Quantitative Risk Analysis of Tunnel Instability in Layered Rock Mass Considering the Spatial Variability of Elastic Modulus

Abstract

Layered rock mass is a typical excavation disturbance sensitive rock mass, which is prone to the large deformation and collapse of soft rock mass under tunnel unloading. This in turn causes the construction safety risk and delays the project construction. As the spatial variability of rock mechanics parameters existed widely, which could make the deterministic calculation results cannot really reflect the safety reserve of the rock mass by supports. Therefore, considering the spatial variability of elastic modulus of layered rock mass for study the risk of tunnel instability both has the theoretical and practical significance. According to the transverse anisotropy characteristics of layered rock mass in Baokang tunnel, China, elastic wave velocities were determined by the acoustic test method at different broken surrounding rock mass. Meanwhile, the elastic modulus was converted into the elastic modulus based on theoretical formula, and a database of the elastic modulus was set up. Using the variograms model of geostatistics, the autocorrelation distances of elastic modulus along the strike and dip of rock strata were determined, respectively. Furthermore, a two-dimensional parameter random field which can characterize the spatial variability of elastic modulus of layered rock mass was constructed by the Karhunen-Loève (K-L) expansion method. Taking the standard value of tunnel allowable deformation as the evaluation index, the limit state equation of tunnel allowable deformation in the soft rock was established. Finally, considering the spatial variability of elastic modulus of layered rock mass, a quantitative risk analysis of surrounding rock instability was realized by the Monte Carlo method and numerical simulation method. The engineering example shows that, this quantitative risk analysis method can effectively evaluate the safety state of the surrounding rock mass, and it can provide a theoretical guidance and technical support for the tunnel construction. This work could provide a reference for other layered rock mass tunnel construction.