堆载预压径竖向固结等体积应变解答

Equal volumetric strain solutions for radial and vertical consolidation with vertical drains under surcharge preloading

现有的含竖向排水体地基固结问题的解析解答大都是在传统的等竖向应变假设基础上建立的,而且在考虑涂抹区土体的渗流和压缩作用方面,还没有真实地体现出涂抹区土体的竖向渗透系数和体积压缩系数,其对地基固结的影响也尚不明确。为此,针对含竖向排水体地基径竖向同时固结的轴对称问题,采用等体积应变假设,考虑井阻作用、涂抹作用、随时间线性堆载预压以及地基附加球应力任意分布,推导了完整的径竖向固结微分方程的解答,给出了超静孔隙水压力和固结度的显式表达式,分析了侧向变形即泊松比效应以及涂抹区土体的竖向渗透系数和三维体积压缩系数对地基整体平均固结度的影响。结果表明,泊松比效应较为明显,基于传统的等竖向应变假设的解答高估了地基的固结速率;不考虑涂抹区土体体积压缩的解答虽然也高估了地基的固结速率,但影响有限;而涂抹区土体的竖向渗透系数对于地基固结的影响则几乎可忽略不计。

The available analytical solutions for ground consolidation with vertical drains are mostly established based on the traditional equal vertical strain assumption. Moreover, in the aspect of considering the effects of seepage and compression of the soil within the smeared zone, the vertical hydraulic conductivity and the coefficient of volume compressibility of the smeared soil are not really embodied, and then their impacts on the ground consolidation are not clear. Therefore, the equal volumetric strain assumption is adopted to solve the axisymmetric problem of radial and vertical ground consolidation with vertical drains. The effects of well resistance and smear are considered, together with a linearly time-varied surcharge preloading and an arbitrarily distributed mean stress increase in the ground. Solutions are derived from a complete set of partial differential equations of radial and vertical consolidation. Explicit expressions for the excess pore water pressure and degree of consolidation are presented. The influences of the lateral deformation, i.e., Poisson＇s ratio effect, the vertical hydraulic conductivity and the three-dimensional coefficient of volume compressibility of the smeared soil, on the overall mean values of degree of ground consolidation are analyzed. It shows that the Poisson＇s ratio effect is significant. The solutions derived based on the traditional equal vertical strain assumption overestimate the consolidation rate of the ground. The solutions derived without consideration of the volume compressibility of the smeared soil also overestimate the consolidation rate, but to a limited extent. Nevertheless, the influence of the vertical hydraulic conductivity of the smeared soil on the ground consolidation is negligible.