GLE/CEE 330: Soil Mechanics Lateral Earth Pressure Geological Engineering University of Wisconsin-Madison

Learning Objectives Learn about key concepts: Lateral earth pressure coefficients At rest, active and passive earth pressure Place in context of Mohr Circle analysis

Lateral Earth Pressure (R.P. Weber) ?? (R.P. Weber)

Water Pressure and Soil Pressure Consider hydrostatic condition Consider “at-rest” (geostatic) condition Anisotropic sx sz Isotropic sz sx ≠ >

Earth Pressure Coefficient “At Rest” K0 = Coefficient of Lateral Earth Pressure at Rest sx sz For normally consolidated soil (Jaky, 1944): For overconsolidated soil (Meyerhoff, 1976): In general:

Calculate lateral total stress (sx) at z = 5 m if K0 = 0.5 (M. Budhu)

Active and Passive Limit Conditions Ka = Coefficient of Active Earth Pressure (Wall Moving Away from Backfill) (small sx) Active Failure Condition movement Active Failure Wedge (45+f/2) Kp = Coefficient of Passive Earth Pressure (Wall Moving Toward Backfill) (large sx) Passive Failure Condition movement Passive Failure Wedge (45 -f/2)

Consider Mohr’s Circles… sx decreases until failure movement Active Failure sx increases until failure movement Passive Failure

Rankine Active Failure Surface Pole Point

Rankine Passive Failure Surface Pole Point

Evolution of lateral stress with wall movement… Stationary (at rest) Movement away from backfill Movement toward backfill Passive Failure at Kp Active Failure at Ka Ka < K0< Kp

Essential Points 1) Coefficient of Lateral Earth Pressure at Rest 2) Active Earth Pressure Coefficient: 3) Passive Earth Pressure Coefficient: 4) Active slip planes at 45˚ + f’/2 to horizontal 5) Passive slip planes at 45˚ - f’/2 to horizontal 6) More wall movement (inward) required for passive failure than active (outward) failure