Correction factors for SSI effects predicted by simplified models: 2D versus 3D rectangular embedded foundations

Abstract

Summary The effects of soil‐structure interaction (SSI) are often studied using two‐dimensional (2D) or axisymmetric three‐dimensional (3D) models to avoid the high cost of the more realistic, fully 3D models, which require 2 to 3 orders of magnitude more computer time and storage. This paper analyzes the error and presents correction factors for system frequency, system damping, and peak amplitude of structural response computed using impedances for linear in‐plane 2D models with rectangular foundations, embedded in uniform or layered half‐space. They are computed by comparison with results for 3D rectangular foundations with the same vertical cross‐section and different aspect ratios. The structure is represented by a single degree‐of‐freedom oscillator. Correction factors are presented for a range of the model parameters. The results show that in‐plane 2D approximations overestimate the SSI effects, exaggerating the frequency shift, the radiation damping, and the reduction of the peak amplitude. The errors are larger for stiffer, taller, and heavier structures, deeper foundations, and deeper soil layer. For example, for a stiff structure like Millikan library (NS response; length‐to‐width ratio ≈ 1), the error is 6.5% in system frequency, 44% in system damping, and 140% in peak amplitude. The antiplane 2D approximation has an opposite effect on system frequency and the same effect on system damping and peak relative response. Linear response analysis of a case study shows that the NEHRP‐2015 provisions for reduction of base shear force due to SSI may be unsafe for some structures. The presented correction factor diagrams can be used in practical design and other applications.

Torsion in symmetric buildings due to soil‐structure interaction: A discussion on code values of accidental eccentricity factor in seismic design

“…These two components, φ * and φ 0 , are usually referred to as the kinematic and inertial motion, respectively. The component φ * is the free‐field ground motion modified by scattered waves from the rigid excavation for the unit amplitude of the incident harmonic wave, and is obtained as follows: $$\begin{equation}{\varphi }_* = K_{{\rm{TT}}}^{ - 1} \mathop \int_{{\Gamma}} \left[ {{{\left( {{G}_\sigma \Lambda } \right)}}^{\rm{T}}{U}_{\rm{f}} - {\Omega }^{\rm{T}}{T}_{\rm{f}}} \right]{\rm{dS,}}\end{equation}$$where K TT denotes the torsional impedance function of the foundation and is computed using the IBEM presented in 26,27 . The element meshing scheme for ensuring the high precision of the impedance functions is listed for different foundation dimensions in Table 1.…”

“…where K TT denotes the torsional impedance function of the foundation and is computed using the IBEM presented in. 26,27 The element meshing scheme for ensuring the high precision of the impedance functions is listed for different foundation dimensions in Table 1. Furthermore, U f (x, y, z) and T f (x, y, z) represent the free-field ground displacement and traction, respectively, Γ denotes the soil-foundation interface, G σ denotes the traction Green's function, Λ denotes the fictitious load of the IBEM, and Ω represents the rigid foundation influence matrix.…”

“…Furthermore, U f (x, y, z) and T f (x, y, z) represent the free-field ground displacement and traction, respectively, Γ denotes the soil-foundation interface, G σ denotes the traction Green's function, Λ denotes the fictitious load of the IBEM, and Ω represents the rigid foundation influence matrix. 26,27 The additional motion φ 0 is computed from the inertial motion as follows:…”

A Study on Possibility of Detrimental Effects of Soil-Structure Interaction in Seismic Design Due to a Shift of System Frequency

“…The method, although widely used among civil engineers, is not accurate and cannot be parametrically quantified. For example, many studies by numerical simulations [16,17] and earthquake damage investigations [1,18] reveal that, structures with some same features in a certain area, exhibit much more serious damage than other structures without the features.…”

Effect of a symmetric V‐shaped canyon on the seismic response of an adjacent building under oblique incident SH waves

“…The dynamic soil-structure interaction (DSSI) is a key research topic in the field of earthquake engineering. [1][2][3][4] Numerical research efforts have been devoted into it by using various experimental, [5][6][7] numerical, [8][9][10][11][12][13][14] analytical, 15 or hybrid 16 methods. While experimental and numerical methods can more easily handle complex and realistic configurations, analytical solutions are of intrinsic significance not only for elucidating the underlying physics but also for serving as benchmarks for calibrating numerical results.…”