Geotechnical Engineering

REVIEW OF CAVITY EXPANSION MODELS

IN SOIL AND ITS APPLICATIONS

By

Nitin S. Pandit

Ronald C. Chaney

Hsai-Yang Fang

Fritz Engineering Laboratory

Department of Civil Engineering

Lehigh University

Bethlehem, Pennsylvania

Harch 1, 1983

Fritz Engineering Laboratory Report No. 462.10

REVIEW OF CAVITY EXPANSION MODELS

IN SOIL AND ITS APPLICATIONS

By

Nitin S. Pandit1

2 Ronald C. Chaney Hsai-Yang Fang 3

ABSTRACT

Various forms of analytical methods and models have

been proposed in the literature to explain the behavior of

a cavity in soil as it undergoes expansion into the surrounding

medium. The models are very complex and not suitable for quick,

routine applications in practice. A review of the cavity ex-

pansion models is presented in this paper. The basic assump-

tions made in each model, their various characteristics, and

applicability are summarized. I~ addition an examination of

the various cavity expansion concepts is conducted to clarify

the pros and cons of its application in interpretation of

pressuremeter tests and the prediction of the axial bearing

capacity of piles.

KEYWORD: Geotechnology, Soil, Model, Construction, Foundation,

Failure, piles, pressuremeters.

1 senior Staff Engineer; Woodward-Clyde Consultants; Solon, Ohio 44139

2 . Assoc~ate Professor; Dept. of Environmental Resources 'Engineering; Humboldt State University; Arcata, Califor~ia 95521

3Professor and Director; Geotechnical Engineering Division; Lehigh University; Bethlehem, Pennsylvania 18015

INTRODUCTION

The theory of soil cavity expansion deals with the

expansion of a cavity in a material of given properties.

The models developed based on this theory find application

in problems dealing with bearing capacity of deep foundations,

interpretation of pressuremeter tests, cratering by blasting

explosives and breakout resistance of ground anchors. Essen-

tially, in all the problems, observations of failure patterns

led to the belief that a certain portion of the soil mass,

associated with failure under load, could be defined as that

which is responsible for the failure. The failure patterns also

indicated that in all these cases, this causative portion - the

cavity - was wedged against and pushing into the soil mass

surrounding it. The model of cavity expansion tries to simu-

late the behavior of this cavity and to offer analytical solu­

tions for its behavior under. various types of loadings.

The scope of this study will be restricted to a review of

the available models and their application in two cases: (1) pre­

diction of the bearing capacity of pile foundations (deep founda­

tions) and (2) the analysis of pressuremeter tests for determi-

nation of soil properties. An attempt has been made to take

into account the observation that in soil mechanics, whether a

theory is used routinely in practice to solve geotechnical prob­

lems is often dependent on the simplicity of application of the

theory.

The use of cavity expansion models for the interpretation

of cone penetration tests is not in the scope of this study.

1

THEORETICAL CONSIDERATION OF CAVITY EXPANSION MODELS OF SOILS

Theory, Concept and Assumptians

The theory of cavity expansion has been developed step­

by-step to model insitu soil behavior utilizing various material

properties and loading conditions. Essentially in any of these

developments, three independent constraints have to be defined

to solve the cavity expansion problem.

1) The shape of the cavity which simulates the

field conditions:

Two cavity ·shapes have been addressed so far

in the literature. These shapes are spherical

and cylindrical.

2) Properties of the soil material surrounding the

cavity:

Many types of soils have been utilized to evaluate

the ability of the individual models to predict soil

behavior. In the majority of the models, the soil

is assumed to be a homogeneous linear elastic-plastic

material. This is a reasonable assumption for materials

not exhibiting strain softening behavior such as loose

sand and soft clay. Recent theoretical work has been

directed toward the utilization of curved failure en~

velopes. This development would allow the more meaning-

ful prediction of soil behavior for stiff clays and

2

dense sands which exhibit strain-softening behavior.

In addition to considering variations in stress-strain

behavior some soil models also consider volume change,

sensitivity, dilatancy, compressibility, time de­

pendency, and annulus disturbance.

3) Loading Conditions:

A review of the literature indicates that very little

attention has thus far been paid to the effects of

varying lo~ding conditions on the solutions offered

by the different models.

It is important to note that some of the models were de-

veloped to solve specific problems. Therefore, they are very

special cases of the overall problem. A summary of the various

models indicating the many assumptions involved is presented in

Table 1. A review of Table 1 indicates that all the models are

derived for very ideal materials.

Models in Use - A Review:

Out of these models, the model proposed by Vesic (1972) is

most commonly used in deep foundations such as piles by Vesic

(1975) and in stone columns by Datye and Nagraju (1977). The

models by Ladanyi (1961), Wroth & Windle (1975), and Baguelin,

et al. (1978) are commonly utilized in the interpretation of

pressuremeter tests.

3

Besides the assumptions, the following points should

be noted regarding these commonly used models.

1) Ladanyi's Models: Ladanyi (1963) showed that

compression and dilatancy characteristics play

an important role in the expansion of a cavity in

granular soils. He gave a trial and error method

for estimating the shear strength of granular soils

in drained conditions. The implicit failure criterion

in this theory is that failure occurs at a constant

stress ratio or constant effective angle of internal

friction (~) and is npt dependent on the stress level

or increasing strain levels. For a c'-¢' soil (effective

cohesion, c'), and especially for a cohesive soil, the

volumetric strains have to be ass~ssed to enable de­

termination of c'-¢'. The computations are rather in­

volved and therefore, the procedure is not favored in

routine practice. Ladanyi (1963) also analyzed the

problem of cavity expansion in a saturated clay in un-

drained conditions. The effects of overconsolidation

on the method were also qualitatively examined. A

modified form of this method was used later to develop

a new method for sensitive clays, Ladanyi (1972).

2) Vesic's Model: Vesic (1972) presented one of the most

simple and usable of all the cavity.expansion models,

which also takes into account volume changes in the

4

plastic range of the stress-strain curve for an

elastic-plastic soil. The main assumptions about the

behavior of the cavity are summarized in Figure 1.

Four variables were considered in the model, namely. c',

¢', volume change and limit pressure. The analysis

does not do away with laboratory testing and in some

applications it is essential that the in situ volume

change be measured or estimated. This is a very diffi-

cult problem which is yet to be resolved. The computa-

tions in applying this model are immensely simplified

by the introduction of the rigidity index,

in Eq. 1.

I r

G s

Shear Modulus Shear Strength

(I ) defined r

(1)

Values of Ir were presented in a tabular form and a

convenient chart form and utilized to compute the ratio

Rp/Ru in Figure 1. The theory was principally worked

out for computing the bearing capacity of piles but was

thought to be applicable to the interpretation of pressure-

meter tests too.

3) Wroth & Windle's Model: Wroth & Windle (1975) presented

a model which also takes into account volume changes.

The method was made for use in the interpretation of

pressuremeter tests. The main drawback of the model is

that field measurements of volume changes are made. In

a companion paper, Windle and Wroth (1975) presented

one of the novel ideas to do so by the resistivity method.

5

4) The French Model: Baguelin, et al. (1978) presented

a number of advanced theoretical techniques to account

for the effects of sensitivity, dilatancy, compress-

ibility, and annulus disturbance characteristics. This

analysis is typically restricted to sands and the data

generated primarily from pressuremeter- tests in France.

A special sectio~ has al~e-be~n dev6ted to _cohesive soils

in undrained conditions. The effects of sensitivity

and annulus disturbance in pressuremeter tests have also

been discussed.

A review of the above models indicates that all require the

measurement of volume change under insitu conditions. A summary

of the various insitu methods for determining volume chqnge has

been presented by Mitchell and Gardner (1975). The selection

of the appropriate method was shown to be dependent on the soil

type.

In soft clays, permeability tests and static penetration

tests are believed to be most appropriate. In routine practice,

permeability tests are expensive and rare in soft clays which

implies that one is usually left with the static penetration

test. In stiff clays or shales, load bearing tests or pressure­

meter tests are felt to be tbe most useful.

In determining the volume change of cohesionless soils,the

screwplate and pressuremeter tests have been found ~o be best

for all density conditions. In addition the static penetration

6

and load bearing tests may be used respectively in loose

and dense cohesionless soils. A summary of the various

methods for insitu determination of volume change is presented

in Table 2.

The State-of-the-Art paper by Mitchell and Gardner (1975)

indicates that the measurement of volume change is not likely

to be very accurate by any of the methods. This raises the

question of the actual utility of most of the models which de-

mand an accuracy to within one percent. The main criterion

for evaluating the validity of the various cavity expansion

models has therefore to be the method which was used to com-

pute volume change and its accuracy. In this situation, labora-

tory testing seems to offer a more accurate solution. However,

practical difficulties, such as quality of sampling and sample

disturbance, have set a limit on the accuracy of laboratory

test data, even if the field loading conditions are adequately

simulated in the laboratory.

7

APPLICATIONS

Pressuremeter

The purpose of pressuremeter tests is the evaluation

of in situ soil properties. The test has been gaining in-

creasing acceptance in the geotechnical field because (1)

it is conceptually attractive, and (2) the ease with which

it can be used in the field to simulate various loading con-

ditions. The pressuremeter like other insitu methods has

its drawbacks and limitations. A discussion of the test

has been presented by Fang (1969), Schmertmann (1975) and

more recently by Winter (1982).

The basic arrangement of the pressuremeter test is shown

in Figure 2a. A review of Fig. 2a shows that the test appara-

tus ~onsists of a main expandable cylindrical pressure cell

with two smaller pressure cells (guard cells) top and bottom

in a prebored hole. The main cell is expanded by pre~surizing

it from the surface and the volume change is noted. The test

is usually run in a stress controlled manner, but it is also

possible to run it with strain control. The length of the

cavity is kept constant by the guard cells. A typical test

curve, after making test corrections, is shown in Figure 2b.

The cavity expansion model has been extensively used to

analyze typical pressuremeter results such as shown in Figure 3.

The use is restricted,however, since the pressuremeter itself

8

only measures total stresses. Attempts to measure pore

pressures have so far been relatively unsuccessful. In

addition, other factors affect the test itself and therefore

the int~rpretation of test results by cavity expansion concepts.

In cohesive soils, the concepts of cavity expansion have

tieen ~pplied to the undrained condition only or in the condition

when the loading rate effects are negligible. However, the

fact that the pressuremeter is normally installed in a prebored

hole amplifies the effects of annulus ·disturbance, which severdy

limits the test. The disturbed annulus of soil around the

pressuremeter is likely to give a value of·cohesion larger than

the value obtained from conventional tests.

The cavity expansion theory has also been applied in

pressuremeter test analysis in granular soils and c'-¢' soils.

The variation of the values of the friction angle, ¢' shows

a wide scatter in comparison with values obtained from conven-

tional tests. The main causes for the discrepancies are the

effects of dilatancy, compressibility and sensitivity. The

table below summarizes typical variations in the estimation of

granular soil properties by analyzing pressuremeter results

using cavity expansion concepts.

¢p ¢ Value obtained from pressuremeter tests (computed using cavity expansion model)

¢c ¢ Value obtained from conventional laboratory tests

9

Property Effect on ¢ Typical Variation(Degrees)

Compressibility ¢p greater than ¢c 6 7

Sensitivity ¢p greater than ¢c 6 - 7

Dilatancy ¢c greater than ¢p 12 - 15

It is evident that the results from pressuremeter tests,

as analyzed by cavity expansion conceptsJare not very reliable

if the above-mentioned factors are an important characteristic

of the soil in question.

Not all the problems arise from the model of cavity ex-

pansion, but are directly incorporated in the data due to the

practical limitations of the pressuremeter test. For instance,

the loading duration of each stress level has to be limited to the

facilitate the test. Thus the utility of the test in saturated,

undrained condition in impermeaBle soils may be open to doubt.

The effect of test procedures on the test results is shown by

Roy, et al. (1975) and Laier (1973). Another problem with the

test is to get it to follow a given stress path for vertical

loading. To solve this problem, two choices become available.

First, one could include the effects of all these variables

of the test into the theory. The second option may be to im-

prove the test and testing procedures by testing under controlled

conditions. The first choice is not attractive since the test

can only be corrected if it is refined to indicate the effects

of these variables. In addition, it is now being widely accepted

that it is neither simple nor cost-effective to obtain parameters

10

required for refining correction factors in complex models.

A recent development was made in the direction of the second

preferable option by the advent of the self-boring pressure­

meter, which reduces annulus disturbance effects of the bore­

hole. This is shown in Figure 3 which shows the stress paths

followed in the conventional and the new test. It is seen that

the portion of the curve due to the effect of the borehole dis­

turbance in a conventional test can be substantially reduced

in the test. The reader is refetred to Drnevich (1975) for

details. The sel!-boring pressuremeter has some practical

limitations which have restricted its applicability. There­

fore, to date (1982) its use is not cost-effective for routine

applications in most instances.

The only lesson to be learned from the notes above is

that there are still many "bugs" in the pressuremeter test

itself which have nothing to do with the modeling by cavity

expansion concepts. Even if the model is corrected for some

of the imperfections, the better option would be to run con­

trolled tests to improve the test itself before attempting to

modify the model further. As in some other developments in

fubd~ling soil behavior, the analytical sophistication of the

cavity expansion model seems to have gone ahead of the much

needed practical refinements in the pressuremeter test techni­

ques/equipment.

11

Piles

The application of cavity expansion concepts to pile

foundations is mainly attributable to Vesic, (1912), (1975),

(1977). He compared the failure patterns of end bearing

piles in model tests and in the field with the failure patterns

developed by cavity expansion to find that the end bearing

capacity could be reasonably predicted by cav~ty expansion con-

cepts.

Conventional theories predicting point resistance of piles

are based on Eq. 2.

where:

Q = c·Nc + q N·q 0

point resistance

( 2 )

cohesion, (1+2Ko)

q = mean normal stress = Qv

Ko coefficient of e~rth pressure at rest, Qv = overburden pressure

3

Nc & Nq - bearing capacity factors; NC = (Nq-l)cot ¢

The modified method, using cavity expansion, accepts the

failure pattern at the pile tip such as the one shown in Figure

4. This pattern was accepted on the basis of photographs and

data from field and model studies of the modes of failure of

end bearing piles. It is supported by data on dense and loose

sands and soft clays. The figure indicates a highly compressed

conical wedge I of soil. This wedge forces its way through

loose sand without forming slip surfaces; whereas in dense

sands, it pushes sideways to force zone II against zone III.

12

If this mechanism is accepted, then it is easy to see

that the pile advances by compression along zones II and I

and by expansion along the boundary AB. It is then assumed

that the average normal stress along AB is equal to the

pressure needed to expand the cavity in the infinite soil

mass around it.

The cavity is then assumed to be elastic-plastic with

strength parameters c-¢, deformation modulus E, poisson's

ratio._ v, and average volume change parameter A. The theory,

presented in Vesi~ (1972) leads to the Eqs. 3 and 4.

* Nq (1 +sin ¢)(I sec ¢)sin ¢/(l +sin¢) rr

I rigidity index of the soil r

A volume change parameter

(3)

whe~e: I =reduced rigidity index of the soil; I =I /(1-I *A) rr rr r r

* * (N - 1) cot ¢ q

(4)

These are now used in the Eq. (2) as the bearing capacity

factors. The values of Nq* and Nc* can be easily computed or

stored as tables or charts. Some typical values of the rigidity

index are given in Table 3.

Vesic (1972) showed that it was necessary to carry out

laboratory tests to determine ¢ (or ¢' in the case of effective

stress analysis) and that plane strain triaxial tests were re-

presentative for this problem. He also indicated that without

these tests, in situ volume change readings are essential to

use the theory.

13

One limitation of this arises from equipment limitations,

cost and the relative unavailability of the plane strain tri-

axial device for routine applications. But the major objection

to the use of Vesic's model (1972) in pile design stems from

the fact that it requires an accurate measurement of the volume

change. The fact.has been taken into account and the model

used in conditions where the accuracy of the volume change pre­

diction was sufficient to enable the use of the model. For

instance, the model has been applied in other types of deep

foundations such as stone columns, by Datye & Nagaraju (1977),

where a similar failure pattern was envisaged.

14

SUMMARY AND CONCLUSIONS

The theory of cavity expansion has been developed into a

series of models by various investigators to analyze the

behavior. of a cavity in soils. All the models developed

thus far assume that the surrounding material is a homogeneous

linear elastic - plastic medium of specified properties and

an assumed failure criteria. A summary of the various cavity

expansion models is presented in Table 1.

Accuracy in the measurement of volume change is the criti­

cal factor in the use of the accepted cavity expansion models.

This parameter may be used to evaluate the validity of appli­

cation of the model in a particular situation.

Cavity expansion models have been used to explain and

predict pressuremeter test results. It is felt however, that

the refinements of the model are not required at this stage

since the test procedure and apparatus itself needs refinements.

Vesic's model (1972) has been commonly used for computing

the bearing capacity of piles. The model is simple to use.

The critical factor in the model is again the accurate· measure­

ment of volume change with one percent error tolerance.

It should be noted that all models assume the soil to be

elastic-plastic. Thus, volumetric strains during shear (dilatancy),

and the decrease in shear strength with strain (strain softening)

are essentially ignored. Unless the basic assumption about the

rheologic properties of soils is changed, corrections will have

to be applied to account for these effects.

15

REFERENCES

Baguelin, F; Jezequel, J.-F; Lemee, E., Le Mehaute, A. (1972)

"Expansion of Cylinderical Probes in Cohesive Soils", JSMFE, ASCE, Vol. 98; SMll,

Proc. Paper 9377, p. 1129-1142.

Baguelin, F; Jezequel, J.-F; Shields, D. H; (1978)

"The Pressuremeter and Foundation Engineering"; Trans Tech. Publications,

Clausthal Germany, p. Appendix.

Baligh, M. M; (1976) "Cavity Expansion in Sands with Curved Envelopes",

JSMFE, ASCE; Proc. Paper 12536, p. 1131-1146.

Bishop, R. F; Hill, R; Mott, N.-F; (1945)

"The The~ry of Indentation and Hardness Tests", Proc. of the Physical Society,

London, No. 57, p. 147-159.

Datye, K. R; Nagraju, S. S. (1977)

"Reinforced Granular Columns - A New Design Approach", IX ICSMFE, Tokyo; Spec.

Session No. 10.

Drnevich, V. P. (197 5); "In Situ Measurement of Inti tal Stresses and Deformation

Characteristics", Proc. Conf. on In Situ Measurement of Soil Properties; Raleigh,

N.C; Vol. II p. 244-253.

Fang, H. Y. (1969); "Discussion of Pressuremeter Correlation Study", Highway Research

·Record, No. 284, p. 61-62

Gibson, R. E; Anderson, W. F; (1961)

"In Situ Measurement of Soil Properties with the Pressuremeter", Civil Engineering,

London; Vol. 56, May, p. 615-620.

16

Hill, R; (1950) "The Mathematical Theory of Plasticity";

Oxford University Press; New York.

Ladanyi, B. (1961); "Etude Theorique et Experimentale de !'expansion

daus un Sol Pulverulent d'une cavite Presintant une Synietrie Spherique ou

Cylindrique"; Annales de Travaux Publics de Belgique; Buxelles No. 2 et 4.

(1963a); "Evaluation of Pressure meter Test in Granular Soils", Proc. 2nd Pan-Am

Conf. on Soil Mech. & Found. Engg; Brazil; Vol. 1, p. 3-20.

(1963b); "Expansion of a Cavity in a Saturated Clay Medium", JSMFE, ASCE: Vol.

90, SM4, Proc. Paper 3577, p. 127-161.

(1972); "In Situ Determination of Undrained Stress Strain Behavior of Sensitive Clays

with the Pressuremeter", Canadian Geotechnical Journal, Vol. 9; No. 3.

Laier, J. E. (197 3); "Effects of Pressure meter Probe Length/Diameter

Ratio and Bore Hole Disturbance on Pressuremeter Test Results in Dry Sand"; Ph.D.

. Thesis; University of Florida.

Menard, L. (1957); "Measure In Situ des Propertes Physiques des Sols",

Annales des Ponts et Chausseis, Paris, No. 14, Mai-Juin, p. 357-377.

(1957); "An Apparatus for Measuring the Strength of Soils in Place", Ph. D. Thesis,

University of Illinois.

Mitchell, J. K; Gardner, W. S.; (197 5);

"In Situ Measurement of Volume Change Characteristics", SOA paper to Session IV,

Proc. ASCE Conf. on In Situ Measurement of Soil Properties, Raleigh, N.C.; Vol. II,

p. 279-346.

Palmer, A. C; (1972}; "Undrained Plane-Strain Expansion of a Cylindrical Cavity

in Clay - A Simple Interpretation of the Pressuremeter Test", Geotechnique; Vol.

22, No. 3, p. 451-457.

17

Roy, M.; Guneau, R.; La Rochelle, P.; Tavenas, F. (1975) "In Situ Measurement of the Properties of Sensitive Clays by Pressuremer Test", Proc. ASCE Conf. on In Situ Measurement of Soil Properties, Vol. 1, p. 350-372.

Salecon, J. (1966); "Expansion Quasi-Static d'une Cavite a Symme­trie Spherique on Cylindrique dans un milieu elasto-plasti-que", Annales des Ponts & Chaussies, Paris, Vol. III, p. 175-187.

Schmertmann, J. H. (1975); "t1easurement of In Situ Shear Strength", State-of-the Art Paper to Session III in Proc. ASCE Conf. on In Situ.Measurement of Soil Properties, Vol. II, p. 57-139.

Vesic, A. S. (1972); Expansion of Cavities in an Infinite Soil Mass", JSMFE, ASCE, Vol. 98, SM3, Proc. Paper 8790, p. 265-290.

----- (1_975); "Principles of Pile Foundation. Design", Soil Mechanics S~ries No. 38, Duke University, N. C. 46p plus 34 figures.

----- (1977); "Design of Pile Foundation", NCHRP Program Publication .. No. 42, Transportation Research Board, National Research Council, 68p.

W in d 1 e , D . ; W r o t h , C • P . (1 9 7 5 ) ; " E 1 e c t r i c a 1 R e s i s t i vi t y Me t h o d f o r Determining Volume Changes that Occur During a Pressuremeter Test", Proc. ASCE Conf. on In Situ Measurement of Soil Pro­perties, Vol. 1, p. 497-510.

Winter, E. (1982); "Suggested Practice for Pressuremeter Testing in Soils'', Geotechnical Testing Journal, ASTM, Vol. 5, No. 3/4, Sept/Dec., p. 85-88.

W r o t h , C . P . ; W in d 1 e , D . ( 1 9 7 5 ) ; "An a 1 y s is o f P r e s s u r em e t e r T e s t .Allowing for _Volume Change", Geotechnique; Vol. 25, No. 3, Technical Notes, p. 598-604.

NOTE:

ASCE - American Society of Civil Engineers

ASTM - American Society for Testing and Materials

ICSMFE - International Conference on Soil Mechanics and Foundation Engineering.

JSMFE - .Journal of Soil Mechanics and Foundation Engineering

18

TABLE I: MODELS, ASSUMPTIONS & LIMITATIONS

r-l :>., Ill (/) (/) "-'

'"d u Q) Q) •,..j Q) ·,..j •,..j •,..j :>

THEORY p. OJ)-1-J "-' 'M 0 H 0 H Q) Q) H "-' r-l 0 r-l Q) s OJ)Q) 'M Q) ~ 0 p. ::l d p. (/)

:> Q) 0 r-l Cll 0 d Q) ..c H o..c H Q)

Q ~p.. :>up.. U)

BISHOP, HILL & MOTT M - -(1945)

HILL (1950) M I u -H H U)

..:t: .....:1 p..

I

MENARD (1957) u s H - -H U)

..:t: rj

GIBSON & ANDERSON (1951) ~ s w - -z

LADANYI (1961)

~I

s Netals Soils

CYL SPH

H .....:1

s I ?

Cylindrical Cavities Only Spherical Cavities Only

I :>., 'M u (/)

d (/)

Ill Q) :>., "-' H "-' C1j p. ·,..j

r-l Sri •,..j 0 •,..j Q u..o

- -

- ?

- -

- -

? ?

:>., u d Q)

'"d c

Q) Q)

s p. •,..j Q)

HQ

-

-

-

-

-

;,

D

~

..._. 0 Q) 0 I 'M u c "-' d Q!W Ill Ill H '"d r-l

(/),0 B ~ a ·rl Ill

::l H :>., r-l •rl rl ::l C1j ::l ~. "-' I 0 H ::l "-' :>r-l 'M Q) H (/) Q) Q) c (/) H •,..j .- ;:.. p. Q) d "-' p. C •,..j ::l Cll g Cll :>... :>·o Cll :>., ..:t:O u~ UH ou ;:<:;H

- - Both - ¢=0

rl

- - Both - Cll H Q)

d Q)

c.:>

- - CYL * C-¢

C=O - - SPH - or

¢=0

r-l Cll

- - Both H - Q)

d Q)

c.:>

Considered in Theory = Effect is Explained

Relevant Data is Used

(/)

"-' d Q)

§ 0 u

For Pressure Meters

For Piles

N 0

THEORY

LADANYI ( 19 63

LADANYI (1963

SALE CON (1966)

:'

VESIC (1972)

LADANYI (1972)

N s

Metals Soils

a)

b)

CYL SPH

TABLE I: MODELS, ASSUMPTIONS & LIMITATIONS

(Continued)

H ;>., C1l UJ UJ .u

"0 u QJ QJ "H QJ "H "H "H :> 0.. M.U .u "H 0

'""' 0

'""' QJ QJ

'""' .u

H 0 H QJ s MQJ "H QJ r.x. 0 0.. ::l j:! 0.. en :> QJ 0 H C1l 0 j:! QJ .c

'""' o.c

'""' QJ

Q P:::P... ::>up... U)

s I -

I s u -H E--< U) ~ '· t-1 p...

I

s u I ? H E-< U) ~ t-1 w

~ s I -w z H t-1

s I D

Cylindrical Cavities Only Spherical Cavities Only

I ;>., "H u (/)

c. en C1l QJ ;>., .u '""' .u C1l 0.. "H H EiH "H 0 ·H Q u.o

I I

- -

? ?

- I

- -

~ 0 QJ 0 I "H

;>., u j:! .u u j:! QJW C1l r:: C1l

'""' "0 H

QJ !1),.0 ::l QJ "H C1l "0 ::l

'""' .u '""' ~ ;>., H "H j:! H ::l C1l ::l ~ .u I 0

'""' QJ QJ ::l .u :> H ( "H QJ

'""' en QJ QJ

s 0.. j:! (/) '-' "H r: :> 0.. QJ j:! .u 0.. "H QJ j:! "H :l C1l g C1l ;>., 68 C1l :>.. E--<Q ~Q u r.x. ~ UE--< ;:;;E--<

'""' C1l

Both H

- - - - ::l j:! C1l

'""' c.!l

"0

Both QJ

- - - D .u en C1l :>..

'""' C1l

::lH .u .u C1l

U)

? ? - Both - ?

H - - - Both - C1l

'""' QJ j:! QJ

c.!l

"0 QJ

* .u

- - - CYL C1l

'""' ::l ;>., .u C1l. c:;:: cUH~ U)U

V Considered in Theory * ~ Effect is Explained D Relevant Data is Used

en .u j:! QJ

~ 0 u

Drained Condition

Only

Undrained Condition

Only

Pile Design

Pressure-Meter: !undrained, IPiane-Strain Cqnditions I

N 1--'

THEORY

PALHER (1972)

BAGUELIN, ET.AL. (1972)

WROTH & WINDLE (1975)

BAGUELIN, ET.AL. (1978)

BALIGH

M

s

(1980)

Hetals Soils

CYL SPH

TABLE I: HODELS, ASSUHPTIONS & L U!ITATIONS

'U Q)

0. 0 H

.--! 0 QJ ~ > QJ

Q

s

s

s

s

s

.--! C\1 Ul () QJ

·ri •ri OOJJ 0 H

.--! QJ 0 0. QJ 0

..r:: H P:::P...

~ w z H ....:1

:>.. Ul JJ QJ ·ri •ri > JJ ·ri

QJ QJ H JJ s OOQJ ·ri :l c 0. Ul

.--! C\1 0 c o..r:: H QJ ;>up... U'l

Cylindrical Cavities Only Spherical Cavities Only

(Continued)

I :>... ·ri () Ul c Ul Cll Q) :>... JJ H JJ C\1 0. ·ri

.--! Sr--I ·ri 0 ·ri Q u.o

"-1 QJ 0 I

:>... () c () c QJ~ r:: C\1 H QJ Ul.O :l QJ 'U :l H JJ H 0 :>-. c .--! :l Cll :l ~ JJ

QJ QJ :l JJ > .--! c •ri QJ El 0. c Ul H ·ri r- > p..

•ri QJ c ·ri :l Cll ~ C\1 :>-. E-tQ ~Q u ~ ~ UE-t

CYL

CYL

CYL

CYL

SPH

,... 0

•ri JJ Cll

'U ·ri .--!

I 0 H Ul QJ c 6'8

?

.--! Cll

•ri H QJ QJ JJ 0. Cll :>-.

::E:E-t

'U QJO JJ II C\l-6-H ::l :>-.

-1-) Cll Cllr--1 U'lU

¢=0

(J)

'U r:: Cll

U'l

V Considered in Theory * - Effect is Explained D = Relevant Data is Used

Ul JJ c QJ

§ 0 u

Pressure­Meter; Un drained, Plane-Strc in Condition

As Above

Drained Condition Only. Undrained Condition Touched Upotn

Pressure­Meter

Modificatioh of

Vesic (1972D Concepts

Material

Soft Clays

Stiff Clays or Shales

Cohesionless Soils

Insitti Test

Permeability Test Static Penetration Test

Load Bearing Tests Pressuremeter Tests

Screw Plate Tests Pressuremeter

TABLE 2 - Insitu Determination of Volume Change (after Mitchell and Gardner, 1975)

22

TABLE ·3

TYPICAL VALUES OF RIGIDITY INDEX, /,

(a) sands and silts

Relative Hean Normal Rigidity Soil censity stress level index Sourc;e

Dr 00 (kg/cm2) I r

0.1 200 Vesic 80\ 1 118 and

~hattahoochee sand 10 52 Clough 100 12 (1958)

20\ <l.l 140 1 85

Otta\.la sand 62\ 0.05 265 Roy (1956) 21\ o.os 89

Piedmont silts 0.70 10-30 Vesic (1972)

(b) clays (undrained conditions)

Plasticity Water oc Effective .Rigidity Soil index content ratio stress level index Source

Ip ,o <J (kg/cm2)

Weald clay 25 23.1\ 1 2.1 99 22.5\ 24 0.35 10

Ladanyi Dra:nmen clay 19 24.9\ 1.5 267 (1963)

25.1\ 1 2.5 259 27.H 4. 0 23 3

Lagunillas 50 65'!.* l 6.5 390 clay 4. 0 300

*prior to consolidation

2 3 -

Figure 1: Vesic's model of an expanding spherical cavity

Assumed initial conditions:

(1) A soil mass is under an isotropic effective stress.

(2) The soil mass is homogeneous.

(3) There exists a spherical cavity of radius Ri (dashed line).

(4) Soil behavior in the elastic range can be described by a modulus of deformation, E,

and a poisson's ratio, V. In the plastic range, it can be described by the Mohr­

Coulomb shear strength parameters, C-tl, and the average volumetric strain (which

can be defined from the knowledge of the state of stress and volume change-stress

relationships in the plastic range).

Assumed loading and behavior:

(1) The internal pressure of the cavity is uniformly increased causing the cavity to

expand.

(2) This causes an annulus of soil around the cavity to go into the plastic range.

(3) At a particular internal pressure Pu, the qwity has a radius, Ru and the liinit of the

annulus in the plastic range is defined by Rp. Beyond this, the soil mass is still in

the elastic range.

24

CONTIO:c!>l. UNIT ~--------~

II =II =1/:::/1=11 :IJ: II= II

(a)

3oREHOLE

(b)

TVPICAL CU!ZVE

VOLUI-1£. CHANGE

Fig. 2 The Pressuremeter

25

..

Q

Horiront•l Strrnrs in Potc Coordin"rs

P:I/2{CTr+CTe)

q:l/2(o-,-o-8)

. Pressuremeter Curve

Shear Stress

Actual ln.Situ Undisturbed

F

c o~-:---+=------.,----­

-a

Q

0

-o

p

c Shear S!rain

Lole E;.;cavation E :r.cavotion

(a)

(c)

Prrssurr mr ter Strru Pothl

E F a

(b) Prtnurcmctf'r Suru-Str•in

Snear Stress

J Pre ssuremeter Curve-

F

/ 1_Actuol

I In Situ

D A

S!rru PJ:tlu

'"' xlf-!lnrinr Prcuun· lnC'!rr

p

c

(d)

1 Undisturbed Curve

Shear Strain

/--+--Insertion of Pressuremeter

Suru StrJin !ot StU-Burin& Prr\\UtC'(I"'('Icr

Fig. 3 R~duction in Annulus Disturbance Usc of Self-Boring Pressurcmeter

with After Drnevich (1975)

26

..

CON IC.AL. WEDC4-e

Fig. 4 Vesic 1 s Model of Pile Behavior

27

Sctt. IN PLASTIC

RA"l~E