斜坡浅埋水平条形锚板抗拔承载力的极限分析
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摘要
针对山区和丘陵等复杂地形下浅埋锚板抗拔承载力计算问题,基于极限分析上限定理、非线性Mohr-Coulomb强度准则及其关联流动法则,构造了斜坡浅埋水平条形锚板的曲线型破裂机制和机动许可速度场,采用变分极值原理获得了其上方土体破裂面方程和抗拔承载力的上限解,分析了斜坡倾角和锚板埋深对锚板抗拔承载力的影响。结果表明:随着斜坡倾角的增大,锚板抗拔承载力逐渐减小,此时其上方两侧土体破裂面不再对称且整体向下坡侧偏移;锚板抗拔承载力及其上方两侧土体破裂面宽度均随着埋深增大而增加;锚板埋深越小,斜坡倾角对其抗拔承载力的影响越大,应在计算中予以考虑,以更合理地反映斜坡浅埋水平条形锚板的抗拔承载特性。
Aiming at calculating the ultimate pullout capacity of a shallow horizontal strip anchor plate embedded in complicated topographical regions,e.g.,mountainous areas,a kinematic admissible velocity field of the curved failure mechanism is constructed for the shallow horizontal strip anchor plate embedded in slope,based on the upper bound limit analysis theorem,the nonlinear Mohr-Coulomb failure criterion as well as the associated flow rules.The ultimate pullout force and failure mechanism are deduced using the variation minimum principle.Influences of the inclination angle and embedded depth on the ultimate pullout force are discussed in detail.The results show that the ultimate pullout force of the anchor plate decreases with the increasing inclination angle and the failure planes of the above ground are no longer symmetrical with an obvious shifting to the down side of the slope.Along with the increasing embedded depth,the ultimate pullout force of the anchor plate increases with a larger failure scope of the above ground.The inclination angle has a greater impact on the ultimate pullout force of the anchor plate with a smaller embedded depth.This effect should be taken into account for reasonably characterizing the ultimate bearing feature of a shallow horizontal strip anchor plate embedded in slope.
Aiming at calculating the ultimate pullout capacity of a shallow horizontal strip anchor plate embedded in complicated topographical regions,e.g.,mountainous areas,a kinematic admissible velocity field of the curved failure mechanism is constructed for the shallow horizontal strip anchor plate embedded in slope,based on the upper bound limit analysis theorem,the nonlinear Mohr-Coulomb failure criterion as well as the associated flow rules.The ultimate pullout force and failure mechanism are deduced using the variation minimum principle.Influences of the inclination angle and embedded depth on the ultimate pullout force are discussed in detail.The results show that the ultimate pullout force of the anchor plate decreases with the increasing inclination angle and the failure planes of the above ground are no longer symmetrical with an obvious shifting to the down side of the slope.Along with the increasing embedded depth,the ultimate pullout force of the anchor plate increases with a larger failure scope of the above ground.The inclination angle has a greater impact on the ultimate pullout force of the anchor plate with a smaller embedded depth.This effect should be taken into account for reasonably characterizing the ultimate bearing feature of a shallow horizontal strip anchor plate embedded in slope.
引文
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[17]ZHANG X J,CHEN W F.Stability analysis of slopes with general nonlinear failure criterion[J].International Journal for Numerical and Analytical Methods in Geomechanics,1987,11(1):33-50.
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[2]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].Engineering Mechanics,2014,31(2):131-138.(in Chinese)]
[3]余生兵,黄茂松.基于组合块体集的浅埋条形锚板上限分析[J].岩石力学与工程学报,2011,30(5):1049-1056.[YU S B,HUANG M S.Upper bound analysis of horizontally embedded anchors based on block set mechanism[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(5):1049-1056.(in Chinese)]
[4]茜平一,刘祖德,刘一亮.浅埋斜拔锚板板周土体的变形破坏特征[J].岩土工程学报,1992,14(1):62-66.[QIAN P Y,LIU Z D,LIU Y L.Distortion and failure characteristics of shallow buried inclined anchors[J].Chinese Journal of Geotechnical Engineering,1992,14(1):62-66.(in Chinese)]
[5]胡伟,刘顺凯,邹贵华,等.竖向条形锚定板水平拉拔极限承载力统一理论解研究[J].岩土工程学报,2018,40(2):296-304.[HU W,LIU S K,ZOU G H,et al.Unified theoretical solution for ultimate bearing capacity of vertical strip anchor[J].Chinese Journal of Geotechnical Engineering,2018,40(2):296-304.(in Chinese)]
[6]许华青,卢伟.粉土中锚板抗拔模型试验研究[J].建筑工程技术与设计,2017(28):1440-1450.[XUH Q,LU W.Uplift test study on strip anchor in silt soil[J].Architectural Engineering Technology and Besign,2017(28):1440-1450.(in Chinese)]
[7]KUMAR J.Uplift resistance of strip and circular anchors in a two layered sand[J].Journal of the Japanese Geotechnical Society of Soils and Foundations,2003,43(1):101-107.
[8]KUMAR J,KOUZER K M.Vertical uplift capacity of horizontal anchors using upper bound limit analysis and finite elements[J].Canadian Geotechnical Journal,2008,45(5):698-704.
[9]黄茂松,余生兵.基于块体集上限法的砂土中条形锚板抗拔承载力分析[J].岩土工程学报,2013,35(2):201-207.[HUANG M S,YU S B.Pull-out capacity of strip anchor plate in sand based on block set mechanism[J].Chinese Journal of Geotechnical Engineering,2013,35(2):201-207.(in Chinese)]
[10]赵炼恒,李亮,杨小礼,等.非线性破坏准则下法向受力条形浅锚抗拔力上限计算方法[J].中南大学学报(自然科学版),2009,40(5):1444-1450.[ZHAO L H,LI L,YANG X L,et al.Calculating method of upper bound for ultimate pullout capacity of Vertically loaded strip plate anchors based on nonlinear Mohr-Coulomb failure criterion[J].Journal of Central South University(Science and technology),2009,40(5):1444-1450.(in Chinese)]
[11]张晓曦,苏谦.倾斜荷载下条形锚板破裂面与极限抗拔承载力[J].地下空间与工程学报,2014,10(1):122-127.[ZHANG X X,SU Q.Ultimate uplift capacity of strip anchor plates and position of failure surfaces under inclined loads[J].Chinese Journal of Undergrourd Space and Engneering,2014,10(1):122-127.(in Chinese)]
[12]黄明华,胡倩,黄炎杰,等.非均质地基浅埋水平条形锚板承载力上限分析[J].水文地质工程地质,2017,44(6):37-43.[HUANG M H,HU Q,HUANG Y J,et al.Upper bound analysis on pullout capacity of shallow horizontal strip anchor plate embedded in non-homogeneous soils[J].Hydrogeology&Engineering Geology,2017,44(6):37-43.(in Chinese)]
[13]MERIFIELD R S,LYAMIN A V,SLOAN S W.Stability of inclined strip anchors in purely cohesive soil[J].Journal of Geotechnical and Geoenvironmental Engineering,2005,131(6):792-799.
[14]MERIFIELD R S,SLOAN S W.The ultimate pullout capacity of anchors in frictional soils[J].Canadian Geotechnical Journal,2006,43(8):852-868.
[15]FRALDI M,GUARRACINO F,Limit analysis of collapse mechanisms in cavities and tunnels according to the Hoek-Brown failure criterion[J].International Journal of Rock Mechanics&Mining Sciences,2009,46(4):665-673.
[16]谭亦高,左仕,胡世红,等.三维圆形浅埋锚板极限抗拔力非线性上限解析[J].铁道科学与工程学报,2017,14(6):1167-1173.[TAN Y G,ZUO S,HU S H,et al.Study on the ultimate pullout capacity of 3-D shallow circle plate anchors[J].Journal of Railway Science and Engineering,2017,14(6):1167-1173.(in Chinese)]
[17]ZHANG X J,CHEN W F.Stability analysis of slopes with general nonlinear failure criterion[J].International Journal for Numerical and Analytical Methods in Geomechanics,1987,11(1):33-50.
[18]DRESCHER A,CHRISTOPOULOS C.Limit analysis slope stability with nonlinear yield condition[J].International Journal for Numerical and Analytical Methods in Geomechanics,1988,12(3):341-345.
[19]胡卫东,谭建辉,曾律弦,等.变形协调条件下非线性破坏准则的加筋土坡临界高度上限解[J].水文地质工程地质,2018,45(4):45-51.[HU W D,TAN J H,ZENG L X,et al.Upper bound solution of critical heights of reinforced soil slope based on the nonlinear failure criterion and compatibility of deformation[J].Hydrogeology&Engineering Geology,2018,45(4):45-51.(in Chinese)]
[20]曹卫华,郭正.最优化技术方法及MATLAB的实现[M].北京:化学工业出版社,2005:58-110.[CAO W H,GUO Z.Optimization technique and its realization in MATLAB software[M].Beijing:Chemical Industry Press,2005:58-110.(in Chinese)]