Soil Stresses (ch10)

2. Soil Stresses(ch10)

3. Stress Assumptions Continuous material Homogeneous (eng. props. = at all locations) Isotropic (Modulus and n are = in all directions) Linear-elastic stress-strain properties

4. Stress Concept

5. x z Stress Concept s normal stresses Ten (-), Comp (+) t shear stresses Clock (+), CC (-)

6. Strain Concept gshear strain enormal strain g = shear strain [radians]

7. Stress vs. Strain = Modulus

8. Stresses in Soils 1. Geostatic Stresses Due to soil’s self weight 2. Induced Stresses Due to added loads (structures) 3. Dynamic Stresses e.g., earthquakes

9. Geostatic Stresses TOTAL VERTICAL STRESS AT A POINT Ground surface z = depth = 5 m Soil , g = 18 kN/m3 A “total vertical stress at A”

10. Geostatic Stresses SHEAR STRESSES If ground surface is flat, all geostatic shear stresses = zero

11. Ground surface hpA Geostatic Stresses PORE WATER PRESSURE AT A POINT z = 5 m Soil , g = 18 kN/m3 A “pore water pressure at A”

12. Geostatic Effective Stress board

13. Example board

14. Special Case Board – submerged soils

15. P g g A A z z Induced Stresses sA = g z sA = g z + ? tA = 0 tA = ?

16. zf Bousinnesq - point loads Point load A See page 324 of your book…

17. P g A z Area loads B L Area, A Terminology: B < or = to L q = bearing pressure = P/A

18. Area loads – sz below corner B L zf sz below corner of a loaded area: see page 327 (book)

19. q zf A Area loads – sz below center Circular loaded area

20. Square loaded area Strip loads Rectangular area Area loads – sz below center See page 332 (text)

21. = Vertical effective stress = = Horiz. eff. stress = ? Lateral Stresses Ground surface z Soil , g = 18 kN/m3 A

22. Lateral Stresses “Coefficient of lateral earth pressure”

23. Superposition We can only add total stresses

24. Stresses on other planes… So far we have sx and sz Now we want Stresses acting on other planes

25.  The Mohr Circle Describes 2-D stresses at a point in a material Plots s and t on an =scale Each point on the MC represents the s and t on one side of an element oriented at a certain angle The angle between two points in the MC is = 2 times the angle between the planes they represent

26. A1 B2 B1 A2 tA2tA1 sB2sB1 tB2tB1  If we change we will get two more points on the same MC. The Mohr Circle t A  s sA2sA1 B

27. The Mohr Circle 1 21

28. The Mohr Circle – Principal Stresses Planes A and B are called principal planes when there are no shear stresses (only normal stresses) acting on them. s1 = major principal stress s3 = minor principal stress

29. The Mohr Circle

30. Direction of max principal stresses is 17 degrees c.c. from the vertical

31. Effective Stress Mohr Circle board

32. Seepage Force board

33. Seepage Force - Example board