At-Rest Earth Pressure Coefficient (Jaky)

Between the active and passive extremes lies the state where nothing has moved at all: the soil sits under the horizontal stress it acquired as it was deposited. József Jáky published K₀ = 1 − sin φ in Hungarian in 1944, and eighty years of measurement have failed to improve on it for normally consolidated soils. At φ = 32° it gives K₀ = 1 − 0.530 = 0.470; at φ = 30°, exactly 0.50. Compare that with $K_a$ = 0.33 at the same friction angle and the message is plain — a wall that cannot yield carries half again the load of one that can.

The trap is over-consolidation. A clay that once had a kilometre of ice on top of it retains locked-in horizontal stress, and K₀ climbs with the over-consolidation ratio roughly as $K_0 = (1 - \sin\varphi)\cdot \mathrm{OCR}^{\sin\varphi}$, reaching 1.0 or even 2.0 in heavily over-consolidated London Clay. Excavate into that and the sides squeeze in far more than a normally consolidated estimate predicts — a well-documented headache on the London Underground extensions. Basement walls, braced excavations, buried culverts and integral bridge abutments all live in the K₀ world, and none of them should be designed with $K_a$.