Lateral Earth Pressure

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1 1 of 11 6/2/2012 4:28 AM Lateral Earth Pressure The magnitude of lateral earth pressure depends on: 1. Shear strength characteristics of soil 2. Lateral strain condition 3. Pore water pressure 4. State of Equilibrium of soil 5. Wall and ground surface shape Previous conditions depends mainly on: a) Drainage conditions b) Interaction between soil and wall Soil state of Equilibrium The state of Equilibrium of soil can be divided into two states : a) State of Elastic Equilibrium When a small change in stress produces a corresponding small change in strain. b) State of Plastic Equilibrium When irreversible strain takes place at a constant stress. The strain state relating to earth pressure calculation fall into three categories: a) At Rest State:

2 2 of 11 6/2/2012 4:28 AM It is the case when state of elastic Equilibrium with no lateral displacement occurs (Figure 1 ). b) Active state: It is the case when plastic equilibrium with lateral expansion takes place (wall moves outward from the soil). ( Figure 2 ). c) Passive state: Plastic equilibrium with lateral contraction takes place (wall moves toward the soil). ( Figure 2 ) Figure 1 (1) Earth Pressure at rest (ko condition ) Figure 2 lateral strain, εh = 0 k o = coefficient of lateral earth presser at rest. k o depends on : Soil type ( sand, silt, clay)

3 3 of 11 6/2/2012 4:28 AM Loading Unloading history Relative density of soil For normally consolidated soil (N.C.) and sand For over consolidated soil (O.C.) where OCR is the over consolidated ratio and in general where is Poisson ratio In this case,the mohre circle is below the shear envelope of this soil (Figure 3). Figure 3

4 4 of 11 6/2/2012 4:28 AM (2) Active Earth pressure (Rankine s Active state ) Rankine s theory neglects friction between soil and wall. when the wall moves outward from the soil, the lateral earth pressure starts to be reduced until it reaches its, minimum Figure 3 value, where, where, ka = coefficient of active earth pressure. (Figure 3) And in this case, the failure plane makes ( 45 Ø/2 ) with the direction of the major principal plane ( usually horizontal axes ). (3) Rankin Passive State If the wall moved toward the soil, the passive condition will take place. The passive pressure will increase until it reaches its maximum value of:

5 5 of 11 6/2/2012 4:28 AM and in this case, the failure place makes ( 45 + Ø/2 ) with the direction of the major principal plane. Earth pressure Distribution for Sand In general, the active earth pressure distribution in sand will be: where γ = soil unit weight H = wall height Figure (4) However the distribution and value of passive earth pressure in sand is, Figure(5)

6 6 of 11 6/2/2012 4:28 AM Figure 5 (b) For clay The value of active earth pressure is (Figure 6) Figure(6) where, c = soil cohesion The passive pressure values are (Figure 7)

7 7 of 11 6/2/2012 4:28 AM Figure(7) Effect of Ground Water Table a) Static water table For static water table the water pressure should be treated separately from soil lateral pressure as shown in Figure(8) Figure(8)

8 8 of 11 6/2/2012 4:28 AM where γ sub = submerged unit weight of soil = γ sat - γ w b) Moving Water Table In this case, the flow net and equipotential lines should be drawn for the wall, Then the pore pressure against the wall can be determined, ( Figure 9) Figure (9 ) Effect of Stratified Soil As an example of stratified soil shown in(figure10)

9 9 of 11 6/2/2012 4:28 AM (Figure 10) Effect of Sloping Ground Surface In this case the active coefficient of lateral earth pressure is and the resultant in this case will be parallel to the ground surface, (Figure 11) Coulomb's Theory for Rough Walls

10 10 of 11 6/2/2012 4:28 AM Figure(12) δ = angle of wall friction for concrete wall and and Strutted Trench sheeting

11 11 of 11 6/2/2012 4:28 AM Figure(13) The location of struts affects the values and distributions of lateral earth pressures Figure(14)

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