基于虚单元法的非连续变形分析方法新格式

doi:10.13722/j.cnki.jrme.2021.0813

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摘要以块体顶点位移为自由度的非连续变形分析(DDA)方法可有效克服DDA原自由度的局限性，但使用多边形有限元形函数构造的格式计算效率明显不足。针对此问题，建立基于虚单元法(VEM)的DDA新格式，使用VEM表达单个块体的位移，同时保留DDA对于块体接触的分析处理。从块体独立位移空间上双线性格式的计算出发，数学推导给出新格式中块体各项势能的矩阵表达，然后基于最小势能原理建立块体系统平衡方程，最后利用滑动模型明确弹性应变能和惯性力势能计算中的稳定项近似乘子取值。采用3个算例考察新格式的有效性和计算效率，结果表明：新格式可以有效克制块体大转动模拟的体积虚假膨胀，保障接触计算精度，且计算效率明显优于已有的块体顶点位移型DDA格式。

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	江巍1
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	徐建城1
	王乐华1
	刘立鹏2
	郑宏3

关键词 ：数值分析, 非连续变形分析(DDA), 自由度, 虚单元法(VEM), 体积膨胀, 计算效率

Abstract：Vertex displacement-based discontinuous deformation analysis(DDA) was recently proposed to avoid the demerits caused by the original degree of freedom in DDA，but the current formulations developed by using the shape functions in polygonal finite element method have an unacceptable computational efficiency. To remedy this issue，a new formulation of DDA，utilizing VEM to define an individual displacement space and to calculate the potential energy for a block，and adopting original DDA to detect and analyze the contacts between blocks，is developed. The matrix expression for the block potential energy is mathematically deduced，and then the global equilibrium equations of the block system are derived based on the principle of minimum potential energy. A sliding block model is employed to determine the values of the multipliers in the approximations of the elastic deformation energy and the inertial force energy. The validity and computational efficiency of the new formulation are testified by three examples. Results show that the new formulation is capable to restrain the false volume expansion when simulating large rotation and to ensure the precision of the contact analysis. Most of all，the new formulation has a higher computational efficiency than the existing formulations of vertex displacement-based DDA.

Key words： numerical analysis discontinuous deformation analysis(DDA) degree of freedom virtual element method(VEM) volume expansion computational efficiency

引用本文:

江巍1，2，徐建城1，王乐华1，刘立鹏2，郑宏3. 基于虚单元法的非连续变形分析方法新格式[J]. 岩石力学与工程学报, 2022, 41(1): 106-119.
JIANG Wei1，2，XU Jiancheng1，WANG Lehua1，LIU Lipeng2，ZHENG Hong3. A novel formulation of discontinuous deformation analysis enlightened by virtual element method. , 2022, 41(1): 106-119.

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http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2021.0813 或 http://rockmech.whrsm.ac.cn/CN/Y2022/V41/I1/106

[28]	AHMAD B，ALSAEDI A，BREZZI F，et al. Equivalent projectors for virtual element methods[J]. Computers and Mathematics with Applications，2013，66：376-391.
[13]	JIANG W，ZHENG H. An efficient remedy for the false volume expansion of DDA when simulating large rotation[J]. Computers and Geotechnics，2015，70：18-23.
[3]	FU X D，SHENG Q，ZHANG Y H，et al. Computation of the safety factor for slope stability using discontinuous deformation analysis and the vector sum method[J]. Computers and Geotechnics，2017，92：68-76.
[4]	邬爱清，丁秀丽，李会中，等. 非连续变形分析方法模拟千将坪滑坡启动与滑坡全过程[J]. 岩石力学与工程学报，2006，25(7)：1 297-1 303.(WU Aiqing，DING Xiuli，LI Huizhong，et al. Numerical simulation of startup and whole failure process of Qianjiangping landslide using discontinuous deformation analysis method[J]. Chinese Journal of Rock Mechanics and Engineering，2006，25(7)：1 297-1 303. (in Chinese))
[6]	焦玉勇，张秀丽，刘泉声，等. 用非连续变形分析方法模拟岩石裂纹扩展[J]. 岩石力学与工程学报，2007，26(4)：682-691.(JIAO Yuyong，ZHANG Xiuli，LIU Quansheng，et al. Simulation of rock crack propagation using discontinuous deformation analysis method[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(4)：682-691.(in Chinese))
[9]	KE T C. The issue of rigid body rotation in DDA[C]// the First International Forum on Discontinuous Deformation Analysis(DDA) and Simulation of Discontinuous Media. Berkeley：TSI Press，1996：318-326.
[11]	高亚楠，高峰，YEUNG M R. 基于有限变形理论的非连续变形分析方法改进[J]. 岩石力学与工程学报，2011，30(11)：2 360-2 365. (GAO Yanan，GAO Feng，YEUNG M R. Modification of discontinuous deformation analysis method based on finite deformation theory[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(11)：2 360-2 365.(in Chinese))
[14]	WU J H，OHNISHI Y，NISHIYAMA S. A development of the discontinuous deformation analysis for rock fall analysis[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2005，29(10)：971-988.
[16]	CHENG Y M，ZHANG Y H. Rigid body rotation and block internal discretization in DDA analysis[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2000，24(6)：567-578.
[19]	JIANG W，WANG Y H，SUN G H，et al. Discontinuous deformation analysis based on Wachspress interpolation function for detailed stress distribution[J]. Mathematical Problems in Engineering，2018，4079035：1-18.
[21]	TALISCHI C，PAULINO G H. Addressing integration error for polygonal finite elements through polynomial projections：A patch test connection[J]. Mathematical Models and Methods in Applied Sciences，2014，24(8)：1 701-1 727.
[23]	GAIN A L，TALISCHI C，PAULINO G H. On the virtual element method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes[J]. Computer Methods in Applied Mechanics and Engineering，2014，282：132-160.
[1]	SHI G H. Discontinuous deformation analysis-a new numerical model for the statics and dynamics of block systems[Ph. D. Thesis][D]. Berkeley：Department of Civil Engineering，University of California，Berkeley，1988.
[29]	ANDERSON O，NILSEN H M，RAYNAUD X. Virtual element method for geomechanical simulations of reservoir models[J]. Computers and Geosciences，2017，1：1-17.
[7]	CHEN G Q，HE M C，FAN F S. Rock burst analysis using DDA numerical simulation[J]. International Journal of Geomechanics，2018，18(3)：04018001.
[17]	FAN H，ZHENG H，ZHAO J D. Discontinuous deformation analysis based on strain-rotation decomposition[J]. International Journal of Rock Mechanics and Mining Sciences，2017，92(2)：19-29.
[24]	WRIGGERS P，REDDY B D，RUST W，et al. Efficient virtual element formulations for compressible and incompressible finite deformations[J]. Computational Mechanics，2017，60：253-268.
[26]	林珊，郭昱葵，孙冠华，等. 边坡稳定性分析的虚单元强度折减法[J]. 岩石力学与工程学报，2019，38(增2)：3 429-3 438.(LIN Shan，GUO Yukui，SUN Guanhua，et al. Slope stability analysis using the virtual element method and shear strength reduction technique[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(Supp.2)：3 429-3 438.(in Chinese))
[27]	卢波，邬爱清，徐栋栋，等. 基于混合高阶非连续变形分析的刚性伺服数值试验方法[J]. 岩石力学与工程学报，2020，39(8)：1 572-1 581.(LU Bo，WU Aiqing，XU Dongdong，et al. Stiff servo- controlled numerical test method based on mixed higher order discontinuous deformation analysis[J]. Chinese Journal of Rock Mechanics and Engineering，2020，39(8)：1 572-1 581.(in Chinese))
[31]	CIHAN M， HUDOBIVNIK B，ALDAKHEEL F，et al. Virtual element formulation for finite strain elastodynamics[J]. Computer Modeling in Engineering and Sciences，2021，http：//dx.doi.org/10.32604/cmes. 2021.016851
[33]	廖秋林，李晓，李守定，等. 三峡库区千将坪滑坡的发生、地质地貌特征、成因及滑坡判据研究[J]. 岩石力学与工程学报，2005，24(17)：3 146-3 153.(LIAO Qiulin，LI Xiao，LI Shouding，et al. Occurrence，geology and geomorphy characteristics and origin of Qianjiangping landslide in Three Gorges reservoir area and study on ancient landslide criterion[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(17)：3 146-3 153.(in Chinese))
[2]	刘泉声，蒋亚龙，何军. 非连续变形分析的精度改进方法及研究趋势[J]. 岩土力学，2017，38(6)：1 746-1 761.(LIU Quansheng，JIANG Yalong，HE Jun. Precision improvement methods and research trends of discontinuous deformation analysis[J]. Rock and Soil Mechanics，2017，38(6)：1 746-1 761.(in Chinese))
[5]	FENG X X，JIANG Q H，ZHANG H C，et al. Study on the dynamic response of dip bedded rock slope using discontinuous deformation analysis(DDA) and shaking table tests[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2020，45(3)：411-427.
[15]	MACLAUGHLIN M M，SITAR N. Rigid body rotations in DDA[C]// The First International Forum on Discontinuous Deformation Analysis (DDA) and Simulation of Discontinuous Media. Berkeley：TSI Press，1996：620-635.
[25]	BREZZI F，MARINI L D. Virtual element methods for plate bending problems[J]. Computer Methods in Applied Mechanics and Engineering，2013，253：455-462.
[8]	中国岩石力学与工程学会. 2016～2017岩石力学与岩石工程学科发展报告[R]. 北京：中国科学技术出版社，2018.(Chinese Society for Rock Mechanics and Engineering. Report on advances in rock mechanics and engineering 2016‐2017[R]. Beijing：China Science and Technology Press，2018.(in Chinese))
[12]	WU J H. The elastic distortion problem with large rotation in discontinuous deformation analysis[J]. Computers and Geotechnics，2015，69：352-364.
[22]	DA VEIGA L B，BREZZI F，MARINI L D，et al. The hitchhiker′s guide to the virtual element method[J]. Mathematical Models and Methods in Applied Sciences，2014，24(8)：1 541-1 573.
[32]	左建平，孙运江，文金浩，等. 岩层移动理论与力学模型及其展望[J]. 煤炭科学技术，2018，46(1)：1-11.(ZUO Jianping，SUN Yunjiang，WEN Jinhao，et al. Theoretical and mechanical models of rock strata movement and their prospects[J]. Coal Science and Technology，2018，46(1)：1-11.(in Chinese))
[10]	KOO C Y，CHERN J C. Modification of the DDA method for rigid block problems[J]. International Journal of Rock Mechanics and Mining Sciences，1998，35(6)：683-693.
[18]	巩师林，凌道盛，胡成宝，等. 非连续变形分析中块体大转动问题研究[J]. 岩土力学，2020，41(11)：3 810-3 822.(GONG Shilin，LING Daosheng，HU Chengbao，et al. Study on large rotation problem of a block in discontinuous deformation analysis[J]. Rock and Soil Mechanics，2020，41(11)：3 810-3 822.(in Chinese))
[20]	JIANG W，XU J J，ZHENG H，et al. Novel displacement function for discontinuous deformation analysis based on mean value coordinates[J]. International Journal for Numerical Methods in Engineering，2020，121：4 768-4 792.
[30]	DOOLIN D M，SITAR N. Displacement accuracy of discontinuous deformation analysis method applied to sliding block[J]. Journal of Engineering Mechanics，2002，128(11)：1 158-1 168.