Current seismic design codes require each building to be designed for its stand-alone seismic response, treating every structure as isolated from its neighbours. Yet in dense urban environments, buildings are dynamically coupled through the common soil — a phenomenon known as structure–soil–structure interaction (SSSI) — and this coupling can either magnify or attenuate a building's seismic response. A 2023 state-of-the-art review by Vicencio, Alexander and Saavedra Flores identified as an open problem that the conditions under which inter-building interaction is beneficial rather than detrimental are not quantified, that constructing a new building next to an existing one can increase or reduce the existing structure's seismic risk in a way that currently constitutes an unquantified liability, and that reduced-order models able to capture multi-building interaction at the city scale — with accuracy sufficient for next-generation seismic codes and risk assessments — do not yet exist. The open problem is to determine, quantitatively, the combinations of inter-building spacing, soil conditions and structural dynamic characteristics under which SSSI attenuates rather than magnifies seismic response and risk, and develop reduced-order models of validated predictive accuracy that capture these effects at city scale. The problem remains open: studies continue to report configuration-dependent amplification and reduction, knowledge gaps remain for multi-building three-dimensional clusters, and no general criterion or code-ready city-scale model has been established.

Background

When an earthquake shakes a building, the building's motion is coupled with the deformation of the ground beneath it: the foundation moves and rocks, and the soil, being deformable, both transmits and radiates energy away. Accounting for this coupling for a single structure is called soil–structure interaction (SSI). When two or more buildings stand close together on a common soil deposit, the motion of each foundation disturbs the soil in a way that also loads the neighbouring foundations: the buildings are dynamically coupled through the soil. This is called structure–soil–structure interaction (SSSI), and when the scale grows to whole districts or cities it is called site–city interaction (SCI). Because seismic waves are modified both by the soil layers (site effects) and by the collective response of the buildings themselves, the seismic demand on a given building in a city can differ substantially from the demand predicted by the standard design assumption that the building stands alone on rigid ground.

The sign of this effect is not fixed. Experimental and numerical studies going back two decades consistently find that inter-building coupling can either reduce (attenuate) or increase (magnify) a building's seismic response, depending on the configuration: Kham, Semblat, Bard and Dangla (2006) showed with simplified numerical models that a city's buildings collectively modify the ground motion and each other's response; Padrón, Aznárez and Maeso (2011) analysed groups of piled buildings with a combined boundary-element/finite-element method (numerical techniques that discretize the soil and the structures into elements to compute their coupled dynamic response); Schwan, Boutin, Padrón, Dietz, Bard and Taylor (2016) combined theoretical, numerical and experimental analyses of site–city interaction; Aldaikh, Alexander, Ibraim and Knappett (2016) confirmed beneficial or detrimental outcomes in shaking-table tests (tests in which model structures on a soil block are excited on a programmable table reproducing earthquake ground motion) of two and three adjacent buildings; and Vicencio and Alexander (2018) showed the interaction persists when the soil behaves nonlinearly. A common physical picture is that neighbouring buildings exchange energy through the soil and modify each other's foundation rocking, so a building can act partly as a tuned mass damper — an auxiliary mass–spring–damper device attached to a structure to absorb its vibration — for its neighbour (attenuation) or can drive the coupled system into resonance (magnification), with the outcome depending on inter-building spacing, the soil's stiffness and damping (including energy radiated away into the soil, called radiation damping), and the dynamic characteristics of the buildings such as their fundamental natural periods and height ratios.

Seismic design codes, however, still require every building to be designed as an isolated structure. The review by Vicencio, Alexander and Saavedra Flores (2023) states the consequence: as urbanization increases building density and land costs push buildings closer together, the seismic risk to an existing structure can be increased — or reduced — by constructing a new building adjacent to it, and this modified risk represents a liability that is currently unquantified within the code framework. The review also identifies the modelling bottleneck: high-fidelity numerical methods (finite element and boundary element analyses, in which the soil and all structures are discretized and integrated in the time domain) are computationally far too expensive for whole cities, so low-fidelity reduced-order models — mechanical idealizations that capture multi-building interaction at low computational cost, for example by concentrating the soil and buildings into a small number of masses, springs and dashpots — with comparable predictive accuracy are needed to make city-scale SSSI/SCI analysis, and eventually code-level treatment, feasible. What such reduced-order formulations exist (for example rotational-spring models of building clusters) have so far been exercised only on specific configurations, and two-scale homogenization approaches (averaging the collective effect of many buildings into an effective medium) have so far been verified only for idealized infinite-city geometries.

Problem Statement

From the state-of-the-art review by Vicencio, Alexander and Saavedra Flores (2023), the open problem has two parts, both directed at quantifying the seismic-risk modification that inter-building soil coupling imposes on existing structures — currently an unquantified liability neglected by seismic codes that treat every building in isolation — so that it can be incorporated into next-generation seismic design codes and risk assessments.

(1) Attenuation-versus-magnification criteria. For buildings dynamically coupled through a common soil deposit under seismic excitation, determine quantitatively under what combinations of inter-building spacing, soil conditions (stiffness, stratigraphy, damping, and nonlinearity), and structural dynamic characteristics (such as fundamental-period and height ratios between adjacent buildings, and foundation type) the structure–soil–structure interaction attenuates rather than magnifies the seismic response and risk of a given structure (measured against the response of the same structure on the same soil without its neighbours, that is, coupled SSSI versus uncoupled soil–structure interaction) — in particular, when the construction of a new building adjacent to an existing one increases the seismic risk borne by the existing structure and when it reduces it. The three factor classes — inter-building spacing, soil conditions, and structural dynamic characteristics — are required jointly: the criterion must address all three together, and the properties named in parentheses are illustrative examples of each class rather than a separately mandatory checklist. The criteria must characterize the risk change with damage-relevant engineering demand measures, assessed independently for each measure: because experimental evidence shows that peak-response and accumulated-energy measures can move in opposite directions, attenuation and magnification are determined measure by measure, so a configuration that reduces one measure while increasing another is reported as attenuating under the first and magnifying under the second and need not be reduced to a single overall verdict.

(2) Reduced-order models adequate for city scale. Develop low-fidelity reduced-order models of multi-building interaction through the soil whose predictive accuracy for these attenuation/magnification effects is demonstrably comparable to that of detailed (high-fidelity) analyses, established by benchmarking against appropriate reference evidence (high-fidelity numerical simulations, physical experiments and/or instrumented-building or field data), and whose computational cost is low enough for city-scale (site–city interaction) seismic response and risk analysis, thereby making the criteria of part (1) usable across realistic urban configurations.

References

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