CH 7 Shear Strength - جامعة تكريتced.ceng.tu.edu.iq/images/lectures/Soil-Mechanics/CH 7...Shear Strength of Soil College of Eng. Civil Eng. Dept Soil Mechanics Dr. Ahmed

Tikrit University

College of Engineering

Civil engineering Department

Soil Mechanics

3rd ClassLecture notes

Up Copyrights 2016

SHEAR STRENGTH

OF SOIL

Shear Strength of Soil

College of Eng. Civil Eng. Dept Soil Mechanics Dr. Ahmed Al-Obaidi

Shear Strength of Soils

Soils consist of individual particles that can slideand roll relative to one another. Shear strengthof a soil is equal to the maximum value of shearstress that can be mobilized within a soil masswithout failure taking place.

The shear strength of a soil is a function of thestresses applied to it as well as the manner inwhich these stresses are applied. A knowledge ofshear strength of soils is necessary to determinethe bearing capacity of foundations, the lateralpressure exerted on retaining walls, and thestability of slopes.

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Mohr Circle of Stresses

In soil testing, cylindrical samples are commonlyused in which radial and axial stresses act onprincipal planes. The vertical plane is usually theminor principal plane whereas the horizontalplane is the major principal plane. The radialstress (sr) is the minor principal stress (s3), andthe axial stress (sa) is the major principal stress(s1).

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College of Eng. Civil Eng. Dept Soil Mechanics Dr. Ahmed Al-Obaidi 4



To visualize the normal and shear stresses acting on anyplane within the soil sample, a graphical representationof stresses called the Mohr circle is obtained by plottingthe principal stresses. The sign convention in theconstruction is to consider compressive stresses aspositive and angles measured counter-clockwise alsopositive.

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Draw a line inclined at angle with the horizontal throughthe pole of the Mohr circle so as to intersect the circle.The coordinates of the point of intersection are thenormal and shear stresses acting on the plane, which isinclined at angle within the soil sample.

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The plane with the maximum ratio of shear stress tonormal stress is inclined at an angle of to the horizontal,where a is the slope of the line tangent to the Mohrcircle and passing through the origin

Mohr-Coulomb Failure Criterion When the soilsample has failed, the shear stress on the failureplane defines the shear strength of the soil. Thus,it is necessary to identify the failure plane. Is itthe plane on which the maximum shear stressacts, or is it the plane where the ratio of shearstress to normal stress is the maximum?

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For the present, it can be assumed that a failure planeexists and it is possible to apply principal stresses andmeasure them in the laboratory by conducting a triaxialtest. Then, the Mohr circle of stress at failure for thesample can be drawn using the known values of theprincipal stresses.

If data from several tests, carried out on different samplesupto failure is available, a series of Mohr circles can beplotted. It is convenient to show only the upper half ofthe Mohr circle. A line tangential to the Mohr circles canbe drawn, and is called the Mohr-Coulomb failureenvelope.

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If the stress condition for any other soil sample isrepresented by a Mohr circle that lies below the failureenvelope, every plane within the sample experiences ashear stress which is smaller than the shear strength ofthe sample. Thus, the point of tangency of the envelopeto the Mohr circle at failure gives a clue to thedetermination of the inclination of the failure plane. Theorientation of the failure plane can be finally determinedby the pole method.

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The Mohr-Coulomb failure criterion can be written as theequation for the line that represents the failureenvelope.The general equation is

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The failure criterion can be expressed in terms of therelationship between the principal stresses. From thegeometry of the Mohr circle,

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Methods of Shear Strength Determination

Direct Shear Test

The test is carried out on a soil sample confined in ametal box of square cross-section which is splithorizontally at mid-height. A small clearance ismaintained between the two halves of the box. The soilis sheared along a predetermined plane by moving thetop half of the box relative to the bottom half. The boxis usually square in plan of size 60 mm x 60 mm. Atypical shear box is shown.

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If the soil sample is fully or partially saturated, perforatedmetal plates and porous stones are placed below andabove the sample to allow free drainage. If the sample isdry, solid metal plates are used. A load normal to theplane of shearing can be applied to the soil samplethrough the lid of the box.

Tests on sands and gravels can be performed quickly, andare usually performed dry as it is found that water doesnot significantly affect the drained strength. For clays,the rate of shearing must be chosen to prevent excesspore pressures building up.

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As a vertical normal load is applied to the sample, shearstress is gradually applied horizontally, by causing thetwo halves of the box to move relative to each other.The shear load is measured together with thecorresponding shear displacement. The change ofthickness of the sample is also measured.

A number of samples of the soil are tested each underdifferent vertical loads and the value of shear stress atfailure is plotted against the normal stress for each test.Provided there is no excess pore water pressure in thesoil, the total and effective stresses will be identical.From the stresses at failure, the failure envelope can beobtained.

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The test has several advantages:

• It is easy to test sands and gravels.

• Large samples can be tested in large shear boxes,as small samples can give misleading results dueto imperfections such as fractures and fissures,or may not be truly representative.

• Samples can be sheared along predeterminedplanes, when the shear strength along fissures orother selected planes are needed.

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The disadvantages of the test include:

• The failure plane is always horizontal in the test, and thismay not be the weakest plane in the sample. Failure ofthe soil occurs progressively from the edges towardsthe centre of the sample.

• There is no provision for measuring pore water pressurein the shear box and so it is not possible to determineeffective stresses from undrained tests.

• The shear box apparatus cannot give reliable undrainedstrengths because it is impossible to prevent localiseddrainage away from the shear plane.

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TriaxialTest

The triaxial test is carried out in a cell on acylindrical soil sample having a length todiameter ratio of 2. The usual sizes are 76 mm x38 mm and 100 mm x 50 mm. Three principalstresses are applied to the soil sample, out ofwhich two are applied water pressure inside theconfining cell and are equal. The third principalstress is applied by a loading ram through thetop of the cell and is different to the other twoprincipal stresses.A typical triaxial cell is shown.

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The soil sample is placed inside a rubber sheath which issealed to a top cap and bottom pedestal by rubber O-rings. For tests with pore pressure measurement,porous discs are placed at the bottom, and sometimesat the top of the specimen. Filter paper drains may beprovided around the outside of the specimen in orderto speed up the consolidation process. Pore pressuregenerated inside the specimen during testing can bemeasured by means of pressure transducers.

The triaxial compression test consists of two stages:

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First stage: In this, a soil sample is set in the triaxialcell and confining pressure is then applied.

Second stage: In this, additional axial stress (alsocalled deviator stress) is applied which inducesshear stresses in the sample. The axial stress iscontinuously increased until the sample fails.

� During both the stages, the applied stresses, axial strain,and pore water pressure or change in sample volumecan be measured.

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TestTypes

There are several test variations, and those usedmostly in practice are:

UU (unconsolidated undrained) test: In this, cell pressure isapplied without allowing drainage. Then keeping cellpressure constant, deviator stress is increased to failurewithout drainage.

CU (consolidated undrained) test: In this, drainage isallowed during cell pressure application. Then withoutallowing further drainage, deviator stress is increasedkeeping cell pressure constant.

CD (consolidated drained) test: This is similar to CU testexcept that as deviator stress is increased, drainage ispermitted. The rate of loading must be slow enough toensure no excess pore water pressure develops.

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In the UU test, if pore water pressure is measured, thetest is designated by . In the CU test, if pore waterpressure is measured in the second stage, the test issymbolized as .

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Significance of Triaxial Testing The first stagesimulates in the laboratory the in-situ conditionthat soil at different depths is subjected todifferent effective stresses. Consolidation willoccur if the pore water pressure which developsupon application of confining pressure is allowedto dissipate. Otherwise the effective stress onthe soil is the confining pressure (or total stress)minus the pore water pressure which exists inthe soil.

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During the shearing process, the soil sample experiencesaxial strain, and either volume change or developmentof pore water pressure occurs. The magnitude of shearstress acting on different planes in the soil sample isdifferent. When at some strain the sample fails, thislimiting shear stress on the failure plane is called theshear strength.

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The triaxial test has many advantages over the direct shear test:

• The soil samples are subjected to uniform stresses and strains.

• Different combinations of confining and axial stresses can be applied.

• Drained and undrained tests can be carried out.

• Pore water pressures can be measured in undrained tests.

• The complete stress-strain behaviour can be determined.

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Total Stress Parameters

� All Mohr circles for UU test plotted in terms of total stresses have the same diameter.

� The failure envelope is a horizontal straight line and hence It can be represented by the equation:

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For tests involving drainage in the first stage, when Mohrcircles are plotted in terms of total stresses, thediameter increases with the confining pressure. Theresulting failure envelope is an inclined line with anintercept on the vertical axis. It is also observed thatcCU ¹ cCD and fCU ¹ fCD

It can be stated that for identical soil samples testedunder different triaxial conditions of UU, CU and CDtests, the failure envelope is not unique.

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Effective Stress Parameters

If the same triaxial test results of UU, CU and CD testsare plotted in terms of effective stresses takinginto consideration the measured pore waterpressures, it is observed that all the Mohr circlesat failure are tangent to the same failureenvelope, indicating that shear strength is aunique function of the effective stress on thefailure plane.

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If is the effective stress acting on the rupture plane atfailure, is the shear stress on the same plane and istherefore the shear strength. The relationship betweenthe effective stresses on the failure plane is

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Pore Water Pressure Parameters

The difference between the total and effective stressesis simply the pore water pressure u. Consequently,the total and effective stress Mohr circles have thesame diameter and are only separated along the s -axis by the magnitude of the pore water pressure.

It is easy to construct a series of total stress MohrCircles but the inferred total stress parameters haveno relevance to actual soil behavior. In principle, theeffective strength parameters are necessary to checkthe stability against failure for any soil constructionin the field. To do this, the pore water pressure in theground under the changed loading conditions mustbe known and in general they are not.

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In an undrained triaxial test with pore pressuremeasurement, this is possible and the effective stressescan then be determined. Alternatively, in drained tests,the loading rate can be made sufficiently slow so as toallow the dissipation of all excess pore water pressure.For low permeability soils, the drainage will requirelonger times.

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In undrained tests, the general expression relating totalpore water pressure developed and changes in appliedstresses for both the stages is:

Du = Du1 + Du2 = B.Ds3+ B.A.(Ds1 - Ds3) = B[Ds3+A(Ds1 - Ds3)]

where Du1 = pore water pressure developed in the firststage during application of confining stress Ds3,

Du2 = pore water pressure developed in the second stageduring application of deviator stress (Ds1 - Ds3), and

B and A are Skempton's pore water pressure parameters.

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Parameter B is a function of the degree of saturation ofthe soil (= 1 for saturated soils, and = 0 for dry soils).Parameter A is also not constant, and it varies withthe over-consolidation ratio of the soil and also withthe magnitude of deviator stress. The value of A atfailure is necessary in plotting the effective stressMohr circles.

Consider the behavior of saturated soil samples inundrained triaxial tests. In the first stage, increasingthe cell pressure without allowing drainage has theeffect of increasing the pore water pressure by thesame amount. Thus, there is no change in theeffective stress. During the second shearing stage, thechange in pore water pressure can be either positiveor negative.

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For UU tests on saturated soils, pore waterpressure is not dissipated in both the stages (i.e.,Du = Du1 + Du2).

For CU tests on saturated soils, pore waterpressure is not dissipated in the second stageonly (i.e., Du = Du2).

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Stress-Strain Behavior of Sands

Sands are usually sheared under drained conditions as they have relatively higher permeability. This behaviourcan be investigated in direct shear or triaxial tests. The two most important parameters governing their behavior are the relative density (ID) and the magnitude of the effective stress (s¢). The relative density is usually defined in percentage as

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where emax and emin are the maximum andminimum void ratios that can be determined fromstandard tests in the laboratory, and e is the currentvoid ratio. This expression can be re-written in termsof dry density as

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where gdmax and gdmin are the maximum andminimum dry densities, and gd is the current drydensity. Sand is generally referred to as dense if ID> 65% and loose if < 35%.

The influence of relative density on the behavior ofsaturated sand can be seen from the plots of CDtests performed at the same effective confiningstress. There would be no induced pore waterpressures existing in the samples.

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For the dense sand sample, the deviator stress reaches a peakat a low value of axial strain and then drops down, whereasfor the loose sand sample, the deviator stress builds upgradually with axial strain. The behaviour of the mediumsample is in between. The following observations can bemade:

• All samples approach the same ultimate conditions of shearstress and void ratio, irrespective of the initial density. Thedenser sample attains higher peak angle of shearingresistance in between.

• Initially dense samples expand or dilate when sheared, andinitially loose samples compress.

Examples

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Documents

CH 7 Shear Strength - جامعة تكريتced.ceng.tu.edu.iq/images/lectures/Soil-Mechanics/CH 7...Shear Strength of Soil College of Eng. Civil Eng. Dept Soil Mechanics Dr. Ahmed