Retaining structures are crucial for preventing the collapse of soil and maintaining soil stability. The accurate determination of lateral earth pressure exerted by the soil is essential to the safety and economic feasibility of foundation pit engineering. Traditional earth pressure theories, however, overlook the displacement mode and displacement magnitude of the wall, wall-soil interaction, and soil arching effect. As a result, the calculated lateral earth pressure is often inaccurate, posing risks to engineering design and construction. To address the problem of active earth pressure in sandy soil under a rigid retaining wall in the rotational and translational coupling (RTT) mode, a more accurate and reliable calculation formula for non-limit active earth pressure in this scenario is developed, considering the interlayer sliding of soil wedges.

The non-limit active earth pressure was investigated under the RTT mode with a combination of discrete element simulations and theoretical derivation. The primary goal was to understand the impact of various factors such as wall displacement, friction angles, and rotation center position on earth pressure. To simulate the physical properties of soil particles accurately, and minimize the influence of resisting rotational moments, an elliptical particle cluster composed of three disks was chosen as the basic particle. The model parameters were selected based on previous research, ensuring the reliability and relevance of the simulation results. The PFC^2D software was used to create a soil model, and three different confining pressures (30 kPa, 60 kPa, and 100 kPa) were applied in a biaxial test setup. The internal friction angle of the soil was found to be 26.1°. To generate the soil model, a gravity deposition method was employed, layering the soil into six distinct layers with a controlled porosity of 0.22. A series of measurement circles were set up to obtain the internal stress and rotation angle of the soil. After the sample was formed, the horizontal displacement speed of the wall was 6 × 10⁻⁴ m/s when the control displacement wall rotated outward. The maximum horizontal displacement of the wall was set to 0.012H to ensure that the soil could reach the ultimate failure state under the RTT mode. Discrete element simulations were carried out for three rotation center positions (rotation center n = 0.5, 1.0, and 5.0) to explore the influence of rotation center position on the active earth pressure, wall-soil friction angle, the development of shear failure surfaces, and the internal stress state of the soil. Based on discrete element simulation analysis, the soil arch shape was assumed to be a middle-symmetric circular arc, and the non-limit slip fracture surface inclination was thus obtained. Taking into account the impact of interlayer staggering of soil wedges, the calculation formula for active soil pressure in the RTT mode was obtained using horizontal layer analysis method. The theoretical solution was further validated through model experiments, with a comparison showing good agreement between the experimental results and the theoretical predictions. Additionally, a comprehensive parameter analysis was conducted to investigate the effects of wall displacement, internal friction angle, wall-soil friction angle, and the rotation center position on the magnitude and distribution of active earth pressure under the RTT mode.

The results of discrete element simulation, simulation verification, and parameter analysis are summarized.　　The simulation results are as follows: 1. The performance of the wall-earth friction angles of soil samples with different rotating center positions in the RTT mode is basically the same. The average wall-soil friction angle of the three groups of models is approximately 21.4°. As wall displacement increases, the wall-soil friction angle gradually mobilizes and reaches its limit value. 2. The distribution of active earth pressure in the RTT mode exhibits characteristics of both translational mode and rotational mode. As wall displacement increases, the pressure distribution transitions from linear to parabolic. A larger n value results in a more linear pressure distribution. 3. With the displacement of the wall, both the internal friction angle φ and the wall-soil friction angle δ gradually mobilize. The soil transitions from a non-limit state to a limit state. The resultant earth pressure becomes essentially stable at S/H = 0.2%. In the RTT mode, the wall-soil friction angle of sand reaches its limiting value faster than the internal friction angle. 4. The soil failure process shows increasing particle rotation with wall displacement, leading to the development of a shear failure surface. The rotation of soil particles is more pronounced for higher n, and the failure surface becomes more distinct. 5. In the RTT mode, the principal stress at the slip surface deflects. In the upper and middle zones of the soil mass, the rotation angle of soil particles behind the wall and at the slip fracture surface is approximately the same. The principal stress deflection in the middle area is small. The soil arching effect occurs inside the soil mass, forming approximately symmetrical semicircular arches.　　Model verification: The theoretical results match well with the experimental results. When n = 0, the RTT mode transforms into a special mode of rotation about the wall top, and the active earth pressure appears as a parabolic distribution with an upward convex shape. When n = ∞, the RTT mode becomes a special translational mode, and the active earth pressure shows a linear distribution.　　Parameter analysis: 1. In the RTT mode, the active earth pressure distribution is a parabolic shape with an upward convex curve. As displacement increases, the active earth pressure decreases and approaches the Coulomb value. 2. The influence of the internal friction angle on the magnitude and distribution of active earth pressure is greater than that of the wall-soil friction angle. The greater the internal friction angle and the wall-soil friction angle, the smaller the active earth pressure. 3. As the n value increases, the pressure distribution becomes less nonlinear and approaches a linear form in the RTT mode. When n ≥ 5.0, calculations in the translational mode are acceptable.

The findings enhance the theoretical understanding of non-limit active earth pressure under RTT displacement and provide practical guidance for the design and construction of retaining structures. Future studies could explore the application of this model to scenarios of more complex retaining wall systems, displacement modes, and soil conditions.