基于数学规划算法的单桩沉降计算分析研究

Calculation and analysis of single pile settlement based on mathematical programming algorithm

基于荷载传递法的土弹簧模型,提出了新假设,并建立了用于单桩沉降计算的数学规划模型。该数学模型以离散的最小势能方程为目标函数,桩顶荷载为约束条件,拟解决如何对各土弹簧进行荷载分配使整个系统势能最小的数学问题。不同于传统的土弹簧模型,论文提出的模型假设某一桩单元沉降值为该桩单元顶部平面沉降与底部平面沉降的平均值。通过算例验证,文章推出的计算方法可行有效,计算得出的Q–s曲线、轴力分布与实测数据吻合较好,并对比发现在桩单元较少的情况下,通过该数学规划模型求解单桩沉降可以达到比位移协调法更高的精度。

Based on the soil spring model of the load transfer method,a new assumption is proposed,and a mathematical programming model for calculating single pile settlement is established.In the mathematical model,the principle of the minimum potential energy is used as the objective function and the working load at the top of the pile is used as constraints,which is a mathematical approach to find how to distribute the load of soil spring to make the whole system potential energy minimum.Different from the traditional soil spring model,the proposed model defines the element value of a pile settlement as the average value of the top and bottom plane settlements of that pile element.Validated by an example,the Q-s curve calculated by the mathematical programming model and the measured data are in good agreement,which illustrates the proposed method is feasible and effective.And a comparison with the displacement coordination method shows that the proposed method has higher precision under the condition of less subdivision element.