Geomechanics 255 (610.255)

1. Geomechanics 255 (610.255) Geomechanics Group School of Civil & Resource EngineeringThe University of Western Australia Part 2: Soil Strength Professor Martin Fahey

2. Outline • Shearing behaviour of sand (cohesionless soil) • friction • dilatancy • concept of critical state (critical void ratio) • Shearing behaviour of clays (cohesive soil) • critical state concept for clayey soils • drained and undrained shear strength in triaxial tests • relationship between pore pressure change in undrained tests, and volume change in drained tests The aim is to show that the shearing behaviour of all soils (sands and clays) can be presented within the unified framework of Critical State Soil Mechanics. This links the volume change behaviour in drained shearing with the pore pressure changes that occur when drainage is not able to occur. For sands, undrained behaviour generally can only occur when the boundary conditions prevent – otherwise, shearing is generally slow enough to allow any pore pressures (positive or negative) that tend to occur to dissipate as the shearing progresses. (The exception may be very fast loading, as in an earthquake, or where the scale of the problem is very large, as with very large offshore gravity platforms). On the other hand, the permeability of clay soils is so low that it is very difficult to apply loads slowly enough for drained conditions to apply, and hence many problems involving applying loads to clayey soils deal with the undrained shear strength.

3. Soil Strength: Angle of Internal Friction f' N N N R f' F F F F f': Angle of internal friction; m: coefficient of friction tan f' = m = F/N f' f' f': Angle of repose of sand heap f': Angle of plank when block slides

4. Principle of Effective Stress N Water pressure u F N F F Note: As u ® s (i.e. s' ® 0)strength (t) ® 0 (liquefaction)

5. Direct Shear Box Apparatus

6. Other Versions at UWA Pneumatic jack (computer controlled) to apply vertical load Load cells Direct Via Lever Hangers for load

7. Behaviour of Sand in Direct Shear Box

8. Direct Shear Tests on Sand D, M, L: Dense, Medium, Loose

9. Direct Shear Box: Summary of Results

10. Relative Density – Density Index (ID) Absolute value of soil density not so important – what matters is how dense is the soil relative to its maximum possible value and its minimum possible value ID Densest possible state (emin, or rdmax) (obtained by vibration under load) 1 or 100% Density index ID (relative density) – where density lies in the range min. to max. - or rather where void ratio lies between loosest (emax) and densest (emin) state 0 Loosest (stable) state (emax, or rdmin)(obtained by pouring with funnel)

11. Apparent Cohesion in Sand Mohr-Coulomb Failure Criterion: tf = c' + s' tan f' • Failure surface is actually curved • Straight line through tests results at s' of 40, 60 and 80 kPa implies a cohesion intercept (c') of 10 kPa • This implies a strength at zero effective stress: NOT CORRECT “Apparent cohesion” c'

12. "Saw-tooth" Model of Dilation • Dilation has effect of increasing the apparent friction angle on interface above the true value (f'cv) • Apparent friction angle from sawtooth model:f'peak = f'cv + n • Dilation angle = n • Observed relationship:f'peak»f'cv + 0.8 n (Bolton) • Collapsing material (negative dilation) shows friction angle less than f'cv

13. Stress-Ratio Dilation Relationship (Taylor) Peak stress ratio (tan f'peak) DENSE Stress ratio (t/s'n) "Constant volume" stress ratio (tan f'cv) LOOSE dy/dx = 0 DENSE dx dy Vertical displacement y (vol. strain) Point of max. slope (nmax) dy/dx = 0 LOOSE dy/dx negative, increasing towards zero

14. Critical State Concept • When sheared, state of soil tends to migrate to a unique line in t - s' - e space. This is called the critical state line (CSL). • CSL has same gradient as NC line (l)

15. Dilation depends on density and stress level Critical State Line (CSL) At low stress, even loose samples may dilate LOOSE Void ratio e At high stress, even dense samples may contract DENSE Normal effective stress s'n (or mean effective stress p')

16. n p' (kPa) º 10 100 1,000 10,000 0.2 (20%) 3.2º 0.5º -2.3 (?) I 0.5 (50%) 17.1º 10.2º 3.3º D 0.8 (80%) (30.9º ?) 19.9º 8.8º Relative Density Corrected for Stress Level • For plane strain, Bolton found that: • nmax (º) = 6 IR for plane strain • f´max – f´cv = 0.8 nmax • f´max – f´cv 5 Irº • For triaxial conditions • Must define 'dilatancy' in general as • where ev is volumetric strain = e1 + e2 + e3. • e1 is the major principal strain (generally ea in triaxial tests) • (negative sign, because expansion - I.e. dilation - is negative by normal sign convention, but want 'dilatancy' to be positive) -2.2º (?)

17. Drained & Undrained Shear Strength Shear stress t Drained strength sd f'cv Undrained strength su Undrained strength su Drained strength sd s'n Void ratio e Positive pore pressure reduces effective stress Suction increases effective stress Dilation Undrained testÞ no volume change allowed Loose states eo Dense states Contraction CSL Normal effective stress s'n (or mean effective stress p')

18. Fa scell Area,A scell u scell Fa Triaxial Test The triaxial test enablesa variety of stress or strain controlled tests to be carried out on cylindrical soil specimens.

19. One of the UWA Triaxial Systems Axial motor drive system Cell cover lowered once sample in place Sample goes here Cell pressure controller Sample, enclosed in rubber membrane, with axial strain measuring devices attached Control and data logging system

20. Triaxial Test: Background • Direct shear test useful, but limited • Know only 1 normal stress (s'n), don't know horizontal normal stresses • Failure plane pre-defined - must coincide with the shear box • Triaxial test still limited: • vertical and horizontal directions still principal directions • horizontal stress equal in all directions • “true triaxial” test would allow different s'1, s'2, s'3 on three faces of cubical sample • even more general - allow shear stresses to be applied to the three faces s'v s'v (=s'1) s'1 thv s'h s'h s'h (=s'2) s'2 s'h (=s'3) s'3 “True triaxial” (s'1s'2 s'3) “Simple shear” Triaxial

21. Triaxial Test: Conduct of Test • Almost always use saturated samples (using high backpressure uo to achieve full saturation) • Almost always consolidate the sample to some stress state (in situ stresses often) before carrying out the strength test • isotropic consolidation: vertical and horizontal stresses equal (increase cell pressure only, allowing drainage against constant back pressure) • s'h = s'3 = sc - uo, and s'1 = s'v = s'h = s'3 in this stage • anisotropic consolidation: generally vertical stress greather than horizontal stress: increase cell pressure and apply additional vertical load • s'h = s'3 = sc - uo, and s'1 = s'v > s'h = s'3 in this stage • “Shearing” phase (in the simplest test): increase the vertical load (stress) until the sample fails • other “stress paths” also possible - see later

22. Stress Paths in Triaxial Tests • Different stress paths in “shearing” phase: • keep cell pressure constant (Dsh = 0) and increase vertical stress (Dsv +) • keep vertical stress constant (Dsv = 0) and reduce cell pressure (Dsh -) • keep vertical stress constant (Dsv = 0) and increase cell pressure (Dsh +) • keep cell pressure constant (Dsh = 0) and reduce vertical stress (Dsv -) • vary both cell pressure and vertical stress in some predetermined way, to produce any type of stress path • Stress path in q-p space:Dq = Dsv - DshDp = (Dsv + 2Dsh)/3 • Dsh = 0 and Dsv = +  Dq = +Dsv and Dp = +Dsv/3 Dq/Dp =3 Shearing phase Shearing phase q q Stress path: a plot showing how the stresses vary during a test. In this case, this is a Total Stress Path (TSP). In this case, shearing starts from an isotropic stress state, following isotropic consolidation. In this case, shearing starts from an anisotropic stress state, following anisotropic consolidation. 3 3 1 1 Anisotropic consolidation phase p p Anisotropic consolidation phase

23. "Standard" stress path: sh constantsv increased to failure sv increasing sh constant Dq = Dsv Dp = D sv/3 Dq/ Dp = 3 Total and Effective Stress Paths (TSP, ESP) q TSP: Total stress path (imposed by apparatus) ESP: Effective stress path (soil response) 3 1 (ESP) Du (+) B q = q' (b') B' (Du may be negative) p, p' p A p' p' = p - Du

24. Drained & Undrained Strength (Clays) CSL Deviator stress q Bd TSP Drained strength sd Au , Bu Du - Undrained strength su Undrained strength su Du + 3 Ad Undrained strength depends on p'oand OCR Drained strength sd ESP 1 A B Void ratio e mean effective stress p' Ad NC line Dilation Undrained testÞ no volume change allowed "Wet of critical" B eo A Contraction OC line Bd "Dry of critical" CSL Mean effective stress p'

25. Initial and Final Undrained Strength q su for NC soil increases after consolidation Tank or GBS ® Dsv su su after consolidation suo CSL NC soil In situ su 1 Depth (m) p' e k In situ eo su after consolidation e after consolidation NCL In situ su su = k.z (k = 1 to 2 kPa/m) (or su = suo + k.z) CSL p' How long for strength increase to occur ??? GBS ® Dsv ® p'

26. Consolidation between increments ESP in undrained loading Staged Loading (Undrained) q CSL Fully drained sd 6 su after two increments 5 4 In situ su Dq due to total load > in situ su ® failure if applied in 1 increment 2 3 TSP 1 p' e 1 2 In situ eo 3 4 NCL e after two increments 5 6 CSL p'

27. Drained Tx Tests: Silica & Calc. Sands Calc. sand (Dog's Bay) Silica sand Dilation Dilation

28. Drained & Undrained Tx Tests, Calc. Sand Dog's Bay Dog's Bay TSP Drained Undrained