Uncertainty Analysis in Tunnel Deformation Using Monte Carlo Simulation

Calculating in situ rock stresses is increasingly imperative due to the complexities and limitations associated with testing techniques, equipment, assumptions, and the subjective interpretation of test results. Estimating in situ stress from hydraulic fracturing tests (HFT) is one of the most effective methods. HFT data rely on three parameters: (1) shut-in pressure, (2) reopening pressure, and (3) fracture orientation. The previously available literature developed a first-order approximation for estimating the effect of these uncertainties on tunnel deformation estimates using Pender’s solution. This study conducts a detailed Monte Carlo analysis across four cases with results compared with the first-order approximate analysis. The cases are defined by the least horizontal principal stress, maximum horizontal principal stress, the direction of the fracture, and angular coordinates concerning the tunnel center. Case b represents maximum tunnel deformation (percentage of tunnel diameter) when the tunnel alignment is along the direction of the maximum horizontal principal stress. Cases c and d represent minimal tunnel deformation (percentage of tunnel diameter) when the tunnel alignment is along the direction of the least horizontal principal stress and the most horizontal principal stress, respectively. It is observed that the first-order analysis provides reasonable results for Cases b, c, and d. However, significant errors exist in Case a, which involves the largest tunnel deformation (percentage of tunnel diameter) when the tunnel alignment is along the direction with the least horizontal principal stress. This case is the most critical and exhibits less fluctuation in the Monte Carlo simulation (MCS) results compared with the first-order approximation (FOA). This study demonstrates that MCS offers a more precise approach to analyzing uncertainties and estimating their impact on tunnel deformation. Specifically, for Case a, a detailed Monte Carlo analysis outperforms the approximate analysis, making MCS a more reliable method for assessing the effects of uncertainty in hydrofracturing parameters on tunnel ovalization estimates. Numerical models are predominantly used in designing rock engineering projects.