用薄层法分析层状地基中条形基础的阻抗函数

Analysis of Impedance Functions of Strip Foundations Embedded in Stratified Soils by Using Thin Layer Method

薄层法是分析和模拟弹性波在层状介质中传播的一种半解析半数值方法,以往薄层法在柱坐标体系中建立求解方程,并通过直角坐标系和柱坐标系的转化关系而得到直角坐标系中的解答,本文从直角坐标直接推导了层状地基在无限长线荷载作用下的计算公式,求解了层状地基在垂直方向和水平方向上无限长线激振荷载作用下薄层法位移基本解。结合容积法得出了层状地基中基础-地基动力相互作用方程及条形基础阻抗函数的计算公式。本文计算了半无限弹性地基以及基岩上覆盖层在无限长简谐线荷载作用下的位移反应,计算了半无限弹性地基以及基岩上覆盖层地基中明置与埋置条形基础的地基阻抗函数。计算结果与已有的研究结果的比较表明两者吻合较好,验证了本文方法的适用性。

The thin layer method（TLM） is a semi- analytical and semi- numerical approach for the analysis of elastic wave propagation in stratified media. TLM usually established the solution equations in the circular cylindrical coordinate system, and obtained the result in Cartesian coordinate by the relationship of the two kinds of coordinate system. The formulas of calculating the response of stratified soil under the harmonic infinite long line load were educed. And the complex displacement of the soil under the vertical and horizontal harmonic infinite long line load were calculated. The governing equation of dynamic soil foundation interaction and the formula of impedance functions and dynamic flexible functions of strip foundation were derived by flexible volume method and fundamental displacement solutions of thin layer method. The method was certified by comparing the complex displacement of a half space and a soil layer on a rigid rock under the harmonic line load with other method. The flexible function of surface strip foundation and embedded foundation in a half space or soil layer on a rigid rock were compared with other numerical result. The results show well agreement with other numerical results. The method is feasible for the analysis of impedance functions of strip foundations in elastic stratified.