Final Report Summary - WAPRO (Wave Propagation in Anisotropic Soil Strata Resting on a Poroelastic Half-plane by the BEM)
Results
An original and efficient knowledge and computational package based on the boundary element method (BEM) was developed, programmed, validated and subsequently used to study two-dimensional (2D), time-harmonic or transient, wave propagation problems. These problems encompass pressure (P), vertically polarised shear (SV) and horizontally polarised SH elastic waves propagating through non-homogeneous geological media. More specifically, the knowledge and software package comprises the following parts:
- displacement-based BEM using fundamental solutions derived analytically by both the Fourier and Radon transformations;
- hypersingular and non-hypersingular, traction-based BEM again based on Fourier and Radon transformations;
- displacement-based and non-hypersingular traction-based BEM using frequency-dependent Green's functions for the elastic anisotropic half-plane subjected to incident SH-waves analytically derived, by Radon transform;
- hybrid WNIM-BEM technique based on the splicing of the semi-analytical wave number integration method (WNIM) and the BEM;
- hybrid FDM-BEM technique based on meshing together the finite difference method (FDM) and BEM.
This particular technique proved indispensable in studying the seismic wave-fields in the urban region of the Thessaloniki, Greece. More specifically, the case study was a North-South cross-section containing a buried Metro station tunnel that is currently under construction and a Roman monument directly above. The new hybrid technique takes into consideration all three main components of the seismic problem, namely:
(i) the seismic source with a prescribed signals emanating from the bedrock interface;
(ii) the topography and material properties of the inhomogeneous wave path travelled by the seismic signal and
(iii) the local (near site) profile with complex material behaviour (poroelasticity, anisotropic and inhomogeneity) plus tunnels and surface relief.
A. Extensive simulation studies were conducted to gauge the sensitivity of the dynamic stress concentration fields and the diffracted wave fields in two-dimensional geological deposits to:
(i) geometry and overall geological composition of the deposit cross-section;
(ii) specific material properties and behaviour;
(iii) boundary conditions and
(iv) type dynamic load and time-harmonic versus transient conditions.
B. Development of a distributed-mass, continuous structural system representation that can be interfaced with base-isolation and foundation systems. This model can directly use the seismic signals generated in the previous part of the project so as to study the seismic response of structures located in the aforementioned geological deposits.
C. A closely-related 2D elastodynamic problem was solved by the methodology developed for the Project, whereby a finite-size deformable continuum (elastic solid) contains multiple cavities and/or elastic inclusions of arbitrary shape and geometrical arrangement is subjected to a dynamic stress field. Furthermore, the cavity surfaces are either traction-free or internally pressurized, while the inclusions have elastic properties ranging from very flexible to nearly rigid. The presence of all these heterogeneities within the elastic matrix gives rise to both wave scattering and stress concentration phenomena. Extensive numerical simulations reveal the complex dependence of the scattered wave fields and of the resulting dynamic stress concentration factors (SCF) on the shape, size, number and geometrical configuration of multiple discontinuities. This problem has applications in fields transcending seismic mechanics, such as composite materials.
Conclusions
The numerical simulations have shown that seismic field development at a given geological site is the result of interplay of different factors such as:
- wave scattering, diffraction and dynamic stress concentration near heterogeneities such as surface relief, layering, cracks, and inclusions;
- complex soil properties including the existence of a material gradient, of anisotropy and of poroelasticity;
- seismic source type, geometry, location, properties and structure of the geological deposits.
Socio-economic impacts
The research work will benefit EU excellence in the broader field of computational earthquake engineering and in the generation of contemporary technological information in this field. The obtained results have a potential for contribution to EU competitiveness regarding earthquake engineering and its associated social component of risk mitigation in the built environment. The created package of knowledge (modelling, computational tools, software, validations and simulations) can be used by the academic society (students and researchers in the fields of computational mechanics, earthquake engineering, fracture mechanics and structural mechanics), practicing engineers in design offices and by emergency management agencies, seismic risk analysts and risk managers.
The interdisciplinary nature of the research work done is precisely what allows the researcher to acquire new, complementary skills that has an impact in reference to her career development. The MC Researcher was appointed in 2012 to the position of full professor in the Department of Solid Mechanics at the Institute of Mechanics, Bulgarian Academy of Sciences (BAS), Sofia in the field 'mathematical modelling and application of mathematics'. This undoubtedly will generate interest and set a precedence for other faculty and researchers working at BAS.
The results obtained within the framework of this project will enable the MC researcher to realise a long-standing project with the scientist-in-charge for producing a collabourative book on wave propagation in non-homogeneous, deformable media for the benefit of graduate students in the field.
An original and efficient knowledge and computational package based on the boundary element method (BEM) was developed, programmed, validated and subsequently used to study two-dimensional (2D), time-harmonic or transient, wave propagation problems. These problems encompass pressure (P), vertically polarised shear (SV) and horizontally polarised SH elastic waves propagating through non-homogeneous geological media. More specifically, the knowledge and software package comprises the following parts:
- displacement-based BEM using fundamental solutions derived analytically by both the Fourier and Radon transformations;
- hypersingular and non-hypersingular, traction-based BEM again based on Fourier and Radon transformations;
- displacement-based and non-hypersingular traction-based BEM using frequency-dependent Green's functions for the elastic anisotropic half-plane subjected to incident SH-waves analytically derived, by Radon transform;
- hybrid WNIM-BEM technique based on the splicing of the semi-analytical wave number integration method (WNIM) and the BEM;
- hybrid FDM-BEM technique based on meshing together the finite difference method (FDM) and BEM.
This particular technique proved indispensable in studying the seismic wave-fields in the urban region of the Thessaloniki, Greece. More specifically, the case study was a North-South cross-section containing a buried Metro station tunnel that is currently under construction and a Roman monument directly above. The new hybrid technique takes into consideration all three main components of the seismic problem, namely:
(i) the seismic source with a prescribed signals emanating from the bedrock interface;
(ii) the topography and material properties of the inhomogeneous wave path travelled by the seismic signal and
(iii) the local (near site) profile with complex material behaviour (poroelasticity, anisotropic and inhomogeneity) plus tunnels and surface relief.
A. Extensive simulation studies were conducted to gauge the sensitivity of the dynamic stress concentration fields and the diffracted wave fields in two-dimensional geological deposits to:
(i) geometry and overall geological composition of the deposit cross-section;
(ii) specific material properties and behaviour;
(iii) boundary conditions and
(iv) type dynamic load and time-harmonic versus transient conditions.
B. Development of a distributed-mass, continuous structural system representation that can be interfaced with base-isolation and foundation systems. This model can directly use the seismic signals generated in the previous part of the project so as to study the seismic response of structures located in the aforementioned geological deposits.
C. A closely-related 2D elastodynamic problem was solved by the methodology developed for the Project, whereby a finite-size deformable continuum (elastic solid) contains multiple cavities and/or elastic inclusions of arbitrary shape and geometrical arrangement is subjected to a dynamic stress field. Furthermore, the cavity surfaces are either traction-free or internally pressurized, while the inclusions have elastic properties ranging from very flexible to nearly rigid. The presence of all these heterogeneities within the elastic matrix gives rise to both wave scattering and stress concentration phenomena. Extensive numerical simulations reveal the complex dependence of the scattered wave fields and of the resulting dynamic stress concentration factors (SCF) on the shape, size, number and geometrical configuration of multiple discontinuities. This problem has applications in fields transcending seismic mechanics, such as composite materials.
Conclusions
The numerical simulations have shown that seismic field development at a given geological site is the result of interplay of different factors such as:
- wave scattering, diffraction and dynamic stress concentration near heterogeneities such as surface relief, layering, cracks, and inclusions;
- complex soil properties including the existence of a material gradient, of anisotropy and of poroelasticity;
- seismic source type, geometry, location, properties and structure of the geological deposits.
Socio-economic impacts
The research work will benefit EU excellence in the broader field of computational earthquake engineering and in the generation of contemporary technological information in this field. The obtained results have a potential for contribution to EU competitiveness regarding earthquake engineering and its associated social component of risk mitigation in the built environment. The created package of knowledge (modelling, computational tools, software, validations and simulations) can be used by the academic society (students and researchers in the fields of computational mechanics, earthquake engineering, fracture mechanics and structural mechanics), practicing engineers in design offices and by emergency management agencies, seismic risk analysts and risk managers.
The interdisciplinary nature of the research work done is precisely what allows the researcher to acquire new, complementary skills that has an impact in reference to her career development. The MC Researcher was appointed in 2012 to the position of full professor in the Department of Solid Mechanics at the Institute of Mechanics, Bulgarian Academy of Sciences (BAS), Sofia in the field 'mathematical modelling and application of mathematics'. This undoubtedly will generate interest and set a precedence for other faculty and researchers working at BAS.
The results obtained within the framework of this project will enable the MC researcher to realise a long-standing project with the scientist-in-charge for producing a collabourative book on wave propagation in non-homogeneous, deformable media for the benefit of graduate students in the field.