针对刚性挡土墙，推导了非极限状态摩擦角与相对位移之间的关系式，分析了最不利情况下墙后土楔的受力情况，得到非极限状态主动土压力计算公式，较好地解释了平动位移模式下的主动土压力分布性状。并通过室内模型试验进行了验算。文中仅对砂性土主动土压力进行研究。

As for rigid retaining walls, the relationship between the friction angles at non-limit state and wall movement is developed. By analyzing the forces acting on soil wedge under the most unfavorable conditions, the formula of calculating earth pressure in the non-limit state is achieved. It can explain the earth pressure distribution of translation movement mode well. And this formula is verified through experiments. The research represents only the active earth pressure of sand soil in this text.

针对平动模式下的刚性挡土墙,提出了考虑土拱效应的非极限主动土压力计算方法。考虑墙体平动位移对墙后填土内摩擦角与墙土界面上的外摩擦角的影响,建立了内外摩擦角与位移之间的关系式。对未达到极限位移的挡土墙,分析墙后小主应力拱的应力状态,并结合位移与摩擦角之间的关系,把主动侧土压力系数与挡土墙位移联系起来,将其用于水平微分单元法求解平动模式下挡土墙非极限主动土压力,给出了考虑土拱效应的非极限主动土压力分布、合力及作用点的理论公式,并与不考虑土拱效应的非极限主动土压力计算方法进行了比较。结果表明:该方法可行有效;土压力合力大小相等,但合力作用点与土压力分布存在明显差别;研究成果可为相关工程提供参考。

Aimed at rigid retaining wall under the mode of translation, a calculation method for active earth pressure under non-limit state, which considered soil arching effect was proposed. Considering the influence of wall translation displacement on the internal friction angle of the backfill soil behind the wall and the outer friction angle on the soil-wall interface, the relationships between the friction angles and the wall displacements were acquired. Stress state of minor principal stress arch behind the retaining wall under non-limit state was analyzed. Then, combined with relation of displacement and friction angle, authors related the coefficient of active earth pressure to displacement of retaining wall. The coefficient in the method of horizontal differential unit was used to compute active earth pressure with the mode of translation under non-limit state. The theoretical formulae of the unit active earth pressure, the resultant force and the action point of the resultant force were derived, which were compared with the calculation method of active earth pressure under non-limit state without considering soil arching. Results show that the method is feasible and effective. The same resultant force can be got by the two methods mentioned in above, but the action point of the resultant force and earth pressure distribution have significant differences. The study results can provide reference for related projects.

朗肯理论局限于求解墙背铅直且光滑,墙后填土位移达到极限状态的土压力,因而开展倾斜粗糙墙背的非极限主动土压力的理论研究具有重大意义。将墙后黏性填土滑裂体分为弹性区和塑性区两部分,并基于非极限状态下的虚功原理,建立了能量守恒方程,推导了张拉裂缝深度及潜在滑裂面的解析式。在此基础上,考虑了土拱效应,并通过摩尔应力圆,得到了水平应力、竖向应力的表达式,由水平层分析法建立受力平衡方程,推求了倾斜挡墙黏性填土非极限主动土压力分布、合力大小、合力作用点深度的理论表达式。当满足朗肯假设时,朗肯裂缝深度、滑裂面倾角、合力值为其特解。由两例模型试验验证了公式的合理性。研究表明:张拉裂缝深度与填土内摩擦角φ_m、填土黏聚力c_m、墙土摩擦角δ_m、墙土黏聚力c_w_m、墙体位移比η呈正相关,与墙背倾角ε呈负相关。潜在滑裂面倾角大小与c_m无关,随ε、φ_m、η的增大而增大,而δ_m、c_m对其影响则相反。墙背光滑时,土压力近似呈线性分布,合力作用点深度与朗肯解接近;墙背粗糙时,土压力则呈凸曲线分布,上部本文解大于朗肯解,下部反之,其大小随η、φ_m、c_m的增加而减小,峰值随ε的减小而有所提高,c_w_m对其影响甚微,合力作用点深度仅在俯斜式挡墙发生较大位移时才可能低于朗肯解。

Rankine’s theory is limited to solving the earth pressure where the wall back is vertical and smooth and the displacement of the fill behind the wall reaches the limit state. It is of great significance to carry out theoretical research for non-limit active earth pressure on inclined rough wall backs. The viscous fill slipper behind the wall is divided into two parts, the elastic region and the plastic region. Based on the principle of virtual work in the non-limit state, an energy conservation equation is established, and the formulas for tension crack depth and potential slip surface are derived. On this basis, the expressions for horizontal stress and vertical stress are obtained through the Mohr stress circle in consideration of the soil arch effect. Moreover, the theoretical expressions for the non-limiting active earth pressure distribution,the magnitude of the resultant force,and the position of the resultant force’s action point are derived by establishing the force balance equation using the horizontal layer analysis method. When the Rankine’s hypothesis is met, the Rankine’s crack depth, slip surface inclination, and resultant force values are special solutions. The validity of the formulas is verified by two model tests. The research manifests that the tensile crack depth is positively correlated with the internal friction angle <i>φ</i>_m of the fill, the cohesion <i>c</i>_m of the fill, the wall-soil friction angle <i>δ</i>_m, the wall-soil cohesion <i>c</i>_wm, and the wall displacement ratio <i>η</i>, while negatively correlated with wall back inclination <i>ε</i>. The inclination angle of the potential slip surface has nothing to do with <i>c</i>_m, but increases with the growth of <i>ε, φ</i>_m, and <i>η</i>, while the influence of <i>δ</i>_m and <i>c</i>_m is opposite. When the wall back is smooth, the earth pressure is approximately linearly distributed, and the position of the resultant force is close to that obtained from the Rankine’s solution; when the wall back is rough, the earth pressure distributes in a convex curve, with the upper part larger than the Rankine’s solution, and the lower part smaller than the Rankine’s solution. Earth pressure declines with the increase of <i>η, φ</i>_m, and <i>c</i>_m, and its peak value increases with the shrinkage of <i>ε</i>, but is rarely affected by <i>c</i>_wm. The position of the resultant force acting point can only be lower than the Rankine’s solution in the presence of large displacement of the inclined retaining wall.

基于扩展的非饱和土抗剪强度公式，假定墙后土体小主应力拱为圆弧拱，分别建立了水平微分单元平均竖向应力、层间剪切力与墙体水平反力的关系，进而通过静力平衡方程推导出非饱和土主动土压力计算公式。分析过程中考虑了水平微分单元体层间剪切作用，弥补了传统土拱效应方法中水平微分单元体受力不平衡的不足。与经典方法获得的非饱和土土压力公式相比，该方法考虑了墙后土体主应力偏转现象，所得主动土压力呈非线性分布，能够反映土体的真实应力状态;与传统的考虑土拱效应的土压力解析解相比，该方法较全面地分析了主动土压力影响因素，考虑了非饱和土物理力学性质、地下水位的影响。该结果可为非饱和土土压力研究提供理论依据，对工程设计有一定参考意义。

With the assumption that the trace of the principal stress arching is a semicircle, the relationships of average vertical stress and interlaminar shear stress of soil differential element vs. counterforce of wall were established, respectively. Then, a static equilibrium equation based on the extended unsaturated soil shear strength formula was set up to solve the active earth pressure. The interlaminar shear action was considered in the process, to make up the shortage of force imbalance of traditional static equilibrium equation. Compared with the earth pressure formula of unsaturated soil deduced from classical approach, principal stress deflection is considered in this study, and the active earth pressure is nonlinear along the height which is closed to the true stress distribution. Compared with the conventional earth pressure calculations considering arching effects, factors on active earth pressure are analyzed in the new method. These factors include the properties of unsaturated soil and groundwater level. The result can provide theoretical basis for earth pressure study and reference for the design of retaining wall.