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Effects of inertial soil–structure interaction on inelastic displacement ratios of SDOF oscillators subjected to pulse-like ground motions

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Abstract

This study is devoted to investigate the effects of inertial soil–structure interaction (SSI) on the constant-strength inelastic displacement ratios of elastoplastic single-degree-of-freedom systems using a suit of 91 pulse-like ground motions. The soil beneath the foundation is simulated based on the cone model. A local minimum for the inelastic displacement ratios around the interacting system-to-pulse period ratio of one is demonstrated. Moreover, the soil flexibility increases the inelastic displacement ratios at all interacting system-to-pulse period ratios. However, the aspect ratio has decreasing and increasing effects on the inelastic displacement ratios before and after a threshold interacting system-to-pulse period ratio, approximately very close to one. It is confirmed that for slender structures, the SSI effects are the lowest at small interacting system-to-pulse period ratios and as this ratio increases, the SSI effects on the inelastic displacement ratios increase. However, for squat structures, the SSI approximately has more significant effects on the inelastic displacement ratios at lower interacting system-to-pulse period ratios and the effects decrease for higher interacting system-to-pulse period ratios. It is noted that the equal displacement rule is not valid as the SSI effects are taken into account. In addition, a formula is proposed to estimate the inelastic displacement ratios of soil–structure systems using nonlinear regression analysis, which is desirable for the displacement assessment of existing structures. Besides, the mean ratios of approximate-to-analytical values, very close to one, emphasize well accuracy of the proposed formula.

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Abbreviations

SSI:

Soil-structure interaction

SDOF:

Single-degree-of-freedom

\(\hbox {C}_{\upmu }\) :

Constant-ductility inelastic displacement ratio

\(\hbox {C}_{\mathrm{R}}\) :

Constant-strength inelastic displacement ratio

\(\hbox {u}_{\mathrm{in}}\) :

Maximum inelastic lateral displacement

\(\hbox {u}_{\mathrm{e}}\) :

Maximum elastic lateral displacement

\(\hbox {u}_{\mathrm{y}}\) :

Maximum yielding lateral displacement

\(\upmu \) :

Structural ductility ratio

R:

Strength reduction factor

\(\hbox {F}_{\mathrm{e}}\) :

Elastic lateral force

\(\hbox {F}_{\mathrm{y}}\) :

Yielding lateral force

\(\upalpha \) :

Post-elastic stiffness ratio

\({\upxi }_{\mathrm{o}}\) :

Structural viscous damping

\(\hbox {T}_{\mathrm{fix}}\) :

Vibration period of fixed-base structure

\(\hbox {M}^{*}\) :

Effective mass of the structure in the first mode

\(\hbox {I}^{*}\) :

Effective mass moment of inertia of the structure around its geometric center

\(\hbox {h}^{*}\) :

Effective height of the structure in the first mode

N:

Number of stories

\(\hbox {C}_{\mathrm{m}}\) :

Effective mass coefficient

\(\hbox {C}_{\mathrm{h}}\) :

Effective height coefficient

r:

Radius of circular plan and foundation

\(\hbox {K}_{\mathrm{fix}}^{*}\) :

Elastic stiffness of the fixed-base structure

\(\hbox {m}_{\mathrm{f}}\) :

Foundation mass

\(\hbox {I}_{\mathrm{f}}\) :

Mass moment of inertia of the foundation

\(\hbox {A}_{\mathrm{f}}\) :

Area of the foundation

\(\hbox {r}_{\mathrm{e}}\) :

Equivalent radius of the non-circular foundation

DOF:

Degree-of-freedom

s:

Sway degree-of-freedom of the foundation

\({\upvarphi }\) :

Rocking degree-of-freedom of the foundation

\(\uptheta \) :

Additional internal rotational degree-of-freedom

\(\hbox {m}_{\uptheta }\) :

Polar mass moment of inertia of additional freedom

\({\upupsilon }\) :

Soil Poisson’s ratio

\(\hbox {V}_{\mathrm{a}}\) :

Soil axial-wave velocity

\(\hbox {V}_{\mathrm{s}}\) :

Soil shear-wave velocity

\(\Delta \hbox {M}_{{\upvarphi }}\) :

Trapped mass moment of inertia

\(\hbox {k}_{\mathrm{s}}\) :

Sway stiffness coefficient of soil

\(\hbox {k}_{{\upvarphi }}\) :

Rocking stiffness coefficient of soil

\(\hbox {C}_{\mathrm{s}}\) :

Sway damping coefficient of soil

\(\hbox {C}_{{\upvarphi }}\) :

Rocking damping coefficient of soil

\(\uprho \) :

Mass density of soil

\({\upomega }_{\mathrm{fix}}\) :

Circular frequency of fixed-base structure

G:

Shear modulus of the soil

\({\upxi }_{\mathrm{M}}\) :

Material damping of the soil

\(\hbox {a}_{0}\) :

Non-dimensional frequency

M:

Mass matrix of soil–structure system

C:

Damping matrix of soil–structure system

K:

Stiffness matrix of soil–structure system

{U}:

Displacement vector of soil–structure system

\(\hbox {u}_{\mathrm{g}}\)(t):

Input acceleration time history

{r}:

Influence vector

\(\hbox {u}^{*}\) :

Absolute displacement of soil–structure system

\(\hbox {u}_{\mathrm{s}}\) :

Sway displacement of the foundation

c:

Structure damping

\(\hbox {T}_{\mathrm{p}}\) :

Pulse period

\(\hbox {T}_{\mathrm{ssi}}\) :

Vibration period of soil–structure system

\({\upbeta }\) :

Ratio of the \(\hbox {C}_{\mathrm{R}}\)-values resulting from the soil–structure systems to those obtained from the fixed-base structures

\({\upbeta }_{\mathrm{ap}}\) :

Approximate value of \({\upbeta }\)

\({\upbeta }_{\mathrm{an}}\) :

Analytical value of \({\upbeta }\)

\(\hbox {E}_{\mathrm{m}}\) :

Mean ratio of \({\upbeta }_{\mathrm{ap}}\) to \({\upbeta }_{\mathrm{an}}\)

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Authors and Affiliations

  1. Faculty of Civil Engineering, Amirkabir University of Technology (Tehran Polytechnic), Hafez Avenue, Tehran, Iran

    Faramarz Khoshnoudian

  2. Department of Civil Engineering, Monash University, Clayton Campus, Melbourne, Australia

    Ehsan Ahmadi

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  1. Faramarz Khoshnoudian
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  2. Ehsan Ahmadi
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Correspondence to Ehsan Ahmadi.

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Khoshnoudian, F., Ahmadi, E. Effects of inertial soil–structure interaction on inelastic displacement ratios of SDOF oscillators subjected to pulse-like ground motions. Bull Earthquake Eng 13, 1809–1833 (2015). https://doi.org/10.1007/s10518-014-9693-y

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  • DOI: https://doi.org/10.1007/s10518-014-9693-y

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