Title Page
 Table of Contents
 Similitude and modeling
 Testing equipment and specimen...
 Instrumentation and data acqui...
 Testing procedures
 Evaluation of test results
 Conclusions and recommendation...
 Biographical sketch

Title: Centrifugal modeling of underground structures subjected to blast loading /
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Permanent Link: http://ufdc.ufl.edu/UF00097401/00001
 Material Information
Title: Centrifugal modeling of underground structures subjected to blast loading /
Physical Description: Book
Language: English
Creator: Tabatabai, Habibollah, 1959-
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Copyright Date: 1987
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Statement of Responsibility: by Habibollah Tabatabai.
 Record Information
Bibliographic ID: UF00097401
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000973737
oclc - 17416937
notis - AEU9301


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Table of Contents
    Title Page
        Page i
        Page i-a
        Page ii
        Page iii
        Page iv
        Page v
    Table of Contents
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        Page 1
        Page 2
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    Similitude and modeling
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    Testing equipment and specimens
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    Instrumentation and data acquisition
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    Testing procedures
        Page 108
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        Page 114
        Page 115
    Evaluation of test results
        Page 116
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    Conclusions and recommendations
        Page 284
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    Biographical sketch
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Full Text







09917 ZS9O9 Z9ZL c


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



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.



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

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


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


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


4.1. Introduction ........................... 39
4.2. Instrumentation......................... 40
4.2.1. Electrical Resistance Strain
Gages ........................... 40 Strain Gage Measurements
in a Centrifuge........ 46 Electronic Circuits For
On-board Strain
Measurements........... 50 Calibration of Strain
Gage Bridges........... 50 Strain Gage Setup on
the Test Structure..... 55
4.2.2. Piezoelectric Shock Pressure
Transducers...................... 59 Introduction to
Piezoelectricity........ 59 Polyvinylidene Fluoride
(PVDF) .................. 61 PVDF Pressure
Transducer.............. 66 Electronic Circuits for
Transducers............. 70 Voltage Measurements.... 71 Charge Amplifiers....... 75 Shock Pressure
Measurements in a
Centrifuge .............. 78 Calibration of PVDF
Pressure Transducers.... 84 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


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


SYSTEM ....................................... 289


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

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



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



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,


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:

Z = 1/3 Equation 2.1

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



-&-- --- --

-^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


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










(Bradley, 1983)

- Soil Modulus

- Soil Cohesion

- Preconsolidation


- Gravity

- Time

- Soil Angle of Friction

- Steel Strain

- Soil Strain

- Concrete Strain

- Steel Poison's Ratio

- Concrete Poisson's Ratio

- Steel Modulus








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)

1 E

'10 H

i= -

a H p
Tr3 =
3 E
n4 -

Tr5 =--7T3--
5 H3 E
6 H

0c C 2c
iT - _ _

8 =



0c C2

12 -


T13 =
T14 =
T15 -

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


Table 2.3

Scaling Relationships (Bradley, 1983)






Explosive Pressure

Explosive Energy



Material Density

Material Modulus

Material Strength

Material Wave Speed





Dynamic Time

Poisson's Ratio

Soil Cohesion

Soil Preconsolidation



Acceleration of Gravity




















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- =
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


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
(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


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


2.3 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


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

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


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

If the force causing the dynamic response is applied on the

system through gravity alone, then

= g

where g is the acceleration of gravity. Therefore the term

in Equation 2.7 can be rewritten in the following form

g t2
TT -

Equating r terms for model and prototype

TT = 7T
In p
gmn m gp pt

1 1


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

2 = l 2
t m 2p
n n P

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

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 = IT
m p
m p
VL 'g vL /g
/ m gm p/' p

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


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






= (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


(c) Spring-Mass System

Figure 2.2. Gravity Effects on Dynamic Time


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


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

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


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)


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


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






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)


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.



,,",,. ", ",. ,DIRECTION C






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.




Figure 3.6. General Shape of the Structural Model



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.


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:

F = --3- Equation 4.1

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


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


R I1 = R 12 and R II1 R2 2

Figure 4.1. Basic Wheatstone Bridge

Thus, for a balanced bridge,

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,

S= 6R Equation 4.4
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,

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 ,

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

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,

6V = V.
0 4R + 25R
g g

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

Substituting equation 4.1 in the above equation,

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

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. 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







z L14






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. 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


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. 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

< D
-0 <

- 0

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

strain can be calculated as follows:

F V.

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


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


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

C 0 0 0 0 0 0 0 0 0
M -500 -159 -158 -162 -162 -160 -160 -158
R -689 -215 -216 -215 -217 -220 -219 -216
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 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








Figure 4.6. Strain Gage Locations on the Structural Model




**:: *. 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


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


C + C,
S=1 Equation 4.7
a 2


S= C Ea Equation 4.9


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

x 4J

II a



w 2

. . :. :. . .
0 l: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). 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. 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


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,


P = do Equation 4.10

where d is the piezoelectric coefficient. In general for a

/ Surface


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



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


P = d31 a + d32 + d33 a

P3 = (d31 + d32 + d33j)


P3 dh o

where dh is the hydrostatic piezoelectric coefficient.


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


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


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


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


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:


0/ <


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. 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. 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



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

V =
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


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






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 =
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
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 ~


(2L WsO.SE FO & *20

hA0111 ACMaLL rm. OF KA.t



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

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




- - - - - - - - -

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). 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


0U 0
0- Z > 0 -

LU 0 :

O <








Z 2



> o

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

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

U, -C


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

0 to

*~ 0


- - - - - - L L L

\ i
- I I



z Z! Z ~
a L.- -I 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


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


K =-- Equation 4.15

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



/A h



Figure 4.16. Test Specimen for Calibrating Pressure Gages


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


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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