Contents

Stress distribution in soil

Some cases[edit]

Finitely loaded area[edit]

If soil is considered homogeneous and isotropic and the surface loading area is finite (a point, circle, strip), the vertical stress in the subsoil decreases as depth and radial distance from the surface loading area increases.

This section needs expansion. You can help by adding to it. (April 2022)

Vertical line load at the surface[edit]

This section needs expansion. You can help by adding to it. (April 2022)

Vertical Point Load at the Surface[edit]

The solution to the problem of calculating the stresses in an elastic half space subjected to a vertical point load at the surface will be of value in estimating the stresses induced in a deposit of soil whose depth is large compared to the dimensions of that part of the surface that is loaded. ${\displaystyle \Delta \sigma _{z}=-{\frac {3P}{2\pi R^{2}}}\cos ^{3}\theta }$ ${\displaystyle \Delta \sigma _{r}={\frac {P}{2\pi R^{2}}}(-3\cos \theta \sin ^{2}\theta +{\frac {1-2\mu }{1+\cos \theta }})}$ ${\displaystyle \Delta \sigma _{t}={\frac {P}{2\pi R^{2}}}(1-2\mu )(\cos \theta -{\frac {1}{1+\cos \theta }})}$ ${\displaystyle \Delta \tau =-{\frac {3P}{2\pi R^{2}}}\cos ^{2}\theta \sin \theta }$ ${\displaystyle \cos \theta ={\frac {z}{R}}}$, ${\displaystyle R={\sqrt {r^{2}+z^{2}}}}$ ${\displaystyle \Delta \sigma _{z}=-{\frac {3Pz^{3}}{2\pi R^{5}}}=-{\frac {3P}{2\pi }}{\frac {z^{3}}{(r^{2}+z^{2})^{5/2}}}=-{\frac {3P}{2\pi z^{2}\left[1+\left({\frac {r}{z}}\right)^{2}\right]^{\frac {5}{2}}}}}$^[3]

Below centre of uniformly loaded circular area[edit]

${\displaystyle \sigma =q\{1-{\frac {1}{[({\frac {R}{z}})^{2}+1]^{3/2}}}\}}$^[4]

References[edit]

Wikimedia Commons has media related to Stress distribution in soil.