Shear Strength of Soil lecture - Soil mechanics 2

Shear Strength of Soil - Mesri

1. QUESTIONS What is meant by the shear strength of soil? What factors affect the shear strength? How is shear strength determined? Are there differences between the shear strengths of dense and loose sands or normally and overconsolidated clays? What are the differences between drained and undrained shear strengths? Under what conditions should the drained shear strength or the undrained shear strength parameters be used? What lab and field tests are used to determine shear strength ?

2. SHEAR STRENGTH OF SOILS Shear stress corresponding to the failure condition is called shear strength.

3. Mohr’s Hypothesis

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

5. Mohr-Coulomb Failure Envelope in terms of Principal Stresses

6. Mohr Circle of stress Soil element s ’ 1 s ’ 1 s ’ 3 s ’ 3 q s ’ t Resolving forces in s and t directions,

7. Mohr Circle of stress t s ’

8. Mohr Circle of stress t s ’ P D = Pole w.r.t. plane q (s ’, t)

9. SHEAR STRENGTH OF SOILS Shear resistance in soils is the result of resistance to movement at the inter-particle contacts. Each contact can transmit normal force from one particle to another across an area which increases or decreases as normal force increases or decreases. Bonds form across the contact areas and together with any interlocking resist tangential force

10. Any mechanism that increases contact area contributes to shear resistance Increase in effective stress produces an increase of interparticle contact area and thus increase in shear resistance.

11. It is a distinctive characteristic of soils that during mobilization of shear resistance, shear deformation is accompanied by a change in either density or effective stress. The nature and magnitude of this change depends on the pre-shear density and effective stress conditions as well as the structure of soil.

12. VARIABLES Density Effective Stress Soil Structure

13. Φ ’ Shape, Gradation Loose Dense rounded, uniform 30 37 rounded, well graded 34 40 angular, uniform 35 43 angular, well graded 39 45

14. Φ ’ Clay Mineral Random H oriented Kaolonite 23-26 8-14 Illite 19-24 6-7 Montmorillonite Ca - 10-14 6 Na - 0-4 0-2

15. The mechanism responsible for volume or pore pressure change is the tendency of soil particles to rearrange themselves during shear If water can leave or enter the soil, the tendency for particles re-arrangement manifest itself as a change in volume and consequently density.

16. Soils of low pre-shear density, such as loose sand and silt and soft clays tend to compress during shear. Soils of high pre-shear density, such as dense sand and gravel and stiff clays and shale tend to expand.

17. The change in shearing resistance that is directly related to the change in effective normal stress, and therefore to physical bonding, is called frictional resistance. The rate of increase of the frictional resistance with effective normal stress is expressed as the angle of friction Φ '.

18. Changes in effective stress directly control physical bonding between soil particles, and indirectly affect chemical bonding if it exists. An increase in effective stress produces an increase in physical bonding, whereas a decrease produces the opposite result. On the other hand, either an increase or a decrease in effective stress from the condition at which interparticle chemical bonding developed leads to breakage of chemical bonds

19. Volumetric Response of Soils

20. Shear strength of Cohesive soils

21. A cylindrical sample of soil having a cohesion of 80 kN /m 2 and an angle of internal friction of 20° is subjected to a cell pressure of 100 kN /m 2 . Determine: ( i ) the maximum deviator stress at which the sample will fail (ii) the angle made by the failure plane with the axis of the sample.

22. A normally consolidated clay was consolidated under a stress of 3150 lb /ft 2 , then sheared undrained in axial compression. The principal stress difference at failure was 2100 lb /ft 2 , and the induced pore pressure at failure was 1848 lb /ft2. Determine (a) the Mohr-Coulomb strength parameters, in terms of both total and effective stresses analytically, (b) compute (  1 /  3 ) f , and ( ’ 1 / ’ 3 ) f , and (c) determine the theoretical angle of the failure plane in the specimen.

23. PLAN VIEW Vane shear test This is one of the most versatile and widely used devices used for investigating undrained shear strength (C u ) and sensitivity of soft clays Bore hole (diameter = D B ) h > 3D B ) Vane D H Applied Torque, T Vane T Rupture surface Disturbed soil Rate of rotation : 6 – 12 per minute Test can be conducted at 0.5 m vertical intervals

24. Vane shear test Since the test is very fast, Unconsolidated Undrained (UU) can be expected C u C u T = M s + M e + M e = M s + 2M e M e – Assuming a uniform distribution of shear strength d/2 d/2 C u h

25. Vane shear test Since the test is very fast, Unconsolidated Undrained (UU) can be expected C u C u M s – Shaft shear resistance along the circumference T = M s + M e + M e = M s + 2M e

26. Vane shear test Since the test is very fast, Unconsolidated Undrained (UU) can be expected C u C u T = M s + M e + M e = M s + 2M e M e – Assuming a triangular distribution of shear strength h d/2 d/2 C u Can you derive this ???

27. Vane shear test Since the test is very fast, Unconsolidated Undrained (UU) can be expected C u C u T = M s + M e + M e = M s + 2M e M e – Assuming a parabolic distribution of shear strength h Can you derive this ??? d/2 d/2 C u