近场动力学理论在区域地面沉降建模中的应用研究

地面沉降是由自然和人类活动共同作用导致的缓变性地质灾害，是区域可持续发展的重要影响因素。以往地面沉降在建模时需要地裂缝等不连续结构的位置、走向、深度等信息，在构建微分方程模拟时需假设模型连续，这对开展地面沉降-地裂缝-地面塌陷一体化模拟带来一定的局限性。于2000年出现的近场动力学理论提出以积分形式描述材料受力过程，方法具有无需先验知识与连续性假设的优点，在材料的疲劳、损伤、断裂等模拟研究中展现出良好的应用前景。本文综述了其在岩石水力压裂、滑坡、饱水岩土材料等领域的研究进展；提出了应用近场动力学进行区域地面沉降建模求解的一般方法；结合InSAR技术获取的沉降信息、三维地震频谱谐振勘探技术获取的地下结构与密度信息等，提出了模型的反演调参与优化方法。以北京东部梨园-台湖镇-张家湾镇区域为实验区，建立了其4 km×6 km范围、0.2 km深度的近场动力学地面沉降模型，以实验区地下水位月均下降速率为边界条件，对2007—2010年地面沉降过程进行模拟。模拟结果与实测值的平均绝对误差为18 mm，表明近场动力学在地面沉降建模中有较好的适用性。

Application of Peridynamic Theory in Regional Land Subsidence Modeling

Land subsidence is an important factor that influences the sustainable development of a region. Due to the complexity of land subsidence, the uncertainty and risk caused by land subsidence disasters are increasing. Therefore, new methods need to be developed to quantify the nonlinear land subsidence processes, identify emerging risk, and improve urban resilience. In this paper, the necessity of introducing peridynamic to land subsidence modeling is discussed by analyzing the progress and shortcomings of current land subsidence modeling. For natural discontinuous structures such as fractures and faults, current deterministic models based on differential equations are insufficient to describe land subsidence. Therefore, the peridynamic theory which is suitable for discontinuous and nonlinear characteristics is introduced. The peridynamic theory (PD) describes the mechanical behavior of matter by solving integral equations and has advantages in analyzing discontinuous and multi-scale problems. The applicability of peridynamic in land subsidence is analyzed from the aspects of material properties and modeling methods, respectively. By establishing a peridynamic model of land subsidence, discontinuous disasters such as ground crack and ground collapse can be included, so as to realize the multi-field and multi-scale recognition of land subsidence under a unified framework. In the light of the “Higher-bigger-deeper” urban construction, combined with the CAS-ESM, the simulation of future evolution of ground subsidence and ground fractures can be carried out. However, there are still problems to be solved in the interdisciplinary research, such as the reasonable generalization of material properties, material structure, and the balance between operation accuracy and operation cost. Then, based on theoretical principles, the modeling method, solving process, and optimization method of peridynamic land subsidence model are given. Besides the establishment, solution and optimization of the model, a variety of spatial monitoring methods and data are also needed, e.g., subsidence data monitored by InSAR technology, the underground structure and density information obtained by Seismic Frequency Resonance Technology (SFRT), bedrock and stratified scale data, groundwater level data, building information data, and road network data. In this paper, a peridynamic land subsidence model with a range of 4km*6km and a depth of 0.2 km is established in Liyuan-Taihu -Zhangjiawan area in the eastern Beijing, and the evolution process of land subsidence is simulated by using the monthly average rate of groundwater level decline from 2007 to 2010 as the boundary condition. The mean absolute error between the simulated and the measured values is 18mm, which verifies the effectiveness of this interdisciplinary research. The peridynamic theory has superiority in the field of materials and the study of fatigue, damage, fracture, and so on. Our study provides new ideas and new methods for regional land subsidence modeling. Furthermore, with the support of big data, cloud computing platforms, and Geo-AI, new opportunities are emerging for preventing, controlling, slowing down, and avoiding land subsidence hazards.