Title: Finite element modeling of Florida soil with the PENCEL Pressuremeter
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Title: Finite element modeling of Florida soil with the PENCEL Pressuremeter
Physical Description: Book
Language: English
Creator: Anderson, Jeremy Brian, 1973-
Publisher: University of Florida
Place of Publication: Gainesville Fla
Gainesville, Fla
Publication Date: 2001
Copyright Date: 2001
 Subjects
Subject: Civil and Coastal Engineering thesis, Ph. D   ( lcsh )
Dissertations, Academic -- Civil and Coastal Engineering -- UF   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )
 Notes
Summary: ABSTRACT: For many years, numerical codes that use the Finite Element Method were restricted to research. Advances in computing power have now enabled these codes to move out of the laboratory and into the hands of geotechnical engineers. Behavior of soil is implemented in these codes by way of constitutive models. These models were typically derived based on theoretical soil mechanics or fitted empirically to a soil test with known boundary conditions. In order to fit these models to a specific soil in question, a set of soil parameters must be passed into the code. In the simplest case, a linear elastic model could be used where the only parameters needed are modulus and Poisson's ratio. In many cases, such a simple representation is not sufficient. Instead of a constant stiffness, the stiffness may change with changes in stress. Strains may include elastic and plastic contributions. Failure or yield surfaces may be implemented to describe soil strength, and other limits. The purpose of this study was to take a critical look at the PENCEL Pressuremeter as a means for developing finite element constitutive model input parameters. The first part of the research looked at eight PENCEL Pressuremeter tests performed where natural sands were sampled for laboratory testing. Triaxial tests on these sands were used to develop baseline input parameters. These parameters were verified by simulating the triaxial tests using two finite element codes. An examination of the PENCEL Pressuremeter field curves yielded no correlation with the triaxial parameters.
Summary: ABSTRACT (cont.): An attempt was then made to "signal match" the triaxial input parameters to match the pressuremeter test. This best match yielded a factor omega by which the triaxial stiffness is multiplied to match the pressuremeter test, where omega is a function of the PENCEL limit pressure. These findings were used to predict the deformations of a cantilevered sheet pile wall. PENCEL Pressuremeter tests were conducted before the wall was installed. Deflections of the wall were measured during excavation. Soil parameters derived from the PENCEL Pressuremeter and the cone penetration test were used in the finite element code to determine the deflections of the wall with depth.
Thesis: Thesis (Ph. D.)--University of Florida, 2001.
Bibliography: Includes bibliographical references (p. 165-167).
System Details: System requirements: World Wide Web browser and PDF reader.
System Details: Mode of access: World Wide Web.
Statement of Responsibility: by Jeremy Brian Anderson.
General Note: Title from first page of PDF file.
General Note: Document formatted into pages; contains viii, 168 p.; also contains graphics.
General Note: Vita.
 Record Information
Bibliographic ID: UF00100778
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: oclc - 49877824
alephbibnum - 002728640
notis - ANK6402

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FINITE ELEMENT MODELING OF FLORIDA SOIL WITH THE PENCEL
PRESSUREMETER




















By

JEREMY BRIAN ANDERSON


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


2001



























To My Father and My Daughter















ACKNOWLEDGMENTS


First I would like to acknowledge my committee members Drs. F. C. Townsend,

D. Bloomquist, J. L. Davidson, M. C. McVay, B. Birgisson, and S. L. Detweiler.

Dr. Townsend's drive to bring the world of cutting-edge research into the grasp of

practicing engineers working in the real world has brought us to this point together. I

respect and admire him as an engineer, teacher, and person. He is not only my committee

chair; Dr. Townsend is my friend.

Dr. Bloomquist taught me how to think outside of the box and that geotechnical

engineering is not always about soil.

I will always be grateful to my friend Paulo Pinto. I enjoyed his company and

that of his family. I respect his wisdom as a teacher and engineer and feel fortunate to

have worked with him at the University of Florida.

I would like to acknowledge Mike Garau, Brian Hathaway and Danny Brown for

their generosity and willingness to always lend a helping hand. I will always cherish the

Breakfast and Lunch Clubs.

I would like to acknowledge my father for his support throughout my educational

career. He never let me settle for good enough and always encouraged me to push harder

and excel. I feel fortunate to still have him in my life.

Finally, I would like to recognize my wife Elizabeth. Her willingness to sacrifice

many things for my lifelong goal will always be remembered.
















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ................................................................................................. iii

A B STRA CT .............. .......................................................................................... vii

CHAPTERS

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

B a c k g ro u n d ........................................................................................................ 1
P problem Statem ent .............. ......... . ... ............................................ ..................... 3
O bje ctiv e s ........................................................... ........ ...... 3
Scope of W ork .................. ............................................................... 3

2 LITER A TU R E R EV IEW ................................................................. ....................... 4

H history of the Pressurem eter .................. ................................................. ........... 4
Previous Work with Full-Displacement Pressuremeters ............................................... 7
P av em ent P ressu rem eter ......................................................... ............................... 7
G e n e ra l ....................................................................................................... 1 0
A p p a ra tu s ..................................................................................................... 1 0
T e st ........................................................................................................................ 1 3
R research ............... ....... ......... ............................... ......... 13
Robertson and Hughes Full Displacement Pressuremeter ...................................... 14
G e n e ra l ....................................................................................................... 1 4
A p p a ra tu s ..................................................................................................... 1 4
T e st ........................................................................................................................ 1 6
R e se a rc h ............................................................................. 1 6
Fugro Prototype Pressuremeters ..................................................................... 23
G e n e ra l ...................................................................................................... 2 3
A p p a ratu s ..................................................................................................... 2 3
T e st ........................................................................................................................ 2 4
R e se a rc h ....................................................................................... 2 4
Finite Element Software .......................................... 30
P la x is ......................................................................................................................... 3 0
P la sF E M ......................................................................................... 3 5





iv









3 T H E O R Y ................................................................................................................. 3 8

S tress an d In v arian ts ......................... .. ........................ ............... ........ ................. .. 3 8
M ohr's C ircles and Stress Paths .................................... .......................................... 39
Invariants for N um erical M odeling ........................................ ...................... 45
P rin cip al store ss ....................................................................... 4 7
Principal deviatoric stress ....................... .............................. ............ .............. 48
U se of the invariants of stress ........................................................................ ... 52
Constitutive M odels for Cohesionless Soil ................................................. ............. 53
P la x is ............... ................................................................................... . . ........... ..... 5 3
M ohr-C oulom b .... ........................ ........ .............................. .............. 54
Hardening soil ....................................................................... .... ......... ................... 55
PlasFEM......................................... 57
Drucker-Prager............................................ 58
Sandler-Dimaggio ................................. ........................... .......... 59
Sensitivity A naly sis ................................................................... 6 1
P laxis param eters ..................................................... .............. 6 1
P lasF E M param eters ....................................................................... 62

4 LABORATORY AND FIELD TESTING ................ .....................................64

T testing E quipm ent ..................................................... 64
Triaxial Test Equipment .. ........... .................. .............. 64
F field T est E quipm ent ....................................................................... 66
PENCEL Pressurem eter.................................... ......... .. 66
University of Florida electric cone truck ................................................... 71
T e st S ite s ................. .... .. .... ...... .. .. ........................................ .............. 7 1
Florida State Road 20 Site Swift/Sanders Creek .................................. ......... .. 72
University of Florida Southwest Recreation Center Site ............. ....................... 77
A lachua C county Landfill................................ ............ ...................... .................. 85

5 FINITE ELEMENT SIMULATIONS ....................................... ... ............... 94

T riax ial T ests .. ..... ........................................... ........ .. .......... ............ .. 94
PEN CEL Pressurem eter ............................................................. .. .............. 107
Discussion of the PENCEL Pressuremeter ................. ................ ................... 107
FEM Modeling of the PENCEL Pressuremeter............................. 108

6 MOFFITT CANCER CENTER SHEET-PILE WALL PREDICTION ......................118

Geotechnical Exploration at Moffitt Cancer Center .................................................. 118
Sheet Piling at M offitt Cancer Center.......................... ............... .............. 132

7 C O N C L U SIO N ......................................................... ............... ........ ............... 138

S u m m ary ...................................... ........................... ..................................... 13 8
C on clu sion s ............................................................................................ 13 8









D isc u ssio n ........................................................................................ 1 3 9
R ecom m endations.................... .. ...................................... .............. ...... 140
Contributions................................... .............. 141

APPENDIX: ADDITIONAL INSITU TEST DATA......................................................144

L IST O F R E F E R E N C E S ........................................................................ .................... 165

BIOGRAPHICAL SKETCH .............................................................. ............... 168















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

FINITE ELEMENT MODELING OF FLORIDA SOIL WITH THE PENCEL
PRESSUREMETER

By

Jeremy Brian Anderson

May 2001


Chairman: F. C. Townsend
Major Department: Civil Engineering

For many years, numerical codes that use the Finite Element Method were

restricted to research. Advances in computing power have now enabled these codes to

move out of the laboratory and into the hands of geotechnical engineers. Behavior of soil

is implemented in these codes by way of constitutive models. These models were

typically derived based on theoretical soil mechanics or fitted empirically to a soil test

with known boundary conditions. In order to fit these models to a specific soil in

question, a set of soil parameters must be passed into the code.

In the simplest case, a linear elastic model could be used where the only

parameters needed are modulus and Poisson's ratio. In many cases, such a simple

representation is not sufficient. Instead of a constant stiffness, the stiffness may change

with changes in stress. Strains may include elastic and plastic contributions. Failure or

yield surfaces may be implemented to describe soil strength, and other limits.









The purpose of this study was to take a critical look at the PENCEL

Pressuremeter as a means for developing finite element constitutive model input

parameters. The first part of the research looked at eight PENCEL Pressuremeter tests

performed where natural sands were sampled for laboratory testing. Triaxial tests on

these sands were used to develop baseline input parameters. These parameters were

verified by simulating the triaxial tests using two finite element codes.

An examination of the PENCEL Pressuremeter field curves yielded no correlation

with the triaxial parameters. An attempt was then made to "signal match" the triaxial

input parameters to match the pressuremeter test. This best match yielded a factor Q by

which the triaxial stiffness is multiplied to match the pressuremeter test, where Q is a

function of the PENCEL limit pressure.

These findings were used to predict the deformations of a cantilevered sheet pile

wall. PENCEL Pressuremeter tests were conducted before the wall was installed.

Deflections of the wall were measured during excavation. Soil parameters derived from

the PENCEL Pressuremeter and the cone penetration test were used in the finite element

code to determine the deflections of the wall with depth.














CHAPTER 1
INTRODUCTION


Background

The age-old dilemma for geotechnical engineers is, "What are the properties of

the soil?" Engineering properties we are mainly concerned about are the strength,

compressibility, and permeability. Sometimes, we go out and carefully collect

undisturbed samples of soil by way of Shelby tubes or piston samplers. Then, samples

are brought into a soils lab where they are classified by grain size and Atterberg Limits

and often separated into several laboratory specimens for the traditional triaxial or direct

shear, permeability, and consolidation tests. These tests were developed at the

universities where soil mechanics was born, MIT or Harvard, due to the problems with

clayey soils in the New England area of the United States. Traditional geotechnical

engineering courses present these tests as the methods for determination of soil

properties, and therefore most engineers are calibrated to these results.

Now, consider regions such as North Carolina's Coastal Plain or Florida. The soil

profile in both places consists primarily of sand, with a rather high water table. In this

case, the method of collecting field specimens for lab testing is not applicable. These

submerged sands are difficult, if not impossible, to sample, and even if collected likely

will not be stable enough to properly trim and place into a testing apparatus. Therefore,

the properties of the soils must be determined insitu.

For testing soil insitu, we often rely on a test that involves hammering a 2.5-inch









diameter steel pipe into the ground with a 140 lb hammer to determine a myriad of soil

properties. The only result of the test is the number of hammer strikes it takes to

penetrate the tube 1 foot into the ground. This is called the Standard Penetration Test

(SPT) and the resulting number is widely referred to as the "blowcount" or "N value."

Most soil data gathered in the State of Florida is in the form of SPT borings.

Traditionally geotechnical engineers were restricted to limiting equilibrium

theories to solve geotechnical problems. Deformations were only considered for

settlement analyses. Enter into the picture the Finite Element Method (FEM). Now that

computing power has evolved, the FEM has been implemented into computer programs

whereby we can attack deformation-based geotechnical problems. In these programs,

constitutive models represent the behavior of soil. Soil is by nature heterogeneous and

nonlinear, and fails when subjected to shearing. In addition, the movement, or lack of

movement, of water through soil necessarily alters its response to loading. In an attempt

to model this complex behavior, many constitutive models have been developed. These

models range in complexity from those that define the failure characteristics of the soil

(limiting equilibrium), to deformation models that attempt to define strength, hardening,

and plasticity.

Some of these models are calibrated to our traditional geotechnical tests and thus

are defined by familiar soil properties. This is convenient and it allows us to easily

implement a program of testing to determine the input parameters if we can test the soil

in the lab. Yet, other models are adopted from other disciplines and often have esoteric

input parameters. Even when these models have been calibrated to soil, they are

calibrated by modeling traditional laboratory tests. Now, when an engineer from Florida









wishes to use an FEM program with one of these constitutive models, he or she often

only has a "blowcount" and a description by which to define a constitutive model.


Problem Statement

From the above discussion, there are two primary issues. First, the classical tests

by which most constitutive models are calibrated often are not performed during

geotechnical investigations on soils in Florida. Second, the method that is used, the

Standard Penetration Test, provides little information for the engineer who wishes to

extrapolate a constitutive relationship. The PENCEL Pressuremeter, which is pushed as a

cone penetrometer, then inflated like a traditional pressuremeter, may provide vastly

more information about the soil by way of a moderately simple insitu stress and strain

test of the soil.


Objectives

The primary objective of this research is to develop a relationship between or

some methodology by which to determine constitutive model parameters from the

PENCEL Pressuremeter test for implementation in finite element codes.


Scope of Work

The following tasks are included in the scope of this project:

1) Literature search and theoretical development
2) Field and laboratory testing
a. Florida state road 20 at Swift/Sanders Creek
b. University of Florida Southwest Recreation Center
c. Alachua County Landfill-Archer
3) Finite element modeling
a. Plaxis
b. PlasFEM
4) Prediction of sheet pile wall deformation at the University of South Florida Moffitt
Cancer Center based on findings from Tasks 2 and 3.















CHAPTER 2
LITERATURE REVIEW

This section consists of two parts. First, the history of the pressuremeter is

examined, with a focus on previous research and development of full displacement

probes. The latter portion of this section introduces the finite element codes utilized in

this research.


History of the Pressuremeter

K6gler, a German, developed the first pressuremeter and used it to determine soil

properties somewhere around 1930. His pressuremeter was a single cell, long, and

hollow device, which he inflated with gas. The results of this early pressuremeter were

often difficult to interpret, and its development was hampered by technological

difficulties (Baguelin et al., 1978). Figure 2.1 shows K6gler's pressuremeter.











100
mm -









Figure 2.1 K6gler's sausage-shaped pressuremeter (Baguelin et al., 1978, reprinted,
with permission, copyright Trans Tech Publications)

4









While working as a density inspector for a new airport runway near Paris, Louis

Menard pondered why he was measuring the density of the soil rather than the strength

and deformation properties. As an answer to his dilemma, Menard developed the modern

soil pressuremeter in 1954 working on his university final year project. This apparatus

was a tri-cell design with two gas-filled guard cells and a central water-filled measuring

cell. Menard continued his work under Peck at the University of Illinois for his Masters

degree, "An Apparatus for Measuring the Strength of Soils in Place." By 1957, Menard

had opened the Center d'Etudes Menard where he produced pressuremeters for practicing

engineers. Figure 2.2 shows a modem Menard Pressuremeter marketed by Roctest, Inc.





















Figure 2.2 A modem version of the Menard Pressuremeter (http://www.roctest.com/
roctelemac/product/product/g-am menard.html)



Although the pressuremeter seemed a radical departure from traditional

geotechnical tests, there were inherent problems with the device. Many believed that the

stresses induced or reduced by drilling the borehole were significant. These stresses were

further complicated by the general quality of drilling. If the hole were too large, the









pressuremeter would possibly not inflate enough to develop a full pressuremeter curve.

On the other hand, if the hole was too small, the insertion of the probe would disturb the

borehole and therefore diminish the quality of the test data.

In an attempt to rectify these drilling issues, engineers at the Saint Brieuc

Laboratory of the Ponts et Chaussees (LPC) in France developed the first self-boring

pressuremeter. As the name implies, this pressuremeter inserts itself into the borehole as

the borehole is being drilled. The premise behind the new device was to prevent

movement of the borehole wall after drilling, and therefore prevent any changes in stress.

A similar device was developed at Cambridge and is sold by Cambridge Insitu called the

Camkometer (Figure 2.3). Data from this pressuremeter proved to be radically different

than that of the Menard. While the self-boring pressuremeter may have seemed to be the

panacea to PMT problems, it suffered from more of its own. These new probes were

extremely complex and required a great deal of experience and maintenance to operate.























Figure 2.3 Self-boring pressuremeter sold by Cambridge Insitu (http://www
.cambridge-insitu. com/csbp leaflet2.htm)









Also to address the problems with drilled pressuremeters, Reid et al. (1982) and

Fyffe et al. (1985) developed a push-in type of pressuremeter. Shown in Figure 2.4, this

new probe was developed primarily for use in the characterization of soils for offshore

drilling structures. This new pressuremeter is hollow much like a Shelby tube. Soil is

displaced into the probe during pushing, thus eliminating the cutting system.

Unfortunately, the probe has to be extracted after every test to clean out the displaced

soil.

A more recent development in pressuremeter technology is the full displacement

or cone pressuremeter. This probe is pushed, as a cone penetration test, and then inflated

as a traditional pressuremeter. This method eliminates the problems associated with

drilling and the complexity of the self-boring equipment. Full displacement probes have

been researched at the University of British Columbia, the University of Ottawa, and

Oxford University. A commercially available full displacement type of pressuremeter is

shown in Figure 2.5.


Previous Work with Full-Displacement Pressuremeters

As mentioned in the introduction, the full displacement type pressuremeter was

the focus of this research. There have been three significant studies into this type of

pressuremeter since the late 1970s.

Pavement Pressuremeter

The first group to develop such a probe was Briaud and Shields (1979). Their

pressuremeter was developed primarily for the pavement industry to test the granular

base and subbase layers and cohesive and granular subgrades. Transport Canada funded

research into alternative methods of determining stiffness of pavement systems for airport

runways. Current practice of the time included nondestructive tests such as

























CHINESI LANTERN









BASE TUBI









STEEL SLEIVIE











LANTERN CLAMP


IL SUPPY LIE


CUTTING SHOE











- MIMMAN[ CLAMP










- MEMBRANE










MEMBRANE CLAMP


Figure 2.4 The push-in pressuremeter (Reid et al., 1982, reprinted, with permission,
copyright Editions Technip)







































Figure 2.5 A full displacement pressuremeter (http://www.cambridge-insitu.com
/specs/ Instruments/CPM.html)


~cc









Benkelman beam, dynaflect, and impulse tests that provided a "bulk" stiffness for the

entire pavement system, rather than specific layers. Other tests were destructive in

nature, (including CBR and plate bearing) were expensive, and often required significant

patching. Lab tests that, were destructive in nature, suffered the typical lab problems of

sample disturbance, small scale, and cost.

General

The pavement pressuremeter was developed as a rugged, inexpensive, portable

apparatus for the direct evaluation of the deformation characteristics of the pavement and

subgrade layers. A traditional Menard type of probe could not be used in the case of

pavement design. The magnitude of the loads and depths of influence due to traffic

loading are very different to that of a shallow foundation. Since the depth of influence

was much smaller, a cone penetration test tip sized monocellular probe with a singular

hydraulic tubing used. The shortened length of the probe facilitated a reasonable amount

of measurements within the relatively shallow zone of influence. Strain control was

chosen to allow for better definition of the elastic portion of the curve since stiffness is

the important measurement. Additionally, strain control also simplified the equipment

and facilitated cyclic testing.

Apparatus

The pavement pressuremeter works by way of a hand-wheel pump that forces

water through the tubing to the probe. The pressure in the water increases as the

membrane is pushed into the soil. Pressure is read on a gauge while the volume change is

monitored by the displacement of a column of red kerosene in a graduated tube. After

the probe is fully inflated, reversing the direction of the hand-wheel easily deflates it.










The probe consists of three parts. The first part, the body, is a 500 mm (19.7 in)

long and 25 mm (0.98 in) diameter pipe threaded at both ends. It has grooves for 0-

Rings at both ends to facilitate sealing of the membrane and two holes to allow water to

pass through the pipe wall during inflation.

The membrane is a rubber tube, 430 mm (16.9 in) long. This portion of the probe

expands when filled with water and is in essence the measuring cell. A Chinese Lantern

of metal strips is glued to the outside to protect the membrane. Strips included, the

membrane has an outside diameter of 31 mm (1.22 in). A sheathed membrane should last

for 100 to 200 tests. Figure 2.6 shows a schematic of the probe.




QUICK CONNECTOR
DRIVING POINT PROBE-EW ROD
CONNECTOR
QUICK RELEASE VALVE 23 CM r 6 MM TUBING
RING EW RODS




3.25 CM -



-RING/ / HOLE FOR INJECTED WATER
CONICAL SLEEVE / \ METAL TUBE (BODY)

RUBBER SLEEVE RUBBER MEMBRANE
METAL STRIPS


Figure 2.6 The pavement pressuremeter probe (Briaud and Shields, 1979, reprinted,
with permission, copyright ASTM)


To restrict the movement of the membrane on the body and seal the system so that

no air enters the membrane, rubber sleeves and conical metal sleeves are forced over the

membrane at the ends of the body. Two metal nuts are screwed on until the length of the

membrane between the sleeves is 230 mm (9.1 in).










A control unit, shown schematically in Figure 2.7, provides pressurization for the

pavement pressuremeter. Pressure is applied to a column of water using a hand pump.

The pressure in the system is displayed on a pressure gauge. Two Plexiglas tubes and

three Plexiglas containers hold the fluid pumped into the probe, and the volume change is

read by graduations on the Plexiglas tubes. The control unit is contained in a plywood

box with dimensions 1200 mm x 600 mm x 300 mm (47.2 in x 23.6 in x 11.8 in). The

probe, tubing, rods, and other accessories are also stored in the box. The box weighs 50

kg (112 lb).

CONTAINER 2
CONTAINER 1 CONTAINER 3




KEROSENE

/


PRESSURE
GAUGE GRADUATED
(KPA) RULER
(CM3)


VOLUMETER
0 3000 / TUBE 1

AJE



HAND PUMP ---- -- VOLUMETER
TUBE 2

F



VALVE F
FLEXIBLE TUBING
TO THE PROBE

Figure 2.7 The pavement pressuremeter control unit (Briaud and Shields, 1979,
reprinted, with permission, copyright ASTM)









Test

To test a pavement and its subgrade with a pavement pressuremeter, first a hole is

drilled though the pavement to a depth of 2000 mm (78.7 in). The probe is inserted

through the 35 mm (1.38 in) hole and tests are performed every 300 mm (11.8 in)

Preparation of the hole takes on the order of 2 to 10 minutes while each test (inflation of

the membrane) takes around 6 to 7 minutes. A single hole could be logged with 6 tests in

about one hour.

Research

The literature only contains two cases where the pavement pressuremeter was

used in research. The first case (Briaud and Shields, 198 la) investigates whether there is

a critical depth for measuring stiffness by the pressuremeter similar to the critical depth

for the development of pile capacity in sand. Briaud and Shields performed 66 tests in

prepared sand and 38 tests in natural clay. Triaxial tests were performed on specimens of

similarly prepared sands as well as Shelby tube specimens of the clay. Vane shear tests

were also performed in the natural clay layer. The increase in stiffness of the sand with

depth as measured by the pavement pressuremeter was attributed to that due to increase

in horizontal stress with depth. In clay, the variation in pressuremeter modulus coincided

with the variation in vane shear strengths with depth. The authors conclude that the

proximity of the ground surface had little to no effect on the small strain deformation

around the probe. As a corollary, the assumption of small strain is valid; therefore, the

same mathematical technique can be used to obtain stiffness from a shallow test as from a

deep test.

The second research study (Briaud and Shields, 1981b) performed with the

pavement pressuremeter was more along the lines of pavement evaluation. The primary









findings were that the pavement pressuremeter tests compare well with McLeod plate

load tests.

Robertson and Hughes Full Displacement Pressuremeter

General

The second study into the full displacement pressuremeter was conducted at the

University of British Columbia (Hughes and Robertson, 1985). As mentioned earlier, the

pressuremeter had already been the subject of much research. Standard practices were

developed for the Menard probe to account for the difficulty of hole preparation. Design

rules were established for use of pressuremeter parameters much like design rules based

on standard penetration tests in the United States. The self-boring pressuremeter was

developed to overcome the installation problems of the Menard probe, but brought along

an entire new set of problems including the complexity of equipment as well as the total

cost. It was proposed if a pressuremeter probe was pushed into the ground before

inflation, that a quantifiable amount of soil disturbance would occur. This disturbance

would be operator independent, since pushing would be identical to the well established

CPT procedure, as well as repeatable.

Apparatus

Instead of developing a new tool, an existing tool was modified for the job. The

full-displacement pressuremeter used during this study was a 76 mm diameter (45.4 cm2

area) self-boring pressuremeter with the cutting shoe removed and a solid 600 cone tip

fitted in place of the cutting shoe. Lateral deformations were measured electronically

with feeler gauges. The center of the pressuremeter membrane was located about 380

mm (14.9 in) behind the cone. A diagram of the full displacement pressuremeter is

shown in Figure 2.8.










Signal Wires
to Surface


Casing Suppor


Air (Pressurized)


Electrical Signal
Conditioners
Pressure Transducer-


Displacement


Flexible Membrane


Solid Cone Tip


Figure 2.8 The full displacement pressuremeter (Hughes and Robertson, 1985,
reprinted, with permission, copyright NRC Research Press)









Test

Because no method for this test was established, the published procedure is

merely summarized. For these full-displacement pressuremeter tests, the tool was pushed

to depth using the UBC research vehicle, which has a 200 kN pushing capacity. The

pressuremeter was pushed at the standard 2 cm/s rate used in cone penetration testing.

The pushing force on the rods and probe was monitored with a load cell. Tests were

performed by expanding the membrane with small increments of gas pressure. The

displacement of the membrane at the feeler gauges was logged continuously.

Research

Robertson proposes that in contrast to the self-boring and push-in pressuremeters,

a full displacement probe would cause a quantifiable amount of disturbance that could be

considered analytically. Thus, the boundary conditions would be much better defined or

well known unlike the predrilled and self boring pressuremeters.

Since a full displacement pressuremeter is much like a CPT when inserted, this

study starts with the considerations of the stress condition around a cone penetrometer.

Hughes and Robertson conclude that the ratio of the lateral sleeve stress to the tip stress

of a penetrometer pushed into sand at, for this example, a depth of 6m, to be 1:70 or

somewhere close to a two orders of magnitude difference. As the tip passes the element,

the ratio of stresses decreases rapidly. When the element of soil is adjacent to the friction

sleeve, the lateral stresses are most likely similar to the insitu lateral stress. This

phenomenon is shown in Figure 2.9. For loose to medium sands, the average lateral

stress at the friction sleeve is very close to the insitu horizontal stress, but for dense sands

at shallow depths, the lateral stresses are higher than the initial horizontal stress.











Advancing Cone McDonald's Form Site
Depth 6m



.--Calculated average lateral stress
on sleeve 90kPa
Friction
Sleeve



Cone Tip '
.- Measured overage
radial stress on
tip 6500kPa

U



0 20 40 60 80
Radial Stress as a Ratio
of the Effective Vertical Stress


Figure 2.9 Zone of high lateral stress around a pushed cone penetrometer (Hughes
and Robertson, 1985, reprinted, with permission, copyright NRC Research
Press)



The penetrated sand has already experienced a complex stress path. Robertson

and Hughes have idealized this stress path in Figure 2.10. With the starting point A

representing the insitu state of stress, the stress path immediately moves toward the

failure surface upon the approach of the cone. During penetration of the cone, the stress

path moves along the failure surface until the tip begins to move past the point in

question. At some point, C, the stresses will begin to diminish and likely reach the

opposite failure surface, then finally settling back to something close to the original state

of stress, but now there is a stress history. Points located some distance from the probe

will, obviously, not feel the same magnitude of stress as those closer. But it is not likely

that their final stress state will be the same as the points on the boundary. There is likely






18




Conslant Rote
o0f P ntrotion



I
I ee
C **
80 --C I
SUltimate b
yield surface


0 -
60-




0 40

o cr



30 /



IE
30-


b >0 2 D



0 E




0 10 20 30 40 50 60
Circumferential Stress (0cr)
as a Ratio of the Effective Vertical Stress


Figure 2.10 Proposed stress path followed by soil adjacent to a cone penetration test
(Hughes and Robertson, 1985, reprinted, with permission, copyright NRC
Research Press)









a zone of high residual stress some distance from the probe probably due to arching

effects. Figure 2.11 shows the level of radial and circumferential (hoop) stresses when

point C is at the cone and point E is somewhere past the cone, most likely in the position

of the friction sleeve. The stresses at point E have reduced, but a residual zone exists at

some radius from the probe.

Since the full displacement pressuremeter membrane is often a short distance

behind the cone tip, the stress distribution around the pressuremeter will not be uniform

and would vary with radial distance from the probe. Additionally, the failure surface may

have shifted inwards due to the enormous (1:70) stress reduction and the fact that the soil

has failed.

Depending on the radial distance of a soil element from the pressuremeter

membrane, the initial stress could fall anywhere on the curve AE'E in the lower part of

Figure 10. Loading from any of these points would begin as linear elastic until the stress

path reaches the first yield surface. Then the loading will continue non-linearly until the

failure condition is reached. Due to the high stresses already experienced by the soil, the

yield and failure surfaces could be very high. Figure 2.12 shows an idealization of the

pressuremeter curve that results from a full-displacement test and the non-linear elastic

yielding nature of sand as the stress path passes through progressive yield surfaces.

To put it all together, the stress paths for an element of soil adjacent to the

membrane of a traditional Menard pressuremeter, a self-boring pressuremeter, and a full

displacement pressuremeter are shown together on the left-hand side of Figure 2.13. The

corresponding pressuremeter expansion curves are shown on the right-hand side of the

figure. The primary difference among the figures is the initial stresses induced by the

























E t Rodius



E




C
t-

E "--Zone of hgqh
3 residual stresses


Notes :
Stress distribution about cone sleeve
Maximum stress distribution
about cone tip

Figure 2.11 Stress field around a pushed cone penetration tip (Hughes and Robertson,
1985, reprinted, with permission, copyright NRC Research Press)


method by which the pressuremeter was advanced to depth. In the case of the prebored

probe, some amount of unloading occurs, but to what extent? Is it repeatable? With both

the self-boring and full displacement probes, the amount of displacement is known and

repeatable, thus the initial condition is better known. Regardless of the method, the

unload-reload cycle should be similar for all tests.

The last part of this study included a small field program to compare/contrast the

full displacement pressuremeter with its self-boring equivalent. With respect to the lift















r a


-- Pressurrem le
element

2ro


Kcr M
I6


'. F
Possible locus -- --
of stress slotes with radius E' r r
I /E


Figure 2.12


I /ar=a L (r:ro) r ,
/ -Yield surfoce
o ai oss cioted ith point e

I 2 3 4 5 6
Circumferential Stress, c ,
os o Ratio of the Effective Vertical Stress

Stress path followed by a full displacement pressuremeter test after
pushing (Hughes and Robertson 1985, reprinted, with permission,
copyright NRC Research Press)


off pressures, although there was a good deal of scatter from both pressuremeters, the

results seem to center somewhere around the assumed initial horizontal stress. Friction

angles estimated based on the self-boring tests were reasonable. Application of the same

method to determine friction angle in with the full displacement were incorrect, likely

due to the very different stress paths the soil experiences before each test is run. And











() Prebored Pressuremeter Test
(M nard)


Strain, E


(b) Self- Boring Pressuremeter
Test


Strain. E
S(c) Full -Displacement
Pressuremeter Tesi


Strain, e

--- Stress Path during Installation
Stress Path during Pressure Expansion Test


Figure 2.13


Comparative stress paths followed by each of the pressuremeter methods
(Hughes and Robertson 1985, reprinted, with permission, copyright NRC
Research Press)


Foilure line









finally, as expected, shear moduli based on unload/reload loops from both were very

similar.

Fugro Prototype Pressuremeters

General

By far the most investigated full displacement pressuremeters have been those

produced in conjunction with Fugro. Work with this family of probes was conducted in

house at Fugro, University of British Columbia, and at Oxford University. The first

description of the cone pressuremeter appeared in work by Withers et al. (1986). The

impetus for the development of this pressuremeter was primarily offshore testing.

Pressuremeters on the market at the time were not suitable for all soil types and strengths.

In addition, the tools were not robust enough to be used in such extreme conditions and

often times needed precoring due to high embedment forces. As with the other probes

discussed, the benefit of this tool would be an accurate measure of shear modulus without

the unpredictable effects of stress relaxation and operator dependency. With that in

mind, Fugro set out to develop a commercial grade full displacement pressuremeter.

Since this pressuremeter was intended for use with CPT equipment, it was thus called the

cone pressuremeter.

Apparatus

The cone pressuremeter was constructed to the same diameter as a standard 15

cm2 ( 2.33 in2) cone penetrometer. The volume measurement system included a Chinese

lantern, internal membrane, and feeler gauges for measuring deformation changes. The

membrane length is 450 mm (17.9 in) and the distance between the center of the

membrane and the cone is 930 mm (36.6in). Circumferential strain is measured at the

midpoint of the membrane at 3 locations 1200 apart. The maximum probe pressure is 10









MPa (1450 psi) and the radial strain capacity is 50%. The prototype probe is inflated

with nitrogen gas, with the production offshore model to be inflated with oil. Behind the

pressuremeter is a module that amplifies the pressuremeter signals. CPT signals pass

through on separate connections. Figure 2.14 shows the prototype Fugro cone

pressuremeter.

Test

Little detail was given as to the method of testing followed for the cone

pressuremeter. Like the pavement pressuremeter, the cone pressuremeter test is strain

controlled. Since this tool is used in conjunction with a traditional CPT, the probe is

pushed to depth using a standard CPT rig. Tests are performed by inflating the

monocellular probe with high pressure gas at carefully strain controlled intervals.

Research

The first study of the prototype Fugro cone pressuremeter was conducted between

the University of British Columbia and Fugro Holland (Withers et al., 1989). Twenty-

five tests were performed at the McDonalds farm site as well as an additional six at

Fugro's test site in Leidschendam, Holland. Being the first examination of the new

pressuremeter, the authors went to great analytical length to use the test results to predict

the friction angle or undrained strength. It was necessary to quantify the states of stress

induced by the pressuremeter, so the authors presented a revised view of the stress path of

soil around the pressuremeter probe. The stress paths and stress concentrations around a

pushed and inflated probe are shown in Figure 2.15. Cylindrical and spherical cavity

expansion and contraction models were attempted, but most over predicted the strength.

On the other hand, as with the previously discussed probes, they found that the shear

modulus compared very well with self-boring pressuremeter tests in the same place.











CONTRACTION
RING




CHINESE LANTERN


MEMBRANE
CLAMP RING


MEMBRANE


ARM COVER
SLEEVE


STRAIN GAJGED
SPRING


3 STRAIN SENSING
ARMS AT
1200 SPACING -.


INSTRUMENT BODY


MEMBRANE


MEMBRANE
CLAMP RING


CHINESE LANTERN -





CONTRACTION
RING
CONNECTION TO
CONE SPACER AND CONE


Figure 2.14


CONNECTION TO
AMPLIFIER SUB
















E
E
CN
C14


E
E






E
E
C4
















43.7 mm


Fugro cone pressuremeter (Withers, et al., 1986, reprinted, with
permission, copyright ASTM)
















(I) BEFORE
CONE PRESSURE IERF
PENETRATION




A R C ) DF 1 0


11I) AFTER
CONE PRESSUREMETER
-77.^ PENETRATION


ELASTIC

INTENSE SHEAR BAND
T 4--

t INTENSE SHEAR RAND


(IIl) AFTER
CONE PRESSUREMETER
EXPANSION


ELASTIC

S r l> r .R e > R o


(IV) AFTER
CONE PRESSUREMETER
/ ''- CONTRACTION


RRe ELASTIC
PLASTIC\ i.w
PIC
Ai
R /\\K^ j ''^!


L~4/


/


A.ho
/


HOOP STRESS Or ,--







PATH FOLLOWED BY A
B/



I/" LOCUS OF STRESSES



HOOP STRESS Oh-*




A
/
B /
PATH FOLLOWED BY A


S/


0 LOCUS OF STRESSES


HOOP STRESS (t.,


HOOP STRESS CT,--


Figure 2.15


Stress paths and stress concentrations during a cone pressuremeter test
(Withers et al., 1989, reprinted, courtesy of Thomas Telford Ltd, London)









The most recent, and perhaps most extensive, research with the cone

pressuremeter has been by Guy Houlsby and his students at Oxford University. For their

studies, Fugro constructed two additional smaller scale pressuremeters. One probe was a

10 cm2 (1.55 in2) version that included a volumetric measurement system in addition to

feeler gauges. The other tool was a 5 cm2 (0.775 in2) version. Due to size limitations,

deformations were only monitored volumetrically.

An early attempt to model the cone pressuremeter using FEM was done by

Houlsby and Yu (1990). The soil was represented by the Mohr-Coulomb constitutive

model with two-noded elements with nonlinear displacement functions to create a simple

cavity expansion mesh to create a right cylindrical model. Limit pressures calculated

agreed well with those measured during calibration chamber tests. A second method was

used to estimate friction angle using the plastic unloading slope. This yielded poor

results.

The research project at Oxford was primarily undertaken to calibrate the cone

pressuremeter much like the cone penetrometer and flat dilatometer were previously.

During the course of the study, it was determined that the size of the calibration chamber

had a significant effect on the results (Schnaid and Houlsby, 1991). Although there was

only one chamber (Figure 2.16) used in the experiment, there were visible trends in limit

pressure, stiffness, and inferred friction angle in relation to the ratio of chamber to probe

diameter. Size effects seem to become more prominent as soil density increases.

Knowing the limitations of the chamber, a program consisting of 34 cone

pressuremeter tests was performed in the calibration chamber (Schnaid and Houlsby,

1992). The 10cm2 probe was used as the primary testing tool with which 21 tests were

completed. There were an additional 5 tests with the 15cm2 tool and 8 with the 5cm2



























Cone pressuremeter


Air-water reservoir
(vertical pressure) Rubber membranes


Figure 2.16 Cone pressuremeter calibration chamber setup at Oxford (Schnaid and
Houlsby, 1992, reprinted, courtesy of Thomas Telford Ltd, London)










Since tests with the cone pressuremeter have shown that the cone resistance and limit

pressure depend primarily on the effective horizontal stress and not the vertical stress, the

testing program varied such parameters as the density, Ko, vertical and horizontal stress.

Analysis of the calibration chamber tests showed almost unique correlations

between qc and Ch' and yf and Ch'. In light of these findings, the authors define a term

called the cone resistance-limit pressure ratio.


Cone resistance-limit pressure ratio = (- h)
(Fv-^ h')

where qc is tip resistance, y1 is the limit pressure, and Ch is, of course, the horizontal

effective stress. Based on this ratio, the friction angle and relative density can be

estimated.


S= 1.45 (q + 26.5



R = 9.0(q a 30
(VI ah')

This is shown graphically in Figure 2.17.

16r 18
0 10 cm2 device
14- 10 cm2 device N 5 cm2 device
5 cm2 device
14- M
12- 0





6-
a% 6U- o
6-o
6 0
4-

S 20 40 60 80 100 30 34 38 42 46 50
R,: % O'p: degrees


Figure 2.17 Relative density and friction angle based on calibration chamber tests
(Schnaid and Houlsby, 1992, reprinted, courtesy of Thomas Telford Ltd,
London)









The last portion of the published research concerned the interpretation of shear

moduli (Houlsby and Schnaid, 1994). Unload-reload loops from the calibration tests

were analyzed. One of the primary findings was that there was no appreciable difference

in the use of feeler gauge measurements or volumetric measurements when calculating

the shear modulus. Furthermore, it was discovered that calculating the modulus using the

two external points of a loop, the apexes, systematically produced a higher value for

modulus than performing a least squares regression of all points in the loop.

Houlsby and Schnaid (1994) used a method proposed by Fahey and Jewel (1990)

for calibration of the Fugro pressuremeter shear modulus for system compliance. The

membrane stiffness correction is carried out as before. On the other hand, the volume

loss correction is applied differently. Instead of just inflating the probe in a steel pipe and

noting the volume, unload-reload loops were performed at ascending increments of cell

pressure. These loops were used to derive the unload-reload shear modulus for the

system. The shear modulus of the soil could then be estimated by first correcting the raw

curve for membrane stiffness and hydrostatic pressure only. Then, the unload-reload

shear modulus is calculated at the desired point on the curve. Next, the unload-reload

shear modulus of the system is calculated. Finally, the unload-reload shear modulus of

the soil can be determined using this equation:

1 1 1
Gcorrected Gmeasured Gsystem


Finite Element Software

Plaxis

Two finite element codes were used in the course of this research. The first code,

Plaxis, was chosen due to its commercial availability and ease of use. Development of









Plaxis began in 1987 at the Technological University of Delft (Plaxis, 1998). Initially,

the code was developed to analyze river embankments over soft soils of Dutch lowlands.

With further development, Plaxis has been extended for use in most geotechnical

problems. Version 7.2 is capable of modeling static plane strain or two-dimensional

axisymmetric problems using 6 or 15 node triangular soil elements. In addition, special

elements are available for modeling tunnels, beams, anchors, geotextiles, and soil-

structure interfaces. Plaxis utilizes several constitutive models for soils including linear

elastic, Mohr-Coulomb, soft soil (clay), and hardening soil (hyperbolic sand).

The true advantage to using Plaxis lies in its user friendliness. The input pre-

processor and output post-processor are completely functional. Inputting the problem

geometry is done easily with cad-like drawing tools. Material properties and boundary

conditions are easily assigned using dialogue boxes and a simple mouse click or drag and

drop. Figure 2.18 shows the Plaxis pre-processor window.

Once the geometry, material properties, and boundary conditions are set, the next

step is mesh generation. Choosing the mesh generation tool in Plaxis will fill each of the

delineated polygon areas of the model with triangular finite elements. The elements will

be placed in the mesh such that nodal points will correspond with cluster interfaces,

boundary conditions, and external loads. It is also possible to degrade the entire mesh or

refine the mesh around individual features such as nodes, lines, or clusters of elements.

An example showing a complex mesh of finite elements is shown in Figure 2.19.

After the mesh generation is complete, the next step in the problem is to define

initial conditions. Plaxis has implemented a module that allows for the specification of

initial pore pressure and flow conditions, staged construction steps, and initial linear

















J/JA-WJ JJ .I / ,1 --I I -,I.


W +4--4


-I .... .,I . .. ... I F


Figure 2.18


View of Plaxis input interface


4 i s7.Oupt- ii ML


pu ., !-li --I'.


tI ;


-i -

..-44.[I


- I~


rt tf r __ M = t n Er


L or.r.. ...,
I ,, -


Figure 2.19 Plaxis automatic mesh generation


', L -


I I

II -


I11P I I


S ha I72 Input I I E cs 1. I I hM I -


i . . I .


I II









elastic stress calculations. Again, all of the options are easily input with dialogue boxes

and mouse clicks.

The main engine portion of the code is referred to as Plaxis Calculations. This

module allows the user to set up multiple chronological loading, excavation, or

consolidation events. If the problem is a simple loading, then the user would simply

enter the load multiplier and the program would automatically step the load up to

calculate the deformations. For fill/excavation problems, the loading events can be edited

graphically by again clicking on and/or off clusters of elements. There is a time interval

input for use in consolidation analyses. Finally, the user is encouraged by the engine to

select a "watch point" that will be monitored during the calculation. The movement and

force at this point are monitored so the user can get visual feedback on the progress of the

analysis. Figure 2.20 shows the main engine window with time stepping and load

multipliers.

The output of a Plaxis analysis can be viewed with one of two output post-

processors. The first is called Plaxis Output. This program reads the output stresses and

deformations from the analysis and plots the results over the original mesh for a single

loading event. The data can be plotted as contours, shadings, or vectors. Plaxis Output

also has scaling, zooming, and printing capabilities. An example plot of vector

displacements can be seen in Figure 2.21.

The second post-processor is called Plaxis Curves. This program allows for the

plotting of monitored variables through the entire analysis. For example, one might

choose the toe point of a dam, or the top of a retaining wall. The movement of that point

can be plotted against the loading multiplier imposed on the model Pore pressure in a

consolidation model can be plotted against time for such a point. Additionally, stress























C i-.,-i .1.,-


P. .. IN

111 1- l O___ ^


I.. I


I .1 I,1



IIL-


S ... I I I r

4 ii i


Figure 2.20 Plaxis Calculation engine window


'2'JiJJ'L! ''


V


T..I,, dlulated.e .
I.=~r .. . I I j, II I i .i i 1ll


I1 I I


Figure 2.21 Plaxis Output example


[l-,- J,.I _,.- '_ .6i ,- "-9

LK~ HU I
n.& -nS _LM- 1^ -::; j *1


Pami 72 Ou-tpu,,t, [Em ,i,.se _


I I I









strain points can be chosen, and a plot of the stress and strain at that gauss point can be

plotted.

PlasFEM

PlasFEM (Pinto, 1998) was the second finite element code used in this research.

It is currently under development at the University of Florida by Dr. Michael McVay.

The program is well suited to handle most geotechnical problems and is capable of

dynamic analysis of dry or saturated soil in ID, 2D or 3D with elements ranging from

simple 2 node truss elements to 27 node bricks. Being primarily a research tool, the code

is extremely versatile. The user can impose very complex loading conditions, initial

stresses, and boundary conditions. Constitutive models available include: linear elastic,

Drucker-Prager, Sandler-Dimaggio, Cam Clay and Modified Cam Clay, viscoplasticity,

and a Mohr-Coulomb interface formulation.

Stresses and deformations can be visualized with the post-processor called

PlasPLOT. In a similar manner to Plaxis Output, the stresses and deformations data can

be represented by different levels of shading. The deformed mesh can also be plotted

with or without a magnification factor. As with Plaxis Output, the resulting plots can be

scaled, zoomed or printed. Figure 2.22 shows an example PlasPLOT session showing

four screens with unreformed mesh, vertical effective stress, pore pressures, and

deformed mesh.

A pre-processor for PlasFEM called PlasGEN is under development by the

University of Florida Geotechnical Numerical Group. Figure 2.23 shows a sample of the

current development version of PlasGEN. Features of this new module will include cad-

like geometry definition and an automatic mesh generator. Loading events will be

defined in the pre-processor, and material properties and boundary conditions will be























































Figure 2.22


PlasPLOT example output


M u ..l, - : I E III IIE I- I r I I I-
1 3-


1- -






U-

vl


a.Nb .. aMb


a a


Figure 2.23 An embankment model in the pre-release version of PlasGEN


. ....... - -
.-., Tk ... .. ..j












T i' .









*I -


IP..POT P1









37


specific to loading events, not global to the problem. Until PlasGEN's full capabilities

are realized, PlasFEM input files must be prepared by hand in ASCII format. Meshes can

easily be implemented on a spreadsheet, but small alterations of a complex problem often

require a complete remeshing.















CHAPTER 3
THEORY


Stress and Invariants

Finite element programs allow the user to determine stresses or deformations in a

soil continuum that is subject to events such as external loadings, prescribed

displacements, or cuts and fills. Therefore, the relationship between stress and strain is of

the utmost importance to the program. In the simplest case, it could be said that there is a

linear relationship between stress and strain. This is known as Hooke's Law.

oa =EE

This relationship is ideal, and may work for some materials, but soils do not often follow

this model. Soil is heterogeneous, exhibits non-linear stress strain behavior, has a

strength limit, and is sensitive to water moving through its pores. Therefore such a

simple representation is not sufficient.

With that in mind, many researchers have attempted to emulate the behavior of

soil by way of constitutive models. So, instead of the simple "E" in Hooke's Law, more

complex mathematical formulations have been developed. Now instead of a constant

stiffness, the stiffness may change as the sample is strained in shear or hydrostatically. In

order to track these changes and impose limits such as failure surfaces or yield surfaces, a

convenient representation for stresses is necessary. Two such idealizations are contained

in the following section. The first is the stress path method as adopted for soil mechanics

by Lambe (1969). A second method is by invariants of stress.









Mohr's Circles and Stress Paths

An element of any material can be idealized as an infinitesimally small cube. The

stresses on such an element can then be represented by a normal stress on each face and a

pair of perpendicular shear stresses on each face. This is shown in Figure 3.1.


I Tl1


T13


T12


T33


Figure 3.1 Stress on an element


This representation is sufficient if the stresses on the 90-degree cubical planes are

the only interest. Often times, the stresses of interest are not on these convenient planes.

It would be useful to have a mechanism where an array of stresses on this element could

be displayed.

Consider now a wedge of material, shown in Figure 3.2, with stresses on each


plane:

































Figure 3.2 Stress on a wedge of material


Assuming a unit area on the hypotenuse face, the force equilibrium can be written


o, sin a zcosa- o, sina = 0


(o cosa +, sina-(To cosa = 0


Then solve for the unknown stresses Ta and Ca in terms of the knowns cy and oy:


2 x 2y x -Cy
(o =( sin2 a + o cos2 a = + cos2a
Y e e)


T, = (Ox y)sina cosa


x O-y sin2a
2


If both equations are squared, then added together, the result is a circle with radius

(cx cy)/2 and center on the horizontal axis radius (xy + Oy)/2. When plotted with

normal stress, o, on the horizontal axis and shearing stress, c, on the vertical axis, it is


ax









known as Mohr's Circle of stress. This is the state of stress at a point in equilibrium.

Figure 3.3 shows an arbitrary plot of Mohr's Circle.












TG














Figure 3.3 Mohr's Circle of stress



Since ox and cy were acting on planes with no shear stress, they are by definition

principal stresses. In this example oy is the major principal stress and Cx is the minor

principal stress. A third principal stress exists called the intermediate principal stress,

but it is often neglected due to the typical assumption of two-dimensional behavior.

Figure 3.4 shows all three principal stresses.

Now that we know the state of stress, we would like to be able to apply a strength

criterion. Through his early work with retaining walls, Coulomb determined that the

shearing strength of soil was the sum of some internal strength and a function of the































Figure 3.4 Principal stresses



normal stress. This is expressed as:

Zff = c + tan4

where c is the internal strength of the material and 4 is an angle that defines the function

of strength with normal stress. This function is often superimposed onto Mohr's Circle

for soil, thus creating the Mohr-Coulomb failure criterion for soil, shown in Figure 3.5.

The Mohr-Coulomb failure criterion is very useful since we can typically estimate

or control the principal stresses so as to limit the amount of shearing stress induced. This

is best demonstrated in Figure 3.6, which is a standard triaxial test where the minor

principal stress is kept constant while increasing the major principal stress until the

material fails.

Notice how the state of stress changes in Figure 3.6. As the difference between

ol and c3 increases, the circle grows until it becomes tangent to the failure envelope. A






43










C











Figure 3.5 Mohr-Coulomb failure criterion


CYl




C73 CN3


Figure 3.6 Triaxial compression test










circle can be defined by the location of its center and its radius. So instead of plotting all

of the Mohr's Circles, we can plot the center and radius of the circle. This is called the

stress path. Figure 3.7 shows this schematically.












2.
":. ... ."." .



-..............


Figure 3.7 Triaxial compression test stress path in T-c space


A better representation of the stress path is in p-q space, where p is the center of

the circle and q is the radius of the circle. This can be expressed in equation form:

',a + (73 q 1 03
p=--- q=-
2 2

The envelope and interecept of the Mohr-Coulomb failure envelope must also be

converted into p-q space. The slope of the failure surface will be Y and the intercept will

be ac. This new failure envelope is called the Kf line. Converting from the Mohr-

Coulomb quantities we have:


sin = tan Vf


a
cosO


The stress path for a standard triaxial compression test is shown in Figure 3.8 as an

example.































Figure 3.8 Stress path for a standard triaxial compression test in p-q space


The concept of the stress path is useful for illustrating how stresses are changing

in an element of soil under multiple loading conditions. In all likelihood, the actual

loading history of a soil element will not be a simple triaxial type. Using a stress path to

visualize the loading history would better show which failure stress states and

mechanisms the engineer should be designing for.

Mohr's Circle represents the full state of stress on an element of soil. The Mohr-

Coulomb failure envelope defines the strength of a soil in terms of the state of stress,

independent of the plane where stresses are measured or known. Finally, the stress path

shows the progression of the state of stress during loading.

Invariants for Numerical Modeling

Advances in computing technology have made the application of the Finite

Element Method to geotechnical problems possible. Although the FEM was developed









many years ago, it has only become practical with the advent of PCs capable of

performing numerous calculations per second.

In a three dimensional finite element code the state of stress must be defined in

terms of three dimensions. The problem lies in the fact that carrying an entire Mohr's

Circle worth of information for each element of soil is computationally impractical.

Therefore, the state of stress needs to be reduced to a manageable set of numbers.

A method that is often employed is called invariants of stress. The convenience

of using this method is that the hydrostatic and deviatoric components of stress are

separated since soil behaviors can often be attributed to changes in these stresses

independently. In tensorial form, the stresses can be defined using the following

derivation.

Much of this development is contained in unpublished course notes of McVay

(1999). Figure 3.9 shows a cut plane through a cubic element. The resultant stress vector

T on any plane which has a unit normal n is

T, = Tln

In order to determine the principal stresses, we must find the unit normal, n, in

the direction of the principal axes. If we let X represent the principal stress, then the

stress vector acting along the normal to n has components kni. (note n, = 6 n ). The

same vector is also given by the expression Tinj. So if we equate the expressions, and

transpose to the same side, we obtain:

Tnj n1 = 0 or Tl n A ,nj = 0






47




^z, 1







T31T



A T232
T33 T23

T32 T13 py,3





T, T




x,2


Figure 3.9 Cut plane through an element with normal n


Collecting Terms:

(Tj, J,1)nJ =0

Principal stress

To determine the principal stresses, we need to take determinant of T11 .

T11 A T12 T13
DET T21 T22 A T23 0
T31 T32 T33 -









Expanding:

(T,, )(T22 T33 + T2T32T13 + T3T12T23

T3 (T22 )T31 T23T32 (T11 )- T21T12(T33- )= 0

Expanding:

TI1T22T33 TII1T22 11 TIIT33T 3- T22T33T + T12 + T22 2 + T33 2 3+ +T21T32T13
+ T31T12T23 T,3T3,T22 + AT13T31 T23T32TI + T23T32 T21T12T33 + AT12T21 = 0

Collecting Terms:

3 + 2 [T11 + T22 +T33 ]+ [- {T1T,22 +T22T3 + TT33}+ T232 + T212T12]

ST11T22T33 + T21T32T13 + T31T12T23 T31T22T13 T11T32T23 T21T12T33 = 0

The coefficients of the k terms become the invariants:

11 [ T, + T22 + T33

12 [-({TIT22 + T22T33 T1T33+T232 + T21 T122

13 = T1T,22T33 + T21T32T13 + T31T12T23 T31T22T13 T,1T32T23 T21T12T33

Ti T12 T13
or 13 =DETT21 T22 T23
T31 T32 T33

Resulting in the cubic equation:

3 + 12 + I2A + 13 = 0 or 3 12 I21 3 = 0

Principal deviatoric stress

As stated before, it will be useful to separate the stress into hydrostatic and

deviatoric components. Figures 3.10 and 3.11 show the new deviatoric and hydrostatic

stress tensors. And since the hydrostatic stress is constant on any plane, then the

principal planes of the stress tensor and the deviatoric stress tensor should align. Say that





























S22 121

Figure 3.10 Deviatoric stress tensor


S11 = T1i (T11 + T22 + T33)/3 = T11 P


T12



S32 T32



S31 T31


the hydrostatic component of stress is P = (T,, + T22 + T33)/3, then Sl = Tj -P. As

before, assume X is the principal deviatoric stress. Then take the determinant of the

deviatoric stress tensor:


T12
S22
T32


T13
T23 0
S33 -


Expanding:

(S )(S22 OXs33 -/)+ T21T32T13 +T31T12T23

T13(S22 -)T31 -T23T32(S,, -)- 21T12(S33 -)= 0


S33


T13




T23


9T


ZZ











P= (T11 + T22 + T33)/3


v ^


P= (T + T22 + T33)/3
P= (Tl + T22 + T33)/3


P= (T11 + T22 + T33)/3


Figure 3.11 Hydrostatic stress tensor



Expanding:

S11S22S33 SlS22A S11S331 S22S33 + 112 + S222 + S33 2 + + T21T32T13
+ 31T12T23 T13T31S22 + T13T31 T23T32S11 + ,T23T32 T21T12S33 + AT12T21 = 0

Collecting Terms:

-3 + [S11s + S22 +S33]+[- {S1S22 +S22S33 +S11S33 }+T232 +T212T122


+ S, S22S33 + T21T32T13 + T31T12T23 T31S22T13 S1T32T23 T21T12S33 = 0


As before, the coefficients of the k terms become the invariants of the deviatoric stress:

Ii' =[S11 +S22 +S33]


12'= [- {SS22 + S22S33 + S,,S33 }+ T232 + T212T122


Si1 T12 T13
3' =DET T21 S22 T23
T31 T32 S33


f
I

f
f
f


.....................................................
.................................. .. 7


,,e










But note that the first invariant of the deviatoric stress is zero by definition:



Since [S, + S22 + S33]= (T1 + T22 + T33)- 3(T1 + T22 +T33)/3 = 0

II' = 0



Also, simplify the second invariant:

Know: S SSi = S,1S,1 + S2S12 + S13813

Si S = S S11 + S21S21 + S31S31 + S12S12 + S22S22 + S23S23 + S13S13 + S23S23 + S33S33

SiS = Sl2 +S222 +S332 + 2T212 + 2T312 +2T232

And: S,1S =(S11 +S22 +S33)S11 +(S11 +S22 +S33)S22 +(S11 +S22 +S33)S33


S11S = S 2 +S 222 +S 332 +211S 22 +2S11S33 +S22 33

12' = SlSl S ,,S


But: SSjj = Il'2 = 0


So: I2'= (S jS

Similar to before, the resulting cubic equation is:

,3 I2'' I3' = 0



It should be noted that the same development holds true for the axisymmetric case. The

axisymmetric stresses on a radian-sized wedge are shown in Figure 3.12. The stress

tensor is similar except the off diagonal terms are zeros due to the plane strain condition.











Tz= Tll





STZR = T


TR = T33



Tz =T31

STe = T22



Figure 3.12 Axisymmetric stress tensor




Tz 0 TZR T,, O T13
Tl= 0 T 0 = 0 T, 0
TRZ 0 TR T31 0 T33

The invariants are calculated exactly as before in the three dimensional case.



Use of the invariants of stress

The invariant I1 will be used to define the hydrostatic portion of the stress and the

square root of the invariant 12'will be used to define the deviatoric portion of the stress.

It is often referred to as AJ2. When plotted in principal stress space, I1 will be the

hydrostatic axis. VJ2 will be perpendicular to the II axis. This is shown in Figure 3.13.

Yield and failure surfaces for constitutive models are often defined in terms of these

invariants. For example, the Drucker-Prager failure surface is a cone centered around the

































S 2

Figure 3.13 Invariants II and A2 in principal stress space


hydrostatic axis with apex zero. The Von-Mises surface is a cylinder and only depends

on the value of VJ2.


Constitutive Models for Cohesionless Soil

Although both of the finite element codes contain many constitutive models,

specific models are more appropriate for sandy soils. The following is a brief discussion

of the models that were used in this research.

Plaxis

Plaxis contains two constitutive models that are appropriate for cohesionless soils.









Mohr-Coulomb

By far the simplest and most familiar is the Mohr-Coulomb model (Plaxis, 1998).

This relationship is the same that is used in common everyday soil mechanics, just

expanded to three dimensions. Figure 3.14 shows the Mohr-Coulomb failure surface in

principal stress space.


2 2 -









--G





3

Figure 3.14 Mohr-Coulomb failure surface (Plaxis, 1998)



The failure surface, in this case, is directional, meaning that it depends on the type

of loading (i.e. triaxial compression, triaxial extension, etc.). The equations for the

failure surface are the following:

fi = i a2' as' + 2 (2' + 3')sin -ccos < 0

f2 = 2 03' + 2a3' + a/')sin -ccos < 0

f3 = 2 0l' C2 + (2s' + 2' )sin -ccos < 0

After the stresses exceed these limits, the material will yield in a perfectly plastic

manner as idealized in Figure 3.15.





















Figure 3.15 An elastic perfectly plastic stress strain curve



The basic parameters necessary to define the Mohr-Coulomb model are the following:

Failure Surface
S Friction Angle
c cohesion

Stiffness
E Young's Modulus
v Poisson's Ratio

Initial Stresses
p unit weight
ko ratio of initial horizontal stress / initial vertical stress


Hardening soil

Although it would seemingly be easy to assume that soil behaves as in the Mohr-

Coulomb model, sands are often more complex. A triaxial test on sand will likely not

appear as the elastic perfectly plastic curve in Figure 3.15. More likely, during shear, the

stiffness of the sand specimen will decrease. In order to emulate this behavior, the

hardening soil model has been implemented in Plaxis. The hardening soil (Plaxis, 1998)

model utilizes the same failure surface as the Mohr-Coulomb. A hyperbolic function

provides the relationship between the vertical strain and deviatoric stress. As with the









Mohr-Coulomb model, when the state of stress reaches the failure surface, perfectly

plastic strains occur.

In addition to the hyperbolic stress strain relationship, the hardening soil model

includes a hardening cap. When a cohesionless material is loaded in isotropic

compression, the material will likely not continually strain elastically as the Mohr-

Coulomb model would imply. In fact, plastic volumetric strains will occur. In order to

describe these strains, a hardening cap was formulated. Figures 3.16 and 3.17 show the

hardening soil model with its cap in both p-q and principal stress space.


q










elastic region



P
c cot(p p

Figure 3.16 Hardening soil model with cap in p-q space (Plaxis 1998)



The basic parameters for the hardening soil model are as follows:

Failure Surface remains the same as before:
S Friction Angle
c cohesion





















shear yield surface




shear yield surface



Figure 3.17 Hardening soil model with cap in principal stress space, (Plaxis 1998)



Hyperbolic Stiffness Parameters
Erf Secant stiffness in standard triaxial test at pref
Eref Tangent Stiffness for primary oedometer loading at pref
m Power for stress level dependency of stiffness
EU Unloading/reloading stiffness
Vur Poisson's Ratio for unloading-reloading
pre Reference Stress for stiffness
Rf Failure ratio
Tension Tension Cutoff

Initial Stresses as before
p unit weight
ko ratio of initial horizontal stress / initial vertical stress

PlasFEM

Similar to Plaxis, PlasFEM contains two constitutive models that can be used to


represent sand.









Drucker-Prager

The Drucker-Prager (1952) model is very similar to the Mohr-Coulomb model

employed by Plaxis. The stresses are limited by a simple two parameter failure surface.

Underneath, any strains are elastic. If the stresses reach the failure surface, shown in

Figure 3.18, any further strains will be perfectly plastic.


Figure 3.18


Drucker-Prager failure surface in invariant stress space (Pinto 1998)
Drucker-Prager failure surface in invariant stress space (Pinto 1998)


The Drucker-Prager failure surface is a cone centered around the hydrostatic axis

in invariant stress space. It can be expressed by the equation:

f = J2 -a 11 = 0


This relationship differs from the Mohr-Coulomb in that it is not dependent on the type of

loading. Figure 3.19 shows both models plotted in principal stress space oriented to the

7T plane.












Mohr
Coulomb

/ Drucker-
Prager






03 C2
Figure 3.19 Mohr-Coulomb and Drucker-Prager failure surfaces viewed in the nt plane

The parameters for the Drucker-Prager model are listed below:

Failure Surface
ca strength intercept (similar to cohesion)
0 strength parameter (similar to friction angle)

Stiffness Parameters:
E Young's Modulus
v Poisson's Ratio

Initial Stresses
p unit weight
Go initial vertical stress in elements
ko ratio of initial horizontal stress / initial vertical stress

Sandler-Dimaggio

Just as in Plaxis, PlasFEM includes a model for cohesionless materials that

includes a hardening cap. The Sandler-Dimaggio (1971) model contains a failure surface

that is an advanced curved version of the Drucker-Prager, as well as a hardening cap.

Unlike the hardening soil model, strains remain linear elastic until the stresses reach the

failure surface or yielding cap. Figure 3.20 shows the Sandler-Dimaggio constitutive

model.










Compressive
Comer Region


J2 \ Fe(I1) = -y e- p1 +061



Failure Surface


Sfl(a)= 2- Fe(Ill) 2 Ep)=(I1 -L)2 -(X L) +R2 =0
Elliptic Cap


Tensile E a
Comer Region Elastic

Tension Cutoff
f3(c)=T-li=0

Ii
T 0 Li X



Figure 3.20 Sandler-Dimaggio cap model (Pinto 1998)



The parameters necessary to defined the Sandler-Dimaggio model are the
following:

Failure Surface
ac strength intercept (similar to cohesion)
0 strength parameter (similar to friction angle)
y strength parameter (curvature)
P strength parameter (curvature)
T tension cutoff stress

Stiffness
E Initial Young's Modulus
v Poisson's Ratio

Hardening Cap
XO preconsolidation pressure
W cap parameter (ep max)
R cap parameter (ellipticity)









D cap parameter (hardening)

Initial Stresses
p unit weight
oo initial vertical stress in elements
ko ratio of initial horizontal stress initial vertical stress


Sensitivity Analysis

A sensitivity analysis was performed using the primary parameters for Plaxis

hardening soil and PlasFEM Sandler-Dimaggio. A single triaxial test, Archer Landfill

Tube 1 Specimen 2, was used as the control case for each. Each parameter was first

varied by -50%, -25%, -10%, -5%, +5%, +10%, +25%, and +50% of their given value.

Less sensitive parameters were given extra intervals of -10 and x 10. In some cases, a

reasonable range could be discerned for the variable through experience. Other variables

have been far less studied and no true range was known. Thus, the above variation was

used arbitrarily.

Since the simulation resulted in a set of numbers, triaxial test curve, rather than a

single value, it was not possible to look at a single figure to determine statistical

significance or variability. Instead, the results of the sensitivity analysis were examined

qualitatively.

Plaxis parameters

Since the hardening soil model contained the same basic parameters as the Mohr-

Coulomb, the sensitivity was examined for hardening soil only. The results are

summarized as follows:

S Natural range 25 to 450 for sand. Most sensitive parameter. Limited

maximum value of deviatoric stress. Small variations -5% resulted in









substantial differences.

E50 This value naturally varied by orders of magnitude. Plaxis parameter

checking will not allow for certain combinations of E50, Eoed and 4 to

occur, thus the arbitrary range was used. Small percentage variations had

little effect on the results while, variation in the -50% range had an

appreciable effect.

Eoed When varied in the arbitrary range, exhibited little effect on results. Low

sensitivity.

m This parameter is -0.5 for sands and 1.0 for clays. Variation of this

parameter had little effect.

V Natural range not very well established. In the case of this research was

found to be close to 1.50. Regardless, it is often very difficult to discern

and calculate. Caused little variation when varied between 1 and 8.

PlasFEM parameters

As with the Plaxis parameters, the Sandler-Dimaggio model contains the basic

parameters from the Drucker-Prager. The sensitivity was examined for the Sandler-

Dimaggio only.



O Similar to 4 from above, the simulation was very sensitive to small

changes in this parameter. When calculated based on a normal range of

4, 0 ranges from 0.189 to 0.356.

E Model was insensitive to small changes on E, but was sensitive to order of

magnitude changes.









[t Model was insensitive to changes in [t between 0 and 0.5.

XO Arbitrary variation affected the initial yielding of the model, but the results

varied little on the whole.

W Small changes reflected small changes in the total strain. Model was very

sensitive to order of magnitude changes.

R Small variations in R had little effect. Large percentage variations affected

strain amounts.

D Order of magnitude variations had a large effect on this parameter while

the model was less sensitive to small variations.














CHAPTER 4
LABORATORY AND FIELD TESTING

Parallel laboratory and field tests were conducted as the experimental phase of the

research. This chapter looks at the methods and equipment used in the tests as well as the

test locations and data from the tests.


Testing Equipment

Triaxial Test Equipment

A new triaxial testing system was assembled for this research. The system is

composed of a loading frame, pressure/volume control board, testing chamber, and data

acquisition. The control panel is a three independent burette system built by Trautwein

Soil Testing Equipment. The test cell, also manufactured by Trautwein, is a three piece

design with dual ports for the top and bottom of the sample. A Humboldt Triscan 50 load

frame was purchased for this testing. It is fully software controlled and features a LCD

and keypad interface. Instrumentation includes an Omegadyne Load Cell, an

Omegadyne Pore Pressure Transducer with internal amplifier, and a Macro Sensors linear

voltage displacement transducer. All of these devices are powered by Omega power

supplies.

The data acquisition system is based on a 16 channel DAQPadTM-MIO-16XE-50

made by National Instruments. The DAQPad is connected to a Pentium 233 PC through

a parallel port interface. Figure 4.1 shows the control panel and loading frame. A close-

up of the triaxial cell and the data acquisition computer are shown in Figure 4.2.
































Figure 4.1 Triaxial testing load frame and control board


Figure 4.2 Triaxial cell and data acquisition computer









Field specimens were collected in accordance with ASTM D1587. All of the

triaxial tests conducted for this research were consolidated and drained. ASTM D4767

was followed with provision for cohesionless free draining soil.

Field Test Equipment

Several insitu tests were conducted for this research. Although the primary focus

of this study was the PENCEL Pressuremeter, standard penetration tests, cone penetration

tests, and dilatometer tests were conducted at each of the sites as well. The following

discussion describes the PENCEL Pressuremeter and the penetration rig necessary to

advance it.

The standard penetration test and the cone penetration tests are covered by ASTM

standards D1586 and D3441, respectively. The dilatometer test currently has no accepted

ASTM standard, but the tests were performed in accordance with the proposed ASTM

standard suggested by Schmertmann (1986).

PENCEL pressuremeter

The testing device used in this study was the PENCEL model pressuremeter. This

is more or less the commercial version of the pavement pressuremeter developed by

Briaud and Shields (1979). Roctest, Inc. manufactures the unit in Canada and markets it

worldwide.

The control unit, shown in Figure 4.3, has been modernized. A volume calibrated

screw piston has replaced the graduated Plexiglas tube with kerosene. The unit is

lightweight and easily transportable. The monocellular tubing was carried on from the

original model. SwagelokTM quick connects are used to, theoretically, allow for the unit,

line, and probe to be presaturated in the lab and then disconnected for easy transport.





























Figure 4.3 The PENCEL Pressuremeter control unit


The probe has undergone a slight modification where, instead of O-rings, metal

protrusions now create the seal between the membrane and the body. Figure 4.4 shows

both an assembled probe with its drive point and friction reducer and a disassembled

probe with the retaining nuts and brass rings. An assembled PENCEL Pressuremeter

system is shown in Figure 4.5.


Figure 4.4 The PENCEL Pressuremeter probe














































Figure 4.5 The PENCEL Pressuremeter probe fully assembled



No ASTM standard exists for the PENCEL Pressuremeter test. Instead, the test

and calibration methods are based on the manual published by Briaud and Shields (1979).

Calibration of the system is conducted in three steps. First, the free air correction is

determined by inflating the probe in air, with no obstruction, at the same elevation as the

pressure gauge. The second calibration is the system compliance or volume loss

correction. The probe is inserted into a steel tube and inflated. Since there is an annular

space between the probe and the tube, some correction will need to be made to the


y.,

T I;


~i~Ei









compliance curve so that is can be used to correct the PENCEL volumes without over

correction. A third curve is generated by detaching the probe and injecting volume into

the control unit and tubing. The latter two corrections are combined to develop the

compliance correction. This construction is shown in Figure 4.6.

PRESSURE
(KPA)
KPA) CURVE B CURVE OF CURVE A
CONTROL UNIT VOLUMEONTROL NIT
2000 + TUBING LOSSES + TU ENG




I /
1500




1000 I




i I
A A /
500 f -I- E




D D
I /


0 2 4 6 8 10 15 20 25 30

VOLUME INJECTED (MM3 x 103)

Figure 4.6 System compliance correction for the PENCEL Pressuremeter (Briaud and
Shields, 1979, reprinted, with permission, copyright ASTM)



As with other pressuremeters, the parameters determined are the limit pressure

and pressuremeter modulus. The PENCEL limit pressure is defined as the pressure

required to double the probe volume, or more simply the maximum pressure during the

test. On the other hand, the modulus could come from many portions of the









pressuremeter curve. Due to probe insertion, the initial modulus, Ei, may not be that

reliable. Other portions of the PENCEL curve that could be used for calculating stiffness

are an unload-reload loop, if available, and the final unload portion of the test. These

moduli are referred to as EUR and EUL, respectively. Figure 4.7 shows these moduli and

the limit pressure on an arbitrary pressuremeter test.


Figure 4.7 PENCEL Pressuremeter curve with limit pressure and moduli denoted



Calculation of the PENCEL Pressuremeter modulus is identical to the Menard

method:


V +V f]f -P


where


[t is Poisson's Ratio

Vc is the initial volume of the pressuremeter

Vo and po are the first point on the linear portion of the pressuremeter curve









Vf and pf are the final points on the linear portion of the pressuremeter curve

University of Florida electric cone truck

All of the insitu tests performed by the University of Florida were done utilizing

the electric cone penetration testing vehicle, shown in Figure 4.8. As the name implies,

the primary use of this vehicle is for cone penetration testing. The truck was purchased

with matching funds from the National Science Foundation and the University of Florida

College of Engineering (Davidson and Bloomquist, 1986). Fortunately, other penetration

type testing devices have been adapted for use with this equipment including, for this

research, the PENCEL Pressuremeter. Other devices include the dilatometer, BAT

groundwater system and piston sampler.






















Figure 4.8 The University of Florida electric cone truck


Test Sites

Three research tests sites were established where field tests were performed and

laboratory samples were collected for analysis.









Florida State Road 20 Site Swift/Sanders Creek

The first specimen tested was collected at State Road 20 Swift/Sanders Creek near

Niceville, Florida. Maintenance problems helped establish this site as a research

location. Differential settlements were occurring around a heavily trafficked five-lane

bridge. Compressible soils on either side of the bridge were causing the approaches to

settle while the bridge maintained level. The FDOT district asked UF to look at the

problem, and then predict what future settlements would occur if different remedial

measures were taken.

FDOT characterized the site by three standard penetration tests and over 50 cone

penetration tests. Since the project was going to be modeled using a finite element

program, the UF Geotechnical Numerical Group desired some stiffness values for the soil

at the site, particularly layers that had not been tested in the lab (i.e. not Shelby tube

sampled).

The University of Florida provided support to FDOT to conduct PENCEL

Pressuremeter and dilatometer tests on the east (STA 381+00) and west (STA 380+25)

sides of the bridge at Swift/Sanders Creek. Of the collected data, a single pressuremeter

test overlapped with the Shelby tubes collected. A consolidated drained triaxial test was

performed on sand from Tube 7 at the Florida Department of Transportation State

Materials Office. Figure 4.9 shows the location of the field borings and soundings.

Stratigraphy based on standard penetration tests is shown in Figure 4.10. The corrected

PENCEL Pressuremeter curves from 5 depths are shown in Figures 4.11 and 4.12.

Finally a triaxial test is detailed in Figures 4.13 and 4.14. Additional insitu test data can

be found in the appendix.




























8-t
C-6 C-7 C-90 c--2


38 -00
C-31 C-1 C-s c-a c-v

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





SB-I


BEGIN BRIDGE
STA. 380*75


END BRIDGE
S7A. 81 -70


Figure 4.9 Plan view of soil exploration at State Road 20 Swift/Sanders Creek







74









10 -- ------------------------------- ---

2 ASPHALT & GROUT
23O_ ~ _PINKISH ifED SIL Y_ SAQ WZ/G.RiOT CQMPAC T (SM)_.
---- &
4 YELLOW SAND WITY SILT, LOOSE (SP-SM)
9
-6 -lo
3 | MUCK, SOFT (ML)
2 SHELBY TUBE I
2 SHELBY TUBE 2
-2 WOH -- SHELBY TUBE 3

3 MUCKSF SHELBY TUBE 5
3 MUCK, SOFT SHELBY TUBE 4
S30 --- ---- - --GWAYISR-WHITE-SICTY-SAND-W7WOOD, LO5EE -rSI-
3 :SHELBY TUBE 6
6e SHELBY TUBE 7
S-408 --4.- SHELBY- IUBEI .8_ _---9---_-----_- ----_---
SGRAY SILTY SAND, DENSE (SM)
38
36
J -50 _"--

57
-60- ---------34-
29
32 -
GRAY SILTY SAND, DENSE (SM)
39 =
30
-O,-

38
-90 -------- -- ------------------------
44 _= ,5-.,


39 GRAY SILTY SAND, DENSE (SM)
36



Figure 4.0 Standard penetration test boring B at State Road 20 SwiftSanders Creek----------------------------------

Figure 4.10 Standard penetration test boring Bl at State Road 20 Swift/Sanders Creek




























(L
-


I-



-











































Figure 4.12
I-




--


-*-10.5 ft















Volume (cm3)

PENCEL Pressuremeter tests at State Road 20 Swift/Sanders Creek at
depths 10.5-25 ft














S-*-35 ft
-U- 45 ft




0 20 100-- -1 1:10


-1




Volume (cm3)

PENCEL Pressuremeter tests at State Road 20 Swift/Sanders Creek at
depths 35-45 ft












70


60


S50


40


30
U,

0 20


10


0


0 2 4 6 8 10 12 14
Axial Strain (%)


Figure 4.13





60

h


U)
S40
U)
U)

U)

0

U)
Cz

0z


Figure 4.14


Consolidated drained triaxial test of tube 7 specimen 2 from State Road 20
Swift/Sanders Creek at depth 34 ft


20 40 60 80 100
Normal Stress (psi)


Mohr-Coulomb envelope for consolidated drained triaxial test of tube 7
specimen 2 from State Road 20 Swift/Sanders Creek at depth 34 ft









Soil parameters from the depth of Tube 7 are shown in Table 1.1. All of the

possible values for PENCEL Pressuremeter modulus are shown in Table 1.2.



Table 4.1 Summary of soil parameters from lab and insitu tests on State Road 20
Swift/Sanders Creek at the depth of tube 7
) E5o ) Ko E M Limit E
Tube Depth TRIAX TRIAX N qc CPT DMT DMT DMT DMT Pressure PMT
(ft.) (0) (psi) (blows) (psi) (0) (o) (-) (psi) (psi) (psi) (psi)

34.0 37.3 2300.0 6.0 486.4 32.0 36.0 0.61 2436.0 3422.0 72.2 3726.5





Table 4.2 Summary of possible PENCEL moduli from pressuremeter a tests at State
Road 20 Swift/Sanders Creek at the depth of tube 7
EUR MAX MIN MAX MIN
Ei apexes EUR Secant E UL Secant E UL Secant EUL Tangent EUL Tangent
Tube Depth PMT PMT PMT PMT PMT PMT PMT
(ft.) (psi) (psi) (psi) (psi) (psi) (psi) (psi)

34.0 556.1 2069.7 (--) 186528.0 1964.8 186528.0 1191.9




University of Florida Southwest Recreation Center Site

Five consolidated drained triaxial tests were conducted on material collected for

the Southwest Recreation Center site on the University of Florida Campus. Boring logs

were secured from the initial construction of (Universal Testing) and the current addition

to (Law/Gibb Engineering) the Southwest Recreation Center. After reviewing borings

from the site, and due to the existence of shallow sand layers, the site was chosen. Cone

penetration tests and a dilatometer test were conducted by the UF Geotechnical insitu

class. Universal Testing donated the time and labor for the collection of eight Shelby

tubes. Finally, two PENCEL Pressuremeter tests were conducted at the site as the

construction project began in the fall of 2000.









Due to time elapsed between the collection of Shelby tubes at this site and triaxial

tests, a complication arose. The moisture contained in the soil caused corrosion of the

tube walls thereby locking the soil inside. The specimens were often difficult to extract,

resulting in lost and disturbed samples. It should be duly noted that all of the specimens

from this site might suffer from preloading and disturbance. Therefore, after testing

material from the first three tubes, the remaining five tubes were abandoned. A total of

five consolidated drained triaxial tests were conducted on material from the three viable

tubes.

The locations of the standard penetration test borings are shown in Figure 4.15.

All of the tests were performed in the vicinity of B 12. The log of standard penetration

test B12 is shown in Figure 4.16. Corrected PENCEL Pressuremeter results are included

as Figures 4.17 through 4.19. Lastly, triaxial tests are shown in Figures 4.20 through

4.25. Additional insitu test data can be found in the appendix.
\\ ----?
Y-- \\ ---
Sa. I I r
SSOFA SOFTBALL
S L-J RELD IEL.D


BKET6L L. 7


4z*L xLLX--A

I5 A- R


Figure 4.15 Plan view of soil exploration at Southwest Recreation Center





















































Figure 4.16 Standard penetration test boring B 12 at Southwest Recreation Center





































Figure 4.17


Figure 4.18


2-

















0 0 20 40 60 80 100 1:


Volume (cm3)

PENCEL Pressuremeter tests at Southwest Recreation Center at depths 8-
16ft


-*- 22 ft
- 26 ft
-A-30 ft


Volume (cm3)

PENCEL Pressuremeter tests at Southwest Recreation Center at depths
22-30 ft


-- 8 ft
-- 12 ft
-A- 16 ft


14 /





8 -









20 1 20 40 60 80 100 1;





















-*-34 ft
-- 38 ft


-20 0 20 40 60 80
Volume (cm3)


Figure 4.19


14


12


=10


8


0 6


PENCEL Pressuremeter tests at Southwest Recreation Center at depths
34-38 ft


2 4 6 8 10
Axial Strain (%)


Figure 4.20


Consolidated drained triaxial test of tube 1
Center at depthl0-12 ft


from Southwest Recreation











12





8


Q.
(a


C 4
C)


0 4 8 12 16 20 24
Normal Stress (psi)


Figure 4.21 Mohr-Coulomb envelope for consolidated drained triaxial test from tube 1
at Southwest Recreation Center at depth 10-12 ft


--Specimen 1
- Specimen 2


Figure 4.22


2 4 6 8 10 12 14 16
Axial Strain (%)



Consolidated drained triaxial tests of tube 2 from Southwest Recreation
Center at depth 14-16 ft


50

45

40

35

S30
25

S20
20

S15

10

5

0

















S 30


0)

C)
15





0


( = 33.4


15 30 45 60 75
Normal Stress (psi)


Figure 4.23 Mohr-Coulomb envelope for consolidated drained triaxial tests of tube 2
from Southwest Recreation Center at depth 14-16 ft



60



50 _



40


S30 _

o -u- Specimen 1
/ -*-Specimen 2
S20







0
0 5 10 15 20
Axial Strain (%)


Figure 4.24


Consolidated drained triaxial tests of tube 3 from Southwest Recreation
Center at depth 18-20 ft










45





30


3 3= 34.2
mb = 33.8






0
0 15 30 45 60 75 90
Normal Stress (psi)

Figure 4.25 Mohr-Coulomb envelope for consolidated drained triaxial tests of tube 3
from Southwest Recreation Center at depth 18-20 ft

Soil parameters corresponding to the depths where Shelby tube samples were

tested are shown in Table 4.3. All of the possible values for PENCEL Pressuremeter

moduli are shown in Table 4.4.




Table 4.3 Summary of soil parameters from lab and insitu tests at the Southwest
Recreation Center
S E50 Ko E M Limit E
Tube Depth TRIAX TRIAX N qc CPT DMT DMT DMT DMT Pressure PMT
(ft.) (0) (psi) (blows) (psi) (o) (0) (-) (psi) (psi) (psi) (psi)

11.0 25.1 540.0 16.0 1830.4 45.0 44.0 2.59 11136.0 36221.0 214.6 42093.5

15.0 34.5 830.0 18.0 839.8 41.0 41.0 3.55 9715.0 34075.0 305.2 44080.0
33.3 2000.0

19.0 33.8 700.0 15.0 686.0 39.0 46.0 2.06 11455.0 35844.0 269.7 48879.5
34.2 1800.0










Table 4.4 Summary of possible PENCEL moduli
Southwest Recreation Center
EUR MAX
Ei apexes EUR Secant E UL Secant
Tube Depth PMT PMT PMT PMT
(ft.) (psi) (psi) (psi) (psi)


from pressuremeter a tests at

MIN MAX MIN
E UL Secant EUL Tangent EUL Tangent
PMT PMT PMT
(psi) (psi) (psi)


11.0 3190.0 160051.0 (-) 421065.5 4988.0 181308.0 4096.3

15.0 4925.7 (-) (-) 919050.6 19436.8 70380.1 3540.9


19.0 4471.8 (--) (--) 594268.0 18188.8 103074.7 3951.3



Alachua County Landfill

To complete the laboratory testing, a third set of Shelby tubes was collected at the

Alachua County Landfill in Archer, Florida. This site was chosen for accessibility. For

several years the Archer Landfill has allowed the University of Florida to conduct

research on their grounds. Furthermore, the landfill staff provided a location where there

was at least forty feet of sand overlying limerock.

With this site secured, CPT tests were conducted to verify the stratigraphy. Once

again, Universal Testing donated time to collect 4 Shelby tubes at the site and perform 4

Standard Penetration Tests. The fourth tube, from depth 19 to 20 ft, had poor take and

may have been disturbed by the drilling crew during collection. The final tests to be

completed at the site were PENCEL Pressuremeter and dilatometer soundings.

Knowing that the material contained in tubes from this location was fairly clean

sand, we realized that extraction might compromise the materials. Therefore, the

decision was made to cut the tubes to test length, and then freeze them for at least 48

hours before extraction and trimming. This method worked extremely well. The average

3 percent moisture provided enough virtual cohesion when frozen to allow for extraction


I


I








and trimming as well as placement of the specimen in the triaxial chamber. Six
specimens were tested from these four tubes.
A sketch of the approximate location of all borings and soundings is shown in
Figure 4.26. The field boring log for the standard penetration test performed at the site is
included as Figure 4.27. Figures 4.28 and 4.29 show the corrected PENCEL
Pressuremeter curves. Finally, the six triaxial tests performed on the Archer Landfill
sands are shown in Figures 4.30 through 4.37. Additional insitu test data can be found in
the appendix.


A Southwest Archer Road


IDD


Figure 4.26


.-::::o O

IApproximate Fence
Location of
ISPT, CPT, i
DMT and
:PMT
L_.... _...... ...


O ,H
H


Closed Landfill


Plan view sketch of soil exploration at the Alachua County Landfill in
Archer, Florida


a



















] FIELD LOG OF BORING B- 1

FRB3T- BENTP WD. NUMBER DATE STARTED
Archer Landfill U of F 502 10/25/00
ILL ED BY: tG. ELEVATE ON(DATU TOTAL DEPH DATE FINiSE
22.5 "


DATE;


S CLASSIFICATn OF MnTERIAL REMARKS

tan fine sand
I


3

4
5- Shelby Tube #1 spooned 6-7.5'

6-
t.f.s.

T-



shelby tube #2
0-
spooned 11-12.5'

2-
t.f.s.

3

4

5
shelby tube #3
6-
7 t.f.s. spooned 16-17.5'

8-


shelby tube #4


I -

2-
3-

4-


6-

7-

8-
9-

--


2-


t.f.s.


Spooned 21-22.5'


S88 Figver EingMnnStg Speence




Figure 4.27 Standard penetration test boring B 1 at Archer Landfill


z





















4










0 20 40 60 80 1


Volume (cm
Volume (cm3)


Figure 4.28



























-20



Figure 4.29
S--













Figure 4.29


PENCEL Pressuremeter tests at Archer Landfill at depths 5-15 ft


0 20 40 60 80

Volume (cm3)


PENCEL Pressuremeter tests at Archer Landfill at depths 20-30 ft


--5 ft
--10 ft
--15 ft


--20 ft
--25 ft
A 30 ft












35


30


25


20


S15





5


0


-5
-5


Axial Strain (%)


Figure 4.30


Consolidated drained triaxial tests of tube 1 from Archer Landfill at depth
4-6 ft


S 20


0)


10
W,


4 = 34.4


0 10 20 30 40 50 6
Normal Stress (psi)
Figure 4.31 Mohr-Coulomb envelope for consolidated drained triaxial tests of tube 1
from Archer Landfill at depth 4-6 ft


--Specimen 1
-*-Specimen 2







































Figure 4.32


S 30
Q.
(n



15





0


2 4 6 8 10
Axial Strain (%)

Consolidated Drained Triaxial tests of tube 2 from Archer Landfill at
depth 9-11 ft


4 = 32.5


15 30 45 60 75
Normal Stress (psi)


Figure 4.33 Mohr-Coulomb envelope for consolidated drained triaxial tests of tube 2
from Archer Landfill at depth 9-11 ft












35


30


-25
U)





.15
S 20






010-


5


0
0




Figure 4.34





30
QI-^






















10
W20









0
o3


2 4 6 8 10
Axial Strain (%)


Consolidated drained triaxial test of tube 3 from Archer Landfill at depth
14-16 ft


10 20 30 40 50
Normal Stress (psi)


Figure 4.35


Mohr-Coulomb envelope for consolidated drained triaxial test of tube 3
from Archer Landfill at depth 14-16 ft












35


30



-25 -



,20
'I
9,

C,
15
0

010



5



0
0



Figure 4.36


20



10
(0









0


Figure 4.37


2 4 6 8 10
Axial Strain (%)


Consolidated drained triaxial test of tube 4 from Archer Landfill at depth
19-21 ft


10 20 30 40 50
Normal Stress (psi)


Mohr-Coulomb envelope for consolidated drained triaxial test of tube 4
from Archer Landfill at depth 19-21 ft




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