Citation
Centrifugal modeling of underground structures subjected to blast loading

Material Information

Title:
Centrifugal modeling of underground structures subjected to blast loading
Creator:
Tabatabai, Habibollah, 1959- ( Dissertant )
Townsend, Frank C. ( Thesis advisor )
Hays, Clifford O. ( Reviewer )
McVay, Michael C. ( Reviewer )
Bloomquist, David G. ( Reviewer )
Smith, Douglas L. ( Reviewer )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1987
Language:
English

Subjects

Subjects / Keywords:
Acceleration ( jstor )
Accelerometers ( jstor )
Amplifiers ( jstor )
Blasts ( jstor )
Centrifugation ( jstor )
Electric potential ( jstor )
Explosives ( jstor )
Pressure gauges ( jstor )
Signals ( jstor )
Velocity ( jstor )
Blast effect
Civil Engineering thesis, Ph.D.
Dissertations, Academic -- Civil Engineering -- UF
Military Technology, Weaponry, And National Defense
Safety
City of Panama City Beach ( local )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
The survivability of underground military structures may be of critical importance in times of crisis. Reliable and economical design of such structures requires a better understanding of the complex parameters involved. Small-scale model testing of such systems offers major cost savings compared to full-scale tests. The laws of similitude and scaling relationships require some form of dead-load compensation to properly account for the effect of gravity stresses in scaled models. This can be accomplished by subjecting the scaled model to an increased acceleration field through an elevator arrangement or, more suitably, a centrifuge. The objectives of this research are to determine the significance of gravity stresses on the response of underground structures subjected to blast loading and to evaluate the scaling relationships. A discussion of the scaling relationships and procedures for model construction are presented. A complete instrumentation set-up for the measurements of shock pressures, strains and accelerations on the structure is designed, built and tested. This includes development of Polyvinyidene Fluoride (PVDF) piezoelectric shock pressure transducers and associated electronics. A series of tests at high-gravity and low-gravity environments are performed on 1/60 and 1/82-scale models of an underground protective structure subjected to a scaled bomb blast. Based on the test results it is concluded that the structural responses in the two gravity fields are different and that such parameters as wave speed, pressure magnitudes and structural strains are higher in the high gravity tests. The centrifuge is believed to be a necessary and viable tool for blast testing on small-scale models of underground structures.
Thesis:
Thesis (Ph.D)--University of Florida, 1987.
Bibliography:
Includes bibliographic references (leaves 307-311).
General Note:
Vita.
Statement of Responsibility:
by Habibollah Tabatabai.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
030515965 ( AlephBibNum )
17416937 ( OCLC )
AEU9301 ( NOTIS )

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Full Text












CENTRIFUGAL MODELING OF UNDERGROUND STRUCTURES
SUBJECTED TO BLAST LOADING












BY

HABIBOLLAH TABATABAI


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA


1987




















09917 ZS9O9 Z9ZL c














ACKNOWLEDGEMENTS


The author wishes to express his sincere appreciation

and gratitude to the chairman of his supervisory committee,

Dr. Frank C. Townsend, for providing him with the

opportunity to conduct this research and for his continued

support and encouragement throughout the course of this

study. Appreciation is also expressed to Dr. David

Bloomquist and Dr. Michael McVay for their help and advice.

Further gratitude is extended to Dr. Clifford 0. Hays, Dr.

Mang Tia and Dr. Douglas Smith for serving on his

supervisory committee.

The author is grateful to Mr. Dan Ekdahl of the Digital

Design Facility for his help in the design and building of

the electronic components, and to Dr. J.C. McGrath of the

Thorn EMI Central Research Laboratories in England for his

help and advice and for providing a PVDF sample for

pressure transducers.

The author is specially thankful to his friend, Mr. Krai

Soongswang, for his help, advice and encouragement

throughout hiis graduate work.

The author wishes to express his love and gratitude






to his parents and family for their continued encouragement

and support.

The funding of this research by the U.S. Air Force is

also acknowledged and appreciated.













Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


CENTRIFUGAL MODELING OF UNDERGROUND STRUCTURES
SUBJECTED TO BLAST LOADING

By

Habibollah Tabatabai


August 1987


Chairperson: Dr. Frank C. Townsend
Major Department: Civil Engineering

The survivability of underground military structures may

be of critical importance in times of crisis. Reliable and

economical design of such structures requires a better

understanding of the complex parameters involved.

Small-scale model testing of such systems offers major

cost savings compared to full-scale tests. The laws of

similitude and scaling relationships require some form of

dead-load compensation to properly account for the effect

of gravity stresses in scaled models. This can be

accomplished by subjecting the scaled model to an increased

acceleration field through an elevator arrangement or, more

suitably, a centrifuge. The objectives of this research are

to determine the significance of gravity stresses on the






response of underground structures subjected to blast

loading and to evaluate the scaling relationships.

A discussion of the scaling relationships and procedures

for model construction are presented. A complete

instrumentation set-up for the measurements of shock

pressures, strains and accelerations on the structure is

designed, built and tested. This includes development of

Polyvinyidene Fluoride (PVDF) piezoelectric shock pressure

transducers and associated electronics.

A series of tests at high-gravity and low-gravity

environments are performed on 1/60 and 1/82-scale models of

an underground protective structure subjected to a scaled

bomb blast. Based on the test results it is concluded that

the structural responses in the two gravity fields are

different and that such parameters as wave speed, pressure

magnitudes and structural strains are higher in the high-

gravity tests. The centrifuge is believed to be a necessary

and viable tool for blast testing on small-scale models of

underground structures.














TABLE OF CONTENTS


Page

ACKNOWLEDGEMENTS ....................................... ii

ABSTRACT ............................................... iv

CHAPTERS

1. INTRODUCTION................................... 1

1.1 General .................................. 1
1.2 Review of Previous Work..... ............ 3
1.3 Objectives .............................. 6
1.4 Scope of Work ........................... 6

2. SIMILITUDE AND MODELING........................ 8

2.1 Introduction............................ 8
2.2 Similitude For Underground Structures.. 11
2.3 Gravity Effects.......................... 18
2.4 Construction of Small-Scale Models..... 25
2.4.1. Micro-Concrete.................. 25
2.4.2. Reinforcement................... 26
2.4.3. Mold And Model Construction.... 27

3. TESTING EQUIPMENT AND SPECIMENS................ 29

3.1. Centrifuge.............................. 29
3.2. Test Specimens........................... 35

4. INSTRUMENTATION AND DATA ACQUISITION.......... 39

4.1. Introduction ........................... 39
4.2. Instrumentation......................... 40
4.2.1. Electrical Resistance Strain
Gages ........................... 40
4.2.1.1 Strain Gage Measurements
in a Centrifuge........ 46
4.2.1.2 Electronic Circuits For
On-board Strain
Measurements........... 50







4.2.1.3 Calibration of Strain
Gage Bridges........... 50
4.2.1.4 Strain Gage Setup on
the Test Structure..... 55
4.2.2. Piezoelectric Shock Pressure
Transducers...................... 59
4.2.2.1 Introduction to
Piezoelectricity........ 59
4.2.2.2 Polyvinylidene Fluoride
(PVDF) .................. 61
4.2.2.3 PVDF Pressure
Transducer.............. 66
4.2.2.4 Electronic Circuits for
Piezoelectric
Transducers............. 70
4.2.2.5 Voltage Measurements.... 71
4.2.2.6 Charge Amplifiers....... 75
4.2.2.7 Shock Pressure
Measurements in a
Centrifuge .............. 78
4.2.2.8 Calibration of PVDF
Pressure Transducers.... 84
4.2.2.9 Pressure Gage Setup on
the Test Structure..... 94
4.3. Piezoelectric Accelerometers............ 94
4.3.1 Coriolis Accelerations......... 94
4.3.2 Accelerometer Setup on the
Test Structure.................. 98
4.4. Detonators............................... 101
4.5. Overall Instrumentation and Data
Acquisition.............................. 103

5. TESTING PROCEDURES............................. 108

6. EVALUATION OF TEST RESULTS................... 116

6.1. Pressures ................................ 116
6.1.1. Pressure Gage P ............... 117
6.1.2. Pressure Gage P2. ............... 127
6.1.3. Pressure Gage P3. ............... 150
6.1.4. Pressure Gage P4... ............ 163
6.1.5. Pressure Gage P5. ............... 167
6.1.6. Pressure Gage P6. ............... 167
6.2. Accelerations............................ 167
6.2.1. Accelerometer Al. ............... 177
6.2.2. Accelerometer A2. ............... 194
6.3. Strains ................................. 211
6.3.1. Strains in Top Slab ............ 212
6.3.2. Strains in Side Wall........... 219
6.3.3. Strains in Bottom Slab ......... 232
6.4. Velocities............................... 249
6.4.1. Velocity V ...................... 255
6.4.2. Velocity V2 .................... 265
6.5. Displacements............................ 270


v i i







6.5.1. Displacement Dl. ................ 270
6.5.2. Displacement D2................. 281

7. CONCLUSIONS AND RECOMMENDATIONS............... 284

7.1. Conclusions.............................. 284
7.2. Recommendations for Future Studies..... 287

APPENDICES

A ELECTRONIC COMPONENTS OF THE INSTRUMENTATION
SYSTEM ....................................... 289

B COMPUTER PROGRAMS WRITTEN ON HP 9816.......... 297

REFERENCES ............................................. 307

BIOGRAPHICAL SKETCH .................................... 312


viii














CHAPTER 1
INTRODUCTION


1.1 General

The survivability of underground military structures may

be of critical importance in times of crisis. Reliable and

economical design of such structures requires a better

understanding of the complex parameters.involved. Although,

in recent years, there have been advances made in the

development of analytical methods for the study of such

systems, structural testing is believed to be essential

considering the existing uncertainties and complexities in

evaluating the performance of underground structures

subjected to blast loads. Defense-related agencies

regularly perform full-scale or scaled model tests on

buried protective structures. Although full-scale testing

may be ideal in terms of evaluating structural response,

the economic costs may be substantial. Small-scale model

testing (1/10 to 1/80) offers major cost savings, thereby

allowing a larger number of tests to be performed for the

purpose of parametric studies or evaluating repeatability.

There are several important factors to be considered in

blast tests on small-scale models. First, the development

of model materials such as microconcrete and miniaturized







reinforcement with properties similar to the prototype is

an important consideration. The ability to build small-

scale models within acceptable tolerances is another major

concern. Second, the development and proper understanding

of the scaling relationships, based on which the scaled

model is designed and the observed response on the model is

extrapolated to predict the response of the full-scale

(prototype) structure, are essential. Third, the

development of instrumentation methods and devices for the

measurements of such parameters as shock pressures, strains

and accelerations on small-scale models is another

important consideration.

Complete adherence to the scaling relationships

developed on the basis of the laws of similitude would

require some form of dead-load compensation to properly

account for the effect of gravity stresses. For example, in

static tests on model bridges, it is customary to account

for the discrepancy between the prototype and model dead-

load stresses by adding sufficient weight to the bridge in

such a way as not to add stiffness to the structure. In

dynamic tests on super small-scale models, this problem

becomes more complicated because of the relatively small-

size structures involved and the problem of accounting for

increased mass in a dynamic test.

An alternative would be to subject the scaled model to

an increased acceleration field through an elevator

arrangement or, more suitably, a centrifuge. Researchers







have generally ignored the effect of gravity on the

response of buried structures based on the argument that,

for shallow-buried structures subjected to blast loading,

gravity stresses are generally much smaller than blast-

induced stresses. Also, the relative complexity of

compensating for gravity stresses has been another

important consideration. However, it is clear that in some

soils, properties such as stiffness and strength are

directly related to gravity stresses (or depth of soil). In

addition, the degree of soil-structure interaction could

very well be a function of gravity stresses. To answer some

of these questions, the U. S. Air Force sponsored this

research project to determine the significance of gravity

stresses (centrifuge testing) on the response of models of

underground structures subjected to blast loading.



1.2 Review of Previous Work

During the last 50 years, the centrifuge has been

frequently used as a tool in geotechnical testing,

especially in Europe and the Soviet Union. In recent years,

there has been an increased interest in using this

technique to study soil mechanics and soil-structure

interaction problems including underground structures.

Many researchers have conducted centrifuge tests to

study varied subjects such as offshore gravity structures

(Prevost et al., 1981), coal waste embankments (Al-Hussaini

et al., 1981), consolidation of phosphatic clay







(Bloomquist, 1982), buried large-span culverts (McVay and

Papadopoulos, 1986), abutments (Randolph et al., 1985),

embankment dams and dikes (Fiodorov et al., 1985), pile

installations (Craig, 1985), and laterally loaded pile

groups in sand (Kulkarni et al., 1985).

Schmidt and Holsapple (1980) conducted a number of blast

tests in a centrifuge to study the effectiveness of the

centrifuge technique for modeling explosive cratering in

dry sand and to validate their derived similarity

requirements. These experiments used 0.5-4 grams of

Pentaerythritol-tetranitrate (PETN) and 1.7 grams of lead-

azide explosives in tests at zero depth of burial and at

gravities as high as 450 g's.

The authors conclude that the centrifuge is an effective

tool for such tests. Based on the observed symmetrical

cratering in these tests, they also suggest that the

Coriolis effects are insignificant (Coriolis effects are

explained in Chapter 4). In addition, the authors recommend

a non-dimensional parameter (discussed in Chapter 2) for

determining an equivalent charge for simulating large

explosive yields with small charges at elevated gravities.

Nielsen (1983) conducted a number of blast tests in a

centrifuge to evaluate the suitability of the centrifuge

technique for the measurement of free-field blast pressures

in soil. In some tests less than 1 gram of

Cyclotrimethylenetrinitramine (RDX) and PETN explosive was

placed in the sand and then detonated at 50 g's. The soil







pressures at different locations were measured. In other

tests, the explosive was placed inside a microconcrete

burster slab (which, in the design of underground

protective structures, serves to prevent deep penetration

of the weapon into the soil). The explosives were detonated

at gravities of up to 90 g's and pressure measurements were

taken at different locations in the sand beneath the

burster slab.

The author suggests that the centrifuge is a suitable

tool for such measurements. The author also recommends the

use of larger centrifuges and improvements in the

instrumentation and data-acquisition arrangements.

Baird (1985) presents a survey of the instrumentation

problems for explosive centrifugal testing and provides a

list of commercially available transducers and data-

acquisition systems that have a potential for use in such

tests. Bradley (1983) and Cunningham et al. (1986) discuss

scaling relationships and model materials for blast testing

in a centrifuge, respectively.

Kutter et al. (1985) report preliminary results of a

number of blast tests on scaled aluminum models of a buried

reinforced concrete pipe (tunnel) at 1, 50 and 100

gravities. The two types of explosive charges used

contained 64 and 512 mg of PETN. Horizontal accelerations

on one side of the models were measured. The authors

suggest that the effect of gravity becomes more important







as the range from the blast source increases and as the

relative size of the explosion decreases.



1.3 Objectives

The objectives of this research program are as follows:

1) To develop instrumentation methods and devices for the

measurement of shock pressures, strains and accelerations

in centrifuge blast tests on small-scale microconcrete

models of underground structures and to develop general

testing procedures for such tests.

2) To perform blast tests on small-scale models of an

underground structure at low-gravity (ig) and high-gravity

(centrifuge) environments, and to study the differences in

response, if any, between the two testing conditions and

thereby ascertain the significance of gravity stresses in

the response of such structures.

3) To evaluate the validity of scaling relationships by

performing and comparing blast tests on two different sized

scaled models (1/60 and 1/82-scale models).



1.4 Scope Of Work

A complete discussion of the scaling relationships for

blast tests on underground structures is presented.

Research work performed by Cunningham et al. (1986) and

Bradley (1983) in the development of model materials and

scaling relationships are summarized.

A complete instrumentation and data acquisition set-up






for the measurements of pressures, strains and

accelerations in a centrifuge is designed, built, and

tested and detailed procedures for such measurements are

recommended. This includes the development of

Polyvinylidene Fluoride (PVDF) piezoelectric pressure

transducers and associated electronics for pressure

measurements at the soil-structure interface and design of

electronic circuits for strain measurements.

A series of tests are performed on 1/60- and 1/82-scale

models of an underground structure subjected to a scaled

500-lb bomb blast at low-gravity (ig) and high-gravity (60-

or 82-g's) environments. The results are evaluated for the

purpose of determining the significance of gravity stresses

(centrifuge testing) and for evaluating the scaling

relationships.














CHAPTER 2
SIMILITUDE AND MODELING


2.1 Introduction

Experimental evaluations of engineering systems are

generally recommended especially when such systems are too

complicated to yield accurate analytical solutions based on

mathematical formulations of the problem. However, prototype

testing can, in many cases, be prohibitively expensive. Tests

on scaled-down models of the prototype offer an alternative

to prototype testing at a generally reduced cost.

The design of a model and the relationships, based on

which the prototype response can be predicted from the

observed response on the model, are based on the laws of

similitude. Murphy (1950) defines models and prototypes as

follows: A model is a device which is so related to a

physical system that observations on the model may be used

to predict accurately the performance of the physical system

in the desired respect. The physical system for which the

predictions are to be made is called the prototype" (p. 1).

Murphy (1950) also comments that the theory of similitude

includes a consideration of the conditions under which the

behavior of two separate entities or systems will be







similar, and the techniques of accurately predicting results

on the one from observations on the other" (p. 1).

Structural models have been widely used to evaluate the

performance "of underground structures subjected to blast

loading. Parametric studies can be performed on such models to

evaluate the significance of different factors such as varying

soil conditions, sizes of threat, structural configurations,

etc.

The most common relationship in blast wave scaling is

based on the Hopkinson or cube-root scaling. This law states

that "self-similar blast (shock) waves are produced at

identical scaled distances when two explosive charges of

similar geometry and the same explosive, but of different

size, are detonated in the same atmosphere" (Baker et al.,

1973, p. 55). The dimensional scaled distance, Z, is defined

by the following equation:

R
Z = 1/3 Equation 2.1
W1/

where R is the distance from the explosive and W is the

energy (or weight) of the explosive. Figure 2.1 illustrates

the Hopkinson blast scaling. Baker et al. (1973) reviewed

several other scaling relationships developed for blast.

A more systematic approach to scaling is through the laws

of similitude and the theory of models. The first and by far

the most important step is to determine the pertinent

variables in the problem. According to the Buckingham's Pi

theorem, the relationship among these variables can be



















R-i



iP>


-&-- --- --

-^A R

p IT


Figure 2.1. Hopkinson Blast Scaling (Baker et al., 1973)
(Reprinted by Permission of the Southwest
Research Institute)







described by a set of S dimensionless and independent terms

called Pi (i) terms which are products of the pertinent

variables.

S = n r Equation 2.2

Where S is the number of T terms, n is the number of

variables and r is the number of fundamental dimensions. In

a dynamic engineering problem, these fundamental dimensions

are generally selected to be either force, length and time,

or mass, length and time. There can be infinite sets of

correct Ti terms. However, in each set the total number of

dimensionless and independent terms is limited to S.

Similitude requirements establishing the relationship

between model and prototype is determined by equating the

dimensionless n terms in the model and prototype. Therefore

7n = T. i = 1,2,...,S Equation 2.3

where m and p denote model and prototype respectively.

More information on similitude requirements for static or

dynamic modeling is presented by Murphy (1950), Langhaar

(1951), Young and Murphy (1964), Tener (1964), Denton and

Flathau (1966), Krawinkler and Moncarz (1973), Sabnis et al.

L1983) and Bradley (1983).



2.2 Similitude for Underaround Structures

Bradley (1983) presents a list of pertinent variables

(Table 2.1), n terms (Table 2.2) and scaling relationships

(Table 2.3) for underground structures subjected to blast

loading. The relationships in Table 2.3 are based on the









Table 2.1

List Of Parameters


- Stress

- Displacement

- Acceleration


a

d

a



P
0
E
n
R

H



C
c
F
c
E
c
Fst

Ast

0
s

C
5


(Bradley, 1983)


- Soil Modulus

- Soil Cohesion

- Preconsolidation

Pressure

- Gravity

- Time

- Soil Angle of Friction

- Steel Strain

- Soil Strain

- Concrete Strain

- Steel Poison's Ratio

- Concrete Poisson's Ratio

- Steel Modulus


g

T

0

est

ES

E
C
c

Lst



E st


- Characteristic Pressure

- Energy

- Radius

- Thickness

- Concrete Mass Density

- Concrete P-Wave Speed

- Concrete Strength

- Concrete Modulus

- Steel Strength

- Area Of Steel

- Soil Mass Density

- Soil P-Wave Speed









Table 2.2

Solution n Terms (Bradley, 1983)


a
1 E
E


Ast
'10 H
H


d
i= -
2
H

a H p
Tr3 =
3 E
c
P
O0
n4 -
E

E
n
Tr5 =--7T3--
5 H3 E
c
R
6 H


0c C 2c
7
C
iT - _ _
,F'


8 =


F'
c
E


0s


0c C2

12 -

E
C

T13 =
E
c
C
T14 =
c
P
c
T15 -
c

H c g
716 -=
c
E T2
c
17 = ----2
C


Fst
9=
E
C










Table 2.3

Scaling Relationships (Bradley, 1983)


Parameter

Stress

Displacement

Acceleration

Velocity

Explosive Pressure

Explosive Energy

Radius

Thickness

Material Density

Material Modulus

Material Strength

Material Wave Speed

Area

Volume

Mass

Strain

Dynamic Time

Poisson's Ratio

Soil Cohesion

Soil Preconsolidation

Pressure

Force

Acceleration of Gravity


Symbol

0

d

a

v

P

E
n
R

H



E

F

C

A

V

M

C

t



c

P
c



F
f


Scaling Law

O = o
m p
d = d /n
m p
a = n a
m p
v = v
m p
P = P
om op
E = E /n3
nm np/

R = R /n

H = H /n
m p
0P =0 p

E = E
m p
F = F
m p
C = C
m p
A = A /n2
m = Vp/n
V = M /n3



m p

t t /n
tm p


C = C
m p

P = P
cm cp


F- =
tm
gin =


F p/n2

n gp








assumption that the same materials are used in the model as in

the prototype, or at least the material properties are kept

constant. Strict adherence to the geometric scaling

requirements in Table 2.3 means that aggregates in concrete or

soil particles would have to be scaled down to meet those

requirements. For soils, large reductions in particle sizes can

lead to major changes in soil properties. Therefore, such

scaling down of all soil particles is not recommended and

only large-size aggregates should be scaled down.

Sabnis and White (1967) suggest using a gypsum mortar mix to

model concrete in small scale models. This would result in

material properties similar to concrete.

Table 2.3 shows that the acceleration of gravity in the

model (gm ) should be n times the acceleration of gravity in

the prototype (g = lg). This condition can be achieved by

subjecting the model to an acceleration field. (An elevator

arrangement or, more suitably, a centrifuge can provide the

desirable acceleration field./

Almost all research involving model tests on underground

structures subjected to blast loads has been performed at ig,

i.e. ignoring the gravity effect and thereby violating one of

the requirements for a true model./An evaluation of the

/ significance or lack of significance of ignoring gravity

effects in such model tests is presented in Section 2.3.)

Modeling explosives is another important consideration in

such tests. The geometric scaling of the shape of cased

explosives may be an important parameter. For example,







cylindrical-shaped charges may be necessary to model some

weapons. Table 2.3 shows that the energy of explosion is

scaled by a factor of 1/n3. For example, a 500 lb bomb

containing 267 lb of TNT can be simulated by a 0.267 lb TNT

explosive in a 1/10 scale model test.

Schmidt and Holsapple (1980) suggest the following N

term for scaling of energy for various types of explosives

for centrifuge testing:

S 1/3

I 1 -- Equation 2.4
Q 6


where Q = Heat of detonation per unit mass of explosive

6 = Initial density of the explosive

W = Mass of the explosive

G = Gravity

By equating the above I term for the model and prototype,

the scaling relationship can be established

IT = T
m p

G W 1/3 G W 1/3
m m p _p

Qm 6m Qp 6p

Or


G 3 Q 3
W = ( ) ( ) m) Wp Equation 2.5
m Qp p
Based on this relationship, Table 2.4 shows calculated

explosive weights for models simulating various size bombs at

different scales or gravities (Nielsen, 1983). The type of







explosive used to model the prototype bombs in these

calculations is Cyclotrimethylenetrinitramine (RDXJ.


Table 2.4

Theoretical Model Explosive Simulation Weights

(Nielsen, 1983)

Centrifuge Environment (Gravities)

Threat 20 g 40 g 60 g 80 g 100 g
Designation
(lb) Weight of RDX in Grams

250 12.35 1.54 0.46 0.19 0.10

500 25.57 3.20 0.95 0.40 0.20

1000 53.43 6.68 1.98 0.83 0.43

2000 106.95 13.37 3.98 1.67 0.86


Schmidt and Holsapple's r term provides satisfactory

results for centrifuge testing. However, this n term implies

that, in order to compensate for the error introduced by

ignoring gravity in simulating explosive energy, the mass of

explosive in the model as predicted by Equation 2.5 should

be increased by a factor of (G m/G )3 or n 3. This is of

course an improper extension of the use of Schmidt and

Holsapple's 7n term. To observe strict adherence to the

similitude requirements, the type of explosive to be used

for modeling should have the same detonating rate as the

prototype explosives to simulate the blast effects

correctly.

There are commercially available detonators such as the

standard Reynolds RP-83 detonator (explained in Section 4.4)







with RDX charges that can be used for model tests. Based on

the information on the available commercial detonators, the

model scale can be calculated using the fr term in Equation

2.4.



2.3 Gravity Effects

In this section the effect of ignoring gravity in model

tests of underground structures subjected to blast loads is

evaluated. In almost all such model tests in the literature,

the effect of gravity is ignored on the basis of the fact

that, for shallow-buried structures, the blast-induced

pressures are generally much higher than gravity stresses.

The effect of neglecting gravity on dynamic time in models

is dependent on the nature of dynamic forces. Consider the

following n term in deriving a relationship for dynamic time:

F t2
S= Equation 2.7
M 1

where F is dynamic force, M is mass, t is dynamic time and 1

is any relevant length. Equating this Tn term for model and

prototype,

m p
Fm 2m Fp p L2
M 1 M 1I

Therefore,
2
t M 1 F
--- ~) J )( -- -
t M 1 F
P p p m
Considering the scaling relationships in Table 2.3,




19




t 2 1 1 2
(---m ) = (----- )(- n2)(n
t n n
p
Or
1
tm = tp Equation 2.8
n

If the force causing the dynamic response is applied on the

system through gravity alone, then

F
= g
M

where g is the acceleration of gravity. Therefore the term

in Equation 2.7 can be rewritten in the following form

g t2
TT -
1

Equating r terms for model and prototype

TT = 7T
In p
gmn m gp pt

1 1

Therefore,

2
t g 1
p gm p
If the effect of gravity is not neglected, then

2 = l 2
t m 2p
n n P

Or
1
t t
m p

Which is the same as the relationship in equation 2.8.







However, if the effect of gravity is neglected, then


2 1
t2 (I --- ) t2
m p
n

Or
1
t = t Equation 2.9
m /-n P

which is substantially different from Equation 2.8. The

following two examples illustrate this effect in systems where

gravity is the only force causing the dynamic response of the

system. An ideal pendulum is one such system in which gravity

is the only force applied on the mass (Figure 2.2(a)). The

period of vibration (T) of an ideal pendulum of length L is

T = 2T /L/g Equation 2.10

If a test is performed on a scaled-down version of this

pendulum, the resulting period of vibration can be

calculated as follows:


T
T = -


T = IT
m p
T T
m p
VL 'g vL /g
/ m gm p/' p

Then
Tm = (/pF /ggm Tp

If gravity is not neglected, then

T = (1/n) T

If gravity is neglected, then

Tm = V(1/nJ)L T
p







Or

T = (1//n) T

Another similar example is the case of determining the time

(t) that it takes for a point mass to drop from a height H

with zero initial velocity (figure 2.2 (b)).

t = v'2H/'g Equation 2.11

This is similar to Equation 2.10 and yields the same

results as in the previous example.

Consider a spring-mass system (Figure 2.2 (c)) which is

in static equilibrium under its own weight. For the case of

a linear spring, the period of vibration (T) of such a

system is only a function of its mass M and its stiffness

(spring constant K) and not a function of gravity

T = 2IT /M/K Equation 2.12

Of course, stress in the spring is a function of gravity

and any other external force applied on the mass. So, if the

system is not linear, K and consequently T would be

functions of gravity too.

Based on the above argument, it would appear at first

that, for underground structures for which gravity stresses

are small compared to blast induced stresses, the response

time would be independent of gravity assuming the loading

functions are che same. However, there are other factors

that must be taken into account. Wong and Weidlinger (1983)

suggest that, in box-type structures, a part of soil mass

around the structure moves with it and therefore the

effective mass for the vibration of the structure under









Tm = (1/-6 ) Tp

Tm = (1/n) Tp


at 1 g

at n g's


(a) Ideal Pend



mgT
H


/7777


(b)





K


ulum


= (1/'1n) tp at 1 g

= (1/n) tp at n g's


Free Fall


Tm = (1/n) Tp at 1 g

Tm = (1/n) Tp at n g's


mg

(c) Spring-Mass System


Figure 2.2. Gravity Effects on Dynamic Time


mg







blast loading increases. If gravity stresses are not scaled

properly, it is believed that the degree of interaction

between soil and structure (in terms of movement of soil

with structure) would be reduced and the effective mass for

structural vibrations would be reduced. This results in

reduced response times (Equation 2.12) and higher

frequencies for models for which gravity effects are

ignored. Other factors may be an increased apparent

stiffness of the structure and soil confinement effects on

the structure due to higher degree of soil-structure

interaction.

Perhaps the most important factor to be considered is the

possible change in characteristics of shock waves in soils

due to gravity. For example, properties such as strength,

wave speed, and stiffness of dry sand or gravel are highly

dependent on gravity or overburden (Baker et al., 1973,

Pan, 1981 and 1982 and Kutter et al., 1985). Therefore, it

is expected that in models in which gravity is not properly

accounted for, there would be a decrease in strength and

stiffness of soil (compared to prototype) and thereby

greater attenuation of shock waves could be expected. For

models subjected to proper acceleration fields (gravity), it

is expected that the shock wave will arrive faster with

smaller rise times (higher frequency content) and higher

magnitudes of pressure.

Denton and Flathau (1966) conducted a series of

load tests on buried circular aluminum arches at different







scales. They reported relatively good agreement in strain and

deflection results due to the applied loads even though

gravity was ignored. However, the applied loads were quasi-

static: that is the load durations were much greater than the

period of vibrations for the structure (Baker et al., 1973).

Baker et al. (1973) report a study performed by Hanna et

al. on half-buried steel containment shells subjected to an

internal blast. It is reported that the peak strain did not

appreciably change in different tests. However, large shells

exhibited increased damping which was attributed to gravity

effects which were not properly scaled.

Young and Murphy (1964) conducted tests on buried aluminum

cylinders at different scales. Load was applied by dropping a

weight on the surface of the sand. However, the drop height

for different size models was kept constant (not scaled) in

order to obtain the same velocity of impact in all tests. This

is equivalent to scaling the drop height and subjecting the

mass to an increased gravity field. The authors attribute some

discrepencies in test results to the fact that the weight of

soil was not scaled.

Gran et al. (1973) compared tests on 1/30 and 1/6-scale

models of a buried cylindrical missile shelter. They

reported good agreement in results. The soil wave speed in

the 1/6 scale test (400 m/s) was higher than that in the

1/30 scale test (250 to 400 m/s). This was attributed to

differences in soil density due to imperfect soil placement.

They also reported that the concrete strain responses were







generally reproduced, although the magnitudes of the strains

differed somewhat.

In summary, the use of centrifuge for model tests on

underground structures subjected to blast loads is warranted

based on the belief that the increased gravity field affects

such things as the characteristics of shock waves in soils and

the degree of interaction between soil and structure resulting

in added mass, stiffness and confinement for the structure.



2.4 Construction of Small Scale Models



2.4.1 Micro-Concrete

The scaling relationships presented in Table 2.3 are

derived on the assumption that the material properties in the

models remain the same as the prototype. Therefore, it is

essential that the micro-concrete used in the small scale

models have the same properties as prototype concrete. Sabnis

and White (1967) recommended gypsum mortar to be used for

small scale model tests. Cunningham et al. (1986) give the

following reasons for choosing gypsum over portland cement in

super small scale modeling:

1. Relatively large particle sizes in portland cement can

cause problems for models smaller than 1/60 scale.

2. Curing time for cement is generally 28 days while gypsum

cures very rapidly and can be removed from its mold within an

hour. In fact when micro-concrete reaches its desired

strength, the surface is coated with shellac to prevent







further variations in strength and eventually brittleness.

3. In very small scale models, shrinkage problems with

portland cement can be severe, while gypsum exhibits very low

distortion upon curing.

The micro-concrete mix selected uses gypsum cement, sand

and water in a ratio of 1:0.8:0.25 by weight. The resulting

properties for such a mix are as follows:

f'c = 4085 psi

f' = 327 psi

y = 130 pcf

E = 3.3 X 106 psi
c


2.4.2 Reinforcement

The primary concern in developing reinforcement for small

scale models is to have similar properties in the model and

prototype. The following three properties and characteristics

are considered important in the development of miniaturized

reinforcement (Cunningham et al., 1986):

1. Yield strength

2. Modulus of elasticity

3. Bond development

The prototype steel generally has a yield strength of 60

ksi and a modulus of elasticity of 29000 ksi. Black-annealed

steel wires (gages 28, 24, 22) were chosen as model

reinforcement. Annealed steel wire has lower yield strength

(40 to 60 Ksi) than cold-rolled steel wire (80 to 100 ksi) and

it is widely available. In order to provide sufficient bond







between micro-concrete and steel wire, a method developed at

Cornell University was utilized. A deforming machine, made up

of two pairs of perpendicularly mounted knurling wheels, was

built.



2.4.3 Mold and Model Construction

An aluminum mold was used to build the micro-concrete box-

type models and a cast acrylic mold was used to build the

burster slab (Gill, 1985). The reason for using an aluminum

mold for the box type model was that there were problems in

removing the cast acrylic mold. The aluminum mold included a

collapsible inner column and break-away outer walls.

Miniaturized reinforcement was placed in the mold by drilling

holes on the molds and stringing the micro-reinforcing wire

prior to casting the concrete (Figure 2.3).











































Figure 2.3. Aluminum Mold for Structural Model (Gill, 1985)














CHAPTER 3
TESTING EQUIPMENT AND SPECIMENS


3.1 Centrifuge

The University of Florida geotechnical centrifuge (Figure

3.1) has a radius of 1 meter and a capacity of 2125 g-kg.

Two buckets containing the test specimen (Figure 3.2) and

the counterweight (Figure 3.3) are attached at the two ends

of the centrifuge arm by means of two aluminum support

fcames. The bucket containing the test specimen has inside

dimensions of 10 in X 12 in X 10 in deep (McVay and

Papadopoulos, 1986). The counterweight is used to balance

the forces applied on the centrifuge arm by the test

specimen.

The test specimen and the counterweight are placed in the

buckets while the buckets are in an up-right position before

spinning the centrifuge. Connections between the buckets and

the support frames are built such that the buckets could

rotate around the point of connection. Figure 3.4 shows that

the center of mass of the bucket (with contents) is below

the point of connection to the support frame. Therefore,

when the centrifuge is accelerated from rest to full speed,

tne net centrifugal force acting on the center of mass of

the bucket produces a net moment around the connection












































Figure 3.1. University of Florida Geotechnical Centrifuge

































Figure 3.2. Bucket Containing Test Specimen


Figure 3.3. Bucket Containing Counterweight






32









LLI E
'4:




-4








0


4-)












0 z 41


0 0I

LU Z) C <
C/ 0








point. This results in the rotation of the bucket by 90

degrees at which point the net moment is zero (Figure 3.5).

The relationship between centrifugal acceleration (a) and

angular velocity of the centrifuge (w) is given in the

following equation:

a = r w2 Equation 3.1

In this case, r is the distance from the center of rotation

of the centrifuge to the center of mass of the test specimen

(soil plus structure) in the rotated position. For example,

to obtain a centrifugal acceleration of 60 g's for a radius

of 36 inches:

(60 g)(32.2 ft/sec2)(12 in/ft) = (36 in) (w2)

Or

w = 25.4 rad/sec or w = 242 rpm

Since the height of the test specimen is small compared

to the length of the centrifuge arm, variations of

centrifugal accelerations along the height of the test

specimen are believed to be negligible.

The rotating nature of a centrifuge makes it impossible

to have instrumentation wires from inside the centrifuge

directly connected to outside devices. These wires must pass

through slip rings, unless other schemes such as telemetry

or on-board data capture and storage are devised. Slip rings

operate based on a sliding contact mechanism. A total of 64

slip rings are available on the U.F. centrifuge.





















CENTER OF
ROTATION .



BUCKET


,,",,. ", ",. ,DIRECTION C
CENTRIFUGE
ACCELERATE




'. AFTER SPINNING


)F
L
ON


SOIL -

STRUCTURE


BEFORE SPINNING


Figure 3.5. Orientation of Bucket Before and After Spinning








3.2 Test Specimens

The original prototype structure considered for

centrifuge model testing in this research effort was a

multi-bay underground structure (with burster slab) designed

for use as shelter for Ground Launched Cruise Missiles

(Bradley, 1983). However, the objectives of this research

program are to develop methods and evaluate modeling

relationships and techniques for centrifuge tests, rather

than to be a detailed study of the performance of a specific

structure. Therefore, a slightly simplified version of the

prototype, which included a one-bay (box-type) structure

(instead of 3 bays) with burster slab, was built at two

different scales of 1/60 and 1/82. Figures 3.6 and 3.7

illustrate the shape and sizes of the models.

A total of three 1/60-scale and two 1/82-scale structures

were built using a gypsum mortar mix as concrete and

deformed steel wire as reinforcement (Chapter 2).

Reinforcement details for 1/60 and 1/82-scale models are

given in Gill (1985). The criteria, based on which, the size

of models for such tests are selected are as follows:

1. Ability to construct small-scale models is a primary

consideration. Super small-scale models may pose

difficulties in terms of building molds or formwork

within acceptable tolerances, designing and obtaining

micro-concrete with specific properties, and providing

for steel reinforcement and its placement within

acceptable tolerances.





36










BURSTER SLAB































ONE-BAY STRUCTURE


Figure 3.6. General Shape of the Structural Model




















































DINJEfJSIOrI
(INCH)


A


B C D E F Deplth


1/,'60 4.0 4.4 1.0 2 8 0 6 1.4 4.0
1/82 2 93 3 22 0 73 2 05 0.44 1.02 2.93


Figure 3.7. Dimensions of 1/60 and 1/82-Scale Models







2. Simulating explosives in small-scale models generally

involves very small-size charges that may have to be

custom-made in order to satisfy geometry and size

(explosive weight) requirements. Another, perhaps more

convenient approach would be to choose from a limited

number of commercially available explosive charges and

calculate the model scale, for which, the commercial

charge would be an appropriate simulation of the size

of the threat on the prototype structure (Section 2.2).

For example, two commercially available explosive

charges (Standard and modified Reynolds RP-83) were

used to simulate a 500-lb bomb threat on 1/60 and 1/82

scale models in this research work. Safety concerns

with regard to detonating large explosive charges in a

centrifuge is also a limiting factor on the model

scale selected.

3. Size and capacity limitations for the centrifuge

should also be considered in selecting a model scale.

Models that are too large may cause obvious problems

in centrifuge tests.

4. The type of instrumentation planned for model tests

may also be dependent on, and limited by, the size of

the model in super small-scale models. A complete

review of instrumentation for centrifuge tests is

given in Chapter 4.

Based on the above arguments, two model scale sizes (1/60

and 1/82) were selected for the tests reported here.















CHAPTER 4
INSTRUMENTATION AND DATA ACQUISITION


4.1 Introduction

Instrumentation and data acquisition in centrifugal

model tests pose unique challenges in that the conventional

methods and instruments may not be adequate to handle the

special conditions associated with a centrifuge. Blast

testing in such an environment also adds to the

complications involved.

There are several factors that should be considered in

the design of effective instrumentation and data

acquisition methods for such a system. The primary concern

is the existence of electrostatic and magnetic noise

sources in the centrifuge which could affect the electrical

signals. In fact, slip rings, through which all signals

have to pass to exit the centrifuge, are inherently noisy

because of their sliding contact mechanism.

Another factor to be considered in small-scale modeling

is the necessity of having measuring instruments small

enough, both in mass and size, compared to the model such

as to minimize distortions in the model response. Finally,

the relatively high frequency signals associated with blast








waves require accurate instruments with sufficiently high

sampling rates to properly record the event.

In this chapter a complete explanation of the

development of methods for the measurement of strains,

pressures, and accelerations in centrifugal testing of

small scale models subjected to blast loading is presented.

However, most of the following discussions equally apply to

other kinds of instrumented testing in a centrifuge.



4.2 Instrumentation

In this section the basic concepts of electrical

resistance strain gages, piezoelectric pressure transducers

and piezoelectric accelerometers are reviewed. Development

of new procedures and modifications to conventional methods

are also discussed.



4.2.1 Electrical Resistance Strain Gages

Electrical resistance strain gages function on the basis

of the change in the electrical resistance of the gage in

response to strain. When properly bonded to a test surface,

these gages exhibit slight changes in resistance (relative

to their original resistance) as a function of strain in

the test specimen. Each gage has a constant factor, called

the gage factor, which determines the relationship between

the relative change in resistance and the strain, according

to the following equation:









.SR
g
R
F = --3- Equation 4.1
c

where F is the gage factor,6R and R are the change in
g g
resistance and the resistance of the gage, respectively,

and E is the strain in the gage.

The usual way to monitor such changes in resistance is

through a Wheatstone bridge (Figure 4.1). The four arms of

the bridge consist of four resistors, one of which is the

strain gage R In such case the circuit is called a

quarter bridge. The bridge is powered by a voltage power

supply Vi.

A bridge is called balanced when the potential level at

points b and d are equal or, in other words, the output

voltage is zero (Figure 4.1). Therefore, voltage drop

across a-d is equal to voltage drop across a-b.


Vad = Vab and Vbc= Vdc

or

R I =R3 I3 and R I =R2 2


where I,, 12, I3, and I represent electrical current in

the four arms of the bridge as shown in Figure 4.1.

Similarly, because of zero voltage across b-d,


I1 = I and 12 = 13

Therefore,

R I1 = R 12 and R II1 R2 2














































Figure 4.1. Basic Wheatstone Bridge









Thus, for a balanced bridge,


R R
g Equation 4.2
R1 R2

In the balanced bridge method of calculating strains,

the Wheatstone bridge has to be first balanced in the 'no-

load' or unstrained condition. This can be accomplished by

using a variable resistor for R1 and changing it until the

output voltage V becomes zero. The bridge must again be

balanced in the strained condition by readjusting R,.


5R = R1(strained) R (unstrained)

From equation 4.2:

Rg = (R3/R2) R1

Since R3 and R2 are constant,

56R = (R3/R2) 6R1 Equation 4.3

However, substituting 6R into Equation 4.1,

R
3
S= 6R Equation 4.4
R RF
2 g

Equation 4.4 is valid only when the bridge is balanced.

This is called the 'balanced bridge' method of calculating

strains. Most regular strain gage indicators are based on

this concept. However, in dynamic tests, where continuous

monitoring of strain is required, the output signal does

not stay constant for a sufficient time to balance the

bridge, specially when several strain gages have to be

monitored simultaneously. The 'unbalanced bridge' method







relates the output voltage of the bridge to the resistance

change, or strain, in the gage. Therefore, bridge balancing

is not required and equation 4.4 does not apply any longer.

Williams and McFetridge (1983) present equations relating

strains to the output voltages at unstrained and strained

conditions, supply voltage and gage factor.


V ab= RI
ab g g

Ig= V./(R g+R)

Therefore, in the unstrained or initial condition,

R
ab= 1
R + R1


And in the strained or final condition,

(R + 6R )
ab= Vi
(R + 6R )+ R
g g 1


6V =f vi = g g 6R R9 V
ab ab ab .

If Ris selected to be equal toR R
If R1 is selected to be equal to R ,


6R
6V ab= 9 V
4R + 26R
g g
However,

6Vo= -6Va
o ab

This is because the potential at d is unchanged and

therefore any change in potential across bd (6V ) must be

due to the change in potential at b. Therefore,








.SR
6V = V.
0 4R + 25R
g g
Or,

6R 4.5V
g_ o
R V.+ 26Vo
9 1

Substituting equation 4.1 in the above equation,

46V
c = -Equation 4.5
F (V + 26V )


Therefore, any change in output voltage from the

unstrained condition indicates a strain which can be

calculated using the above equation. This equation

indicates a nonlinear relationship between strain c, and

6V However, for a strain gage with a gage factor close to

2 and a strain of 10000 micro in./in., the deviation from

linearity is less than 1 percent (Dove and Adams, 1964).

This indicates that 6V is very small compared to V..

Therefore, the linear approximation of equation 4.5 can be

written as


4 6V
c = -- Equation 4.6
F V


In order to accurately measure strains, it is necessary

to use accurate voltage measuring devices. Also, the power

supply must be stable. Another factor to be considered is

the effect of temperature changes on lead wires connecting

the strain gage to the Wheatstone bridge. These changes can








cause resistance variations in the lead wires and thereby

introduce errors in the measurements. For short-term tests

this problem may not be critical because of the small

probability of large temperature variations in a short

period of time. However, this effect can be completely

eliminated by employing a three-wire arrangement instead of

a two-wire setup as shown in Figure 4.2. In this method,

equal lengths of lead wires exist in two adjacent arms of

the bridge and since resistance changes in adjacent arms

make opposite contributions to the output voltage (Dove and

Adams, 1964), the overall effect is thereby eliminated.



4.2.1.1 Strain Gage Measurements in a Centrifuge

The use of commercially available strain indicators may

not be suitable for centrifugal testing. Because of the

size and number of these indicators, they generally have to

be placed outside the centrifuge. Therefore, the gage

connection to the Wheatstone bridge passes through slip

rings. This can cause serious problems because the slip

rings are inherently noisy and resistance changes in slip

rings can be as large as the resistance changes in the

strain gages (Hetenyi, 1950). In addition, in regular

strain indicators, the low-level output voltage of the

bridge is increased with an amplifier. Depending on the

gain, the amplifier has a frequency range in which that

gain remains constant and the amplifier exhibits a linear

response (Figure 4.3). If the signal frequency is beyond







47


















Q)
M

fa


4.J4



.14










00


z L14





U)U





48


























z



-LJ
0L











FREQUENCY


Figure 4.3. Gain Versus Frequency Response of Amplifiers







the frequency range of the amplifier, distortion of the

response associated with that frequency will occur.

Therefore, in blast testing, where higher frequency signals

are expected, the characteristics of the regular strain

indicator may not be suitable.

A solution to these problems can be achieved through on-

board signal conditioning and circuitry. This means that

electronic circuit boards containing multiple Wheatstone

bridges and instrumentation amplifiers can be specially

designed and built. The relatively small size of the

electronic board would permit the attachment of the box

containing the board on the arm of the centrifuge. Of

course, the box has to be located as close to the center of

rotation as possible to reduce unwanted centrifugal

accelerations on the electronic components. Such an

arrangement would eliminate the effect of resistance

changes in the slip rings on the output voltage of the

Wheatstone bridge due to the fact that the slip rings are

not on the arm of the bridge anymore. Also, since the

Wheatstone bridge is relatively close to the gage, the lead

wires are shorter and noise pickup by those wires will be

reduced. In addition, since the output voltage is amplified

with an instrumentation amplifier before the signal passes

through slip rings, the signal to noise ratio will be much

higher.







4.2.1.2 Electronic Circuits For On-Board Strain Measurements

Figure 4.4 illustrates the basic electronic circuit for

each strain gage. The strain gages used in the tests

discussed in this report had a resistance of 120 ohms. The

basic circuit consists of a quarter-bridge (one active

gage) completion unit and an instrumentation amplifier. The

quarter-bridge completion unit consists of one 120-ohm and

two 1000-ohm precision resistors as shown in figure 4.4. It

is very important that the resistors have nigh precisions

in order to reduce errors. The bridge is powered with + 3

DC volts. The same power supply is used to power the

instrumentation amplifiers. In these tests the strain gage

power supply unit was placed outside the centrifuge.

However, batteries can be placed on-board to power the

bridge and the amplifier. The amplifier used is Burr-Brown

Model INA 101 which is a high-accuracy instrumentation

amplifier. It responds only to the difference between the

two input signals and has very high input impedance (1010

ohms).

Characteristics of INA 101 are presented in Appendix A.

The gain for this amplifier is set through an external

resistor. In this case, the gain was set at 100, which for

frequencies below 10000 hertz remains constant.



4.2.1.3 Calibration of Strain Gage Bridges

The output voltage of the bridge can be theoretically

related to strain through equation 4.6. Therefore, for a one











































































K LU
z
< D
-0 <


- 0







volt change in the output voltage of the amplifier (6V oA),

strain can be calculated as follows:


46V
0
Eo
F V.
1

Amplifier Amplifier Bridge
Output = X Output
V o, Gain 6V0


46VOA

F V. (Amplifier Gain)


For F= 2.065, V. = + 3 Volts = 6 Volts


4 x 1
c = =-3.22 X 10-3 Strain/Volt
2.065 x 6 x 100


This is equivalent to 3.22 microstrains per milivolt of

amplifier output.

To verify this relationship, all eight strain gage

channels were calibrated. An aluminium cantilever beam with

a 120 ohm strain gage attached to it was loaded. Three

different loads were applied which produced tensile strains

in the gage. The three tests were then repeated with the

beam in a reversed position which resulted in compressive

strains. In each case the static strain in the gage was

measured both by a commercial strain gage indicator

(Vishay/ Ellis 10) and by each of the eight strain gage

channels. Table 4.1 shows the results and the calibration

values (sensitivities) obtained for a strain gage with a







gage factor of 2.10. Equivalent calibration values

(sensitivities) for strain gages used in the tests which

had gage factors equal to 2.065 and 2.05 are calculated

using the following equation which is derived from equation

4.6.


Sensitivity at Sensitivity at 2.10
New = Gage Factor X
Gage Factor Equal to 2.10 New Gage Factor

Channel No. 3 shows a different calibration factor than

the others which may be due to lack of precision of the

resistors in the Wheatstone bridge.

For noise considerations, it is important that the lead

wires connecting the strain gages to bridge completion

units be twisted and shielded and the shield be grounded

properly at the ground surface on the bridge completion

board. The cable used in these tests was Micro.leasurements'

type 326-DSV which is a stranded tinned-copper wire, 3-

conductor twisted cable with vinyl insulation, braided

shield and vinyl jacket. Separate ground wires were used

for each amplifier. The two-wire outputs for all channels

exited the centrifuge through slip rings. Each pair of

wires corresponding to a strain gage channel was then

connected to a coaxial cable through a BNC connector.

Coaxial cables (30 feet long) then carried the signals to

Nicolet digital storage oscilloscopes. Figure 4.5 shows the

overall schematics of the strain gage setup.















































































............







Table 4.1
Strain Gage Sensitivity Measurements


Amplifier Output Voltage (Milivolts)
For Strain Gage Channels

Micro 1 2 3 4 5 6 7 8
Stra in

T 0 0 0 0 0 0 0 0 0
E
N 500 158 159 202 155 159 162 160 158
S
I 684 216 216 288 211 217 221 217 216
0
N 860 273 274 373 268 274 279 273 273

C 0 0 0 0 0 0 0 0 0
0
M -500 -159 -158 -162 -162 -160 -160 -158
P
R -689 -215 -216 -215 -217 -220 -219 -216
E
S -868 -270 -274 -270 -271 -279 -278 -273

Sensitivities (ustrain/mvolt)

F=2.10 3.179 3.161 2.069 3.181 3.159 3.104 3.138 3.169

F=2.U65 3.233 3.215 2.104 3.235 3.213 3.157 3.191 3.223

F=2.05 3.257 3.238 2.120 3.259 3.236 3.180 3.215 3.246

** Excitation Voltage = + 3 Volts
Out of Range



4.2.1.4 Strain Gage Setup on the Test Structure

A total of eight strain gages were used on each

structure. Their locations are illustrated in Figure 4.6.

Considering the existence of axial strains in the slabs and

walls of the structure unaer loading in addition to

flexural strains, the gages were applied in pairs, one on

the outside and the other on the inside of the structure.

This arrangement would allow calculation of axial and






CENTRIFUGE

S BCKET BURSTER
SLAB
I


A


DETONATOR


SAND
I


!.....


STRAIN GAGES I


Figure 4.6. Strain Gage Locations on the Structural Model


S2 SA


]S6


S8


**:: *. J :-
'-;:*,.*...-.*..







flexural strains froin the total strains measured on the two

gages. Assuming linear strain distributions, total strains

are the algebraic sum of axial and flexural strains (figure

4.7).


S+ E = E
a f o
Ea Cf = Ci

Therefore,

C + C,
S=1 Equation 4.7
a 2

And,


S= C Ea Equation 4.9

Or

E = a Ei Equation 4.9


The size of strain gages used in the tests were chosen

considering several factors. First, the gages have to be

small relative to the size of the structural model. For

example, a gage length of 1/4 inch in a 1/60 scale model is

equivalent to a 15-inch long gage on the prototype

structure. This may or may not be sufficiently small

depending on the strain gradient in the immediate vicinity

of the gage. Second, the gage length has to be several

times larger than the maximum aggregate size in the

microconcrete mix so that the gage readings would be

indicative of overall structural strains rather than local

strains in the aggregate. Third, physical restrictions

related to the application of extremely small gages in














_j Z

LJ >x cc
(/)




L4
x 4J
LU I-


,-4
II a

r,.



-4
0-


w 2



. . :. :. . .
0 l:i I







< <

i-







hard-to-access areas may be important. Considering the

above factors, a gage length of 1/4 inch was selected for

these tests. The gages are manufactured by Micro-

Measurements. The gages were installed according to the

directions recommended by the manufacturer.



4.2.2 Piezoelectric Shock Pressure Transducers

In this study, the pressure transducers were used to

determine the shock pressure applied on the structure due

to blast loading. A piezoelectric material was chosen for

transducer development because of the wide dynamic range

and high resonant frequencies associated with piezoelectric

transducers (Riedel, 1986).



4.2.2.1 Introduction to Piezoelectricity

Piezoelectricity is defined by W. G. Cady (1964) as

"electric polarization by mechanical strain in crystals

belonging to certain classes, the polarization being

proportional to the strain and changing sign with it" (p.

4) In other words, piezoelectric materials generate

electrical charge when subjected to pressure. In fact

piezoelectricity means "pressure electricity" (Kantrowitz,

et al., 1979, p. 308). Pierre and Jacques Curie discovered

this property in 1880 (Cady, 1964).

Some materials such as Rochelle salt, tourmaline and

quartz are naturally piezoelectric. Some other materials,

called ferroelectric, can be made piezoelectric through







artificial polarization, in which material characteristics

can be controlled through the manufacturing process

(Endevco 101, 1986).

The major advantage of piezoelectric materials when used

as shock pressure transducers is their large bandwidth. In

addition, they are self-generating ana do not need a power

supply to generate an output.

In addition to their sensitivity to pressure,

piezoelectric materials also generate electrical charges

when subjected to temperature variations. This effect is

called pyroelectricity and is not a favorable effect in

shock pressure transducers because such pressure variations

are not isothermal. Another disadvantage is that

piezoelectric materials cannot be used for long-term static

or steady-state pressure measurements.

Piezoelectric materials have been widely used in

accelerometers and pressure transducers. Piezoelectric

accelerometers are essentially "spring-mass" systems with

the "spring" being the piezoelectric material and the mass

applying compressive or shear forces (depending on the

accelerometer design) on the spring when the system is

subjected to accelerations.

The piezoelectric material used to develop shock

pressure transducers for the tests reported here was

artificially polarized Polyvinylidene Fluoride (PVDF). In

the next section the general properties of PVDF are

presented.









4.2.2.2 Polyvinylidene Fluoride (PVDF)

Polyvinylidene Fluoride (PVDF) is a semicrystalline

polymer which has been widely used in commercial

applications in chemical, food, and nuclear industries

(Thorn EMI notes, 1986). The fact that this material could

be made piezoelectric was discovered in 1969 (Meeks and

Ting, 1983). The piezoelectric response is achieved through

a special manufacturing process which includes electrical

polarization. In addition to its strong piezoelectric

properties, PVDF has a good acoustic impedance match to

water which makes it suitable for use as hydrophones or

underwater shock sensors (Meeks and Ting, 1984). The

National Bureau of Standards has also conducted research on

developing a stress gage for shock pressure measurements

(Bur and Roth, 1985, Chung et al., 1985 and Holder et al.,

1985). PVDF is manufactured in different shapes, sizes and

thicknesses.

Figure 4.8 shows the three principal directions in a

piezoelectric material with axes 1 and 2 in the plane and

axis 3 perpendicular to the plane of the sample. The

relationship between the generated charge per unit area, p,

and the applied uniaxial stress, o, can be written as (Nye,

1957)


P = do Equation 4.10

where d is the piezoelectric coefficient. In general for a























Electroded
/ Surface


.~,*.


Piezoelectric
Material >0


Figure 4.8. Principle Directions on a Piezoelectric Material


$1:. .:'" '".." t







3-dimensional state of stress equation 4.10 can be

rewritten in matrix form (Nye, 1957):


P = .i a. (1= 1,2,3 : j= 1,2,3,...,6) Equation 4.11

Or in expanded form,


1 i 11 dl2 d 3 d 4 d 5 d 6 Il
P2 = d21 d22 d23 d24 d25 d26 02

P31 d31 d32 d33 d34 d35 d36 03 Equation 4.12

04

05

6
where P is the vector of polarization charge per unit

area, d is the matrix of piezoelectric coefficients, and

a. is the stress vector. The six components of a. represent

the six independent terms in a general stress tensor


l = 11

02 022

3 = 033
04 -= 23

5 = 31

06 = 12


For PVDF, the d matrix has several zero components (Bur

and Roth, 1985):








0 0 0 0 d15 0

d. = 0 0 0 d 0 0

d31 d32 d33 0 0 0


When the two surfaces perpendicular to axis 3 are

electroded, the electrical charge, P3 can be written as


P3 = d31 01 + d32 02 + d33 03


When there is a hydrostatic state of stress

01 = 02 = 03 = o

Therefore,

P = d31 a + d32 + d33 a

P3 = (d31 + d32 + d33j)

Or

P3 dh o


where dh is the hydrostatic piezoelectric coefficient.

Therefore,

dh = d31 + d32 + d33

The PVDF sample used in the tests reported here is

produced by Thorn EMI Central Research Laboratories in

England. The sample contained microvoids in order to

improve its piezoelectric properties. Table 4.2 shows the

properties of the PVDF sample as reported by the

manufacturer.

Meeks and Ting (1983,1984) conducted a series of

hydrostatic and dynamic tests on voided and nonvoided, 0.5

mm thick, PVDF samples. They concluded that relatively high











Table 4.2

General Properties of PVDF Sample


SAMPLE NO
PVDF THICKNESS
ELECTRODE THICKNESS
ELECTRODE/POLYMER ADHESION
Er
dh
gh
SENSITIVITY
d31
d32
d33


3717B1
570 pm
= 10 pm Copper
> 14 MPa
7.8
-1
13.4 pCN
178 mVm1 Pa1
-199.9 dB (rel 1V p.iPa1)
= 15pCN-1
-1
= 0.25 pCN
= -28 pCN-1
= -28 pCN


Provided By THORN EMI Central Research Laboratories







pressures applied on voided samples can cause the collapse

of microvoids and thereby result in a nonlinear,

irreversible response while nonvoided samples exhibited

linear response up to pressures as high as 10000 psi in

both hydrostatic and dynamic tests. However, non-voided

samples show smaller piezoelectric sensitivities. Test

results indicate that for relatively low amplitude

pressures (less than 2000 psi), the response of voided

samples are also close to linear. The degree of linearity

increases with a decrease in the number of voids at the

cost of a decrease in the value of piezoelectric

coefficients. Meeks and Ting (1984) also evaluated the

frequency response of non-voided PVDF for underwater shock-

wave sensor applications. They reported a 2-MHZ Dandwidth

and very little high-frequency ringing. These factors are

both favorable in shock-wave sensors which may encounter

high frequency signals.



4.2.2.3 PVDF Pressure Transducer

The transducer used for the tests reported here was a

1/4 in X 1/4 in square which was cut from a sheet of 570 um

thick, copper electroded PVDF material. The selection of

size was based on several factors. First, the gage size

should be small compared to the size of the structural

model. Second, the gage dimensions have to be at least 10

times the mean soil grain size (Bur and Roth, 1985). Third,

the aspect ratio of gage thickness to gage size should be







less than 1/5 (Bur and Roth, 1985). Of course, the size is

also limited by the practical restrictions in building and

working with small gages.

Two 30-gage stranded wires were attached to the two

electroded surfaces on the gage. These wires can be

satisfactorily soldered to the copper electrodes by

following the procedures recommended by the manufacturer:

1. Clean the solder area by dipping it in a 3% solution

of sulfuric acid for a few seconds. Then wash thoroughly in

water and dry it.

2. Place a small piece of solder on the electrode

surface and place the tinned wire on top of, and

perpendicular to the solder.

3. Apply the soldering iron to the wire and remove it

quickly as soon as the solder melts.

The above procedure provides for a satisfactory

connection. However, when the gage is used at the soil-

structure interface, the gage surface must be smooth enough

to have full contact with the concrete surface. This might

not be possible if there is a blob of solder on the

surface. In addition, if extreme care is not taken, heat

from the soldering iron may deform or damage the PVDF.

Based on these considerations, it was decided to use silver

filled epoxy to attach wires to the electrode surfaces as

suggested by Meeks and Ting (1983, 1984). The following is

a step-by-step procedure used in these tests to obtain

satisfactory wire connections.







1. To clean the gage, dip it in a 3% solution of

sulfuric acid for a few seconds. Then wash it thoroughly in

water ana dry it.

2. Expose a few millimeters of a 30 gage stranded wire

and place it on top of the electroded surface in such a way

that only the exposed wire is on the surface. Tape it down

as shown in Figure 4.9.

3. Mix the two components of silver-filled conductive

epoxy.

4. Apply a small amount of epoxy on the exposed wire.

5. Use a piece of masking tape to cover the epoxy, wire

and the gage. This procedure would level the epoxy to a

smooth surface. Let the epoxy cure for a few hours.

6. Remove the masking tape and check the wire

connection. Repeat steps 2 through 6 for the other

electroded surface.

7. Use polyurethane coating to cover the gage for

protection.

The silver-filled epoxy used was Dexter Hysol's Type

KS0002. The polyurethane coating used was Micro-

Measurements' M-Coat A solution.

Another important consideration is the procedure for

applying the gage on the concrete surface for shock

pressure measurements at the soil-structure interface. The

objective is to measure 03 from the measured charge P3 in

the following equation:






























x
0-
w2
LU


0
z
0/ <
2


0
z-








3 = d31 01 + d32 2 + 33 03

If the gage were to be glued to the concrete surface,

the structural strains in the concrete would result in in-

plane strains and stresses in the gage (Co and o2) which,

in turn, would make unwanted contributions to the measured

charge P3. Therefore, it is essential to decouple the

structural strains from the transducer response. This is

done by taping, rather than glueing, the gage on the

concrete surface. Reinforced nylon strapping tape was used

to apply the gages on the concrete surface. Holder et al.

(1985) used a similar method of gage application.

As mentioned earlier, the pyroelectric effects must be

considered in piezoelectric transducer design. However,

Chung et al. (1985) suggest that the temperature rise, for

stresses below 2000 psi, in a gage embedded in soil is very

small (0.6 OF) and, therefore, temperature correction is

not required.



4.2.2.4 Electronic Circuits For Piezoelectric Transducers

There are two general ways for measuring the electrical

response of piezoelectric transducers. One is based on

voltage sensitivity and the other is based on charge

sensitivity. In this section these two methods are

discussed and compared. Also, the electronic circuitry

designed for the tests reported here is described in

detail.








4.2.2.5 Voltage Measurements

A simplified electronic representation of a

piezoelectric transducer is shown in Figure 4.10(a) (Dove

and Adams, 1964, Endevco 101, 1986). The transducer acts

as a capacitor (C ) which generates electrical charge when

subjected to pressure. The open-circuit voltage output (V )

is related to the generated charge q, and the internal

capacitance of the transducer, C through the following

equation:


q
V
C
p

When this transducer is connected to a voltage measuring

instrument (Figure 4.10b), the capacitance of the connecting

cables and the input capacitance of the measuring

instrument incroouce additional external capacitance Ce, to

the circuit. Therefore, the voltage output V0 is a function

of the total capacitance C + C :
p e

q
V =
C C
p e

The above equation indicates that the voltage output

varies as a function of the external capacitance, and is

therefore dependent on such factors as the length and type

of cable used between the transducer and the instrument.

This is not an ideal situation because each measurement

would require an accurate Knowledge of the total














TRANSDUCER

,.. . . .. -..... \ ... .. .. -..


CHARGE
GENERATOR


TRANSDUCER

------------------------


CHARGE Cp Ce
GENERATOR T T





(b)

Figure 4.10. Voltage Measuring Method









capacitance. This problem can be eliminated by using the

charge measurement method as explained in the next section.

Another consideration is the low frequency response of

the transducer. The time constant of the circuit, which is

the product of the input resistance of the instrument R and

the total caoacitance C + C determines the cut-off point
p e
for the low frequency response of this system. The system

filters out signal frequencies below the cut-off frequency

(f)


1
f =
2n R (C + C )


Gurtin (1961) presents a study of the effect of low-

frequency response on transient measurements. Figure 4.11

shows the effect of variations in the time constant of the

circuit RC, on the accuracy of response to transient

signals. It is clear that as RC is decreased, the accuracy

of the response is decreased. This is equivalent to the

loss of low-frequency component of the signal. In the

limit, when RC approaches zero, the response approaches the

differentiated form of the actual signal. It is necessary

to use devices with very high input impedances (1012 to
14
10 ohms) to accurately measure transient pulses. The high

frequency response of the transducer is a function of its

mechanical characteristics (Endevco 101, 1986).




























HII Sing wAve PuLS(



'
5 ~

-
'3'


(1) MOUT ACCELERATION PUM5C
(2L WsO.SE FO & *20
(31 ESPOPSE FOR 10
to RE SPOSE F C S
0l RESPONSE FOR 2


hA0111 ACMaLL rm. OF KA.t


TwI&ftLAR PULSE


I


Figure 4.11. Effect of Time Constant on Signals (Gurtin, 1961)

(Reprinted by Permission of the Society for
Experimental Mechanics).








4.2.2.6 Charge Amplifiers

In this method, all the charge generated by the

transducer due to applied pressure is transferred to, and

deposited on, a capacitor with a known capacitance. The

voltage across this known capacitor is then measured and

the charge q is calculated from equation:


q = C V


In this case, C is fixed and is independent of cable

capacitance. This is the major advantage of this method

over the voltage sensing method explained earlier. The

basic electronic circuit is shown in Figure 4.12 (Endevco

General Catalog, 1986). The major elements of the circuit

are an operational amplifier and a feedback capacitor C .

This arrangement is called a charge amplifier. The

operational amplifier, through its feedback loop, maintains

point S at virtual common. The charges on the transducer

appear and accumulate on the feedback capacitor Cf as they

are generated. Since point S is at virtual common, the

output voltage of the operational amplifier V is, at any

time, equal to the voltage across Cf (Malmstadt et al.,

1981). The charge q, calculated from the following

equation, is the total accumulated charge by the transducer

at any time, and is proportional to the applied pressure

on the transducer.


q = Cf Vo





















SWITCH CHARGE
AMPLIFIER
FEEDBACK CAPACITOR


Cf


TRANSDUCER (+)
OUTPUT Vo

T OPERATIONAL
AMPLIFIER
- - - - - - - - -


Figure 4.12. Basic Charge Amplifier








An electronic switch placed across the feedback

capacitor is used to discharge the capacitor and reset the

charge amplifier. This prevents the gradual drift in the

output due to long-term integration of low-level leakage

currents (Malmstadt et al., 1981).

Although the voltage output V is not a function of the

length of cables connecting the transducer to the charge

amplifier, long cables can increase the noise level and

therefore should be avoided when possible (Endevco, 1986,

Dove and Adams, 1964). The low frequency response of the

charge amplifier is dependent on the low-frequency response

of the amplifier (Endevco 101, 1986) and on the time

constant RfCf, where Rf is the off-resistance of the

electronic switch, and Cf is the feedback capacitor (Dove

and Adams, 1964). The high frequency response of charge

amplifier is a function of the input capacitance

(transducer plus cable) and any resistance in the cable

connecting the transducer to point S.

A very important consideration for noise reductions in

high impedance piezoelectric transducers is the type of

cable used to connect the transducer to the charge

amplifier. Coaxial cables or shielded twisted-pair cables

are recommended (Endevco, 1986). However, when coaxial cables

are subjected to mechanical distortions such as vibrations,

a separation of the cable dielectric and the outer shield

can occur and thereby create low frequency "triboelectric"

noise signals (Endevco 101, 1986). Therefore, it is







important to reduce the cable length and to prevent the

flexing and vibration of the cable which could be significant

in an explosive test. Specially treated cables can also be

used to minimize this effect (Endevco 101, 1986).



4.2.2.7 Shock Pressure Measurements in a Centrifuge

On-board signal conditioning is recommended for

piezoelectric pressure transducers in a centrifuge based on

two main reasons. First, the reduction in the length of

cable between the transducer and the charge amplifier

reduces the noise level and improves the high frequency

response (Dove and Adams, 1964). Second, such an arrangement

would prevent the integration of noise signals from the

slip rings. In addition to multiple charge amplifiers,

electronic switches are required on-board to discharge the

feedback capacitors.

Figure 4.13 shows a block diagram of the pressure

transducer set-up in the centrifuge. Charge amplifiers and

electronic switches are shown in an instrumentation box

inside the centrifuge. Upon pressing the "fire" knob on the

detonator control unit, a trigger signal is released 2 co

10 microseconds prior to the explosion. A voltage

comparator is used to reduce the rise time of this trigger

signal to less than 10 nanoseconds. This signal is then

used to trigger the oscilloscopes. The relatively fast rise

time of the signal insures that, regardless of the trigger

levels set on individual oscilloscopes, the difference in










t= c




CC 0

c0 0 L

Z < -r














o X
<
0


CO









0U 0
0- Z > 0 -












^LU
LU 0 :













O <


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CD

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LL..
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trigger times on different oscilloscopes would be

negligible (less than 10 ns). Therefore, all

instrumentation channels on the oscilloscopes will have a

common time base.

The output of the comparator is also used to activate

the electronic switches inside the instrumentation box.

However, because of the relatively long distance

(approximately 30 feet) that this high frequency signal has

to travel, it is important to use a line driver to prevent

the distortion of the signal.

Figure 4.14 shows the electronic circuitry for the scope

trigger and the line driver. The trigger signal from the

detonator control unit has an amplitude of 30 volts. This

amplitude is first reduced by using a voltage divider (30V

X 1.1 K2/ 5.6 K2 = 5.9 V ). The noise floor for the

comparator, beyond which the comparator (LM 361) output

goes to the limit (5 Volts), is set at 0.5 Volts by using

another voltage divider ( 12 V X 2KQ/51 KM = 0.5 Volts).

Tne comparator is a very high-gain amplifier with well-

balanced difference inputs and controlled output limits

(Malmstadt et al., 1981). If a signal larger than the

noise floor (0.5 V) appears at pin 3, the comparator

outputs a 5 volt signal with a very fast rise time.

A capacitor (0.68 pF) is used for filtering the

reference voltage and two capacitors (1 pF) on the power

supply are also used as noise filters. The comparator

output is then used to trigger the oscilloscopes located

















> cc










LL
3: .







nearby. A line driver (DS 75450) is used to preserve the

high frequency components of the comparator output over a

distance of 30 feet to the centrifuge. An insolation

transformer is used to float the cable: that is to

disconnect the ground of this circuit from the ground in

the instrumentation box in the centrifuge.

Figure 4.15 shows the charge amplifiers and other

electronic circuitry on-board the centrifuge. A monostable

multivibrator or one-shot (1/2 74221) is used to provide a

window in which to accept data. This window is the time

frame during which the electronic swLtches are activated

and the feedback capacitors are not discharged. This time

is a function of the external capacitance and resistors and

can be changed by adjusting a variable resistor (10 K2).

For the tests reported here, the window was set to exceed

the time covered by the oscilloscope screens. DS 1488 is an

interface driver and is used as a level shifter to

interface two families of logic: CMOS and TTL.

Each charge amplifier has an analog switch (4066) which

is placed across a feedback capacitor (1000 pF). Another

switch (IH 5011) may be used instead in order to obtain

better performance. AD 515 is a very high impedance

electrometer operational amplifier. Information on all

commercial electronic components used in the circuits

explained here are given in Appendix A. A total of eight

charge amplifiers were built and placed in the

instrumentation box on board the centrifuge.




























0 0 0 0
0000


L__
U, -C











Cj












--- -- --- -- --













0 to




Ln
*~ 0



















*1
I.


- - - - - - L L L








\ i
- I I
to




-..

SI I I U I


z Z! Z ~
a L.- -I









4.2.2.8 Calibration of PVDF Pressure Transducers

In general, the output voltage of the charge amplifier

can be related to the applied pressure as follows:


Q A d o
V = --- Equation 4.13
Cf C

where,

V = Output voltage of the charge amplifier

Q = Charge on the feedback capacitor

Cf = Capacitance of the feedback capacitor

A = Surface area of the pressure transducer

d = Piezoelectric constant

a = Applied pressure

When A, d, and Cf are known, output voltage and stress

can be directly related:

V = K a Equation 4.14

Where,

Ad
K =-- Equation 4.15
Cf


The piezoelectric coefficient d33 given in Table 4.2 can

not be used here for pressure measurements at the soil-

structure interface, even though the stress direction is

essentially perpendicular to the gage surface (direction 3).

The reason is that the confining effect of concrete and soil

creates a more complex state of stress in the gage resulting

in a different apparent piezoelectric coefficient (Dragnich








and Calder, 1973). Therefore, it is essential that the

calibration of transducers be conducted under conditions

similar to the actual test.

A special test arrangement was designed for this

calibration. A 1 inch-thick circular micro-concrete slab (3

inch diameter) was built. Three 1/4 in X 1/4 in PVDF gages

were taped on the slab as shown in Figure 4.16. A cardboard

cylinder with an inside diameter of 3 inches was placed

around the slab such that it extended 1/4 inch above the top

of the slab. A 1/4 inch-thick layer of sand was placed on

top of the slab. The test specimen was then placed in an MTS

testing machine to be subjected to cyclic loads. A 1 inch-

thick circular steel plate and a load cell were placed on

the specimen as shown in Figure 4.17.

Sinusoidal loads were applied on the specimen with

varying frequencies of up to 50 hertz. Only one level of

peak stress (162 psi) was tested because of an equipment

malfunction after the first series of tests were completed.

However, because of the relatively low stress levels (less

than 2000 psi), the gage response is expected to be linear

(Meeks and Ting, 1983).

The charge amplifiers and other electronic circuits used

for the actual tests were also utilized for these

calibration tests. The sequence of events was as follows:

first, the load was applied on the specimen. second, the

control unit of the detonator was used to send a trigger

signal (no explosion) to activate the switches and trigger












SAND
SL-AB LAYER


PVDF
TRANSDUCERS

-U
/A h


CARDBOARD
CYLINDER


PVDF
TRANSDUCERS


Figure 4.16. Test Specimen for Calibrating Pressure Gages











MTS TESTING MACHINE


Figure 4.17. Test Setup for Calibrating Pressure Gages







the oscilloscope which, in turn, recorded the outputs of the

load cell and the three charge amplifiers for the pressure

transducers.

Figures 4.18 to 4.21 show the applied load and pressure

gage response curves for different frequencies of up to 50

hertz. These figures indicate that, in all cases, the

pressure gage response is sinusoidal and corresponds to the

applied load. It is interesting to note that some pressure

transducers show negative responses. This is due to the fact

that, when the trigger signal is released, the pressure at

that time is shown as zero on the output. Therefore, any

pressure less than the pressure at trigger time appears as

negative in the output. Thus, calibration is based on the

ratio of peak-to-peak amplitudes of applied load and gage

outputs rather than absolute peaks.

The amplitude of response for the gage closest to the

edge of the slab (cardboard cylinder) is consistently lower

than the other two gages which exhibit similar responses.

The reason for lack of uniformity of pressure near the edge

of the slab is believed to be due to transfer of some of the

load in that immediate area to the cylinder. The response of

the gage located in that area is omitted from the

calculation of calibration factor. Table 4.3 summarizes the

calibration test results. These results indicate that

frequency variations (up to 50 Hz) do not have a major

influence on the calibration values.

The calibration factor (369 psi/volt) can be related to










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I I m

,I /
h I c
i /I a "
I I I Ii IL








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SI I I < i


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a. Ix m I I.









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SI I r n I
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Full Text

PAGE 1

CENTRIFUGAL MODELING OF UNDERGROUND STRUCTURES SUBJECTED TO BLAST LOADING BY HABIBOLLAH TABATABAI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1987

PAGE 2

nil

PAGE 3

^ ACKNOWLEDGEMENTS The author wishes to express his sincere appreciation and gratitude to the chairman of his supervisory committee, Dr. Frank C. Townsend, for providing him with the opportunity to conduct this research and for his continued support and encouragement throughout the course of this study. Appreciation is also expressed to Dr. David Bloomquist and Dr. Michael McVay for their help and advice. Further gratitude is extended to Dr. Clifford 0. Hays, Dr. Mang Tia and Dr. Douglas Smith for serving on his supervisory committee. The author is grateful to Mr. Dan Ekdahl of the Digital Design Facility for his help in the design and building of the electronic couiponents , and to Dr. J.C. McGrath of the Thorn EMI Central Research Laboratories in England for his help and advice and for providing a PVDF sample for pressure transducers. The author is specially thankful to his friend, Mr. Krai Soongswang, for his help, advice and encouragement throughout his graduate work. The author wishes to express his love and gratitude 11

PAGE 4

to his parents and family for their continued ecouragement and support. The funding of this research by the U.S. Air Force is also acknowledged and appreciated. Ill

PAGE 5

Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CENTRIFUGAL MODELING OF UNDERGROUND STRUCTURES SUBJECTED TO BLAST LOADING By Habibollah Tabatabai August 1987 Chairperson: Dr. Frank C. Townsend Major Department: Civil Engineering The survivability of underground military structures may be of critical importance in times of crisis. Reliable and economical design of such structures requires a better understanding of the complex parameters involved. Small-scale model testing of such systems offers major cost savings compared to full-scale tests. The laws of similitude and scaling relationships require some form of dead-load compensation to properly account for the effect of gravity stresses in scaled models. This can be accomplished by subjecting the scaled model to an increased acceleration field through an elevator arrangement or, more suitably, a centrifuge. The objectives of this research are to determine the significance of gravity stresses on the IV

PAGE 6

response of underground structures subjected to blast loading and to evaluate the scaling relationships. A discussion of the scaling relationships and procedures for model construction are presented. A complete instrumentation set-up for the measurements of shock pressures, strains and accelerations on the structure is designed, built and tested. This includes development of Polyvinyidene Fluoride (PVDF) piezoelectric shock pressure transducers and associated electronics. A series of tests at high-gravity and low-gravity environments are performed on 1/60 and 1/82-scale models of an underground protective structure subjected to a scaled bomb blast. Based on the test results it is concluded that the structural responses in the two gravity fields are different and that such parameters as wave speed, pressure magnitudes and structural strains are higher in the highgravity tests. The centrifuge is believed to be a necessary and viable tool for blast testing on small-scale models of underground structures.

PAGE 7

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ii ABSTRACT iv CHAPTERS 1 . INTRODUCTION 1 1 . 1 General 1 1.2 Review of Previous Work 3 1.3 Objectives 6 1 . 4 Scope of Work 6 2. SIMILITUDE AND MODELING 8 2.1 Introduction 8 2.2 Similitude For Underground Structures.. 11 2.3 Gravity Effects 18 2.4 Construction of Small-Scale Models 25 2.4.1. Micro-Concrete 25 2.4.2. Reinforcement 26 2.4.3. Mold And Model Construction.... 27 3. TESTING EQUIPMENT AND SPECIMENS 29 3.1. Centrifuge 29 3.2. Test Specimens 35 4. INSTRUMENTATION AND DATA ACQUISITION 39 4.1. Introduction 39 4.2. Instrumentation 40 4.2.1. Electrical Resistance Strain Gages 40 4.2.1.1 Strain Gage Measurements in a Centrifuge 46 4.2.1.2 Electronic Circuits For On-board Strain Measurements 50 VI

PAGE 8

4.2.1.3 Calibration of Strain Gage Bridges 50 4.2.1.4 Strain Gage Setup on the Test Structure 55 4.2.2. Piezoelectric Shock Pressure Transducers 59 4.2.2.1 Introduction to Piezoelectricity 59 4.2.2.2 Polyvinylidene Fluoride (PVDF) 61 4.2.2.3 PVDF Pressure Transducer 66 4.2.2.4 Electronic Circuits for Piezoelectric Transducers 70 4.2.2.5 Voltage Measurements.... 71 4.2.2.6 Charge Amplifiers 75 4.2.2.7 Shock Pressure Measurements in a Centrifuge 78 4.2.2.8 Calibration of PVDF Pressure Transducers.... 84 4.2.2.9 Pressure Gage Setup on the Test Structure 94 4.3. Piezoelectric Accelerometers 94 4.3.1 Coriolis Accelerations 94 4.3.2 Accelerometer Setup on the Test Structure 98 4.4. Detonators 101 4.5. Overall Instrumentation and Data Acquisition 103 5. TESTING PROCEDURES 108 6. EVALUATION OF TEST RESULTS 116 6.1. Pressures 116 6.1.1. Pressure Gage Pi 117 6.1.2. Pressure Gage P2 127 6.1.3. Pressure Gage P3 150 6.1.4. Pressure Gage P4 163 6.1.5. Pressure Gage P5 167 6.1.6. Pressure Gage P6 167 6.2. Accelerations 167 6.2.1. Accelerometer Al 177 6.2.2. Accelerometer A2 194 6.3. Strains 211 6.3.1. Strains in Top Slab 212 6.3.2. Strains in Side Wall 219 6.3.3. Strains in Bottom Slab 232 6.4. Velocities 249 6.4.1. Velocity VI 255 6.4.2. Velocity V2 265 6.5. Displacements 270 vii

PAGE 9

6.5.1. Displacement Dl 270 6.5.2. Displacement D2 281 7. CONCLUSIONS AND RECOMMENDATIONS 284 7.1. Conclusions 284 7.2. Recommendations for Future Studies 287 APPENDICES A ELECTRONIC COMPONENTS OF THE INSTRUMENTATION SYSTEM 289 B COMPUTER PROGRAMS WRITTEN ON HP 9316 297 REFERENCES 307 BIOGRAPHICAL SKETCH 312 Vlll

PAGE 10

CHAPTER 1 INTRODUCTION 1.1 General The survivability of underground military structures may be of critical importance in times of crisis. Reliable and economical design of such structures requires a better understanding of the complex parameters . involved. Although, in recent years, there have been advances made in the development of analytical methods for the study of such systems, structural testing is believed to be essential considering the existing uncertainties and complexities in evaluating the performance of underground structures subjected to blast loads. Defense-related agencies regularly perform full-scale or scaled model tests on buried protective structures. Although full-scale testing may be ideal in terms of evaluating structural response, the economic costs may be substantial. Small-scale model testing (1/10 to 1/80) offers major cost savings, thereby allowing a larger number of tests to be performed for the purpose of parametric studies or evaluating repeatability. There are several important factors to be considered in blast tests on small-scale models. First, the development of model materials such as microconcrete and miniaturized

PAGE 11

reinforcement with properties similar to the prototype is an important consideration. The ability to build smallscale models within acceptable tolerances is another major concern. Second, the development and proper understanding of the scaling relationships, based on which the scaled model is designed and the observed response on the model is extrapolated to predict the response of the full-scale (prototype) structure, are essential. Third, the development of instrumentation methods and devices for the measurements of such parameters as shock pressures, strains and accelerations on small-scale models is another important consideration. Complete adherence to the scaling relationships developed on the basis of the laws of similitude would require some form of dead-load compensation to properly account for the effect of gravity stresses. For example, in static tests on model bridges, it is customary to account for the discrepancy between the prototype and model deadload stresses by adding sufficient weight to the bridge in such a way as not to add stiffness to the structure. In dynamic tests on super small-scale models, this problem becomes more complicated because of the relatively smallsize structures involved and the problem of accounting for increased mass in a dynamic test. An alternative would be to subject the scaled model to an increased acceleration field through an elevator arrangement or, more suitably, a centrifuge. Researchers

PAGE 12

have generally ignored the effect of gravity on the response of buried structures based on the argument that, for shallow-buried structures subjected to blast loading, gravity stresses are generally much smaller than blastinduced stresses. Also, the relative complexity of compensating for gravity stresses has been another important consideration. However, it is clear that in some soils, properties such as stiffness and strength are directly related to gravity stresses (or depth of soil). In addition, the degree of soil-structure interaction could very well be a function of gravity stresses. To answer some of these questions, the U. S. Air Force sponsored this research project to determine the significance of gravity stresses (centrifuge testing) on the response of models of underground structures subjected to blast loading. 1 . 2 Review of Previous Work During the last 50 years, the centrifuge has been frequently used as a tool in geotechnical testing, especially in Europe and the Soviet Union. In recent years, there has been an increased interest in using this technique to study soil mechanics and soil-structure interaction problems including underground structures. Many researchers have conducted centrifuge tests to study varied subjects such as offshore gravity structures (Prevost et al., 1981), coal waste embankments (Al-Hussaini et al., 1981), consolidation of phosphatic clay

PAGE 13

(Bloomquist, 1982), buried large-span culverts (McVay and Papadopoulos , 1986), abutments (Randolph et al., 1985), embankment dams and dikes (Fiodorov et al . , 1985), pile installations (Craig, 1985), and laterally loaded pile groups in sand (Kulkarni et al . , 1985). Schmidt and Holsapple (1980) conducted a number of blast tests in a centrifuge to study the effectiveness of the centrifuge technique for modeling explosive cratering in dry sand and to validate their derived similarity requirements. These experiments used 0.5-4 grams of Pentaerythritol-tetranitrate (PETN) and 1.7 grams of leadazide explosives in tests at zero depth of burial and at gravities as high as 450 g's. The authors conclude that the centrifuge is an effective tool for such tests. Based on the observed symmetrical cratering in these tests, they also suggest that the Coriolis effects are insignificant (Coriolis effects are explained in Chapter 4). In addition, the authors recommend a non-dimensional parameter (discussed in Chapter 2) for determining an equivalent charge for simulating large explosive yields with small charges at elevated gravities. Nielsen (1983) conducted a number of blast tests in a centrifuge to evaluate the suitability of the centrifuge technique for the measurement of free-field blast pressures in soil. In some tests less than 1 gram of Cyclotrimethylenetrinitramine (RDX) and PETN explosive was placed in the sand and then detonated at 50 g's. The soil

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pressures at different locations were measured. In other tests, the explosive was placed inside a microconcrete burster slab (which, in the design of underground protective structures, serves to prevent deep penetration of the weapon into the soil). The explosives were detonated at gravities of up to 90 g's and pressure measurements were taken at different locations in the sand beneath the burster slab. The author suggests that the centrifuge is a suitable tool for such measurements. The author also recommends the use of larger centrifuges and improvements in the instrumentation and data-acquisition arrangements. Baird (1985) presents a survey of the instrumentation problems for explosive centrifugal testing and provides a list of commercially available transducers and dataacquisition systems that have a potential for use in such tests. Bradley (1983) and Cunningham et al . (1986) discuss scaling relationships and model materials for blast testing in a centrifuge, respectively. Kutter et al . (1985) report preliminary results of a number of blast tests on scaled aluminum models of a buried reinforced concrete pipe (tunnel) at 1, 50 and 100 gravities. The two types of explosive charges used contained 64 and 512 mg of PETN . Horizontal accelerations on one side of the models were measured. The authors suggest that the effect of gravity becomes more important

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as the range from the blast source increases and as the relative size of the explosion decreases. 1. 3 Objectives The objectives of this research program are as follows: 1) To develop instrumentation methods and devices for the measurement of shock pressures, strains and accelerations in centrifuge blast tests on small-scale microconcrete models of underground structures and to develop general testing procedures for such tests. 2) To perform blast tests on small-scale models of an underground structure at low-gravity (Ig) and high-gravity (centrifuge) environments, and to study the differences in response, if any, between the two testing conditions and thereby ascertain the significance of gravity stresses in the response of such structures. 3) To evaluate the validity of scaling relationships by performing and comparing blast tests on two different sized scaled models (1/60 and 1/82-scale models). 1. 4 Scope Of Work A complete discussion of the scaling relationships for blast tests on underground structures is presented. Research work performed by Cunningham et al. (1986) and Bradley (1983) in the development of model materials and scaling relationships are summarized. A complete instrumentation and data acquisition set-up

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for the measurements of pressures, strains and accelerations in a centrifuge is designed, built, and tested and detailed procedures for such measurements are recommended. This includes the development of Polyvinylidene Fluoride (PVDF) piezoelectric pressure transducers and associated electronics for pressure measurements at the soil-structure interface and design of electronic circuits for strain measurements. A series of tests are performed on 1/60and 1/82-scale models of an underground structure subjected to a scaled 500-lb bomb blast at low-gravity (Ig) and high-gravity (60or 82-g's) environments. The results are evaluated for the purpose of determining the significance of gravity stresses (centrifuge testing) and for evaluating the scaling relationships .

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CHAPTER 2 SIMILITUDE AND MODELING 2.1 Introduction Experimental evaluations of engineering systems are generally recommended especially when such systems are too complicated to yield accurate analytical solutions based on mathematical formulations of the problem. However, prototype testing can, in many cases, be prohibitively expensive. Tests on scaled-down models of the prototype offer an alternative to prototype testing at a generally reduced cost. The design of a model and the relationships, based on which the prototype response can be predicted from the observed response on the model, are based on the laws of similitude. Murphy (1950) defines models and prototypes as follows: " A model is a device which is so related to a physical system that observations on the model may be used to predict accurately the performance of the physical system in the desired respect. The physical system for which the predictions are to be made is called the prototype" (p. 1) . Murphy (1950) also comments that " the theory of similitude includes a consideration of the conditions under which the behavior of two separate entities or systems will be 8

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similar, and the techniques of accurately predicting results on the one from observations on the other" (p. 1). Structural models have been widely used to evaluate the performance of underground structures subjected to blast loading. Parametric studies can be performed on such models to evaluate the significance of different factors such as varying soil conditions, sizes of threat, structural configurations, etc . The most common relationship in blast wave scaling is based on the Hopkinson or cube-root scaling. This law states that "self -similar blast (shock) waves are produced at identical scaled distances when two explosive charges of similar geometry and the same explosive, but of different size, are detonated in the same atmosphere" (Baker et al . , 1973, p. 55). The dimensional scaled distance, Z, is defined by the following equation: R Z = -, /.. Equation 2.1 W -^ where R is the distance from the explosive and W is the energy (or weight) of the explosive. Figure 2.1 illustrates the Hopkinson blast scaling. Baker et al. (1973) reviewed several other scaling relationships developed for blast. A more systematic approach to scaling is through the laws of similitude and the theory of models. The first and by far the most important step is to determine the pertinent variables in the problem. According to the Buckingham's Pi theorem, the relationship among these variables can be

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10 AR -jrL T \J Figure 2.1. Hopkinson Blast Scaling (Baker et al., 1973) (Reprinted by Permission of the Southwest Research Institute)

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11 described by a set of S dimensionless and independent terms called Pi (n) terms which are products of the pertinent variables. S = n r Equation 2.2 Where S is the number of it terms, n is the number of variables and r is the number of fundamental dimensions. In a dynamic engineering problem, these fundamental dimensions are generally selected to be either force, length and time, or mass, length and time. There can be infinite sets of correct tr terms. However, in each set the total number of dimensionless and independent terms is limited to S. Similitude requirements establishing the relationship between model and prototype is determined by equating the dimensionless tt terms in the model and prototype. Therefore TT. = IT. i = 1,2,. ..,S Equation 2.3 where m and p denote model and prototype respectively. More information on similitude requirements for static or dynamic modeling is presented by Murphy (1950), Langhaar (1951), Young and Murphy (1964), Tener (1964), Denton and Flathau (1966), Krawinkler and Moncarz (1973), Sabnis et al. (1983) and Bradley (1983). 2 . 2 Similitude for Underground Structures Bradley (1983) presents a list of pertinent variables (Table 2.1), it terms (Table 2.2) and scaling relationships (Table 2.3) for underground structures subjected to blast loading. The relationships in Table 2.3 are based on the

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12 Table 2.1 List Of Parameters (Bradley, 1983) a Stress d Displacement a Acceleration P Characteristic Pressure o E„ Energy n ^-' R Radius H Thickness ^s

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Table 2.2 Solution TT Terms [Bradley, 1983) 13 St c d H a H p '10 11 '12 H P. C2 c s E. TT C E 3 H E R H c c IT, '13 '14 15 '16 '17 E c

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14 Table 2.3 Scaling Relationships (Bradley, 1983) Parameter

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15 assumption that the same materials are used in the model as in the prototype, or at least the material properties are kept constant. Strict adherence to the geometric scaling requirements in Table 2.3 means that aggregates in concrete or soil particles would have to be scaled down to meet those requirements. For soils, large reductions in particle sizes can lead to major changes in soil properties. Therefore, such scaling down of all soil particles is not recommended and only large-size aggregates should be scaled down. Sabnis and White (1967) suggest using a gypsum mortar mix to model concrete in small scale models. This would result in material properties similar to concrete. Table 2.3 shows that the acceleration of gravity in the model (g ) should be n times the acceleration of gravity in m ^ -' the prototype (g = Ig) . This condition can be achieved by subjecting the model to an acceleration field. An elevator arrangement or, more suitably, a centrifuge can provide the desirable acceleration field. Almost all research involving model tests on underground structures subjected to blast loads has been performed at Ig, i.e. ignoring the gravity effect and thereby violating one of the requirements for a true model. ''An evaluation of the y significance or lack of significance of ignoring gravity effects in such model tests is presented in Section 2 . 3 .j Modeling explosives is another important consideration in such tests. The geometric scaling of the shape of cased explosives may be an important parameter. For example.

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16 cylindrical-shaped charges may be necessary to model some weapons. Table 2.3 shows that the energy of explosion is scaled by a factor of 1/n . For example, a 500 lb bomb containing 267 lb of TNT can be simulated by a 0.267 lb TNT explosive in a 1/10 scale model test. Schmidt and Holsapple (1980) suggest the following ir term for scaling of energy for various types of explosives for centrifuge testing: 1 1/3 W — Equation 2.4 6 where Q = Heat of detonation per unit mass of explosive 6 = Initial density of the explosive W = Mass of the explosive G = Gravity By equating the above it term for the model and prototype, the scaling relationship can be established m p m W m 1/3 W 1/3 C— 2— ) m m Or w = m (iL ) c m ) (• m ) W Equation 2.5 m «p p Based on this relationship, Table 2.4 shows calculated explosive weights for models simulating various size bombs at different scales or gravities [Nielsen, 1983). The type of

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17 explosive used to model the prototype bombs in these calculations is Cyclotrimethylenetrinitramine (RDX). Table 2.4 Theoretical Model Explosive Simulation Weights (Nielsen, 1983] Centrifuge Environment [Gravities] Threat Designation

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18 with RDX charges that can be used for model tests. Based on the information on the available commercial detonators, the model scale can be calculated using the ir term in Equation 2.4. 2. 3 Gravity Effects In this section the effect of ignoring gravity in model tests of underground structures subjected to blast loads is evaluated. In almost all such model tests in the literature, the effect of gravity is ignored on the basis of the fact that, for shallow-buried structures, the blast-induced pressures are generally much higher than gravity stresses. The effect of neglecting gravity on dynamic time in models is dependent on the nature of dynamic forces. Consider the following ir term in deriving a relationship for dynamic time: Equation 2.7 F t2 f4 1 where F is dynamic force, M is mass, t is dynamic time and 1 is any relevant length. Equating this tt term for model and prototype, IT = ir m p 2 2 m m _ p p ^rr, Im M 1 mm P P Therefore, t^ M 1 F — iIL_ . c i^)C L)( ^3 t M 1 F P p p m Considering the scaling relationships in Table 2.3,

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19 t„ 2 1 1 o (— JL) = ( ]i )(n2) t n-^ n P Or 1 tj„ = t Equation 2.8 If the force causing the dynamic response is applied on the system through gravity alone, then P = g M where g is the acceleration of gravity. Therefore the term in Equation 2.7 can be rewritten in the following form 9 t2 IT = 1 Equating tt terms for model and prototype IT = TT m p 2 2 g^ ^ g ^ ^m "1 _ ^p p Im Ip Therefore, t' g 1 ^ = ( P )( E. t^^ g„ 1 p ^m p If the effect of gravity is not neglected, then ^ 1 2 n ^ -\-

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20 However, if the effect of gravity is neglected, then t2 U)(— ) t^ n '^ Or 1 t = t Equation 2.9 /^ P which is substantially different from Equation 2.8. The following two examples illustrate this effect in systems where gravity is the only force causing the dynamic response of the system. An ideal pendulum is one such system in which gravity is the only force applied on the mass (Figure 2.2Ca)). The period of vibration (T) of an ideal pendulum of length L is T = 2tt /L/g Equation 2.10 If a test is performed on a scaled-down version of this pendulum, the resulting period of vibration can be calculated as follows: /L/g IT = IT m p T T m p /L/g /L/g m' ^m p^ ^p Then T = (/L /L )(/g /g ) T m m' p^ ^ ^p' ^m"^ p If gravity is not neglected, then T^ = Cl/n) Tp If gravity is neglected, then ^m = v/(l/n)(l) T^

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21 Or T = (l//n) T m P Another similar example is the case of determining the time (t) that it takes for a point mass to drop from a height H with zero initial velocity (figure 2.2 [b)). t = /2H/g Equation 2.11 This is similar to Equation 2.10 and yields the same results as in the previous example. Consider a spring-mass system (Figure 2.2 (c)) which is in static equilibrium under its own weight. For the case of a linear spring, the period of vibration (T) of such a system is only a function of its mass M and its stiffness (spring constant K) and not a function of gravity T = 211 /M/K Equation 2.12 Of course, stress in the spring is a function of gravity and any other external force applied on the mass. So, if the system is not linear, K and consequently T would be functions of gravity too. Based on the above argument, it would appear at first that, for underground structures for which gravity stresses are small compared to blast induced stresses, the response time would be independent of gravity assuming the loading functions are the same. However, there are other factors that must be taken into account. Wong and Weidlinger (1983) suggest that, in box-type structures, a part of soil mass around the structure moves with it and therefore the effective mass for the vibration of the structure under

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22 Tm = (I/nTtI) Tp at 1 g Tm = (1/n) Tp at n g's (a) Ideal Pendulum mg H /V777 tm = (1/^) tp at 1 g tm = (1/n) tp at n g's Tm = (1/n) Tp at 1 g Tm = (1/n) Tp at n g's (c) Spring-Mass System Figure 2.2. Gravity Effects on Dynamic Time

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23 blast loading increases. If gravity stresses are not scaled properly, it is believed that the degree of interaction between soil and structure (in terms of movement of soil with structure) would be reduced and the effective mass for structural vibrations would be reduced. This results in reduced response times (Equation 2.12) and higher frequencies for models for which gravity effects are ignored. Other factors may be an increased apparent stiffness of the structure and soil confinement effects on the structure due to higher degree of soil-structure interaction. Perhaps the most important factor to be considered is the possible change in characteristics of shock waves in soils due to gravity. For example, properties such as strength, wave speed, and stiffness of dry sand or gravel are highly dependent on gravity or overburden (Baker et al . , 1973, Pan, 1981 and 1982 and Kutter et al . , 1985). Therefore, it is expected that in models in which gravity is not properly accounted for, there would be a decrease in strength and stiffness of soil (compared to prototype) and thereby greater attenuation of shock waves could be expected. For models subjected to proper acceleration fields (gravity) , it is expected that the shock wave will arrive faster with smaller rise times (higher frequency content) and higher magnitudes of pressure. Denton and Flathau (1966) conducted a series of load tests on buried circular aluminum arches at different

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24 scales. They reported relatively good agreement in strain and deflection results due to the applied loads even though gravity was ignored. However, the applied loads were quasistatic: that is the load durations were much greater than the period of vibrations for the structure (Baker et al . , 1973). Baker et al. (1973) report a study performed by Hanna et al . on half -buried steel containment shells subjected to an internal blast. It is reported that the peak strain did not appreciably change in different tests. However, large shells exhibited increased damping which was attributed to gravity effects which were not properly scaled. Young and Murphy (1964) conducted tests on buried aluminum cylinders at different scales. Load was applied by dropping a weight on the surface of the sand. However, the drop height for different size models was kept constant (not scaled) in order to obtain the same velocity of impact in all tests. This is equivalent to scaling the drop height and subjecting the mass to an increased gravity field. The authors attribute some discrepencies in test results to the fact that the weight of soil was not scaled. Gran et al. (1973) compared tests on 1/30 and 1/6-scale models of a buried cylindrical missile shelter. They reported good agreement in results. The soil wave speed in the 1/6 scale test (400 m/s) was higher than that in the 1/30 scale test (250 to 400 m/s). This was attributed to differences in soil density due to imperfect soil placement. They also reported that the concrete strain responses were

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25 generally reproduced, although the magnitudes of the strains differed somewhat. In summary, the use of centrifuge for model tests on underground structures subjected to blast loads is warranted based on the belief that the increased gravity field affects such things as the characteristics of shock waves in soils and the degree of interaction between soil and structure resulting in added mass, stiffness and confinement for the structure. 2 . 4 Construction of Small Scale Models 2.4.1 MicroConcrete The scaling relationships presented in Table 2.3 are derived on the assumption that the material properties in the models remain the same as the prototype. Therefore, it is essential that the micro-concrete used in the small scale models have the same properties as prototype concrete. Sabnis and White (1967) recommended gypsum mortar to be used for small scale model tests. Cunningham et al. (1986) give the following reasons for choosing gypsum over portland cement in super small scale modeling: 1. Relatively large particle sizes in portland cement can cause problems for models smaller than 1/60 scale. 2. Curing time for cement is generally 28 days while gypsum cures very rapidly and can be removed from its mold within an hour. In fact when micro-concrete reaches its desired strength, the surface is coated with shellac to prevent

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26 further variations in strength and eventually brittleness. 3. In very small scale models, shrinkage problems with Portland cement can be severe, while gypsum exhibits very low distortion upon curing. The micro-concrete mix selected uses gypsum cement, sand and water in a ratio of 1:0.8:0.25 by weight. The resulting properties for such a mix are as follows: f = 4085 psi c ^ f'^ = 327 psi Y = 130 pcf E = 3.3 X 10^ psi c "^ 2.4.2 Reinforcement The primary concern in developing reinforcement for small scale models is to have similar properties in the model and prototype. The following three properties and characteristics are considered important in the development of miniaturized reinforcement (Cunningham et al . , 1986): 1. Yield strength 2. Modulus of elasticity 3. Bond development The prototype steal generally has a yield strength of 60 ksi and a modulus of elasticity of 29000 ksi. Black-annealed steel wires (gages 28, 24, 22) were chosen as model reinforcement. Annealed steel wire has lower yield strength (40 to 60 ksi) than cold-rolled steel wire (80 to 100 ksi) and it is widely available. In order to provide sufficient bond

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27 between micro-concrete and steel wire, a method developed at Cornell University was utilized. A deforming machine, made up of two pairs of perpendicularly mounted knurling wheels, was built. 2.4.3 Mold and Model Construction An aluminum mold was used to build the micro-concrete boxtype models and a cast acrylic mold was used to build the burster slab (Gill, 1985). The reason for using an aluminum mold for the box type model was that there were problems in removing the cast acrylic mold. The aluminum mold included a collapsible inner column and break-away outer walls. Miniaturized reinforcement was placed in the mold by drilling holes on the molds and stringing the micro-reinforcing wire prior to casting the concrete (Figure 2.3).

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28 Figure 2.3. Aluminum Mold for Structural Model (Gill, 1985)

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CHAPTER 3 TESTING EQUIPMENT AND SPECIMENS 3 . 1 Centrifuge The University of Florida geotechnical centrifuge (Figure 3.1) has a radius of 1 meter and a capacity of 2125 g-kg. Two buckets containing the test specimen (Figure 3.2) and the counterweight (Figure 3.3) are attached at the two ends of the centrifuge arm by means of two aluminum support frames. The bucket containing the test specimen has inside dimensions of 10 in X 12 in X 10 in deep (McVay and Papadopoulos , 1986). The counterweight is used to balance the forces applied on the centrifuge arm by the test specimen . The test specimen and the counterweight are placed in the buckets while the buckets are in an up-right position before spinning the centrifuge. Connections between the buckets and the support frames are built such that the buckets could rotate around the point of connection. Figure 3.4 shows that the center of mass of the bucket (with contents) is below the point of connection to the support frame. Therefore, when the centrifuge is accelerated from rest to full speed, the net centrifugal force acting on the center of mass of the bucket produces a net moment around the connection 29

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30 Figure 3.1. University of Florida Geotechnical Centrifuge

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31 Figure 3.2. Bucket Containing Test Specimen Figure 3.3. Bucket Containing Counterweight

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32 e 0) 3 u-i •H c U
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33 point. This results in the rotation of the bucket by 90 degrees at which point the net moment is zero (Figure 3.5). The relationship between centrifugal acceleration (a) and angular velocity of the centrifuge (w) is given in the following equation: 2 a = r w Equation 3 . 1 In this case, r is the distance from the center of rotation of the centrifuge to the center of mass of the test specimen (soil plus structure) in the rotated position. For example, to obtain a centrifugal acceleration of 60 g's for a radius of 36 inches: (60 g)(32.2 ft/sec^)(12 in/ft) = (36 in) (w^) Or w = 25.4 rad/sec or w = 242 rpm Since the height of the test specimen is small compared to the length of the centrifuge arm, variations of centrifugal accelerations along the height of the test specimen are believed to be negligible. The rotating nature of a centrifuge makes it impossible to have instrumentation wires from inside the centrifuge directly connected to outside devices. These wires must pass through slip rings, unless other schemes such as telemetry or on-board data capture and storage are devised. Slip rings operate based on a sliding contact mechanism. A total of 64 slip rings are available on the U.F. centrifuge.

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34 VX>XX-N.WV CENTER OF ROTATION BUCKET SOIL STRUCTURE DIRECTION OF CENTRIFUGAL ACCELERATION AFTER SPINNING BEFORE SPINNING Figure 3.5. Orientation of Bucket Before and After Spinning

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35 3 . 2 Test Specimens The original prototype structure considered for centrifuge model testing in this research effort was a multi-bay underground structure (with burster slab) designed for use as shelter for Ground Launched Cruise Missiles (Bradley, 1983). However, the objectives of this research program are to develop methods and evaluate modeling relationships and techniques for centrifuge tests, rather than to be a detailed study of the performance of a specific structure. Therefore, a slightly simplified version of the prototype, which included a one-bay (box-type) structure (instead of 3 bays) with burster slab, was built at two different scales of 1/60 and 1/82. Figures 3.6 and 3.7 illustrate the shape and sizes of the models. A total of three 1/60-scale and two 1/82-scale structures were built using a gypsum mortar mix as concrete and deformed steel wire as reinforcement (Chapter 2). Reinforcement details for 1/60 and 1/82-scale models are given in Gill (1985). The criteria, based on which, the size of models for such tests are selected are as follows: 1. Ability to construct small-scale models is a primary consideration. Super small-scale models may pose difficulties in terms of building molds or formwork within acceptable tolerances, designing and obtaining micro-concrete with specific properties, and providing for steel reinforcement and its placement within acceptable tolerances.

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36 BURSTER SLAB ONE-BAY STRUCTURE Figure 3.6. General Shape of the Structural Model

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37 CENTRIFUGE BUCKET BURSTER SLAB DETONATOR SAND DIMENSION (INCH)

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38 2. Simulating explosives in small-scale models generally involves very small-size charges that may have to be custom-made in order to satisfy geometry and size (explosive weight) requirements. Another, perhaps more convenient approach would be to choose from a limited number of commercially available explosive charges and calculate the model scale, for which, the commercial charge would be an appropriate simulation of the size of the threat on the prototype structure (Section 2.2], For example, two coitimercially available explosive charges (Standard and modified Reynolds RP-83] were used to simulate a 500-lb bomb threat on 1/60 and 1/82 scale models in this research work. Safety concerns with regard to detonating large explosive charges in a centrifuge is also a limiting factor on the model scale selected. 3. Size and capacity limitations for the centrifuge should also be considered in selecting a model scale. Models that are too large may cause obvious problems in centrifuge tests. 4. The type of instrumentation planned for model tests may also be dependent on, and limited by, the size of the model in super small-scale models. A complete review of instrumentation for centrifuge tests is given in Chapter 4. Based on the above arguments, two model scale sizes (1/60 and 1/82] were selected for the tests reported here.

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CHAPTER 4 INSTRUMENTATION AND DATA ACQUISITION 4 . 1 Introduction Instrumentation and data acquisition in centrifugal model tests pose unique challenges in that the conventional methods and instruments may not be adequate to handle the special conditions associatea with a centrifuge. Blast testing in such an environment also adds to the complications involved. There are several factors that should be considered in the design of effective instrumentation and data acquisition methods for such a system. The primary concern is the existence of electrostatic and magnetic noise sources in the centrifuge which could affect the electrical signals. In fact, slip rings, through which all signals have to pass to exit the centrifuge, are inherently noisy because of their sliding contact mechanism. Another factor to be considered in small-scale modeling is the necessity of having measuring instruments small enough, both in mass and size, compared to the model such as to minimize distortions in the model response. Finally, the relatively high frequency signals associated with blast 39

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40 waves require accurate instruments with sufficiently high sampling rates to properly record the event. In this chapter a complete explanation of the development of methods for the measurement of strains, pressures, and accelerations in centrifugal testing of small scale models subjected to blast loading is presented. However, most of the following discussions equally apply to other kinds of instrumented testing in a centrifuge. 4 . 2 Instrumentation In this section the basic concepts of electrical resistance strain gages, piezoelectric pressure transducers and piezoelectric accelerometers are reviewed. Development of new procedures and modifications to conventional methods are also discussed. 4.2.1 Electrical Resistance Strain Gages Electrical resistance strain gages function on the basis of the change in the electrical resistance of the gage in response to strain. When properly bonded to a test surface, these gages exhibit slight changes in resistance (relative to their original resistance) as a function of strain in the test specimen. Each gage has a constant factor, called the gage factor, which determines the relationship between the relative change in resistance and the strain, according to the following equation:

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41 5R g_ R F = 2 — Equation 4.1 where F is the gage factor, 5R and R are the change in resistance and the resistance of the gage, respectively, and e is the strain in the gage. The usual way to monitor such changes in resistance is through a Wheatstone bridge (Figure 4.1). The four arms of the bridge consist of four resistors, one of which is the strain gage R . In such case the circuit is called a quarter bridge. The bridge is powered by a voltage power supply V. . A bridge is called balanced when the potential level at points b and d are equal or, in other words, the output voltage is zero (Figure 4.1). Therefore, voltage drop across a-d is equal to voltage drop across a-b. V , = V . and V, = V, ad ab be dc or R I =R-,I-, and R,It=RtI„ gg33 1122 where I, , I„, I,, and I represent electrical current in the four arms of the bridge as shown in Figure 4.1. Similarly, because of zero voltage across b-d, I, = I^ and I„ = I^ i g 2 3 Therefore , R I, = R-,1^ and R, I, = R-I-, gi 32 11 22

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42 Figure 4.1. Basic Wheatstone Bridge

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43 Thus, for a balanced bridge, R R^ — ^ — — Equation 4.2 ^1 ^2 In the balanced bridge method of calculating strains, the Wheatstone bridge has to be first balanced in the 'noload' or unstrained condition. This can be accomplished by using a variable resistor for R, and changing it until the output voltage V becomes zero. The bridge must again be balanced in the strained condition by readjusting R, . 6R-, = R-,( strained) R, [unstrained) From equation 4.2: Rg = (R3/R2) R^ Since R^ and R„ are constant, 6R = [R3/R2) 6R-L Equation 4.3 However, substituting 6R into Equation 4.1, R3 e = 6R-] Equation 4.4 R^ R F 2 g Equation 4.4 is valid only when the bridge is balanced. This is called the 'balanced bridge' method of calculating strains. Most regular strain gage indicators are based on this concept. However, in dynamic tests, where continuous monitoring of strain is required, the output signal does not stay constant for a sufficient time to balance the bridge, specially when several strain gages have to be monitored simultaneously. The 'unbalanced bridge' method

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44 relates the output voltage of the bridge to the resistance change, or strain, in the gage. Therefore, bridge balancing is not required and equation 4.4 does not apply any longer. Williaras and McFetridge (1983) present equations relating strains to the output voltages at unstrained and strained conditions, supply voltage and gage factor. V , = R I ab g g I = V./(R +Ri ) g 1^ ' g 1' Therefore, in the unstrained or initial condition, R ^^ R + R, ' g 1 And in the strained or final condition, ,f V ab" (R + 6R ] __2 2 V. (R + 6R )+ R, ^ g g 1 ^V,K= V^ KV^ , : ab ab ab [R + 5R ) g g [Rg^ 6Rg)^ R^ If R, is selected to be equal to R , R R + R, g 1 V. 5R 6V , = ab 4R + 26R g g ^i However , 6V = -6V ab This is because the potential at d is unchanged and therefore any change in potential across bd (5V ) must be due to the change in potential at b. Therefore,

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45

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46 cause resistance variations in the lead wires and thereby introduce errors in the measurements. For short-term tests this problem may not be critical because of the small probability of large temperature variations in a short period of time. However, this effect can be completely eliminated by employing a three-wire arrangement instead of a two-wire setup as shown in Figure 4.2. In this method, equal lengths of lead wires exist in two adjacent arms of the bridge and since resistance changes in adjacent arms make opposite contributions to the output voltage (Dove and Adams, 1964), the overall effect is thereby eliminated. 4.2.1.1 Strain Gage Measurements in a Centrifuge The use of commercially available strain indicators may not be suitable for centrifugal testing. Because of the size and number of these indicators, they generally have to be placed outside the centrifuge. Therefore, the gage connection to the Wheatstone bridge passes through slip rings. This can cause serious problems because the slip rings are inherently noisy and resistance changes in slip rings can be as large as the resistance changes in the strain gages (Hetenyi, 1950). In addition, in regular strain indicators, the low-level output voltage of the bridge is increased with an amplifier. Depending on the gain, the amplifier has a frequency range in which that gam remains constant and the amplifier exhibits a linear response [Figure 4.3). If the signal frequency is beyond

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47 CO 0) 4J c Q) 6 (U s-i 3 0] 10 0) s Id u u Ul M o M-l 3 U M •H U (U i-l •H I 0) 0) Vh J= El CM 3 •H Eg

PAGE 57

48 < o CE LLj Li. FREQUENCY Figure 4.3. Gam Versus Frequency Response of Amplifiers

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49 the frequency range of the amplifier, distortion of the response associated with that frequency will occur. Therefore, in blast testing, where higher frequency signals are expected, the characteristics of the regular strain indicator may not be suitable. A solution to these problems can be achieved through onboard signal conditioning and circuitry. This means that electronic circuit boards containing multiple Wheatstone bridges and instrumentation amplifiers can be specially designed and built. The relatively small size of the electronic board would permit the attachment of the box containing the board on the arm of the centrifuge. Of course, the box has to be located as close to the center of rotation as possible to reduce unwanted centrifugal accelerations on the electronic components. Such an arrangement would eliminate the effect of resistance changes in the slip rings on the output voltage of the Wheatstone bridge due to the fact that the slip rings are not on the arm of the bridge anymore. Also, since the Wheatstone bridge is relatively close to the gage, the lead wires are shorter and noise pickup by those wires will be reduced. In addition, since the output voltage is amplified with an instrumentation amplifier before the signal passes through slip rings, the signal to noise ratio will be much higher.

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50 4.2.1.2 Electronic Circuits For On-Board Strain Measurements Figure 4.4 illustrates the basic electronic circuit for each strain gage. The strain gages used in the tests discussed in this report had a resistance of 120 ohms. The basic circuit consists of a quarter-bridge (one active gage] completion unit and an instrumentation amplifier. The quarter-bridge completion unit consists of one 120-ohm and two 1000-ohm precision resistors as shown in figure 4.4. It is very important that the resistors have nigh precisions in order to reduce errors. The bridge is powered with + 3 DC volts. The same power supply is used to power the instrumentation amplifiers. In these tests the strain gage power supply unit was placed outside the centrifuge. However, batteries can be placed on-board to power the bridge and the amplifier. The amplifier used is Burr-Brown Model INA 101 which is a high-accuracy instrumentation amplifier. It responds only to the difference between the two input signals and has very high input impedance (10 ohms) . Characteristics of INA 101 are presented in Appendix A. The gain for this amplifier is set through an external resistor. In this case, the gain was set at 100, which for frequencies below 10000 hertz remains constant. 4.2.1.3 Calibration of Strain Gage Bridges The output voltage of the bridge can be theoretically related to strain through equation 4.6. Therefore, for a one

PAGE 60

51 u. CM CM Z) CL HZ) o 'J) CJ3 (0 w o 3 O -H c o >>( o 0) r-( 0) 3

PAGE 61

volt change in the output voltage of the amplifier C
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53 gage factor of 2.10. Equivalent calibration values (sensitivities) for strain gages used in the tests which had gage factors equal to 2.065 and 2.05 are calculated using the following equation which is derived from equation 4.6. Sensitivity at New Gage Factor Sensitivity at Gage Factor Equal to 2.10 X 2.10 New Gage Factor Channel No. 3 shows a different calibration factor than the others which may be due to lack of precision of the resistors in the Wheatstone bridge. For noise considerations, it is important that the lead wires connecting the strain gages to bridge completion units be twisted and shielded and the shield be grounded properly at the ground surface on the bridge completion board. The cable used in these tests was Microi4easurements ' type 326-DSV which is a stranded tinned-copper wire, 3conductor twisted cable with vinyl insulation, braided shield and vinyl jacket. Separate ground wires were used for each amplifier. The two-wire outputs for all channels exited the centrifuge through slip rings. Each pair of wires corresponding to a strain gage channel was then connected to a coaxial cable through a BNC connector. Coaxial cables [30 feet long] then carried the signals to Nicolet digital storage oscilloscopes. Figure 4.5 shows the overall schematics of the strain gage setup.

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54 LU o o LU J|_ 05 o -I Z CO ?;: o CO DC LU i X

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55 Table 4.1 Strain Gage Sensitivity Measurements ** Amplifier Output Voltage [Milivolts) For Strain Gage Channels

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56 CENTRIFUGE BUCKET BURSTER SLAB DETONATOR SAND i \

PAGE 66

57 flexural strains from the total strains measured on the two gages. Assuming linear strain distributions, total strains are the algebraic sum of axial and flexural strains (figure 4.7). ^a ^ ^f = ^o S ^f = ^i Therefore, e + £• e = Equation 4.7 2 And, e, = e e Equation 4.3 f o a ^ Or Gc = E £• Equation 4.9 f a 1 The size of strain gages used in the tests were chosen considering several factors. First, the gages have to be small relative to the size of the structural model. For example, a gage length of 1/4 inch in a 1/60 scale model is equivalent to a 15-inch long gage on the prototype structure. This may or may not be sufficiently small depending on the strain gradient in the immediate vicinity of the gage. Second, the gage length has to be several times larger than the maximum aggregate size in the microconcrete mix so that the gage readings would be indicative of overall structural strains rather than local strains in the aggregate. Third, physical restrictions related to the application of extremely small gages in

PAGE 67

58 CO <^rTT^ co° li < H "^^ < Z OJ (O W "^ CO c (0 (0 3 c CO 111 o < < H LU

PAGE 68

59 hard-to-access areas may be important. Considering the above factors, a gage length of 1/4 inch was selected for these tests. The gages are manufactured by MicroMeasurements. The gages were installed according to the directions recommended by the manufacturer. 4.2.2 Piezoelectric Shock Pressure Transducers In this study, the pressure transducers were used to determine the shock pressure applied on the structure due to blast loading. A piezoelectric material was chosen for transducer development because of the wide dynamic range and high resonant frequencies associated with piezoelectric transducers (Riedel, 1986). 4.2.2.1 Introduction to Piezoelectricity Piezoelectricity is defined by W. G. Cady (1964) as "electric polarization by mechanical strain in crystals belonging to certain classes, the polarization being proportional to the strain and changing sign with it" (p. 4) In other words, piezoelectric materials generate electrical charge when subjected to pressure. In fact piezoelectricity means "pressure electricity" (Kantrowitz, et al., 1979, p. 308). Pierre and Jacques Curie discovered this property in 1880 (Cady, 1964). Some materials such as Rochelle salt, tourmaline and quartz are naturally piezoelectric. Some other materials, called ferroelectric, can be made piezoelectric through

PAGE 69

60 artificial polarization, in which material characteristics can be controlled through the manufacturing process (Endevco 101, 1986) . The major advantage of piezoelectric materials when used as shock pressure transducers is their large bandwidth. In addition, they are self -generating ana do not need a power supply to generate an output. In addition to their sensitivity to pressure, piezoelectric materials also generate electrical charges when subjected to temperature variations. This effect is called pyroelectricity and is not a favorable effect in shock pressure transducers because such pressure variations are not isothermal. Another disadvantage is that piezoelectric materials cannot be used for long-term static or steady-state pressure measurements. Piezoelectric materials have been widely used in accelerometers and pressure transducers. Piezoelectric accelerometers are essentially "spring-mass" systems with the "spring" being the piezoelectric material and the mass applying compressive or shear forces (depending on the accelerometer design) on the spring when the system is subjected to accelerations. The piezoelectric material used to develop shock pressure transducers for the tests reported here was artificially polarized Polyvinylidene Fluoride (PVDF). In the next section the general properties of PVDF are presented.

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61 4.2.2.2 Polyvinylidene Fluoride (PVDF) Polyvinylidene Fluoride (PVDF) is a semicrystalline polymer which has been widely used in commercial applications in chemical, food, and nuclear industries (Thorn EMI notes, 1986). The fact that this material could be made piezoelectric was discovered in 1969 [Meeks and Ting, 1983). The piezoelectric response is achieved through a special manufacturing process which includes electrical polarization. In addition to its strong piezoelectric properties, PVDF has a good acoustic impedance match to water which makes it suitable for use as hydrophones or underwater shock sensors (Meeks and Ting, 1984). The National Bureau of Standards has also conducted research on developing a stress gage for shock pressure measurements [Bur and Roth, 1985, Chung et al . , 1985 and Holder et al . , 1985). PVDF is manufactured in different shapes, sizes and thicknesses . Figure 4.8 shows the three principal directions in a piezoelectric material with axes 1 and 2 in the plane and axis 3 perpendicular to the plane of the sample. The relationship between the generated charge per unit area, p, and the applied uniaxial stress, a, can be written as [Nye, 1957) P = d a Equation 4.10 where d is the piezoelectric coefficient. In general for a

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62 Electroded Surface Piezoelectric Material Figure 4.8. Principle Directions on a Piezoelectric Material

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3-dimensional state of stress equation 4.10 can be rewritten in matrix form [Nye, 1957): ^i "" "^ii '^i ^^^ 1.2,3 : j= 1,2,3,. ..,6) Equation 4.11 Or in expanded form, 63 ^11 ^12 ^13 ^^14 ^15 ^16 ^21 ^22 ^23 ^24 ^25 ^26 ^31 ^32 ^^33 ^34 ^35 ^36 Equation 4.12 where P. is the vector of polarization charge per unit area, d. is the matrix of piezoelectric coefficients, and a. is the stress vector. The six components of a. represent the six independent terms in a general stress tensor '11 a^ = a = a a . = a O:= o 22 33 23 31 = a 12 For PVDF, the d matrix has several zero components [Bur and Roth, 1985) :

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64

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65 Table 4.2 General Properties of PVDF Sample SAMPLE NO 371 7B1 PVDF THICKNESS 570 |im ELECTRODE THICKNESS = 1 |im Copper ELECTRODE/POLYMER ADHESION > 1 4 M Pa Er 7.8 dh 13.4 pCN gh 178 mVm''' Pa"" SENSITIVITY -199.9 dB (rel IV jiPa-"") d31 =15pCN-1 d32 =0.25pCN" d33 =-28pCN"'' Provided By THORN EMI Central Research Laboratories

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66 pressures applied on voided samples can cause the collapse of microvoids and thereby result in a nonlinear, irreversible response while nonvoided samples exhibited linear response up to pressures as high as 10000 psi in both hydrostatic and dynamic tests. However, non-voided samples show smaller piezoelectric sensitivities. Test results indicate that for relatively low amplitude pressures (less than 2000 psi), the response of voided samples are also close to linear. The degree of linearity increases with a decrease in the number of voids at the cost of a decrease in the value of piezoelectric coefficients. Meeks and Ting (1984) also evaluated the frequency response of non-voided PVDF for underwater shockwave sensor applications. They reported a 2-MHZ bandwidth and very little high-frequency ringing. These factors are both favorable in shock-wave sensors which may encounter high frequency signals. 4.2.2.3 PVDF Pressure Transducer The transducer used for the tests reported here was a 1/4 in X 1/4 in square which was cut from a sheet of 570 \im thick, copper electroded PVDF material. The selection of size was based on several factors. First, the gage size should be small compared to the size of the structural model. Second, the gage dimensions have to be at least 10 times the mean soil grain size (Bur and Roth, 1985). Third, the aspect ratio of gage thickness to gage size should be

PAGE 76

67 less than 1/5 (Bur and Roth, 1985]. Of course, the size is also limited by the practical restrictions in building and working with small gages. Two 30-gage stranded wires were attached to the two electroded surfaces on the gage. These wires can be satisfactorily soldered to the copper electrodes by following the procedures recommended by the manufacturer: 1. Clean the solder area by dipping it in a 3% solution of sulfuric acid for a few seconds. Then wash thoroughly in water and dry it. 2. Place a small piece of solder on the electrode surface and place the tinned wire on top of, and perpendicular to the solder. 3. Apply the soldering iron to the wire and remove it quickly as soon as the solder melts. The above procedure provides for a satisfactory connection. However, when the gage is used at the soilstructure interface, the gage surface must be smooth enough to have full contact with the concrete surface. This might not be possible if there is a blob of solder on the surface. In addition, if extreme care is not taken, heat from the soldering iron may deform or damage the PVDF . Based on these considerations, it was decided to use silver filled epoxy to attach wires to the electrode surfaces as suggested by Meeks and Ting (1983, 1984). The following is a step-by-step procedure used in these tests to obtain satisfactory wire connections.

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68 1. To clean the gage, dip it in a 3% solution of sulfuric acid for a few seconds. Then wash it thoroughly in water and dry it. 2. Expose a few millimeters of a 3U gage stranded wire and place it on top of the electroded surface in such a way that only the exposed wire is on the surface. Tape it down as shown in Figure 4.9. 3. Mix the two components of silver-filled conductive epoxy . 4. Apply a small amount of epoxy on the exposed wire. 5. Use a piece of masking tape to cover the epoxy, wire and the gage. This procedure would level the epoxy to a smooth surface. Let the epoxy cure for a few hours. 6. Remove the masking tape and check the wire connection. Repeat steps 2 through 6 for the other electroded surface. 7. Use polyurethane coating to cover the gage for protection. The silver-filled epoxy used was Dexter Hysol's Type KS0002. The polyurethane coating used was MicroMeasurements' M-Coat A solution. Another important consideration is the procedure for applying the gage on the concrete surface for shock pressure measurements at the soil-structure interface. The objective is to measure a^ from the measured charge P-. m the following equation:

PAGE 78

69 U Q LU LU ^ O ^ a5 o Q > Q. Q LU LU O < o CO < QC hLU DC DC LU

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70 ^3 = ^31 -^l ^ ^32 "2 -^ ^^33 <^3 If the gage were to be glued to the concrete surface, the structural strains in the concrete v;ould result in inplane strains and stresses in the gage [o, and a^) which, in turn, would make unwanted contributions to the measured charge P^. Therefore, it is essential to decouple the structural strains from the transducer response. This is done by taping, rather than glueing, the gage on the concrete surface. Reinforced nylon strapping tape was used to apply the gages on the concrete surface. Holder et al. (1985) used a similar method of gage application. As mentioned earlier, the pyroelectric effects must be considered in piezoelectric transducer design. However, Chung et al . [1985) suggest that the temperature rise, for stresses below 2000 psi, in a gage embedded in soil is very small [0.6 °F) and, therefore, temperature correction is not required. 4.2.2.4 Electronic Circuits For Piezoelectric Transducers There are two general ways for measuring the electrical response of piezoelectric transducers. One is based on voltage sensitivity and the other is based on charge sensitivity. In this section these two methods are discussed and compared. Also, the electronic circuitry designed for the tests reported here is described in detail.

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71 4.2.2.5 Voltage Measurements A simplified electronic representation of a piezoelectric transducer is shown in Figure 4.10(a) [Dove and Adams, 1964, Endevco 101, 1986). The transducer acts as a capacitor [C ) which generates electrical charge when It subjected to pressure. The open-circuit voltage output (V ) is related to the generated charge q, and the internal capacitance of the transducer, C through the following equation : q V = o c p When this transducer is connected to a voltage measuring instrument [Figure 4.10bJ, the capacitance of the connecting cables and the input capacitance of the measuring instrument incroauce additional external capacitance C , to the circuit. Therefore, the voltage output V is a function of the total capacitance C + C : p e V = o c + c P e The above equation indicates that the voltage output varies as a function of the external capacitance, and is therefore dependent on such factors as the length and type of cable used between the transducer and the instrument. This is not an ideal situation because each measurement would require an accurate knowledge of the total

PAGE 81

TRANSDUCER \ 72 CHARGE GENERATOR ['^ . Cp Vo ^-.•---•••-.-.-.-.».».-.».-.m«,»«.-.-.»«»,«,«.«»«. TRANSDUCER \ CHARGE GENERATOR l'^. (a) Cp (b) Ce R Vo Figure 4.10. Voltage Measuring Method

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73 capacitance. This problem can be eliminated by using the charge measurement method as explained in the next section. Another consideration is the low frequency response of the transducer. The time constant of the circuit, which is the product of the input resistance of the instrument R and the total capacitance C + C , determines the cut-off point p e' ^ for the low frequency response of this system. The system filters out signal frequencies below the cut-off frequency (f) 2iT R (C^ + C_^) Gurtin (1961) presents a study of the effect of lowfrequency response on transient measurements. Figure 4.11 shows the effect of variations in the time constant of the circuit RC , on the accuracy of response to transient signals. It is clear that as RC is decreased, the accuracy of the response is decreased. This is equivalent to the loss of low-frequency component of the signal. In the limit, when RC approches zero, the response approaches the differentiated form of the actual signal. It is necessary 12 to use devices with very high input inapedances (10 to 10 ohms) to accurately measure transient pulses. The high frequency response of the transducer is a function of its mechanical characteristics (Endevco 101, 1986).

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74 HMJ SIX WAve PMLSe oni ID nmjT ACCtLENATIOM M.SE (31 fttSPOKSt cow X • 10 I4« RESPONSE FOM X • S Bl RESPONSE FOn X • 2 .... , >**SUBgO tCIXLEHATICM ""' UAL ACCELEAATUH OT PUU? 10TWIAHGULAW POCSe OK) SOUAREPIAiE A

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75 4.2.2.6 Charge Amplifiers In this method, all the charge generated by the transducer due to applied pressure is transfered to, and deposited on, a capacitor with a known capacitance. The voltage across this known capacitor is then measured and the charge q is calculated from equation: q = C V In this case, C is fixed and is independent of cable capacitance. This is the major advantage of this method over the voltage sensing method explained earlier. The basic electronic circuit is shown in Figure 4.12 [Endevco General Catalog, 1986]. The major elements of the circuit are an operational amplifier and a feedback capacitor C^. This arrangment is called a charge amplifier. The operational amplifier, through its feedback loop, maintains point S at virtual common. The charges on the transducer appear and accumulate on the feedback capacitor C^ as they are generated. Since point S is at virtual common, the output voltage of the operational amplifier V is, at any time, equal to the voltage across C^ [Malmstadt et al . , 1981). The charge q, calculated from the following equation, is the total accumulated charge by the transducer at any time, and is proportional to the applied pressure on the transducer. q = C. V ^ f o

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76 TRANSDUCER V OPERATIONAL AMPLIFIER CHARGE AMPLIFIER OUTPUT Vo Figure 4.12. Basic Charge Amplifier

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77 An electronic switch placed across the feedback capacitor is used to discharge the capacitor and reset the charge amplifier. This prevents the gradual drift in the output due to long-term integration of low-level leakage currents (Malmstadt et al., 1981). Although the voltage output V is not a function of the length of cables connecting the transducer to the charge amplifier, long cables can increase the noise level and therefore should be avoided when possible (Endevco, 1986, Dove and Adams, 1964). The low frequency response of the charge amplifier is dependent on the low-frequency response of the amplifier (Endevco 101, 1986) and on the time constant R^C^, where R^ is the off-resistance of the electronic switch, and C^ is the feedback capacitor (Dove and Adams, 1964). The high frequency response of charge amplifier is a function of the input capacitance (transducer plus cable) and any resistance in the cable connecting the transducer to point S. A very important consideration for noise reductions in high impedance piezoelectric transducers is the type of cable used to connect the transducer to the charge amplifier. Coaxial cables or shielded twisted-pair cables are recommended (Endevco, 1986). However, when coaxial cables are subjected to mechanical distortions such as vibrations, a separation of the cable dielectric and the outer shield can occur and thereby create low frequency " triboelectric" noise signals (Endevco 101, 1986). Therefore, it is

PAGE 87

78 important to reduce the cable length and to prevent the flexing and vibration of the cable which could be significant in an explosive test. Specially treated cables can also be used to minimize this effect (Endevco 101, 1986). 4.2.2.7 Shock Pressure Measurements in a Centrifuge On-board signal conditioning is recominended for piezoelectric pressure transducers in a centrifuge based on two main reasons. First, the reduction in the length of cable between the transducer and the charge amplifier reduces the noise level and improves the high frequency response (Dove and Adams, 1964). Second, such an arrangement would prevent the integration of noise signals from the slip rings. In addition to multiple charge amplifiers, electronic switches are required on-board to discharge the feedback capacitors. Figure 4.13 shows a block diagram of the pressure transducer set-up in the centrifuge. Charge amplifiers and electronic switches are shown in an instrumentation box inside the centrifuge. Upon pressing the "fire" knob on the detonator control unit, a trigger signal is released 2 to 10 microseconds prior to the explosion. A voltage comparator is used to reduce the rise time of this trigger signal to less than 10 nanoseconds. This signal is then used to trigger the oscilloscopes. The relatively fast rise time of the signal insures that, regardless of the trigger levels set on individual oscilloscopes, the difference in

PAGE 88

79

PAGE 89

80 trigger times on different oscilloscopes would be negligible (less than 10 ns 3 . Therefore, all instrumentation channels on the oscilloscopes will have a common time base. The output of the comparator is also used to activate the electronic switches inside the instrumentation box. However, because of the relatively long distance (approximately 30 feet) that this high frequency signal has to travel, it is important to use a line driver to prevent the distortion of the signal. Figure 4.14 shows the electronic circuitry for the scope trigger and the line driver. The trigger signal from the detonator control unit has an amplitude of 30 volts. This amplitude is first reduced by using a voltage divider (30V X 1.1 K^/ 5.6 KQ. = 5.9 V ). The noise floor for the comparator, beyond which the comparator (LM 361) output goes to the limit (5 Volts), is set at 0.5 Volts by using another voltage divider ( 12 V X 2Kri/51 KQ = 0.5 Volts). The comparator is a very high-gain amplifier with wellbalanced difference inputs and controlled output limits (Malmstadt et al . , 1981). If a signal larger than the noise floor (0.5 V) appears at pin 3, the comparator outputs a 5 volt signal with a very fast rise time. A capacitor (0.68 yF) is used for filtering the reference voltage and two capacitors (1 pF) on the power supply are also used as noise filters. The comparator output is then used to trigger the oscilloscopes located

PAGE 90

cc UJ s (j> 1^ u > •H >>l Q (U C •H 1-^ -o c (0 u 0) D» Oi •H U Eh 0) a O u CO 0) »H 3 •H 1X4

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82 nearby. A line driver (DS 75450) is used to preserve the high frequency components of the comparator output over a distance of 30 feet to the centrifuge. An insolation transformer is used to float the cable: that is to disconnect the ground of this circuit from the ground in the instrumentation box in the centrifuge. Figure 4.15 shows the charge amplifiers and other electronic circuitry on-board the centrifuge. A monostable multivibrator or one-shot (1/2 74221) is used to provide a window in which to accept data. This window is the time frame during which the electronic switches are activated and the feedback capacitors are not discharged. This time is a function of the external capacitance and resistors and can be changed by adjusting a variable resistor (10 Kfl) . For the tests reported here, the window was set to exceed the time covered by the oscilloscope screens. DS 1488 is an interface driver and is used as a level shifter to interface two families of logic: CMOS and TTL. Each charge amplifier has an analog switch (4066) which is placed across a feedback capacitor (1000 pF) . Another switch (IH 5011) may be used instead in order to obtain better performance. AD 515 is a very high impedance electrometer operational amplifier. Information on all commercial electronic components used in the circuits explained here are given in Appendix A. A total of eight charge amplifiers were built and placed in the instrumentation box on board the centrifuge.

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83 13 I o (£>3 3 3 3 Q. a Q. Q. IKII3 3 ID 3 O O O O ®ffi©0-* tn •H a o o 0) U-l a s < en o in 0)

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84 4.2.2.8 Calibration of PVDF Pressure Transducers In general, the output voltage of the charge amplifier can be related to the applied pressure as follows: Q Ada V^ = = Equation 4.13 ° C C ^f ^f where , V = Output voltage of the charge amplifier Q = Charge on the feedback capacitor Cj = Capacitance of the feedback capacitor A = Surface area of the pressure transducer d = Piezoelectric constant a = Applied pressure When A, d, and C^ are known, output voltage and stress can be directly related: V^ = K a Equation 4.14 Where, A d K = Equation 4.15 The piezoelectric coefficient d given in Table 4.2 can not be used here for pressure measurements at the soilstructure interface, even though the stress direction is essentially perpendicular to the gage surface (direction 3). The reason is that the confining effect of concrete and soil creates a more complex state of stress in the gage resulting in a different apparent piezoelectric coefficient [Dragnich

PAGE 94

85 and Calder, 1973). Therefore, it is essential that the calibration of transducers be conducted under conditions similar to the actual test. A special test arrangement was designed for this calibration. A 1 inch-thick circular micro-concrete slab (3 inch diameter) was built. Three 1/4 in X 1/4 in PVDF gages were taped on the slab as shown in Figure 4.16. A cardboard cylinder with an inside diameter of 3 inches was placed around the slab such that it extended 1/4 inch above the top of the slab. A 1/4 inch-thick layer of sand was placed on top of the slab. The test specimen was then placed in an MTS testing machine to be subjected to cyclic loads. A 1 inchthick circular steel plate and a load cell were placed on the specimen as shown in Figure 4.17. Sinusoidal loads were applied on the specimen with varying frequencies of up to 50 hertz. Only one level of peak stress [162 psi) was tested because of an equipment malfunction after the first series of tests were completed. However, because of the relatively low stress levels (less than 2000 psi), the gage response is expected to be linear (Meeks and Ting, 1983). The charge amplifiers and other electronic circuits used for the actual tests were also utilized for these calibration tests. The sequence of events was as follows: first, the load was applied on the specimen, second, the control unit of the detonator was used to send a trigger signal [no explosion) to activate the switches and trigger

PAGE 95

86 SLAB SAND U\YER PVDF TRANSDUCERS 3" CARDBOARD CYLINDER PVDF TRANSDUCERS 3 iliir yOUTPUT TO CHARGE AMPLIFIERS Figure 4.16. Test Specimen for Calibrating Pressure Gages

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87 MTS TESTING MACHINE / SINUSOIDAL LOAD STEEL PLATE LOAD CELL TEST SPECIMEM Figure 4.17. Test Setup for Calibrating Pressure Gages

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88 the oscilloscope which, in turn, recorded the outputs of the load cell and the three charge amplifiers for the pressure transducers . Figures 4.18 to 4.21 show the applied load and pressure gage response curves for different frequencies of up to 50 hertz. These figures indicate that, in all cases, the pressure gage response is sinusoidal and corresponds to the applied load. It is interesting to note that some pressure transducers show negative responses. This is due to the fact that, when the trigger signal is released, the pressure at that time is shown as zero on the output. Therefore, any pressure less than the pressure at trigger time appears as negative in the output. Thus, calibration is based on the ratio of peak-to-peak amplitudes of applied load and gage outputs rather than absolute peaks. The amplitude of response for the gage closest to the edge of the slab (cardboard cylinder) is consistantly lower than the other two gages which exhibit similar responses. The reason for lack of uniformity of pressure near the edge of the slab is believed to be due to transfer of some of the load in that immediate area to the cylinder. The response of the gage located in that area is omitted from the calculation of calibration factor. Table 4.3 summarizes the calibration test results. These results indicate that frequency variations (up to 50 Hz) do not have a major influence on the calibration values. The calibration factor (369 psi/volt) can be related to

PAGE 98

89 M I— CH LlI n: a < < CD < U LlI < LU ct: LO CD U cc: Q_ m in o: a. Ul

PAGE 99

90 1^ M 1— LU X o < a < CD < u LU < LU Z) (/) CO LU a. UJ IE n ui -I a. a. Q 01 a. § o o) en •-• > 2 < HI (J Z3 •-• a tuj a: (C HI u. > < UJ a: = (n en UJ te a. BC Q U. (M Q I Z a en

PAGE 100

91 N ct: LU X a w a: U) O) LU IT a. a. a. < a: Q UJ IT ID en en ui a: a. o: a '-• Q O) > 0. M a CD a II I z a n IT (n en u e a. < ctr QD < u Ll! < CD UJ q: ID CO CO UJ q: Q_ a en > > 1 — -. a a >• u _i _j 2 < •< UJ u u 3 -, , a I1UJ IT (E a: tu UJ o CD a a a cj (\J UJ CO UJ t— I I— o N -p v^
PAGE 101

92 M I— q: LU X o in < a: CD < CJ UJ CD < 1x1 cn CO CO LU (r Q. UJ § tn en ui IE a. _i a. a. S 111 0) < en u UJ a: UI 0. a: a m ui in •-• UJ -1 a: a. a. Q c u. a u. ta a a 01 en > > a a _i _i 2 5 ^^ ^^ 5 5 S X a 01 en UJ 3 a

PAGE 102

93 piezoelectric coefficient d through Equations 4.14 and 4.15. Thus : 1 — = 369 psi/volt K K C^ 1000 pF d = == 5 = 9.66 pC/N A (369 psi/volt) (1/16 in'^)( 4.488 N/lb) Table 4.3 Calibration of Pressure Transducers Frequency (Hertz)

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94 4.2.2.9 Pressure Gage Setup on the Test Structure A total of six PVDF pressure transducers (1/4 in X 1/4 in) were used on each structure. Their locations are shown in Figure 4.22. The gages were distributed around the structure in order to determine pressure distributions on the top slab and the side wall. 4 . 3 Piezoelectric Accelerometers In this study, accelerometers were used to measure accelerations on the top slab and the side wall. Piezoelectric accelerometers are essentially spring-mass systems (Endevco, 1986) in which the mass exerts a force on the spring (piezoelectric material) when the base is subjected to accelerations. The amount of generated charge on the piezoelectric material is then related to acceleration. In small scale model tests, it is important that the mass and size of the accelerometer be as small as possible to prevent distortions in the structure response. Miniature accelerometers are commercially available which can be suitable for blast tests on small scale models. Baird (1984) presents an evaluation of different commercially available accelerometers for such tests. 4.3.1 Coriolis Accelerations Acceleration measurements in a centrifuge may include unwanted components due to the nature of a rotating

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95 CENTRIRJGE BUCKET BURSTER SLAB ^ DETONATOR V irTTTT P1 SAND / P2 mill

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96 coordinate system. Figure 4.23 shows an inertial coordinate system X Y Z and a coordinate system X'Y'Z' which moves and rotates with respect to X Y Z . The following equation relates the acceleration of point P in the two coordinate systems (D'Souza and Garg, 1984 and Baird, 1984): a = a' + £. + 2wxr + wxr + wx(wxr) Equation 4.16 where, a = Acceleration vector for point P with respect to X Y Z (absolute acceleration) a'= Acceleration vector for point 0' with respect to X Y Z r = Position vector for point P with respect to X'Y'Z' r_ = Velocity vector for point P with respect to X'Y'Z' r = Acceleration vector for point P with respect to X'Y'Z' w = Angular velocity vector for X'Y'Z' w = Angular acceleration vector for X'Y'Z' In a centrifuge test, the angular velocity w is constant. Therefore, w = and a' = Therefore, for centrifuge tests equation 4.16 can be rewritten in the following form a = r + 2wxr + wx(wxr) where w X ( w X r) is the centripetal acceleration and 2w X r is the coriolis acceleration. The magnitude of coriolis acceleration is proportional to the angular velocity of the centrifuge and the particle velocity in the rotating coordinate system. The direction of the coriolis

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97 Y' Figure 4.23. Inertial and Rotating Coordinate Systems

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98 acceleration is perpendicular to both the particle velocity and the angular velocity vectors. Accelerometer measurements indicate the component of the absolute acceleration (inertial coordinate system) along the sensitive axis of the accelerometer. In the tests reported here the velocity and acceleration vectors have the same directions (on the top slab and the side wall where accelerometers are located). Therefore, the coriolis acceleration is perpendicular to the sensitive axis of the accelerometer which is in the same direction as the acceleration and velocity vectors. Thus, in this case, the effect of coriolis acceleration on the accelerometer readings is limited to the transverse sensitivity of accelerometer. 4.3.2 Accelerometer Setup on the Test Structure Two Endevco (model 2255A) accelerometers were attached to the structure as shown in Figure 4.24. Characteristics of these accelerometers which have integral electronics are illustrated in Table 4.4. The accelerometers were screwed on a nut and then epoxied on the structure. A sealant was used on the threads to prevent relative motion between the accelerometer and the nut. Figure 4.25 shows the block diagram for acceleration measurements in the centrifuge.

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99 CENTRIFUGE BUCKET BURSTER SLAB ^ V DETONATOR SAND i

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CD 3 100

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101 Table 4.4 Characteristics of Endevco Model 2255A Accelerometers Sensitivity 0.1 mV/g Range, Full Scale 50000 g Frequency Response 50 KHz Mounted Resonant Frequency 270 KHz Transverse Sensitivity 5 % Weight 1.6 grams 4 . 4 Detonators Based on the similitude requirements for modelling a 500 lb bomb (explained in Section 2.2) and the availability of commercial detonators to meet those requirements at 60 and 82 g's, Reynolds Industries' Standard and Modified RP-83 detonators are used. Figure 4.26 shows the standard RP-83 detonator. It consists of an exploding bridge wire, a low density pressing of Pentaerythritol [PETN) , a high density Cyclotrimethyleretrinitramine [RDX) initiator, and a high density output charge. All of these charges are contained in a .007-inch thick aluminum cup. Each of the four RDX pressings weigh 0.200 grams and the composite RDXPETN initiator weighs 0.125 grams (Nielson, 1983, and Gill, 1985). The modified RP-83 used in these tests contains only one pressing of RDX. The exploding bridgewire (EBW) type detonators resist explosion when subjected to heat, friction, and low voltages because of the exclusive use of

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102 PLASTIC HEADER ALUMINUM CAP WIRE BRIDGE OUTPUT CHARGE RDX Figure 4.26. Reynolds Industries' RP-83 Detonator (Nielsen, 1984)

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103 secondary explosives (FSIO Operating Manual, 1981). Reynolds Industries' FS-10 firing system is designed to fire EBW detonators. This system consists of a control unit and a firing module. The control unit provides low voltage (32-40 volts) electrical energy to the firing module which is accumulated on a capacitor. When the capacitor voltage reaches 4000 volts, the system is armed and ready to fire. The signal to release the 4000 volt signal to explode the detonator is released from the control unit by the operator, when the operator presses the "fire" switch, another signal (30 volts) to be used to trigger scopes is also released which precedes the explosion by approximately 2 to 10 microseconds . Figure 4.27 shows a block diagram for the detonator and firing system arrangements in the centrifuge. The firing module is located inside the centrifuge (on the arm) in order to avoid transmitting 4000-volt signals through slip rings. The firing module and the high-voltage cables were at least 10 inches away from the instrumentation wires and equipment at all times to minimize interference. 4.5 Overall Instrumentation and Data Acquisition Figure 4.28 illustrates a block diagram of overall instrumentation and data acquisition for centrifuge testing of small scale models subjected to blast loading. Figure 4.29 shows the instrumentation box attached to the centrifuge arm.

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104

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106 A number of digital oscilloscopes (16 channels) were used to record the signals from the transducers (Figure 4.30). These oscilloscopes were Nicolet models 4094 and 2090. The oscilloscope digitizing rate was selected to be iMHz for pressure transducers and 200 KHz for strain gages and accelerometers (12-bit resolution). The output signals were recorded on 5 1/4 inch diskettes. The waveforms were also transferred to an HP 9816 computer for further analysis and plotting on a digital plotter. Appendix B contains programs written on the HP computer for the transfer of waveforms, plotting on a plotter, and analysis of data.

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107 Figure 4.29. Instrumentation Box on the Centrifuge Arm Figure 4.30. Nicolet Digital Oscilloscopes

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CHAPTER 5 TESTING PROCEDURES The following is a step-by-stap account of the preparations made and the procedures followed in carrying out experiments on the test specimens. Detailed information on the geometry of the test specimens is given in Chapter 3. Small styrofoam panels were used to cover the two open sides of the structural model in order to prevent sand from entering the box structure. Fiberboard panels were used to line the walls and floor of the centrifuge bucket in order to dampen shock wave reflections. The next step was the placement of the structural model and sand inside the bucket. First, a 1-inch layer of dry sand was placed on the bottom of the bucket (Figure 5.1). In all cases, sand was dropped from a height of approximately 10 inches in order to obtain a uniform density distribution. Density of sand was measured by placing a small container inside the bucket when sand was being dropped. The weight and volume of the sand in the container was measured after removing it from the bucket. An average density of 89 pcf was obtained. The box structure was then placed on the bottom sand layer. Great attention was given to the placement of the 108

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structure at the exact center of the bucket. A PVC pipe located at a corner of the bucket was used to shield the instrumentation wires from damage due to explosion (Figure 5.2). More sand was then placed all around the structure (Figure 5.3) . The box structure was subsequently covered with 7 scaled feet of sand (1.4" in 1/60-scale and 1.0" in 1/82-scale models). The exact height of sand above the top of the structure was verified by dipping a metal ruler (marked at the desired height) into the sand. The next step was to place the burster slab on top of the sand and at the exact center of the bucket (Figure 5.4). The burster slab was then covered with 2 scaled feet of sand (0.4" in 1/60-scale and 0.3" in 1/82-scale models) as shown in Figure 5.5. A wooden frame was used to hold the detonator in the exact position on top of the burster slab (Figure 5.6). The detonator was attached to the bottom of the bolt located at the center of the wooden frame. The distance between the bottom of the detonator and the top of the burster slab (standoff distance) varied between 2 scaled feet to zero feet (direct contact between detonator and burster slab) in different tests. The next step was to connect the instrumentation wires from the structure to the instrumentation box on the centrifuge arm using RS-232 type connectors. Output wires from the instrumentation box were connected to binding posts for slip rings. Outside the centrifuge, the

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110 Figure 5.1. A Layer of Sand on the Bottom of the Bucket Figure 5.2. Structural Model Placed Inside the Bucket

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Ill Figure 5.3. Sand Placed Around the Model Figure 5.4. Burster Slab in Place

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112 Figure 5.5. Sand Placed on Top of the Burster Slab Figure 5.6. Wooden Frame to Support the Detonator

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113 output of each instrumentation channel was connected to a digital storage oscilloscope through a 30-foot long coaxial cable. A complete check of the wiring systems, electronic components, mechanical connections, oscilloscopes, power supplies, and detonator control systems was then performed. Necessary measures were taken to insure safety at all times. An explosives expert was in charge of storage, handling, safety, and operation of explosives and associated equipment. Upon completion of the equipment and safety checks, the system was ready for performing experiments. At this point, for tests at Ig, the explosive charge was put in place and the charge was exploded when the signal to detonate was given to the operator. For tests at 60 or 82 g's, the explosive charge was put in place and the centrifuge was spun until it reached the desired speed (242 rpm for 60 g's and 276 rpm for 82 g's). The signal to detonate was then given and the charge was exploded. The resulting waveforms displayed on the oscilloscope screens were then stored on diskettes so that the waveforms could be recalled at a later time for transfer to, and analysis on a computer (Hewlett Packard model 9816). Although some variations existed for some model tests, the general testing sequence for each test specimen was as follows. First, a test was performed at Ig at a standoff distance of 2 scaled feet. Next, the same test was repeated

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114 but at 60 or 82 g's depending on the scale of the model. Subsequently, another test was performed on the same structure at Ig but at a standoff distance of zero. Finally, a test with a standoff distance of zero was performed at 60 or 82 g's. Table 5.1 illustrates the characteristics of the various tests performed on different models. Test No, Model No. Table 5.1 Tests Performed on Structural Models 1/60 scale Al A2 A3 A4 A5 A6 A7 Gravity Cg's) Standoff 2 2 2 2 (scaled ft) 1/82 scale Bl B2 33 34 35 1 60 1 60 1 60 60 2 2 2 1 82 82 82 82 In tests Al and A3 (1/60 scale], the centrifuge was spun to 60 g's before tests at Ig were performed. Therefore, the density of sand for these tests at Ig were expected to be higher than if the centrifuge had not been spun before the tests. In tests A5 (1/60 scale) and Bl (1/82 scale), the centrifuge was not spun before the test. All structures and burster slabs were reinforced, except for the burster slab in model No. 2 which was unreinf orced. There were no tests performed on models no. 2, 3 and 4 at Ig

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115 with a standoff distance of zero. The reason is that tests at zero standoff result in cratering and cracking on the burster slab which render it useless for further tests. Therefore, it was decided to perform the tests at zero standoff for models 2, 3 and 4 only at 60 and 82 g's and not at Ig .

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CHAPTER 6 EVALUATION OF TEST RESULTS In this chapter the test results are presented and evaluated in such a manner as to help answer the questions raised in this research effort. Therefore, the main focus of this chapter is on evaluating the significance of increased gravity (centrifuge] rather than studying the performance and survivability of underground structures subjected to blast loading. Measurements of pressures, accelerations and strains on the models in tests at 1 g and 60 or 82 g's are compared. Also, the scaling relationships are evaluated by comparing tests at 60 and 82 g's. Table 5.1 lists the characteristics of the various tests performed on different models. 6 . 1 Pressures Locations of various pressure gages attached to the structural model and the burster slab are shown in Figure 4.21. In this section, the pressure-time histories at each gage location in different tests are compared and studied. Explosive tests generally have spurious effects on transducer responses. This can be seen in most of the pressure responses during the first few microseconds. 116

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117 6.1.1 Pressure Gage Pi Pressure gage Pi is located on the bottom of the burster slab. Because of the close proximity of this gage to the explosive, the pressure gage (Pl) responses in some tests were not satisfactory. Figure 6.1 is one such example. It shows the pressure response from gage Pl in tests Al and A2 . The slow rise of the signal after the passage of the main shock wave may be attributed to a severe vibration of the cable which could be significant in piezoelectric transducers (see Chapter 4). There were some tests that yielded reasonable responses for Gage Pl. Figure 6.2 shows the response of pressure gage Pl in test A4 (0' standoff, 60 g's). The first peak of the response exceeded the range set on the oscilloscope at approximately 1500 psi. The signal shows a second peak of magnitude 1060 psi at a time of 294 yseconds. This second peak is believed to be a reflection of the main shock wave on the top slab of the box structure. In this case, the average speed of the shock wave in soil is approximately 930 ft/sec. Figure 6.3 shows the pressure response Pl for test A7 (0' standoff, 60 g's). This test is similar to test A4 (Figure 6.2) with one important difference. The burster slab in test A4 was already damaged and cracked during test A3 while test A7 was performed using an intact burster slab. It is not clear wheather the first sharp peak in the response in the A7 test is due to the effects of explosion

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119

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120 z CD < I < en ill a CM a

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121 on instrumentation or a precursor wave front. This effect is observed in almost all of the pressure gage responses. The second peak is considered to be the main shock front and the third peak is believed to be a reflection of the main wave on the top slab of the box structure. It can be seen that at 640 yseconds the wire connection to the gage was cut and the rest of the signal was lost. The main shock front is estimated to have a rise time ( the time it takes for the signal to rise from 10% to 90% of its peak) of approximately 65 yseconds with a peak pressure of 1400 psi which is slightly smaller than the corresponding pressure in test A4 [1500 psi). However, the reflected pressure in test A7 is approximately 1345 psi which is higher than the second peak in test A4 by 27%. The wave speed in soil is calculated to be 1003 ft/sec which is close to the value obtained from test A4 . The accuracy of this speed is verified by checking the time of arrival for pressure gage P2 in tests A4 and A7 which yield very similar results. Figure 6.4 shows the pressure response Pi for test B3 (0' standoff, 82 g's). According to the scaling relationships [Chapter 2), the peak pressures in this test should be the same as in tests A4 and A7 [Figure 6.2 and 6.3). In addition, the arrival times in test B3 should be less than the corresponding arrival times in tests A4 and A7 by a factor of 60/82. The first peak in test B3 exceeded 1500 psi [similar to test A4). However, the second pressure peak in test B3 [662 psi) was less than the second peak in

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123 test A4 (1060 psi] by approximately 37%. The arrival time of the second peak in test B3 was 191 useconds which is equivalent to 261 yseconds on a 1/60 scale model [191 X 82/60 = 261 ). The actual arrival time in test A4 was about 10% higher (294 useconds). Again, the residual observed pressure in test B3 is believed to be due to the vibration of the cable (triboelectric effect) explained in Chapter 4. Figure 6.5 shows the pressure gage response Pi for test B2 (2' standoff, 82 g's). The arrival time for the peak of the main wave is 103 microseconds. It should be noted that this arrival time is the same as the arrival time in test A7 , even though the standoff distances in the two tests are different and the model scales (and therefore the time relationships) are different. If the standoff distances had been the same in both tests, the theoretical arrival time for test 32 (based on scaling laws) would have been 60/82 times the arrival time in test A7 or 75 ^seconds. However, since the standoff distance in test 32 is 0.29 inches (2 scaled ft) compared to zero inches in test A7 , the wave front has to travel a longer distance (40% longer). Assuming equal wave speeds in soil and microconcrete , the arrival time should be 40% longer than 75 yseconds (105 yseconds), which is very close to the arrival time observed in test 32. The rise time of the main signal is about 60 yseconds but the pressure is much smaller (564 psi) than the A4 , A7 or 33 tests because of the larger standoff distance in test

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125 B2. The wave speed in soil is calculated by dividing the distance between the bottom of the burster slab and top of the structure by the time difference between the peaks in Pi and P2 for test B2 . A speed of 918 ft/sec is obtained which is similar to the value obtained in other tests. The second peak on the Pi response has a delay and therefore a lower speed compared to the other tests. Figure 6.6 shows the pressure response Pi in test Bl (2' standoff, Ig) . The arrival time of the main peak is the same as in test B2 . Test B2 is similar to test Bl except that the test is performed at 82 g's. Equal arrival times for the main peak pressure in Pi are expected because gravity mainly affects wave speed in soil but not concrete. The peak pressure in test B2 (564 psij is larger than the peak pressure in Bl (430 psi) by about 31%. This is because of a larger soil stiffness (under the burster slab) due to greater confinement stresses at higher gravities. The speed of shock wave in soil (test Bl) is calculated to be 683 ft/sec by observing the arrival time of the main wave on the top of the structure. The wave speed in test B2 is higher than speed in test Bl by approximately 33%. Although the number of satisfactory pressure responses on the bottom of the burster slab are limited, the results indicate generally repeatable responses in similar tests and larger peak pressure in the test at 82 g's ,,2' standoff) as compared to the test at Ig (2' standoff).

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127 6.1.2 Pressure Gage P2 Pressure Gage P2 is located on top of , and at the center of the top slab of the box structure [Figure 4.21). Figure 6.7 shows the pressure gage P2 response for tests Al (2' standoff, Ig) and A2 [2' standoff, 60 g's). The centrifuge was spun to 60 g's before the test at Ig (Al) was performed. Therefore, the density of sand in both tests were equal and the only difference was the effect of gravity. It can be seen that the shock wave arrives faster in the 60g test and has a slightly larger peak pressure. The two pressure responses show ripple effects before the arrival of the main wave. As mentioned earlier, this effect is seen in almost all the pressure gage responses and it is not clear wheather this is a side effect of explosion on instrumentation or a precursor wave. The exact wave speed in soil can not be determined in this case because of a lack of precise information on the arrival time of the shock wave on the bottom of the burster slab (Pressure Gage Pi in tests Al and A2 did not function properly) . The arrival time of the first peak of the shock wave in test Al is 393 yseconds which is larger than the corresponding arrival time for test A2 (264 ^seconds) by 50%. Also, the arrival time for the second peak in test Al (561 ^seconds) is larger than the corresponding arrival time for test A2 (460 yseconds) by about 22%. The rise time of the signal in test Al is 96 pseconds while the rise time

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129 in test A2 is 68 yseconds which is a reduction of about 30%. The first peak pressure in test Al is 120 psi which is slightly smaller than the first peak pressure in test A2 (123 psi). However, the second peak pressure in test A2 (148 psi) is larger than the corresponding peak pressure in test Al (139 psi) by about 7%. These differences can be explained by considering the fact that the stiffness of sand is a function of gravity stresses. Therefore, in tests at high gravities, the soil stiffness is higher and thus the shock wave arrival times are smaller and the peak pressures are higher. The shape of the pressure response curve is a complex function of the reflections on the burster slab and the structural motion of the box structure in response to the load. Wong and Weidlinger (1983) suggest that the motion of an Underground structure and the loading acting on the structure are closely coupled. Figure 6.8 shows the impulse (area under the pressure time curve) for pressure gage P2 at 1 and 60 g's. The peak impulse (at zero pressure) in test A2 is larger than the peak impulse in test Al by about 28%. Figure 6.9 shows the Pressure Gage P2 responses in tests A5 (2' standoff, Ig) and A6 (2' standoff, 60 g's). Thesa two tests are similar to tests Al and A2 respectively, except that the centrifuge was not spun to 60 g's before test A5 (at Ig) was performed. Therefore, in addition to the difference in gravities between tests A5 and AS, the sand densities were not equal either.

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The arrival time of the first peak in test A5 is 408 yseconds which is larger than the corresponding arrival time for test A6 (361 yseconds] by about 13%. The arrival time for the second peak in test A5 (500 yseconds] is 8% smaller than the corresponding arrival time for test A6 (541 yseconds] . The rise time of the signal in test A5 (137 yseconds] is much larger than the rise time in test A6 (61 yseconds]. The first peak pressure in test A6 is 108 psi which is higher than the corresponding peak pressure in test A5 (99 psi] by about 9%. However, the difference in second peak pressures in these two tests is larger. Test A6 has a second peak of 129 psi which is larger than the second peak in test A5 (105 psi] by 23%. Figure 6.10 illustrates the difference in impulse curves between tests A5 and A6 . The peak impulse in test A6 is larger than the peak impulse in test A5 by about 73%. In order to evaluate the repeatability of tests conducted under similar conditions, tests Al and A2 are compared with tests A5 and A6 respectively. It should be noted that the densities of sand in tests Al and A5 were not equal. Table 6.1 summarizes the results for Pressure Gage P2 . For tests Al and A5 , the difference in the amplitude of the first and second peaks are 21% and 32% respectively. Larger values in test Al can be attributed to a larger density. The arrival time for the first peak in tests Al and A5 are fairly close (4% difference]. The

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135 arrival time for the second peak in test Al is higher the corresponding arrival time in test A5 by 11%. The differences in magnitudes of the first and second peaks in tests A2 and A6 are slightly smaller. Both peaks in test A2 are larger than the corresponding peaks in test A6 by about 14%. However, the difference in arrival times are relatively larger than in tests Al and A5. It should be noted that the selection of the first peak in test A6 may be arbitrary because of a lack of a clear first peak. The comparison of the impulse curves for tests Al and A5 indicate a noticeable difference in the peak impulse between the two tests. However, this difference is much smaller in tests A2 and A6 . Figure 6.11 shows Pressure Gage P2 responses for tests Bl (2' standoff, Ig) and B2 (2' standoff, 82 g's). The centrifuge was not spun to 82 g's before test Bl was performed. These two tests are similar to the two sets of tests explained earlier (Al, A2 and A5 , A6 ) in that the standoff distance is 2 scaled feet. However, tests Bl and B2 are conducted on 1/82-scale models rather than 1/60scale models. It is clear that the arrival time of the main wave in test B2 is faster and the peaks are higher than in test Bl. Table 6.1 includes the results from these two tests. It should be noted that all arrival times for tests on 1/82-scale models as listed in table 6.1 have been multiplied by 82/60 for the purpose of comparing these arrival times with the corresponding arrival times in tests

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137 on 1/60-scale models. The arrival time for the first peak in test Bl is larger than the first peak arrival time in test B2 by 11%. However, the arrival time of the second peak in test Bl is smaller than the corresponding arrival time in test B2 by 24%. The first peak pressure in test B2 (142 psi) is higher than the first peak pressure in test Bl (133 psi) by 7%. The second peak pressure in test B2 (168 psi) is larger than the corresponding pressure in test Bl (163 psi) by 3%. Both pressure responses show residual apparent pressures after the main shock wave has passed. This is believed to be due to the vibration and flexing of the cable. Figure 6.12 illustrates the impulse curves for tests Bl and B2 which show very slight differences. According to the laws of similitude and, assuming that the structure and the explosive charge are scaled properly, the magnitudes of pressures and arrival times (including adjustments for different scale models) should be the same in tests at 2' standoff on 1/60and 1/82-scale models. However, although in selecting the explosive charge the total mass of explosive was scaled properly, the distribution of the mass in the detonator, the relative size of the detonator, thickness of the case, etc. were not taken into account because of limitations with regard to availability of commercial detonators. Therefore, slight differences in pressures and arrival times are to be expected. The first peak pressure in test Bl (133 psi) is

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139 larger than the average of the first peak pressures in tests Al and A5 (110 psi) by 21% [see Table 6.1). Similarly, the second peak pressure in test Bl [163 psi) is larger than the average second peak pressure for tests Al and A5 [122 psi) by 34%. The arrival time [adjusted) of the first peak in test Bl [279 pseconds) is smaller than the corresponding average time in tests Al and A5 [400 useconds) by 30%. The arrival time [adjusted) of the second peak in test Bl [488 yseconds) is smaller than the average arrival time for tests Al and A5 [531 yseconds) by 8%. Figure 6.13 shows the Pressure Gage [P2) response for tests B2 (2' standoff, 82 g's) and B4 [2' standoff, 82 g's). These two tests are conducted under similar conditions and should yield similar results. Table 6.1 indicates that the arrival times for the first peak in both tests are very close [251 and 259 pseconds). However, the first peak in test B2 [142 psi) is larger than the first peak in test B4 [113 psi) by 26%. This situation is reversed for the second peak where the pressure in test B4 [180 psi) is larger than the second peak in test B2 [168 psi) by 7%. Figure 6.14 shows that impulse curves in tests B2 and B4 are very close. The next step is to evaluate tests at zero standoff distance. Only one test [A3) was performed at Ig and at zero standoff distance. The reason for this was that any test at zero standoff destroys the burster slab and further tests on such a slab may not provide accurate information.

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Figure 6.15 shows the Pressure Gage (P2) responses in tests A3 (0' standoff, Ig) and A4 (0' standoff, 60 g's). Test A4 was performed using a burster slab which had a crater and some cracks which appeared during test A3. Test A3 exhibits an unusual response considering the observed responses in tests at 2' standoff explained earlier. The peak pressure in test A3 (277 psi) is higher than the peak pressure in test A4 [163 psi) by 10%. This phenomenon may be explained by considering several factors. First, in tests at zero standoff, the explosive charge rests on the top surface of the burster slab and most of the pressure is expected to transfer to the soil at a point directly beneath the charge. If there is increased soil stiffness (60-g test), the pressure is expected to distribute more evenly on top of the box structure. Second, a part of the total energy of explosion is expended in crater excavation. Crater formation in soils is shown to be a function of gravity (Schmidt and Holsapple, 1980 and Kutter et al., 1985). Assuming that the same holds true for crater formations in concrete, a larger portion of the total energy is used in crater formations at high-gravity environments. Therefore, a smaller portion of the total energy is transmitted to the structure or soil as shock wave. Third, there is a slight possibility that the placement of the model or the explosive may not have been precise in the only test performed at Ig with a standoff distance of zero (test A3).

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144 Figure 6.16 shows the impulse curves for tests A3 and A4. The peak impulse [impulse at zero pressure] in test A3 is 23% larger than the peak impulse in test A4 . Figure 6.17 compares the Pressure Gage (P2) responses in tests A3 (0' standoff, Ig] and A7 (0' standoff, 60 g's). In this case, the burster slab used in test A7 was intact before the test. Again, the pressure peak in test A3 (277 psi) is larger than the peak in test A7 (169 psi) by 64%. Table 6.1 shows the two similar tests (A4 and A7) with very good agreement with respect to the magnitude and the arrival time of the first peak but the values of the second peak have large differences. Figure 6.18 shows a considerably larger impulse values for test A3 compared to test A7. Figure 6.19 shows the Pressure Gage (P2) response curves for tests B3 (0' standoff, 82 g's) and B5 (0' standoff, 82 g's). These two tests are similar. However, even though the arrival time of the shock waves are very close, the peak pressures in test B5 (404 psi and 337 psi) are higher than in test 33 (313 psi and 240 psi) by 29% and 40% respectively. Figure 6.20 shows large impulse values for test B5 compared to test B3. Table 6.1 shows that the first peak pressures in tests on 1/82-scale models at zero standoff are higher than the pressures in tests on 1/60scale models. In summary, Table 6.1 shows that for tests at 2' standoff, the arrival times of the first peak pressure in

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150 Ig tests are consistently and substantially higher than the corresponding arrival times in 60 or 82g tests. Moreover, the impulse curves show larger values in high-gravity tests at 2' standoff. The peak pressures in tests at 60 g's are slightly higher than tests at Ig. For tests at standoff distance, the only test performed at Ig shows larger pressures and impulses as compared to high-gravity tests. These facts indicate the importance of properly accounting for the effect of gravity stresses through centrifuge testing. Comparisons of tests on 1/60 and 1/82scale models indicate slight variations from the theoretical scaling relationships. This can be attributed to inaccurate scaling of the geometry and mass distribution of the explosive charge in 1/82-scale tests. 6.1.3 Pressure Gage P3 Pressure Gage P3 is located on top of the box structure and directly over the side wall [see Figure 4.21). In this section, only the largest peak pressure is used as a basis for comparisons between different tests because, in most cases, only one significant peak appeared in the response of Pressure Gage P3. Figure 6.21 shows the Pressure Gaga CP3) responses in tests Al (2' standoff, Ig) and hi (2' standoff, 60 g's). The peak pressure in the 60-g test (58 psi) is much larger than the peak in test Al (7 psi). Also, the arrival time of the peak in test Al (548 viseconds) is larger than the corresponding arrival time in test A2 (482

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152 yseconds] by 14%. Figure 6.22 shows the impulse curves for the two pressure curves in Figure 6.21. Figure 6.23 shows the Pressure Gage [P3) response in tests A5 [2' standoff, Ig] and A6 [2' standoff, 60 g's). It is clear that the peak pressure in the 60-g test (194 psi) is much larger than the peak pressure in the 1-g test [69 psi) by 131%. Although the arrival time of the peak in test A6 is larger than the arrival time in A5 by 12%, the arrival time of the shock front is clearly smaller in test A6. Comparisons of tests Al and A2 with A5 and A6 respectively indicate that there are wide variations in magnitudes of pressures in similar tests even though the arrival times are close. The reason may be due to an incorrect placement of the burster slab which resulted in the burster slab not being precisely over the box structure in tests Al and A2 . Also, variations in soil density at different locations may be a contributing factor. Figure 6.24 shows much larger impulse for test A6 as compared to A5. Figure 6.25 shows pressure responses in tests Bl [2' standoff, Ig) and B2 (2' standoff, 82 g's) on 1/82-scale models. Test Bl exhibits a very well-defined pressure response. This type of response is expected for Pressure Gage P3 because of its location on top of the side wall. Gage P3 is subjected to much smaller structural deformations and wave reflections than Gage P2 . The arrival

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157 time of the shock front in test B2 is slightly smaller (faster] as expected. However, the peak pressure in test B2 is smaller [double-peak) by about 45%. This unusual behavior may be attributed to a rigid-body movement of the structure when subjected to pressure. The duration of the pressure wave in test B2 is longer than in test Bl. Figure 6.26 illustrates the difference in impulse curves between these two tests. A similar-shape response is obtained in tests A3 (0' standoff, Ig) and A4 [0' standoff, 60 g's) as shown in Figure 6.27. The peak pressure in test A3 [135 psi) is larger than the peak pressure in test A4 [108 psi) by 25%. Figure 6.28 shows the impulse curves for these two tests. Figure 6.29 shows pressure responses in tests A3 [0' standoff, 60 g's) and test A7 [0* standoff, 60 g's). The difference between these two tests and tests A3 and A4 shown in Figure 6.27 is that the burster slab in test A7 was intact before the test was performed while the burster slab in test A4 was damaged during test A3. The peak pressure in test A7 [158 psi) is larger than the peak pressure in test A3 [135 psi) by 17%. The arrival time of the peak in test A7 is also higher by 21%. Figure 6.30 shows the pressure results for tests B3 [0' standoff, 82 g's) and B5 (0' standoff, 82 g's) which are similar. The arrival time of the shock wave and the peaks are very close [206 and 208 yseconds). However, the magnitude of the peak in test B3 is larger by 31% [see

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153 Table 6.2). These two tests show larger pressures and smaller arrival times than the corresponding 1/60-scale tests (A4 and A7 ) . Table 6.2 also shows that 1/82and 1/60-scale tests at high g's have better agreement in tests at 2' standoff. In summary, the peak pressures (P3) in tests at 60 g's (2' standoff) are substantially larger than the corresponding pressures in tests at Ig. The arrival times of the shock, fronts are also faster in the 60g tests. This type of behavior is not observed in tests on 1/82-scale model [Bl and B2) which inay be due to a rigid body movement of the structure in test 82. The peak pressure in the Ig test at standoff is higher than the corresponding test at 60 g's. 6.1.4 Pressure Gage P4 Pressure Gage P4 is located on top of the side wall as shown in Figure 4.21. If the sand used in these tests was saturated, then pressure Gage P4 would register relatively high pressures due to a hydrostatic pressure condition. However, the sand used in these tests were dry and therefore very little pressure is expected at the location of Gage P4 . Figures 6.31 and 6.32 are two examples of P4 responses which are very close to zero.

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167 6.1.5 Pressure Gage P5 Pressure Gage P5 is located in the middle of the side wall as shown in Figure 4.21. Figure 6.33 shows the Pressure Gage (P5) response in tests Al [2' standoff, Ig) and A2 (2* standoff, 60 g's). The peak pressure in the 60-g test (32 psi) is larger than the peak pressure in the Ig test (16 psi) by 100%. Figure 6.34 also indicated larger impulse for the 60-g test. Figure 6.35 shows the pressure responses (P5) for tests A3 (0' standoff, Ig) and A4 (0' standoff, 60 g's). The pressures are very close to zero in both tests. Figure 6.36 shows a similar response for tests A3 and A7 . Pressure Gage (P5) did not perform satisfactorily in tests on 1/82-scale models (B series). Therefore, those results are not presented here. 6.1.6 Pressure Gage P6 Pressure Gage P6 is located on the bottom of the side wall as shown in Figure 4.21. This gage also indicates pressures very close to zero in all tests (low and highgravity tests). Figures 6.37 to 6.40 show the results for Gage P6 in some of the tests. 6 . 2 Accelerations Locations of the two accelerometers (Al and A2 ) used in the tests reported here are shown in Figure 4.23. In this section, the accelerometer waveforms for different tests

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are compared to evaluate the significance of gravity effects in the response of an underground structural model subjected to blast loading. As explained in Chapter 4, the outputs of piezoelectric accelerometers generally drift with time. Prior to conducting each test, the output of each accelerometer was adjusted to zero on the oscilloscope, and the oscilloscopes were then set to trigger when the explosion occurred. During the time period between the adjustment and explosion, the accelerometer output may have a slight drift. Therefore, digital zero on the oscilloscope may not indicate zero acceleration and the absolute acceleration values should be calculated by including the amount of drift in the calculation. The values of accelerations given here in the text and tables are adjusted for the amount of drift. Also, in a way similar to other transducers, explosions have spurious effects on the accelerometer response in the time span of a few microseconds. This effect can be seen in all accelerometer responses presented here. Positive acceleration is directed away from the base. Therefore, for accelerometer Al , positive acceleration is directed downward and for accelerometer A2 , positive acceleration is directed to the right.

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177 6.2.1 Accelerometer Al Accelerometer Al is located in the bottom and at the middle of the top slab of the box structure [Figure 4.23]. Figure 6.41 shows accelerometer response Al in test Al [2' standoff, Ig] . The main accelerometer response occurs at 250 ^seconds which is slightly later than the time shock wave hits the top slab [see Pressure Gage P2). The first peak, has a magnitude of 447 g's and occurs at 285 yseconds [see Table 6.3). Figure 6.42 shows accelerometer response [Al) in test A2 [2' standoff, 60 g's). Comparing Figures 6.41 and 6.42 shows that the peaks in test A2 are larger and the arrival times of the peaks are faster. Table 6.3 shows that the first peak in test A2 [519 g's) is larger than the first peak in test Al [447 g's) by 165^. The difference in the second peak [negative) is as much as 300%. The arrival time for the first peak in test Al [285 ^seconds) is larger than the corresponding arrival time in test A2 [225 useconds) by 21%. The difference in the arrival times of the second peak for these two tests is 18%. Figures 6.43 and 6.44 show accelerometer [Al) responses in tests A5 and A6 . These two tests are similar to tests Al and A2 , respectively, except for the density variations explained earlier. Table 6.3 shows that the magnitude and arrival times of the first peak in test Al and A5 are very close [447 and 453 g's, 285 and 280 yseconds). The second

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183 peaks vary substantially in tnagnitude but are very close with respect to arrival times. Tests A2 and A6 show agreement with respect to arrival times of the first and second peaks. However, the magnitudes of those peaks are substantially smaller in test A6 . This may have been due to a possible problem with the connection of the accelerometer to the surface of the microconcreta. The values presented in Tables 6.3 and 6.4 and discussed here for magnitudes and arrival times of peak accelerations in tests on 1/82-scale models are multiplied by 60/82 and 82/60 respectively to adjust for scaling size differences in 1/60and 1/82-scale models and thereby have a common basis for comparisons. Figures 6.45 and 6.46 show accelerometer (Al) responses in tests Bl and B2 (1/82-scale model]. Both the magnitude and the arrival time of the first peak in test 31 [786 g's, 226 viseconds) are larger than the corresponding valaes in test B2 (677 g's, 198 yseconds) by about 15% (see Table 6.2). The second peak in test Bl (-437 g's] is also larger than the second peak in test B2 (-362 g's] by 21% while the arrival time for the second peak in test Bl (280 ijseconds] is larger than the corresponding arrival time in test B2 (267 yseconds) by 5%. Figure 6.47 shows the Accelerometer (Al] response in test B4 (2' standoff, 82 g's]. This test is similar to test B2. However, the first peak response in test 34 (886 g's)

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187 is higher than the first peak response in test B2 (677 g's) by 31% while the second peak in test B4 (-100 g's) is smaller than the second peak in B2 (-362 g's] by 72%. The arrival time of the first peak in B2 (198 ^seconds) is larger than the corresponding arrival time in test B4 (157 yseconds) by 26%. In summary, acceleration responses in tests at 2' standoff on 1/60-scale models show larger peaks and faster arrival times at 60 g's as compared to tests at Ig. The average first peak acceleration in tests on 1/82-scale models (B2 and B4j is very close to the peak in test Bl while the average second peak is smaller in tests B2 and B4 as compared to test Bl. However, the arrival times in 82-g tests are faster compared to Ig tests on 1/82-scale models. Comparable tests on different scale models (1/60 and 1/82) show larger first peaks and faster arrival times for 1/82scale models. This may be attributed to an improper scaling of the explosive, not in terms of total mass which was properly accounted for, but rather in terms of mass distribution and charge geometry. Also, dimensional tolerances with regard to the placement of structural model in the centrifuge bucket may be harder to maintain in 1/82scale models. Figures 6.48 and 6.49 show accelerometer (Al) responses in tests A3 (0' standoff, Ig) and A4 (0' standoff, 60 g's). The adjusted first acceleration peak (see Table 6.3) in test A3 (1605 g's) is larger than the first acceleration

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190 peak in test A4 (1038 g's] by 55%. The second peak in test A3 (-1247 g's] is also higher than the second peak in test A4 (-501 g's) by 149%. The arrival times for the first and second peaks however, are very close (140 and 144 ^seconds and 190 and 190 yseconds). The higher peak accelerations in the Ig test (A3) is expected here because of an observed higher pressure P2 (see Figure 6.15). Figure 6.50 shows accelerometer (Al) response in test A7 (0' standoff, 60 g's). This test is similar to test A4 except for the damaged and cracked burster slab used in test A4. Test A7 shows higher first peak accelerations than in test A4 (1163 g's compared to 1038 g's) by 12%. The second peak in test A7 (-728 g's) is also higher than the second peak in test A4 (-501 g's) by 45%. The arrival times for the first and second peaks in test A7 (170 and 210 yseconds) are higher than the corresponding arrival times in test A4 (144 and 190 yseconds) by 18% and 11% respectively. Figures 6.51 and 6.52 show Accelerometer (Al) responses in tests B3 (0' standoff, 82 g's) and B5 (0' standoff, 82 g's). These two tests are conducted under similar conditions. Test B5 shows a higher adjusted first peak (3938 g's) as compared to test 33 (2790 g's) by 41%. The second peak in test 85 (-2196 g's) is higher than the second peak in test 33 (-847 g's) by 159%. The arrival times for the first and second peaks in test B3 (123 and 157 yseconds) are larger than the corresponding arrival

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194 times in test B5 [109 and 150 yseconds) by 13% and 5%, respectively. In summary, acceleration responses in tests at zero standoff on 1/60-scale models at 60 g's result in smaller peak accelerations compared to the test at Ig. The arrival times for the peaks in tests at 60 g's are, on the average, higher than in Ig tests. High-g tests on 1/60and 1/82scale models show different responses. 82-g tests [B series) show larger adjusted peak accelerations and faster arrival times as compared to 60-g tests (Table 6.3). As explained earlier, this is believed to be due to an incorrect scaling in terms of the distribution of explosive mass and the geometry of the detonator. 6.2.2 Accelerometer A2 Accelerometer A2 is located on the inside and the middle of the side wall as shown in Figure 4.23. Figures 6.53 and 6.54 show Accelerometer (A2) responses in tests Al (2' standoff, Ig) and A2 (2' standoff, 60 g's). The first response time of Accelerometer A2 in test Al [290 yseconds) has a delay of 40 yseconds compared to the first response time of Accelerometer Al in test Al [250 yseconds). The negative first peak acceleration in these tests indicate an outward direction [on the side wall) for the first acceleration peak. The first peak in test A2 [-121 g's) is higher than the first peak in test Al [-94 g's) by 29% [Table 6.4). The second peak in test A2 [231 g's) is

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198 smaller than the second peak in test Al (248 g's) by 1%. The arrival times for the first and second peaks in test Al (310 and 430 yseconds) are larger than the corresponding arrival times in test A2 (260 and 335 yseconds) by 19% and 28% respectively. Figure 6.55 and 6.56 show Accelerometer (A2] responses in tests A5 (2' standoff, Ig) and A6 (2' standoff, 60 g's). Tests A5 and A6 are similar to tests Al and A2 respectively except for the difference in soil density between tests Al and A5 explained earlier. The first response time of Accelerometer A2 in test A5 (285 yseconds) is 45 yseconds larger than the first response time of Accelerometer Al in test A5 (240 yseconds). Test A6 shows smaller peak accelerations as compared to test A5 . A similar response was obtained from the Accelerometer Al results. The first peak in test A5 (-138 g's) is higher than the first peak in test Al (-94 g's) by 47%. However, the second peak in test A5 (248 g's) is slightly smaller than the second peak in test Al (253 g's). The arrival times for the first and second peaks in test A5 (320 and 420 yseconds) and Al (310 and 430 yseconds) are very close. Although the magnitudes of the first and second peaks in tests A6 and A5 vary substantially, the arrival times for the peaks in these tests are relatively close (270 and 355 yseconds in A5 and 260 and 335 yseconds in A6 ) . Figures 6.57 and 6.58 show Accelerometer (A2) responses in tests Bl (2' standoff, Ig) and B2 (2' standoff, 82 g's)

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203 on 1/82-scale models. The adjusted first and second peaks in test B2 (-173 g's and 475 g's) are smaller than the corresponding peak accelerations in test Bl (-205 and 503 g's) by 16% and 6% respectively. The adjusted arrival times for the first and second peaks in test Bl (246 and 355 yseconds) are larger than the corresponding arrival times in test B2 (239 and 335 viseconds] by 3% and 6% respectively. The time at first response for Accelerometer A2 in test Bl (212 yseconds) is 27 ^seconds larger than the time at first response for Accelerometer Al in the same test. Figure 6.59 shows Accelerometer A2 response in test B4 (2' standoff, 82 g's). This test was conducted under conditions similar to test 32. The first and second acceleration peaks in test B4 (-165 and 503 g's) are relatively close to the first and second peaks in test B2 (-173 and 475 g's), respectively. The arrival time for the first peak in test B2 (239 yseconds) is higher than in test B4 (178 yseconds) by 34%. The arrival times for the second peak in these two tests are close (335 and 301 yseconds). Figures 6.60 and 6.61 show Accelerometer (A2) responses in tests A3 (0' standoff, Ig) and A4 (0' standoff, 60 g's). Both peak accelerations in test A3 (-424 and 902 g's) are higher than the peak accelerations in test A4 (-281 and 594 g's) by about 51%. The arrival time for the peak accelerations in test A4 (175 and 290 yseconds) are

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207 slightly higher than the corresponding arrival times in test A3 (165 and 285 yseconds). Figure 6.62 shows Accelerometer (A2) response in test A7 . Test A7 was conducted under conditions similar to test A4 except that test A4 was performed using a cracked burster slab. The peak accelerations in test A7 (-369 and 638 g's) are higher than the peak accelerations in test A4 (-231 and 594 g's) by 31% and 7% respectively. The arrival times in test A7 (200 and 315 yseconds) are higher than the corresponding arrival times in test A4 (175 and 290 yseconds) by 14% and 9% respectively. Figures 6.63 and 6.64 show Accelerometer (A2) responses in test B3 (0' standoff, 82 g's) and B5 (0' standoff, 82 g's). These two tests were performed under similar conditions. The peak accelerations and arrival times are close as shown in Table 6.4. In summary, blast tests at 2' standoff show consistently faster arrival times for the first and second acceleration peaks (A2) in tests at high gravities as compared to tests at Ig. The only Ig test performed at zero standoff on a 1/60-scale model (A3) shows larger peaks and faster arrival times compared to similar tests at 60 g's. On the other h^nd, high-g tests on 1/82-scale models at 32 g's show larger adjusted peak accelerations and faster arrival times than tests on 1/60-scale models at both Ig and 60-g tests.

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211 6 . 3 Strains A total of eight [four pairs) strain gages were used on each structure. Locations of these strain gages are shown in Figure 4.6. Because of the unavailability of a sufficient number of digital oscilloscopes with disk storage capabilities, results from strain gages 33 and S4 were only recorded photographically. Therefore, results from these two gages were not transferred to the computer (HP 9816) for reduction and analysis. Results from other strain gages [stored on oscilloscope disks) were transferred to the computer through a direct link between the oscilloscopes and the computer after the completion of all tests. During tests of the trigger system for the detonator (before actual explosive tests), it appeared that the trigger signal had an influence on the strain gage responses. This interference lasted for a relatively short period of time. This influence was recorded and subsequently subtracted from corresponding strain gage outputs in different blast tests to compensate for that unwanted effect. However, because of possible variability of such an interference in different tests, the first 150 to 200 microseconds of all strain gage data should be viewed and interpreted cautiously and with due consideration of a great possibility of interference.

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212 Fortunately, the main shock wave arrives at the structure just after this time period has passed. Axial and flexural strains in the slabs and sidewall of each structure in different tests are calculated (on the computer] from the adjusted strain gage data using Equations 4.7 and 4.8 [see Figure 4.7). Strain gages 31 and S2 [top slab) did not function properly in tests on 1/82scale models [B series). 6.3.1 Strains in Top Slab In this section, only the results of tests on 1/60-scale models are presented because strain gages SI and S2 did not work properly in tests on 1/82-scale models. Figure 6.65 shows flexural strains in the top slab for tests Al [2' standoff, Ig) and A2 [2' standoff, 60 g's). As mentioned earlier, the response in the first 150 ijseconds should be considered as influenced by interference from the trigger system and the explosion. In these discussions, only tlie time frame during which the shock wave is applied on the structure is considered. It is clear that the compressive flexural strains [on top of the top slab), which appear in the same time frame as the applied pressure P2 , are substantially larger in the 60g test [93% difference in peak strains). Figure 6.66 shows flexural strains [in top slab) for tests A5 [2' standoff, Ig) and A6 [2' standoff, 60 g's). These two tests are conducted under conditions similar to tests Al and A2

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215 except for a difference in soil density as explained earlier. Again, the flexural strain curves show larger compressive strains in the 60g test CA6) compared to the Ig test [AS]. The peak compressive strain in test A6 is larger than the peak strain in test A5 by 100%. However, these flexural strains are smaller than the corresponding flexural strains in tests Al and A2 . Figure 6.67 shows flexural strains for test A3 [0' standoff, Ig] and A4 (0' standoff, 60 g's). As explained earlier, test A4 was performed on a cracked burster slab. It is clear that the 60g test results are not much larger than the Ig test results. In fact, flexural strains in test A3 [Ig) show slightly larger values at the beginning. This effect can be better seen in Figure 6.68 which shows flexural strains for tests A3 and A7 [0' standoff, 60 g's). Tests A4 and A7 are similar except for the condition of burster slab which was intact in test A7 . Flexural strains in the Ig test (A3) are larger than strains in the 60g test (A7). This effect can be explained by considering the fact that Pressure Gage P2 also recorded higher pressures in test A3. Figure 6.69 shows axial strains in the top slab for tests Al and A2. It appears that, at smaller deflections (times), there is compressive axial strain in the slab and as the deflection (time) increases, the axial strain becomes tensile due to rigidity of the sidewalls. Test A2 shows smaller compressive strains than test Al . Of course,

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219 compressive axial strains (stresses) help with ultimate flexural strength of slabs subjected to dynamic loads (Krauthammer, 1984). Figure 6.70 shows axial strains in tests A5 and A6 . In this case, test A6 shows larger compressive strains than test A5 in the beginning, but then they both show tensile axial strains. Figure 6.71 shows axial strains in tests A3 and A4 . Test A4 shows larger tensile strains than test A3. A similar type response is observed in Figure 6.72 for tests A3 and A7. 6.3.2 Strains in the Side Wall Figure 6.73 shows flexural strains in the side wall for tests Al and A2 . The large tensile strains in test A2 are due to existance of larger pressures on the top slab of the structure in test A2 as compared to test Al . Flexural strain in test Al (on the side wall) fluctuate between compression and tension. Figure 6.74 shows flexural strains in test A5 and A6 . Again, there are larger flexural tensile strains on the outside of the side wall in the 60g test (A6) compared to the Ig test (A5). However, the magnitudes of strains are smaller than in tests Al and A2 . Figure 6.75 shows flexural strains in tests Bl (2* standoff, Ig) and B2 (2' standoff, 82 g's) performed on 1/82-scale models. Larger tensile strains appear in the 82g test (82) compared to the Ig test (Bl). The magnitudes and

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226 shapes of the strain response curves in tests Bl and B2 are similar to the curves in tests Al and A2 (Figure 6.73]. In fact, the arrival time for the first tensile peak in test 32 (during the time the shock wave is applied on structure) is almost exactly 60/82 times smaller than the first comparable peak in test A2 . Figure 6.76 shows flexural strains in tests B2 and B4 (2' standoff, 82 g's). These two tests are similar and they show equal magnitudes for the first tensile peak. The arrival times of this peak are also close. Flexural strains in tests A3 and A4 (Figure 6.77) show equal peak magnitudes of tensile strain on the outside of the side wall. A similar type of response is obtained from tests A3 and A7 (Figure 6.78). Figure 6.79 shows flexural strains in the side wall for test 83 (0' standoff, 82 g's) and B5 (0' standoff, 82 g's). These two tests show very different responses even though they are essentially the same tests. It appears that test B5 presents a more valid response considering the similarity of this response to the results obtained in test A7 . Figure 6.80 shows axial strains in the side wall for tests Al and A2 . It appears that the compressive strains in tests Al and A2 are almost equal even though a larger compressive strain was expected in test A2 considering larger pressures applied on the top slab in this test. This may be explained by pointing out that the increased confinement by the soil on the structure could result in a

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231 n

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232 larger degree of load transfer to the soil. Figure 6.81 shows axial strains in tests A5 and A6 . The magnitudes of strains in this case are smaller compared to tests Al and A2 (Figure 8.80). However, the first compressive peak is larger in the 60g test (A6) compared to the Ig test [A5). Figures 6.82 and 6.83 show axial strains for tests Bl , B2 and 32, B4 respectively. The magnitudes of these strains are smaller than the corresponding strains in tests on 1/60-scale models (A series). Figure 6.84 shows axial strains in tests A3 and A4 . Test A4 shows slightly larger compressive strains than test A3. Considering larger pressures observed on the top slab in test A3, it is expected that compressive strains in test A3 be larger. This effect can be clearly observed in tests A3 and A7 [Figure 6.85). Tests B3 and B5 (Figure 6.86) show substantially different results. It is believed that this is due to a gage malfunction in test B3. 6.3.3 Strains in Bottom Slab Figure 6.87 shows flexural strains in the bottom slab for tests Al and A2. Test A2 shows residual strains after the shock wave has passed. This is due to gravity stresses in the 60g tests which remain after the explosion occurred. Compressive flexural strains on the outside of the bottom slab are consistently and considerably higher in the 60g test (A2). The peak strain in the 60-g test (A2) is 200% larger than the peak strain in the Ig test (Al) . Figure

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240 6.88 shows flexural strains in tests A5 and A6 . Again, flexural compressive strains are larger in the 60g test (A6). The magnitudes of these strains are close to those obtained in tests Al and A2 . Similar tests at 2' standoff on 1/82-scale models (Figure 6.89) exhibit behaviors similar to those observed in tests Al, A2 , A5 and A6 . Peak strains in test B2 are close to peak strains in test A2 . Also, the arrival times for the peak in test 82 is 60/82 times smaller than the corresponding arrival times in test A2. These facts point to the validity of scaling relationships presented in Chapter 2. Tests 32 and B4 which are conducted under similar conditions show very similar responses as shown in Figure 6.90. Tests on 1/60-scale models at zero standoff distance (A3, A4, A7] also show a response similar to tests at 2' standoff (Al, A2 , A5, A6 ) as shown in Figures 6.91 and 6.92. Test A7 shows slightly larger peak compressive strains than test A4 . Figure 6.93 shows flexural responses in tests on 1/82-scale models at zero standoff distance. The do not show similar responses as would be expected and the peak strains are larger than those in tests on 1/60scale models at zero standoff distance. Axial strain curves in the bottom slabs for tests on 1/60-scale models (Figures 6.94 and 6.95] are very similar to the axial strain curves in the top slab for the same tests. The reason may be that the axial strains in the too

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249 slab are transferred to the bottom slab through shear waves in the side walls. Tests on 1/82-scale models at 2' standoff show very little axial strains in the bottom slab (Figures 6.96 and 6.97). Figures 6.98 to 6.100 show axial strains in the bottom slab for tests A3, A4 , A7 , B3 and B5. In summary, tests at 60 or 32 g's show substantially higher flexural strains in the top slab, the side wall, and the bottom slab of the box structure as compared to tests at Ig. Again, these facts illustrate the significance of gravity stresses (centrifuge testing) in the response of these structures. 6 . 4 Velocities Velocities at the center of the top slab and the side wall are calculated by integrating the responses of Accelerometers Al and A2 , respectively. Because of the observed drift in the accelerometer responses prior to the explosions, the digital zero on the accelerometer responses does not indicate zero acceleration. Therefore, a reference voltage (zero acceleration) has to be established for each accelerometer response. This is equivalent to shifting the accelerometer response by a constant value to account for the drift. The reference voltage is determined through the process of trial and error. The selected reference voltage which results in the convergence of velocity and displacement responses to zero after a relatively long

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255 period of time (5 to 10 ms ) is a valid reference point for each accelerometer response. The first 80 pseconds in the response of each accelerometer was set equal to zero so that the effect of explosion on the instrumentation would not be integrated. Positive velocity is directed downward for the top slab, and inward for the side wall. 6.4.1 Velocity VI Velocity VI [top slab) is obtained by integrating the response of accelerometer Al . Figure 6.101 shows Velocity VI responses in tests Al (2' standoff, Ig) and A2 [2' standoff, 60 g's). The peak velocity in test Al (17 in/sec) is larger than the peak velocity in test A2 (14 in/sec) by 21%. The duration of positive velocity in test Al (2400 yseconds) is larger than the corresponding time in test A2 (1150 yseconds) by 109%. Velocity VI in test A2 also has a faster arrival time for the first peak, which is expected considering the observed faster arrival time of the pressure wave on the top slab in test A2 (see Figure 5.7]. The smaller peak velocity in test A2 may be attributed to larger confinement of the structure by the soil at high gravities. Figure 6.102 shows a very similar type of response for tests A5 (2' standoff, Ig] and A6 (2' standoff , 60 g's]. Figure 6.103 shows Velocity VI responses for test Bl (2' standoff, Ig) and B2 (2' standoff, 82 g's). The general

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259 shapes of the two curves are similar to the corresponding responses in tests Al , A2 , A5 , and A6 [Figures 6.101 and 6.102). Based on the scaling relationships [Table 2.3), peak velocities in comparable tests on 1/60and 1/82-scale models should be equal. However, specific times in tests on 1/82-scale models should be smaller than the corresponding tests on 1/60-scale models by a factor of 60/82. Figure 6.103 shows that the peak, velocity in test Bl is 20 in/sec which is slightly larger than the peak velocities in comparable tests Al and A5 [17 in/sec). The peak velocity in test B2 [11 in/sec) is slightly smaller than the peak velocity in test A2 [14 in/sec) and test A6 [13 in/sec). The adjusted time for the duration of positive velocity in test 81 [1536 X 82/60 = 2100 ^seconds) is smaller than the corresponding times in tests Al [2400 yseconds) and A5 [2170 yseconds) by 12% and 3%, respectively. The adjusted time for the duration of positive velocity in test B2 [696 X 82/60 = 951 useconds) is also smaller than the corresponding times in tests Al [1150 ^seconds) and A2 [1200 ijseconds) by 17% and 21%, respectively. Figure 6.104 shows the Velocity VI responses in tests B2 and B4 . These two tests were conducted under identical conditions and should yield similar results. The general shapes of the two curves and the magnitudes of the peak positive velocities are in close agreement. Figure 6.105 shows the Velocity VI responses in tests A3 and A4 . The peak velocity in test A3 [26 in/sec) is larger

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262 than the peak velocity in test A4 (19 in/sec) by 37%. The duration of positive velocity in test A3 (1730 yseconds) is also larger than the corresponding time in test A4 (1310 yseconds) by 32%. Figure 6.106 shows Velocity VI responses in tests A4 and A7 . Tests A7 and A4 were conducted under similar conditions (except for the condition of burster slab explained earlier). Test A7 shows slightly smaller peak velocities as compared to test A4 . Figure 6.107 shows Velocity VI responses in tests B3 and B5. These two tests are also comparable to tests A4 and A7 (Figure 6.106) except for the size of the model (1/82 versus 1/60). Although, the peak velocities for the 1/82scale models are larger, the general shape of the response curves are very similar considering that the times in 1/82scale models are smaller than the corresponding times in 1/60-scale models by a factor of 60/82. For example, the adjusted arrival time of the third peak velocity in test B3 (342 X 82/60 = 467 yseconds) is relatively close to the corresponding arrival time in test A4 (528 yseconds). In general, for tests conducted on 1/60 and 1/82-scale models, the peak velocities (Vl) in tests at Ig are larger than the peak velocities in corresponding tests at 60 and 82 g's. Moreover, the general shape of velocity responses differ significantly for high-gravity and Ig tests. These results are believed to be due to larger confinement of the structure by soil in high-gravity tests. This fact illustrates the significance of gravity stresses

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265 [centrifuge testing) with respect to the structural response of such systems. A high degree of repeatability of velocity responses is evident for tests conducted under similar conditions. 6.4.2 Velocity V2 Velocity V2 (side wall) is obtained by integrating the response of Accelerometer A2 . Figure 6.108 shows Velocity V2 responses in tests Al and A2 . The magnitude of peak velocities [4 in/sec) is much siaaller than the velocity peaks on the top slab (Figure 6.101). As expected, the velocity on the side wall is first directed outward (negative velocity). Figure 6.109 shows Velocity V2 responses in tests A5 and A6 which are in general agreement with the response in tests Al and A2 (Figure 6.108). There was a problem with the convergence of the velocity response in test A5 . Tests Bl and B2 (Figure 6.110) show slightly different velocity responses. The peak negative velocity in test Bl has a magnitude of 6 in/sec which is larger than the corresponding peaks in tests Al (4 in/sec) and A5 (5 in/sec). The adjusted arrival time of the peak velocity in test Bl (215 X 82/60 = 294 useconds) is smaller than the corresponding times in tests Al and A5 (360 useconds). Figure 6.111 illustrates that tests B2 and B4 , which were conducted under similar conditions, show very similar velocity responses.

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270 Figure 6.112 shows Velocity V2 responses in tests A3 and A4. The first negative peak velocity in test A3 [10 in/sec] is larger than the corresponding peak in test A4 (7 in/sec). However, the arrival times of these two peaks are very close. Velocity responses for tests A4 and A7 are shown in Figure 6.113. As expected, the two curves are very similar because the two tests were conducted under similar conditions. This type of similarity in response can also be seen in tests B3 and B5 [Figure 6.114). The first negative peak velocity in test B3 [17 in/sec) is larger than the coreesponding peak in comparable test A4 [10 in/sec). The adjusted arrival time of this first peak in test B3 [138 x 82/60 = 189 ^seconds} is smaller than the corresponding time in test A4 [228 pseconds). 6 . 5 Displacements Displacements at the center points of the top slab and the side wall are calculated through double integration of the responses of Accelerometers Al and A2 , respectively. Positive displacement is directed downward for the top slab and inward for the side wall. 6.5.1 Displacement Dl Displacement Dl [top slab) is obtained by integrating the response of Velocity VI. Figure 6.115 shows the Displacement Dl in tests Al and A2 . Test Al shows a peak displacement of 0.018 in which is larger than the peak in

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21\ test A2 (0.005 in]. This difference in displacements at 1 and 60 g's is due to a larger confinement of the structure by soil at 60 g's which results in a higher stiffness for the top slab. Figure 6.116 shows a similar-type behavior in tests A5 and A6 . The adjusted peak displacement in test Bl [0.015 x 82/60 = 0.02 in) is slightly larger than the corresponding peak displacements in tests Al (0.018 in ] and A5 (0.017 in). The adjusted peak displacement in test B2 (0.003 x 82/60 = 0.004 in) is smaller than the corresponding peaks in tests A2 (0.005 in) and A6 (0.006 in). Figure 6.118 shows the displacement curves for tests B2 and B4 . They show similar responses except for the divergence of the negative displacement in test 84. Figure 6.119 shows the displacement (Dl) curves in tests A3 and A4 . The peak displacement in test A3 (0.022 in) is larger than the peak displacement in test A4 (0.010 in). Again, the increased confinement of the structure in test A4 is believed to be the main reason for this observed difference. Test A4 shows a divergence in displacement response. A similar test (A7) is shown in Figure 6.120. The peak displacement in test A7 is 0.006 which is smaller than the peak in test A4 (0.010 in). In summmary, deflections of the top slab of the structure are much larger in the Ig tests as compared to the tests at high gravities. These observations are believed to be due to larger confinement of the structure

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281 by soil (along the side walls) in high-gravity tests resulting in different (more restrictive) boundary conditions for the top slab as compared to tests at Ig. These results clearly indicate the significance of centrifuge testing in terms of the effect of gravity stresses in modifying the structural response of the system. In addition, the repeatability of deflection responses in similar tests are clearly illustrated and the scaling relationships are, to a large extant, verified. 6.5.2 Displacement D2 Displacement D2 (side wall) is obtained by integrating the velocity response V2 . Most of the displacement curves for the side wall do not converge to zero displacement. This may be because of very small displacements (less than 0.001 in) involved, and the errors introduced in double integrations to obtain such small displacements. Therefore, only Figures 6.121 and 6.122 which indicate more reasonable responses are shown. Displacement scales in these two figures are different from previous figures.

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283 a

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CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS 7.1 Conclusions Based on the tests performed in this research effort, the following conclusions can be made: 1) An effective instrumentation system including piezoelectric shock pressure transducers, strain gages and accelerometers can be designed and built for centrifuge tests on small-scale models of underground structures subjected to blast loading. 2) For blast tests at a standoff distance of 2 scaled feet, the arrival times of pressure waves on the top slab of the box structure are consistently and substantially faster in the high-gravity tests (both 1/60and l/82-3cale) as compared to Ig tests. In addition, the peak pressures in high-gravity tests are also higher. These results are believed to be due to larger stiffness of sand in highgravity tests. Accelerometer and strain gage data also show faster acceleration response times and higher flexural strains in the high-gravity tests. Tests on l/82-3cale models (2' standoff) show larger pressures than similar tests on 1/60-scale models even though equal pressures were expected according to the 284

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285 scaling relationships. The reason for this discrepancy is believed to be due to an improper scaling of the explosive, not in terms of total mass, but rather in terms of mass distribution and charge geometry. Also, dimensional tolerances with regard to the building and placement of very small-scale structural models and explosive charges may be a factor. Despite these differences, the arrival times of peaks in most tests on 1/82-scale models were close to 60/82 times smaller than the corresponding times on the 1/60-scale models. This relationship satisfies the basic time scaling relationship. Based on these tests, it appears that 1/82-scale models may be close to the limit in terms of the smallest acceptable size model to be used in such tests. For blast tests at zero standoff distances, the only test performed at Ig showed larger pressures and accelerations on the top slab of the box structure as compared to high-gravity tests. This condition may be explained by considering that, for tests at higher gravities, the higher soil stiffness (under the burster slab) would distribute the highly localized pressure (zero standoff) more evenly and therefore reduce peak pressures at the center of the top slab of the box structure. In addition, a larger portion of the total explosive energy may be expended in crater formations in tests at high gravities, resulting in smaller energy transmission to the soil. Also, testing errors such as incorrect placement of

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286 the detonator may be a distinct possibility for this specific test. Again, consistent results were obtained for high-gravity tests on 1/60-scale models but tests on 1/82scale models showed some variations. Velocity and displacement responses for tests on 1/60 and 1/82-scale models indicate substantially different results between tests conducted at high gravities and at Ig. This fact illustrates the significant effect of gravity stresses (centrifuge testing) on the soil-structure interaction and the structural response of such systems. A high degree of repeatability of velocity and displacement responses is also evident for tests conducted under similar conditions . 3) Based on the test results reported here, it can be concluded that the centrifuge is a necessary and viable tool for blast testing on small-scale models of underground structures. This method of testing can result in substantial cost savings as compared to full-scale tests and would be ideal for parametric studies on underground structures. Ultimate strength (failure) studies on such systems in a centrifuge should be performed only after a sufficient understanding of the dynamic ultimate strength properties of microconcrete and their relationship to regular concrete is achieved.

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287 7 . 2 Recommendations for Future Studies Further improvements to the instrumentation system should be directed at eliminating the use of slip rings and multiple oscilloscopes. The use of telemetry to bypass slip rings may not be advisable because of the relatively high costs of such systems specially when signals with wide frequency bandwidths (such as blast) are involved. It is recommended that on-board data capture and storage systems be designed for future tests. These systems are technologically and economically feasible. Multiple highspeed, high-accuracy analog-to-digital converters together with storage modules can be designed to store the waveforms for transfer to a computer at a later time. Now that the basic methods and devices for blast tests in centrifuge have been developed and the importance of gravity stresses are established, future such tests should, at first, be directed at understanding the major contributing parameters independent from each other. For example, an study of the characteristics of shock wave propagation in different soils (no structure) should be the first step in that process. Next, a structure with a simple geometry such as a slab should be included in the tests. Finally, complex structures such as box-type structures can be tested for parametric studies on the structural performance of such systems. More information is needed on the dynamic ultimate strength (failure) properties of microconcrete compared to regular concrete specially for

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288 the shear failure mode. This information is needed for performing reliable ultimate strength blast tests in a centrifuge.

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APPENDIX A ELECTRONIC COMPONENTS OF THE INSTRUMENTATION SYSTEM 289

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290 INA101 ! ^M»l^ i Very-High Accuracy INSTRUMENTATION AMPLIFIER FEATURES . ULTHA-LOW VOLTASE OaiFTttZSMV/t • LOW Off SET VOLTAGE -25pU LOW NOHUNEAaJTY O-COZ^, • LCWHOISE13nV/>/i?Z3tf|j= IkHz • HIGHCMR-IOadSatSOliz . HI'lH INPUT IMPEflAMCE • IQ'Op. •iC'ii( COST DESCRIPTION The INAIOI is a high accuracy, muliisiage. integraisU-circuii insirumentadonaaiplificr designed for signal conditioning irqiuremests where very-high pert'ormance is desired. Ail circuits, including the interconnected Ihin-film resiston, are integrated on a single monolithic subsirnte. A multiamplifier design is used to provide the highest perlortnance and maximum versatility with mono lithic construction for low cost. The input stage uses Burr-Brown's ultra-low drift, low noise technology to provide exceptional input characteristics. Gain accuracy is achieved with precision nichrome resistors. This provides high initial accuracy, low TCR (temperature coefficient of resisunce) and TCR matching, with outstanding subility as a function of lime. State-of-the-art wafer-level laser-trimming techniques are used for minimizing offset voltage and offset voltage drift versus temperature. This advanced technique also maximizes common-mode rejection and gain accuracy. The INAIOI introduces premium instrumentation amplifier performance and with the lower cost makes it ideal for even higher volume applications. APPLICATIONS • AMPLiFICATI0!4 OF SIGNALS FROM SOURCES SUCH AS: Strain Gign Tharmoixuples RTD» • REMOTE TRANSOUCERS • LOW LEVEL SIGNALS • MEDICAL INSTRUMEMTATIOM VFOTUUin

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291 ANALOG DEVICES Precision, Low-Power FET-Input Electrometer Op Amp AD515 F6ATUHBUltra Low Bia»CufTOTit: O.OTSpA mm (A061SL> 0.150pAmas(AO515K) 0.300pAnna(AC515J) Low Poww: 1.5mA max Oiiitwrn Cumot lO^SmA typ) Lnw Ofhtt Votaqa: 1.0mV nux (A0519 K & L) Low Drift: IS^V/^C tnaji (A051SK) Low NouK. 4^ p^, 0.1 to 10Hs^ l~« Cort ADSIJ FUNCnONAi. BLOCK DIACSAM -•3551 TO-99 TOP VIEW PRODUCT DESOUPTTON The ADS 1 5 Jenes viously available in ulcn4ow bos aujmt. diouiL All devices are intemaUy conipcnssiBd. frec-of Utch-ap. aod sboR circuit proceaed. The Ai3SlS delivers a. new level of vecutility and precision to a *nde viriery of Uei-tiuuieiei a nd very high unpcdance buffomeiiuremenr situaaota, including pttoto-cmrcnt detection, vacuum ion-gauje measurement, long tenn precaion integration, and low drift sample/hold applications. The device is also in excellent choice for all forms of biomedical instrumentation such is pH/pIon sensitive electrodo, very low current oxygen sensors, and high impedance biological nhcroprobes. In addition, the low cost and pin compatibiliry of die ADS 15 with standard FET op amps will allow designers to upgrade the performance ofpresent systems at litde or no additional cose The 10 ohm commoo mode input impedance, resulting from 1 solid bootstrap input stage, insures that the input bias current IS essentially independent of common mode voltage. .\s>viih previous electrometer amplifier designs from Analog De\ices, :he case is brought out to its own connection (pin 8) io chst the case can be independently connected to a point at tne Sime potential as the input, thus minimizing stray leakage to ihe tise. This feature will also shield the input circuitry trom external noise and supply transients, is well as reducing common mode input capacitance from O.SpF to 0.2pF. The ADS 1 5 is available in three versions of bias current and oit«t voltage, the "J", "K", and "L"; all are specified tor rsteJ performance from to *70°C and supplied in a hermetically veiled TO-99 package. PRODUCT HICHUGHTS 1 . The ADS 1 S provides the lowest bias currents available in an integrated circait amplifier. • The ultia low input bias currents are specified as the maxunum measured at either input with the device fully warmed up on ±IS volt supplies at -^ZS C ambient with o heat sink. This parameter is 100% tested. • By using iS volt supplies, input bias currentxan typically be brought below SOf A. 2. The input offset voltage on all grades is Laser trimmed to a level typically less than SOOfiV. " The offset voltage drift is the lowest available in an FET electrometer amplifier. • If additional nulling is desired, the amount required will have a minimal effect on offset drift (approxiimtely i(iV/°C per millivolt). 3. The low quiescent current drain of 0.3mA typical and l.SmA maxunum, which is among the lowest available in operational amplifier designs of any type, keeps sdfheating effects to a minimum and renders the ADS 15 suitable for a wide range of remote probe situations. 4. The combination of low input noise voltage and very low input noise current is such that for source impedances from much over one .Megohm up to 10 ohm, the Johnson noise of the source will easily dominate the noise characteristic. OPERATIONAL AMPUFI£R5 VOL. /.4.57

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292 National Semiconductor Transmission Line Drivers/Receivers DS14d8 Quad Line Driver Genefat Description Th* 0S14SS is a quad lina drnar vnAidt cu i nw a aandani OTL/TTT. input logtc l«»«t» through oo» Ttsg* of invanion to output lcv«4s whicn ma«i EIA Stantrtnl No. HS-232C and CCJTT Recomnwnd*tion V. 24. Features • Current limited output ilO mA ryp • Pow«f-oH source imoedmo* 3flon min Simple tiew rate control wtttt externa* caMCitor Flexible operstirtq Sipply ranqe JnputJ are OTTL/TTL compaotll^ Schematic and Connection Diagrams OumUn-Uimfwcktft I !• 11 "1 n >9 1 I lOVVtHi Ordw Numsw 0S1«8U or OSIASSM S« NS Packaea J14A w N14A Typical Applications RS232C Data Tr9fWff«n
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293 National Semiconductor PeripheraiyPower Drivers DS55450/DS75450 Series Dual Peripheral Drivers Generai Description Ttw OSS54e0/OS7S45O »nm at dual pwipliant dhvwi «• a famtyat varutil* J ani cai daii^Md 'of ui» in S Y %tm n » that m* TTl. or OTL logic Typtcal aoclicationi inrtiBla high soaad logic bufftn. powr driven, relay dilnMj, lamp drivarv MOS driv«n. bus drivtn ind TTtt 0S5545Q/DS75450 una v* uniqua gantral purpoia drincas «ach faatuhn^ tvao rundard Smi« 54/74 TTL 3attt and tY«o unconMmnad.)>igh currsnt. high voltaga NPN tramisTon. Th*»» dw i cai otttf tfw syjiam dtsJgcMr iha ftaxibilicv of aUomq tha drcuir to th« aoolicabOK. lYn DSS5*S>/DS7545»,DSS5452/OS75452. DSS5453/ DS75453 and 0SS5454/0S75454 ara dual ptrioharat ANO. NANO. OR and NOH drivan. mpactivaty. [poa* tiva logicl vnith tha output of tha logic ^atas irrtemaiiy connactad to Tha basai ot tha NPN outpur transaton. Features 300 m A output: cufTvnt capab>li(y a Hi^ yoltaga outouti No output latch-uo at 2u> High spaad switching Oioica. of iogic hinctioc. "nX or DTL comoaiitila dioda-damoad inputs Standard supoly voltagai Replaeai Tl "A" and "B" lanei Connection Di^QramS (Oual-ln-Una and Matat Ctn PackagtsI 1..

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294 National Semiconductor CD4066BM/CD4066BC Quad Bilateral Switch gan«fal descnption Th^ C040«68M/C040668C • quad tMUnr*4 s«rt« 'noMtad tor m» u a wiii u i u ii or multipUninq oi mi lot or Ji>u< iMfr ^ %. It' « j i i »' ) o n3i i v . compMibl* wntn CO4OieaM/<:04016SC b1SV 0.45 V 00 tvtt S7.5 VorAK ARqn * Sllrvp • Wide 9U(ip^ oo»cjt. B M«^«ad "ON" J » in oiwj o«ar TSV sqnal incut • "OW* ft«t»an«» ftn La »i p »» k m p «»tr signal rang*. • Hi<*t"ON-/*^FF'*eutnutvo(tJ9« ratio 65 dB rvp ^f;,.10 kHz. RllOkn Htgtidayaaof lincanrr < 0.4% distortion xvp ^^tJ1 kHz. V|, -SVo-o. ''00— VsS" lOV, R| -lOkii Eyrramdy la«r"OFP'*s*Htdt iMkaga a.1nAtvp »Voo-VsslOV. ta zs'c • £xtretti«(y ni^control mout lO'^fltyp imoadanc*. Low eronaiic om»«»n swwcrtia*.. -SOdBryo 9 fi,.-a9 MMi. Sl 1 ka Fr»qu»nev rnooma. .vMtcft "ON" 40 MHz tvp applications Analogitgnal iwiiehi.ig/iTTultiQl«]im9 • S'nnal aatinq • Squalen coi-troi • C.'ioooar • ModuUtor/Oemodulatar • Comrmitating switch Oigiial signal switcfiing/imltrpltxing CMOS logic >mp(«nen(aDan Analog-to-digital/digital-to-«naio9Conv«mon Digital control of frequancy, impadancs. pliasa, and analoq-signal gain schefnatic and crmnection diagrams Omf-*.. .iiwPack*^

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295 Using the CMOS Dual Mcnostabie Multivibrator Nationat Semicanductor Application Note 133 Thomas P. Redferrv mrr^oeucnoN Ttm MM54C22T/MM74C(2T fj a duat CMOS mononaftU muiuyibntor. Fjrh o n » iho t >a» Oirea inouu (A, 3 and CLUX^ Md n«o owipua lO Md Q). TTm output pulM. Mtrav is sM tiv an •namat R(T narMork. Th« A and 9 inpuo tnggac an output puiia on a ncqativ* orponrr** input tnnutuai moaetivc^v. Tha CLR input vtrf^anlow r«s«t> tha on»4hot. Oncm tnggarad tha A and B inouti ha«* no furthar comrol on rfm output. •mennY of opchatioi* Figure T jhowi tfiat in its nabta nata, tha ona^ho dampc CgxT to ground by mtrmg Ml ON and hold ttwpaiThv» comparator input at V(.g by lurninq N2 OFF. Th»p»Tfix N i j used to danotw N-cnanr>»« tramwton. Tha ^i^rat, G, gating N2 OFF alaagataa ttia comparator OFP tftaraOr >cc«oing xfn intam* povvar diuipation to an absotuta mmimMm. Tha only powar omipation vWianin tJi» stabta 5tat* ii that ga nat ai e U by tha current thftsugtr RgxTTha buik of tha dissipation ii m Rgxr jirKa tlM yottag* drop acron Ml a vary small for normal o» FIrxT. To tnggar tha on»4/ior tha CU) input must ba high I na ganng. G. on tha comparator is oasiqnad wcit that tha comparator output is high yi^nn tha ona-thpt is. in ia ttabia nata. With ttia CLA input high tha daar input to FF is disablad lilowmg tha flip-Aop to raspond to th* A or 9 input. A nagativa trarmtion on A or a posiliwa transition on B >m Q to a high stata. This m turn gatai N1 OFF and N2 and tha comparator ON 'viting N2 ON cstaplishaa a la f aiai wj of 0.62 V(^ on .r-: comparator'i poutiva ir>put. Sine* thr volraga or» Caxr '^"^ '^°f change lnstamar>aaus^r V1 > OV at thia tima. Tha comparator than voill maintatn irs on» lava* on (ha output. Gatjng N1 OFF allows Ca^^ to itart charging through I^EXT toward V,-^ «xponanT avants. This diagram is idealited by assuming zero risa and fall times and zero propagation delay but it shows the basic operation of tha ona.»hor. Al«3 shown is the effect of taking the CLR input low. Whenever CL3 goes low FF ^ C»^' '^ •it FICURC 1. ^
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296 Voltage Comparators National Semiconductor L!Vl161/LM26iyLlVl361 High Speed Differential Comparators Generat Description Features •Pw CM181AJi«81/LM3St n i vOTy high di >f «w ni a*input, comptamantary TTL output woltag* comoarstor wiin improvxl characrtriidcs ovar th« S&529/NE529 tor mhidi it n i pm-rorgin rcptacamatn. Th» Ortica iMi b««n ogtimiitd 'or 7«si«r spMd p »r< onim i u ind lowar input of]tt MOttaq*. TypicXty d*4av vvm only 3 ns for ov«r-driv« »«rution» of S mV to 500 mV. It mjy b* oparatad from op imp tupptiai (±I5V). CompJamantjryoutputi having minimum sknv art providad. App4icatiom involvt higfi spead analog ta digital canvamn and zaro-croaing datactort in disc lila svnimt. Indtpaodvnt nrobai Guai^ntaad high spaad 20 ra max Tight datay mat^nng on both outpuix • Complamaotary TTL outputi 'Oparaits from op amp supoliai ±15V Low spaad variation with ovardi «« variation Low input offjat voltag* Versatiia supply voltag* ranga Schematic and Connection Diagrams Oiut-livUna l>MJu«> I" » " • I" • I OntarNufnbwLMISU. LM28tJ or LM3S1J Sm NS PvcSiaaa JIAA Ontap Nun*v LM3S1N S— NS fitlini M14A Logic Diagram rjf mIL OrdirNumbw LMISIH. LM261H or LM381M Sm NS l>>clua* HI DC nj nj

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APPENDIX B COMPUTER PROGRAMS WRITTEN ON HP 9816 The following are several computer programs written on an HP 9816 computer for analysis of the test results. One such program is for the retrieval of waveforms from Nicolet 4094 oscilloscopes and storage of data on computer diskettes. Other programs analyze and plot the results on a digital plotter. 297

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3C 10 JSI PROCSAM TO ?LOT ACCSXEHAnON UAVCFORHS OH HP 7470* PLOTTH -^ ;0 IBf ^ FTBRUAilY 1987 — ;o urn -0 3L1 A(204i). 3(2048). ftSI501 30 lapuT -:spoT file nake for isT. vAVEToiw . ns 70 ASSIGN i|Fl TO ns JO ASSIOT ?P TO "05 100 ouTTirr iP:-!N:SPi:iPi350. 2000. 9250. sooo:no OUTPUT 3P;-SC0, 2000. -eSO.SSO:" 120 OUTPUT iaP:-PUO. -650 PD 2000 , -650, 2000. 650.0. 630,0, -S50 PU' 130 OUTPUT ap:-pAO,o po 2000,0 po140 OUTPUT ap;-si. 2, -3.ru,. 3.0" 150 FOR :(-) TO 2000 STEP 200 160 OUTPUT aP:-PA-:X.-.-650:rr;170 IP .(-0 THEM OUTPUT 9P: "CP-l. •1:U:I: " ISO IF X-0 THEN 210 190 IF :«1000 THES OUTPUT !5P: •CP-2. l:La":X<1.3; •" 200 IF :c>-1000 THEM OUTPUT ?P: 'CPO. -1;U:I«1.3; " 210 .VEJtT .1 260 OUTPUT 3P:*PAI0OO, -650:C?-10.-2.5:LBTIMI (HZCSOSECOHDS)" 270 OUTPUT iP:-TlI.5.0280 FOR Y— 600 TO 600 STEP 20O 290 OUTPUT JP:-PAO.-:Y.-YT:300 IF Y-O THEM OUTPUT ap; "CP3 . , 23 ; LSiY; "" 310 IF YOO THEM OUTPUT 'aP:'CP-5.25:LB";T^:«" !20 :)aCT Y 370 L-IPUT -INPUT CEHEIAL TITLE FOT OXAPM'.PtS 384 OUTPUT aP:'PAO.O CP-6.0. -5-.0I0.L;LS ACCELOUrXOS CCS) " 390 OUTPUT ?Pt-PA1250.S50 SI. 2. .3 CPI.14" -00 OUTPUT 3P:-0I1.0 La":Ft1:-* -10 OUTPUT aP: *?U1600, -650 PD1600, -200, 2000, -20O PO" -20 OUTPUT aP;-pui700, -600 PD 1900,-600,1900,-350.1700,-350,1700,-600 PU" -30 3UTPUT ap:-pui730. -S65 PO 1870 , -565 , 1370, 380 . 1730. • 380, 1730, -363 PO' —0 OUTPUT ap;-?ul700, -305 PD L900. 305. 1900. -230. 1700. -250.1700 -303 Pn" -30 lEM -60 R£J( — iHOinSO LOCATIOa OF TEST OACES -^ -61 iOt — Al -70 O UTPUT aP:-?uiaoO.-380 PD 1810 ,380, 1810, -385, 1800, 345. 1800, 380 PO" -71 OUTPUT ap:-SI.l, .13:PA1780, -4lO:LaAi" -36 5EM — A2 -88 OUTPUT ap:-?01730.-475 PO 1730, -465. 1740. -iiS, 1740. .475. 1730 -473 PD' -89 OUTPUT JP:-SI.l. .13;PA1730,-475:UA2* 503 lEM 504 ^EM ^ LEGEND -^ 305 i£H =06 INPUT -INPUT LEGEND TITLE FOR 1ST CURTE, US 307 INPUT -INPUT CALIBRATION VALUE: •, Fttf ;09 OUTP'JT ap:-?uil00 650 PO 1100.-50,2000.450 PO' ilO OUTPirr ap:-pui300.650 PD 1300,-50 PO' 511 OUTPUT aP;-?U1520.630 PO 1520. -SO PO' 512 OUTPUT aP:-?ul6LO,650 PD 1610,450 ?^' 513 OUTPUT ap;-?ui740,650 PD 1740,450 ?rj' 514 OUTPUT aP:-?Uia75,650 ,'D 1375,-50 ."0' 515 OUTPUT ap--puilOO,SSO PD 2000,550 PO' 516 OUTPUT aP:-?ull00,-50 ?D 2000.450 PO' 517 OUTPUT 3P:-SI,l,,15:.»A1150,550:!:P2,-l,3:LaLINE OESCRIPTIOIt TEST SCALZ STAHDOPf 513 OUTPUT 3P:-?A1100.-00:L3NOTE: POSITIVE .^CCELEBAnOM IS SISECTEB AtfAY rROM THE lASE' :20 INPUT -I-VPUT TABLE .'OR 1ST -AVErORM' TIS :22 OUTPUT aP: -'.T523 OUTPUT ap:-puill5,500 PO 1290,300 PO' 524 OUTPOT ap; •PAi3io,500;LS";US:" 523 OUTPUT ap:-?Al550,500:L3-:nS(1.21:'" 529 OUTP'-T ap;-?A1650,300;La-TlS(3,61 ;" 530 OUTPUT aP: ?A1300,500:L3-:T1S[7,31 ;•' 531 :UT?'.T ap; •PA1920, 50O;L3-:TlS[9,101 ;"' 555 OUTPUT ap:-SCO 0000,-1200, 120053~ L'.TZR an,.-4norai,A(*i 533 OUTPUT IP-LT:;9 :UT?'ap -p.w.O PU:-; "OR I-l TO 400 5-1 X":?UT aP: -?AHnoral*'I-l)'lOOOOOO:ACI)«Ffff ;-P0' 551 :l"T?UT ap--?U"

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305 13 .^DI — PROCilM TO PLOT .TLOCITTT VAVtrOWa Jd Hf -i70A FUTTTIl -^ '^ -~ ™IS PSOCllArt LMTTCSATIS ACCSlEEAnOII .•AVCTOiHJ — . -3 JE< .^ rUaUAXY 19«7 ^ -0 JI-H A(20M)..-tS(!0| ,J(20M) :o .:mr: •iKPtrr accel. nii 'iamz roa isr. VAVCToaans :l :X7UT -TSPOT ACCZL. niZ -JAMI TOa 250. .•AVtKllW ^J >i :;ipnT -imput sencxal tttlz Toa ciAra* .•« :<• :;fPOT -TSPtTT LEOEKD TITLE FOa 1ST CCaVTUS 55 l.VPOT -IXTDT IZCDm TITLt .Tia aD CVZTf UJ :7 rimjT •IXPUT CAI^BBATlOll VALUE ivrtff !3 I.TPUT -INPUT TABLE FOa 1ST JAVETOaa' . nj !? ISTCTT •'..IPCTT TAiLE ?oa ZSD JAVETjan* HS " INPUT -lOTuT coaaEcnoii valui ?oa lst cnaviin 55 ispuT -TKPirr coanEcnoii value roa OD amf lai •0 Assici in TO nj '^^ io Assini an TO ns 50 ASSIGN ?P TO 703 lOO OUTTOT 'JP:'T5:SFl::Pi:30.;000,923O.SOOO-' 110 "JUTPUT ap:-sco.:ooo. -tJO.SSO;L:0 31JTPTJT iP: -POT. 430 ?0 20OO. ^iSO.lOOO, 6JO.0. S30.0 .«30 TO* .20 : UIPUT 1P:*?AO.O ?0 2000.3 PU* ^ :UlPUr 1P;'?I.2. J;TL1.3.3" 130 FOax-0 TO 2000 STEP 200 150 =UTPCT 1P:-?AJ..450:.rr:' 120 :r <-j rva ootput ip-'-tp-i .i »»..•.-• 130 :r x-o TMEii 210 130 :r xp:*c7.j. .L:LS-':i«i.3r — ^ S IJir^JJ'f-^'o^^-'-.-^^^iJTM .«c«3s«a™„. 280 oar--400 70 soo step 200 250 linPUT IP: '?A0, • : Y. 'rr: • :oo :r r-o them auTPrrrap: •:?.). • j3-l«*-t-" '•0 '' '''^ ^''°' °''"^"' !'<'•'•• i3;UVy».l0O; — :M 31CTTJT .!P:-?A1J30.,30 SI. 2 3 C?J •<.. 'a/SKI -00 MJTTOT ap--0I1.3 U'-rtS:-' '-° '"P^ aP:-PTisoo, .450 ?01600..;00 2000 200 ?D:fc -S^ l',--i^l°o]T, ^ •'""'OO-'OO.. 530. 1700. .5,0. 1700, .400 TO-0 :s^i^•;s^o^lS5S;l^:;;5^i•^^-::?a^;;^r^J^--oO >D< — SHO.Et— . Ai 'U.uvi -31 JUTTOT ap:.pni73o..,73 ?I) 1730.. .^3. 1740 .*} 17U) .71 1 7in ^•,. _ -39 ;UTTOT aP:-SI.i..IS;PAl730..,73LS73-*»•"«>•••". 1730. .*7J PO:0] UM :0<. IQI — liCETO — :05 lEM ;?n '' ^ "f:-?Uli00.430 ?D UOO. 330. 2000.330 TV 510 l UTPOT >P:-?Tn:00.S30 ?0 1300.330 TV •'.: J gTPUT ap-7171320. 450 ?B L320 330 ?US12 O UTPUT ap;-?ui4io.53o ?o mo 330 ?U" :12 :UT?UT ap:'?ui7ui,450 ?0 i;i0.230 70" :J: '-"^^ 1P:-PU1373.430 TO U73 330 TV' ... ;ur7UT 3P:-?U1100,;50 ?0 ;0OO 530 .^U',:' .'Uju "•?^ll0O..5O ?0 2000.-30 TU" iis ;^ Jp--'AU3o'!oo*tiAOT?°?^SITr^'7S?2.-5 ^f^ST"" '^ '=*" ==*»»" • 22 :JT?'.-T !P:".:tJSi.-.-I VELOCTTr :S OiaCTSD aUAT .TUJN Tai USE;;2 irrr.T 'p-puhij.ioo ?:> -jo ;oo .'u:" rXp"™ !'':'?-*1210.;00:U' LIS.-':; i-"^^-" ?P:-?'n:;3..oo ?o 1:90 .00 ."u" --'TTVT ?P-?M310,.00 L3'L;S •• :23 :\.-r:~ !P:-7.ai;!o.;oo;l3-sii -;••• ::' --"?'" -p-^Aisso :oo u-r.s;3'4i '•• ;; :-"r?'.T ;P-?ai30o. ioo ljTisfT'ai -.. :-. y.-rriT.-Tuno ;oo-:j-r.si9-oi — •-...T-.T !P-?Ai;;o -00:L3* TTSd 'I •• '':fl^~ ?'''^1 = 50 -20:L3— Sc'si'.. ;•I'-TTVT -P: -?.M3C0, -00:L3' — Sr7 31 '-• :-= ::-:?•;P-?.M920.-00:12TTSI9 loi — ;;. ;_'--J'-~ :P-:i:o ;aoo ,s.3.i3.o• •--TTia ?n,.-{nor3i..A(»> -13 :'JT?VT :p-"T--0 ILTPUT 3P:-?A0 yj» '-1 r-v—l '•• ."^S 1-i TO 400 '-''' :.2:^'^f '"' ""•<»«)->(nor.l.)2 , ;.i; -l"'Jv-"^''"°*" ''"''""^"ll'100OO0O:Y-/y:-?5" -1 :VT?-.T ip-p-j" T? -00 t:;e.v 3(.-i — .jo,^ r»»i _3.j -?ff:-.<.„j,.>,:;„^.,, . '^" -"°'^'i'"."-l -IICCCCO

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306 10 Sa — PSIOCSIAM TO PLOT OISPUICEMEKT VAVtrOiUtS OM. HP 'aTO* PIDTTER — :: 3D( — THIS ?ROC!UU< OOUBLE IXTJCRATES ACCn.EIATlbs VAVEFOBMS ^ :0 3n — FESRUARY 1997 — ;0 321 .0 31.1 AiCOiS) ,rtS(50| .3(2048) ;0 INPUT -INPUT ACCEL. FILE 'lAHE rOR IST JAVtrORn. nS 51 :mput -input accel. file name for :nd. javeformvfis 5] INPUT -input OEMESAL TITLE FOR CRAPH" , rc$ 54 INPUT -INPUT LECEHD TITLE FOR 1ST CJSVE' . US 55 INPUT -I.'IPUT LECEHD TITLE FOR STB CURVEVUS 57 INPUT INPUT CALIBRATION VUJII:.Tlli Sa INPUT -INPUT TAiU FOR 1ST JAVETORIl' , Tl 5 59 LNPUT -INPUT TAiLE FOR 2NI) JAVEFORII" , I2S 64 INPUT -IKPUT CORRECTIOM VAUrt FOR 1ST CURVR-.Xn 65 INPUT -INPUT CORRECTIOK 7ALIJI FOR ISO CURVE,Xll2 "0 ASSIGN an TO FIS 30 «sicN irz TO rz% 90 ASSIGN ip TO 705 100 OUTPUT 3P:-IN:SP1.IP1350, 2000, 9250.4000:110 OUTPUT iP:-SCO,:000, -650. 450:120 OUTPUT aP:-?U0.-4S0 ?D :000. -'»50 . 2000. 450.0. 450. , -450 ?U" 130 OUTFJT iP:-PA0.0 ?D 2000.0 TU140 OUTPUT iP:-SI-2.3:TU. 5.0130 FOR X-0 TO 2000 STEP 100 140 OUTPUT 3P:-?A-:X,-. -650:.-1000 TSfOI OUTPUT }P: -cp-s. -1: L»-:X»l. 5 ; " 210 NEXT X 260 OUTPUT ?P:-PM0O0. «50:CP-10.-2.5:LSTIHE (laCTDStCOKDS)270 OUTPUT 1P:-TU.5,0280 FOR Y— •.00 TO 600 STEP 200 290 OUTPUT aP:-?AO.-:Y.-YT:!0O IF Y-) THEM OUTPUT JP: -CP-3 . 25 : LB* :T: •• 110 IF fOO THEN OUTPUT (JP: -C75 . . 2S:L»' : ! OOOl:-' 320 :IEXT t !84 OUTPUT aP:-PA0.0 CP-6.0. -5:010. 1:LS DISPLACIXBrr (HO * 190 0UT7UT aP:-PA1250.450 SI. 2. .3 CP2.14-00 OUTPUT aP:-oii.o LS-:.''tS:--10 OUTPUT ap:-?ul600.-650 P01600.-200. 2000. -200 ?U-20 ;UTPUT aP:-?U1700.-iOO PO 1900.-600.1900. -550.1700. -350. 1700. -600 PO" -30 OUTPUT SP:-?ni730. -565 ?D 1870 . -SSS . 1870 .380 . 1730 180. 1730. • 565 PD* —0 OUTPUT aP:-pui700.-305 PO 1900. 305. 1900. -250. 1700. -250, 1700. . 305 PO* -SO 3E« -oO 3CM ^ SHOVIMC LOCATIOII OF TUT CACU ^ -61 3En -^ Ai -70 OUTPI.-T aP:-?U1800.-380 FO 1310. 390. 1810. -183 . 1800. 3S3. IIOO. 310 BT .71 OUTPUT aP:-SI.l. 15:?A17aO.-«10;LSDl-i6 3EM — A2 -88 OUTPUT }P:-PU1730.-.75 ?0 1730. —«3 . 1740. -^5. 1740. -475.1730. -475 PO* -39 OUTPUT aP:-SI.l. .15:PA17!0..«73:LaOJ• :03 3EM 504 3EM — LEOEMD ^ 505 3EM 509 OUTFJT ap:-pull00.650 PO 1100.350.2000.330 PO510 OUTPUT aP:-PU1300.650 ?D 1300.350 PUSH 3UTPUT aP:-PU1520.SSO ?0 1320.350 PU512 OUTPUT aP:-?U1610.650 ?D 1610.330 PU313 OUTPUT aP:-?ul74O.450 PD 1740.350 PU;1OUTPUT aP:-?U1875.=S0 ?0 1875.350 ?U:13 OLTPUT aP: -PUllOO 5S0 ?0 1000. 550 ?U:16 OUTPUT aP: -PUllOO -SO ?0 2000.-50 PU;:7 lUTP-.-T IP -SI.l. 15:.'A1130.650:C?2..l.!:ULLNE OESCRIPTIOM TEST SCALE STAMDOPT :-3 :UT?UT ap-?A1100.100;LSNOTt: POSITTTE OISPLACEMEBT IS OISECTED ABAT FROM THE SASI' :;: lUTPUT iP-'.T" ;:: :ut?ut iP:-?uiii5.soo ?o 1290. soo ?n;;;-.-T?UT aP:-7Al310. jOO:L3-:US:";;: iutput ;-p:-i.t4.6:Zi I'JTPUT ;P:-?U1115.-00 ?D 1290.-00 .'U:2" -JTFVT ;P: ?A1310. -00 UL2S . •;;3 ICTPUT ::P:-?A1550.;00:L3-:TlS;i.;i:-;:o ILTPUT ap:-?A1650.iOO:L3-:r.S(3.6i .• 131 rUTP'-T ;P-PAiaOO. 300.U' :T1S(~.3| ;•" ;32 lUTPUT aP:-?A1920.500:L3-:TlS(9.10I ;-• :33 OUTP-.T IP: "PAISSO . -00: LS-: T2S( I. 2] : •• :34

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REFERENCES Al-Hussaini, M.M.; Goodings, D.J.; Scofield, A.N.; Townsend, F.C., "Centrifuge Modeling of Coal Waste Embankments," ASCE Journal of the Geotechnical Engineering Division , Vol. 107, No. GT4, April, 1981, pp 481-499. Baird, G.T., Instrumentation for Centrifugal Testing , Task Report, E. H. Wang Civil Engineering Laboratory, Kirtland AFB, New Mexico, 1984. Baker, W.E.; Westine, P.S.; Dodge, F.T., Similarity Methods In Engineering Dynamics , Hayden Book Company, Rochelle Park, New Jersey, 1973. Bloomquist, D. , Centrifuge Modeling of Large Strain Consolidation Phenomena in Phosphatic Clay Retention Ponds , Ph.D. Dissertation, University of Florida, Gainesville, Florida, 1982. Bradley, D.M. , Centrifugal Scaling Laws For Ground Launch Cruise Missile Shelter , Master's Report, University of Florida, Gainesville, Florida, December, 1983. Bur, A.J.; Roth, B.C., "A Polymer Pressure Gage for Dynamic Pressure Measurements," Proceedings of the Second Symposium on the Interaction of Non-nuclear Munitions With Structures , Panama City Beach, Florida, April ISIS, 1985. Cady, W.G., Piezoelectricity; An Introduction to the Theory and Applications of Electromechanical Phenomena in Crystals , 2nd ed . , Vol. 1, McGraw-Hill Book Company, 1964. Chung, R.M.; Bur, A.J.; Holder, J. R. , "Laboratory Evaluation of an NBS Polymer Stress Gage," Proceedings of the Second Symposium on the Interaction of Non-nuclear Munitions with Structures , Panama City Beach, Florida, April 15-18, 1985. Craig, W.H., "Modeling Pile Installations in Centrifuge Experiments," Proceedings of the 11th International Conference on Soil Mechanics and Foundation Engineering , 307

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308 Vol. 2, San Francisco, 1985. Cunningham, C.H.; Townsend, F.C.; Fagundo, F.E., The Development Of Micro-concrete For Scale Model Testing Of Buried Structures , ESL-TR-85-49 , Air Force Engineering And Services Center, Tyndall Air Force Base, Florida, January, 1986. Denton, D.R.; Flathau, W.J., "Model Study of Dynamically Loaded Arch Structures," ASCE Journal Of Engineering Mechanics , Vol. 92, No. EM3, June, 1966, pp 17-32. Dove, R.C.; Adams, P.H., Experimental Stress Analysis and Motion Measurements , C.E. Merrill Books, Columbus, Ohio, 1964. Dragnich, R.G.; Calder, C.A.,"A Sandwich-transducer Technique for Measurement of Internal Dynamic Stress," Experimental Mechanics , May 1973, pp 199-203. D'Souza A.F.; Garg V.K., Advanced Dynamics; Modeling and Analysis , Prentice-Hall, Englewood Cliffs, N.J., 1984. Endevco General Catalog , Endevco Corporation, San Juan Capistrano, California, 1986. Endevco, TPlOl, Endevco Technical Paper 101 , Endevco Corporation, San Juan Capistrano, California, 1986. Fiodorov, I . S . ; Melnik, V.G.; Teitelbaum, A. I.; Sarrina, V.A.; Vogdeo, V.N.; Vutsel, V.I.; Schcherbina, V.I.; Yakoleva, T.G., "Centrifugal Tests of Embankment Dams and Dikes," Proceedings of the 11th International Conference on Soil Mechanics and Foundation Engineering , Vol. 2, San Francisco, 1985. FSIO Owners Manual, Operation of EBW Firing System, Model FS-10 , Reynolds Industries, Inc., San Ramon, California, 1981. Gill, J.J., Centrifugal Modeling Of A Subterranean Structure Subjected To Blast Loading , Master's Report, University of Florida, Gainesville, Florida, December, 1985. Gran, J.K.; Bruce, J.R. ; Colton, J. A., "Scale Modeling Of Buried Reinforced Concrete Structures Under Air-Blast Loading," ACI Special Publication SP 73-7 , 1973, pp 125-142. Gurtin, M.E., "The Effect of Accelerometer Low-Frequency Response on Transient Measurements," Experimental Mechanics , Vol. 18, No. 1, June, 1961, pp 206-208. Hetenyi, M.I., Handbook of Experimental Stress Analysis ,

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309 Wiley, New York, 1950. Holder, J.R.; Chung, R.M. ; Bur, A.J., "Field Evaluation of the Polymer Stress Gage," Proceedings of Second Symposium on the Interaction of Non-nuclear Munitions with Structures , Panama City Beach, Florida, April ISIS, 1985. Kantrowitz, P.; Kousourou, G.; Zucker, L. , Electronic Measurements , Prentice-Hall, Englewood Cliffs, N.J., 1979. Krauthammer, T. , "Shallow-Buried RC Box-Type Structures," ASCE Journal Of Structural Engineering , Vol. 110, No. 3, March, 1984, pp 637-651. Krawinker H. ; Moncarz, P.D., "Similitude Requirements for Dynamic Models," ACI Special Publication SP 73-1 , 197 3. Kulkarni, K.R.; Chandrasekaran , V.S.; King, G.J.W., "Centrifugal Model Studies on Laterally Loaded Pile Groups in Sand," Proceedings of the 11th International Conference on Soil Mechanics and Foundation Engineering , Vol. 2, San Francisco, 1985. Kutter, B.L.; O'Leary, L.M.; Thompson, P.Y., "Centrifugal Modeling of the Effect of Blast Loading on Tunnels," Proceedings of Second Symposium on the Interaction of Non-Nuclear Munitions with Structures , Panama City Beach, Florida, April 15-18, 1985. Langhaar, H.L., Dimensioal Analysis and Theory of Models , John Wiley and Sons, New York, 1951. Malmstadt, H.V.; Enke, C.G.; Crouch, S.R., Electronics and Instrumentation for Scientists , Ben jamin/Cummings Pub. Co., Reading, Mass., 1981. McVay, M.C.; Papadopoulos , P.C., "Long-Term Behavior of Buried Large-Span Culverts," ASCE Journal of Geotechnical Engineering , Vol. 112, No. 4, April, 1986, pp 424-442. Meeks, S.W.; Ting, R.Y., "Effects of Static and Dynamic Stress on the Piezoelectric and Dielectric Properties of PVF2," J. Acoust. Soc. Am. , Vol. 74, No. 6, Dec. 1983, pp 1681-1686. Meeks, S.W.; Ting, R.Y., "The Evaluation of PVF2 for Underground Shock-wave Sensor Application," J. Acoust. Soc. Am. , Vol. 75, No. 3, March, 1984, pp 1010-1012. Murphy, G., Similitude in Engineering , Ronald Press Co., New York, 1950.

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310 Nielsen, J. P., The Centrifugal Simulation Of Blast Parameters , ESL-TR-83-12 , Air Force Engineering And Services Center, Tyndall Air Force Base, Florida, December, 1983. Nye, J.F., Physical Properties of Crystals, Their Representation by Tensors and Matrices , Clarenden Press, Oxford, 1957. Pan, F. , "Analysis of Variation of Poisson's Ratio with Depth of Soil," Proceedings of the International Conference on Recent Advances In Geotechnical Earthquake Engineering a. Soil Dynamics , Vol. 1, St. Louis, April, 1981. Pan, F. , "The Relation Between Dynamic Elastic Parameters and Depth of Soil," Proceedings of Conference on Soil Dynamics a. Earthquake Engineering , Vol. 1, Southampton, U.K., July, 1982. Prevost, J.H.; Cury, B. ; Scott, R.F., "Offshore Gravity Structures: Centrifugal ^4odeling," ASCE Journal of the Geotechnical Engineering Division , Vol. 107, No. GT2, February, 1981, pp 125-141. Randolph, M.F.; Ah-Tech, C.Y.; Murray, R.T., "Centrifuge Study of Spill-Through Abutments," Proceedings of the 11th International Conference on Soil Mechanics and Foundation Engineering , Vol. 2, San Francisco, 1985. Riedel, J., "The Accurate Measurement of Shock Phenomena," Endevco Technical Paper 214 , Endevco Corporation, San Juan Capistrano, California, 1986. Sabnis, G.M.; White, R.N.; "A Gypsum Mortar For Small-Scale Models," ACI Journal , Vol. 64, No. 11, November, 1967, pp 767-774. Sabnis, G.M. ; Harris, H.G.; White, R.N.; Mirza, M.S., Structural Modeling and Experimental Techniques , Prentice-Hall, Englewood Cliffs, N.J., 1983. Schmidt, R.M.; Holsapple, K.A., "Theory and Experiments on Centrifuge Cratering," Journal of Geophysical Research , Vol. 85, No. Bl, January, 1980, pp 235-251. Tener, R.K., "The Application of Similitude to Protective Construction Research," Proceedings of the Symposium on Soil-Structure Interaction , Tucson, Arizona, September, 1964. THORN EMI notes. Information supplied by THORN EMI Central Research Laboratories , Dawley Road, Hayes, Middlesex, England, 1986.

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311 Williams, M. ; McFetridge, G., "Unbalanced-bridge Computational Techniques and Accuracy for Automated Multichannel Strain-measuring Systems," Experimental Techniques , April 1983, pp 32-37. Wong, F.S.; Weidlinger, P., "Design Of Underground Protective Structures," ASCE Journal Of Structural Engineering , Vol. 109, No. 8, August, 1983, pp 19721979. Young, D.F. ; Murphy, G., "Dynamic Similitude Of Underground Structures," ASCE Journal Of Engineering Mechanics , Vol. 90, No. EM3, June, 1964, pp 111-131.

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BIOGRAPHICAL SKETCH Habibollah Tabatabai was born January 10, 1959 in Mashhad, Iran. He studied at the Sharif University of Technology in Tehran, Iran, for two years. In January 1979, he transferred to the University of Florida. He obtained his bachelor's degree in civil engineering with honors from the University of Florida in May 1981. He also obtained his Master of Engineering degree form the University of Florida in August 1982. 312

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. et,oCJ Frank C. Townsend, Chairman Professor of Civil Engineering v^/* Clif|?brd 0. Hay/ Professor of Civil Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. /U^/^i^ Michael C. McfVay Assistant Professor Engineering of Civil I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. P \(7V>\' \(K. Mang Tiai Assistant^-'Prof essor of Civil Engineering

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. David G. Bl^LQmquJLSt Assistant Engineer of Civil Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Douglas ^. Smith Professor of Geology This dissertation was submitted to the Graduate Faculty of the College of Engineering and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. May, 1987 Dean, C6fl.lege of// Engineering Dean, Graduate School

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1"^ t)'