有理函数统一形式的结构性黏土弹黏塑性模型

Elastic-viscoplastic model for structural clays based on a unified form of rational functions

摘要:

针对结构性黏土压缩变形过程中应力应变关系的显著非线性特征,以及传统本构模型存在的数学形式固化与适用性局限问题,本研究提出了一种有理函数统一形式的结构性黏土弹黏塑性本构模型。首先,基于Maxwell力学元件,将总应变分为弹性与黏塑性应变之和,重点探究与结构性相关的黏塑性应变,根据一维压缩试验特征提出有理函数形式的黏塑性应变有效应力等效时间表达式。其次,基于“土体黏塑性应变率仅取决于有效应力和黏塑性应变”的假定,结合等效时间概念推导出结构性黏土的黏塑性应变率表达式,构建结构性黏土一维弹黏塑性模型。再次,介绍模型参数的计算方法,利用线性规划方法,将参数求解问题转化为多元线性回归问题,借用计算机技术进行矩阵求解。最后,在模型验证时推导了突然加载情况下土体应变随实际时间的变化规律,并用本文模型对常规固结试验和蠕变试验进行模拟分析,验证本文模型的适用性和参数计算方法的可行性。研究结果表明,本文提出的结构性黏土等效时间模型能够较好地描述结构性黏土在一维压缩条件下的有效应力黏塑性应变关系和总应变时间关系。

Abstract:

To address the pronounced nonlinearity of stress-strain relationships during the compression deformation of structured clay and the limitations of traditional constitutive models in terms of mathematical rigidity and applicability, this study proposes an elasto-viscoplastic constitutive model for structured clays based on a unified rational function formalism. First, based on Maxwell elements, this study decomposed the total strain into the sum of elastic and viscoplastic strains, with a focus on investigating viscoplastic strain associated with structural effects. A rational function expression for viscoplastic strain-effective stress-equivalent time was established through one-dimensional compression behaviors. Second, under the assumption that “the viscoplastic strain rate of soil depends solely on effective stress and viscoplastic strain,” the viscoplastic strain rate expression for structured clay was derived by integrating the concept of equivalent time, and then a one-dimensional elasto-viscoplastic constitutive model for structured clay was derived. Third, the parameter calculation method was introduced, transforming the problem of solving parameters into a multiple linear regression task by using linear programming techniques, with matrix solutions implemented through computational tools. Finally, during model verification, the strain variation of soil under sudden loading conditions as a function of real time was derived. The model was applied to simulating conventional consolidation tests and creep tests, demonstrating its applicability and the feasibility of the parameter calculation method. The research results indicate that the proposed equivalent time model for structured clay effectively describes both the effective stress-viscoplastic strain relationship and the total strain-time relationship under one-dimensional compression.