Initial Conditions

In all civil or mining engineering projects, there is an in-situ state of stress in the ground, before any excavation or construction is started. By setting initial conditions in the 3DEC model, an attempt is made to reproduce this in-situ state, because it can influence the subsequent behavior of the model. Ideally, information about the initial state comes from field measurements. But, when these are not available, the model can be run for a range of possible conditions. Although the range is potentially infinite, there are a number of constraining factors (e.g., the system must be in equilibrium, and the chosen yield and slip criteria must not be violated anywhere).

In a uniform layer of soil or rock with a free surface, the vertical stresses are usually equal to \(g \rho z\), where \(g\) is the gravitational acceleration, \(\rho\) is the mass density of the material and \(z\) is the depth below surface. However, the in-situ horizontal stresses are more difficult to estimate. There is a common (but erroneous) belief that there is some “natural” ratio between horizontal and vertical stress, given by \(\nu\)/(1 − \(\nu\)), where \(\nu\) is the Poisson’s ratio. This formula is derived from the assumption that gravity is suddenly applied to an elastic mass of material in which lateral movement is prevented.

This condition hardly ever applies in practice, due to repeated tectonic movements, material failure, overburden removal and locked-in stresses due to faulting and localization. Of course, if we had enough knowledge of the history of a particular volume of material, we might simulate the whole process numerically, in order to arrive at the initial conditions for our planned engineering works. This approach is not usually feasible. Typically, we compromise: a set of stresses is installed in the model, and then 3DEC is run until an equilibrium state is obtained. It is important to realize that there are an infinite number of equilibrium states for any given system. In the following sections, we examine progressively more complicated situations, and the ways in which the initial conditions may be specified. The user is encouraged to experiment with the various data files that are presented.