Shear stress distribution and characteristics of deformation for shear band-elastic body system at pre-peak and post-peak

Abstract

The distributed shear stress and the displacement across shear band, the evolution of plastic zones, and the load-carrying capacity of rock specimen were investigated in plane strain direct shear test according to Fast Lagrangian Analysis of Continua (FLAC). And then the shear displacement distribution in normal direction of system composed of localized shear band and elastic rock was analyzed based on gradient-dependent plasticity. The adopted failure criterion was a composite of Mohr-Coulomb criterion, that is, the relation between tension cut-off and post-peak constitutive of rock was linear strain-softening. Numerical results show that shear stress field approximately undergoes three different stages. At first, shear stress is only concentrated in the middle of top and base of specimen. Next, shear stress in the middle of specimen tends to increase, owing to superposition of shear stresses. Interestingly, two peaks of shear stress appear far from the loading ends of specimen, and the peaks approach with the increase in timestep until elements at the center of specimen yield. Finally, relatively lower shear stress level is reached in large part of specimen except in the regions near the two ends. As flow stress decreases, the analytical shear displacement distribution in shear band based on gradient-dependent plasticity becomes steep; outside the band, it is linear and its slope tends to decrease. These theoretical results qualitatively agree with that of the present numerical predicted results. Main advantage of the analytical solution over the numerical results according to FLAC is that it is continuous, smooth and non-linear (except at elastic stage).

Keywords

shear stress / shear displacement / plane strain / strain softening / gradient-dependent plasticity / shear band-elastic body system

References

[1] YinYou-quan, ZhangHong. The softening behaviour of fault zone medium and an instability model of earthquakes[J]. Acta Seismological Sinica, 1984, 6(2): 135-145(in Chinese)

[2] ZhangMeng-tao. The instability theory and numerical simulation of rock burst[J]. Chin J Rock Mech Engrg, 1987, 6(3): 197-204(in Chinese)

[3] PanYi-shan, ZhangMeng-tao, LiGuo-zheng. The study of chamber rockburst by the CUSP model of catastrophe theory[J]. Appl Math Mech (English Edition), 1994, 15(10): 943-951

[4] PanYue, LiuYing, GuShan-fa. Fold catastrophe model of mining fault rockburst[J]. Chin J Rock Mech Engrg, 2001, 20(1): 43-48(In Chinese)

[5] VardoulakisI, PapanastasiouP. Bifurcation analysis of deep boreholes: I. Surface Instabilities [J]. Int J Num Anal Methods Geomech, 1988, 12: 379-399

[6] XieHe-ping, PariseauW G. Fractal character and mechanism of rock bursts[J]. Chin J Rock Mech Engrg, 1993, 12(1): 28-37(in Chinese)

[7] FengTao, PanChang-liang. Lamination spallation bucking model for formation mechanism of rock burst [J]. Chin J Nonferrous Met, 2000, 10(2): 287-290(in Chinese)

[8] WangGui-yao, SunZong-qi, QingDu-gan. Fracture mechanics analysis of rock burst mechanism and prediction[J]. Chin J Nonferrous Met, 1999, 9(4): 841-845(in Chinese)

[9] TangLi-zhong, PanChang-liang, WangWengxing. Surplus energy index for analyzing rock burst proneness[J]. J Cent South Univ Technol (Natural Science), 2002, 33(2): 129-132(in Chinese)

[10] YinGuang-zhi, ZhangDong-ming, DaiGao-fei, et al.. Damage model of rock and the damage energy index of rockburst[J]. J Chongqing Univ, 2002, 25(9): 75-79(in Chinese)

[11] JiHong-guang, WangJin-an, CaiMei-feng. Relativity and unity physical and geometrical characteristics of rockbursting events[J]. J Chin Coal Soc, 2002, 28(1): 31-36(in Chinese)

[12] XuLin-sheng, WangLan-sheng, LiYong-lin. Study on mechanism and judgment of rockbursts[J]. Rock Soil Mech, 2002, 23(3): 300-303(in Chinese)

[13] TangLi-zhong, PanChang-liang, XieXue-bin, et al.. Analysis and prediction of rock burst dangerous areas in Dongguashan Copper Mine under deep well ming[J]. J Cent South Univ Technol (Natural Science), 2002, 33(4): 335-338(in Chinese)

[14] QiQing-xin, ShiYuan-wei, LiuTian-quan. Mechanism of instability caused by viscous sliding in rock burst[J]. J China Coal Soc, 1997, 22(2): 144-148(in Chinese)

[15] XuZe-min, WuPei-guan, WangSu-da, et al.. Analysis of energy released in process of rock burst[J]. J Natural Disasters, 2003, 12(3): 104-110(in Chinese)

[16] PanChang-liang, ZhuFang-cai, CaoPing, et al.. Characteristics of acoustic emission of bursting-induced rocks under unaxial compression[J]. J Cent South Univ Technol(Natural Science), 2001, 32(4): 336-338(in Chinese)

[17] CaiMei-feng, LaiXing-ping. Study and application of monitoring for subsiding area in a composite hars rock roadway[J]. Chin J Rock Mech Engrg, 2003, 22(3): 391-394(In Chinese)

[18] PanLi-you, JiangYu-jing, LiXing-wei, et al.. Dilation theory of rock burst[J]. Chin J Rock Mech Engrg, 2002, 22(Supple): 2301-2303(In Chinese)

[19] WuAi-xiang, SunYe-zhi, GourS, et al.. Characteristics of rockburst and its mining technology in mines[J]. J Cent South Univ Technol(English Edition), 2002, 9(4): 255-259

[20] CaiMei-feng, WangJin-an, WangShuang-hong. Prediction of rock burst with deep mining excavation in Linglong Gold Mine[J]. J Univ Sci Technol Beijing, 2001, 8(4): 241-243

[21] LiuJian-Xin, TangChun-an, ZhuWan-cheng, et al.. Rock-coal model for studying the rockburst[J]. Chin J Geotech Engrg, 2004, 26(2): 276-280(In Chinese)

[22] WangXue-bin, HaiLong, HuangMei. Quantitative calculation of dissipated energy of fault rock burst based on gradient-dependent plasticity [J]. J Univ Sci Technol Beijing, 2004, 11(3): 197-201

[23] WangXue-bin, PanYi-shan, MaJin. Analysis of strain (or the ratio of strain) in the shear band and a criterion on instability based on the energy criterion [J]. Chin J Engrg Mech, 2003, 20(2): 111-115 in Chinese)

[24] WangXue-bin, YangXiao-bin, PanYi-shan. Dynamic analysis of fault rockburst based on gradient-dependent plasticity and energy criterion[J]. J Univ Sci Technol Beijing, 2004, 11(1): 5-9

[25] WangXue-bin. Analysis of progressive failure of pillar and instability criterion based on gradient-dependent plasticity[J]. J Cent South Univ Technol (English Edition), 2004, 11(4): 445-450

[26] WangXue-bin, PanYi-shan, MaJin. Theoretical analysis of stability and unstable sliding of the system composed of shear band and elastic rock[J]. Chin J Geotech Engrg, 2002, 24(3): 360-363(in Chinese)

[27] WangXue-bin, PanYi-shan, HaiLong. Instability criterion of fault rock burst based on gradient-dependent plasticity [J]. Chin J Rock Mech Engrg, 2004, 23(4): 588-591(in Chinese)

[28] WangXue-bin, HuangMei, ZhaoYang-feng, et al.. Analysis on relation between snap-back of specimen and snap-back of system composed of direct shear testing machine and specimen[J]. Chin J Rock Mech Engrg, 2004, 23(3): 379-382(in Chinese)

[29] WangXue-bin, DaiShu-hong, HaiLong, et al.. Analysis of localized shear deformation of ductile metal based on gradient-dependent plasticity[J]. J Nonferrous Met Soc China, 2003, 13(6): 1348-1353

[30] WangXue-bin, YangMei, YuHai-jun, et al.. Localized shear deformation during shear band propagation in Titanium considering interactions among microstructures[J]. J Nonferrous Met Soc China, 2004, 14(2): 335-339

[31] WangXue-bin, PanYi-shan, ShengQian, et al.. Simulation of triaxial compression and localization of deformation[J]. Rock Soil Mech, 2001, 22(3): 323-326(in Chinese)

[32] WangXue-bin, PanYi-shan, ShengQian, et al.. Numerical simulation of development of dynamic strain localization and size effect[J]. Chin J Comput Mech., 2002, 19(4): 500-503(in Chinese)

[33] WangXue-bin, PanYi-shan, DingXiu-li, et al.. Simulation of multiple shear bands in strain softening rock in plane strain[J]. Rock Soil Mech, 2002, 23(6): 717-720(in Chinese)

[34] WangXue-bin, PanYi-shan, ShengQian, et al.. Numerical simulation of localized deformation field for rock in plane strain state[J]. Chin J Rock Mech Engrg, 2003, 22(4): 521-524(in Chinese)