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2 ENCE 3610 Soil Mechanics Lecture 12: Shear Strength Theory Methods of Determining Shear Strength Properties

3 Review of Soil Strength Tension in soil is seldom (if ever) used Even rock is seldom used in tension Two questions we need to ask with soil strength What constitutes soil strength? How to we test for it? All applications of soil as an engineering material are in compression The most important failure The two are not mode to consider is shear failure unrelated, but they are The shear strength of the soil not identical either is the key property to determine The way shear strength acts in a soil depends upon the soil type

4 (in consolidated or drained condition)

5 Types of Tests for Shear Strength

6 Direct Shear Test

7 Direct Shear Test The most obvious way to test for shear strength Failure mechanism in direct shear test is different than in most actual soils Reproducibility is problematic Is used in some cases, but not the most common test for shear strength

8 Triaxial Test

9 Testing for Various Soil Conditions

10 Ductile and Brittle Failure Ductile Failure Brittle Failure

11 Use of Mohr's Circle to Determine Failure Envelope Deviator Stress Δσd

12 Results of Shear Strength Tests Cohesionless Soils Soils with a combination of both Cohesive Soils

13 Shear Failure in Cohesionless and Cohesive Soils

14 Typical for Cohesive Soils InSitu: =0, cu > 0 Typical for Cohesionless Soils: cu = 0, > 0 (but effects from overconsolidation must be considered) Triaxial Shear Test Relationships

15 Shear Strength Purely Cohesionless Soils Shear strength of cohesionless soils is only developed with the presence of effective stress Shear strength increases with increasing effective stress The increase of shear strength depends upon the internal friction angle of the soil

16 Cohesion in Soils True 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 Cohesion Negative pore water pressure Negative excess pore water pressures due to dilation (expansion) Apparent mechanical forces Cannot be relied on for soil strength

17 Purely Cohesive Soils All of the strength of the soil is developed from the cohesion of the soil The strength of the soil is essentially independent of the effective stress qu = unconfined compression strength c = cohesion or shear strength DO NOT CONFUSE THE TWO

18 Soils with Both Cohesion and Internal Friction Ideally soils are either purely cohesive or cohesionless 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

19 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 = psf Find Value of, drained and undrained

20 Undrained Triaxial Test Example Equation for failure envelope and Mohr's Circle Solve for sin ϕ Simplification for c = 0 Simplification for c = 0

21 Undrained Triaxial Test Example Undrained Condition Drained Condition

22 Example 2 Given Find Granular soil (c = 0) Shearing Strength 4m Unit Weight = 19.6 below surface before 3 kn/m installation of structure Internal Friction Angle Whether soil will shear = 35º with additional load Proposed Structure Whether soil will shear Causes vertical stress to with additional load and increase 60 kpa at 4m elevation of water table depth Also consider case where water table increases to ground surface

23 Example 2 Solution No Structure Load Overburden pressure w/o structure 4 m = (19.6 kn/m3)(4 m) = 78.4 kpa This becomes your confining stress σ3 Shearing stress s = (78.4)tan(35) = 54.8 kpa 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 Principal Stresses for two load cases Case 1 σ3 = 60 kpa σ1 = = kpa Case 2 Soil overburden pressure = ( )(4) = 39.2 kpa σ3 = 39.2 kpa Σ1 = = 99.2 kpa

24 Example 2 Formula for failure criterion for Mohr-Coulomb failure for both cohesive and cohesionless soils (and mixed ones too) with principal stresses known σ 1 σ 3 2 c cos(ϕ) (σ 1 +σ 3 )sin (ϕ)=f By direct substitution Case 1: f = kpa Case 2: f = kpa In both cases f < 0; however, Case 2 is closer to failure and thus should be considered with greater care

25 Drained Triaxial Tests on Clay Example Given Drained (S or CD) Triaxial Test on Saturated Clay Sample 1 Confining Pressure = 70 kpa Failure Pressure = 200 kpa Sample 2 Confining Pressure = 160 kpa Failure Pressure = kpa Find Cohesion and Internal Friction Angle Governing equation Noting that 1 sin 2 tan 1 sin 4 2 (angles in radians)

26 Drained Triaxial Tests on Clay Example Governing equation becomes 1 3 tan 2 2c tan Governing equation reduces further to 1 3 N 2c N Substituting: Define: N tan N 2c N N 2c N

27 Drained Triaxial Tests on Clay Example Solving these equations N 2c N N 2c N Results in c kpa N radians 20

28 Unconfined Compression Test No confining pressure Only applicable to purely cohesive soils Best way to determine the unconfined compression strength and cohesion (qu/2) of a cohesive soil

29 Other Methods of Determining Shear Strength

30 Typical Values for Cohesionless Soils Friction Angle vs. Relative Density (very dependent upon grain size)

31 Values of Internal Friction Angle

32 Typical Values of Cohesion Very approximate; for preliminary purposes only

33 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

34 Procedure for Vane Shear Test

35 Vane Shear Test Calculations Torque of vane shear 2r T 2 cu r 2 L 3 T cu 2r 2 r 2 L 3 cu = undrained shear strength T = maximum torque applied r = radius of vanes L = length of vanes Assumes uniform shear strength distribution Corrections for vane shear test Correction for plasticity index: Application of correction factors: cu corrected = μ cu uncorrected

36 Sensitivity and Vane Shear Undrained and undisturbed strength determined by measuring maximum torque while rotating vanes at 0.1 deg./sec. Remoulded shear strength measured by rotating vane about ten (10) times, then recording a final torque value Sensitivity St = undisturbed shear strength/remoulded shear strength

37 Field and Laboratory Tests for Various Soil Types

38 Questions?