Soil Failure Criteria SHEAR STRENGTH OF SOIL Knowledge about the shear strength of soil important for the analysis of: Bearing capacity of foundations, Slope stability, Lateral pressure on retaining structures, etc. Soils fail in shear. Rutgers University Soil Mechanics Shear Strength 1 Rutgers University Soil Mechanics Shear Strength 2 Basic Concept of Shearing Resistance and Strength (from Murthy, 2003) Coulomb s Law s c tan Shear force F P tan a n m m where is angle of friction and tan the coefficient of friction. Shear stress is Fa Pn s tan tan A A Failure OK c cohesion angle of internal friction Rutgers University Soil Mechanics Shear Strength 3 Rutgers University Soil Mechanics Shear Strength 4 1
Coulomb s Law Shear Strength Parameters Typical Values of Drained Angle for Sands and Silts The shear strength parameters, c and, depend on: Past history of soil, The initial state with respect to the degree of saturation, Permeability of soil, Drainage conditions during loading (test), etc. Rutgers University Soil Mechanics Shear Strength 5 Rutgers University Soil Mechanics Shear Strength 6 Cohesion c Mohr s Circle for a Cylinder Specimen (from Murthy, 2003) For sands and inorganic silts = 0. For normally consolidated clays = 0. For overconsolidated clays > 0. Rutgers University Soil Mechanics Shear Strength 7 Rutgers University Soil Mechanics Shear Strength 8 2
Variation of and with a (from Murthy, 2003) Inclination of the Failure Plane (from Murthy, 2003) Rutgers University Soil Mechanics Shear Strength 9 Rutgers University Soil Mechanics Shear Strength 10 Inclination of the Failure Plane Inclination of the Failure Plane Normal and shear stresses on the inclined plane are 1 3 1 3 cos2a 2 2 For failure in the plane 1 3 2 sin 2a c tan Substituting normal and shear stresses 1 3 1 3 1 3 sin 2a c cos2a tan 2 2 2 3 tan c leads to 1 3 1 2 sin 2a cos a tan 2 From all possible solutions that touch or intersect the Coulomb s line, we look for the minimum value of 1. Rutgers University Soil Mechanics Shear Strength 11 Rutgers University Soil Mechanics Shear Strength 12 3
Inclination of the Failure Plane The minimum is obtained when 1 2 sin 2a cos a tan is maximum, or 2 d 1 2a 2 sin cos a tan 0 da 2 0 The minimum is obtained for a 45 / 2 The principal stresses at failure are 2 0 0 tan ( 45 / 2) 2c tan( 45 / 2) 1 3 Failure Plane and 1 (from Murthy, 2003) 2 0 0 tan ( 45 / 2) 2c tan( 45 / 2) 3 1 Rutgers University Soil Mechanics Shear Strength 13 Rutgers University Soil Mechanics Shear Strength 14 Inclination of the Failure Plane Alternatively, 2 0 N 2c N where N tan ( 45 / 2) 1 3 where N is called the flow value. For cohesionless soils For zero friction angle Special Cases N 1 3 for c 0 1 3 2c for 0 For no lateral pressure ( unconfined ) q 2c N for 0 1 u 3 q 2c for 0 & 0 1 u 3 Rutgers University Soil Mechanics Shear Strength 15 Rutgers University Soil Mechanics Shear Strength 16 4
Mohr Diagram for c- Soils Mohr Diagrams for c=0 (Left) and =0 (Right) Soils Rutgers University Soil Mechanics Shear Strength 17 Rutgers University Soil Mechanics Shear Strength 18 Failure Envelope in Terms of Effective Stresses Rutgers University Soil Mechanics Shear Strength 19 Shear Strength Tests 1. Shear Tests a) Direct Shear Laboratory test. Works well on sands, however it can be used for clays too. b) Simple Shear Laboratory test. Works well on both sands and clays. c) Torsional Shear Laboratory test. Works well on both sands and clays. d) Bore Hole Direct Shear Field test. Measures friction angle and cohesion on all soils in the field. e) Vane Shear Field test. Works well on cohesive fine-grained soils only. Measures undrained strength. Rutgers University Soil Mechanics Shear Strength 20 5
Shear Strength Tests 2. Compression Tests a) Triaxial Test Laboratory test. Works well on both sands (gravels) and clays. I Consolidated-Drained (CD) or slow II Consolidated-Undrained (CU) III Unconsolidated-Undrained (UU) or quick b) Unconfined Compression Test Uniaxial. Special case of UU test that measures the undrained shear strength. Principle: 1. Apply normal load. Direct Shear Test 2. Apply shear force until failure occurs. Two types of tests: 1. Stress controlled (controlled horizontal force). 2. Strain controlled. (Better for dense and overconsolidated clays.) Rutgers University Soil Mechanics Shear Strength 21 Rutgers University Soil Mechanics Shear Strength 22 Schematic of Direct Shear Test Schematic of Direct Shear Apparatus (from Murthy, 2003) Rutgers University Soil Mechanics Shear Strength 23 Rutgers University Soil Mechanics Shear Strength 24 6
Stress Controlled Direct Shear Test (Murthy, 2003) Strain Controlled Direct Shear Test (Murthy, 2003) Rutgers University Soil Mechanics Shear Strength 25 Rutgers University Soil Mechanics Shear Strength 26 Direct Shear Apparatus Direct Shear Apparatus Rutgers University Soil Mechanics Shear Strength 27 Rutgers University Soil Mechanics Shear Strength 28 7
Mohr Diagram for Direct Shear Test at Failure (from Murthy, 2003) Direct Shear Tests on Dense and Loose Dry Sands Rutgers University Soil Mechanics Shear Strength 29 Rutgers University Soil Mechanics Shear Strength 30 Strength Parameters from Direct Shear Test Shear Strength for Dense and Loose Sands (from Murthy, 2003) Rutgers University Soil Mechanics Shear Strength 31 Rutgers University Soil Mechanics Shear Strength 32 8
Drained Direct Shear Test on Overconsolidated Clay Failure Envelopes from Drained Direct Shear Rutgers University Soil Mechanics Shear Strength 33 Rutgers University Soil Mechanics Shear Strength 34 Peak and Ultimate Friction Angles for Granular Soils (from Murthy, 2003) Interface of Foundation and Soil Rutgers University Soil Mechanics Shear Strength 35 Rutgers University Soil Mechanics Shear Strength 36 9
Direct Shear Testing of Interface Friction Angle Variation of Friction Angle with Void Ratio Rutgers University Soil Mechanics Shear Strength 37 Rutgers University Soil Mechanics Shear Strength 38 Simple Shear Device Comparison of Simple and Direct Shear (from Murthy, 2003) Rutgers University Soil Mechanics Shear Strength 39 Rutgers University Soil Mechanics Shear Strength 42 10
Torsional Shear Device Schematic of Iowa Borehole Shear Device Rutgers University Soil Mechanics Shear Strength 43 Rutgers University Soil Mechanics Shear Strength 45 Iowa Borehole Shear Device Rutgers University Soil Mechanics Shear Strength 46 c c u u Vane Shear Test A very good device for measurement of the undrained shear strength of very soft clays, sludge, etc. f ( T, h, d) T 2 3 d h d 2 4 depends on the assumption of the shear stress distribution at the end surfaces. Rutgers University Soil Mechanics Shear Strength 47 11
Stress Distributions (after Das, 2002) =0.5 Vane Shear =2/3 =3/5 Rutgers University Soil Mechanics Shear Strength 48 Rutgers University Soil Mechanics Shear Strength 49 Rectangular and Tapered Vanes (ASTM Standards) Vane Shear Testing Rutgers University Soil Mechanics Shear Strength 50 Rutgers University Soil Mechanics Shear Strength 51 12
Laboratory Vane Shear Device Vane Shear - Torvane Rutgers University Soil Mechanics Shear Strength 52 Rutgers University Soil Mechanics Shear Strength 53 Triaxial Test Triaxial Test A very reliable test for evaluation of shear strength parameters. Tests conducted on cylindrical specimens of at least 2 (height) to 1 (diameter) ratio. Not a true triaxial test, since the lateral pressure in two directions cannot be varied. The test has two phases: 1. Consolidation phase The sample is subjected to hydrostatic (consolidation, cell) pressure. 2. Loading phase The sample is subjected to additional axial (deviatoric) loading until failure. Rutgers University Soil Mechanics Shear Strength 54 Rutgers University Soil Mechanics Shear Strength 55 13
Triaxial Test Based on the type of consolidation and loading, three test types: I Consolidated-Drained (CD) or slow II Consolidated-Undrained (CU) III Unconsolidated-Undrained (UU), or undrained, or quick test. Schematic of Triaxial Device Rutgers University Soil Mechanics Shear Strength 56 Rutgers University Soil Mechanics Shear Strength 57 Triaxial Device System Sample Saturation and Test Setup Rutgers University Soil Mechanics Shear Strength 58 Rutgers University Soil Mechanics Shear Strength 65 14
Consolidated-Drained Test (CD) Consolidated-Drained Triaxial Test Procedure: 1. Increase cell pressure 3 and allow dissipation of excess pore water pressure. 2. Deviatoric stress increased slowly so the Du d =0. At time t=0, increase in pore water pressure is expressed through Skempton s parameter B. u c B 3 Rutgers University Soil Mechanics Shear Strength 67 Rutgers University Soil Mechanics Shear Strength 68 Stress-Strain Curves for Three Dense Sand Samples (from Murthy, 2003) Mohr Envelope for Dense Sand (from Murthy, 2003) 3(3) 3(2) 3(1) Rutgers University Soil Mechanics Shear Strength 69 Rutgers University Soil Mechanics Shear Strength 70 15
Theoretical Values of B at Complete Saturation Volume change - consolidation Loose sand & NC clay Consolidated Drained Test (after Das, 2002) Dense sand & OC clay Deviatoric stress vs. axial strain Volume change vs. axial strain Rutgers University Soil Mechanics Shear Strength 71 Rutgers University Soil Mechanics Shear Strength 72 Effective Stress Envelope for CD Test Effective Stress Envelope for CD Test Sand and normally consolidated clay Overconsolidated clay Rutgers University Soil Mechanics Shear Strength 75 Rutgers University Soil Mechanics Shear Strength 76 16
Effect of Plasticity Index on sin (after Kenney, 1959) CD Test Example (Das 11.1) Rutgers University Soil Mechanics Shear Strength 77 Rutgers University Soil Mechanics Shear Strength 78 CD Test Example (Das 11.1) CD Test Example (Das 11.7) Rutgers University Soil Mechanics Shear Strength 79 Rutgers University Soil Mechanics Shear Strength 80 17
CD Test Example (Das 11.7) Consolidated-Undrained Test (CU) Procedure: 1. Increase cell pressure 3 and allow dissipation of excess pore water pressure. 2. During application of the deviatoric stress D d (D 1 ), the drainage valve is closed and the excess pore water pressure buildup Du d (Du 1 ) is recorded. Skempton s pore pressure parameter u d A D D d Rutgers University Soil Mechanics Shear Strength 81 Rutgers University Soil Mechanics Shear Strength 82 Stresses and Pore Water Pressure During CU Test During consolidation End of consolidation During application of d At failure ' D u 3 3 D 1 3 ' D u 1 1 df df df 3 ' 3 u ' 3 3 ' D u 3 3 D 1 3 ' D u 1 1 ' ' 1 3 1 3 d d d Consolidated- Undrained Test (after Das, 2002) A loose sands and normally consolidated clays. B dense sands and overconsolidated clays. Volume change - consolidation A Deviatoric stress B Pore water pressure A B Rutgers University Soil Mechanics Shear Strength 83 Rutgers University Soil Mechanics Shear Strength 84 18
Total and Effective Stress Failure Envelopes - CU Test Total Stress Failure Envelope for CU Test 1 3 1 / 3 1 sin / 1 1 3 1 3 Overconsolidated clay Rutgers University Soil Mechanics Shear Strength 85 Rutgers University Soil Mechanics Shear Strength 86 Mohr Circles for Undrained Shear Test on Partially Saturated Clay (from Murthy, 2003) Total Stress Envelope for Unstaurated Soil vs. Initial S Rutgers University Soil Mechanics Shear Strength 87 Rutgers University Soil Mechanics Shear Strength 88 19
CD and CU Example (Das, 11.6) CD and CU Example (Das, 11.6) Rutgers University Soil Mechanics Shear Strength 89 Rutgers University Soil Mechanics Shear Strength 90 CD and CU Example (Das, 11.6) CU Test Example (Murthy, 8.10) Rutgers University Soil Mechanics Shear Strength 91 Rutgers University Soil Mechanics Shear Strength 92 20
CU Test Example (Murthy, 8.10) CU Test Example (Murthy, 8.10) Rutgers University Soil Mechanics Shear Strength 93 Rutgers University Soil Mechanics Shear Strength 94 CU Test Example (Murthy, 8.15) CU Test Example (Murthy, 8.15) Rutgers University Soil Mechanics Shear Strength 95 Rutgers University Soil Mechanics Shear Strength 96 21
Unconsolidated-Undrained (UU) Test Loading Stages and Excess Pore Water Pressure - UU Test (from Murthy, 2003) No consolidation or dissipation of excess pore water pressure is allowed during either phase of the test => The load (a part of load) is carried by the excess pore water pressure. Total excess pore water pressure is u B A( ) u D u 3 1 3 c d Rutgers University Soil Mechanics Shear Strength 97 Rutgers University Soil Mechanics Shear Strength 98 Total Stress Failure Envelope from UU Test The =0 Concept in UU Test Fully saturated cohesive soil Rutgers University Soil Mechanics Shear Strength 99 Rutgers University Soil Mechanics Shear Strength 100 22
Unconfined Compression Test Unconfined Compression Device q u unconfined compression strength c u unconfined shear strength Rutgers University Soil Mechanics Shear Strength 101 Rutgers University Soil Mechanics Shear Strength 102 General Relationship of Consistency and q u of Clays q u for Undisturbed and Remolded Clay Rutgers University Soil Mechanics Shear Strength 103 Rutgers University Soil Mechanics Shear Strength 104 23
Classification of Clays Based on Sensitivity Behavior of Thixotropic Material S t q u( undisturbed ) q u( remolded ) Rutgers University Soil Mechanics Shear Strength 105 Rutgers University Soil Mechanics Shear Strength 106 Direct Shear Test Example (Murthy 8.3) Direct Shear Test Example (Murthy 8.3) Rutgers University Soil Mechanics Shear Strength 108 Rutgers University Soil Mechanics Shear Strength 109 24