Mekanika Tanah - Triaxial shear test
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The document discusses triaxial shear testing of soils. It begins by explaining that soils fail primarily in shear and defining shear strength. It then details the process of a triaxial shear test, including sample preparation and testing stages. The key types of triaxial tests - consolidated drained (CD), consolidated undrained (CU), and unconsolidated undrained (UU) - are explained. Specifically, the document focuses on CD testing, showing how volume change is monitored during shearing and how stress-strain behavior varies with soil density. It also demonstrates how shear strength parameters (c, φ) are determined from CD test results and how the parameters relate to effective stresses and long-term soil behavior analysis.
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Mekanika Tanah - Triaxial shear test
- 1. Triaxial Shear Test CEP 701 - Soil Engineering Laboratory
- 2. Strength of different materials Steel Tensile strength Concrete Compressive strength Complex behavior Soil Shear strength Presence of pore water
- 3. Shear failure of soils Soils generally fail in shear Embankment Strip footing Failure surface Mobilized shear resistance At failure, shear stress along the failure surface (mobilized shear resistance) reaches the shear strength.
- 4. Shear failure of soils Soils generally fail in shear Retaining wall
- 5. 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.
- 6. Shear failure mechanism failure surface The soil grains slide over each other along the failure surface. No crushing of individual grains.
- 7. Shear failure mechanism σ τ τ At failure, shear stress along the failure surface (τ) reaches the shear strength (τf).
- 8. Mohr-Coulomb Failure Criterion (in terms of total stresses) τ τ f = c + σ tan φ failu Cohesio n re τf c σ φ e elop env Friction angle σ τf is the maximum shear stress the soil can take without failure, under normal stress of σ.
- 9. Mohr-Coulomb Failure Criterion (in terms of effective stresses) τ τ f = c'+σ ' tan φ ' re ailu f Effective cohesion τf c’ σ’ e elop env σ ' =σ −u φ’ u = pore water pressure Effective friction angle σ’ τf is the maximum shear stress the soil can take without failure, under normal effective stress of σ’.
- 10. Mohr-Coulomb Failure Criterion Shear strength consists of two components: cohesive and frictional. τ τ f = c'+σ ' f tan φ ' τf φ’ c’ σ’f tan φ’ c’ σ’f iv hes co t nen po com e frictional component σ' c and φ are measures of shear strength. Higher the values, higher the shear strength.
- 11. Mohr Circle of stress σ’ 1 σ’ σ’ Soil element 3 τ σ’ 3 θ σ’ 1 Resolving forces in σ and τ directions, σ 1' − σ 3' τ= Sin 2θ 2 σ 1' + σ 3' σ 1' − σ 3' σ' = + Cos 2θ 2 2 ' σ +σ τ + σ − 2 2 ' 1 ' 2 3 σ −σ = 2 ' 1 ' 2 3
- 12. Mohr Circle of stress σ’1 σ’ σ’3 τ θ Soil element σ’3 σ’1 τ ' σ +σ τ + σ − 2 2 ' 1 ' 2 3 σ −σ = 2 ' 1 ' 2 3 ' σ 1' − σ 3 2 ' σ3 ' σ 1' + σ 3 2 σ 1' σ’
- 13. Mohr Circle of stress σ’1 σ’ σ’3 σ’3 τ θ Soil element σ’1 τ ' σ +σ τ + σ − 2 2 ' 1 ' 2 3 σ −σ = 2 ' 1 (σ’, τ) ' 2 3 θ ' σ3 ' σ 1' − σ 3 2 ' σ 1' + σ 3 2 PD = Pole w.r.t. plane σ 1' σ’
- 14. Mohr Circles & Failure Envelope τ Failure surface X Y τ f = c'+σ ' tan φ ' X Y σ’ Soil elements at different locations Y ~ stable X ~ failure
- 15. Mohr Circles & Failure Envelope The soil element does not fail if the Mohr circle is contained within the envelope GL ∆σ σc Y σc σc Initially, Mohr circle is a point ∆σ σc+∆σ
- 16. Mohr Circles & Failure Envelope As loading progresses, Mohr circle becomes larger… GL σc Y ∆σ σc σc .. and finally failure occurs when Mohr circle touches the envelope
- 17. Orientation of Failure Plane σ’1 Failure envelope σ’ σ’3 τ σ’3 θ σ’1 (σ’, τ f) (90 – θ) θ φ’ ' σ3 ' σ 1' + σ 3 2 PD = Pole w.r.t. plane Therefore, 90 – θ + φ’ = θ θ = 45 + φ’/2 σ 1' σ’
- 18. Mohr circles in terms of total & effective stresses σv X σ v’ σh = X u σ h’ + X u τ effective stresses σh ’ σv’ σh total stresses u σv σ or σ’
- 19. Failure envelopes in terms of total & effective stresses σv X If X is on failure σ v’ σh τ = X u σ h’ Failure envelope in terms of effective stresses φ’ effective stresses c’ c σh ’ σv’ σh + X u Failure envelope in terms of total stresses φ total stresses u σv σ or σ’
- 20. Mohr Coulomb failure criterion with Mohr circle of stress σ’v = σ’1 X τ Failure envelope in terms of effective stresses σ’h = σ’3 effective stresses X is on failure Therefore, φ’ c’ σ’3 c’ Cotφ ’ (σ ’1 + σ ’3 )/ 2 ' ' σ 1' + σ 3 σ 1' − σ 3 Sinφ ' = c' Cotφ '+ 2 2 (σ ’1 − σ ’3 )/ 2 σ’1 σ ’
- 21. Mohr Coulomb failure criterion with Mohr circle of stress ' ' σ 1' + σ 3 σ 1' − σ 3 c' Cotφ '+ 2 Sinφ ' = 2 (σ ' 1 ) ( ) ' ' − σ 3 = σ 1' + σ 3 Sinφ '+2c' Cosφ ' σ (1 − Sinφ ') = σ (1 + Sinφ ') + 2c' Cosφ ' ' 1 ' 3 σ =σ ' 1 ' 3 (1 + Sinφ ') + 2c' Cosφ ' (1 − Sinφ ') (1 − Sinφ ') φ' φ' σ = σ Tan 45 + + 2c' Tan 45 + 2 2 ' 1 ' 3 2
- 22. Determination of shear strength parameters of soils (c, φ or c’, φ’) Laboratory tests on specimens taken from representative undisturbed samples Most common laboratory tests to determine the shear strength parameters are, 1.Direct shear test 2.Triaxial shear test Other laboratory tests include, Direct simple shear test, torsional ring shear test, plane strain triaxial test, laboratory vane shear test, laboratory fall cone test Field tests 1. 2. 3. 4. 5. 6. 7. Vane shear test Torvane Pocket penetrometer Fall cone Pressuremeter Static cone penetrometer Standard penetration test
- 23. Laboratory tests Field conditions A representative soil sample z σvc σhc σhc σvc Before construction σvc + ∆σ σhc σhc σvc + ∆σ After and during construction z
- 24. σvc + ∆σ Laboratory tests Simulating field conditions in the laboratory 0 σvc 0 0 0 Representative soil sample taken from the site st e lt ia x ra T Di σhc rect sh ea r σhc σvc σhc σvc + ∆σ σvc te τ st τ σvc Step 1 Set the specimen in the apparatus and apply the initial stress condition σhc Step 2 Apply the corresponding field stress conditions
- 25. Triaxial Shear Test Piston (to apply deviatoric stress) Failure plane O-ring impervious membrane Soil sample Soil sample at failure Perspex cell Porous stone Water Cell pressure Back pressure Pore pressure or pedestal volume change
- 27. Triaxial Shear Test Specimen preparation (undisturbed sample) Sampling tubes Sample extruder
- 28. Triaxial Shear Test Specimen preparation (undisturbed sample) Edges of the sample are carefully trimmed Setting up the sample in the triaxial cell
- 29. Triaxial Shear Test Specimen preparation (undisturbed sample) Sample is covered with a rubber membrane and sealed Cell is completely filled with water
- 30. Triaxial Shear Test Specimen preparation (undisturbed sample) Proving ring to measure the deviator load Dial gauge to measure vertical displacement
- 31. Types of Triaxial Tests σc Step 2 Step 1 σc σc deviatoric stress (∆σ = q) σc σc σ c+ q σc Under all-around cell pressure σ c Is the drainage valve open? yes Consolidated sample no Shearing (loading) Is the drainage valve open? yes no Unconsolidated Drained Undrained sample loading loading
- 32. Types of Triaxial Tests Step 2 Step 1 Under all-around cell pressure σ c Shearing (loading) Is the drainage valve open? yes Consolidated sample Is the drainage valve open? no yes Unconsolidated no CD test Undrained loading sample Drained loading UU test CU test
- 33. Consolidated- drained test (CD Test) = Total, σ Neutral, u + Effective, σ’ Step 1: At the end of consolidation σ VC Drainage σ’VC = σ VC σ hC 0 σ’hC = σ hC Step 2: During axial stress increase σ VC + ∆σ Drainage σ hC σ’V = σ VC + ∆σ = σ’1 0 σ’h = σ hC = σ’3 Step 3: At failure σ VC + ∆σ f Drainage σ hC σ’Vf = σ VC + ∆σ f = σ’1f 0 σ’hf = σ hC = σ’3f
- 34. Consolidated- drained test (CD Test) σ 1 = σ VC + ∆σ σ 3 = σ hC Deviator stress (q or ∆σ d) = σ 1 – σ 3
- 35. Consolidated- drained test (CD Test) Expansion Time Compression Volume change of the sample Volume change of sample during consolidation
- 36. Consolidated- drained test (CD Test) Stress-strain relationship during shearing d Dense sand or OC clay Expansion a ro i t Compression Volume change of the sample ve D , ssert s σ ∆ (∆σ d)f (∆σ d)f Loose sand or NC Clay Axial strain Dense sand or OC clay Axial strain Loose sand or NC clay
- 37. CD tests How to determine strength parameters c and φ (∆σ d)f c σ 3c Confining stress = σ 3b Confining stress = σ 3a r o a ve D t i , ssert s σ ∆ d Confining stress = (∆σ d)f b σ1 = σ3 + (∆σ d)f σ3 (∆σ d)f a Axial strain φ r ae h S , ssert s τ Mohr – Coulomb failure envelope σ 3a σ 3b σ 3c σ 1a (∆σ d)f (∆σ d)fb σ 1b σ 1c σ or σ ’
- 38. CD tests Strength parameters c and φ obtained from CD tests Since u = 0 in CD tests, σ = σ’ Therefore, c = c’ and φ = φ’ cd and φ d are used to denote them
- 39. CD tests Failure envelopes For sand and NC Clay, cd = 0 φd r ae h S , ssert s τ Mohr – Coulomb failure envelope σ 3a σ 1a (∆σ d)f a σ or σ ’ Therefore, one CD test would be sufficient to determine φ d of sand or NC clay
- 40. CD tests Failure envelopes For OC Clay, cd ≠ 0 τ NC OC φ c σ3 (∆σ d)f σ1 σc σ or σ ’
- 41. Some practical applications of CD analysis for clays 1. Embankment constructed very slowly, in layers over a soft clay deposit Soft clay τ τ = in situ drained shear strength
- 42. Some practical applications of CD analysis for clays 2. Earth dam with steady state seepage τ Core τ = drained shear strength of clay core
- 43. Some practical applications of CD analysis for clays 3. Excavation or natural slope in clay τ τ = In situ drained shear strength Note: CD test simulates the long term condition in the field. Thus, cd and φd should be used to evaluate the long term behavior of soils
- 44. Consolidated- Undrained test (CU Test) = Total, σ Neutral, u + Effective, σ’ Step 1: At the end of consolidation σ VC Drainage σ’VC = σ VC σ hC 0 Step 2: During axial stress increase σ VC + ∆σ No drainage σ hC ±∆ u Step 3: At failure σ hC σ’V = σ VC + ∆σ ± ∆u = σ’1 σ’h = σ hC ± ∆u = σ’3 σ’Vf = σ VC + ∆σ f ± ∆uf = σ’1f σ VC + ∆σ f No drainage σ’hC = σ hC ±∆uf σ’hf = σ hC ± ∆uf = σ’3f
- 45. Consolidated- Undrained test (CU Test) Expansion Time Compression Volume change of the sample Volume change of sample during consolidation
- 46. Consolidated- Undrained test (CU Test) Stress-strain relationship during shearing d Dense sand or OC clay r t i + o a ve D , ssert s σ ∆ (∆σ d)f (∆σ d)f Loose sand or NC Clay Axial strain ∆u Loose sand /NC Clay - Axial strain Dense sand or OC clay
- 47. CU tests How to determine strength parameters c and φ (∆σ d)f Confining stress = σ 3a σ3 (∆σ d)f a Total stresses at failure Axial strain φ cu Mohr – Coulomb failure envelope in terms of total stresses r ae h S , ssert s τ r o a ve D t i , ssert s σ ∆ d σ 3b Confining stress = b σ1 = σ3 + (∆σ d)f ccu σ 3a σ 3b (∆σ d)fa σ 1a σ 1b σ or σ ’
- 48. CU tests How to determine strength parameters c and φ σ’1 = σ 3 + (∆σ d)f uf Mohr – Coulomb failure envelope in terms of effective stresses σ’3 = σ 3 - uf uf Effective stresses at failure φ’ φ cu r ae h S , ssert s τ Mohr – Coulomb failure envelope in terms of total stresses C’ ccu σ’3b σ’3a σ 3a ufa σ 3b σ’1a (∆σ d)fa ufb σ’1b σ 1a σ 1b σ or σ ’
- 49. CU tests Strength parameters c and φ obtained from CD tests Shear strength parameters in terms of total stresses are ccu and φ cu Shear strength parameters in terms of effective stresses are c’ and φ’ c’ = cd and φ’ = φd
- 50. CU tests Failure envelopes For sand and NC Clay, ccu and c’ = 0 Mohr – Coulomb failure envelope in terms of effective stresses φ’ φ cu r ae h S , ssert s τ Mohr – Coulomb failure envelope in terms of total stresses σ 3a σ 3a σ 1a σ 1a (∆σ d)f σ or σ ’ a Therefore, one CU test would be sufficient to determine φ cu and φ’(= φ d) of sand or NC clay
- 51. Some practical applications of CU analysis for clays 1. Embankment constructed rapidly over a soft clay deposit Soft clay τ τ = in situ undrained shear strength
- 52. Some practical applications of CU analysis for clays 2. Rapid drawdown behind an earth dam τ Core τ = Undrained shear strength of clay core
- 53. Some practical applications of CU analysis for clays 3. Rapid construction of an embankment on a natural slope τ τ = In situ undrained shear strength Note: Total stress parameters from CU test (ccu and φcu) can be used for 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
- 54. Unconsolidated- Undrained test (UU Test) Data analysis Initial specimen condition No drainage Specimen condition during shearing σC = σ3 σC = σ3 No drainage σ 3 + ∆σ d Initial volume of the sample = A0 × H0 Volume of the sample during shearing = A × H Since the test is conducted under undrained condition, A × H = A0 × H 0 A ×(H0 – ∆H) = A0 × H0 A ×(1 – ∆H/H0) = A0 A0 A= 1− ε z σ3
- 55. Unconsolidated- Undrained test (UU Test) Step 1: Immediately after sampling 0 0 Step 2: After application of hydrostatic cell pressure σ’3 = σ 3 - ∆uc σC = σ3 No drainage σC = σ3 = ∆uc + σ’3 = σ 3 - ∆uc ∆uc = B ∆σ 3 Increase of pwp due to increase of cell pressure Increase of cell pressure Skempton’s pore water pressure parameter, B Note: If soil is fully saturated, then B = 1 (hence, ∆uc = ∆σ 3)
- 56. Unconsolidated- Undrained test (UU Test) Step 3: During application of axial load No drainage σ’1 = σ 3 + ∆σ d - ∆uc σ 3 + ∆σ d σ3 = σ’3 = σ 3 - ∆uc + ∆ud ∆ud ∆uc ± ∆ud ∆ud = A∆σ d Increase of pwp due to increase of deviator stress Increase stress Skempton’s pore water pressure parameter, A of deviator
- 57. Unconsolidated- Undrained test (UU Test) Combining steps 2 and 3, ∆uc = B ∆σ 3 ∆ud = A∆σ d Total pore water pressure increment at any stage, ∆u ∆u = ∆uc + ∆ud ∆u = B ∆σ 3 + A∆σ d ∆u = B ∆σ 3 + A(∆σ 1 – ∆σ 3) Skempton’s pore water pressure equation
- 58. Unconsolidated- Undrained test (UU Test) = Total, σ Neutral, u + σ’V0 = ur Step 1: Immediately after sampling 0 0 σ’h0 = ur -ur Step 2: After application of hydrostatic cell pressure No drainage σC σC -ur + ∆uc = -ur + σ c (S = 100% ; B = 1) r Step 3: During application of axial load No drainage σ C + ∆σ σC -ur + σ c ± ∆u σ C + ∆σ f σC σ’VC = σ C + ur - σ C = ur σ’h = ur σ’V = σ C + ∆σ + ur - σ c ∆u σ’h = σ C + ur - σ c σ’Vf = σ C + ∆σ f + ur - σ c Step 3: At failure No drainage Effective, σ’ -ur + σ c ± ∆uf ∆u ∆uf = σ’1f σ’hf = σ C + ur - σ c = σ’3f ∆u f
- 59. Unconsolidated- Undrained test (UU Test) = Total, σ Neutral, u σ C + ∆σ f σC Effective, σ’ σ’Vf = σ C + ∆σ f + ur - σ c Step 3: At failure No drainage + ∆uf = σ’1f σ’hf = σ C + ur - σ c = σ’3f -ur + σ c ± ∆uf ∆u 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 τ σ’3 ∆σ σ’1 σ’ f
- 60. Unconsolidated- Undrained test (UU Test) = Total, σ Neutral, u σ C + ∆σ f σC Effective, σ’ σ’Vf = σ C + ∆σ f + ur - σ c Step 3: At failure No drainage + ∆uf = σ’1f σ’hf = σ C + ur - σ c = σ’3f -ur + σ c ± ∆uf ∆u Mohr circles in terms of total stresses Failure envelope, φ u = 0 τ cu ub σ 3a σ’3 3b ∆σ f ua σ 1a σ’1 1b σ or σ’ f
- 61. Unconsolidated- Undrained test (UU Test) Effect of degree of saturation on failure envelope τ S < 100% σ 3c σ 3b S > 100% σ 1c σ 3a σ 1b σ 1a σ or σ’
- 62. Some practical applications of UU analysis for clays 1. Embankment constructed rapidly over a soft clay deposit Soft clay τ τ = in situ undrained shear strength
- 63. Some practical applications of UU analysis for clays 2. Large earth dam constructed rapidly with no change in water content of soft clay τ Core τ = Undrained shear strength of clay core
- 64. Some practical applications of UU analysis for clays 3. Footing placed rapidly on clay deposit τ = In situ undrained shear strength Note: UU test simulates the short term condition in the field. Thus, cu can be used to analyze the short term behavior of soils
- 65. Unconfined Compression Test (UC Test) σ 1 = σ VC + ∆σ σ3 = 0 Confining pressure is zero in the UC test
- 66. σ 1 = σ VC + ∆σf Shear stress, τ Unconfined Compression Test (UC Test) σ3 = 0 qu Normal stress, σ τf = σ1/2 = qu/2 = cu