Numerical simulation of seismic wave propagation: solution verification

岩土地震工程建模的未来将几乎完全基于基于性能的地震设计理念，即基于位移或变形的设计理念。岩土结构在地震作用下变形的真实数值模拟是非常复杂的。虽然有许多先进的工具可用，但在评估数值分析结果时提出的一个主要问题是：“我们可以(应该)在多大程度上相信数值模拟？”通过验证和验证，获得了对数值分析结果的信任。验证确定数值模型是否正确地解决了所需的数学方程，而验证确定了模型的代表性程度。这项提案将对FLAC3D程序进行详细和关键的验证，以解决地震波传播问题。验证将包括通过将程序的性能与一套关于弹性动力学和孔弹性动力学问题的数学解进行比较来评估程序的数值精度。数值模拟的关键要素，如空间和时间离散，以及初始和边界条件，将与嵌入的固体-流体相互作用的耦合公式一起研究。此外，程序中新实现的高级非线性模型将与OPENSEES程序中的模型进行比较，以解决各种验证问题。这些计算平台和预期的模型在学术界和高级工程实践中得到了越来越多的应用，因此，这项研究是朝着支持进一步研究高级地震波传播数值模拟的方向迈出的重要一步。这项建议的结果还将使人们更好地了解地震波建模过程中的作用机理，使加拿大的专业实践能够利用这项研究的结果来开发更安全、更可靠和更经济的设计。

The future of modeling in geotechnical earthquake engineering will be based almost exclusively onPerformance-Based Seismic Design philosophy that is based on displacements or deformations. A realisticnumerical simulation of deformation of geo-structures subjected to earthquake loading is very complex. Whilethere are many advanced tool available, one of the main questions raised when results of a numerical analysisare evaluated is: "How much can (should) we trust numerical simulations?" Trust in results obtained fromnumerical analysis is gained through verification and validation. Verification determines if the numericalmodel is correctly being solved for the intended mathematical equation of interest, while validation establishesthe level of representativeness of the model. This proposal will conduct a detailed and critical verification ofthe program FLAC3D for the problem of seismic wave propagation. The verification will consist on evaluatingthe numerical accuracy of the program by comparing its performance to a suite of mathematical solutionsregarding elastodynamic and poroelastodynamic problems. Crucial elements of numerical modeling such asspatial and temporal discretization, and initial and boundary conditions will be investigated together with theembedded coupled formulation of solid-fluid interaction. Furthermore, an advanced nonlinear model newlyimplemented in the program will be evaluated in comparison to the one in OPENSEES program for a variety ofverification problems. These computational platforms and the intended model are being increasingly used inacademia and advanced engineering practice, and for that reason this study is a paramount step towardssupporting further research on advanced numerical simulation of seismic wave propagation. Results from thisproposal will also allow a better understanding of the mechanics at play during modelling of earthquake wavesenabling the Canadian professional practice to use outcomes of this study to develop safer, more reliable, andmore economical designs.