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ENCE 3610Soil Mechanics

Lecture 12: Shear Strength TheoryMethods of Determining Shear Strength Properties

Review of Soil StrengthTension in soil is seldom (if Tension in soil is seldom (if ever) usedever) used

Even rock is seldom used in tension

All applications of soil as an All applications of soil as an engineering material are in engineering material are in compressioncompressionThe most important failure The most important failure mode to consider is shear mode to consider is shear failurefailureThe shear strength of the soil The shear strength of the soil is the key property to is the key property to determinedetermineThe way shear strength acts in The way shear strength acts in a soil depends upon the soil a soil depends upon the soil typetype

Two questions we need Two questions we need to ask with soil strengthto ask with soil strength

What constitutes soil strength?How to we test for it?

The two are not The two are not unrelated, but they are unrelated, but they are not identical eithernot identical either

(in consolidated or drained condition)

Types of Tests for Shear Strength

Direct Shear Test

Direct Shear Test

The most The most ““obviousobvious”” way way to test for shear strengthto test for shear strengthFailure mechanism in Failure mechanism in direct shear test is direct shear test is different than in most different than in most actual soilsactual soilsReproducibility is Reproducibility is problematicproblematicIs used in some cases, Is used in some cases, but not the most but not the most common test for shear common test for shear strengthstrength

Triaxial Test

Testing for Various Soil Conditions

Ductile and Brittle Failure

Ductile Failure Brittle Failure

Use of Mohr's Circle to Determine Failure Envelope

Deviator Stress Δσd

Shear Envelope for Multiple Effective Stresses (σ3)

Assume that the smaller Assume that the smaller principal stress principal stress σσ33 is:is:

Horizontal StressConfining Stress

Assume that the larger Assume that the larger principal stress principal stress σσ11 isis

Vertical StressThen the Then the σσ33 stress is the stress is the effective stress of the soileffective stress of the soilVertical stress Vertical stress σσ11 includes includes effective stress and effective stress and foundation loadingfoundation loadingThese conditions will be These conditions will be different in some situations, different in some situations, but illustrate the significance but illustrate the significance of varying of varying σσ33

Results of Shear Strength Tests

Cohesionless SoilsCohesionless Soils

Soils with a combination Soils with a combination of bothof both

Cohesive SoilsCohesive Soils

Shear Failure in Cohesionless and Cohesive Soils

Triaxial Shear Test Relationships

Typical for Cohesive Soils In-Situ: φ =0, cu > 0

Typical for Cohesionless Soils: cu = 0, φ > 0 (but effects from overconsolidation must be considered)

Shear StrengthPurely Cohesionless Soils

Shear strength of Shear strength of cohesionless soils is only cohesionless soils is only developed with the developed with the presence of effective presence of effective stressstressShear strength increases Shear strength increases with increasing effective with increasing effective stressstressThe increase of shear The increase of shear strength depends upon strength depends upon the internal friction angle the internal friction angle of the soilof the soil

φστ tan'=

Cohesion in Soils

True CohesionTrue CohesionCementation

Due to the presence of cementing agents such as calcium carbonate or iron oxide

Electrostatic and electromagnetic attractionsPrimary valence bonding (adhesion)

Occurs primarily during overconsolidation

Apparent CohesionApparent CohesionNegative pore water pressureNegative excess pore water pressures due to dilation (expansion)Apparent mechanical forcesCannot be relied on for soil strength

Purely Cohesive SoilsAll of the strength of the All of the strength of the soil is developed from the soil is developed from the cohesion of the soilcohesion of the soilThe strength of the soil is The strength of the soil is essentially independent of essentially independent of the effective stressthe effective stress

qu = unconfined compression strengthc = cohesion or shear strengthDO NOT CONFUSE THE TWO

Soils with Both Cohesion and Internal Friction

Ideally soils are either purely cohesive or Ideally soils are either purely cohesive or cohesionlesscohesionlessThis is frequently not the case because:This is frequently not the case because:

Composition of soils are mixed (combinations of sands, clays and silts)Drainage and/or remoulding of clays produces conditions similar to drained triaxial or direct shear conditions

Undrained Triaxial Test Example

Given– Dry

Cohesionless Soil

– Tested to determine φ

– Drained test– Confining

pressure = 720 psf

– Deviator stress at failure = 600 psf

Undrained Triaxial Test ExampleEquation for failure Equation for failure envelope and Mohr's envelope and Mohr's CircleCircle

Simplification for c = 0Simplification for c = 0

Solve for sin Solve for sin ϕϕ

Simplification for c = 0Simplification for c = 0

Undrained Triaxial Test Example

Undrained Condition Drained Condition

Example 2

• Given– Granular soil (c = 0)– Unit Weight = 19.6 kN/m3

– Internal Friction Angle = 35º– Proposed Structure causes

vertical stress to increase 60 kPa at 4m depth

– Also consider case where water table increases to ground surface

• Find– Shearing Strength 4m below

surface before installation of structure

– Whether soil will shear with additional load

– Whether soil will shear with additional load and elevation of water table

• Solution– Simplest way to solve last two

parts is to compute failure criterion f

• If f is negative, failure should not occur

• If f is positive, failure will most likely occur

σ1− σ3− 2ccos(φ)− (σ1+σ3)sin(φ)=f

Example 2

• Principal Stresses for two load cases– Case 1

• Soil overburden pressure = (19.6 kN/m3)(4) = 78.4 kPa

• σ3 = 78.4 kPa• σ1 = 60 + 78.4 = 138.4 kPa

– Case 2• Soil overburden pressure =

(19.6-9.81)(4) = 39.2 kPa• σ3 = 39.2 kPa• σ1 = 39.2 + 60 = 99.2 kPa

• Formula for failure criterion for Mohr-Coulomb failure for both cohesive and cohesionless soils (and mixed ones too) with principal stresses known

• By direct substitution• Case 1: f = -64.4 kPa• Case 2: f = -19.4 kPa• In both cases f < 0; however,

Case 2 is closer to failure and thus should be considered with greater care

Example 3:Drained Triaxial Test on Clay

GivenDrained (S or CD) Triaxial Test on Saturated ClaySample 1

Confining Pressure = 70 kPaFailure Pressure = 200 kPa

Sample 2Confining Pressure = 160 kPaFailure Pressure = 383.5 kPa

FindCohesion and Internal Friction Angle

SolutionSee online

presentation on p-q diagrams; best way to solve the problem

Unconfined Compression TestNo confining No confining pressurepressureOnly applicable to Only applicable to purely cohesive purely cohesive soilssoilsBest way to Best way to determine the determine the ““unconfined unconfined compression compression strengthstrength”” and and cohesion (qcohesion (quu/2) of a /2) of a cohesive soilcohesive soil

Other Methods of Determining Shear Strength

Typical Values for Cohesionless Soils

Friction Angle vs. Relative Density (very dependent upon grain size)

Values of Internal Friction Angle

Typical Values of Cohesion

Very approximate; for preliminary purposes only

Vane Shear TestUseful for a quick determination of shear stress in situApplicable to cohesive soilsGood for determining undrained shear strength

Best if qu < 1 ksf or 50 kPa

Test proceduresASTM D3573AASHTO T 223-74

Procedure for Vane Shear Test

Vane Shear Test CalculationsTorque of vane shearTorque of vane shear

cu = undrained shear strengthT = maximum torque appliedr = radius of vanesL = length of vanes

Assumes uniform shear Assumes uniform shear strength distributionstrength distribution

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

32r2ππ

32r2ππ

2

2

+L

T=c

+Lr=T

u

u

Corrections for vane Corrections for vane shear testshear test

Correction for plasticity index:

Application of Application of correction factorscorrection factors::

cu corrected = μ cu uncorrected

Sensitivity and Vane ShearUndrainedUndrained and and undisturbed strength undisturbed strength determined by measuring determined by measuring maximum torque while maximum torque while rotating vanes at 0.1 rotating vanes at 0.1 deg./sec.deg./sec.Remoulded shear Remoulded shear strength measured by strength measured by rotating vane about ten rotating vane about ten (10) times, then recording (10) times, then recording a final torque valuea final torque valueSensitivity SSensitivity Stt = = undisturbed shear undisturbed shear strength/remoulded shear strength/remoulded shear strengthstrength

Field and Laboratory Tests for Various Soil Types

Questions?