1. Faculty of Applied Engineering and Urban Planning Civil Engineering Department Soil Mechanics ECGD3303 Weight-Volume Relationships Lecture 3 Week 2 1 st Quadester 2007/2008 UP Copyrights 2007

2. Content Phase Diagram Specific Gravity Volume and Weight Relationships (Porosity, Saturation, Void Ratio, Moisture Content, Unit Weight) Relationships Relative Density

3. Specific Gravity GsGs is defined as the ratio of the unit weight of a given material to the unit weight of water.

4. Specific Gravity

5. Phase Diagram Air Water Solids 3 Phase System

6. Phase Diagram Air Solids 2 Phase System (Dry)

7. Phase Diagram Water Solids 2 Phase System (Saturated)

8. Phase Diagram

9. WTotal WeightVTotal Volume W w Water WeightV w Water Volume W s Solids WeightV s Solids Volume W a Air Weight = 0V a Air Volume

10. Phase Diagram W= W w +W s V=V s +V w +V a V v =V w +V a V=V s +V v

11. Volume Relationships Porosity (n) Void Ratio ( e ) Degree of Saturation ( S ) Prove!!

12. Volume Relationships Moisture Content (w) Unit Weight ( γ ) Dry Unit Weight ( γ d ) Prove!!

13. Questions?!

14. Basic Relations

15. γ, e, w, G s Relationships Solids Weight in Terms of Specific Gravity G s Water Weight in Terms of Specific Gravity G s

16. γ, e, w, G s Relationships Soil Unit Weight Divide by V s

17. γ, e, w, G s Relationships With the same substitution for W s we got: Dry Unit Weight Void Ratio Saturation

18. γ, e, w, G s Relationships Group Work Prove that for Saturation Condition:

19. Questions?!

20. Soil Unit Weight Divide by V s γ, n, w, G s Relationships Substitute for (e) by

21. Soil Unit Weight γ, n, w, G s Relationships Dry Soil Unit Weight (w=0) Saturated Soil Unit Weight (W w = nV)

22. Questions?!

23. Various Unit-Weight Relationships

24. Typical Values

25. Example 3.2

27. Example 3.4