基于Mogi-Coulomb准则的弹塑性损伤本构模型及其数值实现
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摘要
Mogi-Coulomb准则能够较好的描述真三轴条件下岩石的破坏强度特征,基于Mogi-Coulomb准则,同时考虑岩石材料的塑性及损伤共同作用,建立了岩石弹塑性损伤本构模型,并基于塑性增量理论,构建了模型的本构关系,实现了模型在FLAC~(3D)软件中的二次开发.对比分析不同岩性试样在真三轴压缩路径下室内试验与数值计算结果.结果表明:本文模型计算结果与试验结果吻合度较高,误差较小,对大理岩、红砂岩和水泥砂浆3种试样极限八面体剪应力和应力极限点ε_1的最大计算误差仅为1.60%和3.56%,验证了模型的合理性和优越性.与Mohr-Coulomb模型相比,本文模型能更准确的描述岩石材料在真三轴应力状态下的破坏条件及变形特征,更适合深部三维应力状态下地下工程分析.
Due to the Mogi-Coulomb criterion can well describe the failure strength characteristics of rock under true triaxial condition, an elastoplastic damage constitutive model for rock material was established based on Mogi-Coulomb criterion. The elastic damage and plastic flow of rock were both examined in the new constitutive model. Based on the plastic increment theory, the constitutive relation of the model was established, and the constitutive model was implemented in FLAC~(3 D). In order to verify the validity and superiority of the model, comparisons between laboratory test results and numerical results of different lithologic specimens under true triaxial compression path were conducted. The results show that the FLAC~(3 D) numerical simulation results with self-defined constitutive model accord with the test results, the maximum calculation errors of ultimate octahedral shear stress and ε_1 at the critical point for three different lithologic specimens were 1.60% and 3.56% respectively. Compared with Mohr-Coulomb model, the self-defined model can more accurately describe the failure conditions and deformation characteristics of rock materials under true triaxial stress state, which is more suitable for computing analysis of underground engineering.
Due to the Mogi-Coulomb criterion can well describe the failure strength characteristics of rock under true triaxial condition, an elastoplastic damage constitutive model for rock material was established based on Mogi-Coulomb criterion. The elastic damage and plastic flow of rock were both examined in the new constitutive model. Based on the plastic increment theory, the constitutive relation of the model was established, and the constitutive model was implemented in FLAC~(3 D). In order to verify the validity and superiority of the model, comparisons between laboratory test results and numerical results of different lithologic specimens under true triaxial compression path were conducted. The results show that the FLAC~(3 D) numerical simulation results with self-defined constitutive model accord with the test results, the maximum calculation errors of ultimate octahedral shear stress and ε_1 at the critical point for three different lithologic specimens were 1.60% and 3.56% respectively. Compared with Mohr-Coulomb model, the self-defined model can more accurately describe the failure conditions and deformation characteristics of rock materials under true triaxial stress state, which is more suitable for computing analysis of underground engineering.
引文
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[22] 杨永杰,王德超,郭明福,等.基于三轴压缩声发射试验的岩石损伤特征研究[J].岩石力学与工程学报,2014,33(1):98-104.YANG Yongjie,WANG Dechao,GUO Mingfu,et al.Study of rock damage characteristics based on acoustic emission tests under triaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(1):98-104.
[23] 段力群,董璐,马林建,等.泡沫混凝土单轴压缩下声发射特征试验研究[J].中国矿业大学学报,2018,47(4):742-747.DUAN Liqun,DONG Lu,MA Linjian,et al.Experimental study of acoustic emission characteristics of foamed concrete under uniaxial compression[J].Journal of China University of Mining & Technology,2018,47(4):742-747.
[24] FENG X T,ZHANG X W,KONG R,et al.A novel Mogi type true triaxial testing apparatus and its use to obtain complete stress-strain curves of hard rocks[J].Rock Mechanics and Rock Engineering,2016,49(5):1649-1662.
[2] 孟庆彬,韩立军,乔卫国,等.应变软化与扩容特性极弱胶结围岩弹塑性分析[J].中国矿业大学学报,2018,47(4):760-767.MENG Qingbin,HAN Lijun,QIAO Weiguo,et al.Elastic-plastic analysis of the very weakly cemented surrounding rock considering characteristics of strain softening and expansion[J].Journal of China University of Mining & Technology,2018,47(4):760-767.
[3] 贾善坡,陈卫忠,杨建平,等.基于修正Mohr-Coulomb准则的弹塑性本构模型及其数值实施[J].岩土力学,2010,31(7):2051-2058.JIA Shanpo,CHEN Weizhong,YANG Jianping,et al.An elastoplastic constitutive model based on modified Mohr-Coulomb criterion and its numerical implementation[J].Rock and Soil Mechanics,2010,31(7):2051-2058.
[4] 朱合华,黄伯麒,张琦,等.基于广义Hoek-Brown准则的弹塑性本构模型及其数值实现[J].工程力学,2016,33(2):41-49.ZHU Hehua,HUANG Boqi,ZHANG Qi,et al.Elastoplastic rock constitutive model based on generalized hoek-brown strength criterion and its numerical implementation[J].Engineering Mechanics,2016,33(2):41-49.
[5] 张慧梅,彭川,杨更社,等.考虑冻融效应的岩石损伤统计强度准则研究[J].中国矿业大学学报,2017,46(5):1066-1072.ZHANG Huimei,PENG Chuan,YANG Gengshe,et al.Study of damage statistical strength criterion of rock considering the effect of freezing and thawing[J].Journal of China University of Mining & Technology,2017,46(5):1066-1072.
[6] MOGI,KIYOO.Fracture and flow of rocks under high triaxial compression[J].Journal of Geophysical Research,1971,76(5):1255-1269.
[7] HAIMSON B,CHANG C D.A new true triaxial cell for testing mechanical properties of rock,and its use to determine rock strength and deformability of Westerly granite[J].International Journal of Rock Mechanics and Mining Sciences,2000,37:285-296.
[8] CHANG C D,HAIMSON B.True triaxial strength and deformability of the German Continental Deep Drilling Program(KTB)deep hole amphibolite[J].Journal of Geophysical Research,2000,105(B8):18999-19013.
[9] EWY R T.Wellbore-stability predictions by use of a modified Lade criterion[J].SPE Drilling and Completion,1999,14(2):85-91.
[10] ZHANG L Y.A generalized three-dimensional Hoek-Brown strength criterion[J].Rock Mechanics and Rock Engineering,2008,41(6):893-915.
[11] ALAJMI A M,ZIMMERMAN R W.Relation between the Mogi and the Coulomb failure criteria[J].International Journal of Rock Mechanics and Mining Sciences,2005,42(3):431-439.
[12] CHANG C D,HAIMSON B.A failure criterion for rocks based on true triaxial testing[J].Rock Mechanics and Rock Engineering,2012,45(6):1007-1010.
[13] 张黎明,王在泉,石磊.硬质岩石卸荷破坏特性试验研究[J].岩石力学与工程学报,2011,30(10):2012-2018.ZHANG Liming,WANG Zaiquan,SHI Lei.Experimental study of hard rock failure characteristic under unloading condition[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(10):2012-2018.
[14] 李地元,谢涛,李夕兵,等.Mogi-Coulomb强度准则应用于岩石三轴卸荷破坏试验的研究[J].科技导报,2015,33(19):84-90.LI Diyuan,XIE Tao,LI Xibing,et al.On the Mogi-Coulomb strength criterion as applied to rock triaxial unloading test[J].Science and Technology Review,2015,33(19):84-90.
[15] BENZ T,SCHWAB R.A quantitative comparison of six rock failure criteria[J].International Journal of Rock Mechanics and Mining Sciences,2008,45(7):1176-1186.
[16] SALARI M R,SAEB S,WILLAM K J,et al.A coupled elastoplastic damage model for geomaterials[J].Computer Methods in Applied Mechanics and Engineering,2004,193:2625-2643.
[17] 王军祥.岩石弹塑性损伤MHC耦合模型及数值算法研究[D].大连:大连海事大学,2014:125-127.WANG Junxiang.Study on elastoplastic damage and MHC coupling model of rock and numerical algorithm[D].Dalian:Dalian Maritime University,2014:125-127.
[18] ZHU Q Z,SHAO J F,MAINGUY M.A micromechanics-based elastoplastic damage model for granular materials at low confining pressure[J].International Journal of Plasticity,2010,26(4):586-602.
[19] 袁小平,刘红岩,王志乔.基于Drucker-Prager准则的岩石弹塑性损伤本构模型研究[J].岩土力学,2012,33(4):1103-1108.YUAN Xiaoping,LIU Hongyan,WANG Zhiqiao.Study of elastoplastic damage constitutive model of rocks based on Drucker-Prager criterion[J].Rock and Soil Mechanics,2012,33(4):1103-1108.
[20] 张治亮,徐卫亚,王伟,等.韧性岩石常规三轴压缩试验及变形与损伤演化规律研究[J].岩石力学与工程学报,2011,30(增2):3857-3862.ZHANG Zhiliang,XU Weiya,WANG Wei,et al.Investigation on conventional triaxial compression tests of ductile rock and law of deformation and damage evolution[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(Sup 2):3857-3862.
[21] 蒋邦友.深部复合地层隧道TBM岩爆孕育及控制机理研究[D].徐州:中国矿业大学,2017:34-50.JIANG Bangyou.Evolution and control mechanism of rockburst induced by TBM excavation in deep mixed ground tunnel[D].Xuzhou:China University of Mining and Technology,2017:34-50.
[22] 杨永杰,王德超,郭明福,等.基于三轴压缩声发射试验的岩石损伤特征研究[J].岩石力学与工程学报,2014,33(1):98-104.YANG Yongjie,WANG Dechao,GUO Mingfu,et al.Study of rock damage characteristics based on acoustic emission tests under triaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(1):98-104.
[23] 段力群,董璐,马林建,等.泡沫混凝土单轴压缩下声发射特征试验研究[J].中国矿业大学学报,2018,47(4):742-747.DUAN Liqun,DONG Lu,MA Linjian,et al.Experimental study of acoustic emission characteristics of foamed concrete under uniaxial compression[J].Journal of China University of Mining & Technology,2018,47(4):742-747.
[24] FENG X T,ZHANG X W,KONG R,et al.A novel Mogi type true triaxial testing apparatus and its use to obtain complete stress-strain curves of hard rocks[J].Rock Mechanics and Rock Engineering,2016,49(5):1649-1662.
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