Retaining Wall Pressure Calculator

Lateral earth pressure is the horizontal stress a soil mass exerts on a vertical face, and its magnitude depends on how much the wall is allowed to move. Three states bracket the problem. At rest, with no movement, K0 is approximated by Jaky's expression 1 - sin(phi). If the wall yields away from the backfill, the soil mobilizes its shear strength to help hold itself up and pressure falls to the active state, Ka = tan^2(45 - phi/2). If the wall is driven into the soil, pressure rises to the passive state, Kp = tan^2(45 + phi/2), which is the reciprocal of Ka. For a friction angle of 30 degrees these give Ka = 0.333, K0 = 0.500, and Kp = 3.000, a tenfold spread that explains why the assumed wall movement matters as much as the soil property. Reaching the active state takes very little yielding, roughly 0.001 times the wall height in dense sand, but full passive resistance requires 2 to 5 percent of the height, so passive pressure at the toe is usually discounted. Pressure increases linearly with depth, so at the base it is Ka x gamma x H, and the resultant thrust per foot of wall is the area of that triangle, 0.5 x Ka x gamma x H^2, acting at H/3 above the base. A uniform surcharge q adds a rectangular block of Ka x q acting at mid-height; a common highway traffic surcharge is 250 psf, equivalent to about 2 feet of soil. Soil unit weights typically run 110 to 130 pcf for compacted granular backfill, with friction angles near 30 to 36 degrees for sands and 20 to 28 degrees for clays. Two caveats dominate. Rankine theory assumes a frictionless vertical face and level backfill, so it is slightly conservative for rough concrete. More critically, these coefficients apply only to drained conditions: if drainage fails and the backfill saturates, hydrostatic pressure at 62.4 pcf adds to the buoyant soil pressure and roughly doubles the thrust. Inadequate drainage, not underestimated earth pressure, is the usual cause of wall failure.

The subject begins with Charles-Augustin de Coulomb, better known for his work in electrostatics, who in 1773 presented and in 1776 published an essay applying the principles of maxima and minima to problems in statics relevant to architecture. Working from experience with military fortification, Coulomb treated the backfill as a rigid wedge sliding along a plane failure surface and searched for the wedge orientation producing the greatest thrust on the wall. His formulation accounts for friction between the wall and the soil and can accommodate inclined faces and sloping backfill, and it remains in use essentially unchanged. William John Macquorn Rankine, professor of civil engineering at Glasgow, published a different approach in 1857 in the Philosophical Transactions of the Royal Society, analyzing the stress state within a semi-infinite soil mass on the verge of plastic failure rather than the equilibrium of a discrete wedge. Rankine's method yields the simpler tan-squared expressions used above but assumes no wall friction. The two theories coexisted, and their reconciliation came with Karl Terzaghi, whose 1925 Erdbaumechanik founded soil mechanics as a discipline and established effective stress as the governing principle, clarifying why drainage and pore water pressure determine whether classical earth pressure theory applies at all. Jozsef Jaky, a Hungarian engineer, published the empirical at-rest relationship K0 = 1 - sin(phi) in 1944, filling the gap between the two limiting states for walls too stiff to yield.