### Solved problem of the "at-rest" lateral earth pressure upon an unyielding wall

Articles > Solved problem of the "at-rest" lateral earth pressure upon an unyielding wall

### Question:

Fin the lateral "at-rest" force F0 on the wall and its location with respect to the top of the wall.

Given: Sand #1 has a unit weight of 105 pcf, c =0 and friction angle of 30; sand #2 has a unit weight of 122 pcf, c=0 and friction angle of 30.

### Solution:

From Jaky's empirical relation: k0 = 1 - sinφ' = 1-sin30 = 0.5

at z = 0 feet σ'h = 0 ksf because there is no surcharge loading upon the surface of sand #1

at z = 10 feet σ'h = K0σ'v = 0.5(0.105 kcf)(10ft)=0.525 ksf

at z = 20 feet σ'h = K0σ'v = 0.5[ (0.105 kcf)(10ft) + (0.122 - 0.0624)10]=0.823 ksf

σw = γwh = (0.0624 pcf) (10ft) = 0.624 ksf

F0 = F1 + F2 + F3 + F4 = 1/2 (0.525)(10) + (0.525)(10) + 1/2 (0.302)(10) + 1/2 (0.624)(10) = 2.63 + 5.25 + 1.49 + 3.12 = 12.5 kip/ft

$z = \frac{2.63*6.67 + 5.25*15 + 1.49*16.67 + 3.12*16.67}{12.5kip} = \frac{173.1kips-ft}{12.5kip}$

z = 13.8ft from the top of the wall