基于最小势能原理的加筋垫层与路堤桩土相互作用研究

Interaction of reinforced cushion and pile-soil system in embankments based on principle of minimum potential energy

桩承式加筋路堤由于涉及桩–桩间土–垫层–加筋体的相互作用问题而使其承载机理复杂,适用于分层土的简化计算方法尚需要深入研究。在广义桩–广义土物理模型的基础上引入加筋垫层,考虑桩土荷载传递及加筋体拉伸产生的弹性势能,推导了整个系统的总势能方程,并将其离散化,建立了一个无约束非线性数学规划模型。该数学模型以总势能方程作为目标函数,采用下降迭代算法求解总势能方程的最小值,可求得桩、土、垫层垂直方向上的变形。通过一个未加筋的算例对数学规划模型进行了验证,并结合某堆煤筒仓实际工程对该方法计算的加筋处理效果进行了讨论。

The bearing mechanism of piled embankments is complex as it involves the interaction of piles, soil columns, sand cushions and reinforced geogrids, and its simplified calculation method for layered soils still lacks researches. A mathematical model is proposed for a generalized pile-soil model with geogrids. Considering the potential energy generated by pile-soil load transfer and geotextile tensile, the potential energy equations for the whole system are derived and discreted. An unconstrained nonlinear mathematical optimization model is established, with the potential energy equation as an objective function. The minimum value of the total potential energy equation is obtained by a descent iterative algorithm, and in this way the deformations of piles, soils and sand cushions in the vertical direction are solved. The mathematical model for piled embankment and the solving method are validated through an example without geogrid. The effect of the geogrid interaction is discussed in another engineering example.