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Figure 1 below shows the cross section of a retaining wall. Weight of Wedge ABC From Triangle ABC, Area of Triangle ABC = Therefore: – Again, Area of   Triangle of Forces for W, Pp and R From the sine rule, Substituting the value of W from the equation (3.34) into (3.35) we get, In order to get the maximum value of Pp,     Where, Note: When, (leveled backfilled), (no wall friction) and (vertical interface between wall and backfill), then, . The point of application of Pp is at a…

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Coulomb’s made the following assumptions in the development of his theory and hence it is called Coulomb’s Wedge Theory. The assumptions made by Coulomb while giving his theory was: The soil is isotropic and homogeneous. The surface of rupture is a plane. The failure wedge is a rigid body. There is friction between and the wall. Back of wall need not be vertical. Failure is two dimensional. The soil is cohesion-less. Coulomb’s equation of shear strength is valid. Coulomb made his derivation based on limit equilibrium approach. Derivation of Active…

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In this article we will discuss about derivation of equation by trial wedge method for passive case. The equation is derived as follows. A planar failure wedge IJM is considered. There are distributed normal stresses along IJ and JM and distributed along JM. The resultants of these stresses are carried out in the analysis. In this case, the force F acts above the normal and the angle between the force F and weight W will be . The forces acting at the free body IJM are: Weight of wedge =…

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Derivation of Equation by Trial Wedge Method for Active Case: Figure 1 below shows the application of the trial Wedge method to the problem of simple retaining wall without wall friction. A planar failure wedge IJM is considered. There are distributed normal stresses along IJ and JM and distributed shear stress along JM. The resultants of these stresses are carried out in the analysis. The forces acting at the free body IJM are: let’s start the derivation of equation by trial wedge method Weight of wedge =     Pa…

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The trial wedge method of analysis is shown in Fig.1 below. The following steps are to be followed to make the analysis. Step 1 –   a mass of soil behind the wail is considered as a free body. The force P, which must exist between the free body and the wall, is found by writing the equation of equilibrium for the free body as a whole. Step 2 – a different free body is considered, having a different boundary through the soil. Once again the required force between the…

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In this article we will discuss about Rankine Earth Pressure for passive case. Figure 1 shows the Mohr’s circle in which point B indicates the vertical stress and point E represents the passive pressure. The wall carries a uniform surcharge q. The circle is tangent to the failure envelope. For this case the relation between Pa and  is given by:   ———-(1) Where,  Pressure Distribution of passive case in cohesive soil Figure 2 given below shows the pressure distribution behind a wall retaining a cohesive backfill. The total resultant passive…

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In this article we will discuss about Rankine Earth Pressure for active case. Figure 1 shows the Mohr’s circle in which point B indicates the vertical stress and point E represents the active pressure. The circle is tangent to the failure envelope. For this case the relation between Pa and  is given by: ———-(1)  ———-(2)   Where, In the above equation (2) where z = 0 The negative sign indicates that the pressure is negative and tensile, As a result there would be gap between backfill and wall. The tensile…

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What are Effect of Sloping Surcharge in Passive Case? In previous article we had already posted Effect of Sloping Surcharge in Active Case, now in this article we are dealing with Effect of Sloping Surcharge in Passive Case. The Mohr Circle for the passive case of a retaining wall carrying a sloping backfill is shown in Fig.1. Consider an element subjected to a stress in the  in the vertical direction and  in the direction parallel to the backfill. As these stresses in one plane are parallel to the direction of another…

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What are the Effect of Sloping Surcharge in Active Case? in this article we will discuss about Effect of Sloping Surcharge in Active Case. A wall carrying a sloping backfill is shown in Fig.1. Consider an element subjected to a stress  in the vertical direction and  in the direction parallel to the backfill. As these stresses in one plane are parallel to the direction of another plane, these stresses are conjugate stresses and the planes are the conjugate planes. The equivalent vertical stress acting parallel to the surface of backfill is…

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What is Active Earth Pressure for Partially submerged Sand with Surcharge? In Figure 1 active earth pressure for partially submerged sand and surcharge is shown. The height of the wall is Z and the position of the water table is at a depth of Z1 and the surcharge acting at the top of horizontal surface of the wall is q. The height of the wall below water table is Z2. The unit weight of the sand above water table is  and that below water table is . CASE 1 | Active Earth…

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