The outlined theory forms the framework for detecting an initiation of a failure state by means of propagating waves. By approaching the failure state the speed of a specific wave decreases and eventually degenerates in a stationary discontinuity for the class of materials considered. This result even holds for including a fluid phase in a porous continuum. It remains to be proven that other effects such as inhomogenieties and stress concentrations do not significantly interfere in geological materials.
For the containment of materials in earth structures the detection of discontinuities in otherwise homogeneous materials is of prime importance. Not only from a mechanical point of view but also from a migration standpoint, because the migration through a cracked medium can be of an entirely different nature then through a homogeneous material (Streltsova 1978). Bhanging the geometry of an earthstructure generally changes the stress state within the earth structure. If the stress state changes to a point where discontinuities arise in a former homogeneous material, a new situation is created. As reasoned above the prediction of the initiation of discontinuities is of crucial importance to many engineering situations in earth materials. One approach would be to determine in detail the constitutive behaviour of the geological material. Apart from the great difficulties in formulating such behaviour ~n detail, one faces the enormous task to determine the in situ parameters and initial state accurately.
For reference purpose will derive the now well-known result of the description of wave propagation in prestressed materials.
(Equation in full paper)
Increasing D will increase the speed of the fastest propagating discontinuity and decrease the speed of the slowest discontinuity. If AF - D2 = 0 then the slowest discontinuity degenerates into a statipnary discontinuity; at that point the material will be in a neutrally stable condition. If this condition can be correlated with failure of the material, we would be able to detect and predict the onset of failure by measuring the speed of the discontinuities.
The example here chosen is a relative simple one. Other types of constitutive relations for earth materials could be examined, especially on the more pretentious question whether by exercising this philosophy it would be possible to detect the stress state in an earth material. Van der Kogel, et al, 1980 used a saturated porous medium and studied the propagation of discontinuities in this type of material. A similar conclusion can be drawn as above for this type of material.
We have shown that prestressing an isotropic non-linear elastic material can give rise to the appearance of an induced anisotropic behaviour for small strain waves. This induced anisotropy has significant implications with respect to propagating waves, especially the degeneration of propagating discontinuities into stationary discontinuities. Correlation of this neutrally stable behaviour with failure of a geological material might lead to a method of detecting and predicting the onset of failure.
