The relationship between the 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 modelling. 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 for the parameters related to the fracture-system geometry and boundary conditions. Accordingly, the relations between the inflow rate to the tunnel and the effective parameters, as well as their interactions, 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 impact on the value of the inflow rate. Furthermore, the impact of the tunnel radius on the unit inflow rate is negligible. Using numerical simulations, two empirical equations have been developed for the calculation of the 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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