Roughness of fracture surfaces in Discrete Element Model triaxial deformation experiments

The roughness of fracture surfaces is important for a range of geological processes such as the mechanical behaviour of faults or the fluid flow in jointed rocks or fault zones. However, the processes and parameters controlling the details of the fracture roughness are not fully understood yet. We therefore use numerical simulations based on the Discrete Element Method (DEM) to study the formation of fractures in triaxial deformation experiments under a wide range of stress conditions and to quantify the geometric properties of the resulting fracture surfaces. In the numerical experiments a DEM-model of a box-shaped rock sample is subjected to a displacement controlled load along its x-axis while a defined confining stress is applied to the other surfaces.

Based on the data from 131 numerical simulations the roughness of 388 fracture surfaces has been analysed. For this purpose the surface point clouds extracted from the Discrete Element models have been converted to height fields relative to a "best-fit" plane and the height distributions quantified. The results show that the heights are normally distributed. We observe no dependence on the confining stress except that models with equal confining stress in y- and z-direction show a higher standard deviation of the height distribution than those with differing y- and z-confinement. An analysis of the height-height correlation functions for those surfaces shows that they follow a power-law, demonstrating that the surfaces are self-affine. The Hurst exponent H describing the scaling of the roughness can be derived from the power-law relation. Values obtained are in the range H=0.2-0.6 for the full suite of experiments, while the mean of the Hurst exponents for each group of fracture surfaces generated under the same stress conditions is H=0.3-0.45. A weak decreasing trend of the Hurst exponent with increasing confining stress can be observed, but contrary to the standard deviation of the height distribution there is no dependence on the ratio of the confining stresses. There is also no difference between fractures generated in tensile (mode 1) or compressive conditions (mode 2).

Additionally, surfaces of rock samples fractured in triaxial tests in the laboratory have been analysed using the same methods. The surfaces show similar self-affine characteristics as those in the numerical experiments, although with significantly higher Hurst exponents H=0.6-0.8.

A comparison between our numerical models and laboratory experiments and data obtained from literature shows that natural and lab-created fracture surfaces and their numerically modelled counterparts are similar regarding the normally distributed heights and the self-affine scale, but the Hurst exponents do not match exactly. While the majority of field and experimental studies find significantly higher Hurst exponents of about 0.8, there are some studies, for example on Sandstone, which find H=0.4-0.5, falling into the range observed in our numerical experiments.