BG
Aims and Methodology
The analysis of buried infrastructure to seismically induced ground motions requires the use of sophisticated and dedicated software packages. The main idea behind this proposal is to modify existing large-scale commercial finite element method (FEM) software (e.g., ANSYS, ABAQUS) so that it can realistically model the semi-infinite, far-field geological region through which seismic waves travel as a macro finite element (MFE). This element will be synthesized from analytical, semi-analytical or even numerical solutions of the elastodynamic problem describing waves travelling through complex, graded anisotropic media and will furthermore satisfy the Sommerfeld’s radiation condition at infinity. More specifically, it is possible to create a library of MFE taking into consideration various categories of mechanical models representing soil anisotropy, inhomogeneity, poroelasticity, viscosity, etc. The prime candidate for modelling of the far-field semi-infinite zone is a boundary element method (BEM) platform for casting the underlying boundary value problem (BVP) in an algebraic system of equations that are compatible with the systems obtained by the FEM.
The proposed strategy is to model the finite near-field region of the problem that contains the different types of underground structures and the heterogeneous structure of the surrounding soil including any free surface relief by the FEM, while the external problem with the semi-infinite, wider geological region will be imported as a macro element in the FEM commercial code The research objectives can be summarized as follows, see also Figure 2: 1. Problem decomposition into a semi-infinite far-field region modeled by the BEM and a near field region with finite layers containing the buried structures and modelled by the FEM. 2. Conversion of the far field region model into one macro-finite element (MFE). 3. Importing the MFE in commercial FEM software. 4. Solving the coupled problem for various environmental load scenarios, e.g., seismic actions.
Figure 2
More specifically, the research methodology is as follows: 1. Development of numerical 3D models for elastic wave propagation in continuously inhomogeneous (Figure 3(c)) or with graded layers (Figure 3(b)) semi-infinite regions. This involves full development of the BEM, which starts with an integral equation formulation of the governing differential equations involving fields on the boundary only is realized. 2. The derivation of fundamental solutions is a separate step in itself and will be carried out for two families of graded geomaterials, (a) proportional material parameter variation yielding a constant wave phase velocity; (b) variable phase velocity with depth. 3. Development of a library of fundamental solutions and Green’s functions modelling geological media under point forces. 4. Software development for solution of wave motion in semi-infinite media by (a) transient BEM formulations, (b) transformed domain BEM formulations and (c) approximate transient formulations augmented with the convolution quadrature formula of Lubich.
Figure 3
5. Embedment of the numerical models for the far-field regions in FEM software as macro-finite elements. 6. FEM modelling of the seismic behaviour of the near field, multi-layered geological regions containing the underground structures such as tunnels and piping systems. 7. Examination of different cases of buried structures under various seismic motion scenarios. The end product will be the development of a hybrid FEM–hosted computational technique. Furthermore, useful engineering conclusions will be drawn regarding the performance of buried structures in an active seismic environment, including recommendations on their performance, maintenance and rehabilitation.