广义位势理论从数学原理出发,将主空间的应力应变关系转换成六维空间的应力应变关系,从而建立岩土材料的本构模型,具有明确的数学依据和更少的物理假设。然而,将广义位势理论的本构模型开发到大型数值分析软件,并在六维应力应变空间中进行数值计算和验证的工作尚不多。为此,介绍了广义位势理论的多重势面模型和二重势面模型,详细分析了2种模型用于数值计算的弹塑性矩阵,并以2个二重势面模型(不考虑剪胀性的类剑桥模型和考虑剪胀性的类剑桥模型)为例,在数值分析软件FLAC3D中实现2个模型的开发。将开发的本构模型在FLAC3D的六维应力应变空间中进行计算分析,通过对比数值计算结果和室内三轴试验成果,说明了广义位势理论的本构模型在六维应力应变空间的计算精度是较高的,从而验证了理论模型的科学性和开发软件的正确性。
Abstract
In line with the mathematical principle, the generalized potential theory transforms the stress-strain relationship in the main space into stress-strain relationship in six-dimensional stress-strain space, thus establishing the constitutive model of rock and soil materials which has clear mathematical basis and fewer physical assumptions. However, few researches have been conducted to apply the constitutive model of generalized potential theory to large-scale numerical analysis software, let alone the numerical calculation and verification in the six-dimensional stress-strain space. In view of this, the multiple potential surface model and the double potential surface model of the generalized potential theory are introduced, and the elasto-plastic matrices of the two models used in numerical calculation are analyzed in detail. Two double potential surface models (the Similar Cam-clay model without dilatancy and the Similar Cam-clay model with dilatancy) are taken as examples to develop the model in numerical analysis software FLAC3D. The developed constitutive models are calculated and analyzed in the six-dimensional stress-strain space of FLAC3D. Comparison of the results of numerical calculation with the results of laboratory triaxial tests reveals high computational accuracy of the constitutive model of generalized potential theory in the six-dimensional stress-strain space, thus verifying the scientific nature of the theoretical model and the correctness of the development software.
关键词
广义位势理论 /
本构模型 /
模型开发 /
类剑桥模型 /
六维应力应变空间
Key words
generalized potential theory /
constitutive model /
model development /
Similar Cam-clay model /
six-dimensional stress-strain space
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基金
国家自然科学基金项目(51778152);广东省基础与应用基础研究基金项目(2020A1515110215);2021年度广东水利电力职业技术学院教育教学改革研究与实践项目(GX0205JGXM003)
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