Chapter 13-Shear Strength

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    CHAPTER 13

    SHEAR STRENGTH OFSOIL

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    Shear Strength

    The shear strength of the soil is the internal resistance perunit area that the soil mass can offer to resistfailing/failure and sliding along any plane inside it.

    Mohr (1900) presented a theory saying that rupture (orfailure) in material is because of a critical combination of

    normal stress and shearing stress and not from eithermax. normal or shear stress alone.

    For most soil mechanics problems, it is sufficient toapproximate the shear stress on the failure plane as linearfunction of the normal stress (Coulomb, 1776). This linearfunction is :

    )('tan''

    tan

    stresseffectiveoftermsincor

    c

    f

    f

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    Factors That Affect The ShearStrength of Soil

    Cohesionless soil

    1. Soil type

    2. Soil density

    3. Grain size distribution

    4. Mineral type, angularity and particle size

    5. Deposit variability-because of variations insoil types, particle arrangements etc., theeffective friction angle is rarely uniform withdepth.

    6. Etc.

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    Factors That Affect The ShearStrength of Soil

    Cohesive soil

    1. Soil type the more plastic the soil (higherPI), the lower the values of c and .

    2. Particle Bonding

    3. Stress history

    4. Peak and ultimate shear strength

    5. Etc.-such as sample disturbance, strainrate, anisotropy etc.

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    Shear Strength

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    Inclination of The Plane of FailureCaused by Shear

    As stated by the Mohr-Coulomb failure criterion, failure fromshear will occur when the shear stress on a plane reaches a valuegiven by:

    'tan'' cf

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    Inclination of The Plane of FailureCaused by Shear

    From Figures 11.2 and 11.3, angle bad = 2 = 90+

    or

    and

    2

    '45

    2

    '

    45tan'22

    '

    45tan''

    2

    '45tan

    'sin1

    'sin1

    2

    31

    2

    cGeneralformula

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    Drained and Undrained Conditions

    The drained condition exists when the rate ofloading is slow compared to the rate ofdrainage. Thus, water is able to easily flow into

    or out of the voids and essentially no excesspore water pressures develop in the soil.

    The undrained condition exists when the rateof loading is rapid compared to the rate ofdrainage. Thus, water is not able to flow into orout of the voids quickly enough, and excesspore water pressures develop in the soil.

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    Laboratory Tests For Detemination ofShear Strength Parameters

    We do tests to get shear strength parameterssuch as c, , c, , etc. There are several testsconducted in the laboratory.

    1. Direct shear test

    2. Triaxial test

    3. Unconfined compression test

    4. Vane shear test

    5. etc.

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    Direct Shear Test

    Size of specimen is 100mm X 100mm

    Can be either stress or strain controlled

    Normal stress of specimen max. is approximately 1050 kN/m2

    Resisting shear force of the soil corresponding to any sheardisplacement can be measured by a horizontal proving ring or load

    cell.

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    Direct Shear Test

    In the direct shear test arrangement, the shearbox that contains the soil specimen is generallykept inside a container that can be filled with

    water to saturate the specimen. A drained test is made on a saturated soil

    specimen by keeping the rate of loading slowenough so that the excess pore water pressuregenerated in the soils is dissipated completelyby drainage.

    Pore water from the specimen is drainedthrough two porous stone.

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    Direct Shear Test

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    Direct Shear Test

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    Direct Shear Test

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    Direct Shear Test

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    Triaxial Test

    In triaxial test, specimen issubjected to a confining pressure(3) by compression of the fluid inchamber.

    To cause shear failure, axial stressis applied through a verticalloading ram. This axial stress issometimes called deviator stress.

    The axial load applied by the

    loading ram corresponding to agiven axial deformation ismeasured by a proving ring orload cell attached to the ram.

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    Triaxial Test

    There are three standard types ofTriaxial Test:

    1. Consolidated-drained test or drained test(CD Test)

    2. Consolidated-undrained test or

    undrained test (CU Test)3. Unconsolidated Undrained test (UU Test)

    C lid t d D i d T t

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    Consolidated-Drained Test(CD)

    Because the pore water pressure developedduring the test is completely dissipated,therefore u=0.

    From 3(Total) = u + 3

    when u=0 3 = 0 + 3

    3 = 3

    Total and effective axial stress at failure

    = 3 + ( d)f= 1 = 1

    f= tan

    Consolidated-drained triaxial test on clayeysoil may take several days to complete. Thistime period is required because deviatorstress must be applied very slowly to ensure

    full drainage. For this reason the CD type isuncommon.

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    Consolidated-Drained Test (CD)

    Loose sand andnormallyconsolidated clay

    Dense sand andover consolidatedclay

    Loose sand andnormallyconsolidated clay

    Dense sand andover consolidatedclay

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    Consolidated-Undrained Test(CU)

    Major principal stress at failure (total): 3(t)+(d)f=1(t)

    Major principal stress at failure (effective): 1(t)-(ud)f= 1

    Minor principal stress at failure (total): 3(t)

    Minor principal stress at failure (effective): 3(t) -(ud)f=3

    Where (ud)f= pore water pressure at failure

    1(t)- 3(t) = 1- 3

    f= tan(cu)

    Consolidated-undrained is the most common type oftriaxial test. Because drainage is not allowed in these testsduring the application of deviator stress, they can beperformed quickly.

    (a)Specimen underchamber confiningpressure

    (b) Deviator stressapplication

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    Consolidated Undrained Test (CU)Loose sand and normallyconsolidated clay

    Dense sand andoverconsolidated clay

    Loose sand andnormally consolidatedclay

    Dense sand andoverconsolidated clay

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    Unconsolidated Undrained Test(UU)

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    Unconsolidated Undrained Test(UU)

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    Discussion on Triaxial Test

    Laboratory test generally is divided into 2 categories.

    1. Shear strength tests based on total stress:

    Also known as undrained shear strength test

    To get undrained shear strength, Su, c, - total stress

    Test type vane shear test, unconfined compression,

    unconsolidated undrained (UU), consolidated undrained (CU) Performed exclusively on plastic (cohesive) soil

    Normally for evaluation of foundation and embankment supportedby cohesive soil

    Analysis for rapid loading or unloading conditions

    Conditions applicable to field situations where change in shear

    stress occurs quickly enough that soft cohesive soil does not havetime to consolidate

    Known as short term analysis

    Will give a bigger value of strength carried out with the same cellpressure in triaxial test.

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    Discussion on Triaxial Test

    2. Shear strength test based on effective stress.

    To get effective strength c, ,etc.

    Referred to as drained shear strength test.

    Test include direct shear test, CD, CU, etc.

    Performed on plastic (cohesive) soil and nonplastic (cohesionless)soil

    Effective shear parameters used for long-term analysis wherecondition are relatively constant.

    Eg. includes long term stability of slopes, embankments, earthsupporting structure, foundation etc.

    Effective shear stress analysis fundamentally models the shearstrength of soil

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    Discussion on Triaxial Test

    Strength tests conducted on samples of a stiffoverconsolidated clay gave lower strengths for CDtests than CU tests because since anoverconsolidated specimen tends to expand duringshear (in undrained condition), the pore waterpressure decreases or even goes negative and thus

    the effective stress is increased.

    Because 3(f) = 3(f)-(-uf)or 1(f) = 1(f)-(-uf)the effective stresses are greater than the totalstress.Thus the undrained strength is greater than thedrained strength, which is opposite to the behavior

    of normally consolidated clay.

    Therefore, in normally consolidated clayShear strength of CD>CUIn CD, soil becomes stiffer due to the reduction ofvolume because (1-3)fcd>(1-3)fcu