Stability analysis of a vertical excavation reinforced with horizontal nails using three-dimensional finite elements limit analysis

Abstract

Three-dimensional stability analysis of a vertical excavation, reinforced with grouted horizontal nails, has been carried out by using the three dimensional lower and upper bounds based finite elements limit analysis (FELA) using Optum G3. The nail along with the surrounding grouted cementitious material is assumed to behave as a single monolithic cylindrical block which was assumed to be either rigid or an elasto-plastic material following the Von-Mises yield criterion. The excavation is assumed to fail on account of either an interface shear slippage between nails and surrounding soil mass or on an account of axial tensile rupture of the composite nail material for a few typical cases as well. The soil unit weight has been varied to induce the ultimate shear failure of the soil nailed excavation. The unit weight of the soil mass at which the failure of the nailed wall occurs is termed as γcr. Two different types of boundary conditions along the base of the excavation have been considered. In the first case, the in-situ soil mass behind the excavation is extended below the base as well (Case 1) and in the second case, the excavation is assumed to simply lie on a hard stratum (Case 2). The results have been provided in the form of a non-dimensional stability number N=γcrHc as a function of soil friction angle φ, Sv/H, SH/H, d/H, L/H and m; where H refers to height of the wall, d is diameter of the grouted nail, Sv and SH imply centre to centre vertical and horizontal spacing of the nails, and m is the mobilization factor between grouted nails and adjoining soil mass. The results from the analysis have been found to compare well with the data reported in literature. All the results have been presented in the form of non-dimensional stability charts, which will be useful for design for any given values of height H and cohesion c. From the observed failure mechanisms, an analysis has also been carried out to determine the optimized lengths of nails. The optimized lengths of nails for both Cases 1 and 2 have been also provided. The type of failure mechanism, base or face failure, dictates the optimized lengths of the nails.