Semi-Analytical Solution for Passive Earth Pressure in Unsaturated Narrow Soils Behind Retaining Walls With a Log-Spiral Failure Surface Based on the Principal Stress Trajectory Method

Most existing passive earth pressure theories are not completely suitable for the calculation of unsaturated backfill in practical engineering, especially for narrow backfill cases. In view of this, this study establishes a modified analytical model for the passive earth pressure of narrow backfill behind a retaining wall under unsaturated steady-state seepage conditions, based on the log-spiral failure mechanism and the arched differential element method. The distribution, total force magnitude, and the height of the application point of passive earth pressure for narrow backfill under the rotation about the wall toe (RB) mode are calculated by the fourth order Runge–Kutta method within the framework of the generalized effective stress principle. To validate the proposed method, a comparative analysis is conducted by integrating experimental, theoretical, and OptumG2 simulation results. Moreover, the effect of main parameters on passive earth pressures is investigated through a parametric analysis. The results show that as the wall–soil interface friction angle increases gradually, the passive earth pressure distribution curve transitions from convex towards the wall back to concave towards the wall back; with the increase of aspect ratio, the passive earth pressure curve gradually shifts from curved to nearly straight; with a small air entry pressure parameter, the total passive earth pressure force increases as the air entry pressure parameter increases, while the height of the application point of total force initially decreases and then increases; the hysteresis effect reduces the total passive earth pressure force and decreases the height of the application point of the total force.