Predicting three-dimensional roughness of rock discontinuity based on limited outcrop information during tunnel construction

Three-dimensional (3D) roughness of the rock discontinuity plays a controlling function on the rock mass stability of excavation face during deep buried tunnel construction, which can be predicted based on the discontinuity outcrop from excavation face. However, there exist some disturbing factors such as dust and debris which affect the non-contact measurement accuracy on the outcrop information under construction environment. In this study, a new method to predict three-dimensional roughness of rock discontinuity (JRC_3d) based on the limited outcrop and drilling test information from the rock mass of excavation face is proposed. Two-dimensional roughness of rock discontinuity (JRC_2d) is derived based on different asperity orders firstly. The first-order profile roughness is calculated by combining drilling test result, and the second-order profile roughness is predicted on establishing the statistical relationship between the geometrical parameter of the outcrop and the entire profile. Based on the prediction of JRC_2d, JRC_3d is characterized probabilistically with the improved Bayesian theory where the bootstrap method is used to deal with the difficulty of obtaining μ and σ of the prior distribution because the sample size is limited. A rock tunnel engineering in southwest China is taken as the engineering application, and the relative errors of the predicting JRC_3d are lower than 11 %. Finally, the effect of outcrop width on the predicting JRC_3d results is investigated. For Barton standard profiles, the statistical parameters of the first k climbing angles of the second-order roughness profiles are calculated to estimate the appropriate outcrop width as 16 mm. A rock discontinuity is generated to study the effect of discontinuity size on the predicting JRC_3d, and the relative error of the predicting JRC_3d is lower than 12 %, thereby validating the method applicability across a broad spectrum of discontinuity sizes, ranging from small to large.