非均质地基浅埋水平条形锚板承载力上限分析
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摘要
考虑地基土体的非均质特性,采用非线性Mohr-Coulomb强度准则及其关联流动法则构造了浅埋水平条形锚板的曲线型破裂机制与机动许可速度场,根据极限分析上限定理推导了条形锚板抗拔承载力的表达式。利用变分极值原理求得了锚板抗拔承载力及其上方土体破裂面的上限解,分析了锚板埋深、土体非均质和非线性强度特性对锚板抗拔承载特性的影响,并将该上限解与已有计算方法进行了对比。结果表明:锚板埋深、土体非均质和非线性强度特性对其抗拔承载力与破裂面特征具有明显的影响。锚板埋深和土体非均质系数越大以及土体非线性强度系数越小,锚板抗拔承载力和土体破裂面深度、宽度均是越大。该上限解与极限平衡和极限分析有限元方法的计算结果基本一致,验证了所采用的曲线型破裂机制和地基非均质变化规律有效性,为条形锚板设计提供了一定的参考。
Considering the heterogeneity of soils,a kinematic admissible velocity field was constructed to characterize a proposed curve failure mechanism of soils above the shallow strip anchor plate on the basis of the nonlinear Mohr-Coulomb criterion and the associated flow rule. The ultimate pullout force and failure mechanism of the shallow strip anchor plate were derived using the upper bound analysis method and the variation minimum principle. The influences of the embedded depth,heterogeneity and nonlinear strength features on its ultimate pullout force and failure mechanism were discussed,and comparisons between this upper bound solution and the existing solutions were also conducted. The results show that the embedded depth,heterogeneity and nonlinear strength features have obvious effects on the ultimate pullout force and failure mechanism of the shallow strip anchor plate. With the increases in the embedded depth and heterogeneity coefficient as well as the decrease in the nonlinear strength coefficient,the ultimate pullout force of the shallow strip anchor plate increases together with the failure zone(depth and width) of soils. The calculation results of this upper bound solution show good agreements with those of the limit equilibrium method and limit analysis by the finite element method,which shows the effectiveness of this proposed curve failure mechanism and heterogeneity law of soils,and provides some references for the design of shallow strip anchor plates.
Considering the heterogeneity of soils,a kinematic admissible velocity field was constructed to characterize a proposed curve failure mechanism of soils above the shallow strip anchor plate on the basis of the nonlinear Mohr-Coulomb criterion and the associated flow rule. The ultimate pullout force and failure mechanism of the shallow strip anchor plate were derived using the upper bound analysis method and the variation minimum principle. The influences of the embedded depth,heterogeneity and nonlinear strength features on its ultimate pullout force and failure mechanism were discussed,and comparisons between this upper bound solution and the existing solutions were also conducted. The results show that the embedded depth,heterogeneity and nonlinear strength features have obvious effects on the ultimate pullout force and failure mechanism of the shallow strip anchor plate. With the increases in the embedded depth and heterogeneity coefficient as well as the decrease in the nonlinear strength coefficient,the ultimate pullout force of the shallow strip anchor plate increases together with the failure zone(depth and width) of soils. The calculation results of this upper bound solution show good agreements with those of the limit equilibrium method and limit analysis by the finite element method,which shows the effectiveness of this proposed curve failure mechanism and heterogeneity law of soils,and provides some references for the design of shallow strip anchor plates.
引文
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[14]邹新军,王英宇,赵明华,等.基于能量法的非均质地基中单桩受扭弹塑性分析[J].水文地质工程地质,2016,43(2):54-61.[ZOU X J,WANG Y Y,ZHAO M H,et al.Elastic-plastic analysis of a torsional single pile in non-homogeneous subsoil based on energy principle[J].Hydrogeology&Engineering Geology,2016,43(2):54-61.(in Chinese)]
[15]MERIFIELD R S,SLOAN S W,YU H S.Stability of plate anchors in undrained clay[J].Géotechnique,2001,51(2):141-153.
[16]刘嘉,董志良,郭伟玲.非均质饱和黏土中平板锚基础的抗拉力[J].水运工程,2008(7):1-6.[LIU J,DONG Z L,GUO W L.Uplift capacity of plate anchor foundation in saturated heterogeneous clay[J].Port&Waterway Engineering,2008(7):1-6.(in Chinese)]
[17]THO K K,CHEN Z R,LEUNG C F,et al.Pullout behaviour of plate anchor in clay with linearly increasing strength[J].Canadian Geotechnical Journal,2014,51(51):92-102.
[18]WU X N,CHOW Y K,LEUNG C F.Behavior of drag anchor in clay with linearly increasing shear strength under unidirectional and combined loading[J].Applied Ocean Research,2017,63:142-156.
[19]王洪涛,王琦,尤春安,等.考虑土体非均质和各向异性的锚索极限抗拔力研究[J].岩土力学,2013,34(8):2204-2210.[WANG H T,WANG Q,YOU C A,et al.Study of ultimate pullout force of anchor cable considering non-homogeneity and anisotropy of soil mass[J].Rock and Soil Mechanics,2013,34(8):2204-2210.(in Chinese)]
[20]CHEN W F.Limit analysis and soil plasticity[M].New York:Elsevier Scientific Publishing Company,1975.
[21]黄茂松,秦会来,郭院成.非均质和各向异性黏土地基承载力的上限解[J].岩石力学与工程学报,2008,27(3):511-518.[HUANG M S,QIN H L,GUO Y C.Upper bound solution for bearing capacity of non-homogeneous and anisotropic clay foundation[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(3):511-518.(in Chinese)]
[22]梁桥,杨小礼,张佳华,等.非均质土体中盾构隧道开挖面支护力上限分析[J].岩土力学,2016,37(9):2585-2592.[LIANG Q,YANG X L,ZHANG J H,et al.Upper bound analysis for supporting pressure of shield tunnel in heterogeneous soil[J].Rock and Soil Mechanics,2016,37(9):2585-2592.(in Chinese)]
[23]张迎宾,李亮,赵炼恒.基于非线性破坏准则的边坡稳定性极限分析[J].岩土力学,2011,32(11):3312-3318.[ZHANG Y B,LI L,ZHAO L H,et al.Limit analysis of slope stability based on nonlinear failure criterion[J].Rock and Soil Mechanics,2011,32(11):3312-3318.(in Chinese)]
[24]工程地质手册编委会.工程地质手册[M].4版.北京:中国建筑工业出版社,2011:255-300.[Editorial Board.Handbook of engineering geology[M].4th ed.Beijing:China Architecture&Building Press,2011:255-300.(in Chinese)]
[2]何思明.抗拔锚板基础承载力研究[J].地下空间,2002,22(2):145-148.[HE S M.Research on pullout capacity of anchor plate[J].Underground Space,2002,22(2):145-148.(in Chinese)]
[3]GUNN M J.Limit analysis of undrained stability problems using a very small computer[C]//Proceedings of the symposium on computer applications in geotechnical problems in highway engineering,Cambridge University,1980:5-30.
[4]MEYERHOF G G,ADAMS J I.The ultimate uplift capacity of foundations[J].Canadian Geotechnical Journal,1968,5(4):225-244.
[5]MURRAY E J,GEDDES J D.Uplift of anchor plates in sand[J].Journal of Geotechnical Engineering,1987,113(3):202-215.
[6]YU H S.Cavity expansion methods in geomechanics[M].Dordrecht:Kluwer Academic Publishers,2000.
[7]王洪涛,李术才,王琦,等.非线性破坏准则下水平浅埋条形锚板抗拔承载力的极限分析[J].工程力学,2014,31(2):131-138.[WANG H T,LI S C,WANG Q,et al.Limit analysis of ultimate pullout capacity of shallow horizontal strip anchor plate based on nonlinear failure criterion[J].EngineeringMechanics,2014,31(2):131-138.(in Chinese)]
[8]黄阜,杨小礼,赵炼恒,等.基于Hoek-Brown破坏准则的浅埋条形锚板抗拔力上限分析[J].岩土力学,2012,33(1):179-175.[HUANG F,YANG X L,ZHAO L H,et al.Upper bound solution of ultimate pullout capacity of strip plate anchor based on HoekBrown failure criterion[J].Rock and Soil Mechanics,2012,33(1):179-175.(in Chinese)]
[9]MERIFIELD R S,LYAMIN A V,SLOAN A W.Stability of inclined strip anchors in purely cohesive soil[J].Journal of Geotechnical and Geoenvironmental Engineering,2005,131(6):792-799.
[10]SARAN S,RANJAN G,NENE A S.Soil anchors and constitutive laws[J].Journal of Geotechnical Engineering,1986,112(12):1084-1100.
[11]WANG D,HU Y X,RANDOLPH M F.Threedimensional large deformation finite-element analysis of plate anchors in uniform clay[J].Journal of Geotechnical and Geoenvironmental Engineering,2010,136(2):355-365.
[12]SINGH B,MISTRI B.Pullout capacity of horizontal and inclined plate anchors in clayey soils[J].International Journal of Engineering Science and Technology,2011,3(11):7967-7974.
[13]李海亮,黄润秋,吴礼舟,等.非均质土坡降雨入渗的耦合过程及稳定性分析[J].水文地质工程地质,2013,40(4):70-76.[LI H L,HUANG R Q,WU L Z,et al.Rainfall infiltration coupling process and stability analysis of a heterogeneous soil slope[J].Hydrogeology&Engineering Geology,2013,40(4):70-76.(in Chinese)]
[14]邹新军,王英宇,赵明华,等.基于能量法的非均质地基中单桩受扭弹塑性分析[J].水文地质工程地质,2016,43(2):54-61.[ZOU X J,WANG Y Y,ZHAO M H,et al.Elastic-plastic analysis of a torsional single pile in non-homogeneous subsoil based on energy principle[J].Hydrogeology&Engineering Geology,2016,43(2):54-61.(in Chinese)]
[15]MERIFIELD R S,SLOAN S W,YU H S.Stability of plate anchors in undrained clay[J].Géotechnique,2001,51(2):141-153.
[16]刘嘉,董志良,郭伟玲.非均质饱和黏土中平板锚基础的抗拉力[J].水运工程,2008(7):1-6.[LIU J,DONG Z L,GUO W L.Uplift capacity of plate anchor foundation in saturated heterogeneous clay[J].Port&Waterway Engineering,2008(7):1-6.(in Chinese)]
[17]THO K K,CHEN Z R,LEUNG C F,et al.Pullout behaviour of plate anchor in clay with linearly increasing strength[J].Canadian Geotechnical Journal,2014,51(51):92-102.
[18]WU X N,CHOW Y K,LEUNG C F.Behavior of drag anchor in clay with linearly increasing shear strength under unidirectional and combined loading[J].Applied Ocean Research,2017,63:142-156.
[19]王洪涛,王琦,尤春安,等.考虑土体非均质和各向异性的锚索极限抗拔力研究[J].岩土力学,2013,34(8):2204-2210.[WANG H T,WANG Q,YOU C A,et al.Study of ultimate pullout force of anchor cable considering non-homogeneity and anisotropy of soil mass[J].Rock and Soil Mechanics,2013,34(8):2204-2210.(in Chinese)]
[20]CHEN W F.Limit analysis and soil plasticity[M].New York:Elsevier Scientific Publishing Company,1975.
[21]黄茂松,秦会来,郭院成.非均质和各向异性黏土地基承载力的上限解[J].岩石力学与工程学报,2008,27(3):511-518.[HUANG M S,QIN H L,GUO Y C.Upper bound solution for bearing capacity of non-homogeneous and anisotropic clay foundation[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(3):511-518.(in Chinese)]
[22]梁桥,杨小礼,张佳华,等.非均质土体中盾构隧道开挖面支护力上限分析[J].岩土力学,2016,37(9):2585-2592.[LIANG Q,YANG X L,ZHANG J H,et al.Upper bound analysis for supporting pressure of shield tunnel in heterogeneous soil[J].Rock and Soil Mechanics,2016,37(9):2585-2592.(in Chinese)]
[23]张迎宾,李亮,赵炼恒.基于非线性破坏准则的边坡稳定性极限分析[J].岩土力学,2011,32(11):3312-3318.[ZHANG Y B,LI L,ZHAO L H,et al.Limit analysis of slope stability based on nonlinear failure criterion[J].Rock and Soil Mechanics,2011,32(11):3312-3318.(in Chinese)]
[24]工程地质手册编委会.工程地质手册[M].4版.北京:中国建筑工业出版社,2011:255-300.[Editorial Board.Handbook of engineering geology[M].4th ed.Beijing:China Architecture&Building Press,2011:255-300.(in Chinese)]
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