Generalized Block Theory for the Stability Analysis of Blocky Rock Mass Systems Under Seismic Loads

The stability analysis of rock blocks on man-made excavation faces (e.g. tunnel, cavern, and slope) subject to seismic loads is an important issue in the field of rock engineering. This paper proposes a generalized block theory (GBT) by combining a pseudo-static method and the traditional block theory to evaluate the stability of blocky rock masses during earthquake activities. In our analysis, the basic safety factors are derived considering time-varying seismic loads to determine the stability of a rock block at each time step. Afterwards, two new parameters, Pu and Vu, are used to evaluate the seismic stability of a rock block, where Pu is the instability probability defined as the ratio of the time for the block becoming unstable to the total seismic loading time, and Vu is the probabilistic instability volume defined as Pu times the block volume. As for a blocky rock mass system, its probabilistic instability volume is the sum of Vu of all seismically unstable blocks and the instability probability is the ratio of its probabilistic instability volume and total volume of seismically unstable blocks. Through the simulation of a generic slope excavation, we observe that seismic loads significantly affect the stability and kinematics of a rock block during an earthquake. For a blocky rock mass, both Pu and Vu decay with the epicentral distance, in general following an inverse power law trend. Furthermore, it is found that the local site effect also has a strong influence on the slope stability under seismic loads.