双剪统一边界面塑性本构模型的有限差分算法及其数值验证

doi:10.13722/j.cnki.jrme.2022.0124

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摘要双剪统一边界面塑性本构模型(BUST模型)能反映低偏应力水平下岩土材料的塑性应变累积行为，这不同于经典双剪统一弹塑性本构模型。为了将BUST模型应用于滑坡或边坡的静、动力响应分析，构建并编译了BUST模型的有限差分算法，且通过数值模拟分析验证了该算法的可靠性。首先，推导BUST模型在一般应力空间和主应力空间的有限差分计算格式，给出了边界面、加载面、映射变量、塑性乘子、塑性修正、角点奇异性处理等的具体数学形式；其次，编写BUST模型的C++程序，并在FLAC3D软件平台开展一系列数值计算，比较BUST模型与双剪统一弹塑性本构模型结果差异性，预测软岩三轴剪切应力–应变关系，模拟黄土–泥岩边坡坡体内部加速度响应。结果表明所构建的双剪统一边界面塑性本构模型有限差分算法计算结果可靠，可用于分析边坡或滑坡的静、动力响应。

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	康孝森1
	廖红建2
	黄强兵1
	王作辰1
	马宗源3

关键词 ：边坡工程, 统一强度理论, 边界面塑性, 本构模型, FLAC3D, 数值模拟

Abstract：The twin shear unified bounding surface plasticity model(BUST model) can capture the plastic strain accumulation of geomaterials in small deviatoric stress state，which can?t be well predicted by classical twin shear unified elastoplastic constitutive model(UST model). To apply the BUST model in analyzing static and dynamic response of slopes or landslides，its finite difference format is formulated and compiled，and its reliability is further analyzed using numerical simulation. Firstly，the finite difference format of the BUST model is formulated both in general stress space and principal stress space. Specifically，the mathematical form of bounding surface，loading surface，mapping rule variable，plastic multiplier，plastic correction，and corner singularity treatment are derived. Secondly，the finite difference format of BUST model is compiled using C++ language，and its dynamic link library file is generated. Finally，a list of numerical simulation is conducted using FLAC3D software including a unit test for comparing BUST model and UST model，a triaxial compression test for predicting the stress-strain relationship of soft rock，a loess-mudstone slope simulation for predicting acceleration response. The results indicate that the finite difference method of the BUST model is reliable，and it can be applied in analyzing static and dynamic response of slopes or landslides.

Key words： slope engineering unified strength theory bounding surface plasticity constitutive model FLAC3D numerical simulation

引用本文:

康孝森1，廖红建2，黄强兵1，王作辰1，马宗源3. 双剪统一边界面塑性本构模型的有限差分算法及其数值验证[J]. 岩石力学与工程学报, 2023, 42(1): 65-75.
KANG Xiaosen1，LIAO Hongjian2，HUANG Qiangbing1，WANG Zuochen1，MA Zongyuan3. Finite difference method of a twin shear unified bounding surface plasticity model and its numerical validation. , 2023, 42(1): 65-75.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2022.0124 或 https://rockmech.whrsm.ac.cn/CN/Y2023/V42/I1/65

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