斜坡地基单侧滑移破坏模式及承载力上限解

ONE-SIDE SLIP FAILURE MECHANISM AND UPPER BOUND SOLUTION FOR BEARING CAPACITY OF FOUNDATION ON SLOPE

首先建立了斜坡地基单侧滑移破坏模式,其破坏区域中的刚性滑块绝对速度在过渡区径向和切向可同时发生变化,形成网格状刚性滑块体系。刚性滑块的速度相容和塑性流动约束条件由速度矢量场所确定。增加刚性滑块数目,可引入较多的优化变量,间接减少构造破坏模式时的假定条件,得到更为灵活破坏模式的图式和较优的地基承载力系数上限解。其次利用Matlab编制求解程序。根据破坏模式和速度场的几何条件及上限原理进行参数递推,得到地基承载力系数的目标函数及约束条件,将其转化为数学优化问题进行求解。最后进行斜坡地基承载力系数计算分析,得到不同条件下斜坡地基承载力系数Nγ和Nc的计算图表,探讨了斜坡地基承载力的影响因素及经优化得到的破坏模式和相应速度场的图式。

Firstly,a one-side slip failure mechanism was proposed,wherein the foundation on slope behaves like a system of mesh-like rigid blocks with changeable velocities and directions in transition area.The velocity compatibility and plastic flow rule were satisfied by the corresponding velocity field.More optimization variables were introduced and a flexible failure mechanism was obtained by increasing the number of the rigid blocks.It was shown that some assumptions associated with the failure mechanism can be relieved,yielding a better upper bound solution for the bearing capacity factor.Secondly,calculation program was created using Matlab software.Calculation parameters were deduced based on the upper bound theory and geometric conditions of the failure mechanism and the velocity field.The calculation of bearing capacity factors were converted into a mathematical optimization problem when the object function and constrain conditions were established.Finally,the bearing capacity factors of foundation on slope were analyzed and the computation chart of Nγ and Nc was obtained.And,the influence factors of bearing capacity factor and the figures of the optimized failure mechanism and velocity field were also discussed.