2.1. Characterization of Random Contact Processes
Due to the porous nature of geomaterials, the porosity is used to describe the random contact process on rough surfaces, as shown in Fig. 1. Therefore, the contact between two rough surfaces is considered as a process in which the pore volume is continuously reduced and the real contact area is continuously increased until the porosity is zero. The increase in the real contact area is caused by the continuous increase of the contacting asperities, so a parameter is introduced to represent the true contact ratio, which can be expressed as , where n is the number of asperities in contact, is the number of contact asperities after full contact. The porosity in initial contact is , and the is considered to be zero at this time. As contact occurs, gradually decreases to 0, and gradually increases to 1. Therefore, the relationship between and can be described by an exponential function
where, A is a fitting parameter that can be determined experimentally. The complex random contact process is now characterized by a piecewise exponential function.