Gibson地基与均匀地基承载力之间的相似关系
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摘要
应用弹性理论和太沙基塑性区发展的理论,探讨Gibson非均质地基的承载能力.理论推导在条形均布荷载作用下此类非均匀地基临塑区的边界方程,分析地基的临塑荷载和临界荷载.通过与均匀地基临界荷载的经典解答进行比较,考察此类非均匀地基与均匀地基临界荷载之间的相似性,进而得到各承载力系数之间解答的相似转换关系,给出相应转换系数的解析表达式.借助均匀地基承载力的解答,可将非均匀地基承载力问题求解转化为相似转化系数的计算问题,从而为非均匀地基承载力的求解提供便捷有效的途径,便于工程应用.
By means of application of elastic theory and plastic zone development theory,the bearing capacity of Gibson non-homogeneous foundation was explored.The boundary equation of this category of non-homogeneous foundation plastic zone was theoretically deduced and the critical plastic load and critical load upon the foundation were analyzed under strip uniform load.By means of comparing to the classic solution of critical load upon homogeneous foundation,the analogy of critical load between this category of non-homogeneous and homogeneous foundation was investigated,the analogous transformation relation of the solution of every capacity factor coefficients was further obtained,and the analytic expressions of corresponding transformation coefficients were given out.The problem of solutions of bearing capacity of nonhomogeneous foundation can be converted into a computation problem of analogous transformation coefficients,so that providing a easy,quick,and effective way for the solution of bearing capacity of non-homogeneous foundation and conveniencing its application in engineering.
By means of application of elastic theory and plastic zone development theory,the bearing capacity of Gibson non-homogeneous foundation was explored.The boundary equation of this category of non-homogeneous foundation plastic zone was theoretically deduced and the critical plastic load and critical load upon the foundation were analyzed under strip uniform load.By means of comparing to the classic solution of critical load upon homogeneous foundation,the analogy of critical load between this category of non-homogeneous and homogeneous foundation was investigated,the analogous transformation relation of the solution of every capacity factor coefficients was further obtained,and the analytic expressions of corresponding transformation coefficients were given out.The problem of solutions of bearing capacity of nonhomogeneous foundation can be converted into a computation problem of analogous transformation coefficients,so that providing a easy,quick,and effective way for the solution of bearing capacity of non-homogeneous foundation and conveniencing its application in engineering.
引文
[1]崔江余,宋金峰.地基临塑荷载的分析[J].工程力学,1998,15(4):96-99.
[2]ZHOU F X,LAI Y M,SONG R X.Propagation of plane wave in non-homogeneously saturated soils[J].Science China(Technological Sciences),2013,56(2):430-440.
[3]GIBSON R E,KALSI G S.The surface settlement of a linearly inhomogeneous cross-anisotropic elastic half-space[J].Zeitschrift Für Angewandte Mathematik und Physik ZAMP,1974,25(6):843-847.
[4]GIBSON R E,BROWN P T,ANDREWS K R F.Some results concerning displacements in a non-homogeneous elastic layer[J].Zeitschrift F¨ur Angewandte Mathematik und Physik ZAMP,1971,22(5):855-864.
[5]GIBSON R E,SILLS G C.On the loaded elastic half-space with a depth varying Poisson’s ratio[J].Zeitschrift Für Angewandte Mathematik und Physik ZAMP,1969,20(5):691-695.
[6]BOOKER J R,BALAAM N P,DAVIS E H.The behaviors of an elastic non-homogeneous half-space:PartⅠLine and point loads[J].International Journal for Numerical and Analytical Methods Geomech,1985,9(4):353-367.
[7]方晔,徐长节,蔡袁强.Gibson地基半透水边界一维固结分析[J].浙江大学学报(工学版),2003,37(6):646-651.
[8]ZHANG Q Y,LUAN M T,WANG Z T.Study on failure mechanism and bearing capacity of three-dimensional rectangular footing subjected to combined loading[J].China Ocean Engineering,2008,22(2):313-330.
[9]张其一,栾茂田,张小玲.复合加载下非均质地基上矩形基础的极限承载力[J].北京工业大学学报,2009,30(7):970-975.
[10]栾茂田,金崇磐,林皋.非均匀地基上的极限承载力[J].岩土工程学报,1988,10(4):14-27.
[11]秦会来,黄茂松,王玉杰,等.非均匀与各向异性地基承载力系数Nc计算[J].岩土工程学报,2010,32(8):1194-1197.
[12]赵少飞,栾茂田,范庆来,等.非均质地基承载力及破坏模式的FLAC数值分析[J].岩土力学,2006,27(11):1910-1921.
[13]李世荣,高颖,张靖华.功能梯度板与均匀板固有频率之间的相似转换[J].兰州理工大学学报,2012,38(2):158-163.
[14]徐华,李世荣.一阶剪切理论下功能梯度梁与均匀梁静态解之间的相似关系[J].工程力学,2012,29(4):161-167.
[15]周凤玺,赖远明,米海珍.非均匀地基与均匀地基解答之间的相似关系[J].岩土力学,2013,34(12):3372-3376.
[16]周凤玺,贺钇铭,赖远明.非均匀地基与均匀地基一维固结解答之间的转换关系[J].工程地质学报,2015,23(2):260-264.
[17]周凤玺,贺钇铭.非均匀地基与均匀地基承载力上限解之间的转化关系[J].兰州理工大学学报,2016,42(1):115-118.
[2]ZHOU F X,LAI Y M,SONG R X.Propagation of plane wave in non-homogeneously saturated soils[J].Science China(Technological Sciences),2013,56(2):430-440.
[3]GIBSON R E,KALSI G S.The surface settlement of a linearly inhomogeneous cross-anisotropic elastic half-space[J].Zeitschrift Für Angewandte Mathematik und Physik ZAMP,1974,25(6):843-847.
[4]GIBSON R E,BROWN P T,ANDREWS K R F.Some results concerning displacements in a non-homogeneous elastic layer[J].Zeitschrift F¨ur Angewandte Mathematik und Physik ZAMP,1971,22(5):855-864.
[5]GIBSON R E,SILLS G C.On the loaded elastic half-space with a depth varying Poisson’s ratio[J].Zeitschrift Für Angewandte Mathematik und Physik ZAMP,1969,20(5):691-695.
[6]BOOKER J R,BALAAM N P,DAVIS E H.The behaviors of an elastic non-homogeneous half-space:PartⅠLine and point loads[J].International Journal for Numerical and Analytical Methods Geomech,1985,9(4):353-367.
[7]方晔,徐长节,蔡袁强.Gibson地基半透水边界一维固结分析[J].浙江大学学报(工学版),2003,37(6):646-651.
[8]ZHANG Q Y,LUAN M T,WANG Z T.Study on failure mechanism and bearing capacity of three-dimensional rectangular footing subjected to combined loading[J].China Ocean Engineering,2008,22(2):313-330.
[9]张其一,栾茂田,张小玲.复合加载下非均质地基上矩形基础的极限承载力[J].北京工业大学学报,2009,30(7):970-975.
[10]栾茂田,金崇磐,林皋.非均匀地基上的极限承载力[J].岩土工程学报,1988,10(4):14-27.
[11]秦会来,黄茂松,王玉杰,等.非均匀与各向异性地基承载力系数Nc计算[J].岩土工程学报,2010,32(8):1194-1197.
[12]赵少飞,栾茂田,范庆来,等.非均质地基承载力及破坏模式的FLAC数值分析[J].岩土力学,2006,27(11):1910-1921.
[13]李世荣,高颖,张靖华.功能梯度板与均匀板固有频率之间的相似转换[J].兰州理工大学学报,2012,38(2):158-163.
[14]徐华,李世荣.一阶剪切理论下功能梯度梁与均匀梁静态解之间的相似关系[J].工程力学,2012,29(4):161-167.
[15]周凤玺,赖远明,米海珍.非均匀地基与均匀地基解答之间的相似关系[J].岩土力学,2013,34(12):3372-3376.
[16]周凤玺,贺钇铭,赖远明.非均匀地基与均匀地基一维固结解答之间的转换关系[J].工程地质学报,2015,23(2):260-264.
[17]周凤玺,贺钇铭.非均匀地基与均匀地基承载力上限解之间的转化关系[J].兰州理工大学学报,2016,42(1):115-118.