Evaluating of optimal length and spacing of nails in stabilization of soil pits using finite element and limit equilibrium methods

Nowadays, nailed retaining structures are one of the most practical methods of stabilizing pit walls in urban environments and slopes. This study evaluates the optimal distance and placement length of nails in various conditions using Plaxis and GeoSlope software, taking advantage of the findings of other studies to increase the reliability and stability of the pits. In this study, three examples of common urban pits with a height of 4, 8, and 12 meters were selected, and the variable distances of the nails were evaluated as 0.5, 1, 1.5, 2, and 2.5 meters in each pit. The results of various modeling are presented in 3-dimensional forms, taking into account the state of stability and the maximum displacement, to achieve the minimum amount of the total length of nails used (economic efficiency) in different conditions. For example, the three-dimensional results of the simultaneous investigation of safety factor and displacement along with the total length of nails in an 8-meter pit show that the most suitable safety factor is 1.4 for nails with a distance of 1.5 meters (5 rows of nails with lengths of 10, 9, 8, 6, 4 meters) and with a maximum displacement of 10 mm. In the best case, the total length of nails is 37 meters. Also, the second priority is nails with a distance of 1 meter with a total length of nails of 45 meters, which is not economical. Although shorter distances of nails produce better results, special attention should be given to the parameter of the total length of used nails. In addition, there is a good agreement between the results of the finite element method (FEM - Plaxis) and Limit Equilibrium Method (LEM – GeoSlope/w). Furthermore, a relationship is proposed to relate the response parameters of the pit (i.e., maximum displacement, optimal length of nails, and factor of safety) to the input parameters, such as pit height and nails distance. The results show that the proposed formula has good accuracy and efficiency in predicting the response parameters and gives reliable estimates in comparison to finite element simulations.