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# Geotechnical Engineering-II [Lec #23: Rankine Earth Pressure Theory]

Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.

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### Geotechnical Engineering-II [Lec #23: Rankine Earth Pressure Theory]

1. 1. 1 Geotechnical Engineering–II [CE-321] BSc Civil Engineering – 5th Semester by Dr. Muhammad Irfan Assistant Professor Civil Engg. Dept. – UET Lahore Email: mirfan1@msn.com Lecture Handouts: https://groups.google.com/d/forum/geotech-ii_2015session Lecture # 23 29-Nov-2017
2. 2. 2 RANKINE THEORY OF ACTIVE EARTH PRESSURE ASSUMPTIONS 1. The soil is homogeneous and isotropic. 2. The most critical shear surface is a plane. In reality, it is slightly concave upward, but this is a reasonable assumption (especially for the active case) and it simplifies the analysis. 3. The backfill surface is planar (although it does not necessarily need to be horizontal). 4. There is no friction between wall and soil. 5. The wall is infinitely long so that a representative two- dimensional section of the wall may be analyzed, assuming there is no strain in the direction perpendicular to the section. We refer to this as a plane strain condition.
3. 3. 3 RANKINE THEORY OF ACTIVE EARTH PRESSURE If wall AB is not allowed to move  Shearstress,t Effective Normal stress, s’so’Koso’sa’ a sh’ b c s’h = Ko s’o Stress condition in soil  Mohr’s circle a If wall is allowed to move away from soil mass  horizontal principal stress will decrease   Circle b  Circle c
4. 4. 4 RANKINE THEORY OF ACTIVE EARTH PRESSUREShearstress,t Effective Normal stress, s’so’ Koso’ sa’A O D C f c
5. 5. 5 RANKINE THEORY OF ACTIVE EARTH PRESSURE
6. 6. 6 RANKINE THEORY OF ACTIVE EARTH PRESSURE
7. 7. 7 RANKINE THEORY OF ACTIVE EARTH PRESSURE For cohesionless soils, c’ = 0
8. 8. 8 RANKINE THEORY OF ACTIVE EARTH PRESSURE f ff s s              sin1 sin1 2 45tan2 o a aK aaa KczK  2s                2 45tan'2 2 45tan2 ff s cza
9. 9. 9 RANKINE ACTIVE PRESSURE DIAGRAM aaa KczK  2s aa K2c-Kz z zC aK2c-aK2c- Kz a WALL WALL WALL
10. 10. 10 RANKINE ACTIVE PRESSURE DIAGRAM aa K2c-Kz z zC aK2c- WALL
11. 11. 11 RANKINE THEORY OF ACTIVE EARTH PRESSURE -- DEPTH OF UNSUPPORTED CUT -- aaa KczK  2s aa K2c-Kz z zC aK2c- General Case (c-f soil) 0Cz aac KcKz  20  At zC a a c K Kc z    2 a c K c z    2 Cohesionless Soils (c’=0) Cohesive Soils (f=0) Ka = Height of unsupported cut (hC)  Zero Net force acting on wall  c zc   2 WALL hC = Ht. of Unsupported Cut CC zh  2  s’a = 0 1
12. 12. 12 RANKINE THEORY OF PASSIVE EARTH PRESSURE Wall movement towards soil Shearstress,t Effective Normal stress, s’so’Koso’ sp’A O D C f c
13. 13. 13 RANKINE THEORY OF PASSIVE EARTH PRESSURE Derivation: similar to that for active state For cohesionless soils, c’ = 0
14. 14. 14 RANKINE THEORY OF PASSIVE EARTH PRESSURE f ff s s              sin1 sin1 2 45tan2 o p pK                2 45tan'2 2 45tan2 ff s czp ppp KczK  2s
15. 15. 15 RANKINE THEORY OF PASSIVE EARTH PRESSURE ppp KczK  2s
16. 16. 17 RANKINE THEORY ACTIVE PRESSURE -- SUMMARY -- f ff s s              sin1 sin1 2 45tan2 o a aK aaa KczK  2s a c K c z    2
17. 17. 18 RANKINE THEORY PASSIVE PRESSURE -- SUMMARY -- f ff s s              sin1 sin1 2 45tan2 o p pK ppp KczK  2s
18. 18. 19 RANKINE THEORY -- INCLINATION OF FAILURE PLANE --         2 45tan f ninclinatioplaneFailure         2 45tan f ninclinatioplaneFailure Active Case Passive Case
19. 19. 20 Practice Problem #3 f ff s s              sin1 sin1 2 45tan2 o a aK aaa KczK  2s
20. 20. 21 CONCLUDED REFERENCE MATERIAL Principles of Geotechnical Engineering – (7th Edition) Braja M. Das Chapter #13 Essentials of Soil Mechanics and Foundations (7th Edition) David F. McCarthy Chapter #17 Geotechnical Engineering – Principles and Practices – (2nd Edition) Coduto, Yueng, and Kitch Chapter #17