不完全透水边界条件的数学物理描述及其固结理论

Fully drained or undrained consolidation boundary is not many observed in engineering practice. Impeded drainage boundary opens up the space for studying consolidation problems. However, a comprehensive literature review reveals that the impeded drainage boundary condition is presently man-made constructed and expressed in a single form. In this proposal horizontal sand blanket and woven geotextile are studied. The two media are representative in engineering practice but have significant differences in thickness, seepage path and seepage law. Experimental and theoretical analyses are carried out to establish the mathematical and physical descriptions of their boundary conditions. Analytical solutions for the corresponding consolidation theory are derived. For the horizontal sand blanket, predominated horizontal seepage path and impervious top are considered. A plane strain consolidation test apparatus is developed. Its boundary condition and influencing parameter are determined from the analysis using the seepage and consolidation theories. Analytical solutions are derived for two-dimensional consolidation and axisymmetrical radial and vertical simultaneous consolation. For the woven geotextile, a seepage test apparatus is developed considering various water pressures and heads. Its seepage law, boundary condition and influencing parameter are determined from the experimental study and hydrodynamics analysis. Analytical solutions are derived for one-dimensional consolidation and axisymmetrical radial consolation. Finally the above-mentioned research achievements will be applied to the consolidation deformation calculation in the ground improvement techniques, and the slurry-filled geo-tube or geo-bag embanking and dewatering techniques.

完全透水或不透水的固结边界在现实工程中并不多见，不完全透水（俗称半透水）边界为固结问题研究开辟了新的空间。然而，综观现状发现，不完全透水边界条件形式单一且纯属人工构造。为此，以水平砂垫层和有纺土工织物这两种有工程代表性但厚差明显的介质为研究对象，针对其渗流路径和渗透规律的不同特点，通过试验和理论分析，建立其边界条件的数学物理描述，并推求相应的固结理论解答。对于水平砂垫层，考虑水平向为主的渗流路径及其顶面完全不透水的工况，研制平面应变固结实验装置，并运用渗流和固结理论分析，确定其边界条件和影响参数，推求二维固结和轴对称径竖向同时固结的解析解答。对于有纺土工织物，研制不同水压力和水头差作用下的渗透实验装置，通过试验研究并结合水动力学分析，确定其渗透定律，建立边界条件和影响参数，推求一维固结和轴对称径向固结的解析解答。最终将研究成果应用于解决地基处理、土工管袋充泥筑堤和脱水技术中的固结变形计算。

针对软土地基处理工程实践中常遇的不完全透水边界条件下的固结问题，研制了模拟含水平排水砂垫层地基的平面应变固结实验装置，以及土工织物多功能渗透实验装置，通过试验研究，揭示了水平排水砂垫层参数对地基固结效率的影响规律、土工织物覆土条件下的渗透特性、以及土工织物作为不完全透水边界条件下的固结特性。通过数值和解析分析，提出了评估地基固结效率的综合考虑待固结土体参数、不完全透水介质参数、以及塑料排水板参数的集总参数，分析了集总参数与地基固结效率之间的关系，确定了集总参数的最优控制指标，并建立了满足完全透水边界条件的不完全透水介质参数的简化设计计算方法。此外，还运用Laplace变换和分离变量法，综合考虑井阻和涂抹作用、加载过程、附加应力的分布等因素，推导得到了涵盖不完全透水边界和完全透水边界条件下一维、二维和轴对称固结理论的解析解答。通过计算结果与工程现场实测结果的对比，验证了所建立的理论方法的适用性。所建立的不完全透水边界条件下的固结理论是对传统固结理论的有益补充和完善，并为软土地基排水固结法处理的设计计算提供理论依据。

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