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Shear Strength of Soil © 2004 Brooks/Cole Publishing / Thomson Learning™ Direct shear test in sand: (a) schematic diagram of test equipment; (b) plot of test results to obtain the friction angle φ’ 1 © 2004 Brooks/Cole Publishing / Thomson Learning™ Variation of friction angle φ’ with void ratio for Chattachoochee River sand (after Vesic, 1963) Soil Sampling σ’1 σ’3 σ’3 = K σ’1 σ’1 2 Sequences of stress application in triaxial test © 2004 Brooks/Cole Publishing / Thomson Learning™ Triaxial Test Equipment 3 © 2004 Brooks/Cole Publishing / Thomson Learning™ Plot of deviator stress vs. axial strain-drained triaxial test Triaxial Testing Application of cell pressure (sigma 3): UNCONSOLIDATED (U) – No drainage allowed e constant (fixed) if Sr =1 - CONSOLIDATED (C) – Drainage allowed when applying cell pressure e decreases due to sample consolidation. 4 Triaxial Testing Application of deviatoric stress (σ1): Deviator stress = σ1 – σ3 Undrained (U) No drainage allowed e constant (fixed) if Sr =1 - Drained (D) Drainage allowed when applying cell deviator stress e decreases due to consolidation. Stress applied so slow no excess pwp Triaxial Tests UU – Unconsolidated Undrained UD – Unconsolidated Drained CU - Consolidated Undrained CD - Consolidated Drained 5 Undrained Soil Strength Parameters (Su, φ = 0) Note: Always test soil at void ratio on the field Skempton’s Porewater Coefficients B= Δμ Δσ 3 Developed “B” for a measure of degree of Water saturation 6 © 2004 Brooks/Cole Publishing / Thomson Learning™ Peak- and residual-strength envelopes for clay 7 Skempton’s Porewater Coefficients Developed “A” parameter for indication of sample OCR A= Δμi (σ 1 − σ 3 )i where : Δμi = ( μi − μ o ) μ o = initail pore pressure μi = pore pressure at point of interest (σ 1 − σ 3 )i = deviatoric stress at point of interest What about negative values of Af Soil Strength M-C Failure Envelope Test 1 Failure Circle Sample will fail at intersection with envelope τfailure (2) τ’ τfailure (1) Test 2 Failure Circle c’ σ1(2) σ3(1) σ1(1) σ1(3) σ1(Failure) σ3(2) σ1(1) σ1(2) σ1(3) σ1(Failure) σ’n NOTE: all stresses are effective Each test is performed at a set void ratio 8 Drained Soil Strength Parameters (c’, φ’) Soil Strength Envelope 9 Soil Strength Stress Path of Sample sinφ’ = tanα’ (σ1 - σ3)/2 = t Radius of Circle 3 α’ 2 t t = d' + S tan α' 1 S d d = c' cos φ' tan ψ = sin φ' s s = (σ1' + σ3')/2 Centre of Circle Unconfined compression test in progress (courtesy of Soiltest, Inc., Lake Bluff, IL) 10 © 2004 Brooks/Cole Publishing / Thomson Learning™ Unconfined compression test: (a) soil specimen; (b) Mohr’s circle for the test; (c) variation of qu with the degree of saturation © 2004 Brooks/Cole Publishing / Thomson Learning™ Variation of friction angle φ’ with plasticity index for several clays (after Bjerrum and Simons, 1960) 11