Shear Strength o Soil Hsin-yu Shan Dept. o Civil Engineering National Chiao Tung University
Normally Consolidated Clays s u ( ) = 2 1 z c p = s u c 1 is the index o mobilization o shear strength The shear strength is ully mobilized when this ratio reaches maximum. Normally, during R test, ailure occurs at a axial strain o 1.0 6.0%
Drained Tests (Slow Tests) ( ) 1 expansion ε a 20% ε v contraction
Eective Stress Failure Envelope τ φ c 0 φ tends to decrease as P.I. increases
c u determined rom Q test is the strength not cohesion It comes rom the eect o locked-in stress or stress the soil had been subjected to It has nothing to do with cohesion
S test NC clay Strain concentration tends to lead to compression OC clay Strain concentration tends to lead to dilation Water lows outward rom shear zone Strength increase Water lows inward to shear zone Strength decrease
OC clay Undrained tests 1 c Plane strain 1 u c ~12% ε a
Pore water pressure decreases as eective stress goes up 1 Ater peak the clay is still consolidating Since the eective conining stress is increasing, the strength is still mobilizing in terms o absolute value o 1
NC clay 1 R envelope R envelope ( 1 ) u c
R ( ) 1 vs. R envelope R Overconsolidated Eective stress ailure envelope Normally consolidated Due to u < 0 Total stress (R) ailure envelope Overconsolidated ( 1 ) Normally consolidated c u or
S vs. R envelope ( ) 1 Eective stress (S) ailure envelope Overconsolidated Normally consolidated Due to u < 0 R > S Overconsolidated Total stress (R) ailure envelope ( 1 ) Normally consolidated c u or
NC (lightly OC) S strength > R strength Stability during loading is critical Heavily OC R strength > S strength Stability during excavation is critical ( ) 1
NC Clay ( ) 1 ( 1 ) max ( 1 ) max Eective stress path or undrained test u increases or
OC Clay ( ) 1 ( 1 ) max ( 1 ) max E. stress path or undrained test, u decreases or
NC at ( 1 ) max, the shear strength has not been ully mobilized, 1 ( ) is still increasing OC the dierence is smaller than NC. reaches maximum irst and ( ) 1 is still increasing 1 ( Actually the dierence in ( 1 ) max between NC and OC is not very large )
Cohesion c usually comes rom the eect o itting a straight line through the data points to get the envelope Its just the intercept on the vertical axis It is usually the apparent cohesion, not the real cohesion To test i the cohesion is real, just put the soil specimen in water i it holds, there is true cohesion
Factors Inluencing Undrained Shear Strength Initial eective stress Eective stress shear strength parameters c and φ o N.C. clay show no anisotropy c and φ o O.C. clay has anisotropic eect Pore water pressure generated during shear For N.C. clay, the change o pore pressure is not aected by the orientation o principal stress The pore water pressure o O.C. clay is dependent on the orientation o principal stress
Curved Failure Envelope Dilatancy eect at lower stress level Crushing o particles at high stress level Rearrangement o particle orientation under higher stress (tend to be more parallel) Higher φ Lower φ
Lee and Morrison (1970) q p Compacted kaolinite Compacted Higgens clay = 100 psi φ = 26 =100 psi φ = 25 = 2500 psi φ =12 =1200 psi φ =19
Bishop, Webb, and Lewin (1965) q London clay φ = 0 φ = 10 p
Sensitivity Strength o the soil (in an undisturbed state) divided by the strength in a completely remolded state at the same water content For most soil, sensitivity, s t, ranges between 1.5 ~ 10
Six Factors Aecting Sensitivity Metastable soil structure Cementation Weathering Thixotropic hardening Leaching and ion exchange Eect o addition o dispersive agents
1000 Sensitivity, St (log) 1 Liquidity Index, L.I.
Eect o Salt Concentration Eect on diuse double layer w % L.L. w % P.L. Shear strength Salt concentration Salt concentration
Thixotropy An isothermal, reversible, time-dependent increase in strength at a constant water content Aging Disturbance, Remold Shear strength Remolded strength Time, t
shear Time, t Pore pressure, u
Cementation Eect o removal o the cementation bonds in the soil Test No. 4 5 Leaching solution Original pore liquid Sea water EDTA (disodium salt o ethylene diamene tetra acetic acid) Max. shear strength 11,000 ps 12,000 ps 4,000 ps
Residual Strength Peak strength Shear strength Residual strength ε a
Residual Strength Occurs: At large shear strain/displacement Under drained condition S tests are appropriate tests or measuring the residual strength Especially or clay We should not use peak strength or design involving high-sensitivity clay
For overconsolidated clays, usually φ > φ r p τ φ p φ r c p c r 0
Measuring Residual Strength Direct shear (allowed displacement has to be large enough) Ring shear Consolidated-drained triaxial test
Strain-Rate Eect Mainly or undrained loading Equilibrium o pore water pressure Creep o soil structure under load
Undrained creep test Time, t Strain
( ) 1 ( 1 ) logt 20 % / log cycle R test 1 10 100 1000 10000 Time, logt (min)
Clay Mexico City clay ( 1 ) logt (% / log 6 cycle) Bearpaw clay shale 7 9 Oche bentonite 7 10 Cucaracha clay shale 8 21
Olson and Parola (1968) Q tests on compacted clay t 100 min 10 min 1 min 6 sec 600 milli sec 60 milli sec 6 milli sec ( 1 ) 2 (+ increase) 4 5 9 17 22 (%)
Seed and Chan (1966) Undisturbed S.F. Bay mud S t 0.1sec 140 160% S conventional,t 10-20 min Compacted Vicsburg silty clay and Pittsburg sandy clay S t 0.1sec 10 140% S conventional,t 10-20 min 0.1 sec 10 min.8 log 10 cycles
Eect o Stain Rate on Modulus Negligible eect o strain rate on strain at ailure Negligible eect o strain rate on modulus
Dynamic loading Eect o loading requency Transient strength decreases as loading requency increases For compacted clays the strength remain almost the same For sensitive clays the strength decreases 10 20% Strain at ailure increases as loading requency increases Sot sensitive clays are more aected
Anisotropy Lean sensitive clays are more aected by rotation o principal planes than highly plastic clays o low sensitivity 1 1
Inherent anisotropy Isotropy in c, φ more obvious in OC clays, NC clays don t have this eect Dierence in inherent tendency or pore water pressure to be induced by shear more likely or OC clays, NC clays don t have this dierence Stress-induced anisotropy
Aas (1965) vane shear τ h τ v Site Aserum Drammen Manglerud Lierstronta OCR Slightly > 1 1 1 1 τ h /τ v 1.1 1.5 1.6 2.1 Why?
Ladd and Foott (1974) Type o test/loading condition Plane strain active ( 1 vertical) Triaxial compression ( 1 vertical) Triaxial extension ( 1 horizontal) τ / 0.4 0. 0.16 Direct simple shear 1 0.20 Plane strain passive ( 1 horizontal) 0.19
1 PSA TC 1 DSS PSP TE 1
Triaxial Extension Test Decrease vertical stress ( v ) to induce ailure 1 = 0 1 u 0 hc v
0 u v = = ) (0 ) ( 0 0 u A u B u + + + = ) ( ) ( 1 0 1 1 o u K + = = i B =1 ] ) (1 ) 1)[( ( ) 1)( ( 1 0 o K A u A u + = + + =
Mohr-Coulomb Equation: φ φ ]sin 2 [ sin 2 2 ) ( 0 1 1 1 u u + = + = 0 1 1 1 1 ) ( 2 2 2 u K o + + = + = +
τ = ( 1 ) / 2 = [1 A (1 Ko)]sinφ = [1 (1 2A )sinφ] c p For N.C. clay, the parameters in the above equations are somehow independent o consolidation pressure c p constant
Triaxial Compression Test Increase vertical stress ( v ) to induce ailure = 0 = + u 0 1 u 0 hc = hc + u 0 v
1 = v = 1 u0 i B =1 = 0 u = A ( ) 0 1 u
Mohr-Coulomb Equation: φ φ ]sin 2 [ sin 2 2 ) ( 0 1 1 1 u u + = + = 0 1 1 1 ) ( ) ( u K o + + = + = 0 1 1 1 2 2 2 u K o + + = + = +
τ = ( 1 ) / 2 = [ Ko + A (1 Ko)]sinφ = [1 (1 2A )sinφ] c p For N.C. clay, the parameters in the above equations are somehow independent o consolidation pressure c p constant
φ = o 2 A = 0.9 K = 0.5 Triaxial compression Triaxial extension τ τ 0.5 0.20
This is due to stress-induced anisotropy instead o inherent anisotropy Specimens o triaxial extension tests will experience larger shear deormation The direction o major principal stress has to rotate 90
Direct Simple Shear Under the condition o the applied stresses, it can assumed that: Pure shear applied to horizontal and vertical planes The ailure plane is not horizontal, α=φ/2 The horizontal plane is the plane o maximum shear stress at ailure τ τ φ/2 τ max, τ v = h =0
τ h = 0.19 ( ) 1 / 2 = 0.2 1 DSS Roscoe Four plates Pure shear is applied to horizontal and vertical plane DSS NGI Rubber membrane and circular rings Horizontal plane is the plane o maximum shear stress Failure plane is not horizontal (Most reasonable) τ h ( 1 ) / 2 = 0.25 = Direct Shear τ h ( 1 ) / 2 = 0.19 = 0.22
Determination o Undrained Shear Strength Take undisturbed samples Subject specimens to all-around conining pressure Shear the specimens to ailure with no drainage τ τ cos φ τ φ/2 = max, s u τ τ max,
Lab. Strength is Probably Lower Than the Field Strength Because: Specimens tested in the lab are disturbed Lab conining pressure is less than that in the ield Some drainage will occur in the ield (higher eective stress)
Lab. Strength is Probably Higher Than the Field Strength Because: Strain rates in the lab are much higher than the strain rate in the ield Lab s Q strengths based on triaxial compression (s DSS < s T.C. ) s u (= τ max, ) > τ
SHANSEP procedure (Ladd and Foott) Stress History And Normalized Soil Engineering Properties Normalized Soil Parameters NSP Major advantages: as more and more NSP data become available, less tests are needed NSP τ h This value o a soil is a constant or assumed: (1) OCR and (2) loading path (e.g. TC, TE, or DSS)
( 1 ) OCR=4 OCR=2 Overconsolidated Normally consolidated, OCR=1 or
The (c/p)=const concept have been recognized or NC clays or a long time Ladd and Foott extend the concept to OC clays Consolidate the clay back onto the virgin curve, unload to the desired OCR, and get the shear strength
Eect o Sampling N.C. clay, OCR=1 e or w% Field consolidation (beore sampling) Swelling The sample swells and takes in water No swelling Stress relie only (in sampling tube) log
= + u 0 = + u 0 hc = Ko + u 0 u 0 u + = K o + u 0 In the ield During sampling
In the lab. Beore setup. 1 = 0 20 0 % = = 0 = = = 1 = u 0 = = [1 0 u = u 0 A(1 K 0 A(1 K [ ( ) 0 )] ( + u + u 0 0 ) u ) + A( K 0 + )] 0. 5 For Ko = 0.5, A = 1.0, 1 = = 0 = = 2 2 (Elastic) For Ko 0.5, A =, 1 = = 0 =
NC Clay Ater N.C. clay goes through the sampling process, it may behaves like O.C. clay e or w% Virgin consolidation curve (actually, we don t have it) v, ield c log
To Obtain Field Undrained Shear Strength o N.C. clay Compute v, ield Measure shear strength in the lab Compute ield strength τ τ s u = ( ) lab v, ield
O.C. clays e or w% Virgin consolidation curve (actually, we don t have it) Highly disturbed v, ield max, ield v,lab max, lab log
To Obtain Field Undrained Shear Strength o O.C. clay Compute Measure shear strength in the lab or the ield τ OCR v, ield Compute ield strength τ s u = ( ) lab v, ield τ constant max, ield For a given OCR
O.C. clays in the lab in the ield Virgin consolidation curve (actually, we don t have it) e or w% Shear v, ield max, ield v,lab max, lab log
For a given OCR τ constant τ OCR
Comments Ladd and Foott s procedure eliminate the error o sampling, thus overestimate the shear strength on the unsae side Soil must have relatively insensitive structure, because using this procedure will consolidate and shear a lot o soil specimens