# Overburden pressure

Overburden pressure, also called lithostatic pressure, confining pressure or vertical stress, is the pressure or stress imposed on a layer of soil or rock by the weight of overlying material.

The overburden pressure at a depth z is given by

$p(z) = p_0 + g \int_{0}^{z} \rho(z) \, dz$

where ρ(z) is the density of the overlying rock at depth z and g is the acceleration due to gravity. p0 is the datum pressure, like the pressure at the surface.

It may be noted that the above equation implies that gravitational acceleration is a constant over z since it is placed outside of the integral. Strictly speaking, for almost all boundary conditions, g should appear inside the integrand since g is a function of the distance from mass. However, since g varies little over depths which are a very small fraction of the Earth's radius, it is placed outside of the integral in practice for most near-surface applications which require an assessment of lithostatic pressure. In deep-earth geophysics/geodynamics, gravitational acceleration varies significantly over depth, demanding that g be taken, at least, as a function of depth.