Hoek-Brown准则奇异屈服面的圆化方法及其强度折减技术与应用
|
摘要
为克服基于Hoek-Brown强度准则的屈服面数值奇异问题,提出新的棱角处屈服面圆化方法,在此基础上,借助ABAQUS二次开发平台,采用FORTRAN语言编制理想弹塑性模型子程序,应力更新算法为完全隐式的向后欧拉积分算法;提出基于Hoek-Brown准则的有限元强度折减技术,并将其嵌入到圆化后的屈服函数中,探讨了强度折减技术应用于Mohr-Coulomb强度准则和Hoek-Brown非线性强度准则的异同点。对某圆形隧洞的模拟分析表明,围岩应力和塑性区的数值计算结果和解析结果吻合很好;对某岩质边坡的模拟分析表明,与等效Mohr-Coulomb模型的线性强度折减技术相比,基于Hoek-Brown模型的非线性强度折减技术获得的潜在滑动面位置较浅、形状较陡,更符合岩质边坡滑动面的特征,两个算例验证了该圆化方法和非线性强度折减技术的正确性和适用性。
To overcome the numerical singularity of the yield surface based on the Hoek-Brown strength criterion,a new approach was presented to smooth the edges of the yield surface. The ideal elasto-plastic constitutive model was implemented in ABAQUS software with the fully implicit backward Euler integral algorithm employed in the stress updating. The strength reduction method in finite element method based on the Hoek-Brown criterion was implemented with the smoothed yield function. The similarities and differences of the strength reduction techniques applied with the Mohr-Coulomb strength criterion and the Hoek-Brown nonlinear strength criterion were discussed. The modeling on a circular tunnel shows that the numerical results of stresses and plastic zones in the surrounding rock agree well with the analytical results. The modeling on a rock slope shows that in comparison with the linear strength reduction technique of the equivalent Mohr-Coulomb model,the nonlinear strength reduction technique based on the Hoek-Brown model produced the slip surface which agree better with the characteristics of the slip surface of a rock slope,which are shallower in location and steeper in shape.
To overcome the numerical singularity of the yield surface based on the Hoek-Brown strength criterion,a new approach was presented to smooth the edges of the yield surface. The ideal elasto-plastic constitutive model was implemented in ABAQUS software with the fully implicit backward Euler integral algorithm employed in the stress updating. The strength reduction method in finite element method based on the Hoek-Brown criterion was implemented with the smoothed yield function. The similarities and differences of the strength reduction techniques applied with the Mohr-Coulomb strength criterion and the Hoek-Brown nonlinear strength criterion were discussed. The modeling on a circular tunnel shows that the numerical results of stresses and plastic zones in the surrounding rock agree well with the analytical results. The modeling on a rock slope shows that in comparison with the linear strength reduction technique of the equivalent Mohr-Coulomb model,the nonlinear strength reduction technique based on the Hoek-Brown model produced the slip surface which agree better with the characteristics of the slip surface of a rock slope,which are shallower in location and steeper in shape.
引文
[1]HOEK E,BROWN E T.Empirical strength criterion for rock masses[J].Journal of Geotechnical and Geoenvironmental Engineering,1980,106(9):1 013–1 035.
[2]DRUCKER D C,PRAGER W.Soil mechanics and plastics analysis or limit design[J].Quarterly of Applied Mathematics,1952,10(2):157–165.
[3]ALEJANO L R,BOBET A,Drucker-Prager criterion[J].Rock Mechanics and Rock Engineering,2012,45(6):995–999.
[4]WAN R G.Implicit integration algorithm for Hoek-Brown elasticplastic model[J].Computers and Geotechnics,1992,14(3):149–177.
[5]NAYAK G C,ZIENKIEWICZ O C.Convenient form of stress invariants for plasticity[J].Journal of the Structural Division,1972,98(ST4):949–954.
[6]MATSUOKA H,NAKAI T.Stress-deformation and strength characteristics of soil under three different principal stresses[J].Proceedings of JSCE,1974,232(9):59–70.
[7]LADE P V,DUNCAN J M.Elastoplastic stress-strain theory for cohesionless soil[J].Journal of Geotechnical Engineering,1975,101(10):1 037–1 053.
[8]OWEN D R J,HINTON E.Finite elements in plasticity:Theory and practice[M].Swansea,UK:Pineridge Press Limited,1980:430–566.
[9]ABBO A J,LYAMIN A V,SLOAN S W,et al.A C2 continuous approximation to the Mohr Coulomb yield surface[J].International Journal of Solids and Structures,2011,48(21):3 001–3 010.
[10]KOITER W T.Stress-strain relations uniqueness and variational theorems for elastic-plastic materials with a singular yield surface[J].Quaterly of Applied Mathematics,1953,11(1):350–354.
[11]RISTINMAA M,TRYDING J.Exact integration of constitutive equations in elasto-plasticity[J].International Journal for Numerical Methods in Engineering,1993,36(15):2 525–2 544.
[12]CLAUSEN J,DAMKILDE L,ANDERSEN L.Efficient return algorithms for associated plasticity with multiple yield planes[J].International Journal for Numerical Methods in Engineering,2006,66(6):1 036–1 059.
[13]HOEK E,CARRANZA-TORRES C,CORKUM B.Hoek-Brown failure criterion-2002 edition[J].Proceedings of NARMS-Tac,2002,1(1):267–273.
[14]HAMMAH R E,YACOUB T E,CORKUM B C,et al.The shear strength reduction method for the generalized Hoek-Brown criterion[C]//Alaska Rocks 2005,The 40th US Symposium on Rock Mechanics(USRMS).[S.l.]:American Rock Mechanics Association,2005:ARMA–05–810.
[15]BENZ T,SCHWAB R,KAUTHER R A,et al.A Hoek-Brown criterion with intrinsic material strength factorization[J].International Journal of Rock Mechanics and Mining Sciences,2008,45(2):210–222.
[16]HOEK E.Strength of jointed rock masses[J].Geotechnique,1983,33(3):187–223.
[17]HOEK E.Strength of rock and rock masses[J].ISRM News Journal,1994,2(2):4–16.
[18]HOEK E,WOOD D,SHAH S.A modified Hoek–Brown failure criterion for jointed rock masses[C]//Rock Characterization:ISRM Symposium,Eurock?92,Chester,UK,14–17 September 1992.[S.l.]:Thomas Telford Publishing,1992:209–214.
[19]BISHOP A W.The use of the slip circle in the stability analysis of slopes[J].Geotechnique,1955,5(1):7–17.
[20]赵尚毅,郑颖人,时卫民,等.用有限元强度折减法求边坡稳定安全系数[J].岩土工程学报,2002,24(3):343–346.(ZHAO Shangyi,ZHENG Yingren,SHI Weimin,et al.Analysis on safety factor of slope by strength reduction FEM[J].Chinese Journal of Geotechnical Engineering,2002,24(3):343–346.(in Chinese))
[21]朱合华,张琦,章连洋.Hoek-Brown强度准则研究进展与应用综述[J].岩石力学与工程学报,2013,32(10):1 945–1 963.(ZHU Hehua,ZHANG Qi,ZHANG Lianyang.Review of research progresses and applications of Hoek-Brown strength criterion[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(10):1 945–1 963.(in Chinese))
[22]DAWSON E,YOU K,PARK Y.Strength-reduction stability analysis of rock slopes using the Hoek-Brown failure criterion[J].ASCE Geotechnical Special Publication,2000,102(1):65–77.
[23]FU W,LIAO Y.Non-linear shear strength reduction technique in slope stability calculation[J].Computers and Geotechnics,2010,37(3):288–298.
[24]符文熹,王启鸿,刘长武.非线性Hoek-Brown强度折减技术[J].地质灾害与环境保护,2010,21(2):82–87.(FU Wenxi,WANG Qihong,LIU Changwu.Non-linear Hoek-Brown strength reduction technique[J].Journal of Geological Hazards and Environment Preservation,2010,21(2):82–87.(in Chinese))
[25]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):2 051–2 058.(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):2 051–2 058.(in Chinese))
[26]CARRANZA-TORRES C,FAIRHURST C.The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion[J].International Journal of Rock Mechanics and Mining Sciences,1999,36(6):777–809.
[27]CARRANZA-TORRES C.Elasto-plastic solution of tunnel problems using the generalized form of the Hoek-Brown failure criterion[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(41):480–481.
[28]HOEK E,BROWN E T.Practical estimates of rock mass strength[J].International Journal of Rock Mechanics and Mining,1997,34(8):1 165–1 186.
[2]DRUCKER D C,PRAGER W.Soil mechanics and plastics analysis or limit design[J].Quarterly of Applied Mathematics,1952,10(2):157–165.
[3]ALEJANO L R,BOBET A,Drucker-Prager criterion[J].Rock Mechanics and Rock Engineering,2012,45(6):995–999.
[4]WAN R G.Implicit integration algorithm for Hoek-Brown elasticplastic model[J].Computers and Geotechnics,1992,14(3):149–177.
[5]NAYAK G C,ZIENKIEWICZ O C.Convenient form of stress invariants for plasticity[J].Journal of the Structural Division,1972,98(ST4):949–954.
[6]MATSUOKA H,NAKAI T.Stress-deformation and strength characteristics of soil under three different principal stresses[J].Proceedings of JSCE,1974,232(9):59–70.
[7]LADE P V,DUNCAN J M.Elastoplastic stress-strain theory for cohesionless soil[J].Journal of Geotechnical Engineering,1975,101(10):1 037–1 053.
[8]OWEN D R J,HINTON E.Finite elements in plasticity:Theory and practice[M].Swansea,UK:Pineridge Press Limited,1980:430–566.
[9]ABBO A J,LYAMIN A V,SLOAN S W,et al.A C2 continuous approximation to the Mohr Coulomb yield surface[J].International Journal of Solids and Structures,2011,48(21):3 001–3 010.
[10]KOITER W T.Stress-strain relations uniqueness and variational theorems for elastic-plastic materials with a singular yield surface[J].Quaterly of Applied Mathematics,1953,11(1):350–354.
[11]RISTINMAA M,TRYDING J.Exact integration of constitutive equations in elasto-plasticity[J].International Journal for Numerical Methods in Engineering,1993,36(15):2 525–2 544.
[12]CLAUSEN J,DAMKILDE L,ANDERSEN L.Efficient return algorithms for associated plasticity with multiple yield planes[J].International Journal for Numerical Methods in Engineering,2006,66(6):1 036–1 059.
[13]HOEK E,CARRANZA-TORRES C,CORKUM B.Hoek-Brown failure criterion-2002 edition[J].Proceedings of NARMS-Tac,2002,1(1):267–273.
[14]HAMMAH R E,YACOUB T E,CORKUM B C,et al.The shear strength reduction method for the generalized Hoek-Brown criterion[C]//Alaska Rocks 2005,The 40th US Symposium on Rock Mechanics(USRMS).[S.l.]:American Rock Mechanics Association,2005:ARMA–05–810.
[15]BENZ T,SCHWAB R,KAUTHER R A,et al.A Hoek-Brown criterion with intrinsic material strength factorization[J].International Journal of Rock Mechanics and Mining Sciences,2008,45(2):210–222.
[16]HOEK E.Strength of jointed rock masses[J].Geotechnique,1983,33(3):187–223.
[17]HOEK E.Strength of rock and rock masses[J].ISRM News Journal,1994,2(2):4–16.
[18]HOEK E,WOOD D,SHAH S.A modified Hoek–Brown failure criterion for jointed rock masses[C]//Rock Characterization:ISRM Symposium,Eurock?92,Chester,UK,14–17 September 1992.[S.l.]:Thomas Telford Publishing,1992:209–214.
[19]BISHOP A W.The use of the slip circle in the stability analysis of slopes[J].Geotechnique,1955,5(1):7–17.
[20]赵尚毅,郑颖人,时卫民,等.用有限元强度折减法求边坡稳定安全系数[J].岩土工程学报,2002,24(3):343–346.(ZHAO Shangyi,ZHENG Yingren,SHI Weimin,et al.Analysis on safety factor of slope by strength reduction FEM[J].Chinese Journal of Geotechnical Engineering,2002,24(3):343–346.(in Chinese))
[21]朱合华,张琦,章连洋.Hoek-Brown强度准则研究进展与应用综述[J].岩石力学与工程学报,2013,32(10):1 945–1 963.(ZHU Hehua,ZHANG Qi,ZHANG Lianyang.Review of research progresses and applications of Hoek-Brown strength criterion[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(10):1 945–1 963.(in Chinese))
[22]DAWSON E,YOU K,PARK Y.Strength-reduction stability analysis of rock slopes using the Hoek-Brown failure criterion[J].ASCE Geotechnical Special Publication,2000,102(1):65–77.
[23]FU W,LIAO Y.Non-linear shear strength reduction technique in slope stability calculation[J].Computers and Geotechnics,2010,37(3):288–298.
[24]符文熹,王启鸿,刘长武.非线性Hoek-Brown强度折减技术[J].地质灾害与环境保护,2010,21(2):82–87.(FU Wenxi,WANG Qihong,LIU Changwu.Non-linear Hoek-Brown strength reduction technique[J].Journal of Geological Hazards and Environment Preservation,2010,21(2):82–87.(in Chinese))
[25]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):2 051–2 058.(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):2 051–2 058.(in Chinese))
[26]CARRANZA-TORRES C,FAIRHURST C.The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion[J].International Journal of Rock Mechanics and Mining Sciences,1999,36(6):777–809.
[27]CARRANZA-TORRES C.Elasto-plastic solution of tunnel problems using the generalized form of the Hoek-Brown failure criterion[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(41):480–481.
[28]HOEK E,BROWN E T.Practical estimates of rock mass strength[J].International Journal of Rock Mechanics and Mining,1997,34(8):1 165–1 186.