基于Baker准则浅埋巷道掌子面稳定性的上限分析（英文）
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摘要
将非线性Baker破坏准则引入到极限分析上限定理中,分析浅埋巷道掌子面的稳定性问题。从能量角度分析极限状态下掌子面的受力状态,计算破坏过程中所产生的外功率和内能损耗率,推导围岩压力的解析解,采用Matlab软件序列二次规划算法得到围岩压力的最优上限解。研究结果表明,非线性Baker破坏准则中的三个无量纲参数A,T,n对掌子面围岩压力以及破坏范围的影响均各不相同。A的影响最大,n次之,T最小;并且当A减小时掌子面的围岩压力和破坏范围均非线性增大。结合浙江省丽水市隧下隧道的实际监测资料,对计算结果进行了验证。建议针对软岩巷道应及时加强掌子面的支护措施,防止发生坍塌事故。
The nonlinear Baker failure criterion is introduced into the upper-bound limit analysis to examine the face stability of a shallow tunnel.The tunnel face under the ultimate limit state is analyzed from the perspective of energy balance.The work rates of external forces and internal energy dissipation are calculated.An analytical solution of necessary face pressures is derived.The optimal upper-bound solution of the face pressures is obtained by optimization.The results show that the three dimensionless parameters A, T, n of nonlinear Baker failure criterion have different effects on the necessary face pressures and the pattern failure mechanisms ahead of tunnel face.A is the most important one; n takes the second place, and T is the least one.The computed necessary face pressures are nonlinearly increasing when A is reduced.Combined with the actual monitoring data of Taxia tunnel, the calculation results in this paper is verified.It is suggested that the tunnel face supports should be strengthened timely in soft rocks to prevent the occurrence of face collapse.
The nonlinear Baker failure criterion is introduced into the upper-bound limit analysis to examine the face stability of a shallow tunnel.The tunnel face under the ultimate limit state is analyzed from the perspective of energy balance.The work rates of external forces and internal energy dissipation are calculated.An analytical solution of necessary face pressures is derived.The optimal upper-bound solution of the face pressures is obtained by optimization.The results show that the three dimensionless parameters A, T, n of nonlinear Baker failure criterion have different effects on the necessary face pressures and the pattern failure mechanisms ahead of tunnel face.A is the most important one; n takes the second place, and T is the least one.The computed necessary face pressures are nonlinearly increasing when A is reduced.Combined with the actual monitoring data of Taxia tunnel, the calculation results in this paper is verified.It is suggested that the tunnel face supports should be strengthened timely in soft rocks to prevent the occurrence of face collapse.
引文
[1]CHEN W F.Limit analysis and soil plasticity[M].Amsterdam:Elsevier Scientific Pub.Co,1975.
[2]ZHU J Q,YANG X L.Probabilistic stability analysis of rock slopes with cracks[J].Geomechanics and Engineering,2018,16(6):655-667.
[3]ZHANG Biao,WANG Xuan,ZHANG Jia-hua,CHENGHao.Safe range analysis of clear distance of twin shallow tunnels based on limit analysis and reliability theory[J].Journal of Central South University,2018,25(1):196-207.
[4]WANG Hui,ZHEN Peng-qiang,ZHAO Wen-juan,TIANHong-ming.Application of a combined supporting technology with U-shaped steel support and anchor-grouting to surrounding soft rock reinforcement in roadway[J].Journal of Central South University,2018,25(5):1240-1250.
[5]VAGHEFI M,AHMADI A,FARAJI B.Variation of hydraulic parameters with different wing of a T-shape spur dike in bend channels[J].Journal of Central South University,2018,25(3):671-680.
[6]ABID A,LYAMIN A V,HUANG J S,SLOAN S W,CASSIDY M J.Undrained stability of a single circular tunnel in spatially variable soil subjected to surcharge loading[J].Computers and Geotechnics,2017,84:16-27.
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[9]XU Jing-shu,YANG Xiao-li.Seismic stability of 3D soil slope reinforced by geosynthetic with nonlinear failure criterion[J].Soil Dynamics and Earthquake Engineering,2019,118:86-97.
[10]SALVADOR S,RAFAEL J.A tunnel face failure mechanism for layered ground,considering the possibility of partial collapse[J].Tunnelling and Underground Space Technology,2015,47:182-192.
[11]NIMA K,HISHAM M,MOHSEN H,BEHZAD F.The stability of shallow circular tunnels in soil considering variations in cohesion with depth[J].Tunnelling and Underground Space Technology,2015,49:230-240.
[12]GUAN Z,ZHU W C,NIU L L,WANG Q Y.Threedimensional upper bound limit analysis of supported cavity roof with arbitrary profile in Hoek-Brown rock mass[J].Tunnelling and Underground Space Technology,2017,69:147-154.
[13]LI Zheng-wei,YANG Xiao-li.Active eearth thrust considering tension crack,pore-water pressure and soil nonlinearity[J].KSCE Journal of Civil Engineering,2019,23(1):56-62.
[14]LI Yong-xin,YANG Xiao-li.Three-dimensional seismic displacement analysis of rock slopes based on Hoek-Brown failure criterion[J].KSCE Journal of Civil Engineering,2018,22(11):4334-4344.
[15]XU Jing-shu,LI Yong-xin,YANG Xiao-li.Seismic and static 3D stability of two-stage slope considering joined influences of nonlinearity and dilatancy[J].KSCE Journal of Civil Engineering,2018,22(10):3827-3836.
[16]PAN Qiu-jing,DIAS D.Upper-bound analysis on the face stability of a non-circular tunnel[J].Tunnelling and Underground Space Technology,2017,62:96-102.
[17]PAN Qiu-jing,DIAS D.Three dimensional face stability of a rock tunnel subjected to seepage forces[J].Tunnelling and Underground Space Technology,2018,71:555-566.
[18]MEHDI P,HAMID K,MOHAMMAD A,HAMID A,JAFAR A M.Stability analysis of shallow tunnels subjected to eccentric loads by a boundary element method[J].Journal of Rock Mechanics and Geotechnical Engineering,2016,4(8):480-488.
[19]LI T Z,YANG X L.Probabilistic stability analysis of subway tunnels combining multiple failure mechanisms and response surface method[J].International Journal of Geomechanics,2018,18(12):04018167.
[20]JAGDISH P S,JYANT K.Stability of a circular tunnel in presence of pseudostatic seismic body forces[J].Tunnelling and Underground Space Technology,2014,42:264-276.
[21]SEUNG H K,FULVIO T.Face stability and required support pressure for TBM driven tunnels with ideal face membrane-Drained case[J].Tunnelling and Underground Space Technology,2010,5(25):526-542.
[22]ZHANG Cheng-ping,HAN Kai-hang,ZHANG Ding-li.Face stability analysis of shallow circular tunnels in cohesive-frictional soils[J].Tunnelling and Underground Space Technology,2015,50:345-357.
[23]YANG X L,ZHOU T,LI W T.Reliability analysis of tunnel roof in layered Hoek-Brown rock masses[J].Computers and Geotechnics,2018,104:302-309.
[24]DONALD I B,CHEN Zu-yu.Slope stability analysis by the upper bound approach:Fundamentals and methods[J].Canadian Geotechnical Journal,1997,34(11):853-862．
[25]BAKER R.Non-linear strength envelopes based on triaxial data[J].ASCE Journal of Geotechnical and Geoenvironmental Engineering,2004,130(5):498-506.
[26]JIANG J C,BAKER R,YAMAGAMI T.The effect of strength envelope nonlinearity on slope stability calculations[J].Canadian Geotechnical Journal,2003,40(2):308-325.
[27]BAKER R,FRYDMAN S.Upper bound limit analysis of soil with non-linear failure criterion[J].Soils and Foundations,1983,23(4):34-42.
[28]ZHAO Yan-lin,WANG Yi-xian,WANG Wei-jun,WANWen,TANG Jin-zhou.Modeling of non-linear rheological behavior of hard rock using triaxial rheological experiment[J].International Journal of Rock Mechanics and Mining Sciences,2017,93:66-75.
[29]ZHANG Dao-bing,LIU Zhi-zhen,ZHANG Jia-hua.A new failure mechanism for deep cavity and upper bound solution of supporting pressure[J].Journal of Central South University,2017,24(9):2082-2091.
[30]LI Zheng-wei,YANG Xiao-li.Active earth pressure for soils with tension cracks under steady unsaturated flow conditions[J].Canadian Geotechnical Journal,2018,55(12),1850-1859.
[31]LI Yong-xin,YANG Xiao-li.Soil-slope stability considering effect of soil-strength nonlinearity[J].International Journal of Geomechanics,2019,19(3):04018201.
[32]LUO W J,YANG X L.3D stability of shallow cavity roof with arbitrary profile under influence of pore water pressure[J].Geomechanics and Engineering,2018,16(6):569-575.
[33]MOLLON G,PHOON K K,DIAS D,SOUBRA A H.Validation of a new 2d failure mechanism for the stability analysis of a pressurized tunnel face in a spatially varying sand[J].Journal of Engineering Mechanics,2010,137:8-21.
[34]ZHANG J H,WANG W J,ZHANG D B,ZHANG B,MENG F.Safe range of retaining pressure for threedimensional face of pressurized tunnels based on limit analysis and reliability method[J].KSCE Journal of Civil Engineering,2018,22(11):4645-4656.
[2]ZHU J Q,YANG X L.Probabilistic stability analysis of rock slopes with cracks[J].Geomechanics and Engineering,2018,16(6):655-667.
[3]ZHANG Biao,WANG Xuan,ZHANG Jia-hua,CHENGHao.Safe range analysis of clear distance of twin shallow tunnels based on limit analysis and reliability theory[J].Journal of Central South University,2018,25(1):196-207.
[4]WANG Hui,ZHEN Peng-qiang,ZHAO Wen-juan,TIANHong-ming.Application of a combined supporting technology with U-shaped steel support and anchor-grouting to surrounding soft rock reinforcement in roadway[J].Journal of Central South University,2018,25(5):1240-1250.
[5]VAGHEFI M,AHMADI A,FARAJI B.Variation of hydraulic parameters with different wing of a T-shape spur dike in bend channels[J].Journal of Central South University,2018,25(3):671-680.
[6]ABID A,LYAMIN A V,HUANG J S,SLOAN S W,CASSIDY M J.Undrained stability of a single circular tunnel in spatially variable soil subjected to surcharge loading[J].Computers and Geotechnics,2017,84:16-27.
[7]DANIEL W W,ANDREW J A,SCOTT W S,ANDREI V L.Undrained stability of a square tunnel where the shear strength increases linearly with depth[J].Computers and Geotechnics,2013,49:314-325.
[8]KENTARO Y,ANDREI V L,DANIEL W W,SCOTT W S,ANDREW J A.Stability of dual circular tunnels in cohesive-frictional soil subjected to surcharge loading[J].Computers and Geotechnics,2013,50:41-54.
[9]XU Jing-shu,YANG Xiao-li.Seismic stability of 3D soil slope reinforced by geosynthetic with nonlinear failure criterion[J].Soil Dynamics and Earthquake Engineering,2019,118:86-97.
[10]SALVADOR S,RAFAEL J.A tunnel face failure mechanism for layered ground,considering the possibility of partial collapse[J].Tunnelling and Underground Space Technology,2015,47:182-192.
[11]NIMA K,HISHAM M,MOHSEN H,BEHZAD F.The stability of shallow circular tunnels in soil considering variations in cohesion with depth[J].Tunnelling and Underground Space Technology,2015,49:230-240.
[12]GUAN Z,ZHU W C,NIU L L,WANG Q Y.Threedimensional upper bound limit analysis of supported cavity roof with arbitrary profile in Hoek-Brown rock mass[J].Tunnelling and Underground Space Technology,2017,69:147-154.
[13]LI Zheng-wei,YANG Xiao-li.Active eearth thrust considering tension crack,pore-water pressure and soil nonlinearity[J].KSCE Journal of Civil Engineering,2019,23(1):56-62.
[14]LI Yong-xin,YANG Xiao-li.Three-dimensional seismic displacement analysis of rock slopes based on Hoek-Brown failure criterion[J].KSCE Journal of Civil Engineering,2018,22(11):4334-4344.
[15]XU Jing-shu,LI Yong-xin,YANG Xiao-li.Seismic and static 3D stability of two-stage slope considering joined influences of nonlinearity and dilatancy[J].KSCE Journal of Civil Engineering,2018,22(10):3827-3836.
[16]PAN Qiu-jing,DIAS D.Upper-bound analysis on the face stability of a non-circular tunnel[J].Tunnelling and Underground Space Technology,2017,62:96-102.
[17]PAN Qiu-jing,DIAS D.Three dimensional face stability of a rock tunnel subjected to seepage forces[J].Tunnelling and Underground Space Technology,2018,71:555-566.
[18]MEHDI P,HAMID K,MOHAMMAD A,HAMID A,JAFAR A M.Stability analysis of shallow tunnels subjected to eccentric loads by a boundary element method[J].Journal of Rock Mechanics and Geotechnical Engineering,2016,4(8):480-488.
[19]LI T Z,YANG X L.Probabilistic stability analysis of subway tunnels combining multiple failure mechanisms and response surface method[J].International Journal of Geomechanics,2018,18(12):04018167.
[20]JAGDISH P S,JYANT K.Stability of a circular tunnel in presence of pseudostatic seismic body forces[J].Tunnelling and Underground Space Technology,2014,42:264-276.
[21]SEUNG H K,FULVIO T.Face stability and required support pressure for TBM driven tunnels with ideal face membrane-Drained case[J].Tunnelling and Underground Space Technology,2010,5(25):526-542.
[22]ZHANG Cheng-ping,HAN Kai-hang,ZHANG Ding-li.Face stability analysis of shallow circular tunnels in cohesive-frictional soils[J].Tunnelling and Underground Space Technology,2015,50:345-357.
[23]YANG X L,ZHOU T,LI W T.Reliability analysis of tunnel roof in layered Hoek-Brown rock masses[J].Computers and Geotechnics,2018,104:302-309.
[24]DONALD I B,CHEN Zu-yu.Slope stability analysis by the upper bound approach:Fundamentals and methods[J].Canadian Geotechnical Journal,1997,34(11):853-862．
[25]BAKER R.Non-linear strength envelopes based on triaxial data[J].ASCE Journal of Geotechnical and Geoenvironmental Engineering,2004,130(5):498-506.
[26]JIANG J C,BAKER R,YAMAGAMI T.The effect of strength envelope nonlinearity on slope stability calculations[J].Canadian Geotechnical Journal,2003,40(2):308-325.
[27]BAKER R,FRYDMAN S.Upper bound limit analysis of soil with non-linear failure criterion[J].Soils and Foundations,1983,23(4):34-42.
[28]ZHAO Yan-lin,WANG Yi-xian,WANG Wei-jun,WANWen,TANG Jin-zhou.Modeling of non-linear rheological behavior of hard rock using triaxial rheological experiment[J].International Journal of Rock Mechanics and Mining Sciences,2017,93:66-75.
[29]ZHANG Dao-bing,LIU Zhi-zhen,ZHANG Jia-hua.A new failure mechanism for deep cavity and upper bound solution of supporting pressure[J].Journal of Central South University,2017,24(9):2082-2091.
[30]LI Zheng-wei,YANG Xiao-li.Active earth pressure for soils with tension cracks under steady unsaturated flow conditions[J].Canadian Geotechnical Journal,2018,55(12),1850-1859.
[31]LI Yong-xin,YANG Xiao-li.Soil-slope stability considering effect of soil-strength nonlinearity[J].International Journal of Geomechanics,2019,19(3):04018201.
[32]LUO W J,YANG X L.3D stability of shallow cavity roof with arbitrary profile under influence of pore water pressure[J].Geomechanics and Engineering,2018,16(6):569-575.
[33]MOLLON G,PHOON K K,DIAS D,SOUBRA A H.Validation of a new 2d failure mechanism for the stability analysis of a pressurized tunnel face in a spatially varying sand[J].Journal of Engineering Mechanics,2010,137:8-21.
[34]ZHANG J H,WANG W J,ZHANG D B,ZHANG B,MENG F.Safe range of retaining pressure for threedimensional face of pressurized tunnels based on limit analysis and reliability method[J].KSCE Journal of Civil Engineering,2018,22(11):4645-4656.