Overburden pressure, lithostatic pressure, and vertical stress are terms that denote 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
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.
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