Influence of spatially varying thickness on load-bearing capacity of shotcrete

A common approach to verify a shotcrete layer's ability to secure blocks that can exist between rockbolts in a tunnel is to use analytical calculations. For this situation, an attractive approach to account for variability in the shotcrete parameters is to use reliability-based methods. Variability can then be accounted for by assigning suitable probability distributions to all relevant input parameters. Structural safety can be ensured by verifying that the probability of limit exceedance is smaller than an acceptable target probability of failure. However, even though analytical calculations and reliability-based methods can be used to design shotcrete support, one of the commonly made basic assumptions is that the load-bearing capacity of the shotcrete is governed by the spatial average of the input parameters. Thus, the spatial variability of the parameters are neglected. As a result, if the capacity is governed by the lowest value of a certain parameter, this assumption is non-conservative. In this paper, we present a novel approach in which the minimum of either the spatial average of a shotcrete slab of varying thickness, or the spatial average along the periphery of a loose block of that same slab, is used to estimate the load-bearing capacity of the shotcrete in a tunnel. The approach is based on results from numerical simulations of a shotcrete slab that we perform to investigate the effect that a spatially varying thickness has on the flexural load-bearing capacity of the slab. The results from the simulations show that the shotcrete's flexural load-bearing capacity might be overestimated when using the spatial average of shotcrete thickness between four rockbolts in design. Using the presented approach, the spatial variability of shotcrete thickness can be accounted for in practical design of tunnels without complex and time-consuming numerical simulations.