基坑分级开挖作用下均质饱和地基Biot固结解析解

ANALYTICAL SOLUTION OF BIOT CONSOLIDATION FOR A HOMOGENEOUS SATURATED SOIL UNDERGOING STAGED EXCAVATION

  • 摘要: 基坑开挖带来的卸荷作用不可避免地导致坑底土体发生逆固结变形。基于Biot固结理论,建立了基坑分级开挖作用下均质饱和地基逆固结模型,利用Laplace-Fourier变换法进行求解,得到地基土体的位移和超静孔压解析解。通过与数值模拟结果和现场监测数据的对比,验证了解答的正确性。参数分析表明:地基水平渗透系数越大,则固结速率越快,开挖结束时的坑底回弹量越大;地基回弹模量的增大会减小坑底回弹量,加快固结速率,能够有效地控制基坑稳定性;地基泊松比对基坑开挖期间的坑底回弹量几乎无影响;开挖结束时的坑底回弹量会随开挖工期的增加而增大;在工期不变的多级开挖情况下,最后一级的开挖速率越大则开挖结束时的坑底回弹量越小,累积的负超静孔压越大。

     

    Abstract: The rebound at the bottom of a foundation pit inevitably occurs due to the excavation’s unloading effect. This effect induces reverse consolidation deformation in the bottom soil. Based on the Biot’s consolidation theory, the reverse consolidation model of a homogeneous saturated foundation subjected to staged excavation is established. The Laplace-Fourier transform method is employed to solve the model, yielding analytical solutions for displacement and excess pore-water pressure of foundation soils. The solutions are validated by comparing them with numerical simulation results and field monitoring data. Parameter analysis shows that a larger horizontal permeability coefficient accelerates consolidation and increases rebound after excavation. An increased foundation rebound modulus reduces rebound and speeds up consolidation, effectively enhancing foundation pit stability. The Poisson's ratio of the foundation has minimal influence on soil rebound during excavation. The total rebound at the end of excavation increases with the construction period’s duration. In multi-stage excavation with the same total construction period, a higher excavation rate in the last stage results in a smaller rebound and a larger accumulated negative excess pore-water pressure.

     

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