SHEAR STRENGTH OF SOILSDr. Nalin De SilvaStrength of different materialsSteelTensile strengthConcreteCompressive strengthSoilShear strengthPresence of pore waterComplexbehaviorWhat is shear strength ????Is the external resistance per unit area that the soil mass can ofer to resist failure and sliding along any plane inside itParameter of soil shear strengthc = cohesion = friction angleUSE OF SHEAR STRENGTHOne must understand the nature of shear resistance in order to analyze soil stability problem such as :a. Bearing capacityb. Slope stabilityc. Lateral earth pressure on earth-retainingstructureEmbankmentStrip footingSoils generally fail in shearAtfailure,shearstressalongthefailuresurface (mobilizedshearresistance)reachestheshear strength.Failure surfaceMobilized shear resistanceBearing capacit Slope stabilit!etaining wallAtfailure,shearstressalongthefailuresurface (mobilizedshearresistance)reachestheshear strength.Failure surfaceMobilized shear resistanceSoils generally fail in shearEarth retaining structureCOULOMB METHODThe fundamental shear strength equation proposed by the French engineer Coulomb (1776) is:s = c + tan The relationship between the various parameters of Coulomb's equation is shown in fgure belowIn Coulomb's equation c and are empirical parameters, the values of which for any soil depend upon several factors: i. The past history of the soil.ii. The initial state of the soil, i.e., whether itis saturated or unsaturated.iii. The permeability characteristics of the soil.iv. The conditions of drainage allowed to take place during the test.MOHR METHODMohr (1900)presented a theory for rupture in materials that contended that a material fails because of a critical combination of normal stress and shearing stress and not from either maximm normal or shear stress alone.to the friction between them. The fundamental shear strength equation proposed by the Frenchengineer Coulomb (1776) iss = c + This equation expresses the assumption that the cohesion c is independent of the normalMOHR-COULOMBFAILURE CRITERION(IN TERMS OF TOTAL STRESSES)fisthemaximumshearstressthesoilcantakewithout failure" under normal stress of #cfailure envelopeCohesionFriction anglef tan + cfMOHR-COULOMBFAILURE CRITERION(IN TERMS OF EFFECTIVE STRESSES)fisthemaximumshearstressthesoilcantakewithout failure" under normal effective stress of $#c$failure envelopeEfective cohesionEfectivefriction anglefu = pore water pressure' tan ' ' + cfu 'MOHR-COULOMB FAILURE CRITERIONShear strength consists of two components% cohesive and frictional#ff'c$ ccohesive componentf tan frictional component' tan ' ' f fc + c and are measures of shear strength.Higher the values, higher the shear strength.Mohr Circle of stressSoil element$1$1$3$3$!esolving forces in and directions" 22 222'3'1'3'1''3'1CosSin++2'3'12'3'1' 22 2

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+ + Mohr Circle of stressSoil element1133Soil element Soil element11331133$2'3'12'3'1' 22 2

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+ + 2'3'1 +2'3'1 '3'1Mohr Circle of stressSoil element1133Soil element Soil element11331133$PD = Pole w.r.t. plane(, )2'3'12'3'1' 22 2

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+ + 2'3'1 +2'3'1 '3'1Soil elements at different locationsFailure surfaceMohr Circles & Failure Envelope&XXfailure'YYstable' tan ' ' + cfMohr Circles & Failure Envelope'ccc(nitiall" Mohr circle is a pointc+)he soil element does not fail if the Mohr circle is contained within the envelopeGLMohr Circles & Failure Envelope'cccGL*s loading progresses" Mohr circle becomes larger+## and finall failure occurs when Mohr circle touches the envelope$PD = Pole w.r.t. plane(, f)Orientation of Failure Plane$11331133Failure envelope(90 , ))herefore"90 , + $ - 45 + $2 2'3'1 +'3'1Mohr circles in terms of total & effective stresses-&v$h$&uu.v$ h$effective stressesuvh&vhtotal stresses or $Failure envelopes in terms of total & effective stresses-&v$h$&uu.v$ h$effective stressesuvh&vhtotal stresses or $(f & is on failurec!a"lureen#elope"n ter$s of total stresses$c$!a"lureen#elope"nter$s of effect"#e stressesMohr Coulomb failure criterion with Mohr circle of stress&$v - $/$h - $0& is on failure$/$0effective stresses$$c$!a"lureen#elope"nter$s of effect"#e stressesc Cot(1+ 3)/2(1 3)/2%&erefore,

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++2'2' ''3'1'3'1 Sin Cot cMohr Coulomb failure criterion with Mohr circle of stressMohr Coulomb failure

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++2'2' ''3'1'3'1 Sin Cot c( ) ( ) ' ' 2 ''3'1'3'1 Cos c Sin + + ( ) ( ) ' ' 2 ' 1 ' 1'3'1 Cos c Sin Sin + + ( )( ) ( ) ' 1'' 2' 1' 1'3'1 SinCoscSinSin++

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+ 2'45 ' 22'452 '3'1 Tan c TanCRITERIA FAILURE OF GANULAR SOIL, COHESION SOIL AND GRANULAR-COHESION SOIL1ther laborator tests include"2irectsimplesheartest"torsionalring sheartest"planestraintriaxialtest" laboratorvanesheartest"laborator fall cone testDeterminationofshearstrengthparametersof soils c! or c$, $)3aboratortestson specimenstakenfrom representativeundisturbed samplesField testsMostcommonlaboratorteststo determinetheshearstrength parameters are"/# 2irect shear test4# )riaxial shear test/# 5ane shear test4# )orvane0# Pocket penetrometer6# Fall cone7# Pressuremeter8# Static cone penetrometer9# Standard penetration test"aborator# testsField conditions' #c#c&c&cBefore construction* representative soil sample' #c + &c&c*fter and during construction#c + "aborator# testsSimulating field conditions in the laboratorStep /Set the specimen in theapparatusand appltheinitial stress conditionvcvchchc!epresentative soilsample takenfromthe site::::Step 4*pplthe correspondingfield stress conditionsvc . hchcvc . )raxial testvcvc2irect shear testDIRECT SHEAR TESTSchematic diagram of the direct shear apparatusDIRECT SHEAR TESTPreparation of a sand specimenComponents of the shear box Preparation of a sand specimenPorous platesDirectsheartestismostsuitableforconsolidateddrainedtests speciall# on granular soils e$g$% sand& or stiff cla#sDIRECT SHEAR TEST3eveling the top surface of specimenPreparation of a sand specimenSpecimen preparation completedPressure plateDIRECT SHEAR TESTTest procedurePorous platesPressure plateSteel ballStep /% *ppl a vertical load to the specimen and wait for consolidationPProving ring to measure shear forceSDIRECT SHEAR TESTStep 4% 3ower box is sub;ected to a horizontal displacement at a constant rateStep /% *ppl a vertical load to the specimen and wait for consolidationPTest procedurePressure plateSteel ballProving ring to measure shear forceSPorous platesDIRECT SHEAR TESTShear box3oadingframeto appl vertical load2ialgaugeto measurevertical displacement2ialgaugetomeasure horizontal displacementProving ringto measure shear forceDirect shear test'nal#sis of test results 1C claf3oose sand> 1C Cla3oose sand>