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李亮,高超,吴利华.饱和两相介质动力固结问题时域求解的精细时程积分方法[J].计算力学学报,2017,34(1):27~34

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饱和两相介质动力固结问题时域求解的精细时程积分方法

Precise time-integration method for the time-domain solution of the dynamic consolidation problem of fluid-saturated porous media

投稿时间：2015-11-18 修订日期：2016-03-08

DOI：10.7511/jslx201701003

中文关键词: 饱和两相介质动力固结 u-p波动方程精细时程积分向后差分

英文关键词:fluid-saturated porous media dynamic consolidation u-p dynamic formulation precise time-integration method backward difference algorithm

基金项目:国家自然科学基金面上项目（51178011）；国家重点基础研究发展计划973计划（2011CB013602）资助项目

作者	单位
李亮	北京工业大学城市与工程安全减灾教育部重点实验室, 北京 100124
高超	北京工业大学城市与工程安全减灾教育部重点实验室, 北京 100124
吴利华	北京工业大学城市与工程安全减灾教育部重点实验室, 北京 100124

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中文摘要:

针对u-p形式的饱和两相介质波动方程，采用精细时程积分方法计算固相位移u，采用向后差分算法求解流体压力p，建立了饱和两相介质动力固结问题时域求解的精细时程积分方法。针对标准算例，对该方法的计算精度进行了校核。开展了该方法相关算法特性的研究，对采用不同数值积分方法计算非齐次波动方程特解项计算精度的差异进行了对比研究，并对采用不同积分点数目的高斯积分法计算特解项条件下计算精度的差异进行了对比研究。研究结果表明，（1）该方法具有良好的计算精度。（2）计算非齐次波动方程特解项的数值积分方法中，梯形积分法的计算精度最差，高斯积分法、辛普生积分法和科茨积分法都具有较好的计算精度。（3）增加高斯积分点数目对于提高计算精度的作用并不显著。

英文摘要:

A precise time-integration method for the time-domain solution of the dynamic consolidation problem of fluid-saturated porous media is proposed on the basis of u-p dynamic formulation.The solid-phase displacement u is computed by the precise time-integration algorithm,and the pore fluid pressure pis computed by the backward difference algorithm.The proposed method is verified by a standard numerical example.The characteristic of the proposed method is also investigated.The computational accuracy is compared when several numerical integral methods are employed to calculate the special solution term of u-p dynamic formulation.The computational accuracy of Gauss integral method is also compared when different numbers of integral points are employed.It is shown that (1) the proposed precise time-integration method has fine computational accuracy.(2) Gauss integral method,Simpson integral method and Coates integral method all have fine computational accuracy,while trapezoidal integral method has poor computational accuracy when used to compute the special solution term.(3) the effect of the number of Gauss integral points on computational accuracy is insignificant.

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