Earth Pressure on Buildings

by Helmut Schmidhofer

Buildings are rigid objects that do not yield. Consequently, active earth pressure (Ka) from a sliding wedge of soil cannot develop. The load on the building is the lateral pressure exerted by a soil at rest, ph = pv*K0 where:

ph = lateral (horizontal) pressure on building (wall friction does not develop);

pv = vertical soil stress at depth z, pv = q + gamma*z where q = superimposed live load and gamma = design unit weight of soil and water;

K0 = the at-rest earth pressure coefficient, which is usually greater than the active earth pressure coefficient, Ka.

Two methods are used to determine K0:

for granular soils, K0 = (1 - sin(PHI))/(1 - sin(BETA)) where PHI = effective angle of internal friction and BETA is the surface angle to the horizontal (by Kezdi, 1972); or

for cohesive soils (clay and rock), K0 = Nu/(1 - Nu) where Nu = Poisson's ratio.

Of course, K0 = 1 for water. It is reasonable to assume that the water table can be at the surface after prolonged rain, therefore, the lateral pressure comprises two components:

1. water pressure pw = 9.807*z and
2. soil pressure ps = (q + (gam_sat - 9.807)*z)*K0 where gam_sat is the saturated unit weight of the soil.

Then ph = pw + ps

R_top = (q*K0*D^2/2 + (9.807+(gam_sat-9.807)*K0)*D^3/6)/H

R_btm = q*K0*D + (9.807+(gam_sat-9.807)*K0)*D^2/2 - R_top

The quadratic equation (9.807+(gam_sat-9.807)*K0)/2*z^2 + q*K0*z - R_top = 0 produces z where the moment is maximum...

M_max = R_top*(H - D + z) - (q*K0*z^2/2 + (9.807+(gam_sat-9.807)*K0)*z^3/6)

Some common values for PHI are (by J. E. Bowles, 1996):
    sandy gravel - 35 to 50 degrees
    dense saturated sand - 33 to 44 degrees
    loose saturated sand - 28 to 34 degrees
    dense silt or silty sand - 25 to 30 degrees
    loose silt or silty sand - 20 to 22 degrees
    saturated clay - 0 degrees

Typical values for Poisson's ratio are (by J. E. Bowles, 1996):
    Saturated clay - 0.4 to 0.5
    Rock - 0.1 to 0.4
    Sand, gravelly sand - 0.3 to 0.4
    Silt - 0.3 to 0.35
    Sandy clay - 0.2 to 0.3
    Loess - 0.1 to 0.3

You should do at least one calculation manually, for two reasons:
1. to check the spreadsheet so you can have confidence in its results; and
2. to appreciate how much time the spreadsheet saves.

Please support the ongoing maintenance of this site. Donate $7 and I shall send you the Excel spreadsheet so you can satisfy yourself that the program uses the equations correctly.

When you have the ultimate design moment and shear forces, go to Reinforced Concrete Slab & Wall Design.

Earth pressure on buildings
Given:
unit weight of saturated soil, gam_sat				kN/m3
effective angle of internal friction, PHI				degrees
Poisson's ratio if clay or rock (set PHI = 0)
superimposed live load, q				kPa
surface angle to horizontal, BETA				degrees
depth of soil to base, D				m
height between top and bottom supports, H				m
Then:
at-rest earth pressure coefficient, K0
reaction at top, R_top				kN/m
reaction at base, R_btm				kN/m
position of maximum moment, z				m
maximum wall moment, M_max				kNm/m