Stability analysis of soil behind a vertical free-face between supporting piles

• Stability analysis method for soil between supporting piles is established.
• The validity of the analytical approach is checked by 3D FLAC analysis.
• The influence of h, w, γ, c, and φ to factor of safety of soil is studied.
• The stability analysis method is extended to include seismic conditions.

Estimating soil stability between supporting piles is of practical significance in geotechnical engineering. However, few methods exist that can solve this problem with proper usability. The primary purpose of this paper is to present a new analytical approach that can be used to calculate the factor of safety of soil with a vertical free-face between two adjacent supporting piles. This analytical approach combines the upper bound method with the strength reduction technique. After an appropriately simplified model of a three-dimensional slip surface is developed, the input energy and the energy dissipation of the instability mechanism can be calculated algebraically. Then, the factor of safety of the soil between the supporting piles can be obtained using the work–energy balance equation. A single-variable method is used to analyze the influence of geometry and soil properties on the factors of safety. The magnitude of the factor of safety is generally found to decrease nonlinearly with increasing height of the vertical free-face of the soil, decrease nonlinearly with increasing clear spacing between the two adjacent piles, increase with increasing internal friction angle and increase linearly with increasing soil cohesion.Numerical analyses are performed with the explicit finite difference code FLAC3D, confirming these results. The relationships between the factor of safety and the input parameters obtained from the theoretical procedure are found to be generally similar to that obtained from the FLAC3D numerical analyses. The factors of safety calculated by FLAC3D show acceptable differences from the theoretical results in most calculation domains. In addition, an estimation approach of the seismic stability of soil between the supporting piles is proposed by combining the upper bound method with the pseudo-static method.