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A framework for multi-scale seismic simulation of a city block considering site-city interaction
Abstract
This study presents a novel approach for a multi-scale seismic analysis of a city block capable of capturing the site-city interaction (SCI) effect, which is usually disregarded in practice for buildings in dense urban areas. An automated multi-scale modeling framework is developed in which a region of interest of a city block is modeled with a finite element software, while a building of interest is modeled in detail using an independent analysis tool. The dynamic interaction between the two models is fully captured through a dynamic integration scheme and the generalized multi-platform simulation framework developed at the University of Toronto. The framework is applied to an idealized soil domain and three building structures to demonstrate its applicability. The dynamic response of one of the three buildings from the multi-scale seismic analysis is compared to the common two-step approach, where the base motion at the building location is evaluated first and then the dynamic analysis of a fixed-base building is conducted with the base motion. A verification example of the proposed framework is also presented that confirms the accuracy of the framework in capturing the dynamic responses of both the building and soil domain considering SSI. The analysis case with SCI shows 2% less base shear force compared to the case when the two-neighboring buildings are ignored in analysis.
... Studies have shown that structures partake in SCI (a) passively and/or (b) actively by contaminating ground motions and altering their surrounding structures' response. [12][13][14][15][16][17][18][19] Active effects are feedback vibrations from the structures at resonance while passive effects are wave reflections/refractions due to building inertia and the pinning effects of foundations. The nature of SCI is still unclear however, the consensus is that closely-spaced structures and soil form an integrated dynamic system and should be investigated as such. ...
This study assesses the 3D amplification effects in shallow basins and quantifies the effects of site-city interaction (SCI) on high-rise buildings. A regional-scale 3D spectral element simulation is conducted on the Tuen Mun-Yuen Long basin, which contains multiple subbasins with heterogeneous and nonlinear soil profiles, while 3D city models with various building layouts are fully integrated into the basin model for our SCI study. We found a good correlation between spectral amplification factors and soil depths. Site response is significantly amplified at basin edges and centers due to surface waves generated at basin edges and the focusing effects stemming from 3D basin geometry. Transfer functions of 3D basins can be up to fourfold at fundamental frequencies as compared to 1D response, and further amplifications occur at high frequencies due to surface waves. In the SCI simulations, we observe wave trapping in the open space amid buildings resulting in energy concentration and up to twofold PGA amplifications. The wave trapping effect diminishes as the space between buildings increase beyond their range of influence (∼100 m). The SCI analyses show that destructive kinetic energy in superstructures increases 28% in one horizontal direction but decreases 22% in the other. Our study concluded that, 1D site response analysis can significantly underestimate the seismic demand in shallow basins. Site-city interaction of high-rise buildings increases the short-period spectra of ground motions, leading to an increase in their story accelerations by up to 50% and to a substantial decrease in the seismic safety of short structures in their vicinity.
... Potential application of the proposed method was demonstrated through two verification examples. Due to the page limit, more application examples based on the proposed method, such as the soil-structure interaction analysis of a nuclear containment structure (Huang, 2019) as well as the multi-scale seismic simulation of a city block considering site-city interaction (Sayed, Huang, & Kwon, 2019), are not presented in this paper. It is also worth noting that the proposed method may reduce computation time by distributing analysis into different analysis software. ...
Partitioned methods have been widely used in multiphysics and large‐scale structure‐media problems since they allow decomposition of a complex system into smaller subsystems. Although they have been considered to be superior to monolithic methods in terms of software reuse, difficulties still exist in the implementation process. This paper addresses these difficulties and proposes a new method to ease the coupling of the dynamic subsystems analyzed with different finite element codes. This is enabled by the development of a new staggered approach such that each involved program acts as a black box that is accessible only through model input and output, that is, displacements and forces, at the interface boundary. The accuracy and stability of the proposed method are numerically evaluated. A practical method to determine the maximum time step for stable solutions is also proposed. Two application examples are presented to verify the algorithm and demonstrate potential of the proposed method.
Researchers and engineers have shown a keen interest in the impact of soil-structure interaction (SSI) on seismic
response of structures throughout the past three decades. Less research has been done on the experimental
investigation, with the majority of these studies concentrating on theoretical analysis. When the structure,
foundation, and soil medium work together, the actual behavior of the structure is significantly different from
what would be expected if only the structure were taken into account. The building frames’ overall stiffness is
reduced by the flexible earth medium beneath the foundation, increasing the system’s natural period. The term
“soil-structure interaction” refers to a group of processes that affect both the responsiveness of soils to the
presence of structures and the response of structures to the flexibility of their foundation soils. The combined
structure-foundation-soil system is often ignored by analytical and numerical methods for dynamic analysis. It
has been acknowledged that SSI impacts could have a big effect, especially when larger constructions and soft
soil are involved. In this work, investigations on the interactions between neighboring structures’ soil properties
are reviewed. These studies are divided into two groups: theoretical/numerical studies of SSI and experimental
studies of SSI. It was determined that taking into account various factors, including soil structure interaction, soil
type, building stiffness, infill wall stiffness, wall location, distance between adjacent buildings, and building
height, significantly affected the displacement of the building frame’s base and its time course. The significance
of taking the underlying soil into account decreases as the soil stiffness rises.
Seismic safety of congested metropolitan environments are of key importance for sustainable urban development. Closely spaced high-rise buildings are often adjacent to underground structures in settings such as transportation hubs that yield complex dynamic phenomena during earthquakes. Structures in mega-cities are nonetheless designed using conventional earthquake engineering practices despite reports on multiple interactions between soil and structures (SSSI), for instance erratic structural damage patterns after large earthquakes. This study is set to explore Soil-Underground structure-Soil Interaction (SUSSI) and Site-City Interaction (SCI) through realistic 3D models of Kowloon station, in Hong Kong. A discontinuous Galerkin spectral element method is adopted via the computational platform, SPEED that can efficiently deal with non-conforming meshes, thus easing some key challenges of complex 3D wave propagation problems. For comparative purposes two models are considered, one representing solely the building-foundation systems at the transportation hub, while the other includes a subsurface metro station. A viscoelastic layer-cake model represents the substratum; whereas the metro station and building-foundation systems are modeled by a closed rigid box and homogeneous block models capturing their principal dynamic and geometric properties, respectively. Key findings highlight SUSSI, SCI, moreover how special urban layouts, such as squares, along with structural weight distribution and foundation depth alter surface ground motions.
The main objective of this thesis is to build a framework for performing
earthquake simulations capable of including nonlinear soil behavior
and the presence of the built environment in highly heterogeneous
basins, and to study their influence on the final response of the
ground in large urban areas exposed to high seismic hazard. To this
end, we use a finite elements approach and extend the capabilities
of Hercules, the parallel octree-based earthquake simulator developed
by the Quake Group at Carnegie Mellon.
Nonlinear soil behavior is incorporated in ground motion simulations
employing a rate-dependent plasticity approach to predict the nonlinear
state of the material explicitly at every time step. The soil is
modeled as a perfectly elastoplastic material. The presence of urban
structures is modeled representing buildings as homogeneous blocks
made up of the same type of hexahedral elements used in the mesh.
These elements are generated automatically through a new set of application
programming interfaces, which extend Hercules' meshing capabilities
while preserving its core octree-based formulation.
Both implementations are tested under realistic earthquake conditions
in heterogeneous geological structures. In the case of nonlinear
ground motion modeling, results indicate that soil nonlinearities
greatly modify the ground response, confirming previous observations
for deamplification effects and spatial variability, and evidencing
three-dimensional basin effects not fully observed before. In turn,
the presence of building clusters causes multiple soil-structure
interaction phenomena that change both the near ground-motion and
the individual performance of the buildings themselves. This substantiates
the argument that in soft-soil basins may it not be longer valid
to ignore the presence of neighboring structures.
These new implementations represent important advances in computational
seismology and help make a direct connection to subjects of interest
in earthquake engineering. The analysis drawn from the applications
presented here confirms aspects known from previous, though limited
studies, and broadens our knowledge of the effects of nonlinear soil
and the built environment on the ground motion due to earthquakes
at a regional level not explored before.
It is most generally admitted that seimic ground motion is the convolution of source, path and site effects. The question addressed here is whether a fourth term, called "Site-City Interaction" (SCI), should be added for densely urbanized areas, corresponding to feedback effects from the shaken buildings in the soil. After a short overview of various, consistent observations, several specific experimental and numerical results are briefly summarized, that clearly evidence the wave radiation from isolated buildings and the possibilty of interactions between close buildings as well. The seismic response of a simple "city model" represented by a group of buildings is then addressed through a series of numerical simulations, which allow to determine under which conditions such SCI effects may be significant. These findings are consistent with a very simple "rule of thumb" approach based on the comparison between kinematic energies in soils and buildings, pointing to the significance of SCI effects for dense cities where building and soil periods coincide. The last section thus discusses the practical consequences of such SCI effects, and some possible directions to get unambiguous experimental evidence in real cities.
The analysis of seismic site effects generally disregards the influence of surface structures on the free field motion in densely urbanized areas. This paper aims at investigating this particular problem called site-city interaction especially by comparison to the "free-field" amplification process. Several evidences (experimental, analytical, numerical) of the site-city interaction phenomenon have been given in previous work (Gu\'eguen, Bard, Semblat 2000). The influence of site city-interaction could be large for structures having eigenfrequencies close to that of the surface soil layers. Furthermore, the density of structures is also an important governing parameter of the problem. Considering a specific site (Nice, France) where site-city interaction is supposed to be significant, we start from detailed experimental and numerical studies of seismic site effects giving both amplification levels and occuring frequencies, as well as the location of the maximum amplification areas. The influence of site-city interaction is then investigated through various numerical models considering the boundary element method. The effect of surface structures with variable urban densities is analysed to estimate the contribution of overall site-city interaction on surface motion distribution. The main goal of the paper is to estimate the influence of site-city interaction not only on amplification levels (the influence can be small), but also on the modification of both main amplification frequencies and location of the maximum amplification areas. The main conclusion of this work is to show the modifications of the free-field amplification due to site-city interaction and leading to a specific urban field amplification. Comment: 8 p
This work focuses on the analysis of the multiple interactions between soil layers and civil-engineering structures in dense urban areas submitted to a seismic wave. To investigate such phenomena, called site-city interaction (SCI) herein, two simplified site-city configurations are considered: a homogeneous, periodically spaced city and a heterogeneous, nonperiodically spaced city, both on a constant- depth basin model. These 2D boundary-element method models are subjected to a vertically incident plane SH Ricker wavelet. A parametric study of the city parameters (density of buildings and their natural frequencies) and the thickness of the basin is carried out to characterize the SCI and to investigate its sensitivity to some governing parameters. The following parameters are analyzed: building vibrations, induced ground motion, ground-motion perturbations inside and outside the city, spatial coherency, and kinetic energy of the "urban wave field." A so-called site-city resonance is reached when the soil fundamental frequency and structure eigenfrequencies coincide; building vibrations and ground motion are then significantly decreased and the spatial coherency of the urban field is also strongly modified. Building density and city configuration play a crucial role in the energy distribution inside the city.
Partitioned analysis methods have been mostly used in multiphysics and large-scale media problems since they allow decomposition of a complex system into smaller problems. Although they have been considered to be superior to monolithic methods in terms of software reuse, difficulties still exist in the implementation process. This study addresses these difficulties and proposes a new method to ease the coupling of the substructures analyzed with different Finite Element (FE) codes. This is enabled by the development of a staggered partitioned approach such that each involved program acts as a black box which is accessible through standard model input and output, i.e. displacements and forces at the boundary of each model. In addition, the substructures can be numerically integrated using any α-modified integration scheme (explicit or implicit). A general stability proof is provided to determine the maximum time step to ensure a stable solution. An example application will be presented which demonstrates potential of the developed integrated simulation method.
Seismic damage simulation of buildings on a regional scale is important for loss estimation and disaster mitigation of cities. However, the interaction among densely distributed buildings in a city and the site, i.e., the “site-city interaction (SCI) effects”, is often neglected in most regional simulations. Yet, many studies have found that the SCI effects are very important in regional simulations containing a large number of tall buildings and underground structures. Therefore, this work proposed a numerical coupling scheme for nonlinear time-history analysis of buildings on a regional scale considering the SCI effects. In this study, multiple-degree-of-freedom (MDOF) models are used to represent different buildings above the ground, while an open source spectral element program, SPEED, is used for simulating wave propagation in underlying soil layers. The proposed numerical scheme is firstly validated through a shaking table test. Then, a detailed discussion on the SCI effects in a 3D basin is performed. Finally, a nonlinear time-history analysis of buildings on a regional scale is performed using the Tsinghua University campus in Beijing as a case study. The Tsinghua University campus case results show that the SCI effects will reduce the seismic responses of most buildings. However, some buildings will suffer much more severe damage when the SCI effects are considered, which may depend on the input motions, site characteristics and building configurations.
Soil-structure interaction (SSI) analysis is generally a required step in the calculation of seismic demands in nuclear structures, and is currently performed using linear methods in the frequency domain. Such methods should result in accurate predictions of response for low-intensity shaking, but their adequacy for extreme shaking that results in highly nonlinear soil, structure or foundation response is unproven. Nonlinear (time-domain) SSI analysis can be employed for these cases, but is rarely performed due to a lack of experience on the part of analysts, engineers and regulators. A nonlinear, time-domain SSI analysis procedure using a commercial finite-element code is described in the paper. It is benchmarked against the frequency-domain code, SASSI, for linear SSI analysis and low intensity earthquake shaking. Nonlinear analysis using the time-domain finite-element code, LS-DYNA, is described and results are compared with those from equivalent-linear analysis in SASSI for high intensity shaking. The equivalent-linear and nonlinear responses are significantly different. For intense shaking, the nonlinear effects, including gapping, sliding and uplift, are greatest in the immediate vicinity of the soil-structure boundary, and these cannot be captured using equivalent-linear techniques.
The collective excitation of city structures by a seismic wavefield and the subsequent multiple Structure-Soil-Structure Interactions (SSSIs) between the buildings are usually disregarded in conventional seismology and earthquake engineering practice. The objective here is to qualify and quantify these complex multiple SSSIs through the design of an elementary study case, which serves as a benchmark for theoretical, numerical and experimental crossed-analysis. The experimental specimen consists of an idealized site-city setup with up to 37 anisotropic resonant structures arranged at the top surface of an elastic layer and in co-resonance with it. The experimental data from shaking table measurements is compared with the theoretical and numerical results provided respectively by an equivalent city-impedance model derived analytically from homogenization in the long-wavelength approximation and a model based on boundary elements. The signatures of the site-city interactions are identified in the frequency, time and space domain, and in particular consist of a frequency-dependent free/rigid switch in the surface condition at the city resonance, beatings in the records and the depolarization of the wavefield. A parametric study on the city density shows that multiple SSSIs among the city structures (five are sufficient) can have significant effects on both the seismic response of its implantation site and that of the buildings. Key parameters are provided to assess site-city interactions in the low seismic frequency range: They involve the mass and rigidity of the city compared to those of the soil and the damping of the building.
This paper shows the quantitative effect that foundation compliance has on the maximum base
shear force and the fundamental period of vibration in typical tall buildings subjected to strong-motion
earthquakes. A study was made of five-, ten-, and fifteen-story building models on the
Electric Analog Computer, subjecting them to the ground accelerations of actual earthquakes.
The base shear forces were measured, the foundation compliance of the models being changed
through a very wide range.
The properties specified for the building models are shown to be similar to the properties found
in real buildings. The experimental results imply that the maximum base shear forces in typical
buildings of five stories and higher during strong-motion earthquakes will be essentially unaffected
by any degree of foundation compliance that can be expected in normal building practice. The
fundamental period of typical buildings will be increased by about 10 per cent if the foundation
compliance is the maximum that can be expected in standard building practice.
A study is made of the dynamic interaction, through the soil, between two parallel infinite shear walls placed on rigid foundations. The steady-state response of both structures for a vertically incident SH wave is obtained and compared with the corresponding values resulting from consideration of only one structure.
It is found that the additional interaction effects caused by the presence of a second structure are especially important at low frequencies and in the neighborhood of the fixed-base natural frequencies of the second structure. For high frequencies it is sufficient to consider the interaction between each structure and the soil, ignoring the presence of other structures.
The finite element analysis of dynamic problems in an infinite, isotropic medium is examined. To simulate the physically infinite system by a finite model, an energy absorbing boundary is proposed. This boundary is frequency independent and proves to be very efficient in absorbing stress waves. The boundary constants are calculated for the particular cases of plane strain and axisymmetry for isotropic materials.
The concept of structure–soil–structure dynamic interaction was introduced, and the research methods were discussed. Based on several documents, a systematic summary of the history and status of the structure–soil–structure dynamic interaction research that considers adjacent structures was proposed as a reference for researchers. This study is in the initial stage, given its complexity and excessive simplification of the model for soil and structures, and should be carried forward for its significance. An attempt was made to summarize the common major computer programs in this area of study. Furthermore, the advantages, disadvantages, and applicability of such programs were discussed. The existing problems and the future research trend in this field were also examined.
We study the interaction between the buildings of a city through a fully coupling structure–soil–structure model. The main issues are to emphasize the collective behavior of the buildings during a seismic excitation (city effect) and to compute the global response of the city.The anti-plane shearing of an elastic half space with a part of its boundary formed by the rigid foundations of the buildings is considered. The buildings are modeled as elastic springs which relate two concentrated masses. The associated mathematical problem is a partial differential equation coupled with an ordinary differential equation through a special class of boundary conditions. To focus on the coupling structure–soil–structure (city frequencies) the associated spectral problem is rewritten in terms of a nonlinear scalar equation involving the eigenvalues of a symmetric matrix. A numerical approach, involving an integral method, is proposed to numerically investigate the city effect.The asymptotic limit of the principal eigenvalue with respect to the ratio between the width of the building and the width of the city points out the principal frequency of the city. This value does not depended on the number of buildings which compose the city but it is specific to each city via the specific properties of the buildings. The collective behavior of the buildings during a seismic excitation is emphasized through the shape of the first eigenfunction. Finally a numerical illustration of a the propagation in the city of the impact on the top of one of the buildings (a 9/11 type event) is presented.
The Pseudodynamic (PSD) test method combines the numerical integration of the motion equations of a structure condensed at selected degrees-of-freedom (d.o.f.) with the on-line measurement of the reaction forces needed to impose this computed motion. The results obtained with this testing method can be strongly corrupted by the spurious propagation of experimental errors. The α-operator splitting (α-OS) scheme, a convenient linearisation of the so-called α-method, is a non-iterative implicit time integration scheme. As such, it is a good candidate for PSD testing since it provides the unconditional stability sometimes needed when the number of d.o.f. is large, while preserving the implementation simplicity of explicit schemes. The properties of the α-OS scheme are presented with special emphasis on its error propagation characteristics. These properties are compared with the ones of corresponding iterative implicit schemes. It is shown in particular that, in contrast with what is observed using iterative schemes, the selective damping possibility associated with the α factor become a crucial ingredient for the success of the α-OS scheme.
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