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ENCE 3610Soil Mechanics

Lecture 12: Shear Strength TheoryMethods of Determining Shear Strength Properties

Review of Soil Strength

Tension 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 compressioncompression

The most important failure The most important failure mode to consider is shear mode to consider is shear failurefailure

The shear strength of the soil The shear strength of the soil is the key property to is the key property to determinedetermine

The 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 “obvious” way The most “obvious” way to test for shear strengthto test for shear strength

Failure mechanism in Failure mechanism in direct shear test is direct shear test is different than in most different than in most actual soilsactual soils

Reproducibility is Reproducibility is problematicproblematic

Is 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

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: =0, c

u > 0

Typical for Cohesionless Soils: c

u = 0, > 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 stressstress

Shear strength increases Shear strength increases with increasing effective with increasing effective stressstress

The 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

Cohesion in Soils

True CohesionTrue Cohesion Cementation

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

Electrostatic and electromagnetic attractions

Primary valence bonding (adhesion)Occurs primarily during

overconsolidation

Apparent CohesionApparent Cohesion Negative pore water

pressure

Negative excess pore water pressures due to dilation (expansion)

Apparent mechanical forces

Cannot be relied on for soil strength

Purely Cohesive Soils

All 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 soil

The 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 strength

c = cohesion or shear strength

DO 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 cohesionlesscohesionless

This 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 – Drained test

– Confining pressure = 720 psf

– Deviator stress at failure = 600 psf

– Pore water pressure at failure = 496.2 psf

Find– Value of , drained and

undrained

Undrained Triaxial Test Example

Equation for failure Equation for failure envelope and Mohr's Circleenvelope and Mohr's Circle

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

GivenGiven Granular soil (c = 0)

Unit Weight = 19.6 kN/m3

Internal Friction Angle = 35º

Proposed StructureProposed Structure Causes vertical stress to

increase 60 kPa at 4m depth

Also consider case where water table increases to ground surface

FindFind 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

Example 2

Solution – No Structure LoadSolution – No Structure LoadOverburden pressure w/o structure load @ 4 m = (19.6 kN/m3)(4 m) = 78.4 kPaThis becomes your confining stress σ3

Shearing stress s = (78.4)tan(35) = 54.8 kPaSimplest way to solve last two parts is to compute failure criterion f

If f is negative, failure should not occurIf f is positive, failure will most likely occur

Principal Stresses for two Principal Stresses for two load casesload cases

Case 1σ3 = 60 kPa

σ1 = 60 + 78.4 = 138.4 kPa

Case 2Soil overburden pressure = (19.6-9.81)(4) = 39.2 kPa

σ3 = 39.2 kPa

Σ1 = 39.2 + 60 = 99.2 kPa

Example 2

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

By direct substitutionBy direct substitution

Case 1: f = -64.4 kPaCase 1: f = -64.4 kPa

Case 2: f = -19.4 kPaCase 2: f = -19.4 kPa

In both cases f < 0; however, Case 2 is closer to In both cases f < 0; however, Case 2 is closer to failure and thus should be considered with greater failure and thus should be considered with greater carecare

σ1−σ3−2c cos(ϕ)−(σ1+σ3)sin (ϕ)=f

Drained Triaxial Tests on Clay Example

GivenGiven Drained (S or CD) Triaxial

Test on Saturated Clay Sample 1

Confining Pressure = 70 kPa

Failure Pressure = 200 kPa

Sample 2Confining Pressure =

160 kPaFailure Pressure = 383.5

kPa FindFind

Cohesion and Internal Friction Angle

Governing equationGoverning equation

Noting thatNoting that

(angles in radians)(angles in radians)

24tan

sin1

sin1 2

Drained Triaxial Tests on Clay Example

Governing equation Governing equation becomesbecomes

Define:Define:

Governing equation Governing equation reduces further toreduces further to

Substituting:Substituting:

24tan2

24tan 2

31

c

24tan2

N

NcN 231

NcN

NcN

21605.383

270200

Drained Triaxial Tests on Clay Example

Solving these equationsSolving these equations

Results inResults in

NcN

NcN

21605.383

270200

20radians 349.0

04.2

kPa 06.20

N

c

Unconfined Compression Test No confining No confining

pressurepressure

Only applicable to Only applicable to purely cohesive purely cohesive soilssoils

Best way to Best way to determine the determine the “unconfined “unconfined compression compression strength” and strength” 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 Test

Useful for a quick determination of shear stress in situ

Applicable to cohesive soils

Good for determining undrained shear strength

Best if qu < 1 ksf or 50 kPa

Test procedures ASTM D3573 AASHTO T 223-74

Procedure for Vane Shear Test

Vane Shear Test Calculations

Torque of vane shearTorque of vane shear

cu = undrained shear

strength T = maximum torque

applied r = radius of vanes L = length of vanes

Assumes uniform shear Assumes uniform shear strength distributionstrength distribution

3

22

3

22

2

2

rLr

Tc

rLrcT

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 Shear

Undrained and Undrained 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 value

Sensitivity SSensitivity Stt = = undisturbed shear undisturbed shear strength/remoulded shear strength/remoulded shear strengthstrength

Field and Laboratory Tests for Various Soil Types

Questions?