Shear Strength GLE/CEE 330 Lecture Notes Soil Mechanics William J. Likos, Ph.D. Department of Civil and Environmental Engineering University of Wisconsin-Madison

Applications Slope Stability Bearing Capacity Retaining Walls Others… Tunnel Linings Roadway Base Excavations (USC) (bp0.blogger.com)

Consider Bearing Capacity s’h t uw s’v Is there a plane within the soil mass where the induced shear stresses exceed the shear strength of the soil (c’, f’) ? Will a “failure plane” develop? How does shear strength depend on effective stress?

Shear Strength Dilation s’v t Failure plane Particles must move to create shear plane Results in positive (increase) in volume Total resistance depends on confining pressure Angular particles result in more dilation (so more shear resistance. Failure plane occurs at particle contacts particles themselves generally do not fail (except @ high s’) Sources of shear resistance: 1) Dilation & frictional resistance: Dependent on effective stress (s’) Captured with material property f’ 2) Cohesive resistance: Independent of stress Captured with material property c’ Important for clays (“cohesive soils”)

Mohr-Coulomb Failure Criterion s’v shear strength frictional component (dependent on s’, the effective stress on the shear surface) cohesive component c’ = effective cohesion intercept (units of stress – kPa, psf, psi, etc.)) f’ = effective angle of internal friction (degrees)

Mohr-Coulomb Failure Criterion c’ = effective cohesion intercept f’ = effective friction angle s’ = effective stress on failure plane This is a straight line in s’-t space t failure M-C Failure Envelope no failure s’1 t s’ s’3 f’ Mohr’s Circle c’ s’3 s’1 s’

Factors Affecting f’ Mineralogy (e.g., quartz vs. mica) Grain shape (e.g., angular vs. rounded) Grain size distribution (e.g., well-graded vs. poorly-graded) Void ratio, density, porosity (e.g., compacted vs. loose) Organic material (very weak) (mica) (Coduto, 1999)

(Bardet, 1997)

Cohesion Factors affecting c’: 1) Cementation (e.g., CaCO3) 2) Electrostatic attraction – van der Waals forces appreciable for small, high-surface area materials 3) Negative pore pressure (unsaturated soils) 4) Interlocking Caliche layer exposed in southern Kansas (KGS)

(Bardet, 1997)

Mohr-Coulomb Failure Criterion c’ = effective cohesion intercept f’ = effective friction angle s’ = effective stress on failure plane This is a straight line in s’-t space t failure M-C Failure Envelope no failure s’1 t s’ s’3 f’ Mohr’s Circle c’ s’3 s’1 s’

Consider a triaxial shear test: First apply isotropic compression (s1’ = s3’) Hold s3’ constant and increase s1’ until failure s’1 tf s’f s’3 a M-C Failure Envelope t Stress on failure plane (s’f, tf) Mohr’s Circle at Failure f’ f’ c’ 2a s’ s’3 s’1f So, the higher c’ and f’, the stronger the soil

Consider stress-strain response for loose sand and dense sand Loose Sand (Dr = 38%) Dense Sand (Dr = 100%) ea s’3 ev Observations: Loose sand: ductile Dense sand: brittle Low s3: brittle High s3: ductile Loose: compressive Dense: dilative Dense: low failure ea Same strength and small volume change at “critical state” compression dilation compression dilation (Bardet, 1997)

How do we define failure? Loose Peak strength (Use to find f’p) ea Peak strength Dense (Use to find f’p) Residual strength (Use to find f’res) f’p> f’res (see table 4) Want to use strength appropriate for problem! ea

Consider a laboratory “direct shear” (DS) test on loose sand failure plane (Coduto, 1999) sC’ > sB’ > sA’ tC tC Test C Test C (sC’ = P/A) f’ Test B Construct M-C failure envelope to determine f’ and c’ tB tB Test B (sB’ = P/A) Shear Stress (t = V/A) Shear Stress (t ) Test A tA tA Test A(sA’ = P/A) sA’ sB’ sC’ Shear Displacement Effective Normal Stress, s’

(Coduto, 1999)

Sensitivity – Rissa Landslide (Norway) Occurred 1978 ~0.13 square miles 7-8 million cubic yards 45 minutes 1 fatality (Sukumaran)

Sensitivity, St Sensitive or “Quick” clay: Significant loss of strength when disturbed (remolded) Typically marine clay/silt that has been uplifted and leached with fresh water (Scandinavia). Leads to an unstable flocculated structure Edge-face particle orientation

Shear Strength Measurement Laboratory Methods: Unconfined Compression Test (UCT) Direct Shear Test (DS) Ring Shear Test (residual strength) Triaxial Compression Tests Unconsolidated-Undrained (UU) (aka Q-test) Consolidated-Undrained (CU) (aka R-Test) Consolidated-Undrained with Pore Pressure Meas. (aka CU-bar test) Consolidated-Drained (CD) (aka S-Test) Note: First letter (U or C) describes consolidation phase, second letter (U or D) describes shear phase

Shear Strength Measurement Field (In-situ) Methods: Vane Shear Test Pocket Penetrometer Pocket Torvane Standard Penetration Test (SPT) Cone Penetration Test (CPT) Undrained shear strength (su) Empirical correlation to f’

Unconfined Compression Test Specimen tends to bulge due to end constraint. A0 s 3 = 0 Af s = P/A ea Failure plane Trimmed Cylindrical Specimen (clay/silt) t Loading Frame (CRS) su = undrained shear strength qu = unconfined compressive strength su s3 = 0 qu = s1f s

(Bardet)

Triaxial Compression Test u Control of s3, s1, and u (effective stress)

Unconsolidated-Undrained (UU) Test (Q-Test) Used for undrained shear strength (su) of fine-grained soils Minimizing sample disturbance is critical Relatively inexpensive because test is fast (~2 hours) Better test than UCT (unconfined compression) because we can simulate field stress Step 1: Sample Trimming Step 2: Set up in triaxial cell

Unconsolidated-Undrained (UU) Test (Q-Test) Step 3: Apply isotropic confining stress (s3 = s1) no drainage allowed (so no consolidation occurs) we do not know effective stress (but we know total stress) confining stress selected to simulate stress from depth where sample taken typically s3 (psi) = 0.75(z) (this assumes a total unit weight of ~100 pcf) s 3 u= ? z (ft) g ~100 pcf s (psi)~ 0.75(z)

Unconsolidated-Undrained (UU) Test (Q-Test) Step 4: Apply deviator stress (s1) and monitor stress-strain until failure typical axial strain rate is 1% per minute typically go to about 15%-25% axial strain Step 5: Calculate undrained shear strength (su) s 1f u= ? shear stress (t) s 3 su Test 1 Test 2 s3 s1f s3 s1f total normal stress (s)

Consolidated-Undrained (CU) Test (R-Test) Used to determine fcu Sample is consolidated to some initial effective stress (to represent field) Sheared with no drainage allowed Must analyze in terms of total stress Plot results from multiple tests to find fcu shear stress (t) fcu Test 1 Test 2 s3 s1f s3 s1f

Consolidated-Undrained Test with pore pressure measurements (CU-bar Test) Used to determine c’ and f’ Sample is consolidated to some initial effective stress (to represent field) Sheared with no drainage allowed BUT u measured with transducer Can analyze in terms of effective stress Plot results from multiple tests to find c’ and f’ shear stress (t) f’ c’ Test 1 Test 2 s’3 s’1f s’3 s’1f

Example of CU-bar test ….. (Coduto 13.10)

Vane Shear Test (Field Vane) In-situ test for determining undrained shear strength (su) Very common in soft clays and silts (ASTM D2573) Typically conducted at bottom of borehole Torque required to fail soil related to su apply correction factors for failure mode, disturbance, rate effects, organics... = correction factor (Coduto Fig 13.35) Tf = failure torque d = vane diameter torque rate: 1 deg per 10 sec (Durham Geo) (Geoengineer.org)

Pocket Penetrometer and Torvane Commonly used in field on samples At ends of Shelby tube after sampling Side walls of test pits Split spoon samples “Chunk” samples Applicable for soft to stiff clays and silts Pocket penetetrometer estimates qu (su = qu/2) Torvane estimates undrained shear strength (su) Does not account for rate effects, failure mode, etc. but good indication of strength variation with depth. torvane (source: ODP) Pocket penetrometer

Standard Penetration Test (SPT)

Cone Penetration Test (CPT)