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 \int_{0}^{z} \rho(z) \, dz 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. 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 between the average of the horizontal stresses and the vertical stress, using the following equation: :\frac{(\sigma_H + \sigma_h)}{2} = \bar{\sigma}_H = K\sigma_v = Kp(z) and therefore :K = \frac{\bar{\sigma}_H}{\sigma_v} where \sigma_H and \sigma_h are respectively the maximum and minimum horizontal stresses, \bar{\sigma}_H is the average horizontal stress, and K is called the
lateral stress coefficient. In 1952
Terzaghi, evaluating the conditions of the rock mass as a load-bearing body whose lateral expansion (deformation) is prevented during vertical loading, suggested that the value of the parameter k was independent of depth but a function of the
Poisson's ratio, specific to the rock present at depth
z, according to the equation: :k = \frac{\nu}{1-\nu} In consolidated rocks the values of Poisson's ratio generally vary between 0.2 and 0.3, consequently k would vary between 0.25 and 0.43. This equation treats the behaviour of the rock mass as comparable to that of an
elastic material and does not consider the contribution of tectonic stresses to horizontal pressure values. Although it is widely used for a first rough estimate of the stress ellipsoid (assuming equality of stresses along the x and y axes), decades of measurements indicate that it is not always accurate. Measured values of k are often higher than theoretical values at shallow depths and decrease with increasing depth, within the following range: :100/z + 0.3 k k = 1 is still commonly accepted and used in some branches of the
Earth sciences that do not require the use of the stress ellipsoid, such as
petrology. By contrast, in disciplines requiring quantitative and directional evaluation of stresses within the Earth—such as
civil engineering,
mining engineering,
structural geology analysis and
geomechanics—it is no longer considered adequate except as a simple reference model. Geomechanics researchers have suggested that such anisotropies may exist for at least 50 km within the
Earth's crust, with values of around 20,000 psi. == Geobaric gradient ==