轴对称条件下非饱和土地基固结理论及其验证研究

In the design and construction of freeway and high-speed railway subgrade, sand drains, replacement, dynamic compaction etc. are usually adopted to reinforce the soft foundation, and the foundation deformation is dominated ty the consolidation settlement. While, the major portion of soil deposits above a phreatic line may be unsaturated. Therefore, it is important to study the theory and behavior of consolidation for unsaturated soils. The applicant proposes to obtain the semi-analytical solutions to the axisymmetric consolidation equations of unsaturated soils by using the finite sine (cosine) and Laplace transforms to investigate the consolidation behavior based on the axisymmetric consolidation theory. The main research contents are as follows:.1) Axisymmetric consolidation of unsaturated soils under homogeneous and mixed drainage boundaries subjected to time-dependent loading;.2) Axisymmetric consolidation of unsaturated soils considering the influence of sand cushion at the top surface subjected to time-dependent loading;.3) Axisymmetric consolidation of unsaturated soils considering the smear effect of sand drains subjected to time-dependent loading..Then, the verification will be done by using the methods of generated solution, the finite difference solution and experiment. Finally, the axisymmetric consolidation behavior of unsaturated soil will be outlined. The expected results will provide a theoretical basis for the consolidation settlement control of the unsaturated soil foundation in the national major engineering. Moreover, it is of great significance to extend the practical application of the consolidation theory for unsaturated soils.

在高速公路和高速铁路路基的设计和施工中，通常采用砂井、换填和强夯等方法进行地基处理，处理后的地基以固结沉降变形为主。而位于地下水位线以上的地基土往往处于非饱和状态，因此研究非饱和土地基固结理论并进行固结特性分析非常必要。本项研究基于轴对称非饱和土固结理论，采用有限正（余）弦变换和拉普拉斯变换，求解以下情况的轴对称非饱和土地基固结方程，并对其进行相应的固结特性研究：1）任意荷载作用下考虑均质边界和混合边界的轴对称非饱和土地基固结；2）任意荷载作用下考虑表面砂垫层影响的轴对称非饱和土地基固结；3）任意荷载作用下考虑砂井涂抹效应的轴对称非饱和土地基固结。然后采用退化法、有限差分法和试验方法验证一系列半解析解的正确性，最终提出完整的轴对称非饱和土地基固结特性。预期成果将为国家重大工程非饱和土地基处理的固结沉降控制提供理论依据，也对拓展非饱和土固结理论的实际应用具有重要意义。

本项目基于Fredlund等提出的非饱和土天然地基固结理论对非饱和土中超孔隙水压力和超孔隙气压力控制方程进行解耦简化，得到了非饱和土天然地基的超孔隙气压力和水压力的偏微分方程，应用傅里叶变换(Fourier变换)、拉普拉斯变换(Laplace变换)、微分算子法、有限汉克尔变换(Hankel变换)对所得到的偏微分方程进行求解，具体从如下几方面取得了研究进展：.1).考虑应力扩散效应，将外荷载假设为沿深度和时间同时变化的荷载作用，将其引入一维非饱和土固结理论，分别得到了考虑荷载沿深度和时间同时变化条件下的单层和多层一维非饱和土固结问题的解答；.2).考虑到地基处理过程中砂垫层或排水板非满铺的情况，将两维平面应变非饱和土体表面的边界当作分布式边界条件，并将其与两维平面应变非饱和土固结理论相结合，得到了相应的半解析解答，并开展了分布式边界条件下两维平面应变非饱和土固结特性。.3).目前考虑非饱和土固结理论研究中考虑到的都是随时间连续变化的荷载，而实现工程中，往往随着施工进度的不同会存在各种各样的分段循环荷载，因此考虑分段循环荷载作用，对等应变条件下轴对称非饱和土固结问题开展了研究。.4).轴对称固结问题往往会存在等应变假设和自由应变假设两种情况，既有研究往往都是在等应变条件下完成的，但是自由应变和等应变条件下的非饱和土固结显然存在明显区别，因此作者针对自由应变条件下考虑均质边界和混合边界对轴对称非饱和土固结问题进行研究。