Lecture 11 Shear Strength of Soil CE240
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Shear Strength of Soil Shear strength in soils Introduction Definitions Mohr-Coulomb criterion Introduction Lab tests for getting the shear strength Direct shear test Introduction Procedure & calculation Critical void ratio
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Lecture 11 Shear Strength of Soil CE240
- 1. CE 240 Soil Mechanics & Foundations Lecture 11.1 Shear Strength of Soil I (Das, Ch. 11)
- 2. • Shear strength in soils – Introduction – Definitions • Mohr-Coulomb criterion – Introduction – Lab tests for getting the shear strength • Direct shear test – Introduction – Procedure & calculation – Critical void ratio Class Outlines
- 3. Shear Strength • The strength of a material is the greatest stress it can sustain; • So that the unit of strength is the same as stress (Pa in SI unit system);
- 4. Significance of Shear Strength • The safety of any geotechnical structure is dependent on the strength of the soil; • If the soil fails, the structure founded on it can collapse. • Understanding shear strength is the basis to analyze soil stability problems like: – lateral pressure on earth retaining structures (Chs. 12, 13), – slope stability (Ch. 14), and – bearing capacity (Ch. 15).
- 5. Shear Failure in Soils
- 6. Slope Failure in Soils Failure due to inadequate strength at shear interface
- 7. Static: Transcosna Grain Elevator Canada (Oct. 18, 1913) West side of foundation sank 24-ft
- 9. Dynamic: Foundation failure by liquefaction after the 1964 Niigata Earthquake. (USGS)
- 10. Dynamic: Lateral Spreading caused by the 1906 San Francisco Earthquake at Moss Landing, CA (USGS Professional Paper 993)
- 11. Shear Strength in Soils • The shear strength of a soil is its resistance to shearing stresses. • It is a measure of the soil resistance to deformation by continuous displacement of its individual soil particles • Shear strength in soils depends primarily on interactions between particles • Shear failure occurs when the stresses between the particles are such that they slide or roll past each other
- 12. Shear Strength in Soils (cont.) • Soil derives its shear strength from two sources: – Cohesion between particles (stress independent component) • Cementation between sand grains • Electrostatic attraction between clay particles – Frictional resistance between particles (stress dependent component)
- 13. Shear Strength of Soils: Cohesion Cohesion (C), is a measure of the forces that cement particles of soils Dry sand with no cementation Dry sand with some cementation Soft clay Stiff clay
- 14. Shear Strength of Soils; Internal Friction Internal Friction angle (φ), is the measure of the shear strength of soils due to friction
- 15. Mohr-Coulomb Failure Criteria • This theory states that a material fails because of a critical combination of normal stress and shear stress, and not from their either maximum normal or shear stress alone.
- 16. Mohr-Coulomb Failure Criterion Shear Strength,S φ = φ′ C′ Normal Stress, σn = σ′ = γ h
- 17. ' ' tan (11.2) tan ' (11.3) f n n f n n c c c c τ σ φ µσ τ σ φ µ σ = + = + ′ ′ ′= + = + f where shear strength c = cohesion; c =effective cohesion φ = angle of internal friction; φ = effective angle of internal friction = coefficient of friction; ' = effective coefficient of frictio τ µ µ = ′ ′ n.
- 19. Mohr-Coulomb shear failure criterion σ1 σ1 σ3 σ3σn τf σ1 σ3 σ τ 2θ τf = c’ + µ’σn’ c’ φ φ Failed Zone (σ, τ) σff
- 21. From trigonometric equalities we have
- 23. Way 1: Increase the normal stress in one direction σ1 σ1 major principle stress σn τf σ3 σ3 Minor principle stress Confining stress
- 24. Way 2: directly apply the shear stress Consider the following situation: - A normal stress is applied vertically and held constant - A shear stress is then applied until failure Shear stress τ Normal stress σn Normal stress σn
- 25. Determination of Shear Strength Parameters The shear strength parameters of a soil are determined in the lab primarily with two types of tests: 1) Direct Shear Test; and 2) Triaxial Shear Test. (1) (2) Soil Normal stress σn Shear stress σ3 σ3 σ1
- 26. Direct Shear Test • Direct shear test is Quick and Inexpensive • Shortcoming is that it fails the soil on a designated plane which may not be the weakest one • Used to determine the shear strength of both cohesive as well as non-cohesive soils • ASTM D 3080
- 27. Direct Shear Test (cont.) • The test equipment consists of a metal box in which the soil specimen is placed • The box is split horizontally into two halves • Vertical force (normal stress) is applied through a metal platen • Shear force is applied by moving one half of the box relative to the other to cause failure in the soil specimen Soil Normal stress σn Shear stress σ3
- 32. Direct Shear Test Data Shearstress Residual Strength Peak Strength
- 33. Direct Shear Test Data: Volume change ∆H
- 34. Direct Shear Test: Procedure 1.Measure inner side or diameter of shear box and find the area 2.Make sure top and bottom halves of shear box are in contact and fixed together. 3.Weigh out 150 g of sand. 4.Place the soil in three layers in the mold using the funnel. Compact the soil with 20 blows per layer. 5.Place cover on top of sand 6.Place shear box in machine. 7.Apply normal force. The weights to use for the three runs are 2 kg, 4 kg, and 6 kg if the load is applied through a lever arm, or 10 kg, 20 kg, and 30 kg, if the load is applied directly. Note: Lever arm loading ratio 1:10 (2kg weight = 20 kg)
- 35. Direct Shear Test: Procedure 8. Start the motor with selected speed (0.1 in/min) so that the rate of shearing is at a selected constant rate 9. Take the horizontal displacement gauge, vertical displacement gage and shear load gage readings. Record the readings on the data sheet. 10. Continue taking readings until the horizontal shear load peaks and then falls, or the horizontal displacement reaches 15% of the diameter.
- 36. Calculations 1. Determine the dry unit weight, γd 2. Calculate the void ratio, e 3. Calculate the normal stress & shear stress 1−= d wGs e γ γ A V A N == τσ ;
- 37. Figures Peak Stress s3 s2 s1 Shearstress,s N3 = 30 kg N2 = 20 kg N1 = 10 kg Horizontal displacement, ∆H
- 40. Reading Assignment: Das, Ch. 11 HW: Problem 11.1