Pressure is force magnitude applied over an area. Overburden pressure is a geology term that denotes the pressure caused by the weight of the overlying layers of material at a specific depth under the earth's surface. Overburden pressure is also called lithostatic pressure, or vertical stress. This pressure is usually indicated as σ v {\displaystyle \sigma _{v}} , or alternatively σ z {\displaystyle \sigma _{z}} , in the coordinate system of the stress ellipsoid. At any depth in the subsurface, a point subjected to stresses can be analysed by resolving these stresses along three mutually perpendicular axes, constructing the stress ellipsoid whose axes correspond respectively to the directions of maximum, minimum and intermediate stress. In tectonically stable regions, or under an extensional tectonic regime, the major axis of this ellipsoid is oriented vertically and corresponds in direction and magnitude to lithostatic pressure.
Definition and quantitative determination Lithostatic pressure increases with depth. In a stratigraphic layer that is in hydrostatic equilibrium; the overburden pressure at a depth z, assuming the magnitude of the gravity acceleration is approximately constant, is given by Stevin's Law, following the function:
P ( z ) = P 0 + g ∫ 0 z ρ ( z ) d z {\displaystyle P(z)=P_{0}+g\int _{0}^{z}\rho (z)\,dz} where:
z {\displaystyle z} is the depth in meters.
P ( z ) {\displaystyle P(z)} is the overburden pressure at depth z {\displaystyle z} .
P 0 {\displaystyle P_{0}} is the pressure at the surface.
ρ ( z ) {\displaystyle \rho (z)} is the density of the material above the depth z {\displaystyle z} .
g {\displaystyle g} is the gravity acceleration in m / s 2 {\displaystyle m/s^{2}} . In deep-earth geophysics/geodynamics, gravitational acceleration varies significantly over depth and g {\displaystyle g} should not be assumed to be constant, and should be inside the integral. The unit of measurement commonly used in geology is the bar or kilobar. One bar equals 10^5 Pa ≈ 0.9869 atmospheres. For quick calculations, the lithostatic pressure (P_l) at a given depth can be estimated using the simplified equation: P_l = ρgZ where ρ = average density of the rocks forming the overlying rock column; g = acceleration due to gravity; Z = height of the column. Some sections of stratigraphic layers can be sealed or isolated. These changes create areas where there is not static equilibrium. A location in the layer is said to be in under pressure when the local pressure is less than the hydrostatic pressure, and in overpressure when the local pressure is greater than the hydrostatic pressure. Numerous measurements of vertical stresses carried out in mines, tunnels and other conditions related to geomining activities, subsurface engineering or underground scientific research have confirmed the general validity of the above equation regarding the variation of pressure along the vertical, with some exceptions mainly in surveys conducted at shallow depths. By contrast, it is not easy to experimentally determine and estimate the value of horizontal stresses at a depth z. For convenience and simplicity of analysis this problem is addressed by considering the ratio k {\displaystyle k} between the average of the horizontal stresses and the vertical stress, using the following equation:
( σ H + σ h ) 2 = σ ¯ H = K σ v = K p ( z ) {\displaystyle {\frac {(\sigma _{H}+\sigma _{h})}{2}}={\bar {\sigma }}_{H}=K\sigma _{v}=Kp(z)}
and therefore
K = σ ¯ H σ v {\displaystyle K={\frac {{\bar {\sigma }}_{H}}{\sigma _{v}}}}
… excerpt ends here. Continue reading the full article.
