地下洞室三维弹塑性动力显式有限元锚杆模拟
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摘要
锚杆的数值模拟方法是分析地震灾变中锚杆的作用机理及锚杆支护对地下洞室围岩抗震的加固效果的关键。基于地震动荷载作用下锚杆围岩联合受力机理,在对FLAC3D锚杆模拟算法进行一定改进的基础上,提出了一种适用于抗震分析的全长粘结式锚杆模拟方法,并将该方法应用到自主开发的地下洞室三维显式动力有限元程序中,取得较好效果。该方法继承了FLAC3D中对锚杆、锚杆与砂浆接触面、锚固砂浆、砂浆与围岩接触面及围岩本身共5种结构材料的受力破坏情况的详细模拟,但不再进行相邻锚杆计算段之间的受力平衡迭代,而是将各锚杆计算段的受力转移到单元结点上,将锚杆求解与单元求解相统一,从而降低动力求解中锚杆的计算耗时。同时,详细推导了锚杆各结构材料的屈服极限表达式,缩短了锚杆结构材料屈服判断及应力修正耗时。该锚杆模型与FLAC3D中的模型假定不同,认为锚杆变形由围岩变形引起,各锚杆计算段间受力相对独立,受力并不连续,与地震中围岩锚杆的受力情况较吻合。采用该方法对某地下厂房洞室群进行地震动力时程分析,表明该模拟方法提高了求解速度,充分反映了锚杆对围岩的支护效果。
Numerical simulation method of anchor bolts is a key issue for understanding the working mechanism of anchor bolts and their reinforcing effects in analysis of the seismic disaster process of underground caverns.Based on the joint loading mechanism of anchor bolts and surrounding rock under earthquake impact,the numerical algorithm of anchor bolts adopted by FLAC3D is improved and a new algorithm,suitable for the aseismic analysis,is proposed to simulate fully-grouted anchor bolts.This new algorithm was implemented through an independently-developed explicit 3D elastoplastic dynamic FEM code,and satisfactory results were obtained.This method takes advantages of FLAC3D algorithms for simulating five types of damage under loading conditions,i.e.anchor bolts,anchor-bolts contacting mortar,anchor mortar,mortar contacting surrounding rock,and surrounding rock.It transfers the force bear by each computation section of anchor bolts to the FEM nodes,rather than iterating for loading equilibrium.Thus,it unifies the solution of anchor bolts and elements and reduces the computational cost of anchor blots in dynamic analysis.Moreover,analytical expressions of yield limit for various types of anchor bolt materials are derived in details,which leads to a cost saving in yield state determination and stress modification.The proposed anchor bolts model adopts an assumption different from those of FLAC3D model,i.e.the deformation of anchor bolts is induced by the deformation of surrounding rock.Under this condition,the force bear by each section of anchor bolts is independent from each other,and the forces along an anchor bolt are not continuous.This assumption agrees with the real earthquake process.A dynamic analysis case study for a practical underground cavern indicates that the proposed method enhances the computation speed and fully reflects the supporting effects of anchor bolts to surrounding rock.
Numerical simulation method of anchor bolts is a key issue for understanding the working mechanism of anchor bolts and their reinforcing effects in analysis of the seismic disaster process of underground caverns.Based on the joint loading mechanism of anchor bolts and surrounding rock under earthquake impact,the numerical algorithm of anchor bolts adopted by FLAC3D is improved and a new algorithm,suitable for the aseismic analysis,is proposed to simulate fully-grouted anchor bolts.This new algorithm was implemented through an independently-developed explicit 3D elastoplastic dynamic FEM code,and satisfactory results were obtained.This method takes advantages of FLAC3D algorithms for simulating five types of damage under loading conditions,i.e.anchor bolts,anchor-bolts contacting mortar,anchor mortar,mortar contacting surrounding rock,and surrounding rock.It transfers the force bear by each computation section of anchor bolts to the FEM nodes,rather than iterating for loading equilibrium.Thus,it unifies the solution of anchor bolts and elements and reduces the computational cost of anchor blots in dynamic analysis.Moreover,analytical expressions of yield limit for various types of anchor bolt materials are derived in details,which leads to a cost saving in yield state determination and stress modification.The proposed anchor bolts model adopts an assumption different from those of FLAC3D model,i.e.the deformation of anchor bolts is induced by the deformation of surrounding rock.Under this condition,the force bear by each section of anchor bolts is independent from each other,and the forces along an anchor bolt are not continuous.This assumption agrees with the real earthquake process.A dynamic analysis case study for a practical underground cavern indicates that the proposed method enhances the computation speed and fully reflects the supporting effects of anchor bolts to surrounding rock.
引文
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[3]Itasca Consulting Group Inc..FLAC3D users'manual[R].Minneapolis:Itasca Consulting Group Inc.,2005.
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[5]肖明.地下洞室隐式锚杆柱单元的三维弹塑性有限元分析[J].岩土工程学报,1992,14(5):47-56.XIAO Ming.3D elastoplastic finite element analysis of implicit cylindrical anchor bar element for underground opening[J].Chinese Journal of Geotechnical Engineering,1992,14(5):47-56.(in Chinese)
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[8]张强勇,向文,朱维申.三维加锚弹塑性损伤模型在溪洛渡地下厂房工程中的应用[J].计算力学学报.2000,17(4):475-482.ZHANG Qiangyong,XIANG Wen,ZHU Weishen.Application of3D elastoplastic damage model with bolts to Xiluodu underground powerhouse[J].Chinese Journal of Computational Mechanics,2000,17(4):475-482.(in Chinese)
[9]陆士良,汤雷,杨新安.锚杆锚固与锚固技术[M].北京:煤炭工业出版社,1998.LU Shiliang,TANG Lei,YANG Xin-an.Anchoring force and anchoring technique for anchor bolts[M].Beijing:China Coal Industry Publishing House,1998.
[10]朱训国,杨庆,栾茂田.岩体锚固效应及锚杆的解析本构模型研究[J].岩土力学,2007,28(3):527-532.ZHU Xunguo,YANG Qing,LUAN Maotian.Study of reinforcement effect of anchored rock masses and analytic constitutive equation for rock bolt[M].Rock and Soil Mechanics,2007,28(3):527-532.(in Chinese)
[11]张雄,王天舒.计算动力学[M].北京:清华大学出版社,2007.ZHANG Xiong,WANG Tianshu.Computational dynamics[M].Beijing:Tsinghua University Press,2007.(in Chinese)
[12]钱向东,任青文,赵引.一种高效的等参有限元逆变换算法[J].计算力学学报,1998,15(4):437-441.QIAN Xiangdong,REN Qingwen,ZHAO Yin.An algorithm for inverse isoparametric mapping in FEM[J].Chinese Journal of Computational Mechanics,1998,15(4):437-441.(in Chinese)
[13]张志国,肖明,张雨霆,等.大型地下洞室三维弹塑性损伤动力有限元分析[J].岩石力学与工程学报.2010,29(5):982-989.ZHANG Zhiguo,XIAO Ming,ZHANG Yuting,et al.Dynamic finite element analysis of large-scale complex underground caverns with three-dimensional elastoplastic damage model[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(5):982-989.(in Chinese)
[2]谢和平,邓建辉,台佳佳,等.汶川大地震灾害与灾区重建的岩土工程问题[J].岩土工程学报,2008,27(9):1781-1791.XIE Heping,DENG Jianhui,TAI Jiajia,et al.Wenchuan lager earthquake and post-earthquake reconstruction-related geotechnicalproblems[J].Chinese Journal of Geotechnical Engineering,2008,27(9):1781-1791.(in Chinese)
[3]Itasca Consulting Group Inc..FLAC3D users'manual[R].Minneapolis:Itasca Consulting Group Inc.,2005.
[4]CHEN S H,QIANG S,CHEN S,et al.Composite element model of the fully grouted rock bolt[J].Rock Mechanics and RockEngineering,2004,37(3):193-212.
[5]肖明.地下洞室隐式锚杆柱单元的三维弹塑性有限元分析[J].岩土工程学报,1992,14(5):47-56.XIAO Ming.3D elastoplastic finite element analysis of implicit cylindrical anchor bar element for underground opening[J].Chinese Journal of Geotechnical Engineering,1992,14(5):47-56.(in Chinese)
[6]郭凌云,肖明,任祎.端锚式锚杆数值模拟及其受力分析[J].岩石力学与工程学报,2007,26(增2):4221-4226.GUO Lingyun,XIAO Ming,Ren Yi.Numerical simulation and mechanical analysis of end-anchored bolts[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(supp2):4221-4226.(in Chinese)
[7]朱维申,李术才,陈卫忠.节理岩体破坏机理和锚固效应及工程应用[M].北京:科学出版社,2002.ZHU Weishen,LI Shucai,CHEN Weizhong.Fracture Mechanism and Anchoring Effect of Joint Rock Mass in Engineering[M].Beijing:Science Press,2002.(in Chinese)
[8]张强勇,向文,朱维申.三维加锚弹塑性损伤模型在溪洛渡地下厂房工程中的应用[J].计算力学学报.2000,17(4):475-482.ZHANG Qiangyong,XIANG Wen,ZHU Weishen.Application of3D elastoplastic damage model with bolts to Xiluodu underground powerhouse[J].Chinese Journal of Computational Mechanics,2000,17(4):475-482.(in Chinese)
[9]陆士良,汤雷,杨新安.锚杆锚固与锚固技术[M].北京:煤炭工业出版社,1998.LU Shiliang,TANG Lei,YANG Xin-an.Anchoring force and anchoring technique for anchor bolts[M].Beijing:China Coal Industry Publishing House,1998.
[10]朱训国,杨庆,栾茂田.岩体锚固效应及锚杆的解析本构模型研究[J].岩土力学,2007,28(3):527-532.ZHU Xunguo,YANG Qing,LUAN Maotian.Study of reinforcement effect of anchored rock masses and analytic constitutive equation for rock bolt[M].Rock and Soil Mechanics,2007,28(3):527-532.(in Chinese)
[11]张雄,王天舒.计算动力学[M].北京:清华大学出版社,2007.ZHANG Xiong,WANG Tianshu.Computational dynamics[M].Beijing:Tsinghua University Press,2007.(in Chinese)
[12]钱向东,任青文,赵引.一种高效的等参有限元逆变换算法[J].计算力学学报,1998,15(4):437-441.QIAN Xiangdong,REN Qingwen,ZHAO Yin.An algorithm for inverse isoparametric mapping in FEM[J].Chinese Journal of Computational Mechanics,1998,15(4):437-441.(in Chinese)
[13]张志国,肖明,张雨霆,等.大型地下洞室三维弹塑性损伤动力有限元分析[J].岩石力学与工程学报.2010,29(5):982-989.ZHANG Zhiguo,XIAO Ming,ZHANG Yuting,et al.Dynamic finite element analysis of large-scale complex underground caverns with three-dimensional elastoplastic damage model[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(5):982-989.(in Chinese)
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