Probabilistic generic transformation model between two rock mass properties: specific fracture energy and P-wave velocity

Abstract

This study proposed a probabilistic generic transformation model between two rock mass properties, specific fracture energy, Ev, and P-wave velocity, VP. To build the transformation model, 12 pairwise data sets of Ev and VP were collected from six different construction sites involving construction of mountain tunnels in Japan. This database is labeled as “RockMass/2/350”. A probabilistic transformation model was built based on a bivariate standard normal distribution with these 350 data points. The model is generic, because it is based on a variety of sites. The performance of the constructed transformation model was evaluated through a cross-validation. It was found that 98.2% of the validation data fell within the computed 95% confidence interval of the model estimation, and this result provides a preliminary validation of the probabilistic transformation model. Unlike existing deterministic transformation models for estimating VP from Ev, the proposed model can explicitly evaluate the transformation uncertainty with a quantitative metric such as a percentile. For practical application, a 3D model of the spatial distribution for Young’s modulus, E, was visualized based on the proposed transformation model. Since the proposed model is probabilistic, it can provide the spatial distribution for percentiles of E values. The constructed 3D model presented in this paper can be directly used as an input data for finite element or finite difference analysis, and probabilistic evaluation of excavation simulation is feasible based on the proposed probabilistic model. The quantitative information on such uncertainty can be useful in decision-making for tunnel constructions, such as selection of a cautious characteristic value.