A new mathematical approach for representing the deformation mechanism of rocks under constant load

Abstract

Rock masses will remain under constant load due to the engineering structures in rocks. Particularly, weak rocks undergo time-dependent deformation under constant load following the initiation of mining or civil engineering works. Initially, deformations in rock masses are caused by the closure of discontinuities. Following the completion of discontinuity closures, the rock material will also be subjected to deformation depending on the load applied. On this occasion, deformation characteristics of rock may become important for the stability of an engineering structure in the rock mass. If there is no intervention on completion of the construction work, deformations will diminish and it will come to an end. This phase is the phase in which secondary stresses come into equilibrium. Insertion of certain parameters in empirical equations in designing rock structures should be considered instead of expensive and time-consuming in-situ tests. Generally, empirical equations that determine the deformation modulus are based on rock mass classification systems. Many empirical equations developed by different researchers  can be used to determine the deformation modulus. These equations use the uniaxial compressive strength (UCSi) and elastic modulus (Ei) values of rocks obtained in the laboratory as parameters, such as of rocks obtained from laboratory tests. Those parameters, which are used in empirical equations to state deformation and strength characteristics of rocks, may be reliably used particularly in engineering designs by numerical modelling. In all rock types, deformations will start with the closure of discontinuities; however, pre-failure deformation characteristic of the rock mass will be a factor for the timing of failure. In this study, time-dependent deformational characteristics were analysed under constant load on 12 different rock types from different locations. The results indicate that the rocks deformed in a different manner under various constant loads. In addition, meaningful equations of time–load–deformation were derived from the results of laboratory experiments conducted on different rock types under various constant loads.