准静态应变率下的煤岩非线性力学特性
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摘要
为研究开挖扰动下煤岩的非线性力学特征,利用MTS815伺服刚性试验机对芙蓉白皎煤矿煤岩进行10~(-5)～10~(-2)s~(-1)准静态应变率下的单轴压缩试验,分析准静态应变率下煤岩的应力-应变曲线、抗压强度、弹性模量、泊松比等力学特性的变化规律,基于煤岩显著的非线性力学特征,修正并验证黏弹性损伤本构模型的合理性。研究表明:①煤岩单轴压缩荷载作用下具有明显的压密、线弹性、塑性屈服、峰后破坏4个阶段;煤岩力学特性应变率相关性突出,随着应变率的增加,压密阶段缩短,线弹性阶段增长,屈服阶段应力强化特征及峰后破坏阶段应力软化特征趋于明显;②由于原生裂隙的闭合和扩展,煤岩受载作用下,各阶段均呈现显著的非线性力学特征,随着应变率的增加,压密阶段和线弹性阶段表现出的明显非线性特征呈减弱趋势;③准静态应变率10~(-5)～10~(-2)s~(-1)范围内,抗压强度随应变率增加由8. 83 MPa增加至12. 57 MPa,增长率42. 35%;弹性模量随应变率增加总体呈现先增加后减小的变化趋势,在10~(-5)～10~(-4)s~(-1)应变率区间,弹性模量由1 644 MPa增加至1 825 MPa,随后在10~(-4)～10~(-2)s~(-1)应变率区间内减小,变化趋势发生明显转折;泊松比在准静态应变率下随应变率增加而呈现逐渐减小的变化趋势,从1. 53下降到0. 71,减小53. 59%;整个准静态应变率范畴下,煤岩的力学特征参数(抗压强度、弹性模量、泊松比)均表现出显著的非线性变化趋势,均在临界应变率10~(-3)s~(-1)附近发生转折。④利用一个损伤体和一个Maxwell模型并联方式,综合考虑准静态应变率下煤岩的非线性变化特征后,引入材料常数a对胡克定律进行修正,推导得出准静态应变率下煤岩的非线性损伤演化本构方程,并结合煤岩单轴压缩试验对其合理性进行验证。
In order to study the nonlinear mechanical characteristics of coal rock under excavation disturbance,the uniaxial compression test of quasi-static strain rate of 10~(-5)-10~(-2)s~(-1) was carried out by MTS815 servo rigidity testing machine on the coal rock of Fu Rong,Bai Jiao Coal Mine,China. The variation of mechanical properties such as stressstrain curve,compressive strength,elastic modulus and Poisson's ratio of coal rock under quasi-static strain rate were analyzed. Based on the significant nonlinear mechanical characteristics of coal rock,the viscoelastic damage constitutive model was modified and verified. The research shows that ① Under uniaxial compression loading,the coal rock has four stages,such as compaction,linear elasticity,plastic yield and post-peak damage. The strain rate correlation of coal rock mechanical properties is outstanding. With the increase of strain rate,the compaction phase is shortened,the linear elastic phase is increased,and the stress strengthening characteristics in the yielding stage and the stress softening characteristics in the post-peak failure stage tend to be obvious. ② Due to the closure and expansion of the primary fissures,each stage of the loading coal rock presents remarkable nonlinear mechanical characteristics. With the increase of strain rate,the obvious nonlinear characteristics of the compaction stage and the linear elastic stage show a weakening trend. ③ In the range of quasi-static strain rate 10~(-5)-10~(-2)s~(-1),the compressive strength increases with the strain rate from 8.83 MPa to 12. 57 MPa,the growth rate is 42. 35%. The modulus of elasticity generally increases first and then decreases with the increase of strain rate. In the range of 10~(-5)-10~(-4)s~(-1) strain rate,the elastic modulus increases from 1 644 MPa to 1 825 MPa,followed by 10-4-10-2 s-1 is reduced within the strain rate interval,and the trend of change is obviously turning. The Poisson's ratio shows a decreasing trend with the increase of strain rate under the quasi-static strain rate,which decreases from 1.53 to 0.71,and decreases value by 53.59%. The mechanical characteristics parameters(compressive strength,elastic modulus,Poisson's ratio) of coal rock under the whole quasistatic strain rate category all shows significant nonlinear changes,and all of them turn around the critical strain rate of 10~(-3)s~(-1). ④ Using a damage body and a Maxwell model in parallel,considering the nonlinear variation characteristics of coal rock under quasi-static strain rate,the material constantais used to modify the Hooke's law,and the constitutive equation of nonlinear damage evolution of coal rock under quasi-static strain rate is derived. The constitutive equation' rationality is verified with the combination of the uniaxial compression test of coal rock.
In order to study the nonlinear mechanical characteristics of coal rock under excavation disturbance,the uniaxial compression test of quasi-static strain rate of 10~(-5)-10~(-2)s~(-1) was carried out by MTS815 servo rigidity testing machine on the coal rock of Fu Rong,Bai Jiao Coal Mine,China. The variation of mechanical properties such as stressstrain curve,compressive strength,elastic modulus and Poisson's ratio of coal rock under quasi-static strain rate were analyzed. Based on the significant nonlinear mechanical characteristics of coal rock,the viscoelastic damage constitutive model was modified and verified. The research shows that ① Under uniaxial compression loading,the coal rock has four stages,such as compaction,linear elasticity,plastic yield and post-peak damage. The strain rate correlation of coal rock mechanical properties is outstanding. With the increase of strain rate,the compaction phase is shortened,the linear elastic phase is increased,and the stress strengthening characteristics in the yielding stage and the stress softening characteristics in the post-peak failure stage tend to be obvious. ② Due to the closure and expansion of the primary fissures,each stage of the loading coal rock presents remarkable nonlinear mechanical characteristics. With the increase of strain rate,the obvious nonlinear characteristics of the compaction stage and the linear elastic stage show a weakening trend. ③ In the range of quasi-static strain rate 10~(-5)-10~(-2)s~(-1),the compressive strength increases with the strain rate from 8.83 MPa to 12. 57 MPa,the growth rate is 42. 35%. The modulus of elasticity generally increases first and then decreases with the increase of strain rate. In the range of 10~(-5)-10~(-4)s~(-1) strain rate,the elastic modulus increases from 1 644 MPa to 1 825 MPa,followed by 10-4-10-2 s-1 is reduced within the strain rate interval,and the trend of change is obviously turning. The Poisson's ratio shows a decreasing trend with the increase of strain rate under the quasi-static strain rate,which decreases from 1.53 to 0.71,and decreases value by 53.59%. The mechanical characteristics parameters(compressive strength,elastic modulus,Poisson's ratio) of coal rock under the whole quasistatic strain rate category all shows significant nonlinear changes,and all of them turn around the critical strain rate of 10~(-3)s~(-1). ④ Using a damage body and a Maxwell model in parallel,considering the nonlinear variation characteristics of coal rock under quasi-static strain rate,the material constantais used to modify the Hooke's law,and the constitutive equation of nonlinear damage evolution of coal rock under quasi-static strain rate is derived. The constitutive equation' rationality is verified with the combination of the uniaxial compression test of coal rock.
引文
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[3]何江.煤矿采动动载对煤岩体的作用及诱冲机理研究[D].徐州:中国矿业大学,2013.HE Jiang.Study on the effect of coal mining dynamic load on coal and rock mass and its mechanism of trapping[D].Xuzhou:China University of Mining and Technology,2013.
[4]李明,茅献彪,曹丽丽,等.高应变率下煤力学特性试验研究[J].采矿与安全工程学报,2015,32(2):317-324.LI Ming,MAO Xianbiao,CAO Lili,et al.Experimental study on mechanical properties of coal under high strain rate[J].Journal of Mining&Safety Engineering,2015,32(2):317-324.
[5]刘晓辉,张茹,刘建锋.不同应变率下煤岩冲击动力试验研究[J].煤炭学报,2012,37(9):1528-1534.LIU Xiaohui,ZHANG Ru,LIU Jianfeng.Experimental study on impact dynamics of coal and rock under different strain rates[J].Journal of China Coal Society,2012,37(9):1528-1534.
[6]江红祥,杜长龙,刘送永.冲击速度对煤岩破碎能量和粒度分布的影响[J].煤炭学报,2013,38(4):604-609.JIANG Hongxiang,DU Changlong,LIU Songyong.Effect of impact velocities on cracking energy and particle distribution of coal and rock[J].Journal of China Coal Society,2013,38(4):604-609.
[7]王登科,刘淑敏,魏建平,等.冲击载荷作用下煤的破坏特性试验研究[J].采矿与安全工程学报,2017,34(3):594-600.WANG Dengke,LIU Shumin,WEI Jianping,et al.Experimental study on failure characteristics of coal under impact loading[J].Journal of Mining and Safety Engineering,2017,34(3):594-600.
[8]解北京,崔永国,王金贵.煤冲击破坏力学特性试验研究[J].煤矿安全,2013,44(11):18-21.XIE Beijing,CUI Yongguo,WANG Jingui.Experimental study on mechanical properties of coal impact failure[J].Coal Mine Safety,2013,44(11):18-21.
[9]李海涛.加载速率效应影响下煤的冲击特性评价方法及应用[D].北京:中国矿业大学(北京),2014.LI Haitao.Evaluation method and application of impact characteristics of coal under the influence of loading rate effect[D].Beijing:China University of Mining and Technology(Beijing),2014.
[10]郝宪杰,袁亮,卢志国,等.考虑煤体非线性弹性力学行为的弹塑性本构模型[J].煤炭学报,2017,42(4):896-901.HAO Xianjie,YUAN Liang,LU Zhiguo,et al.Elastoplastic constitutive model considering nonlinear elastic mechanical behavior of coal[J].Journal of China Coal Society,2017,42(4):896-901.
[11]杨小彬,丁元伟,秦跃平,等.煤岩非线性损伤试验及理论模型[J].辽宁工程技术大学学报(自然科学版),2009,28(6):884-887.YANG Xiaobin,DING Yuanwei,QIN Yueping,et al.Nonlinear damage test and theoretical model of coal and rock[J].Journal of Liaoning Technical University(Natural Science Edition),2009,28(6):884-887.
[12]王超,杨小彬,郭伟旗,等.煤岩单轴加载统计损伤本构模型[J].煤矿安全,2015,46(11):10-13.WANG Chao,YANG Xiaobin,GUO Weiqi,et al.Statistical damage constitutive model for coal and rock uniaxial loading[J].Coal Mine Safety,2015,46(11):10-13.
[13]郭子红,刘新荣,刘保县,等.基于塑性体积应变的岩石损伤变形特性实验研究[J].实验力学,2010,25(3):293-298.GUO Zihong,LIU Xinrong,LIU Baoxian,et al.Experimental study on rock damage and deformation characteristics based on plastic volumetric strain[J].Laboratory Mechanics,2010,25(3):293-298.
[14]潘红宇,董晓刚,张天军,等.单轴压缩下松软煤样破裂损伤演化特性研究[J].西安科技大学学报,2018,38(2):202-209.PAN Hongyu,DONG Xiaogang,ZHANG Tianjun,et al.Study on rupture damage evolution characteristics of soft coal under uniaxial compression[J].Journal of Xi’an University of Science and Technology,2018,38(2):202-209.
[15]杨卫忠,王博.基于细观损伤的岩石受压本构关系模型研究[J].郑州大学学报(工学版),2010,31(6):6-9.YANG Weizhong,WANG Bo.Research on rock compression constitutive relation model based on mesoscopic damage[J].Journal of Zhengzhou University(Engineering Science),2010,31(6):6-9.
[16]蔡灿,伍开松,袁晓红,等.中低应变率下的岩石损伤本构模型研究[J].岩土力学,2015,36(3):795-802.CAI Can,WU Kaisong,YUAN Xiaohong,et al.Study on constitutive model of rock damage under medium and low strain rate[J].Rock and Soil Mechanics,2015,36(3):795-802.
[17]单仁亮,程瑞强,高文蛟.云驾岭煤矿无烟煤的动态本构模型研究[J].岩石力学与工程学报,2006,25(11):2258-2263.SHAN Renliang,CHENG Ruiqiang,GAO Wenjiao.Dynamic constitutive model of anthracite in Yunjialing Coal Mine[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(11):2258-2263.
[18]郭德勇,吕鹏飞,赵杰超,等.煤岩冲击变形破坏特性及其本构模型[J].煤炭学报,2018,43(8):2233-2242.GUO Deyong,LüPengfei,ZHAO Jiechao,et al.Impact deformation and constitutive model of coal rock[J].Journal of China Coal Society,2018,43(8):2233-2242.
[19]李会云.考虑高围压和高应变率的岩石类材料弹塑性损伤本构模型[D].天津:天津大学,2017.LI Huiyun.Elastoplastic damage constitutive model for rock materials considering high confining pressure and high strain rate[D].Tianjin:Tianjin University,2017.
[20]胡时胜,王道荣.冲击载荷下混凝土材料的动态本构关系[J].爆炸与冲击,2002,22(3):242-246.HU Shisheng,WANG Daorong.Dynamic constitutive relations of concrete materials under impact loading[J].Explosion and Shock Waves,2002,22(3):242-246.
[21]付玉凯,解北京,王启飞.煤的动态力学本构模型[J].煤炭学报,2013,38(10):1769-1774.FU Yukai,XIE Beijing,WANG Qifei.Dynamic mechanical constitutive model of coal[J].Journal of China Coal Society,2013,38(10):1769-1774.
[22]李晓锋,李海波,刘凯,等.冲击荷载作用下岩石动态力学特性及破裂特征研究[J].岩石力学与工程学报,2017,36(10):2393-2405.LI Xiaofeng,LI Haibo,LIU Kai,et al.Dynamic mechanical properties and fracture characteristics of rock under impact loading[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(10):2393-2405.
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