Reliability-based roof stability charts for cavities in heterogeneous jointed rock masses

This paper reports on a simple yet sound way to estimate the factor of safety of the roof of underground cavities through a reliability-based approach, taking into account the uncertainties due to the spatial variability of rock strength and the presence of discontinuities. The safety factor was calculated for eight numerical models with the 2D finite difference Code FLAC, considering the typical shapes of the underground cavities in Napoli as detected during a recent extensive urban-scale survey. Four hundred analyses were executed to investigate the effect of the variability of rock resistance, by randomly assigning the cohesion according to a Gaussian distribution calibrated on available experimental data. The discontinuities were introduced by modelling a thin horizontal layer in the roof with a reduced resistance. One hundred and forty-four analyses were executed by changing the mechanical properties and the position of the less resistant layer. The results allowed to generate a stability chart expressing the ratio between the rock uniaxial compressive strength and the acting vertical stress as a function of the cavity span normalized to the roof thickness. Within the framework of reliability-based approaches, curves associated with different probabilities of failure were obtained. By using this chart for a large number of well-known cavities in Napoli, it is shown that, consistently with the experimental evidence, their safety margins are slightly influenced by the variability of rock strength and largely worsened by the presence of joints. The chart may be seen as a tool to plan preservation activities at an urban scale, upgrading the deterministic approach previously available to this aim.