层状粘弹性地基一维固结特性
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作者简介：刘加才（1970），男，副教授，主要从事软土特性及地基处理研究、本构关系与数值分析、现场原位测试及边坡稳定研究，（Email）。摘要：采用Merchant 流变模型模拟土体的粘弹性，针对层状黏弹性地基一维固结偏微分方程，利用Galerkin加权残值方法推导了该问题有限元矩阵表达式。将求解方法编制成应用程序，通过单层黏弹性地基和双层线弹性一维固结问题解答与解析解答对比，验证了求解方法和程序的有效性。采用程序对三层黏弹地基一维固结问题进行了算例分析，研究了处于不同深度处土层在不同时刻受土体粘滞性影响程度，以及粘弹性参数η1对土体孔压消散的影响。分析结果表明，黏滞性土体孔压消散慢于线弹性土体，且随着时间的增加和土层距离排水面距离的增加，这种现象更明显，在土层固结度达到80%～90%时两者差异达到最大值。粘弹性参数η1越大，粘滞性土体与线弹性土体固结度差异越大，且对土体的固结度影响也越提前。
关键词：层状；有限元；黏滞性；一维固结
中图分类号：TU471.2文献标志码：A文章编号：16744764（2012）03003405
One Dimensional Consolidation Analysis of Layered Clay
Soils Exhibiting Rheological Characteristics
LIU Jiacai, MA Qiang
（College of Transportation Science & Engineering, Nanjing University of Technology, Nanjing 210009, P. R. China）
Abstract:The rheological characteristics of clay soils were described by Merchant mode. The governing equation for consolidation of layered clay soils exhibiting rheological characteristics was solved using the finite element method. Matrix formulation was derived by Galerkins weighting residual method. The proposed FE procedure was encoded in a program. The presented formulation and program code were examined by using the analytical results of two simplified problems, a onelayer clay soil exhibiting rheological characteristics and a doublelayer elastic clay soil. The comparison shows that the numerical results agree well with those of analytical results. A threelayer clay soil exhibiting rheological characteristics was used to analyze influence of rheological characteristics and its parameter η1 on different layers at different time. The results show that consolidation of clay exhibiting rheological characteristics is slower than that of clay exhibiting elastic characteristics. The phenomenon becomes more obvious over time and the distance between the clay and the pervious plane increases. Difference between the pore pressure dissipation of rheological clay and that of elastic clay reaches its climax when the consolidation degree of clay is in the range from 80% to 90%. Difference between the consolidation degree of rheological clay and that of elastic clay becomes larger and the influence time is earlier with higher creep parameter η1.
Key words:layered; finite element; rheological characteristics; one dimensional consolidation地基的固结问题一直是工程界和理论界关心的热点问题之一。Terzaghi最早提出一维固结理论，为固结理论的发展奠定了基础。近年来一维固结理论有了较大发展，可以考虑较为复杂的情况，如加载随时间变化［1］、渗透力对土体固结的影响［2］、土体非饱和［3］、有限应变［4］、土体材料非线性［5］、非达西渗流［6］。软粘土具有粘弹性，地基土层通常具有成层性。一些学者将Terzaghi固结理论推广到成层地基情况，如Xie等［7］、Lee等［8］。另外一些学者考虑土体的黏滞性，研究了土体的一维固结问题，如赵维炳［9］、Hawlader等［10］、Li等［11］、Xie等［12］。由于问题的复杂性，同时考虑土体的成层性和黏滞性的文献并不多见。Cai等［13］基于Kelvin流变模型，运用Laplace变换、矩阵传递法以及Laplace变换求解了任意荷载下成层粘弹性地基一维变形问题。Kelvin流变模型可以反映弹性后效，却不能反映应力松弛。为了全面反映土体的粘弹性质，刘加才等［14］提出了基于广义Voigt流变模型的双层黏弹性地基求解方法，但求解过程较为复杂，不利于工程应用。本文采用岩土工程中应用较广的Merchant 流变模型，提出了层状黏弹性地基的一维固结有限元分析方法，并对其固结特性进行了研究。〖=D(〗刘加才，等：层状粘弹性地基一维固结特性〖=〗1问题描述