Shear Strength of Soils
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1 Shear Strength of Soils
2 STRESSES IN A SOIL ELEMENT t s v Analyze Effective Stresses (s ) Load carried by Soil t Where: s H t t s H s = t f = s v = s H = t = s v Stresses in a Soil Element after Figure 8.1a. Das FGE (2005)
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7 Shear Stress (t) MOHR FAILURE ENVELOPE Failure Cannot Exist Stable t f = f(s ) Failure Envelope Normal Effective Stress (s ) Mohr Functional Relationship after Figure 8.1b. Das FGE (2005) t f f (s )
8 Shear Stress (t) FACTORS AFFECTING EFFECTIVE FRICTION ANGLE (f ) Cohesionless Soils (c 0) MC Failure Criteria Failure Cannot Exist t Stable f c s tanf Normal Effective Stress (s ) c 0 for sands, inorganic silts,& NC clays MC Failure Criteria after Figure 8.1b. Das FGE (2005)
9 TYPICAL DRAINED FRICTION ANGLES (f ) Table 8.1. Das FGE (2005) Soil D r f ( ) Sand (Rounded) Sand (Angular) Gravels (w/ some sands) Loose Medium Dense Loose Medium Dense Silts 26-35
10 TYPICAL DRAINED FRICTION ANGLES (f ) Coarse Grained Soils Figure 7. NAVFAC DM 7.01 (1986)
11 Shear Stress (t) INCLINATION OF FAILURE PLANE PRINCIPAL STRESSES s 1 MC Failure Criteria h s 3 s 3 q d Where: s 1 s 1 = Major Principal Stress s 3 = Minor Principal Stress f f g O c 2q e b a s 3 Normal Stress (s ) s 1 Normal Stress (s ) Inclination of Failure Plane with Major Principal Plane Figure 8.2. Das FGE (2005)
12 Shear Stress (t) INCLINATION OF FAILURE PLANE PRINCIPAL STRESSES MC Failure Criteria h Angle dab = 2q = 90 + f or From Figure 8.2 d f f g c 2q e b s 3 Normal Stress a (s ) s 1 Normal Stress (s ) Substituting Figure 8.2. Das FGE (2005)
13 Shear Stress (t) INCLINATION OF FAILURE PLANE PRINCIPAL STRESSES MC Failure Criteria h From Previous Slide d or f f g c 2q e b a s 3 Normal Stress (s ) s 1 Normal Stress (s ) Trigonometry Identities and Figure 8.2. Das FGE (2005) Therefore MC Failure Criteria in Terms of Failure Stresses
14 SHEAR STRENGTH LABORATORY TESTING SUMMARY Test ASTM Pore Pressure Soil Types Drained Undrained Coarse Grained Fine Grained Direct Shear D3080 Y N Y See Note 1 Triaxial CD - WK3821 CU D4767 UU D2850 Y Y Y Y Unconfined Compression D2166 N Y N Y NOTES: 1. Possible, but not recommended. Takes 2-5 days to allow for drained conditions.
15 s = Confining Stress = Normal Force/Area DIRECT SHEAR TESTING t t Figure 8.3. Das FGE (2006). Photograph courtesy of ELE.
16 s = Confining Stress = Normal Force/Area DIRECT SHEAR TESTING t t Figure 8.3. Das FGE (2006).
17 s = Confining Stress = Normal Force/Area DIRECT SHEAR TESTING t t Figure 8.3. Das FGE (2006). NOTE: Cross-section Area (A) is from start of test
18 Components of Shear Strength for Cohesionless Soils (Rowe, 1962) Friction Resistance:. DIRECT SHEAR TESTING Direct Shear Test Results Dry Sands Dilation:. Ultimate = Residual Interference: Figure 8.5. Das FGE (2006).
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20 DIRECT SHEAR TESTING. Typical Direct Shear Results Dry Sand (c = 0) Peak Results Only Figure 8.3. Das FGE (2006).
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24 DIRECT SHEAR TESTING EXAMPLE #1 GIVEN: A Poorly Graded Sand (SP) from a Local Sand Pit with the following Direct Shear Test Results. Test Confining Stress (s) (psi) Shear Stress (t) (psi) Peak Residual REQUIRED: Determine the peak friction angle (f peak ) and residual Friction angle (f residual ) for this material.
25 DIRECT SHEAR TESTING EXAMPLE #1 20 Shear Stress (t) (psi) Confining Stress (s) (psi)
26 DIRECT SHEAR TESTING EXAMPLE #2 GIVEN: A Clayey Sand (SC) from a Local Sand Pit with the following Direct Shear Test Results. Test Confining Stress (s) (psf) Shear Stress (t) (psf) Peak Residual REQUIRED: Determine the peak friction angle (f peak ) and residual Friction angle (f residual ) for this material.
27 DIRECT SHEAR TESTING EXAMPLE # Shear Stress (t) (psf) Confining Stress (s) (psf)
28 DIRECT SHEAR TESTING INTERFACIAL SHEAR t f c a s tan FOUNDATION t t SOIL Where: t f = Shear Stress on Failure Plane s = Normal Effective Stress on Failure Plane c a = Adhesion = Effective Interfacial Friction Angle APPLICATION EXAMPLES: Interfacial Shear between Foundation and Soil after Figure 8.7. Das FGE (2006). Deep Foundations Retaining Walls
29 DIRECT SHEAR TESTING INTERFACIAL SHEAR STANDARDS (Geomembrane Interfacial Shear Testing): ASTM D Standard Test Method for Determining the Coefficient of Soil and Geosynthetic or Geosynthetic and Geosynthetic Friction by the Direct Shear Method BS 6906:1991 (British Standard) GDA E (German Recommendation for Landfill Design). Direct Shear Interfacial Testing for Geomembranes (after Mofiz, 2000)
30 Other Interfacial Testing Methods: The Dual Interface Apparatus - Paikowsky et al. (1995) INTERFACIAL FRICTION ANGLE General Rule of Thumb Relating and f: 1/3f < < 2/3f Table 1. NAVFAC DM 7.02 (1986)
31 TRIAXIAL SHEAR TESTING Figure 7-7a. FHWA NHI
32 TRIAXIAL SHEAR TESTING Test Samples: Diameter: 35 to 75 mm 2 D/L Ratio 2.5 D = Diameter L = Length Figure 7-7d. FHWA NHI
33 TRIAXIAL SHEAR TEST SETUP Connection determines cheap or good triaxial setup Axial Load Pressure Source Chamber Filled w/ water or glycerine Triaxial Cylinder (Plexiglass) Porous Stone Soil Sample Membrane Valve Drainage Connection Pore Pressure Measurement Valve Figure 8.9. Das FGE (2006). Porous Stone Base Inlet for Filling
34 s 1 = P/A Applied Stress TRIAXIAL SHEAR TESTING u Soil s 3 u Figure 5. NAVFAC DM 7.01 (1986). Ds d s 1 - s 3
35 s 1 TRIAXIAL SHEAR TESTING BASIC TRIAXIAL TESTS u Test Type ASTM Simple Abbr. Consolidated Drained WK3821 CD Letter S Slow Soil s 3 Consolidated Undrained D4767 CU R Rapid Unconsolidated Undrained D2850 UU Q Quick Figure 5. NAVFAC DM 7.01 (1986). u Full Test Abbreviations (Example): C I D C (L) Consolidation State (Consolidated/Unconsolidated) Consolidation Condition (Isotropic, Anisotropic (e.g. K o )) Loading/Unloading Compression/Extension Drained/Undrained
36 s 3 CONSOLIDATED DRAINED (CD) TEST Check for Saturation (Skempton s Pore Pressure Parameter B) s 3 u c = 0 (Drained prior to test) s 3 After Isotropic Consolidation Prior to Drainage u c s 3 (i.e. B 1) Water takes the Load s 3 Where: B = Skempton s Pore Pressure Parameter B 1 for Saturated Soils (see Table 8.2 below) u c = Pore Pressure Increase due to Confining Stress s 3 = Confining Stress Table 8.2. Theoretical Values of B at S = 100% (Das FGE 2006).
37 Ds d CONSOLIDATED DRAINED (CD) TEST S Slow Test s 3 s 3 Du d = 0 s 3 and s 3 Ds d During Axial Compression Loading
38 Shear Stress (t) CONSOLIDATED DRAINED (CD) TEST RESULTS Sands and Normally Consolidated Clays Total Stress Envelope = Effective Stress Envelope t f = s tanf + c Test 1 Test 2 Test 3 f c 0 s 3f s 3f s 3f s 1f s 1f (Ds d ) f s 1f Normal Stress (s ) Total and Effective Stress Failure Envelope from CD Tests Figure Das FGE (2006). Should use a Minimum of Three Tests
39 Shear Stress (t) CONSOLIDATED DRAINED (CD) TEST RESULTS Overconsolidated Clays Test 1 Test 2 Test 3 Test 4 OC s vm NC t f = s tanf f = f NC t f = s tanf + c f 1 = f OC c s 3f s 3f s 1f s 3f s 1f s 3f (Ds d ) f s 1f Normal Stress (s ) s 1f Total and Effective Stress Failure Envelope from CD Tests Figure Das FGE (2006).
40 CONSOLIDATED DRAINED (CD) TEST RESULTS CD Test Volume Change with Time during Consolidation (DV c ) Figure 8.11a. Das FGE (2006).
41 CONSOLIDATED DRAINED (CD) TEST RESULTS Loose Sands and Normally Consolidated Clays Change in Deviator Stress (Ds d ) vs. Axial Strain (e v ) Figure 8.11b. Das FGE (2006). Volume Change (DV d ) vs. Axial Strain (e v ) Figure 8.11d. Das FGE (2006).
42 CONSOLIDATED DRAINED (CD) TEST RESULTS Dense Sands and Overconsolidated Clays Change in Deviator Stress (Ds d ) vs. Axial Strain (e v ) Figure 8.11c. Das FGE (2006). Volume Change (DV d ) vs. Axial Strain (e v ) Figure 8.11e. Das FGE (2006).
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46 CONSOLIDATED UNDRAINED (CU) TEST Ds d Skempton s Pore Pressure Parameter Ā s 3 s 3 Du d 0 s 3 Where: Ā = Skempton s Pore Pressure Parameter Du d = Pore Pressure Increase due to Deviator Stress Ds d = Deviator Stress s 3 Ds d Setup same as CD Test. Check for Saturation (B parameter). Close drainage valve prior to test to make undrained (i.e. allow pore pressure buildup within sample). Pore pressure can be measured during test to determine effective stresses.
47 CONSOLIDATED UNDRAINED (CU) TEST Ds d R Rapid Test s 3 DO NOT allow drainage of sample during testing. Therefore, pore pressures within the soil sample buildup during shear (i.e. Du d 0). Therefore: s 3 Du d 0 s 3 Where: s 3 Ds d During Axial Compression Loading s 3f = Minor Principal Stress at Failure s 3f = Minor Principal Effective Stress at Failure (Ds d ) f = Deviator Stress at Failure (Du d ) f = Pore Pressure Increase at Failure s 1f = Major Principal Stress at Failure s 1f = Major Principal Effective Stress at Failure
48 Shear Stress (t) CONSOLIDATED UNDRAINED (CU) TEST RESULTS Sands and Normally Consolidated Clays Effective Stress Envelope t f = stanf + c f f Total Stress Envelope t f = stanf + c c & c 0 (Du d ) f s 3f s 3f s 1f s 1f (Ds d ) f (Ds d ) f Normal Stress (s ) (Du d ) f * Still Need a Minimum of Three Tests!
49 CONSOLIDATED UNDRAINED (CU) TEST RESULTS CU Test Volume Change with Time during Consolidation (DV c ) (Still allowing drainage during Consolidation) Figure 8.17a. Das FGE (2006).
50 CONSOLIDATED UNDRAINED (CU) TEST RESULTS Loose Sands and Normally Consolidated Clays Change in Deviator Stress (Ds d ) vs. Axial Strain (e v ) Figure 8.17b. Das FGE (2006). Pore Pressure Change (Du d ) vs. Axial Strain (e v ) Figure 8.17d. Das FGE (2006).
51 CONSOLIDATED UNDRAINED (CU) TEST RESULTS Dense Sands and Overconsolidated Clays Change in Deviator Stress (Ds d ) vs. Axial Strain (e v ) Figure 8.17e. Das FGE (2006). Pore Pressure Change (Du d ) vs. Axial Strain (e v ) Figure 8.17g. Das FGE (2006).
52 UNCONSOLIDATED UNDRAINED (UU) TEST Ds Q Quick Test d s 3 Drainage of sample not permitted during application of confining stress s 3 or during testing (i.e. application of Ds d ). Therefore, pore pressures within the soil sample at any stage of testing is: s 3 u 0 s 3 Therefore: Where: s 3 Ds d s 3 = Minor Principal Stress s 1 = Major Principal Stress Ds d = Deviator Stress Du d = Pore Pressure Increase due to Deviator Stress B = Skempton s Pore Pressure Parameter Ā = Skempton s Pore Pressure Parameter
53 Shear Stress (t) UNCONSOLIDATED UNDRAINED (UU) TEST RESULTS Test 1 Test 2 Test 3 Total Stress Mohr s Circles at Failure Failure Envelope f = 0 c u c u = S u Undrained Shear Strength s 3f s 3f s 1f s 1f s 3f s 1f (Ds d ) f (Ds d ) f constant regardless of confining stress (s 3 ) Figure Das FGE (2006). Normal Stress (s)
54 t UNCONSOLIDATED UNDRAINED (UU) TEST RESULTS Test 1 Test 2 Total Stress Mohr s Circles at Failure Failure Envelope f = 0 c u s 3f s 3f s 1f s 3f s 1f (Ds d ) f (Ds d ) f (Ds d ) f s 1f s (Du d ) f Ds 3 = Du c Figure Das FGE (2006).
55 UNCONFINED COMPRESSION TEST Cohesive Soils UC Test Setup (Courtesy of Durham Geo) Figure Das PGE (2006).
56 Shear Stress (t) UNCONFINED COMPRESSION TEST Cohesive Soils Where: q u = Unconfined Compression Strength c u = Undrained Shear Strength s 1 Failure Envelope f = 0 Soil c u = q u /2 Total Stress Mohr s Circle at Failure s 3 s 1 = q u Normal Stress (s ) s 1 q u Figure Das FGE (2006).
57 UNCONFINED COMPRESSION TEST General Relationship between Consistency and q u of Cohesive Soils Table 8.3 Das FGE (2006) Consistency q u (tsf) q u (kn/m²) Very Soft Soft Medium Stiff Very Stiff Hard > 4 > tsf = 95.8 kpa 100 kpa
58 Shear Stress (t) UNCONFINED COMPRESSION (UC) & UNCONSOLIDATED UNDRAINED (UU) TEST COMPARISON Test 1 - UC Test 2 - UU Test 3 - UU Actual Failure Envelope Theoretical Failure Envelope f = 0 c u s 3 q u = s 1f s 1 s 3 s 1 Figure Das FGE (2006). Normal Stress (s )
59 SENSITIVITY OF COHESIVE SOILS S t Sensitivity Undisturbe d Shear Strength Disturbed Shear Strength Disturbed = Remolded Unconfined Compression Strength for Undisturbed and Remolded Clays Example: Unconfined Compression S u( undisturbed ) u( disturbed Figure Das FGE (2006). ) t q q
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