广义Gibson地基内部作用线源荷载的基本解

针对广义Gibson地基在埋藏线源荷载作用下的静力学问题,通过将内源线荷载等效为在相同深度范围内连续的集中点荷载的累加,采用Hankel积分变换方法,再结合具体的边界条件,推导得到地基土体在内源点荷载作用下的Hankel变换域中的解,并利用Hankel逆变换将变换域内的解转换为物理域内的积分形式解。然后对该解沿深度方向积分求得了地基土体在三种沿深度分布线荷载作用下的竖向位移解,并对地基内部沿深度分布线源荷载作用下地基表面土体变形问题通过具体算例,运用数值积分计算方法,分析了地基土体的非均质性、荷载分布深度等因素对地基表面土体竖向位移的影响。结果表明:①地基土体的非均质性对地基表面竖向位移有较大影响,相对而言,线源荷载竖向分布深度及荷载分布形式对地表竖向位移的影响较小,且地表竖向位移主要受浅层荷载的影响;②荷载分布深度对地表位移的影响主要体现在土体非均质性较小情况下,且在荷载沿深度减小分布时最为显著。

The basic solution of the line source load in the generalized Gibson subgrade

For the static problem of the generalized Gibson subgrade under the burial line source load, the Hankel integral transformation method is combined with the specific boundary conditions by equating the internal source load with the accumulation of continuous concentrated point loads in the same depth range. The solution of the subgrade soil in the Hankel transform domain under the internal source load is derived, and the Hankel inverse transform is used to transform the solution in the transform domain into the integral form solution in the physical domain.Then the vertical displacement solutions of the subgrade soil under three kinds of depth distribution line loads are obtained by integrating the solution along the depth direction, and the influence of the heterogeneity of the subgrade soil and the depth of load distribution depth on the vertical displacement of the subgrade surface soil is analyzed by using the numerical integral method for the deformation problem of the subgrade surface under the action of the depth distribution line source load. The results show that: (1) the heterogeneity of subgrade soil has a great influence on the vertical displacement of subgrade surface. Relatively speaking, the vertical distribution depth and load distribution form of line source load have little effect on the vertical displacement of the surface, and the vertical displacement of the surface is mainly affected by the shallow load. (2) the influence of load distribution depth on surface displacement is mainly reflected in the case of small soil heterogeneity, and it is the most significant when the load decreases along the depth.