Advances in statistical mechanics of rock masses and its engineering applications

To efficiently link the continuum mechanics for rocks with the structural statistics of rock masses, a theoretical and methodological system called the statistical mechanics of rock masses (SMRM) was developed in the past three decades. In SMRM, equivalent continuum models of stress–strain relationship, strength and failure probability for jointed rock masses were established, which were based on the geometric probability models characterising the rock mass structure. This follows the statistical physics, the continuum mechanics, the fracture mechanics and the weakest link hypothesis. A general constitutive model and complete stress–strain models under compressive and shear conditions were also developed as the derivatives of the SMRM theory. An SMRM calculation system was then developed to provide fast and precise solutions for parameter estimations of rock masses, such as full-direction rock quality designation (RQD), elastic modulus, Coulomb compressive strength, rock mass quality rating, and Poisson’s ratio and shear strength. The constitutive equations involved in SMRM were integrated into a FLAC3D based numerical module to apply for engineering rock masses. It is also capable of analysing the complete deformation of rock masses and active reinforcement of engineering rock masses. Examples of engineering applications of SMRM were presented, including a rock mass at QBT hydropower station in northwestern China, a dam slope of Zongo II hydropower station in D.R. Congo, an open-pit mine in Dexing, China, an underground powerhouse of Jinping I hydropower station in southwestern China, and a typical circular tunnel in Lanzhou-Chongqing railway, China. These applications verified the reliability of the SMRM and demonstrated its applicability to broad engineering issues associated with jointed rock masses.