Fractures in geomaterials driven by spatial stress fluctuations

Stress field in geomaterials is not uniform; in particular due to the presence of spatial fluctuations. These are induced under external loading due to multiple randomly located heterogeneities and small-scale defects/fractures or by fluid transport. Stress fluctuations can be a form of residual stresses caused for instance by phase transformation (e.g. magma solidification), or as a result of strong seismic events. Subsequently, the stress field can be represented as a superposition of slowly changing large scale stress and small scale self-equilibrating spatial stress fluctuations (random stress field with zero average).

At the first glance, the field of spatial stress fluctuation taking alone is not supposed to cause any large scale development of fractures considered as linear objects (fracture opening linearly depending upon the applied load) since the average stress is zero. However, often the fractures are not independent of the stress field but produced in the zone where the stress fluctuations exhibit high tensile stress. The fracture initial size is of the order of the characteristic size of the zone of high tensile stress, that is the correlation length of the random field of stress fluctuations. The fracture will then be able to propagate further. The simplest model of such a fracture is a disc-like crack opened in the centre by a pair of concentrated forces with magnitude equal to the total force of the tensile stress in that zone [1].

Model [1] predicts the extensive fracture growth to be stable that is further increase in its size would require increase in the concentrated forces that is increase in the amplitude of stress fluctuations. In the case when the stress fluctuations represent residual stress, it is not possible as the residual stress can only decrease [2]. Yet, self-equilibrating residual stresses can cause macroscopic failure. This requires a new paradigm of crack/fracture growth in self-equilibrating field of stress fluctuations. To this end we accept that (1) the fracture opening is bilinear such that the local compressive stress just closes the fracture and hence cannot equilibrate the corresponding local tensile stress; (2) the fracture growth is not planar as passing through zones of compression is not possible leading to local overlapping.

The simplest model that accommodates the above features of fracture growth is a fracture with distributed bridges (fracture with constraint opening represented as a crack with Winkler layer [4]). We show that such a fracture will exhibit unstable growth forming a mechanism of both breakage due to residual stress and large (e.g. geological) scale fracture formation.

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Acknowledgement. The authors acknowledge support from the Australian Research Council through project DP210102224.