1. AN ACTIVE LEARNING ASSIGNMENT ON Guided By : Prof. B.M. PUROHIT 2015 SOIL MECHNICS(2150609) DEPARTMENT OF CIVIL ENGINEERING GOVERNMENT ENGINEERING COLLEGE, DAHOD Prepared By: BAMANIA AMIT G. 130180106004 DAMOR KAMLESH M. 130180106024 MAHIDA RAGHUVIRSINGH B. 130180106058 BAKLIYA AKSHY D. 120180106064 WJM Rankine (1820-1872)

2. Content Rankine’s theory of earth pressure 1. Dry or moist backfill with no surcharge 2. Submerged backfill 3. Backfill with uniform surcharge 4. Backfill with sloping surcharge 5. Inclined back and surcharge

3. Rankine’s theory of earth pressure Rankine(1857) cosided the equilibrium of a soil element within a soil mass bounded by a plane surface. The following assumptions were made by rankine for the derivation of earth pressure: 1) The soil mass is homogeneous and semi-infinite. 2) the soil dry and cohesion less. 3) the ground surface is plane, which may be horizontal or inclined. 4) the back of the retaining wall is smooth and vertical. 5) the soil element is in state of plastic equilibrium, i.e at the verge of failure.

4. Active earth pressure by rankine theory(for cohesionless soils) We shall consider the following cases of a cohesioless backfill: 1. Dry or moist backfill with no surcharge 2. Submerged backfill 3. Backfill with uniform surcharge 4. Backfill with sloping surcharge 5. Inclined back and surcharge

5. 1) Dry or moist backfill with no surcharge Pressure at the base of the wall,

7. This pressure acts at H/3 above the base of the wall. If the soil is dry, is the dry weight of soil If the soil is moist, is the moist weight of soil

8. 2) Submerged backfill In this case, the sand behind the retaining wall is saturated with water. The lateral earth pressure is made up of two components. i) Lateral pressure due to submeged weight ′ of soil =Ka. ′.H i) Lateral pressure due to water = w.H Total pressure at base

10. 3)Uniform Surcharge Load The soil upto depth H1 is moist whereas Below this point for depth H2 is submerged. At depth H1 at the level of the water table At depth H we have the lateral pressure due to surcharge, the moist soil for depth H1, the submerged soil for depth H2 and water pressure for depth H2. 10

12. The total pressure Pa acting per unit length of the wall may be written as equal to: The point of application of Pa above the base of the wall can be found by taking moments of all the forces acting on the wall about A.

13. 4) BACKFILL WITH SLOPING SURFACE p a = k a  H at the bottom and is parallel to inclined surface of backfill k a = Where  =Angle of surcharge  Total pressure at bottom =P a = k a  H 2 /2

15. 5) Inclined back First of all, total pressure p1 is calculated on vertical face BC. Now; resultant (P) of pressure P1 and weight of soil wedge W is calculated as P. P= [(P1)2+(W)2]2 Where,

17. Solved Example A cantilever retaining wall of 7 meter height (Fig. Ex. 11.2) retains sand. The properties of the sand are: e = 0.5, ɸ = 30° and G = 2.7. Using Rankine's theory determine the active earth pressure at the base when the backfill is (i) dry, (ii) saturated and (iii) submerged, and also the resultant active force in each case. In addition determine the total water pressure under the submerged condition.

20. Reference Dr. R. P. Rethaliya,Soil Mechanics Wikipedia.com