采水型地裂缝的数学模型和数值模拟研究

Earth fissure caused by excessive groundwater withdrawal is called ‘Earth Fissure Caused by Pumping Water’. It has occurred in many regions in China, such as Shanxi Province, Shaanxi Province, Hebei Province, Henan Province, Shandong Province, Anhui Province, Jiangsu Province and Beijing City etc., totally more than ten provinces and cities involved. It seriously influences the safety of people and stable development of society. The successful numerical simulation of earth fissure to large extent depends on the good simulation of three-dimensional land subsidence. It is necessary to develop the coupled model of three-dimensional land subsidence and earth fissures with viable parameters based on the complicated deformation. The finite element method (FEM) and interface element(IE) method will be combined to solve the three-dimensional land subsidence model and earth fissure model. The vulnerability assessment method will be developed based on the typical earth fissure conceptual models and the sensitivity analysis of the main impacts and parameters. Numerical simulation of a couple of earth fissures in the typical Su-Xi-Chang area with earth fissures occuring will be a case study of the proposed three dimensional land subsidence and earth fissure coupled models and the combination of FEM and IE. No similar study was reported.

过量开采地下水引发的地裂缝称为“采水型”地裂缝,在我国的山西、陕西、河北、河南、山东、安徽、江苏和北京等十余省市均有发育，严重影响人类安全和社会稳定发展。地裂缝模拟是否成功很大程度上依赖于三维地面沉降模拟精度，有必要建立复杂变形条件下三维变系数地面沉降与地裂缝耦合模型。将有限元方法和界面元方法联合求解三维地面沉降和地裂缝耦合模型。针对典型地裂缝概念模型中主要影响因素和参数的敏感性分析，建立地裂缝脆弱性评价方法。通过苏锡常典型地裂缝发育区多条地裂缝模拟，对所建三维地面沉降和地裂缝耦合模型，对有限元与界面元联合的数值方法进行检验。国内外未见同类研究。

过量开采地下水引发的地裂缝称为“采水型”地裂缝,在我国的山西、陕西、河北、江苏和北京等十余省市均有发育，严重影响人类安全和社会稳定发展。政府部门在制定城市发展规划及地裂缝防治对策时，迫切需要知道未来地裂缝的发展趋势，希望提供地裂缝的预警预报。要做好这样的预警预报一个好的地裂缝模型是必不可少的。此外，地裂缝的成因机制虽有认识但远不够深入，因此也需要建立基于地裂缝成因机制的数学模型，进一步厘清地裂缝的诱发因素，揭示地裂缝发育过程。本次研究总结了三种最典型的地裂缝概念模型，即“基岩潜山型地裂缝”，“先期断层型地裂缝”和“含水层厚度突变型地裂缝”。建立三维变系数地面沉降与地裂缝耦合模型，具体包括三维地质力学模型(Geomechanical Model-GM)和地裂缝模型(Earth Fissure Model-EF Model)。应用有限元和界面元联合的数值方法实现了所建立的GM-EF耦合地裂缝模型的求解。开展了地裂缝数学模型的广义混沌多项式展开（generalized polynomial chaos expansion-GPC） 替代模型和梯度提升树（gradient boosting tree-GBT）替代模型研究。采用Sobol法、RBD-FAST法、以及基于GPC和GBT替代模型进行了地裂缝发生及发育程度的参数敏感性分析。对于三种典型地裂缝发育的敏感性分析均表明含水系统的特殊几何结构特征和孔隙水压力变化分别是控制地裂缝开裂第一和第二敏感参数。通过参数的多元回归分析，提出对应三种典型地裂缝脆弱性的简单易用的评估方法。通过无锡光明村野外3条地裂缝的成功模拟，验证了所建GM-EF地裂缝模型和所采用的有限元-界面元数值方法的有效性，可以有效刻画实际野外多条地裂缝的发育过程。上述研究成果从理论上建立了可靠的包括地裂缝数学模型和数值算法的地裂缝数值模拟体系，通过参数敏感性分析和脆弱性分析研究推进了对地裂缝成因机理的认识；从实际应用上为苏锡常等地裂缝灾害区的灾害防治提供了科学支撑。

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