Stochastically Determined Safety of Underground Structures According to Eurocode

Eurocode allows the use of stochastic methods to determine an allowable degree of safety or to reduce inaccuracy in the initial data. Quality assurance methods and the nature and extent of the damage may be taken in account. In this paper we describe how this approach may be applied to conventional design. Two case examples will be presented. Principles on how to operate on limited data are stated. Simplifying design assumptions will be used and proof of their validity will be stated. Numerical sampling method (Monte Carlo method) is used as a design aid to solve the probability equations rapidly with reasonable engineering accuracy. The method is applied to predicting non-violent spalling probability and nominal damage depth. Another case example is shown for circular shaft wedge stability and reinforcement design. A comparison with conventional (empirical) design methods shows that the improved design accuracy has a significant effect on reinforcement amount without reducing the level of safety. Also, as it will be shown, the scalability of the methods is very high, ranging spatially from one meter tunnel section to hundreds of meters and source data ranging from sketchy estimates to detailed laboratory tests and in-situ determined parameters.