Relationship between inflow rate to a rocky tunnel and the effective parameters controlling the inflow rate, e.g., aperture, spacing, orientation, tunnel radius, and water head is investigated by numerical modeling. Response surface methodology is adopted to optimize the number of simulations and their meaningful interpretation, and Design-Expert software is used for this purpose. Consequently, numerical simulations are performed using 3DEC version 7 software for 88 scenarios, based on different values of parameters related to fracture system geometry and boundary conditions. Accordingly, the relations between the inflow rate to the tunnel and the effective parameters as well as their interaction are determined and presented in the form of empirical equations. In addition, the mean value of each parameter is used to develop another equation for calculating the inflow rate. Specifically, the aperture and spacing, as well as the interaction between these parameters and other effective parameters, have the most important impacts on the value of the inflow rate. Furthermore, the impact of tunnel radius on the unit inflow rate is negligible. Using numerical simulations, two empirical equations have been developed for calculation of unit inflow rate to the tunnel: one for exact values of parameters and another for their mean values.

Supplementary material: Supplementary information on the interaction between the parameters and the statistical analysis are available at

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