Surcharge Lateral Pressure on a Wall from a Line Load (Boussinesq)
Lateral pressure a concentrated surface load puts on a wall, by Boussinesq.
Example
You enter
- Line load qL (lb/ft, parallel to wall) 1000
- Wall height H (ft) 10
- Setback of the load x (ft) 4
- Depth to evaluate z (ft) 3
You get
- M ratio 0.4
- N ratio 0.3
- Lateral pressure sigma_h 97.4 psf
Details, formula, and sources
The bulge of lateral pressure a concentrated surface load (a footing, wheel line, or crane outrigger set back from a wall) puts on it - which the uniform Ka q surcharge never captures: the NAVFAC DM-7.2 modified-Boussinesq sigma_h = (0.203 qL/H) n/(0.16 + n^2)^2 for m <= 0.4, doubled for a rigid non-deflecting wall (m = x/H, n = z/H). A 1,000 lb/ft line 4 ft back from a 10 ft wall peaks near 97 psf at shallow depth; set it farther back and it pushes less and deeper. Line load, single depth. A design aid; the geotechnical engineer of record governs.
m = x/H, n = z/H; m <= 0.4: sigma_h = (0.203 qL/H) n/(0.16 + n^2)^2; m > 0.4: sigma_h = (1.28 qL/H)(m^2 n)/(m^2 + n^2)^2.
The NAVFAC DM-7.2 modified-Boussinesq line-load lateral pressure on a rigid wall, the doubled elastic Boussinesq solution for an unyielding wall, by name.
NAVFAC DM-7.2 is public-domain and free online; the modified-Boussinesq surcharge relations are public.
Estimate. AHJ and licensed professional govern.
Field names used by the API: ql_plf, h_ft, x_ft, z_ft, m_ratio, n_ratio, sigma_h_psf
- Modified Boussinesq the two m-branch forms with m = x/H, n = z/H; doubled for a rigid non-deflecting wallNAVFAC DM-7.2
- Line load a load per unit length parallel to the wall; point/strip loads use the companion formsNAVFAC DM-7.2
- Single depth pressure at one z; the integrated resultant thrust is a separate stepscope of this tile