多级拼装悬臂式挡墙地震永久位移计算方法

Calculation method for seismic permanent displacement of assembled multi-step cantilever retaining walls

为确定新型的多级拼装悬臂式挡墙的地震永久位移,基于墙-坡系统整体滑面过最下一级墙踵板下边缘的旋转滑动破坏模式,采用极限分析上限法及拟静力法,得出墙-坡系统地震屈服加速度系数表达式,进而结合Newmark滑块法,对系统产生的转动角加速度进行二次积分得到其角位移,分别推导出了Ⅱ级、Ⅲ级和Ⅳ级拼装悬臂式挡墙各级墙顶地震水平永久位移计算公式。通过与Ⅲ级墙、Ⅱ级墙模型振动台试验及数值模拟对比,表明在不同地震波作用下,理论算法得到的Ⅲ级墙、Ⅱ级墙模型各级墙顶水平永久位移比试验值分别约大10%~40%、10%~30%,但其与数值模拟结果较为接近。实例分析进一步表明,理论算法一般比数值模拟结果相对偏保守;填土内摩擦角、黏聚力和单级墙体高度对墙-坡系统的水平屈服加速度分别呈较显著的正相关和负相关影响,而各级墙体间的平台宽度、单级墙底板长度和厚度对其影响较小;多级墙的分级数对水平屈服加速度有明显的非线性与正相关的影响特征;填料颗粒越细,对限制墙-坡系统地震永久位移的效果就越显著。

To determine seismic permanent displacement of a new type of assembled multi-step cantilever retaining walls,based on overall rotation-sliding failure mode of the wall-slope system with potential slip surface passing by the bottom edge of the heel plate of the lowest wall member,the seismic yield acceleration coefficient of the wall-slope system is proposed by the upper bound limit analysis and pseudo-static method.Moreover,according to Newmark’s block method,calculation formulas of seismic horizontal permanent displacement at the top of each step of the wall including two,three,and four steps are derived via angular displacement of the wall-slope system determined by quadratic integration of the rotational angular acceleration.Compared with shaking table tests and numerical simulations of the wall models with two and three steps,the horizontal permanent displacements under two-step and three-step walls calculated by the proposed analysis method are 10-40% and 10-30% larger than those by the tests,respectively.However,the theoretical results are relatively close to the numerical simulation results.Analysis results of the practical example show that the proposed method is generally more conservative than the numerical simulation method.Internal friction angle and cohesion of the backfill have greatly positive correlation with the horizontal yield acceleration of the wall-slope system,while the height of a wall member has obvious negative correlation with the horizontal yield acceleration of the wall-slope system.However,width of the bench between vertically adjacent wall members,length and thickness of bottom plate of a wall member have little effect on it.In addition,the total number of the vertically assembled walls has nonlinear and positive correlation with the horizontal yield acceleration,and the seismic horizontal permanent displacement of the system is decreasing as the filling soil particle size decreases gradually.