Soil Strength Parameters for the Sustainable Design of Unsupported Cuts Under Drained Conditions Using Reliability Analysis

Unsupported excavations are frequently performed in several geological and geotechnical projects, particularly for constructing roads and railways, and they are often carried out in different materials. The design of such cuts in soils needs the determination of representative values of its mechanical properties, particularly of the strength parameters, and the application of adequate safety factors. The procedure should ensure a sustainable design of those cuts, allowing for economical solutions that guarantee a low probability of geological–geotechnical failure. This paper assesses the reliability of unsupported cuts in soils, under drained conditions, assuming a Mohr–Coulomb strength criterion. Statistical meshes are generated considering the spatial variability of the friction angle and of the true effective cohesion, which are assumed to be uncorrelated. In this process, typical values of the coefficients of variation and of the horizontal and vertical scales of fluctuation are applied. Soil characterisation is simulated in each statistical mesh, and the characteristic values of the strength parameters are determined using statistical methods. Unsupported cuts of different heights and inclinations are designed using typical safety factors. Slope stability analyses are carried out using Random Finite Element Limit Analysis. The uncertainty in the actions is considered, and the probability of failure is determined by direct reliability analysis. The results show the relevance of the ratio between the scale of fluctuation and the excavation depth, the slope inclination, and the characteristic value of the soil strength parameters on the probability of failure. Values of adequate safety factors are proposed towards obtaining an appropriate probability of failure, compatible with the sustainable design of the cuts.