CEL 610 Foundation Engineering

Shear Strength of Soils CEL 610 Foundation Engineering

Strength of different materials Steel Concrete Soil Tensile Compressive Shear strength strength strength Complex behavior Presence of pore water

Shear failure of soils Soils generally fail in shear Strip footing Embankment Failure surface Mobilized shear resistance At failure, shear stress along the failure surface (mobilized shear resistance) reaches the shear strength.

Shear failure of soils Soils generally fail in shear Retaining wall

Shear failure of soils Soils generally fail in shear Retaining wall Mobilized shear resistance Failure surface At failure, shear stress along the failure surface (mobilized shear resistance) reaches the shear strength.

Shear failure mechanism failure surface The soil grains slide over each other along the failure surface. No crushing of No crushing of individual grains.

Shear failure mechanism At failure, shear stress along the failure surface () reaches the shear strength ( f ).

Mohr-Coulomb Failure Criterion (in terms of total stresses) ) f c tan Cohesion c f Friction angle f is the maximum shear stress the soil can take without failure, under normal stress of.

Mohr-Coulomb Failure Criterion (in terms of effective stresses) ) c f tan Effective cohesion c f Effective fiti friction angle u u = pore water pressure f is the maximum shear stress the soil can take without failure, under normal effective stress of.

Mohr-Coulomb Failure Criterion Shear strength consists of two components: cohesive and frictional. c tan f f f frictional f tan c c f component

cand are measures of shear strength. Higher the values, higher the shear strength.

Mohr Circle of stress 1 3 3 Soil element 1 Resolving forces in and directions 2 3 1 Sin Resolving forces in and directions, 2 2 2 2 2 3 1 3 1 C Sin 2 3 1 2 3 1 2 2 2 2 2 2 3 1 3 1 Cos 2 2

Mohr Circle of stress 1 Soil element 3 3 1 2 2 2 1 3 1 3 2 2 2 1 3 3 2 1 3 1

Mohr Circle of stress 1 Soil element 3 3 1, 2 2 2 1 3 1 3 2 2 2 1 3 3 2 P D = Pole w.r.t. plane 1 3 1

Mohr Circles & Failure Envelope Failure surface c tan f X Y X Y Soil elements at different locations Y ~ stable X ~ failure

Mohr Circles & Failure Envelope The soil element does not fail if the Mohr circle is contained within the envelope GL Y c c Initially, Mohr circle is a point c c +

Mohr Circles & Failure Envelope As loading progresses, Mohr circle becomes larger GL Y c c c.. and finally failure occurs when Mohr circle touches the envelope

Orientation of Failure Plane 1 Failure envelope 3 3 1, f 3 2 1 3 1 P D = Pole w.r.t. plane Therefore, = 45 45 + /2

Mohr circles in terms of total & effective stresses v = X v u X h h + X u effective stresses total stresses h h v v h or h u v

Failure envelopes in terms of total & effective stresses v = X v u X h h + X u If X is on failure Failure envelope in terms of effective stresses effective stresses Failure envelope in terms of total stresses total stresses c c h h v v h or h u v

Mohr Coulomb failure criterion with Mohr circle of stress X v = 1 Failure envelope in terms of effective stresses h = 3 effective stresses c X is on failure 3 1 Therefore, 3 c Cot Sin 2 c Cot 1 1 3 2

Mohr Coulomb failure criterion with Mohr circle of stress of stress 3 1 3 1 Cot Sin c 2 2 Cot Sin c 2 C S 2 3 1 3 1 Cos c Sin 2 1 1 Cos c Sin Sin 2 1 1 3 1 Cos c Sin Sin 2 1 Cos c Sin 1 2 1 3 1 Sin c Sin 45 2 45 2 Tan c Tan 2 45 2 2 45 1 3 Tan c Tan

Determination of shear strength parameters of soils (c, or c Laboratory tests on Field tests specimens taken from representative undisturbed samples Most common laboratory testst 1. Vane shear testt to determine the shear strength 2. Torvane parameters are, 3. Pocket penetrometer 4. Fall cone 1.Direct shear test 5. Pressuremeter 2.Triaxial shear test 6. Static cone penetrometer Other laboratory tests include, 7. Standard penetration test Direct simple shear test, torsional ring shear test, t plane strain ti triaxiali test, laboratory vane shear test, laboratory fall cone test

Laboratory tests Field conditions A representative soil sample vc z vc + z hc hc hc hc vc vc + Before construction After and during construction

Laboratory tests Simulating field conditions in the laboratory 0 vc hc vc + hc vc + 0 0 hc hc vc 0 vc Representative Step 1 soil sample Set the specimen in Step 2 taken from the site the apparatus and Apply the apply the initialiti corresponding field stress condition stress conditions vc

Direct shear test Schematic diagram of the direct shear apparatus

Direct shear test Direct shear testt is most suitable for consolidated d drained d testst specially on granular soils (e.g.: sand) or stiff clays Preparation of a sand specimen Porous plates Components of the shear box Preparation of a sand specimen

Direct shear test Preparation of a sand specimen Pressure plate Leveling the top surface of specimen Specimen preparation completed

Direct shear test Test procedure Porous plates P Steel ball Pressure plate S Proving ring to measure shear force Step 1: Apply a vertical load to the specimen and wait for consolidation

Direct shear test Test procedure Porous plates P Steel ball Pressure plate S Proving ring to measure shear force Step 1: Apply a vertical load to the specimen and wait for consolidation Step 2: Lower box is subjected to a horizontal displacement at a constant rate

Direct shear test Shear box Dial gauge to measure vertical displacement Proving ring to measure shear force Loading frame to Dial gauge g to apply vertical load measure horizontal displacement

Direct shear test Analysis of test results Normal stress Area of Normal force (P) cross section of the sample Shear stress Shear resistance Area of developed d at the sliding surface cross section of the sample (S) Note: Cross-sectional area of the sample changes with the horizontal displacement dspace e

Direct shear tests on sands Stress-strain relationship She ear stre ess, f f Dense sand/ OC clay Loose sand/ NC clay Shear displacement height mple hange in the sam Ch of Expansi ion Compres ssion Dense sand/oc Clay Shear displacement Loose sand/nc Clay

Direct shear tests on sands How to determine strength parameters c and She ear stress s, f3 f2 Normal stress = 3 Normal stress = 2 Normal stress = 1 f1 Shear displacement Shea ar stress s at failure, f Mohr Coulomb failure envelope Normal stress,

Direct shear tests on sands Some important facts on strength parameters c and of sand Sand is cohesionless hence c = 0 Direct shear tests are drained and pore water pressures are dissipated, hence u = 0 Therefore, = and c = c = 0

Direct shear tests on clays In case of clay, horizontal displacement should be applied at a very slow rate to allow dissipation of pore water pressure (therefore, one test would take several days to finish) Failure envelopes for clay from drained direct shear tests Shear stress at failure e, f Overconsolidated clay y( (c 0) Normally consolidated clay (c = 0) Normal force,

Interface tests on direct shear apparatus Inmany foundation design problems and retaining i wall problems, it is required to determine the angle of internal friction between soil and the structural material (concrete, steel or wood) P Soil S Foundation material f c a tan Where, c a = adhesion, = angle of internal friction

Triaxial Shear Test Piston (to apply deviatoric stress) Failure plane O-ring Soil sample at failure Perspex cell Soil sample impervious membrane Porous stone Water Cell pressure Back pressure pedestal Pore pressure or volume change

Triaxial Shear Test Specimen preparation (undisturbed sample) Sampling tubes Sample extruder

Triaxial Shear Test Specimen preparation (undisturbed sample) Edges of the sample are carefully trimmed Setting up the sample in the triaxial cell

Triaxial Shear Test Specimen preparation (undisturbed sample) Sample is covered with a rubber membrane and sealed Cell is completely filledwithwater

Triaxial Shear Test Specimen preparation (undisturbed sample) Proving ring to measure the deviator load Dial gauge to measure vertical displacement

Types of Triaxial Tests Step 1 c Step 2 deviatoric stress ( = q) c c c c c Under all-around cell pressure c c + q Shearing (loading) Is the drainage valve open? Is the drainage valve open? yes no yes no Consolidated Unconsolidated d sample sample Drained Undrained d loading loading

Types of Triaxial Tests Step 1 Step 2 Under all-around aro cell pressure c Shearing (loading) Is the drainage valve open? Is the drainage valve open? yes no yes no Consolidated Unconsolidated Drained Undrained sample sample loading loading CD test UU test CU test

Consolidated- drained test (CD Test) Total, = Neutral, u Effective, Step 1: At the end of consolidation VC + VC = VC hc 0 Drainage 0 hc = hc Step 2: During axial stress increase Drainage VC + V = VC + = 1 hc 0 h = hc = 3 Step 3: At failure VC + f Vf = VC + f = 1f Drainage hc 0 hf = hc = 3f

Consolidated- drained test (CD Test) 1 = VC + 3 = hc Deviator stress (q or d ) = 1 3

Consolidated- drained test (CD Test) Volume change of sample during consolidation Time Volume change of the sample Compression Expansion

Consolidated- drained test (CD Test) Stress-strain relationship during shearing r stress s, d Deviato d ) f d ) f Dense sand or OC clay Loose sand or NC Clay Axial strain hange mple olume ch the sam Vo of Expansi ion Compres ssion Dense sand or OC clay Axial strain Loose sand or NC clay

CD tests How to determine strength parameters c and ress, d Dev viator str d d) fc 1 = 3 +( ( d ) f = 3b Confining stress = 3c Confining i stress d ) fb Confining stress = 3a 3 d ) fa She ear stre ess, Mohr Coulomb failure envelope 3a 3b Axial strain 3c 1a 1b 1c or ( d ) fa ( d ) fb

CD tests Strength parameters c and obtained from CD tests Since u = 0 in CD Therefore, c = c tests, = and = c d and d are used to denote them

CD tests Failure envelopes For sand and NC Clay, c d = 0 stress s, Mohr Coulomb failure envelope d Shear 3a ( d ) fa 1a or Therefore, one CD test would be sufficient to determine d Therefore, one CD test would be sufficient to determine d of sand or NC clay

CD tests Failure envelopes For OC Clay, c d 0 OC NC c 3 1 c or ( d ) f

Some practical applications of CD analysis for clays 1. Embankment constructed very slowly, in layers over a soft clay deposit Soft clay = in situ drained shear strength

Some practical applications of CD analysis for clays 2. Earth dam with steady state seepage Core = drained shear strength of clay core

Some practical applications of CD analysis for clays 3. Excavation or natural slope in clay = In situ drained shear strength Note: CD test simulates the long term condition in the field. Thus, c d and d shouldbeusedtoevaluatethelong term behavior of soils

Consolidated- Undrained test (CU Test) Total, = Neutral, u Effective, Step 1: At the end of consolidation VC + VC = VC hc 0 Drainage 0 Step 2: During axial stress increase VC + hc = hc V = VC + ± u = 1 No drainage hc ±u h = hc ± u= 3 Step 3: At failure VC + f Vf = VC + f ± u f = 1f No drainage hc ±u f hf = hc ± u f = 3f

Consolidated- Undrained test (CU Test) Volume change of sample during consolidation Time Volume change of the sample Compression Expansion

Consolidated- Undrained test (CU Test) Stress-strain relationship during shearing r stress s, d Deviato d ) f d ) f Dense sand or OC clay Loose sand or NC Clay Axial strain + Loose sand /NC Clay u - Axial strain Dense sand or OC clay

CU tests How to determine strength parameters c and Shear stress, ress, d Dev viator str d ) fb d) fb 1 = 3 +( d ) f Confining stress = 3b Confining stress = 3a d ) fa Axial strain Mohr Coulomb failure envelope in terms of total stresses 3 Total stresses at failure cu c cu 3a 3b 1a 1b ( d ) fa or

CU tests How to determine strength parameters c and 1 = 3 + ( d ) f -u f Shea ar stres ss, Mohr Coulomb failure envelope in terms of effective stresses Mohr Coulomb failure envelope in terms of total stresses u f = 3 -u f Effective stresses at failure cu C u fa u fb c cu 3b 1b 3a 3a 3b 1a 1a ( d ) fa 1b or

CU tests Strength parameters c and obtained from CD tests Shear strength Shear strength parameters in terms parameters in terms of effective stresses of total stresses are are c and c cu and cu c = c d and = d

CU tests Failure envelopes For sand and NC Clay, c cu and c = 0 ress, Mohr Coulomb failure envelope in terms of effective stresses Mohr Coulomb failure envelope in terms of total stresses cu hear st Sh 3a 3a 1a 1a or ( d ) fa Therefore, one CU test would be sufficient to determine cu and = d ) of sand or NC clay

Some practical applications of CU analysis for clays 1. Embankment constructed rapidly over a soft clay deposit Soft clay = in situ undrained shear strength

Some practical applications of CU analysis for clays 2. Rapid drawdown behind an earth dam Core = Undrained shear strength of clay core

Some practical applications of CU analysis for clays 3. Rapid construction of an embankment on a natural slope = In situ undrained shear strength Note: Total stress parameters from CU test (c cu and cu ) canbeusedfor stability problems where, Soil have become fully consolidated and are at equilibrium with the existing stress state; Then for some reason additional stresses are applied quickly with no drainage occurring

Unconsolidated- Undrained test (UU Test) Data analysis Initial specimen condition Specimen condition during shearing No drainage C = 3 C = 3 No drainage 3 + d 3 Initial i volume of the sample = A 0 H 0 Volume of the sample during shearing = A H Since the test is conducted under undrained condition, A H = A 0 H 0 A (H 0 H) = A 0 H 0 A (1 H/H 0 ) = A 0 A A 0 1 z

Unconsolidated- Undrained test (UU Test) Step 1: Immediately after sampling 0 0 Step 2: After application of hydrostatic cell pressure C = 3 3 = 3 - u c No drainage C = 3 u c 3 = 3 - u c drainage = + Increase of pwp due to increase of cell pressure u c = B 3 Skempton s pore water pressure parameter, B Increase of cell pressure Note: If soil is fully saturated, then B = 1 (hence, u c = 3 )

Unconsolidated- Undrained test (UU Test) Step 3: During application of axial load 1 = 3 + d - u c u d No drainage 3 + d 3 = + 3 = 3 - u c u d u c ± u d u d = AB d Increase of pwp due to increase of deviator stress Increase of deviator stress Skempton s pore water pressure parameter, A

Unconsolidated- Undrained test (UU Test) Combining steps 2 and 3, u c =B 3 u d = AB d Total pore water pressure increment at any stage, u u=u c + u d u=b [ 3 + A d ] u=b [ 3 + A( 1 3 ] Skempton s pore water pressure equation

Unconsolidated- Undrained test (UU Test) Total, = Neutral, u Effective, Step 1: Immediately after sampling 0 + V0 =u r 0 -u r Step 2: After application of hydrostatic cell pressure No drainage C C -u r u c = -u r c (S r = 100% ; B = 1) h0 =u r VC = C + u r - C = u r h =u r Step 3: During application of axial load V = C + + u r - c u C + No drainage C -u r c ± u h = C +u r - c u Step 3: At failure Vf = C + f + u r - c u f = 1f C + No f drainage hf = C +u r - c u C -u f r c ± u f = 3f

Unconsolidated- Undrained test (UU Test) Total, = Neutral, u Effective, Step 3: At failure Vf = C + f + u r - c u f = 1f + C f No drainage hf = C +u r - c u C -u f r c ± u f = 3f Mohr circle in terms of effective stresses do not depend on the cell pressure. Therefore, we get only one Mohr circle in terms of effective stress for different cell pressures + 3 1 f

Unconsolidated- Undrained test (UU Test) Total, = Neutral, u Effective, Step 3: At failure Vf = C + f + u r - c u f = 1f + C f No drainage hf = C +u r - c u C -u f r c ± u f = 3f + Mohr circles in terms of total stresses Failure envelope, u = 0 c u u b u a 3a 3b f 1a 1b 3 1 or

Unconsolidated- Undrained test (UU Test) Effect of degree of saturation on failure envelope S < 100% S > 100% 3c c or 3b 3a b a

Some practical applications of UU analysis for clays 1. Embankment constructed rapidly over a soft clay deposit Soft clay = in situ undrained shear strength

Some practical applications of UU analysis for clays 2. Large earth dam constructed rapidly with no change in water content of soft clay Core = Undrained shear strength of clay core

Some practical applications of UU analysis for clays 3. Footing placed rapidly on clay deposit = In situ undrained shear strength Note: UU test simulates the short term condition in the field. Thus, c u can be used to analyze the short term behavior of soils

Unconfined Compression Test (UC Test) 1 = VC + 3 = 0 3 Confining pressure is zero in the UC test

Unconfined Compression Test (UC Test) 1 = VC + f 3 = 0 She ear stres ss, q u Normal stress, τ f = σ 1 /2 = q u /2 = c u

Various correlations for shear strength For NC clays, the undrained shear strength (c u ) increases with the effective overburden pressure, 0 c u 0 0.11 0.0037( PI) Skempton (1957) Plasticity Index as a % For OC clays, the following relationship is approximately true c u cu 0. 8 (OCR) 0 0 Overconsolidated NormallyConsolidated Ladd (1977) For NC clays, the effective friction angle ( ) is related to PI as follows Sin 0.814 0.234 log( IP) Kenny (1959)

Shear strength of partially saturated soils In the previous sections, we were discussing the shear strength of saturated soils. However, in most of the cases, we will encounter unsaturated soils Water Pore water pressure, u Air Water Pore air pressure, u a Pore water Solid Effective stress, Solid pressure, u w Effective stress, Saturated soils Unsaturated soils Pore water pressure can be negative in unsaturated soils

Shear strength of partially saturated soils Bishop (1959) proposed shear strength equation for unsaturated soils as follows f c ( u ) ( u u ) tan n a a w Where, n u a = Net normal stress u a u w = Matric suction = a parameter depending on the degree of saturation ( = 1 for fully saturated soils and 0 for dry soils) Fredlund et al (1978) modified the above relationship as follows f c ( n u a ) tan ( u a u w ) b tan Where, tan b = Rate of increase of shear strength with matric suction

Shear strength of partially saturated soils f c ( n u a ) tan ( u a u w ) b tan Same as saturated soils Apparent cohesion due to matric suction Therefore, strength of unsaturated soils is much higher than the strength of saturated soils due to matric suction - u a

How it become possible build a sand castle f c ( u ) tan ( u n a a u w ) b tan Same as saturated soils Apparent cohesion due to matric suction Apparent cohesion - u a