Shear Strength of Soils

1. Shear Strength of Soils

2. failure surface mobilised shear resistance Shear failure Soils generally fail in shear embankment strip footing At failure, shear stress along the failure surface reaches the shear strength.

3. failure surface Shear failure The soil grains slide over each other along the failure surface. No crushing of individual grains.

4.    Shear failure At failure, shear stress along the failure surface () reaches the shear strength (f).

5. f  Mohr-Coulomb Failure Criterion   failure envelope friction angle cohesion c  f is the maximum shear stress the soil can take without failure, under normal stress of .

6.  f f tan   frictional component cohesive component c c f  Mohr-Coulomb Failure Criterion Shear strength consists of two components: cohesive and frictional.

7. c and  are measures of shear strength. Higher the values, higher the shear strength.

8. Y X Mohr Circles & Failure Envelope  X  Y Soil elements at different locations X ~ failure Y ~ stable

9.  c c  Mohr Circles & Failure Envelope The soil element does not fail if the Mohr circle is contained within the envelope GL Y c c+ Initially, Mohr circle is a point

10.  c c Mohr Circles & Failure Envelope As loading progresses, Mohr circle becomes larger… GL Y c .. and finally failure occurs when Mohr circle touches the envelope

11. Y 45 + /2 45 + /2  c c Orientation of Failure Plane Failure plane oriented at 45 + /2 to horizontal GL  90+ Y c c+

12. v v’ u h h’ u X X X effective stresses total stresses u Mohr circles in terms of  & ’ = + h’ v’ h v

13. c c c c Envelopes in terms of  & ’ Identical specimens initially subjected to different isotropic stresses (c) and then loaded axially to failure f uf Initially… Failure c,  in terms of  At failure, 3= c; 1 = c+f 3’= 3 – uf ; 1’ = 1 - uf c’, ’ in terms of ’

14. failure plane O-ring impervious membrane soil sample at failure porous stone water Triaxial Test Apparatus piston (to apply deviatoric stress) perspex cell cell pressure pore pressure or volume change back pressure pedestal

15. Types of Triaxial Tests deviatoric stress () Under all-around cell pressure c Shearing (loading) Is the drainage valve open? Is the drainage valve open? no yes yes no Consolidated sample Undrained loading Drained loading Unconsolidated sample

16. Types of Triaxial Tests Depending on whether drainage is allowed or not during • initial isotropic cell pressure application, and • shearing, there are three special types of triaxial tests that have practical significances. They are: Consolidated Drained (CD) test Consolidated Undrained (CU) test Unconsolidated Undrained (UU) test

17. For unconsolidated undrained test, in terms of total stresses, u = 0 For normally consolidated clays, c’ = 0 & c = 0. Granular soils have no cohesion. c = 0 & c’= 0

18. CD, CU and UU Triaxial Tests Consolidated Drained (CD) Test • no excess pore pressure throughout the test • very slow shearing to avoid build-up of pore pressure Can be days!  not desirable • gives c’ and ’ Use c’ and ’ for analysing fully drained situations (e.g., long term stability, very slow loading)

19. CD, CU and UU Triaxial Tests Consolidated Undrained (CU) Test • pore pressure develops during shear Measure  ’ • gives c’ and ’ • faster than CD (preferred way to find c’ and ’)

20. CD, CU and UU Triaxial Tests Unconsolidated Undrained (UU) Test • pore pressure develops during shear = 0; i.e., failure envelope is horizontal Not measured ’ unknown • analyse in terms of   gives cu and u • very quick test Use cu and u for analysing undrained situations (e.g., short term stability, quick loading)

21. 1 X 3 X soil element at failure 1 3 1- 3 Relation at Failure

22. v h X t  stress point (v-h)/2 s  (v+h)/2 Stress Point stress point v h

23. t  s  Stress Path During loading… Stress path is the locus of stress points Stress path Stress path is a convenient way to keep track of the progress in loading with respect to failure envelope.

24. t   s c  Failure Envelopes failure tan-1 (sin ) stress path c cos  During loading (shearing)….

25. 1 3 Y u = ? Pore Pressure Parameters A simple way to estimate the pore pressure change in undrained loading, in terms of total stress changes ~ after Skempton (1954) Skempton’s pore pressure parameters A and B

26. Pore Pressure Parameters B-parameter B = f (saturation,..) For saturated soils, B  1. A-parameter at failure (Af) Af = f(OCR) For normally consolidated clays Af 1. For heavily overconsolidated clays Af is negative.