考虑非达西渗流的比奥固结有限元分析

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摘要在经典Biot固结理论基础上,建立了考虑非达西渗流影响的固结方程,并用有限元法进行了求解.首先,引入目前广泛应用的Hansbo非达西渗流定律,简要分析了该模型及其参数情况.通过对孔压梯度进行一定简化,结合流量连续条件和力的平衡条件,获得了考虑非达西渗流的Biot固结理论控制方程.在此基础上,基于加权残数法和空间八结点单元,推导了相应的有限元方程.通过在已有程序基础上编制非达西渗流模块,实现了对上述有限元方程组的求解.最后通过与解析理论对比,验证了数值方法的可靠性.结果发现相比于考虑非达西渗流的解析理论,有限元解法误差随非达西渗流控制参数的增大而增大,但总体误差在10%以内;非达西渗流会延缓固结速率,且该影响随着非达西渗流参数的增大而变得明显.

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	邓岳保
	谢康和
	李传勋

关键词 ： Biot固结理论, 非达西流, 有限元法, 加权残数法

Abstract：Based on the classic Biot’s consolidation theory, the consolidation equation considering non-Darcian flow is set up and then solved numerically with the aid of the finite element method. Firstly, the well-known Hansbo’s non-Darcian flow model is incorporated and the selection of the input parameters is analyzed correspondingly. Then, with a further simplification of the hydraulic gradient combining with the flow continuity condition and the force equilibrium condition, the governing equations for the Biot’s general consolidation theory with non-Darcian flow are formulated. Based on this, the finite element formulations for the spatial eight-node block element are deduced by means of the weighted residual method. A program considering the effect of the non-Darcian flow is developed based on an existing procedure correspondingly. With this modified program, the obtained governing equations can be solved numerically. Finally, the reliability of the numerical method is verified against the established theoretical solutions. The results show that (1) the difference of the calculated results for the two methods increases with the increase of the non-Darcian flow parameters, and the maximum difference is smaller than 10%; (2) the consolidation rate will slow down when considering the effect of non-Darcian flow, and this effect is significant when the property of the non-Darcian flow is apparent.

Key words： Biot’s consolidation theory non-Darcian flow finite element method weighted residual method

收稿日期: 2011-10-19

TU43

基金资助:基金项目:国家自然科学基金项目(51179170,50708093)

作者简介: 邓岳保(1983– )，男，湖南岳阳人，博士研究生，主要研究方向为固结理论数值分析和软土地基处理。E-mail: dengyuebao@yahoo.com.cn

引用本文:

邓岳保, 谢康和, 李传勋. 考虑非达西渗流的比奥固结有限元分析[J]. 岩土工程学报, 2012, 34(11): 2058-2065. DENG Yue-bao, XIE Kang-he, LI Chuan-xun. Finite element analysis of Biot’s consolidation with non-Darcian flow. Chinese J. Geot. Eng., 2012, 34(11): 2058-2065.

链接本文:

http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/ 或 http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/Y2012/V34/I11/2058

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