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 © Learning™ / Thomson Publishing 2004 Brooks/Cole 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 Triaxial Test Equipment

Sequences of stress application in © Learning™ / Thomson Publishing 2004 Brooks/Cole triaxial test

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

Δμ B = 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

Δμ A = i (σ1 −σ3)i where :

Δμi = (μi − μo ) μo = initail pore pressure μi = pore pressure at point of interest (σ1 −σ3)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 τfailure (2) with envelope 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

sinφ’= tanα’ Stress Path of Sample (σ1 - σ3)/2 = t 3 Radius of Circle α’

2

t

1 t = d' + S tan α' S

d = c' cos φ' d 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 Unconfined compression test: © Learning™ / Thomson Publishing 2004 Brooks/Cole

(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)

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