Presentation on Civil Engineering (Project)

Group 7 presentation

1. Rankine And Coulombs Theories Of Lateral Earth Pressure Group Members #7 Tasawar Abbas BCEF14M013 Muzammil Abbas BCEF14M021 M.Ahmed Fraz BCEF14M028 Muhammad Nabeel (G.L) BCEF14M031 Noman khan BCEF14M038

2. Lateral earth pressure Lateral earth pressure is the pressure that soil exerts in the horizontal direction.

3. Why We Study Lateral Earth Pressure? The lateral earth pressure is important because it affects the consolidation behavior and strength of the soil and because it is considered in the design of geotechnical engineering structures such as retaining walls, basements, tunnels, deep foundation sand braced excavations. Earth retaining structures are common in a manmade environment.

4. Contd.. Lateral earth pressure is a function of Type and amount of wall movement Shear strength parameter of soil Unit weight of soil

5. Lateral Earth Pressure There are 3 states of lateral earth pressure Ko = At Rest Ka = Active Earth Pressure (wall moves away from soil) Kp = Passive Earth Pressure (wall moves into soil) Passive is more like a resistance

6. Definition of key Terms Coefficient (K) It is defined as the ratio of the horizontal effective stress σ h to the vertical effective stress σ v . K = σ h / σ v Coefficient of earth pressure at rest ( Ko ): It is the ratio of horizontal and vertical principal effective stresses when the retaining wall does not move at all, i.e. it is “at rest”.

7. Coefficient of earth pressure at rest ( Ko ) K o can be calculated as follows: K o = 1 – sin φ for coarse grained soils K o = .44 + .42 [PI / 100] for NC soils K o ( oc ) = K o (NC) (OCR) 1/2 for OC soils

8. Active Earth Pressure Coefficient ( Ka ) It is the ratio of horizontal and vertical principal effective stresses when a retaining wall moves away (by a small amount) from the retained soil .

9. Passive earth pressure coefficient ( Kp ): It is the ratio of horizontal and vertical principal effective stresses when a retaining wall is forced against a soil mass .

10. Earth Pressure Theories Two classic Earth pressure theories has been put forward in the eighteen and nineteen centuries by Coulomb and Rankine respectively. Coulomb’s(1776) Earth Pressure Theory Rankine (1857) Earth Pressure Theory

11. Rankine's earth pressure theory Rankine's theory, developed in 1857, is a stress field solution that predicts active and passive earth pressure. The Rankine theory assumes that there is no wall friction and the ground and failure surfaces are straight planes, and that the resultant force acts parallel to the backfill slope (i.e., no friction acting between the soil and the backfill)

12. Rankine's earth pressure theory Note that φ' is the angle of shearing resistance of the soil and the backfill is inclined at angle β to the horizontal. The equations for active and passive lateral earth pressure coefficients are given in next slide.

13. Rankine's earth pressure theory

14. Rankine's earth pressure theory

15. Assumptions Soil is non-cohesive (c = 0) dry, isotropic and homogenous. Backfill is horizontal. Wall is vertical, Wall friction is neglected. Failure is a plain strain problem.

16. Coulomb's earth pressure theory Coulomb (1776) first studied the problem of lateral earth pressures on retaining structures. He used limit equilibrium theory, which considers the failing soil block as a free body in order to determine the limiting horizontal earth pressure.

17. Coulomb's earth pressure theory

18. Coulomb's earth pressure theory Since the problem is indeterminate, a number of potential failure surfaces must be analyzed to identify the critical failure surface (i.e. the surface that produces the maximum or minimum thrust on the wall). Mayniel  later extended Coulomb's equations to account for wall friction, symbolized by δ. Müller-Breslau further generalized Mayniel's equations for a non-horizontal backfill and a non-vertical soil-wall interface.

19. Assumptions The backfill is a dry, cohesion less, homogeneous, isotropic soil. The backfill surface is planar and can be inclined. The back of the wall can be inclined to the vertical. The failure surface is a plane surface which passes through the heel of the wall. The position and the line of action of the earth pressure are known.

20. Coulomb's earth pressure theory The limiting horizontal pressures at failure in extension or compression are used to determine the  K a  and  K p  respectively. 

21. Coulomb's earth pressure theory

22. References: Soil Mechanics & Foundation Eng. – Arora . Soil Mechanics – V.N.S.Murthy Müller-Breslau H., (1906) Erddruck auf St utzmauern, Alfred Kroner, Stuttgart. Kramer S.L. (1996) Earthquake Geotechnical Engineering, Prentice Hall, New Jersey

23. Thank You