(

NSF/CEE-82007

PB82-21SS 49

FINAL REPORT

AN EVALUATION OF LABORATORY TESTINGTECHNIQUES IN SOIL DYNAMICS

National Science FoundationGrant No. PFR79-026l2

by

Adel S. Saada*

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CASEWeSTE:RN-RESERVEUNIVERSITV

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INFORMATION RESOURCES \NATIONAL-SCIENCE FOUNDATION.

50272-101

REPORT DOCUMENTATION 11. REPORT NO.

PAGE NSF/CEE-82007.t. Title and Subtitle

Evaluation of Laboratory Testing Techniquesin Soil Dynamics, 1982 Final Report

/--------------- ---------- ------------7. Author(s)

A.S. Saada, G. Fries, C.C. Ker9. Performing Organization Name and Address

Case Western Reserve UniversityDepartment of Civil EngineeringCleveland, OH 44106

3. Recipient's Accession No.

5. Report Date

March 19826.

8. Performing Organization Rept. No.

10. Project/Task/Work Unit No.

11. Contract(C) or Grant(G) No.

(C)

PFR7902612(G)

14.

13. Type of Report & Period Covered

Fi nalf----------------

12. Sponsoring Organization Name and Address

S.C. Liu, CEEDirectorate for Engineering (ENG)National Science FoundationWashington, DC 20550

I----'---=-----:...-=-.:..-=--~--.::.-------- -------------------------'- -----------------115. Supplementary Notes

Submitted by: Communications Program (OPRM)National Science FoundationWashington, DC 20550

---------- ----- ------ ---------16. Abstract (Limit: 200 words)

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

An extensive soil testing program was conducted on clay and sand materials usingthree different devices: the standard triaxial; the N.G.I. simple shear device;and the thin long hollow cylinder. Both monotonic and cycling loadings were usedand led to results emphasizing the influence of the boundary conditions present ineach device. The use of the simple shear test to simulate the conditions that pre­vail during landslides or earthquakes is found to lead to erroneous results whencompared to the thin long hollow cylinder. For both static and dynamic tests, thetriaxial test is definitely an improvement over the simple shear one. The thinlong hollow cylinder is shown to be the most desirable configuration to be used inthe soils laboratory for studies related to strength and stability under both staticand earthquake situations.

1--------------------------------------------------117. Document Analysis a. Descriptors

SoilsSoi 1 testsSandsCl aysb. Identifiers/Open·Ended Terms

Ground motionTri axi al testSimple shear test

c. COSATI Field/Group

Cl ay soil sLandslidesCyclic loadsEarthquakes

A.S. Saada, /PI

Bounda ri esTesting equipmentIns trumentsShear properties

18. Availability Statement 19. Security Class (This Report) 21. No. of Pages

20. Security Class (This Page)NTIS I----------------j---------

22. Price

(See ANSI-Z39.18) See InstructIons on Reverse OPTIONAL FORM 272 (4-77)(Formerly NTIS-3S)Department of Commerce

AN EVALUATION OF LABORATORY TESTING

TECHNIQUES IN SOIL DYNAMICS

by

Adel S. Saada

This report is the condensation of two Master's degree disser-

tat ions by Messrs. G. Fries and C. Ker working under the direction of

the principal investigator. The proposed investigation has been fully

completed and significant results obtained. The report, with some edi-

torial adjustments will soon be submitted for publication in an

international journal.

The following pages contain:

1 - An abstract of the report g~v~ng a very shortsummary of the research conducted.

2 - A list of personnel involved in this research.

3 - The actual report to be published soon.

One of the master's thesis by Mr. Fries is enclosed as well as

two papers already published which have resulted from this work. The

thesis by Mr. Ker is being written and when completed in a couple of

months will be sent to the National Science Foundation. The two thesis

contain all the details and test results.

Within the framework of this grant the Principal Investigator

attended:

1 - The Symposium on Laboratory Shear Strength of Soilheld in Chicago in June, 1980, where he presentedthe state of the art on soil testing (enclosed).

} I

2 - The International Conference on Recent Advances inGeotechnical Earthquake Engineering and Soil Dynamicsheld in St. Louis in April, 1981, where he presentedtwo papers, one supported by a previous NSF grant andone supported by this grant (enclosed).

3 - The Tenth International Conference on Soil Mechanicsand Foundation Engineering held in Stockholm in June,1981, where he presented a paper summarizing a studysupported by a previous NSF grant.

We trust the National Science Foundation finds this report

satisfactory.

Respectfully submitted,

/')' / / l' . ,/,/./7' -" ..' /," l'/.. "< /' (.. /... :. \/ ' .... -/.. \,;,:' (. ,-'\

Adel S. SaadaProfessor and ChairmanDept. of Civil Engineering

, . ,I I t

ABSTRACT

An extensive soil testing program was conducted on clay and sand

materials using three different devices, namely the standard triaxial,

the N.G.I. simple shear device and the thin long hollow cylinder.

Both monotonic and cycling loadings were used and led to results that

dramatize the influence of the boundary conditions present in each

device. The use of the simple shear test to simulate the conditions

that prevail during landslides or earthquakes is found to lead to

erroneous results when compared to the thin long hollow cylinder. For

both static and dynamic tests the triaxial test is definitely an im-

provement over the simple shear one. The thin hollow cylinder is shown

to be most desirable configuration to be used in the soils laboratory

for studies related to strength and stability under both static and

earthquake situations.

ii

<

I V

r

I /

/

PERSONNEL

First Year:

Principal Investigator: Adel S. Saada

1 Graduate Student: Gerardo Fries

Student help and shop technicians

Second Year:

Principal Investigator: Adel S. Saada

1 Graduate Student: Ching-Chang Ker

Student help and shop technicians

iii

v

AN EVALUATION OF LABORATORY TESTING TECHNIQUES

IN SOIL MECHANICS

by

Adel S. Saada*, Gerardo Fries** and Ching-Chang Ker ***

A Paper

To be submitted for evaluation and possible publication in

Soils and Foundations

*Professor and Chairman, Department of Civil Engneering, CaseWestern Reserve University, Cleveland, Ohio.

**Engineer, Woodward-Clyde, Consultants, Houston, Texas.

***Graduate Student, Case Western Reserve University, Cleveland, Ohio.

Vi

INTRODUCTION

The influence of the boundary conditions on the numerical values

of the results obtained in laboratory soil tests has been the subject

of many dissertations. The object of laboratory testing is to study

the behavior of a given soil under conditions similar to those en­

countered in the field and to obtain those parameters which describe

this behavior in a set of constitutive equations. In a laboratory

test the specimen is intended and generally assumed to represent a

single point in a soil medium. The validity of this assumption de­

pends on the uniformity of stress and strain distributions within the

soil samples. This uniformity will depend on the configuration of

the specimen and the control and measurement of stress and strain on

its surface.

In the present study, after a discussion of the stress and strain

distributions in the simple shear device, the standard triaxial and

the thin long hollow cylinder, the results of actual tests on clay and

sand materials are given. Both static and dynamic tests were con­

ducted and attempts were made to obtain equivalent conditions in the

various apparatuses.

In their State of the Art on Laboratory Strength Testing of Soils

SaadaandTownsend (20) discussed in great detail a large number of

devices under static conditions; but they did not give or compare

1

2

results obtained on the same soils simply because such data was not

available. Here this comparison is made for normally consolidated

as well as overconsolidated materials and for stress controlled as

well as strain controlled tests.

STATE OF STRESS IN THE VARIOUS DEVICES

A - The Simple Shear Device

Two types are in use: The Roscoe type with a square cross section

and rigid boundaries and the N.G.I. type with a circular section and

a reinforced membrane. The N.G.I. type, minus the reinforcement has

recently been placed inside a triaxial cell and the sample pressuri-

zed hydrostatically. The stress distribution when the specimen is

subjected to shearing stresses has been studied at length theoreti-

cally and using finite elements (20). A closed form solution was

found for the Roscoe type (13,16) with and without slippage at the

boundaries. A photoelastic study was conducted for both types (25):

Fig. 1 from Ref. 25 shows the shearing stress distribution in the

Roscoe type and Fig. 2 that in the N.G.I. type.

The interest of researchers has primarily been directed at the

nonuniform state of stress resulting from the application of shear-

ing forces to the specimen. However, it was found ( 7 ) that the

lack of uniformity in the axial (0 ) radial (0 ) and circumferentialz r

(Oe) normal stresses was just as, if not more, serious when the specimen

is subjected to axial loads alone in a wire reinforced membrane or

to axial loads in a pressurized cell. The top and bottom platens

of the simple shear device are rigid and often have ribs (or similar

arrangements) to avoid slippage. Under such conditions there is

3

4

often very little relation between the normal stresses acting on

the lateral surface of the sample in a pressurized cell and ° andr

08 within the specimen. The physical dimensions as well as the

boundary conditions prevent any sort of uniformity to prevail.

Fig. 3 shows the results of a linear elastic finite elements

analysis conducted on a specimen of standard size subjected to an

axial displacement of 0.0238 in (0.6045mm) and a lateral cell pres-

sure of 30 psi (207 Kpa) . Young's modulus is chosen to be 2844 psi

(19h09 Kpa). On this figure one notices that for an imposed vertical

displacement the distribution of the three normal stresses is a

function of Poisson's ratio V and varies from the edge to the cen-

ter. This is true on the upper and lower boundaries as well as

the central section. The average value of ° also varies with V.z

However, more important is the fact that or and 08 are indeed

quite different from the 30 psi Q07 Kpa) applied in the cell.

Actually, depending on v, those two components of the state of

stress can be in the larger part of the sample closer to ° thanz

they are to the laterally applied stress. As seen in Fig. 3 only

a very thin layer close to the lateral faces "sees" the applied

30 psi Q07 Kpa) .

Of equal interest are the radial shearing stresses l imposedrz

by the end platens to the specimen because slippage is not allowed

there. Fig. 3 shows the distribution for various values of

v. The magnitude of l due to axial normal force alone could berz

5

higher than the one due to the application of the shearing force

supposed to place the specimen in a state of simple shear. Notice

that depending on the value of V the effect of the lateral stresses

may overcome that of the vertical ones so that T changes in sign.rz

The results of a complete finite element analysis for various

height to diameter ratios and a wide range of Poisson's ratios are

given in the appendix. This analysis applies to both the simple

shear and the triaxial tests.

The discussion above refers to linear elastic materials and does

not introduce any interaction between the shearing and normal components

of the stress and strain tensors. As pointed out by Bishop et al.

(2), when the end platens are rigid a nonuniform shearing stress

distribution will result in nonuniform tendencies to expand or

contract; thus leading to nonuniform normal stresses. The end

result is a totally intractable stress distribution with extremely

high concentrations that lead to premature failure when data based

on average values are compared to that obtained in other devices.

Indeed Bjerrum and Landva (3) concluded that the undrained shear

strength of specimens consolidated in the N.G.I. apparatus was

approximately equal to 2/3 of the average value measured in corres-

ponding triaxial tests. Similar results were found by LaddandEdgers

(8).

6

Finally, Bjerrum and Landva (3) write that the constant volume

test is equivalent to an undrained test and the change in applied

vertical stress on the specimen is equivalent to the change in

pore pressure which would have occured in the specimen if the

specimen had been prevented from draining for a condition of con­

stant applied vertical stress. They also write that the validity

of their assumption was demonstrated in one single truly undrained

test in which the pore pressures were measured at the base of the

specimen. The experiments conducted in this research in the N.G.I.

device show that the drop in the vertical stress in the constant

volume test was several times larger than the increase in pore

pressure in the constant vertical stress test for the same consoli­

dation pressure and the same shearing strain. The results will be

shown in the coming sections.

B - The Triaxial Test

The nonuniformities of the stress distributions within the

specimen are primarily due to the effects of the friction on the

end plates. The problem of the influence of end restraint during

uniaxial or unconfined compression of cylinders has been under in­

vestigation since the latter part of the nineteenth century. Ref.

20 reviews most of the studies conducted on this subject. Of parti­

cular interest are the papers by Balla (1) who summarizes previous

work and brings new insight to the problem, Moore (11) who examined

7

the effects of six Poisson ratios, a height to diameter ratio of

one and two and lateral confinement, and Radhakrishnan (18) who

used finite elements to study linear and nonlinear problems for

height to diameter ratios of one and two.

A feature that is common to all the linear solutions mentioned

above is the drop in the normal contact stress as one moves towards

the center, and a high concentration onthe edges. However, as shown

in the appendix the situation becomes different as the height to

diameter ratio decreases. The concentrations at the ends remain,

followed by a drop, then a substantial increase in the stresses as

one moves to the center of the sample. This is brought about among

others by the zones of influence of the end platens interfering with

each others. More complete information can be found in the references

cited in the State of the Art of Laboratory Strength Testing of Soils

by Saada and Townsend (20).

End restraints can be minimized by using rubber sheeting and

silicone grease to obtain frictionless contacts (17) • However,

Norris (12) showed that one could obtain different stress-strain

curves for sands depending on the number of layers of greased rubber

sheeting and the size of the grains.

C - The Thin Long Hollow Cylinder

When the inner and outer pressures on a hollow cylinder are equal

the radial and circumferential normal stresses across the thickness

8

are equal. Under a superimposed axial stress the nonuniformities

in the distribution of the state of stress are due to the radial

frictional forces that the end platens generate when the specimen

is prevented from expanding or contracting. Those forces are self-

equilibrating and their influence vanishes as one moves away from

the ends. References 20 and 25 contain detailed analyses of the

conditions within the hollow cylinder. In a hollow cylinder the

thickness as well as the mean radius play an important part in the

pressure distribution. The previous references give proportions

for whichfue end effects are reduced to a minimum. If the length

is 2 and the inner and outer radius are r. and r it is recommended1 0

that

,,> 5.44 /r 2o

and nr.

1 ~ 0.65r

o

Such proportions were checked by photoelasticity and by finite element

analysis (4) as well as experimentally (9) and found quite sat is-

factory.

Ifhen the hollow cylinder is subjected to torsional stresses both

shearing stresses and strains vary across the thickness. The larger

the ratio n, the smaller the nonuniformity and the more justified

is the assumption of a uniform distribution equal to the average.

In addition, as the deformation increases one moves towards a uni-

formity of stress. A combination of axial and torsional stresses,

added to a change inthe hydrostatic stress (the same inside and

outside the cylinder ) allow one to rotate the principal stresses

9

at will as well as generate practically any stress path desired.

By keeping the ratios of axial to torsional stress constant any

inclination of principal stress can be maintained during a given

test; and changed from test to test. If this is coupled with a

synchronized change in the cell pressure the inclination may remain

constant and the mean stress varied at will. Saada and his coworkers

have used hollow cylinders to study the properties of anisotropic

clays and sands for years. Ref. 20 lists many of their studies

and describes various stress paths made possible by this particular

configuration.

Finally, it ought to be mentioned that when studying cross

anisotropic materials the hollow cylinder device is rather unique.

Because the system of stress used is axially symmetric cross aniso­

tropy around the axis will be maintained even though its degree

might change due to induced strains. This is not the case for

prismatic samples, be they cubic or parallellepedic: Indeed

as soon as the planes of the prism parallel to the axis of symmetry

move a new kind of anisotropy is created, most probably of the

orthotropic type. States of pure shear stress and simple shear

strain can be studied using hollow cylinders without many of the

boundary effects that plague other devices.

D - Some Comparisons Among the Results Obtained in Various Devices

Until very recently, few systematic studies were made to compare

results obtained in the various devices. Investigators have tried

to match the stress conditions on a horizontal plane in a simple

10

shear apparatus to those on a 45 g plane in the triaxial test. It

is important to remember that all the components of the stress

tensor affect the behavior of the sample and not just what happens

on a particular plane. As mentioned previousl~ Bjerrum and Landva

(3) and Ladd and Edgers (8) found very substantial differences

between the shearing strengths measured in the simple shear device

and the equivalent triaxial tests. Seed and Peacock (23) found that

cyclic strength in simple shear were about 30 to 50 percent smaller

than comparable cyclic triaxial strengths. Park and Silver (14)

attempted to compare the shear moduli and damping ratios measured

in cyclic triaxial tests with results obtained by Thiers and Seed

(24) using cyclic simple shear. They found close agreement when

the comparison was made under conditions of equal mean effective

stress; however, it must be remembered that the mean effective

stress is not known in the simple shear device. This brings into

the picture the whole subject of normalization. While normalizing

has obvious advantages it seems to be used primarily as a curve

fitting technique. When normalizing with respect to some parameter

does not work another is used until the desired coincidence is

obtained _ In view of the results shown in Fig. 3 and in the

appendix, which value of the normal stress is one supposed to take?

Pyke (15) presented a comparison of shear moduli and damping

ratios of sand similar to that made by Park and Silver. He tried

to match the static and cyclic shear stresses on the horizontal

11

plane in the simple shear test and the 45 0 plane in the triaxial

test; realizing that there are differences in the overall states of

stress in the two tests. For example the normal stress in the simple

shear test is constant while its value on the 45 0 plane of the tri-

0daxial test varies by ± :f where 0 d is the difference in the principal

stresses. Pyke points out the difference in the loops obtained in

the two apparatuses: While that of the simple shear is sYmmetric,

the one obtained in the triaxial test is not.

Finally Lee (10) found that, while not perfect the cyclic tri-

axial test offered a reasonable compromise for obtaining dynamic

properties of saturated sand.

The only comparison involving the thin hollow cylinder subjected

to torsional stresses has been made by Saada (22); it is a part of

the study reported herein.

EQUIPMENT AND SPECIMEN PREPARATION

A - Testing Machines

The simple shear tests were conducted using the standard wire

reinforced norwegian membrane. The top and bottom caps were modified

to allow for saturation and measurement of pore water pressure. They

were fitted with thin very short blades to avoid any possible slippage.

The triaxial tests were conducted in norwegian cells with rotat-

ing bushings. Enlarged and greased caps were used for clay samples

and regular caps were used for sand samples. Positive attachment was

provided between the piston and the cap to allow for tension during

cyclic loading.

The hollow cylinder tests were conducted using a specially de-

signed cell allowing for axial and torsional loads to be applied

to the sample. A transducer can be placed both inside and outside

the cell for accurate measurements. A special bushing and piston

assembly allows for the proper balancing of the forces so that both

extension and compression can be applied to the specimen.

K consolidation in the triaxial cell and the hollow cylindero

cell was obtained by means of a servo-system (19) which applies to a

sample a vertical displacement such that it keeps the same cross sec-

tion during consolidation.

12

13

Both controlled stress static and dynamic tests on solid and

hollow cylinders were conducted using a stress controlled SPAC.

This pneumatic analog computer can be programmed to subject speci­

mens to static and slow dynamic axial extension and compression

alone. and pure torsion alone)or to all combined in a synchronized

way (20). The cyclic nature of the loading is controlled by an

electro-pneumatic signal generator that can induce various wave

shapes. A sinusoisal shape was used in this investigation. The

computer and its loading frame are shown in Fig. 4.

Dense soils have a peak stress beyond which the stress strain

curve falls off to the so called residual value. To go beyond this

peak, strain controlled machines are needed. ~fhilea standard Whykam

Farrance loading machine was used for axial loading, two special

frames and a strain controlled SPAC were designed and built for

use with the hollow cylinder. In the first,a torsional displace­

ment is applied to the specimen and the resulting torsional stress

measured with a transducer. The output of this transducer is

amplified or reduced, transformed to a pneumatic signal and fed to

an axial actuator to give a proportional axial stress. One can

thus twist a sample beyond the peak and have principal stresses

which maintain the desired constant inclination on the axis of

symmetry; the torsional mechanical resistance of the sample being

the controlling one. In the second,an axial deformation is applied

to the specimen and the resulting axial stress measured with a

14

transducer. The output of this transducer is amplified or reduced,

transformed to a pneumatic signal and fed to a torque actuator to

give a proportional shearing stress. Here one can go axially

beyond the peak and the axial mechanical resistance is the con-

trolling one. The two frames and their SPAC are shown in Fig. 5.

B - Materials and Specimens Preparation

Both clay and sand materials were used in this comparative study.

The clay was Edgar Plastic Kaolin which has been extensively used in

research on cohesive soil. Its liquid limit is 56.3 percent an plastic

limit is 37.5 percent. The specific gravity of the solid particles is

2.62. Slurries at 125 percent water content were one dimensionally con-

solidated in an 8 in. (203.2 mm) conso1idometer. From the resulting blocks

samples for the simple shear, the triaxial test and the hollow cylinder

were cut and stored. Before each test the specimens were trimmed to:

1.4 in. (35.6mm) diameter and 3.25in. (82.55mm) height for the triaxial

test; 3.16 in. (80. 26mm) diameter and 1 in. (25.4mm) height for the simple

shear; 2.8 in. (71. 12mm) outside diameter, 2 in. (50.8mm) inside diameter

and about 6 in. (152.4mm) height for the hollow cylinder. Those specimens were

then K consolidated in their respective devices. A back pressure of 18 psio

(124.1 Kpa) was used for triaxial and hollow cylinder specimens.

Two sands were tested. One is a well known sand called Reid

Bedford sand and the other a south american sand which will be called

Latin Sand. The Reid Bedford sand is a typically uniform fine sand

with a specific gravity of 2.65 a coefficient of unformity Cu ~ 1.52

15

and a DIO

= 0.125mm. Its minimum void ratio as given by Durham

and Townsend (5) is 0.529 and its maximum void ratio is 0.816.

Its granulometric distribution is shown in Fig. 6. The Latin

Sand contains some fine shell fragments and shows a larger than

usual volumetric compressibility under hydrostatic stresses. Its

granulometric curve is shown in Fig. 7. Samples were prepared to

a void ratio of 0.72 by vibration on a shaking table for the Reid

Bedford sand and to a void ratio of 0.68 by tamping in moist con-

dition for the Latin Sand. Saturation was obtained using vacuum

followed by percolation of CO2

and deaired water; and back pressure

in case of triaxial and hollow cylinder specimens.

c - Convent ions Used in J:-.~~_Ev_alu~~ion of the Experimer~tal Reslil t~

When comparing the tests results, the current conventions will

be followed. This means that the average shearing stress and strain

in the simple shear device will be compared to the maximum shearing

stress and strain in a triaxial compression test:

T45

= Tmax

~(O - 0 )1 31,(02 1 1,0

2 d

where 0d is the excess axial stress also called the deviator.

Y45 = Ymax

where E is the axial strain and no volume change takes place.z

The shear modulus G is the secant modulus equal to T/Y and also

Eequal to 3 where E is Young's modulus. In the hollow cylinder the

16

shearing stresses and strains due to torsion are the ones in questiC:T]

In dynamic testing, the specific damping ratios and the secant

moduli obtained from the various devices will be compared. The

specific damping ratio A is defined as the specific damping capacity

divided by 4n; the specific damping capacity being defined as the

energy loss per unit volume (represented by the area of the hysteresis

loop) divided by the maximum potential energy, ~TY or ~Gy2. The

shear modulus is given by the ratio of T from peak to peak and

y from peak to peak. This definition is necessary because in the

triaxial test the loop is not symmetric and centered at the origin.

Fig. 8 and its caption shows the various definition.

~orm21iza io~ which is the process used to bring down results

to the same common denominator will be discussed as the data is

presented.

STUDY OF CLAY SOILS IN THE VARIOUS DEVICES

A - Testing Program for Clay Soils

All the tests conducted on clay soils were stress controlled.

The following tests were conducted in the standard triaxial cell CST):

Static compression

Cyclic axial

The following tests were conducted in the hollow cylinder device (HC):

Static compression

Cyclic axial

Static torsion with constant length

Cyclic torsion with constant length

Static torsion with constant axial force

Cyclic torsion with constant axial force

The following tests were conducted in the NGI simple shear device (SS):

Static shear with constant length

Cyclic shear with constant length

Static shear with constant axial force

Cyclic shear with constant axial force

The constant length tests in the simple shear device are also

known as constant volume tests. The changes in the axial stress are

measured with a very stiff diaphragm type transducer whose displacement

is negligible.

A test in the standard triaxial or hollow cylinder has an

"equivalent" test in the simple shear device. The equivalence is

17

18

obtained by using the same effective consolidation stress, monitoring

the water content and following similar testing patterns. Once the

static strength is known, the cyclic loading is applied in percentages

of the failure load, 20, 30, 40 percent until failure occurs. 60

cycles per level of stress were used for nearly all of the tests at

about one cycle per minute. During all the tests constant recording

was made of stresses, strain and pore water pressures. Hand calcu-

lations were complemented by a computerized data acquisition system

which reduced immensely the processing time.

Three different consolidation pressures were used for the clay

soil. They are referred to as 58-18, 48-18 and 38-18. The first

number represents the cell pressure and the second the back pressure

during consolidation and just before the undrained shear process be-

gain; both in pounds per square incn Ko consolidation was obtained

through an additional axial load automatically generated by SPAC.

Whenever axial loads were involved in the static or cyclic loading

procedure the excess load producing K consolidation was released,o

equilibrium allowed then the sample tested undrained from a hydro-

static state of stress.

Pure torsion tests in the hollow cylinder be they static or

cyclic started with the axial stress which produced the Ko consoli-

dation. This stress was kept constant during the constant axial

force tests, while static or cyclic torsional stresses were applied

to the sample. On the other hand this stress constantly dropped

19

during the constant length tests, while static or cyclic torsional

stresses were applied to the sample.

Simple shear tests were conducted in a manner similar to that

used for the hollow cylinder tests. The vertical consolidation

pressure was the same as the one indicated by SPAC during the Ko

consolidation ofthe equivalent hollow cylinder test. Then depend-

ing on whether the test was a constant force (CF) or a constant

length one (eL) this stress would be kept constant, or the length

fixed and the stress allowed to drop during shear. Pore water pres-

sures were also measured during simple shear tests. This is not

adviseab1e since the flexibility of the norwegian membranes is quite

large. It was decided, however, to make the measurements in the

most popular devices.

Only static tests were conducted on one type of clay with over-

consolidation ratios of 2, 4 and 8.

The reason for conducting constant length (also called con-

stant volume) tests and constant force (also called undrained) tests

in the simple shear device was to check the validity of Bjerrum's

assumption regarding the equality of the drop in the vertical stress

in one to the increase in the pore water pressure in the other. For

comparison purposes the same type of tests were conducted on hollow

cylinders subjected to static and cyclic torsional stresses.

B - Results Obtained from Static Tests

Fig. 9 shows the results of static tests obtained with the 48-18

clay and normalized with respect to an effective normal stress 0 .n

20

The shearing stress T in the ordinate is the shearing stress on a 45~

plane in triaxial compression test on solid or hollow cylinders; and

the normal stress 0 is the effective normal stress on that plane.n

For the simple shear test and hollow cylinder subjected to torsion,

T and 0 are the shearing and normal effective stresses acting on then

horizontal plane. The shear strain y corresponds to the stresses de-

fined above. In Fig. 9 as well as in all the ones to follow, (HC)

refers to hollow cylinder, (SS) to simple shear, (ST) to standard

triaxial, (C) to compression, (CL) to constant length and (CF) to

constant force. One notices that for strains as high as five per-

cent the triaxial compression tests give the steepest curves. The

lowest strength was obtained from the simple shear test at constant

force and the largest from the hollow cylinder at constant length.

Identical results were obtained for the 58-15 and the 33-18 clays.

Fig. 10 shows the secant shear modulus G(= !) normalized withy

-respect to 0. One notices that the results of the simple shearn

test, whether they are conducted with constant length (constant

volume) or constant force (undrained) are still the lowest. The

differences are very noticeable for small strains where the simple

shear test gives results two to three times smaller than corresponding

hollow cylinder and standard triaxial tests. Here too the three con-

solidation pressures yielded similar results.

The changes in the effective vertical stresses and in the pore

water pressure which take place during constant length (constant

21

volume) and constant force (undrained) tests were recorded during

simple shear and hollow cylinder tests. Fig. 11 shows that whether

it is the simple shear test or the hollow cylinder test the pore

pressure in the undrained test is very different from the drop in

the axial effective stress in the constant volume test. The measure-

ments of the pore water pressures in the simple shear device were

certainly not accurate because of the flexibility of the reinforced

membrane, but it was decided to use the most popular device in this

investigation.

Various normalization parameters were used on the K consoli-­o

dation clays (6) but none of them brought any improvement to the

data shown in Figs. 9 to 11. A normalization of the shear modulus

with respect to the undrained shear strength which is sometimes

used in practice was also found to be totally unacceptable.

c - Results Obtained From Dynamic Tests

For each level of stress a minimum of 60 cycles was applied to

the samples. The results given herein refer to the lath cycle. The

shear moduli and damping ratios were calculated as shown in Fig. 8.

In the constant force cyclic hollow cylinder tests HC(CF) only the

lrysteresis loops connected to torsion were considered. Fig. 12

shows the shear moduli obtained for the 48-18 clay plotted against

the peak to peak value of the shearing strain 2y. Similar results

were obtained for the 55-18 and the 33-18 clays. For small values

of 2y « 2 percent) the differences in the magnitudes of the moduli

22

obtained in the various devices are quite noticeable. The hollow

cylinder seems to yield the highest values and the simple shear the

lowest ones.

It is well known that for small strains the damping ratio in-

creases with strain. However, as the strain becomes larger this

ratio remains more or less constant (21). This seems to be true in

this investigation too. Figure 13 shows the data obtained in this

investigation at the tenth cycle. Again, each device gives a different

answer for the same material.

Finally, it must be noticed that the hysteresis loops kept a

reasonable symmetry with respect to the origin for the simple shear

and torsional tests on hollow cylinder. On the other hand there

was a constant shifting of the loops during axial cyclic tests since

the behavior of K consolidated clays is different in tension ando

compression (21).

D - Analysis of Results for Overconsolidated Clay

Tests on overconsolidated clays were conducted only on the

48-18 clay and for 3 overconsolidation ratios, namely 8, 4 and 2.

Only static tests were conducted; static compression in the standard

triaxial cell, pure torsion at constant length in the hollow cylin-

der device and simple shear at constant length (constant volume).

The results are similar to those obtained for K consolidated clays.o

Various normalizing procedures did not bring the results to coincidence

(6). Fig. 14 shows the value of the shear moduli versus strain for

the tests conducted.

STUDY OF SAND SOILS IN THE VARIOUS DEVICES

A - Testing Program on Sand Soils

Stress controlled tests were conducted on the Reid Bedford sand

and strain controlled tests were conducted on the latin sand.

The simple shear tests and hollow cylinder tests involving torsion

conducted on the Reid Bedford sand were identical to the ones conducted

on K consolidated clay; with K assumed equal to 0.5. The specimenso a

tested in the standard triaxial cell were consolidated under a hydro-

static stress equal to the mean stress acting on the corresponding

simple shear or hollow cylinder test. If for example a specimen at a

void ratio of 0.72 is subjected to a vertical consolidation stress of

10 psi (68.9 Kpa) in the simple shear device, the corresponding conso-

1idation effective stress in the triaxial test would be 20/3 psi. One

void ratio, 0.72 and three consolidation pressures were used for the

Reid Bedford sand. All the tests will be identified in terms of Ko

and the vertical consolidation pressure. For example (0.5-10) means

that during consolidation the vertical effective stress was 10 psi

(68.9 Kpa) and the 1attera1 was 5 (34.47 Kpa~and (1-15) means that

the consolidation was hydrostatic at an effective normal pressure of

15 psi (103.4 Kpa). This latter case applies to the standard triaxial

tests. In all three vertical consolidation pressures of 10 (68.9), 20

(137.8) and 30 psi (206.8 Kpa) were used.

In the strain controlled tests conducted on the Latin sand one

void ratio 0.68 and one consolidation pressure 6.1 psi (42 Kpa) were

23

24

used. The hollow cylinders were all tested under a hydrostatic

consolidation pressure of 6.1 psi (42 Kpa). In the simple shear test

two vertical consolidation pressures were used namely 6.1 (42) and 9.1

psi (62.74 Kpa). In the standard triaxial test a hydrostatic pressure

of 6.1 psi (42 Kpa) was used. For dynamic tests the amplitudes of

the shearing strains were 0.15 percent and 0.34 percent.

B - Results Obtained From Static Tests on the Reid Bedford Sand

Fig. 15 shows the results of static tests obtained with the (0.5-

30) sand normalized with respect to the effective normal stress 0 asn

was done for the K consolidated clay. On the same figure the curveo

obtained with the (1-20) sand is also shown. From those curves one

can see that depending on the type of test one obtains different stress-

strain curves; and that normalization with respect to a mean or a

normal effective stress does not bring them into coincidence. The

differences are quite pronounced for values of strain less than 5 per-

cent. Similar results were obtained with the (0.5-10) and (0.5-20)

sands (27).

Fig. 16 shows the secant shear modulus G for the (0.5-20) sand.

The results vary from device to device with the simple shear test at

constant force showing the smallest G at strains below 5 percent.

Similar results were obtained for the (0.5-10) and (0.5-20) sands.

As in the case of clays the change in the effective vertical

stresses and in the pore water pressure which take place during con-

stant length (constant volume) and constant force (undrained) were

25

recorded during simple shear and hollow cylinder tests. While one

would expect that a drop in the vertical effective stress of a constant

length test would correspong to "at least some increase" of pore water

pressure in an undrained test, as happened for clays, the opposite

took place in the hollow cylinder. Fig. 17 shows the drop in vertical

effective stress of the constant length hollow cylinder test and the

"decrease" in pore water pressure in the undrained test. Fig. 20 shows

the results recorded for the simple shear tests: There the trends are

what they are expected to be but the magnitudes are totally different.

Part of the above is, of course, due to the free 1attera1 movement that

can take place in the hollow cylinder and the "relative" rigidity of

the N.G.I. reinforced membrane. Indeed Fig. 21 shows the measured

volumetric strains in the constant length hollow cylinder and the so

called constant volume simple shear test.

Similar results were obtained with the (0.5-10) and (0.5-20)

sands.

c - Results Obtained From Dynamic Tests on Reid Bedord Sand

Fig. 20 shows the results obtained from dynamic tests on the (0.5­

30) sand for the 10th cycle. Here too the results obtained with the

(1-20) sand are shown; and again depending on the type of the test the

moduli can vary very widely.

The damping ratios for the 10th cycle are shown in Fig. 21 and

they vary from test to test. Similar results were obtained with the

(0.5-10) and (0.5-20) sands.

26

D - Results Obtained From Tests on Latin Sand

Fig. 22 shows the shear moduli versus the number of cycles for

shearing strains y = 0.15% and 0.34% respectively. Here again, for

the smaller number of cycles the modu1ii vary very widely depending

on the cycle number and consequently on the degradation of the reacting

stress: The triaxial and hollow cylinder tests give the higher magni­

tudes of shear moduli when compared to the simple shear tests.

The damping ratios as a function of the number of cycles are shown

in Fig. 23. The simple shear constant force test is once more at the

bottom of the set of curves.

CONCLUSIONS

The analysis of the states of stress in the most popular testing

devices in soil mechanics has shown that the boundary conditions affect

the stress distribution in a very pronounced way. The extensive testing

program conducted on both clay and sand soils supports this analysis.

The standard triaxial test is still the favorite when it comes to static

or dynamic testing in axial extension or compression; but extrapolations

made to simulate shearing conditions leave a lot to be desired.

The simple shear test originally conceived to simulate soil condi-

tions during landslides and earthquakes underestimates the soil proper-

ties by very substantial amounts. The strength, the dynamic and static

shear moduli, the damping ratios it yields are consistently a small

fraction of their true values as measured in the thin long hollow

cylinder. This test underpredicts every parameter it is supposed to

measure. The contention that the drop of the vertical stress is a so

called constant volume test is equal to the increase in porewater

pressure in an undrained test has absolutely nothing to support it either

theoretically or, as shown in this study, experimentally. The volume

in this constant volume test is not constant at all and the reinforced

membrane has substantial flexibility. Using a standard membrane and

placing the device in a cell does not result in any improvement. since,/

as shown by the finite element analysis the sample in general does not

see the applied latteral stresses beyond a thin skin. No calibration

constant could be found to justify the continued use of this device in

27

28

research or commercial laboratories to study either static or dynamic

problems. As stated by Saada and Townsend (20) its proper place is

in the hands of designers who have calibrated their thinking in terms

of the results of those tests and have successfully applied those re­

sults in their practice.

In the thin long hollow cylinder the natural cross anisotropy is

maintained and shearing stresses can be applied to horizontal planes

without resulting in the kind of stress concentrations and noninformities

present in the simple shear device. It does require a special cell

which)although not as simple as that of the standard triaxial test,is

much simpler than the ones required for prismatic elements.

Making a hollow cylinder of sand is not more complicated than

making a solid cylinder, once the cell is made. Any clay that can be

cut with a piano wire can provide a hollow cylindrical specimen. It

is obvious that many natural clays cannot be easily trimmed; but the

same critisim holds when one is trying to prepare a standard triaxial

specimen. The thinner the specimen the closer to uniform are the

shearing stresses and strains.

In conclusion it is felt that the thin long hollow cylinder with

the same inner and outer pressues and subjected to axial and torsional

stresses is the most reliabile and most versatile tool available today

to test soil. Phenomena of cyclic mobility and liquefaction can be

studied with it far more accurately than any laboratory tool of its kind.

It is recommended that it be adopted for standard laboratory investi­

gations of earthquake related problems.

REFERENCES

1. Balla, A., "Stress Conditions in Triaxial Compression", Journalof the Soil Mechanics and Foundation Division, ASCE, Vol. 86,No. SM6, Dec., 1960.

2. Bishop, A.W., Green, G.E., Garga, V.K. and Brown, J.D., "A NewRing Shear Apparatus and its Application To the Measurement ofResidual Strength", Geotechnique, Vol. 21, No.4, pp. 273-328, 1971.

3. Bjerrum, L. and Landva, A., "Direct Simple-Shear Tests on a NorwegianQuick-Clay", Geotechnique, Vol. XVI, No.1, 1966, pp. 1-20.

4. DeNatale, J.S., Shen, C.K., Herrmann, L.R. and Vrymoed, J.L.,"Analysis of Stress Distribution in Torsional Shear Testing", Pro­ceedings of the International Conference on Recent Advances inGeotechnical Earthquake Engineering and Soil Dynamics Vol. 1, pp.145-148, St. Louis, Missouri, 1981.

5. Durham, G.N. and Townsend, F.C., "Effect of Relative Density on theLiquefaction Susceptibility of a Fine Sand Under Controlled-StressLoading", Evaluation of Relative Density and its Role in Geotechni­cal Projects Involving Cohesionless Soils, ASTM, STP523, pp. 319-331,1973.

6. Fries, G., "Strength Characteristics of Clays Tested in DifferentLaboratory Devices", Thesis submitted to the faculty of Case WesternReserve University in partial fulfillment of the degree of Master ofScience in Civil Engineering, 1981.

7. Ker, C.C., "Strength Characteristics of Sands Tested in DifferentLaboratory Devices", Thesis submitted to the faculty of Case WesternReserve University in partial fulfillment of the degree of Master ofScience in Civil Engineering, 1982.

8. Ladd, C.C. and Edgers, L., "Consolidated-Undrained Direct-SimpleShear Tests on Saturated Clays", Massachusetts Insitute of Technology,Research Report No. 72-82, Soils Publication 284, July, 1972.

9. Lade, P.V., "Torsion Shear Apparatus for Soil Testing", LaboratoryShear Strength of Soil, ASTM, STP 740, pp. 145-163, 1981.

10. Lee, K.L., "Fundamental Considerations for Cyclic Triaxial Tests onSaturated Sand", BOSS 76, Behavior of Offshore Structure, The NorwegianInstitute of Technology, pp. 1-19, 1976.

11. Moore, W.M., "Effect of Variations in Poisson's Ratio on Soil TriaxialTesting", Highway Research Record No. 108, pp. 19-25, 1965.

29

30

12. Norris, G.M., "Effect of End Membrane Thickness on the Strenghtof Frictionless Cap and Base Tests", Laboratory Shear Strengthof Soil, ASTM, STP 740, pp. 303-314, 1981.

13. Prevost, J.B. and Boeg, K., "Reanalysis of Simple Shear SoilTesting", Canadian Geotechnical Journal, Vol. 13, No.4, 1976,pp. 418-429.

14. Park, T.K. and Silver, M.L., Dynamic Triaxial and Simple ShearBehavior of Sand", Journal of the Soil Mechanics and FoundationsDivision, ASCE, Vol. 101, No. GT6, pp. 513-529, June, 1975.

15. Pyke, R.M., "Settlement and Liquefaction of Sands Under Multidirec­tional Loading, Thesis, University of California, 1973.

16. Roscoe, K.B., "An Apparatus for the Application of Simple Shear toSoil Samples", Proceedings, Third International Conference on SoilMechanics and Foundation Engineering, Vol. 1, pp. 186-191, Zurich,1953.

17. Rowe, P.W. and Barden, L., "Importance of Free Ends in TriaxialTestings", Journal of the Soil Mechanics and Foundations Division,ASCE, Vol. 90, No. SMl, pp. 1-27, 1964.

18. Radhakrishman, N., "Analysis of Stress and Strain Distributionsin Triaxial Tests Using the Method of Finite Elements", TechnicalReport S-73-4, U.S. Army Engineer Waterways Experiment Station,Vicksburg, Mississippi, 1973.

19. Saada, A.S., "One Dimensional Consolidation in Triaxial Cell",Journal of the Soil Mechanics and Foundations Division, ASCE,Vol. 96, No. SM3, May, 1970.

20. Saada, A.S. and Townsend, F.C., "State of the Art: LaboratoryStrength Testing of Soils", Laboratory Shear Strength of Soil,ASTM, STP740, pp. 7-77, 1981.

21. Saada, A.S. and Shook, L.P., "The Behavior of Clays Subjected toSlow Cyclic Loading", Proceedings of the International Conferenceon Recent Advances in Geotechnical Earthquake Engineering and SoilDynamics, Vol. 1, pp. 369-376, St.Louis, Missouri, 1981.

22. Saada, A.S., A Discussion on the "Strength of Soils", Proceedingsof the International Conference on Recent Advances in GeotechnicalEarthquake Engineering and Soil Dynamics, Vol. 3, pp. 911-913,St. Louis, Missouri, 1981

31

23. Seed, H.B. and Peacock, W.H., "Test Procedures for Measuring SoilLiquefaction Characteristics, "Journal of the Soil Mechanics andFoundation Division, ASCE, Vol. 97, No. SM8, pp. 1099-1119, August,1971.

24. Thiers, G.R. and Seed, H.B., "Strength and Stress-Strain Charac­teristics of Clays Subjected to Seismic Loading Conditions", ASTM,STP450, pp. 3-56, 1969.

25. Wright, D.K., Gilbert, P.A., Saada, A.S., "Shear Devices for Deter­mining Dynamic Soil Properties", Proceedings of the GeotechnicalEngineering Division Specialty Conference on Earthquake Engineeringand Soil Dynamics, ASCE, Pasadena, pp. 1056-1075, June, 1978.

!.=oa

0.6

1.0

0.2

1.2

0.4

5

4-

,-~\'- 0.8'I

. ~

.

X

;z:

~-><--

--2a~/.36~

tJ.l

~

, .00.5o-0.5o ' ! ! ! ;

-, .0

xa

Figure 1. Shear Stress Distribution in the Roscoe Simple Shear Device.

1.00.'5a

~.--~' ............. z~ " ........... £R=O.90

\" 1:.. - """'-' •.\ '-LR-O.60

", ~ ~ .---

-0.'5

FINITEELEMENT

1.4

1.2

I .0

0.8

>- 0.6~l~

0.4

0.2

0-1.0

x

'(

..

a... 1/ '1>

'00')7

/'" I ....'" .9~ ~.6

L t= l·~

~

\~

xR

Figure 2. Shear Stress Distribution in the NGI Device.

11 q;v11 ~v H/D-1/3 H/D-1/32 2 0.499 184.3001 0.499 184.3176 0; . 30 psi 0.45 135.9994 C; • 30 psi2 0.45 135.9994 0.25 81. 9463 0.25 81.946 0.10 70.62034 0.10 70.6203

00 · 1 .2 .3 .4 .5 .6 .7 .8 .9 00 . 1 .2 .3 .4 .5 .6 .7 .8 .9I"/R I"/R

2 11 ~v H/D=1/3 2 IJ ~v H/D=1/30.499 184.3176 OJ = 30 psi

0.499 184.300 OJ • 30 psi

0.45 135.9994 0.45 135.99940.25 81.946 0.25 81. 9460.10 70.6203 0.10 70.6203

.. ..I 4 I

c1r-1c1av

• 1 .2 .3 .4 .5I"/R

.6 .7 .8 .9 • 1 .2 .3 .4 .5I"/R

.6 .7 .8 .9

2 lJ 6...... H/D=1/32 IJ C{.V H/D=1/3

0.499 184.3176 0; • 30 psi0.499 184.3176 0; . 30 psi

0.45 135.9994 0.45 135.99940.25 81. 946 0.25 Hl. 9460.10 70.6203 0.10 70.6203

::: :~ :~: 0;.~1 -1

dv ~v

3 • ....• 3

.00

· 1 .2 .3 .4 .5 .6 .7 .8 .9 00 . 1 .2 .3 .4 .5 .6 .7 .8 .9I"/R

I"/R

TOP .6 11 ~vH/D=1/3 CENTER

.5 0.499 184.3176 "3 • 30 psi0.45 135.99940.25 81.946

.4 0.10 70.6203

.3

.2Trz • 1~v

11'-

-. 1-.2-.3

-.40 • 1 .2 .3 .4 .5 .6 .7 .8 .9

r/R

Figure 3. Results of Finite Elements Analysis for Different \).

~4-<.-" !

•

•

oC I 19

I.. ~

Ij

•

\.l-. I

Figure 4. Controlled-Stress Pneumatic Analog Computer SPAC.

35

Figure 5. Controlled Deformations Pneumatic Analog Computer SPAC.

36

100

80

...Q) 60c:

c:Q)()...Q)

a.. 40

20

o

Gravel Sand Fines

Coarse to Fine Silt Claymedium

U.S. standard sieve sizesI I

0 f3 8 ~.!: '<t ~ Sf ~

'<t ci ci ci ci ci ci..... zC') z z z z ZI I I I

f1~

I1I I !I

"I

I II11\ I 'I

I II I I

I I I II

I! I II I I II 1 1 I 11I I ! I I!I I I I II I I I II II

II II

I Ii 1 I II I I I

III I I I IiI I I I II I I ! III [l 1

I III Ii I III I 1\1I I I

~I

I I! I !IiI I I I 1

0 <0 ~:;r~

O>~ '<t (; lI'l

8~ ": :!o r-- 8co '<t 0 c:i'<t c:i c:i c:i c:i c:i c:i

Grain diameter, mm

Figure 6. Granulometric Distribution of Reid Bedford Sand.

37

gci

..,8ci

oci

Gravel Sand Fines

Coarse to Fine Silt Claymedium

U.S. standard sieve sizesI I

= 0 ~ 0 ~ 008 &'Ot ..... ,.., ..,.,<.0 .....'Ot 0 0 0 .. o 0 <:> 0 0M z z z z z Z. 2.% Z

J. I t[T '"

-, III I r-.. I !I II II I III d I I!1 I I \

1"I,! II I I I

I I T III I I \ I I!I I I \ I II I I I II II

II I

I d I \t II I

~II

I I I I!I I I I II !I I I II 11 I1 I I

I 1\I II I I I I

~'"I ,! I I I! ,.......I

0 I T I

20

80

100

...Q) 60c--cQ)o...Q)

a. 40

Grain diameter, mm

Figure 7. Granulometric Distribution of Latin Sand

3d"

21

1 (or 0)

1max

YmaxI

1

II

1 . Im1.nI I

I

-'J'k"'------- 2y ----------'1.'\,..-

y (or E)

1 - 1max min

1 =2

1 - 1

Gmax min 1-

Y - Y Ymax - Y Ymax min minY 2

(4n) (~ 1Y)

Where lI'0

6'0(4n)(~ Gy2) = Specific Damping Ratio

Total Energy Lost per Unit Volume,and represented by the Area of theHysteresis Loop.

Figure 8. Hysteresis Loop and Definitions of Specific DampingRatio (A) and Secant Modulus (G).

~.~

L LQ rrJE' OJo .C

U (J)___. 06 1 I

OJC CC11 0 . g

23

------lI

JHC(CFl--

0: )

---1 _i.0

Sh e a l' S t r ad n

(48-18) STATIC .- HOLLOH CYLINfJLR

STRNDRR.D TRIRXIAL , 8- SIMPLE SHEAR.

• HC (C)~__ z-< . -~_- . ST(C)

~ ~",S(CL)ti

· 1

.2

.5

· 3

· 7

.8

.G

0-(!)

s.-o

rn rOJ ---"

"TI11l

(!)

-{.I' ~c: L

\.:)

o +JI tJl

(!)

(1ill +JL

L+J OJ(fj>

'I-\1-

'+- '+-W W'. "-(1 C1

(!)C1

QJ OJ

LL

+J +JUJ (Jj

LL

I" "QJ a)-t;..c(Jj) (fJ

Figure 9. Normalized Shear Stress vs. Shear StrainCurves from Ko-consolidated Clay, (48-18) series

------_.--,

2.00 rc-----

5

d

<f:3I,I

._----~

-~~-=::-=:-.-

z

Shea,- Strai.n c-n

(48-18) S"fRTIC- HOLLOW CYL..INDt.R

STANDARD TRIRXIAL . ~ SIMPLE SH~RR

II

Sv ,_. ; Iljl 1

(3

100

~L

L roQ.. vE ...c() lf)

U'-' 00

(lJ c::c 0(Ij .-- (JlQ r...

0-ן"

m .....QJ

-0VIIf)Q!

'" (lJ

LC

+'I a (J1-+-(I')

"l +'QJI LL.

<1J~ >(fl

" q-'+ 4-4- i..JLJ """-au (')0 'L:L

L'- irJttl

II)V'...c~U1(fI

Figure 10_ Normalized Shear Modulus vs. Shear Strainfrom Ko-consolidated Clay, (48-18) series

(48-18) STATIC SIMPLE SHEAR

2010

Vl....

VV

V

V/

VI

/ -pp

j -~ I--D

D

10

20

30

40

50

~

~.::

e ..o atL c:o •

io...J

• •a.. ••

• La. ..II)

c:- ...e ~• •II>eL •o ...c: ...

1"41&1

....• •c: c:88

Shear S~rafn (~)

(18-18) STATIC TORSION HOLLOW CYLINDER

2010

V J....-~

~~

~~--- I--'

l.-- t---I--

/,..."....

./

V".,.,

//

/

It ~~

V ~II>

oo

10

20

40

30

50

• •a.. ••• La.. ..(J)

c:- ...e L• •II>•L •0 ...c: ...

1"41&1

· .....• •c: c:88.., ..,

....~.::·..o at~ c:o •io...J

c:- ~...Q.(J)o a..~ ..,

Q..

Shea,. S~rafn (~)

Figure 11. Comparison of the Increase in Pore Pressure to the Drop inEffective Vertical Stress in Simple Shear and Hollow Cylin­der Tests. (1 psi = 6.9 Kpa)

(48-18) DYN8MICSTANDARD TRIRXIRL

,.

12000

11000

10000

;::; 9000(J)n. 8000....,

~7000

~ I:; 6000~

"00 50130L:

L 40001lJ0

.c. 3000Ul

2000

1000

00 1 2

HOLLOW CYL!NDER~ SIMPLE SHEAR

SS(CL)

3 i:l 5

Shear Stra1n (~) PEAK-TO-PEAK

Figure 12. Shear Modulus Corresponding to 10th Cycle vs. Shear StrainKo-consolidated Clay, (48-18) series. (1 psi = 6.9 Kpa)

~

(48-19) DYNAMICSTANDARD TRIRXIAL ,

HOLLOW CYLINDER •&. SIMPLE SHE~R

30. •

"I !P>'

'......., 20

ST(AX),

0 I.... / I.LV,v.L}.. ~

III

•

...J:. I':..-4:: c-Q..E 10III

Q

54321oI. I

o

She ar St r a' n 00 PEAK-TO-PEAK

Figure 13. Specific Damping Ratio (10th Cycle) vs. Shear StrainKo-conso1idated Clay, (48-18) series.

(48'-18) STATIC .- O\/[R-CONSOLIDATED CLAYHOLLOW CYLINDER, STANDARD TRIAXIAL. & SIMPLE SHEAR

5000 r- I

5421

~~~~_'w, __n ~

HC(CL).OCR-ti ST(C) ~SS(~ ~ '" "" .~o I v,",,&.'\.-v V\JI.'-U Uy \ y ..... I 'VY1.),-" ,ll\l \ \/J.,f I • vy,n y ,

o

She at" St r<l i '1 on

Figure 14. Shear Moduli vs. Shear Strain Over­consolidated Clay, OCR = 2.4 and 8. (1 psi = 6.9 Kpa)

,.. ,..L. L.Q."E aoocUUl\J

aalSc., c 1-0Q.-

" .9• L.moa .... • 8"t7\J

In " .7V'"a.Sl 1/c L. 7

O~

Ul

~ " .5" .",-."

.,~

L. L.+' a .4Ul>

.3ct-ct-ct-ct-a a .2

"" "" " • 1a aL. L.+'~ 0UlUl 0L. L.., .,a I).s:oC(n (n

(0.5-30) STATIC - HOLLOW CYLINDERSTANDARD TRIAXIAL & SIMPLE SHEAR

LegendNO. TYPE

1- HC(CF)2. HC(CL)3. ST(HY)

5 l~.• ST(Ko)

4- 5. SS(CF)

~

46. SS(CL)

7 7. . HC (C)2

10

SHEAR STRAIN (Y.)

Figure 15. Normalized Stress-Strain Curves for Various Devices.:

20

(0.5-30) STATIC - HOLLOW CYLINDERSTANDARD TRIAXIAL & SIMPLE SHEAR

20

6

10

8000

,....... 7000~Q...

'-' 6000tn:3 5000:::J~

~ ~ 4000

-....J~ 3000a:

~2000~~ ---- 31000 .5- ~ 7

1

SHEAR STRAIN (~)

Figure 16. Shear Moud1i for Various Devices. (lpsi = 6.9 Kpa)

(0.5-30) STATIC - HOLLOW CYLINDER

1098765

PP HC(CF)

4

HC(CL)

321

13 ....<? I I I I tit I I I

113

-213

-113

-313 ..o

c-,...-0. ~l

o Q.~ .....

(:I

olS ,..."'.cGl+OII en"- t:o III

Lt..-J

· ·........Co' Ii)C Co 0

r-.. UU""'t- ..... 'V

~ CIl

• (IIa. QJ· "-0.+0If)

c:- ·+'G) ...III G)Ill>III... ·O~

Ct+-..... W

SHEAR STRAIN (%)

Figure 17. Comparison of the Increase in Pore Pressure to the Drop ofEffective Vertical Stress in the Hollow Cylinder Tests.

(0.5-30) STATIC - SIMPLE SHEAR

e~""-o.~

00. 10L. ......

Cl SIoc'S 8""",I;;:.I) .... 7omL. e 6a mu...-l

5· ·........ 4~ ~

e e 3a a-\:. uu

'-J '-J 2~

~· ~ 1Q..m· "-n. .... 0(/)

c: -1·.... -2I) L.

" m«1> -3I)L. · -40 ....e ....HW -5

0 1 2 3 4 5

SS(CL)

6 7 8 9 10 11 12 13 14 15

SHEAR STRAIN (Yo)

Figure 18. Comparison of the Increase in Pore Pressure to the Drop ofEffective Vertical Stress in the Simple Shear Device.

(0.5-30) STATIC - HOLLOW CYLINDER & SIMPLE SHEAR

\r,~

.12112

.12111

.01

.I2II21S

.12108

.01217lSI'oJ

> .1211216"-,..H .12105'oJ

"'0.1211214>

.1211213

.1211212

.01211

121

l12I 1 2 3 4 5 s 7 8 9 1121

SHEAR STRAIN (%)

Figure 19. Volume Changes in the So Called "Constant Volume" Tests.

(0.5-30) DYNAMIC - HOLLOW CYLINDERSTRNDARD TRIRXIAL & SIMPLE SHEAR

5

5

4

LegendNO. TYPE

l. HC (cF)2. HC(CL)3. ST(HY)4. ST(Ko)5. SS(CF)6. SS(CL)

632

~~_ 9.1

12000 r73

\11000 ' ,

,..., 10000-II) 90000..-.J

(f) 8000:J...J 7000:Jr::l

~0 6000E-- 0:: 5000a:w 4000:r:(J1

3000

2000

1000

00

SHERR STRAIN (Yo) peak to peak

Figure 20. Dynamic Shear Moduli at the 10th Cycle forVarious Devices. (1 psi = 6.9 Kpa)

(0.5-30) DYNAMIC - HOLLOW CYLINDERSTANDARD TRIAXIAL & SIMPLE SHEAR

Legend

v,~

"~...,o....t­a:0:

CJZ....~a:~

40

30

20

10

1 2 3

1

NO. TYPE1. HC(CF)2. HC(CL)3. ST(HY)4. ST(Ko)5. SS(CF)6. SS(CL)

5

4 5

SHEAR STRAIN (%) peak ~o peak

Figure 21. Damping Ratio for Various Devices.

LATIN SAND (1-6.1) ~ (0.5-9.1) DYNAMIC - HOLLOW CYLINDERLegendSTANDARD TRIAXIAL ~ SIMPLE SHEAR

NO. TYPE

l. HC (cF) 1).1

Y 0.15% 2. HC (eL) 9.15

20012l 3. ST(HY)6.14. ST(Ko)9.155. SS(CF)9.15

~6. SS(CL)9.157. SS(cF)6.1-

~-:SS(CL)6.161 8.

0.. :~

2til

3 :~-l 4~00 10001:

Q!: 6et

8~til

1

01 I I I I ! I I I I I

0 10 2~ 30 413 50 60 70 80 90 100

NO. OF CYCU:S

LATIN SAND (1-5.1) ~ (8.5-S.1) DYNAMIC - HOLLOW CYLINDERSTANDARD TRIAXIRL ~ SIMPLE SHEAR

2

1200

1100

11300-~ 90130......,

Ul 800:J-l 7130::J00 600L

Q: 500a:w 400J:Ul

300

2013

100

00

s

NO. OF CYCLES

y 0.34%

• 8 •

Figure 22. Variation of the Shear Moduli With the Number of Cyclesfor Controlled Strain Tests. (1 psi ~ 6.9 Kpa)

53

LATIN SAND (1-6.1) & (13.5-9.1) DYNAMIC - HOLLOH CYLINDERSTANDARD TRIAXIAL & SIMPLE SHEAR

•

y = 0.15%313 \

2.~_:=__-=._~_~.---tR~-4 .~ • •

oHt­o:IX

~HIl.:f:0:Q

._------------

l-__-L--~~---.ll---..ll---l::!__~!~--'!'=_-__:_:..I::_-_::::.':---::,1Be 113 213 30 0+13 sa 60 713 80 913 11313

NO. OF CYCLES

LATIN SAND (1-6.1) & (13.5-9.1) DYNAMIC - HOLLOW CYLINDERSTANDARD TRIAXIAL & SIMPLE SHEAR

y = 0.34%

o....t­o:It:

ClZ....Il.:f:0:Q 10

7~

• •5

a I I I Ia 40 513 613 79 80 S0 109

NO. Of CYCLES

Figure 23. Variation of the Damping Ratios With the Number ofCycles for Controlled Strain Tests.

APPENDIX I

Elastic finite elements analysis of

the stresses induced in a cylinder

subjected to axial deformation and

lateral pressures.

55

A linear elastic finite element analysis was made to investigate

themagnitudeof the stresses generated in short circular cylinders

subjected to axial displacement with rigid end platens and lateral

stress; no slippage being allowed between the specimens and the platens.

The use of a fine grid helped bring out the stress concentrations at

the edges (Fig. Al). Four Poisson ratios namely 0.499, 0.45, 0.25 and

0.1 were used, as well as lateral pressures of 0, 20, and 30 psi

(10, 137.9, 206.8 Kpa). For a Poisson ratio of 0.45 and no lateral

stress, the problem was solved for height to diameter ratios HID of

.167, 1/3, 1/2, 1 and 2. This last step was taken to compare the re­

sults of this study with published results (1, 11, 18) as well as to

extend such results to smaller height to diameter ratios. The results

have been normalized with respect to the average vertical stress 0av

which is the total axial force divided by the area. Young's modulus

was chosen to be 2844 psi (19609 Kpa) and the average axial strain 2.38

percent. Under such conditions "if the ends are perfectly smooth and

do not have any effect on the sample" the average stress should be

67.55 psi (465.73 Kpa). This indeed is not the case and this average

stress varies with both HID and Poisson's ratio, it is written on each

of the figures so that the actual magnitudes of the elastic stresses

can be computed.

Figure A2 shows the distribution of Oz at the top and the middle

section of an unconfined specimen for a Poisson ratio of 0.45 and five

different HID ratios. The curves related to HID equal to 2 and 1 at

SG

azthe top of the sample are characterized by a ratio aav

along 70 percent of the radius followed by high stress

close to unity

concentration

along the edges. This is in line with previously published results.

However, as HID decreases the stresses increase substantially in the

central part then vary as shown in the figure. Notice that the proximty

of the curves may be misleading since each ordinate has to be multi-

plied by a different a to obtain a .av z

Figures A3 and A4 show the distributions of a , a , 0 8 and Lz r rz

for the same HID = ~ which relates to the NGI size of specimen, and

values of 0 3 equal to 0 and 20 psi (137.9 Kpa). Each figure shows four

different Poisson ratios. The common features of all these figures are

1that at a ratio HID = 3' the pressure distribution as well as the average

vertical stress are highly dependent on Poisson's ratio and vary very

substantially as one moves along the radius as well as across the thick-

ness of the sample. The values of or and 0 8 , for the higher values of

Poisson's ratio, have very little resemblance to the laterally applied

stress; in other words, except for a thin outer shell, the sample is

very highly affected by the friction of the platens. The value of Trz

is, of course, equal to zero on the middle section, but against the

platens it reaches values that can be higher than the applied shearing

stresses during a shear test; in addition, depending on the lateral

stresses and Poisson's ratio it can take positive or negative values.

The analysis above shows that it is practically impossible to

talk about some average representative value of the state of stress

57

within the simple shear device. The combination of a shearing force

and the normal displacement studied above results in a very strongly

nonuniform distribution of stress and strain in the sample. Normali­

zation of test results appears to be an exercise in forced curve fitting.

\.l1(',- .......}

,----(------; - I

~ :: ~0: L._______ cf. psi

3 777777 7777 77 7/777777777/ 3

Diameter= D = 2R = 3.16 inInitial Height= H 2

~ E= 2844 psi (200 kg/em) »

I E= 2.4%

I

_,-1 211f- 1 r,nUTOP SECTION

2 LV

4221 40

3t---+_-+_-+--+--+--+--+--4--4-~-+-+-+--l--+--+--I--I--+---J '-;3'J

B/2 4141---j----t--t---t---t---t--+--1--+--l--l-+--+-HH-+-+---W

68I 34

5 61 80

t105

~ 81 gP r~IDDLE SECTION

1('-'i 1.26 <t.

,~ R .,

~

Figure AI. Finite Element Grid for Simple Shear Device

TOP

2

OJ = 0 psi

HID1 .1672 1/33 1/24 15 2

~v161. 7775115.9147

93.520878.218672.9414

324

~I

Figure A2. Distribution of Vertical Stresses In An Unconfined Condition.

60

C1<iV'154.3539115.914776.123868.3262

1/1 0.4992 0.453 0.254 0.10

4

2H/D-l/3C'J • 0 psi

C>UV154.3646115.9147

76.123868.3262

V0.4990.450.250.10

2

_3

_4

00 • 1 .2 .3 .4 .5 .6 .7 .B .913

0 • 1 .2 .5 .6 .7 .8 .9r/R r/R

2 1/ ~H/D=1/3 2 H/D"l/31/ ~

0.499 154.3646OJ • 0 psi

0.499 154.3646 "3 . 0 psi

0.45 115.9147 0.45 115.91470.25 76.1238 0.25 76.12380.10 68.3262 0.10 68.3262

=:: :~

c

~1 C>e 1dv C>dV

-••• --13

0 . 1 .2 .3 .4 .5 .6 .7 .B .9 °13 . 1 .2 .3 .4 .5 .6 .7 .B .<J -1r/R r/R

TOP CENTER

.6 1/ C>eW H/D-l/3

.5 1 0.499 154.3646 ~ • 0 psi

2 0.45 115.91473 0.25 76.1238

.4 4 0.10 68.3262

.3

.21rzC1' .1dv

13

-. 1

-.2

-.3

-.413 . 1 .2 .3 .4 .5 .6 .7 '.8 • S

r/R

00 • 1 .2 .3 .4 .5 .6 .7 .B .913

13 . 1 .4 .5 .6 .7 .8 .9

r/R r/R

V C>d\( H/D-l/3 2 V 0,;10' H/D-l/32

0.499 154.3646 OJ • 0 psi 0.499 154.3646 ~ • 0 psi

0.45 115.91470.25 76.1238

0.45 115.9147

0.10 68.32620.25 76.12380.10 68.3262

C>r C>r

d 1 -1

dv~v

dV

Figure A3. Results of Finite Element Analysis for Different V.

H/D=1/3C'j ° 20 psi

v 0CIV2 0.499 174.3359

Ir

0.45 12Q.2673 0.25 79.5674 0.10 69.9361

~, .........--...-::::'-----:~~ j, 4-dV

2V

1 0.4992 0.453 0.254 0.10

~v174.3256129.267

79.56769.9361

H/D=I/3OJ • 20 psi

""0 .2 .3 .4 .5 .6 .7 .8 .900 .5 .6 .7 .8 .9 . 1. 1 .2 .3 .4

r/Rr/R

H/D=1/3 2 II ~vH/D=1/3

2 J) q;v c.3 = 20 psi 1 0.499 174.3359OJ =20 psi

1 0.499 174.3359 2 0.45 129.2672 0.45 129.267 3 0.25 79.5673 0.25 79.567 4 0.10 69.93614 0.10 69.9361

~ ~ ~ :c5

~:6,-1

~ ~ ~ ~;1 ~v

;~~!<IV

•• •• • 3. 3 •.~4, ,

1 °0 .3 .4 .5 .6 .7 .8 .9°0 .5 .6 .7 .8 .9 . 1 .2• 1 .2 .3 .4r/Rr/R

2 J) cr.v H/D= 1/3 Eo 2844 psi

2 J)H/D= 1/3 Eo 2844 psi

1 0.499 174.3359 0; = 20 psi cr.v OJ = 20 psi2 0.45 129.267 0.499 174.32563 0.25 79.567 0.45 129.2674 0.10 69.9361 0.25 79.567

0.10 69.9361

~ :: ::5" :~0;.

Ci 1 --0:- 1,>I,~

• 3 • • • •• ....3..40

0 00

1 2• 1 .2 .3 .4 .5 .6 .7 .8 .9 . 1 .2 .3 .4 .5 .6 .7 .8 .9 'Ir/R

r/R

CENTER

.9.8.7.6.5r/R

.4.3

v ~v H/D=1/30.499 174.3359 OJ = 20 psi0.45 129.2670.25 79.5670.10 69.9361

.2• 1

.6

.5

.4

.3

.2r,.z 1

d • t~~;.l;;;~~=:'l'=::=:E=!:~=~~~~~~.av 0

-. 1

-.2

-.3

-.40

TOP

Figure A4. Results of Finite Element Analysis for Different v.