# Shear Strength of Soil

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Shear Strength of SoilsCEL 610 Foundation Engineering

Strength of different materials

Shear failure of soilsSoils generally fail in shearAt failure, shear stress along the failure surface (mobilized shear resistance) reaches the shear strength.

Shear failure of soilsSoils generally fail in shear

Retaining wallShear failure of soilsAt failure, shear stress along the failure surface (mobilized shear resistance) reaches the shear strength.Soils generally fail in shear

Shear failure mechanismThe soil grains slide over each other along the failure surface.No crushing of individual grains.

Shear failure mechanismAt failure, shear stress along the failure surface () reaches the shear strength (f).

Mohr-Coulomb Failure Criterion(in terms of total stresses)f is the maximum shear stress the soil can take without failure, under normal stress of .

Mohr-Coulomb Failure Criterion(in terms of effective stresses)f is the maximum shear stress the soil can take without failure, under normal effective stress of .u = pore water pressure

Mohr-Coulomb Failure CriterionShear strength consists of two components: cohesive and frictional.

c and are measures of shear strength.Higher the values, higher the shear strength.

Mohr Circle of stressResolving forces in s and t directions,

Mohr Circle of stress

Mohr Circle of stress

Mohr Circles & Failure Envelope

Mohr Circles & Failure EnvelopecThe soil element does not fail if the Mohr circle is contained within the envelopeGL

Mohr Circles & Failure EnvelopeYcGL

sOrientation of Failure PlanefFailure envelope

Mohr circles in terms of total & effective stresses=

Failure envelopes in terms of total & effective stresses=If X is on failure

Mohr Coulomb failure criterion with Mohr circle of stress

Mohr Coulomb failure criterion with Mohr circle of stress

Other laboratory tests include,Direct simple shear test, torsional ring shear test, plane strain triaxial test, laboratory vane shear test, laboratory fall cone testDetermination of shear strength parameters of soils (c, f or c, f)

Laboratory testsField conditions

Laboratory testsSimulating field conditions in the laboratoryStep 2Apply the corresponding field stress conditions

Direct shear testSchematic diagram of the direct shear apparatus

Direct shear testPreparation of a sand specimenDirect shear test is most suitable for consolidated drained tests specially on granular soils (e.g.: sand) or stiff clays

Direct shear testPreparation of a sand specimen

Direct shear testTest procedure

Direct shear testStep 2: Lower box is subjected to a horizontal displacement at a constant rate

Direct shear test

Direct shear testAnalysis of test resultsNote: Cross-sectional area of the sample changes with the horizontal displacement

Direct shear tests on sandsStress-strain relationship

Direct shear tests on sandsHow to determine strength parameters c and f

Direct shear tests on sandsSand is cohesionless hence c = 0Direct shear tests are drained and pore water pressures are dissipated, hence u = 0Therefore, f = f and c = c = 0

Direct shear tests on claysFailure envelopes for clay from drained direct shear testsIn case of clay, horizontal displacement should be applied at a very slow rate to allow dissipation of pore water pressure (therefore, one test would take several days to finish)

Interface tests on direct shear apparatusIn many foundation design problems and retaining wall problems, it is required to determine the angle of internal friction between soil and the structural material (concrete, steel or wood)

Triaxial Shear Test

Triaxial Shear TestSpecimen preparation (undisturbed sample)

Triaxial Shear TestSpecimen preparation (undisturbed sample)

Triaxial Shear TestSpecimen preparation (undisturbed sample)

Triaxial Shear TestSpecimen preparation (undisturbed sample)

Types of Triaxial TestsIs the drainage valve open?Is the drainage valve open?

Types of Triaxial Tests

Consolidated- drained test (CD Test)Step 1: At the end of consolidationStep 2: During axial stress increaseStep 3: At failure

Deviator stress (q or Dsd) = s1 s3Consolidated- drained test (CD Test)

Volume change of sample during consolidationConsolidated- drained test (CD Test)

Stress-strain relationship during shearingConsolidated- drained test (CD Test)

CD tests How to determine strength parameters c and f

CD tests Since u = 0 in CD tests, s = sTherefore, c = c and f = f cd and fd are used to denote them

CD tests Failure envelopesFor sand and NC Clay, cd = 0Therefore, one CD test would be sufficient to determine fd of sand or NC clay

CD tests Failure envelopesFor OC Clay, cd 0

Some practical applications of CD analysis for clays t = in situ drained shear strength1. Embankment constructed very slowly, in layers over a soft clay deposit

Some practical applications of CD analysis for clays 2. Earth dam with steady state seepage

Some practical applications of CD analysis for clays 3. Excavation or natural slope in clayt = In situ drained shear strength Note: CD test simulates the long term condition in the field. Thus, cd and fd should be used to evaluate the long term behavior of soils

Consolidated- Undrained test (CU Test)Step 1: At the end of consolidationStep 2: During axial stress increaseStep 3: At failure

Volume change of sample during consolidationConsolidated- Undrained test (CU Test)

Stress-strain relationship during shearingConsolidated- Undrained test (CU Test)

CU tests How to determine strength parameters c and f

CU tests How to determine strength parameters c and ffcuMohr Coulomb failure envelope in terms of total stressesccuEffective stresses at failureuf

CU tests Shear strength parameters in terms of total stresses are ccu and fcuShear strength parameters in terms of effective stresses are c and f

c = cd and f = fd

CU tests Failure envelopesFor sand and NC Clay, ccu and c = 0Therefore, one CU test would be sufficient to determine fcu and f(= fd) of sand or NC clay

Some practical applications of CU analysis for clays t = in situ undrained shear strength1. Embankment constructed rapidly over a soft clay deposit

Some practical applications of CU analysis for clays 2. Rapid drawdown behind an earth damt = Undrained shear strength of clay coreCore

Some practical applications of CU analysis for clays 3. Rapid construction of an embankment on a natural slope Note: Total stress parameters from CU test (ccu and fcu) can be used for stability problems where, Soil have become fully consolidated and are at equilibrium with the existing stress state; Then for some reason additional stresses are applied quickly with no drainage occurring

Unconsolidated- Undrained test (UU Test)Data analysisInitial volume of the sample = A0 H0Volume of the sample during shearing = A HSince the test is conducted under undrained condition,A H = A0 H0A (H0 DH) = A0 H0A (1 DH/H0) = A0

Unconsolidated- Undrained test (UU Test)Step 1: Immediately after sampling=+Step 2: After application of hydrostatic cell pressureDuc = B Ds3Note: If soil is fully saturated, then B = 1 (hence, Duc = Ds3)

Unconsolidated- Undrained test (UU Test)Step 3: During application of axial loadDud = ABDsd=+

Unconsolidated- Undrained test (UU Test)Combining steps 2 and 3,Du = Duc + DudTotal pore water pressure increment at any stage, DuDu = B [Ds3 + ADsd]

Unconsolidated- Undrained test (UU Test)Step 1: Immediately after samplingStep 2: After application of hydrostatic cell pressureStep 3: During application of axial loadStep 3: At failure

Unconsolidated- Undrained test (UU Test)Mohr circle in terms of effective stresses do not depend on the cell pressure. Therefore, we get only one Mohr circle in terms of effective stress for different cell pressures

Unconsolidated- Undrained test (UU Test)Mohr circles in terms of total stresses

Unconsolidated- Undrained test (UU Test)Effect of degree of saturation on failure envelopeS < 100%S > 100%

Some practical applications of UU analysis for clays t = in situ undrained shear strength1. Embankment constructed rapidly over a soft clay deposit

Some practical applications of UU analysis for clays 2. Large earth dam constructed rapidly with no change in water content of soft clay

Some practical applications of UU analysis for clays 3. Footing placed rapidly on clay deposit Note: UU test simulates the short term condition in the field. Thus, cu can be used to analyze the short term behavior of soils

Unconfined Compression Test (UC Test)s1 = sVC + Ds s3 = 0 Confining pressure is zero in the UC test

Unconfined Compression Test (UC Test)f = 1/2 = qu/2 = cu

Various correlations for shear strengthFor NC clays, the undrained shear strength (cu) increases with the effective overburden pressure, s0For OC clays, the following relationship is approximately trueFor NC clays, the effective friction angle (f

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