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Lateral Earth Pressures Lateral Earth Pressures Lateral Support In geotechnical engineering, it is often necessary to prevent lateral soil movements. We have to estimate the lateral soil pressures acting on these structures, to be able to design them. Tie rod Anchor Sheet pile Cantilever Braced excavation Anchored sheet pile retaining wall 2 1 Earth Pressure at Rest In a homogeneous natural soil deposit, GS v’ ’ h X the ratio h’/v’ is a constant known as coefficient of earth pressure at rest (K0). Importantly, at K0 state, there are no lateral strains. 3 Estimating K0 For normally consolidated clays and granular soils, K0 = 1 – sin ’ For overconsolidated clays, sin K0,overconsolidated = K0,normally consolidated (OCR) From elastic analysis, K Poisson’s 0 1 ratio 4 2 Active/Passive Earth Pressures - in granular soils Wall moves away from soil Wall moves A towards soil B smooth wall Let’s look at the soil elements A and B during the wall movement. 5 Active Earth Pressure - in granular soils v’ = z Initially, there is no lateral movement. v’ z ’ = K ’ = K z ’ h 0 v 0 h A As the wall moves away from the soil, v’ remains the same; and h’ decreases till failure occurs. Active state 6 3 Active Earth Pressure - in granular soils As the wall moves away from the soil, Initially (K0 state) Failure (Active state) v’ active earth pressure decreasing h’ 7 Active Earth Pressure - in granular soils WJM Rankine (1820-1872) [h’]active v’ [ h ']active K A v ' Rankine’s coefficient of 1 sin active earth pressure K tan2 (45 / 2) A 1 sin 8 4 Active Earth Pressure - in granular soils As the wall moves away from the soil, h’ decreases till failure occurs. h’ K0 state v’ z Active ’ h A state wall movement 9 Active Earth Pressure - in cohesive soils Follow the same steps as for granular soils. Only difference is that c 0. [ h ']active K A v '2c K A Everything else the same as for granular soils. 10 5 Passive Earth Pressure - in granular soils Initially, soil is in K0 state. As the wall moves towards the soil, v’ remains the same, and ’ v ’ increases till failure occurs. ’ h h B Passive state 11 Passive Earth Pressure - in granular soils As the wall moves towards the soil, Initially (K0 state) Failure (Passive state) passive earth pressure v’ increasing h’ 12 6 Passive Earth Pressure - in granular soils v’ [h’]passive [ h ']passive KP v ' Rankine’s coefficient of 1 sin passive earth pressure K tan2 (45 / 2) P 1 sin 13 Passive Earth Pressure - in granular soils As the wall moves towards the soil, h’ increases till failure occurs. h’ Passive state v’ ’ h B K0 state wall movement 14 7 Passive Earth Pressure - in cohesive soils [ h ']passive KP v '2c KP Everything else the same as for granular soils. 15 8 9 Earth Pressure Distribution - in granular soils [h’]active PA and PP are the resultant active and passive thrusts on the wall [h’]passive H 2 PA=0.5 KAH h 2 PP=0.5 KPh KPh KAH 19 Rankine’s Earth Pressure Theory [ h ']active K A v '2c K A [ h ']passive KP v '2c KP Assumes smooth wall Applicable only on vertical walls 20 10 [ h ']active K A v '2c K A As given in Figure. σo=0 that z=0 and σo= H at z=H. The pressure distribution shows that at z=0 the active pressure equals indicating a tensile stress that decreases with depth and becomes zero at a depth z=zc The depth zc is usually referred to as the depth of tensile crack, because the tensile stress in the soil will eventually cause a crack along the soil– wall interface. 11 Lateral Earth Pressure at Rest At any depth z below the ground surface, the vertical subsurface stress is 23 the total force per unit length of the wall, P0 12 13 14 Rankine’s Earth Pressure Coefficient for sloped ground 15 A Generalized Case for Rankine Active Pressure -Granular Backfill 16 Coulomb’s coefficients of Earth Pressure Coulomb’s coefficients of Earth Pressure • Take into consideration Wall roughness Inclined walls Where : angle between the wall’s back face and the vertical : angle of friction between the soil and the backside of the wall a : angle of the slope for the backfill behind the wall 17 Lateral Earth Pressure Due to Surcharge 2 p a sin a cosa 2 x 18.
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