Geomechanical model for fracture deformation under hydraulic, mechanical and thermal loads

Hydraulic flow and transport (heat and solute) within crystalline rocks is dominated by the fracture systems found within them. In situ stress conditions have a significant impact on the hydraulic, mechanical and thermal coupled processes, and quantification of these processes provides a key to understanding the often transient time-dependent behaviour of crystalline rocks. In this paper, a geomechanical model is presented which describes fracture closure as a function of effective stress and the changes in parameters such as storage, permeability, porosity and aperture. Allowing the fracture closure to be defined by the change in normal effective stress provides a link to the numerical consideration of parametrical changes due to rock stress alterations caused for example by changes in fracture fluid pressure, stress release, tectonic stress, thermal stress, orientation of the natural fracture in the pervasive stress system and local changes in a rock mass due to stress alteration. The model uses geometrical considerations based on a fractal distribution of apertures on the fracture surface, and applies well-established analytical elastic deformation solutions to calculate the deformation response to changes in effective stress. Analysis of the fractal generation method allows a standard normal distribution of fracture apertures to be predicted for all common fractal dimensions relating to a 2D surface. Changes in the fracture aperture are related to hydraulic functions such as permeability, storage and porosity of the fracture. The geomechanical model is experimentally validated against laboratory scale experimental data gained from the closure of a fractured sample recovered at a depth of 3,800 m from the KTB pilot borehole. Parameters for matching the experimental data were established externally, the only fitting parameters applied were the minimum and maximum contact area between the surfaces and the number of allowable contacts. The model provides an insight into the key processes determining the closure of a fracture, and can act as a material input function for numerical models linking the effects of changes in the stress field, hydraulic or thermal conditions, to the flow and transport parameters of a fractured system.