基于应力梯度理论的锚杆合理预紧力
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摘要
巷道围岩的稳定性不仅与岩体强度有关,还与围岩应力场梯度密切相关。为研究锚杆在巷道围岩支护中合理支护强度的确定方法,在特定的地质条件中提出合理的预紧力,以连续损伤力学模型为基础并引入材料力学领域中的应力梯度理论,推导出了考虑围岩塑性区与弹性区交界面处的平衡方程和边界条件,建立了基于Mohr-Coulomb准则、Drucker-Prager准则以及Hoek-Brown准则下的围岩应力梯度求解模型;以Mohr-Coulomb准则为例,借助FLAC3D对比出模拟结果与理论计算值吻合度为93%且变化趋势一致,验证了提出的应力梯度求解方式适用性,发现随着锚杆预紧力的增加,巷道围岩的塑性区应力梯度相应增加,弹性区应力梯度不断减小,岩体劣化程度减弱。提出应力补偿系数,模拟计算出不同锚杆预紧力下巷道围岩应力梯度分布规律和支护效果,发现预紧力的变化与巷道围岩的锚固效果呈正相关趋势,塑性区范围随预紧力的增加不断减小,围岩稳定性随应力梯度的增加不断提高,并据此得出了锚杆预紧力与围岩应力梯度的对应补偿关系并提出最优补偿比。在现场实践中对巷道变形控制效果提高40%以上,并且应力梯度补偿系数高于0. 65,高于该矿围岩变形安全控制要求,为确定锚杆合理支护强度提供了一种研究思路。
The stability of roadway surrounding rock is not only related to the strength of rock mass,but also closely related to the stress field gradient of surrounding rock.In order to study the determination method of reasonable support strength of bolt in roadway surrounding rock support,a reasonable pre-tightening force is put forward in some specific geological conditions.This paper is based on the continuum damage mechanics model and introduces the stress gradient theory in the field of material mechanics. The equilibrium equation and boundary conditions of the interface between the plastic zone and the elastic zone of the surrounding rock are derived,and the stress gradient solution model of surrounding rock is established based on Mohr-Coulomb criterion,Drucker-Prager criterion and Hoek-Brown criterion.Taking the Mohr-Coulomb criterion as an example,using the FLAC3 D numerical software,the simulation results are compared with the theoretical values,which are 93 percent consistent with the change trend,which verifies the applicability of the stress gradient solution method proposed in this paper.It is found that the stress gradient in the plastic area of roadway surrounding rock increases correspondingly with the increase of the pre-tightening force of bolt,the stress gradient in the elastic area decreases continuously,and the degradation degree of rock mass decreases.The authors put forward the stress compensation coefficient. The stress gradient distribution law and supporting effect of roadway surrounding rock under different bolt preloads are calculated by simulation. It's found that the change of pre-tightening force is positively correlated with the bolting effect of roadway surrounding rock,and the range of plastic zone decreases with the increase of pre-tightening force,and the stability of sur-rounding rock increases with the increase of stress gradient.Based on these conclusions,the corresponding compensation relation between the bolt's pretension force and the stress gradient of surrounding rock is obtained and the optimal compensation ratio is proposed.In the field practice,the control effect of roadway deformation is improved by more than 40%,and the stress gradient compensation coefficient is higher than 0.65,which is higher than the safety control requirements of surrounding rock deformation,and provides a research idea for determining the reasonable support strength of the bolt.
The stability of roadway surrounding rock is not only related to the strength of rock mass,but also closely related to the stress field gradient of surrounding rock.In order to study the determination method of reasonable support strength of bolt in roadway surrounding rock support,a reasonable pre-tightening force is put forward in some specific geological conditions.This paper is based on the continuum damage mechanics model and introduces the stress gradient theory in the field of material mechanics. The equilibrium equation and boundary conditions of the interface between the plastic zone and the elastic zone of the surrounding rock are derived,and the stress gradient solution model of surrounding rock is established based on Mohr-Coulomb criterion,Drucker-Prager criterion and Hoek-Brown criterion.Taking the Mohr-Coulomb criterion as an example,using the FLAC3 D numerical software,the simulation results are compared with the theoretical values,which are 93 percent consistent with the change trend,which verifies the applicability of the stress gradient solution method proposed in this paper.It is found that the stress gradient in the plastic area of roadway surrounding rock increases correspondingly with the increase of the pre-tightening force of bolt,the stress gradient in the elastic area decreases continuously,and the degradation degree of rock mass decreases.The authors put forward the stress compensation coefficient. The stress gradient distribution law and supporting effect of roadway surrounding rock under different bolt preloads are calculated by simulation. It's found that the change of pre-tightening force is positively correlated with the bolting effect of roadway surrounding rock,and the range of plastic zone decreases with the increase of pre-tightening force,and the stability of sur-rounding rock increases with the increase of stress gradient.Based on these conclusions,the corresponding compensation relation between the bolt's pretension force and the stress gradient of surrounding rock is obtained and the optimal compensation ratio is proposed.In the field practice,the control effect of roadway deformation is improved by more than 40%,and the stress gradient compensation coefficient is higher than 0.65,which is higher than the safety control requirements of surrounding rock deformation,and provides a research idea for determining the reasonable support strength of the bolt.
引文
[1] ALAM A K M B,NIIOKA M,FUJII Y,et al. Effects of confining pressure on the permeability of three rock types under compression[J].International Journal of Rock Mechanics and Mining Sciences,2014,65(1):49-61.
[2] SUKPLUM W,WANNAKAO L. Influence of confining pressure on the mechanical behavior of Phu Kradung sandstone[J].International Journal of Rock Mechanics and Mining Sciences,2016,86:48-54.
[3] LI Xibing,TAO Ming,WU Chenqing,et al.Spalling strength of rock under different static pre-confining pressures[J].International Journal of Impact Engineering,2017,99:69-74.
[4] SCHMIDT R A,HUDDLE C W.Effect of confining pressure on fracture toughness of Indiana limestone[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1977,14(5):289-293.
[5] CHI T N,NGUYEN G D,DAS A,et al.Constitutive modelling of progressive localised failure in porous sandstones under shearing at high confining pressures[J]. International Journal of Rock Mechanics and Mining Sciences,2017,93:179-195.
[6] ANTUNES M A,SILVA C R M D,Rêgo E M F D.Stress intensity factor solutions for fretting fatigue using stress gradient factor[J].Engineering Fracture Mechanics,2017,186:331-346
[7] VANTADORI S,FORTESE G,RONCHEI C,et al.A stress gradient approach for fretting fatigue assessment of metallic structural components[J].International Journal of Fatigue,2017,101:1-8.
[8] ARAJO J A,ALMEIDA G M J,FERREIRA J L A,et al. Early cracking orientation under high stress gradients:The fretting case[J].International Journal of Fatigue,2017,100:611-618.
[9] GATES N,FATEMI A.Notch deformation and stress gradient effects in multiaxial fatigue[J]. Theoretical and Applied Fracture Mechanics,2016,84:3-25.
[10] HE Jiang,DOU Linming.Gradient principle of horizontal stress inducing rock burst in coal mine[J].Journal of Central South University,2012,19(10):2926-2932.
[11] SU G,ZHAI S,JIANG J,et al.Influence of radial stress gradient on strainbursts:An experimental study[J]. Rock Mechanics and Rock Engineering,2017,50(10):2659-2676.
[12] CARTER B J. Size and stress gradient effects on fracture around cavities[J].Rock Mechanics and Rock Engineering,1992,25(3):167-186.
[13] CHAPPELL B A.Size effects,stress and couple stress gradients in jointed rock[J].Mining Science and Technology,1990,11(1):1-18.
[14] JESSLL M. The failure of rock[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1965,2:389-403.
[15] GEREK H. An elastic solution for stresses around tunnels with conventional shapes[J]. International Journal of Rock Mechanics and Mining Sciences,1997,34(3-4):96.
[16] BARTON N,LIEN R,LUNDE J. Engineering classification of rock masses for the design of tunnel support[J].Rock Mechanics,1974,6(4):189-236.
[17] CAI Y,ESAKI T,JIANG Y. A rock bolt and rock mass interaction model[J]. International Journal of Rock Mechanics and Mining Sciences,2004,41(7):1055-1067.
[18] MOORE I D.Analysis of rib supports for circular tunnels in elastic ground[J]. Rock Mechanics and Rock Engineering,1994,27(3):155-172.
[19] KANG Hongpu. Support technologies for deep and complex roadways in underground coal mines:A review[J].International Journal of Coal Science&Technology,2014,1(3):261-277.
[20] BOBET A.Elastic solution for deep tunnels application to excavation damage zone and rockbolt support[J]. Rock Mechanics and Rock Engineering,2009,42(2):147-174.
[21] LIU G F,FENG X T,FENG G L,et al.A method for dynamic risk assessment and management of rockbursts in drill and blast tunnels[J].Rock Mechanics and Rock Engineering,2016,49(8):3257-3279.
[22] BARPI F,VALENTE S,CRAVERO M,et al. Fracture mechanics characterization of an anisotropic geomaterial[J]. Engineering Fracture Mechanics,2012,84:111-122.
[23]左建平,魏旭,王军,等.深部巷道围岩梯度破坏机理及模型研究[J].中国矿业大学学报,2018,47(3):478-485.ZUO Jianping,WEI Xu,WANG Jun,et al. Investigation of failure mechanism and model for rocks in deep roadway under stress gradient effect[J].Journal of China University of Mining and Technology,2018,47(3):478-485.
[24]张绪涛,张强勇,向文,等.基于应变梯度理论的分区破裂机制分析研究[J].岩石力学与工程学报,2016,35(4):724-734.ZHANG Xutao,ZHANG Qiangyong,XIANG Wen,et al. Zonal disintegration mechanism based on strain gradient theory[J]. Chinese Journal of Rock Mechanics and Engineering,2016,35(4):724-734.
[25]王明洋,解东升,李杰,等.深部岩体变形破坏动态本构模型[J].岩石力学与工程学报,2013,32(6):1112-1120.WANG Mingyang,XIE Dongsheng,LI Jie,et al. Dynamic constitutive model for deformation and fracture of deep rock mass[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(6):1112-1120.
[26]刘会波,肖明,陈俊涛.复杂地下洞室围岩开挖扰动空间效应参数化研究[J].四川大学学报(工程科学版),2012,44(3):47-54.LIU Huibo,XIAO Ming,CHEN Juntao. Parametric analysis of spatial effect of excavation damaged/disturbed zone around complex underground openings[J].Journal of Sichuan University(Engineering Science Edition),2012,44(3):47-54.
[27] CHEN Z H. Stress distribution characteristics in rock surrounding heading face and its relationship with temporary supporting[J]. Applied Mechanics and Materials,2014,568-570:1684-1689.
[28]侯公羽,牛晓松.基于Levy-Mises本构关系及Hoek-Brown屈服准则的轴对称圆巷理想弹塑性解[J].岩石力学与工程学报,2010,29(4):765-777.HOU Gongyu,NIU Xiaosong. Perfect elastoplastic solution of axisymmetric cylindrical cavity based on levy-mises constitutive relation and Hoek-Brown failure criterion[J]. Chinese Journal of Rock Mechanics and Engineering,2010,29(4):765-777.
[29] IX C. Fundamentals of rock mechanics[M]. Blackwell:Blackwell publishing,1976:132-166.
[30] OBERT L,DUVALL W I.Rock mechanics and the design of structure in rock[M].New York:John Wiley and Sons,1967,71-78.
[31]蔡美峰.岩石力学与工程[M].北京:科学出版社,2013:21-41.
[2] SUKPLUM W,WANNAKAO L. Influence of confining pressure on the mechanical behavior of Phu Kradung sandstone[J].International Journal of Rock Mechanics and Mining Sciences,2016,86:48-54.
[3] LI Xibing,TAO Ming,WU Chenqing,et al.Spalling strength of rock under different static pre-confining pressures[J].International Journal of Impact Engineering,2017,99:69-74.
[4] SCHMIDT R A,HUDDLE C W.Effect of confining pressure on fracture toughness of Indiana limestone[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1977,14(5):289-293.
[5] CHI T N,NGUYEN G D,DAS A,et al.Constitutive modelling of progressive localised failure in porous sandstones under shearing at high confining pressures[J]. International Journal of Rock Mechanics and Mining Sciences,2017,93:179-195.
[6] ANTUNES M A,SILVA C R M D,Rêgo E M F D.Stress intensity factor solutions for fretting fatigue using stress gradient factor[J].Engineering Fracture Mechanics,2017,186:331-346
[7] VANTADORI S,FORTESE G,RONCHEI C,et al.A stress gradient approach for fretting fatigue assessment of metallic structural components[J].International Journal of Fatigue,2017,101:1-8.
[8] ARAJO J A,ALMEIDA G M J,FERREIRA J L A,et al. Early cracking orientation under high stress gradients:The fretting case[J].International Journal of Fatigue,2017,100:611-618.
[9] GATES N,FATEMI A.Notch deformation and stress gradient effects in multiaxial fatigue[J]. Theoretical and Applied Fracture Mechanics,2016,84:3-25.
[10] HE Jiang,DOU Linming.Gradient principle of horizontal stress inducing rock burst in coal mine[J].Journal of Central South University,2012,19(10):2926-2932.
[11] SU G,ZHAI S,JIANG J,et al.Influence of radial stress gradient on strainbursts:An experimental study[J]. Rock Mechanics and Rock Engineering,2017,50(10):2659-2676.
[12] CARTER B J. Size and stress gradient effects on fracture around cavities[J].Rock Mechanics and Rock Engineering,1992,25(3):167-186.
[13] CHAPPELL B A.Size effects,stress and couple stress gradients in jointed rock[J].Mining Science and Technology,1990,11(1):1-18.
[14] JESSLL M. The failure of rock[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1965,2:389-403.
[15] GEREK H. An elastic solution for stresses around tunnels with conventional shapes[J]. International Journal of Rock Mechanics and Mining Sciences,1997,34(3-4):96.
[16] BARTON N,LIEN R,LUNDE J. Engineering classification of rock masses for the design of tunnel support[J].Rock Mechanics,1974,6(4):189-236.
[17] CAI Y,ESAKI T,JIANG Y. A rock bolt and rock mass interaction model[J]. International Journal of Rock Mechanics and Mining Sciences,2004,41(7):1055-1067.
[18] MOORE I D.Analysis of rib supports for circular tunnels in elastic ground[J]. Rock Mechanics and Rock Engineering,1994,27(3):155-172.
[19] KANG Hongpu. Support technologies for deep and complex roadways in underground coal mines:A review[J].International Journal of Coal Science&Technology,2014,1(3):261-277.
[20] BOBET A.Elastic solution for deep tunnels application to excavation damage zone and rockbolt support[J]. Rock Mechanics and Rock Engineering,2009,42(2):147-174.
[21] LIU G F,FENG X T,FENG G L,et al.A method for dynamic risk assessment and management of rockbursts in drill and blast tunnels[J].Rock Mechanics and Rock Engineering,2016,49(8):3257-3279.
[22] BARPI F,VALENTE S,CRAVERO M,et al. Fracture mechanics characterization of an anisotropic geomaterial[J]. Engineering Fracture Mechanics,2012,84:111-122.
[23]左建平,魏旭,王军,等.深部巷道围岩梯度破坏机理及模型研究[J].中国矿业大学学报,2018,47(3):478-485.ZUO Jianping,WEI Xu,WANG Jun,et al. Investigation of failure mechanism and model for rocks in deep roadway under stress gradient effect[J].Journal of China University of Mining and Technology,2018,47(3):478-485.
[24]张绪涛,张强勇,向文,等.基于应变梯度理论的分区破裂机制分析研究[J].岩石力学与工程学报,2016,35(4):724-734.ZHANG Xutao,ZHANG Qiangyong,XIANG Wen,et al. Zonal disintegration mechanism based on strain gradient theory[J]. Chinese Journal of Rock Mechanics and Engineering,2016,35(4):724-734.
[25]王明洋,解东升,李杰,等.深部岩体变形破坏动态本构模型[J].岩石力学与工程学报,2013,32(6):1112-1120.WANG Mingyang,XIE Dongsheng,LI Jie,et al. Dynamic constitutive model for deformation and fracture of deep rock mass[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(6):1112-1120.
[26]刘会波,肖明,陈俊涛.复杂地下洞室围岩开挖扰动空间效应参数化研究[J].四川大学学报(工程科学版),2012,44(3):47-54.LIU Huibo,XIAO Ming,CHEN Juntao. Parametric analysis of spatial effect of excavation damaged/disturbed zone around complex underground openings[J].Journal of Sichuan University(Engineering Science Edition),2012,44(3):47-54.
[27] CHEN Z H. Stress distribution characteristics in rock surrounding heading face and its relationship with temporary supporting[J]. Applied Mechanics and Materials,2014,568-570:1684-1689.
[28]侯公羽,牛晓松.基于Levy-Mises本构关系及Hoek-Brown屈服准则的轴对称圆巷理想弹塑性解[J].岩石力学与工程学报,2010,29(4):765-777.HOU Gongyu,NIU Xiaosong. Perfect elastoplastic solution of axisymmetric cylindrical cavity based on levy-mises constitutive relation and Hoek-Brown failure criterion[J]. Chinese Journal of Rock Mechanics and Engineering,2010,29(4):765-777.
[29] IX C. Fundamentals of rock mechanics[M]. Blackwell:Blackwell publishing,1976:132-166.
[30] OBERT L,DUVALL W I.Rock mechanics and the design of structure in rock[M].New York:John Wiley and Sons,1967,71-78.
[31]蔡美峰.岩石力学与工程[M].北京:科学出版社,2013:21-41.