Validation and further development of the perfectly matched layer technique for the numerical treatment of elastodynamic boundary value problems

• Applicant: Professor Dr.-Ing. Stavros A. Savidis
• Subject Area: Geotechnics, Hydraulic Engineering
• Term: from 2014 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 255685298

• Final Report Year: 2021

Final Report Abstract

The objective of the project is the validation and further development of the Perfectly Matched Layer (PML) method for 2D dynamic soil structure interaction problems in frequency domain. The PML technique is an alternative approach to Local Transmitting Boundaries, according to which a perfectly matched material layer is applied as absorbing boundary around the finite region of interest, absorbing and attenuating all waves propagating outward from the bounded region of all non-tangential angles-of-incident and all non-zero frequencies. The PMLs are designed in such a way that no reflections are generated from the bounded region-PML interface. Due to the fact that PML material layer is not entirely based on physical properties makes mechanically reasonable statements to the numerical quality of the PML formulation not possible. Therefore, the quality of a chosen PML formulation cannot be forecasted, leading to a lack of mathematical-theoretical research to the convergence of PML formulations for no simple boundary value problems. In this context, the parameters affecting the performance of the FE/PML method are extensively investigated in the frame of the present project and recommendations are given for the proper selection of the PML parameters which will increase the performance of the method. Sensitivity analyses are conducted, in attempt to quantify the influence of the combination of different PML parameters on the accuracy of the FE/PML solutions. An alternative approach for the stretching function is proposed along with the optimal choice of the accompanied PML parameters. Moreover, two different approaches for the implementation of the PML method in the FE are applied and successfully implemented into a commercial FE software increasing the applicability of the method. The stretching behavior responsible for the wave absorption within the PML, is expressed in the one approach as a change in the material properties and in the other approach as a stretching of the coordinates. A FE/PML numerical scheme is developed in which both PML formulations are applied and successfully implemented as a macro-finite element in a commercial FEM program. A detailed implementation procedure of both PML formulations in a commercial software is proposed accompanied with proper stretching function and PML parameters for both formulations. The proposed FE/PML computational schemes increase the computational efficiency and applicability of the method by means of the followings: (i) the implementation of PMLs in a commercial software aims to achieve great flexibility but also high accuracy in modeling of surface and underground constructions under dynamic loading; (ii) proper PML parameters are recommended, that will increase the computational efficiency of the method without loss of accuracy (smaller PML domains or coarser discretization). The new developed FE/PML numerical schemes are verified against analytical or semi-analytical solution for 2D wave propagation problems in homogeneous and inhomogeneous geological media accounting for layer and tunnel constructions. The FE/PML computational scheme can be easily applied for 3D problems, however to this end an advanced sensitivity analysis for the calibration of the FE/PML model and for the proper selection of the PML parameters has to be applied. Moreover, the results of the present project serve as a base for further development of the FE/PML model in time domain in order to consider the nonlinear effects in the bounded FE region.

Publications

• Auslegung effizienter absorbierender Schichten zur Simulation von dynamischen Boden-Bauwerk Interaktion Problemen In: Vortragsband der 15. D-A-CH Tagung, Erdbebeningenieur und Baudynamik 21-22 September 2017, Weimar, DGEB-Publikation Nr. 17, 188–200
  Fontara, I. K; Schepers, W; Savidis, S. A; Rackwitz, F.
  
• FE/PML numerical schemes for dynamic soil-structure interaction and seismic wave propagation analysis In: Procedia Engineering 199 pp. 2348– 2353 (2017) – 10th International Conference on Structural Dynamics, EURODYN, 10-13 September 2017, Rome, Italy
  Fontara, I. K; Schepers, W; Savidis, S. A; Rackwitz, F.
  
• Finite Element Implementation of efficient absorbing layers for time harmonic elastodynamics of unbounded domains. In: Soil Dynamics and Earthquake Engineering (2018) – Vol. 114, pp. 625-638
  Fontara, I. K; Schepers, W; Savidis, S. A; Rackwitz, F.
  
• Vergleich von absorbierenden Rändern bei dynamisch belasteten Gründungen. In: 6. VDI-Fachtagung Baudynamik, 17-18 April 2018, Würzburg, Deutschland
  Fontara, I. K; Schepers, W; Savidis, S. A; Rackwitz, F.