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Lecture 25

# Lecture 25 - EP1 LATERAL EARTH PRESSURE Pressure on...

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EP1 LATERAL EARTH PRESSURE Pressure on Structures Geostatic Stresses, At Rest Pressure (at a point, overburden only) o Coefficient of Earth Pressure at Rest, K 0 , is the ratio of horizontal effective to vertical effective stress. The at rest horizontal pressure develops naturally due to weight of the overburden soils. v h 0 ' ' K σ σ = (K 0 = 1 for water, i.e. same pressure both directions) Cantilever Retaining Wall Gravity Retaining Wall Anchor Sheet Pile Wall Braced Excavation Culverts, Tunnels, Sewers, Pipes Dry (or unsaturated) γ m , z σ v = Σγ mi z i σ v = σ v σ h = K 0 σ v σ h = σ h Submerged σ v = Σγ i z i u = γ w z w σ v = σ v - u σ h = K 0 σ v σ h = σ h + u z γ m γ sat , z w

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EP2 o In general the total stresses must be calculated including water pressure and v h 0 K σ σ o For NC soils the Jaky equation is commonly used: ) sin 1 ( K 0 φ - = o Overconsolidation may lock in some of the higher past horizontal stress (soils have a “memory”). For OC soils Mayne and Kulhawy (1982) developed the following equation: o The at rest Mohr’s circle plots beneath the failure envelope: o If we could insert a rigid wall into the soil without disturbance, the horizontal pressure distribution on the wall would be triangular, linearly increasing with depth as the vertical stress increases. o In a dry soil, cohesionless, the pressure distribution and resultant, P 0 , shown at right would act against the wall: (note: soils possessing cohesion can stand on a vertical cut without any wall – more on cohesion later) o If water is present (undesirable) we must also add a triangular water pressure distribution and the at rest effective stress is no longer triangular. H/3 (centroid of triangle) H σ h = K 0 γ H at z = H σ h = 0 at z = 0 P 0 = ½(K 0 γ H)(H) = ½K 0 γ H 2 H σ h = K 0 ( γ H 1 + γ ’H 2 ) at z = H σ h = 0 at z = 0 H 1 H 2 σ h = K 0 ( γ H 1 ) at z = H 1 u = 0 at z = H 1 u = γ w H 2 at z = H 2 σ h = K 0 ( γ H 1 ) at z = H 1 σ h = [K 0 ( γ H 1 + γ ’H 2 ) + γ w H 2 ] at z = H σ h = 0 at z = 0 Shear Stress, τ Normal Stress, σ c σ 3 = σ h = K 0 σ v σ 1 = σ v φ Mohr-Coulomb Failure Envelope τ f = c + σ tan φ OCR ) sin 1 ( K sin 0 φ φ - =
EP3 o For braced excavations, basements and pipes we do design for at rest pressure. For walls, in general, we consider two limit states at the plastic equilibrium (where every point in the soil mass is on the verge of failure): o Active case (K a ): wall moves away from soil, vertical stress remains constant but horizontal stress decreases to the minimum allowable without failure.

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