桩基三维弹性波动方程变步长交错网格有限差分数值计算

Numerical calculation of three-dimensional elastic wave equation of piles staggered grid finite difference using method with variable step lengths

为了提高桩基低应变数值模拟的计算效率,在传统差分方法的基础上,将变步长交错网格有限差分法引入到三维桩土模型的数值计算中,通过对三维弹性波动方程进行差分,并在计算模型界面处引入吸收边界条件,计算得到了桩在瞬态纵向激振力作用下的低应变数值模拟响应。计算结果表明:在保证计算精度的同时,由于该方法自身可变化的差分网格,使得计算过程更加灵活简便,降低了内存需求量,减少了计算时间。吸收边界可以有效吸收到达计算模型界面处的入射波,该方法在对低应变实测曲线的拟合和非对称缺陷桩的数值模拟中取得了良好的应用效果。

To improve the computational efficiency of low-strain numerical simulation of piles,the variable step staggered grid finite difference method is introduced into the calculation of three-dimensional pile-soil model based on the traditional difference method.By differentiating three-dimensional elastic wave equation and introducing absorbing boundary conditions on the computational model interface,the low-strain numerical simulation of the response of piles is calculated under transient vertical excitating force.The results show that the computational accuracy is guaranteed and the computational process is more flexible and simple because of varied difference grids.The process can also reduce the memory requirements and the computational time.The absorbing boundary which absorbs the incident waves reaching the computational model interface is effective.The proposed method has achieved good effects on fitting low-strain measured curve and numerical simulation of asymmetric defective piles.