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Abstract

The computational demand of the soil-structure interaction (SSI) analysis for the design and assessment of structures, as well as for the evaluation of their life-cycle cost and risk exposure has led the civil engineering community to the development of a variety of methods towards the model order reduction of the coupled soil-structure dynamic system in earthquake regions. Different approaches have been proposed in the past as computationally efficient alternatives to the conventional FEM simulation of the complete soil-structure domain, such as the nonlinear lumped spring, the macroelement method and the substructure partition method. Yet no approach was capable of capturing simultaneously the frequency-dependent dynamic properties along with the nonlinear behavior of the condensed segment of the overall soil-structure system under strong earthquake ground motion, thus generating an imbalance between the modeling refinement achieved for the soil and the structure. To this end, a dual frequency-and intensity-dependent expansion of the Lumped Parameter Modeling method is proposed in the current paper, materialized through a multi-objective algorithm , capable of closely approximating the behavior of the nonlinear dynamic system of the condensed segment. This is essentially the extension of an established methodology, also developed by the authors, in the inelastic domain. The efficiency of the proposed methodology is validated for the case of a bridge foundation system, wherein the seismic response is comparatively assessed for both the proposed method and the detailed finite element model. The above expansion is deemed a computationally efficient and reliable method for simultaneously considering the frequency and amplitude dependence of soil-foundation systems in the framework of nonlinear seismic analysis of SSI systems.
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... Lesgidis et al. [116] have recently developed a frequency-dependent macroelement method that is able to reproduce the dynamic properties of the system across various levels of increasing seismic intensity. The proposed macroelement can be divided in two elementary components: a frequency-independent macroelement (i.e., a standard elastoplastic or hypoplastic macroelement can be used according to the literature and depending on the problem to be solved) that manages the nonlinear pseudo-static response of the system and a frequency and intensity-dependent lumped [117] and Li et al. [122,123] parameter model that is intended to capture the dynamic response of the system. ...
... Frequency-dependent and intensity-dependent macroelement approach proposed by Lesgidis et al.[116] ...
Thesis
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The dynamic response of a structure supported by pile foundations is a complex Soil-Structure Interaction (SSI) problem. Under earthquake loading, the piles are subjected to loadings due to the deformation imposed by the soil (kinematic interaction) and to the inertial forces transmitted by the superstructure (inertial interaction). The design of deep foundations under seismic loadings is often carried out by means of conservative methods that aim to assure zero damage of the foundation. Most of these methods consider the behavior of the foundation as linear elastic. As a result, the capability of the foundation to dissipate energy during seismic loading due to nonlinear mechanisms is neglected. This approach was justified in the past due to the lack of information about the nonlinear behavior of foundations and the absence of adapted numerical tools. Such limitations are becoming more and more obsolete, as a relevant number of experimental and numerical results are now available as well as new design methods (Pecker et al. 2012). In this Ph.D, the behavior of single piles and pile groups under seismic loading is studied using both experiments and finite element calculations. Dynamic centrifuge tests are carried out with a multilayered soil profile, several foundation configurations and a series of earthquakes and sinusoidal base shakings. Nonlinear finite element calculations are also performed and compared to experimental results to investigate the ability of current computational models to satisfactorily reproduce the nonlinear response of foundations. A novel macroelement for pile group foundations under seismic loading is developed and numerically validated. It allows taking into account the group effects and their variation with the loading frequency (pile-soil-pile interaction) as well as the nonlinearity developed in the system. Finally, the macroelement model for pile groups is used to perform an Incremental Dynamic Analysis (IDA) of the main pylon of a cable-stayed bridge.
... Lowfidelity, linear, and nonlinear spring models can be used at the foundation of the building structure (e.g., Stewart et al., 1999;Sotiriadis et al., 2020). Lesgidis et al. (2018) proposed frequencyand intensity-dependent spring models for SSI. ...
Article
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The rapid growth of the urban population and associated environmental concerns are challenging city planners and developers to consider sustainable and cost-efficient building systems. Timber-based buildings, such as sustainable systems, are increasingly used. The timber buildings, however, being lighter and flexible, can be vulnerable to earthquakes and wind loads. This paper gives a state-of-the-art review on performance-based design (PBD) considerations and future direction for timber and timber-based hybrid buildings. The PBD review covered both earthquake and wind loads and multi-hazard design considerations. The review also provided 1) current practice and future direction in consideration of hazard, response, and loss assessment within the multi-hazard PBD, 2) damping and energy dissipation devices, 3) optimization under uncertainty, and 4) future of surrogate and multi-fidelity modeling in PBD.
... Although these models can account for the soil's elastoplastic response and interface nonlinearity, such as uplifting, the frequency dependency of IFs has never been considered. A new macroelement model for the incorporation of the frequency-dependent IFs of shallow foundations, using modified GLPMs, was presented in Lesgidis et al. (2018). They considered nonlinearity in their work in order to approximately simulate the FEM results of simplified soil foundation systems by employing a dynamic trait extraction approach. ...
Article
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This paper proposes a phenomenological model that represents both the frequency and intensity dependencies of the dynamic force–displacement relationship at the head of horizontally loaded piles. The present model consists of a bilinear spring unit with hysteretic characteristics and a so-called “Gyro-Lumped Parameter Model (GLPM)” unit arranged in series. The former unit represents the static yielding procedure of soil-pile systems, while the latter represents the frequency-dependent characteristics of impedance functions. Firstly, this study validates the general behavior of the proposed model and then verifies it by simulating the experimentally obtained pile head impedance functions of a single pile for small to large amplitudes of loading in a wide range of frequencies. The results show that the proposed model can sufficiently reproduce variations in the frequency-dependent characteristics of impedance functions for a wide range of loading amplitudes.
... The impedance matrix is calculated using the predominant frequency of the input motion according to the common assumption in the literature [23,49,62,63]. This hypothesis may not be accurate under certain conditions that the input motions are rich in a wide range of frequencies [64,65]. Therefore, it is suggested to verify it with a suitable continuum model. ...
Article
Most of the common monorail bridges in the world are non-isolated ones due to their low superstructure weight. Recently, a limited study on the innovative isolated monorail bridges demonstrated that seismic isolation systems can be beneficial to monorail bridges. In this study, a parametric analysis of soil-pile-bridge-train (SPBT) interaction during frequent earthquakes was performed to better understand the seismic behavior of the novel isolated monorail bridges compared to the traditional non-isolated monorail bridges and the conventional railway bridges. To evaluate the influence of train-bridge interaction (TBI) on the seismic response of bridges under the combined vertical and horizontal ground motions, Taiwan Railway Bridge (TRB), and Qom Monorail Bridge (QMB) with and without isolators were selected. A total of 2268 time history analyses, including different isolator shear modulus, train locations in two vehicle modeling approaches, pier heights, and ground motions in different directions, were performed using the substructuring method. The results were verified by comparing the 3D continuum finite elements. The observations indicated that when lateral and vertical excitations were applied simultaneously, for monorail bridges where the trains’ weight usually reached up to 50% of the weight of a couple of the guideway beams, the presence of the train led to creating the critical conditions. However, for the conventional railway bridges with relatively low train-to-deck weight ratios (less than 30%) ignoring the train could cause the most critical responses in the SPBT system, regardless of the vehicle modeling approach. It was also found that the efficiency of seismic isolation systems for conventional railway bridges is higher than that for monorail bridges.
... Based upon the Saito's model in 2012, Lesgidis, Sextos, & Kwon (2018) further developed a new dynamic macroelement method capable of emulating the inelastic dynamic behavior of the soil-foundation system. The efficiency of the methodology proposed by Lesgidis et al. was validated for the case of a bridge foundation resting on uniform soil. ...
Article
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Numerous physical models using frequency-independent elements have been developed to reproduce impedance functions for the purposes of time-domain soil–foundation interaction analysis. Most of the models have been developed to simulate homogeneous soils. However, the physical models developed in past research for layered soils are mostly focused on surface foundations only. Accordingly, this study proposes a representative simplified model to simulate the three-dimensional layered soil for square foundations embedded in a non-uniform layer, overlying a uniform half-space, subjected to vertical forced vibrations. The non-uniform layer has shear-wave velocities linearly varying with depth. Non-dimensional charts are presented to determine the model parameters as per foundation embedment ratios, layer depth ratios, and shear-wave velocity ratios of layered soil. The capability of the proposed model is demonstrated through the analysis of frequency-response curves of the foundation to a constant-force type oscillator in the frequency domain and of the displacement history of the foundation to a non-periodic loading in the time domain. The proposed model is found to give results consistent with those obtained from a dynamic soil-structure interaction analysis program. The proposed model may be of practical value for analysis of dynamically loaded foundations.
... Similarly, 1D FEMs are developed to study various soil-structure interaction problems, where details for considering soil nonlinearity, soil impedance, as well as kinematic interaction are often approximated through simplified material laws, springs, and dashpots, respectively [9][10][11][12]. For more insightful quantification on wave propagation effects, soil fatigue, discontinuity at the soil-pile interface, advanced nonlinear 3D soil models with detailed material constitutive laws are often preferred [13][14][15][16][17][18][19][20]. Independently of the modeling approach, each computational model must be defined in terms of structural parameters such as mass, stiffness, damping, strength, boundary conditions, etc. ...
Article
The cross-section and the structural twist angle of a typical wind turbine blade vary along its span. This complicates its realistic modeling in nonlinear dynamic analysis of wind turbines when seismic performance estimates are sought. As a result, the lumped mass approach is most commonly used to model the rotor-nacelle-assembly (RNA). The RNA is eccentric to the tower top, and the blades tend to induce rotary inertia on the tower. The exclusion of this rotary inertia and the rotor eccentricity can impact the structural response of the wind turbines as the RNA contributes significantly to the total mass of the system. Moreover, the blades are long, slender structural components that can vibrate and deform independently under seismic excitation. The lumped mass approach intrinsically considers the rigid-body inertia for the RNA, which inevitably acts as a part of the tower top. This can affect the seismic vulnerability estimation of the offshore wind turbines (OWT) at a degree that has not yet been properly quantified. To explore this issue, the present study discusses the effects of the three key RNA parameters, i.e., (i) rotary inertia of the blades, (ii) rotor eccentricity, and (iii) blades' flexibility, on the seismic failure and fragility of OWT under shallow crustal earthquakes. Results show that the rotary inertia affects the higher modes, which in turn influence the height of the tower failure zones. It is also shown that different levels of RNA modeling refinement affect the predicted failure probabilities, particularly under pulse-like ground motions, while the same estimates are overestimated if the conventional rigid body lumped mass rotary inertia is used. Even worse, they can be underestimated (thus less safe) when the rotary inertia is completely ignored, compared with the refined modeling of flexible turbine blades. These results are revealing as they highlight that seismic hazard can indeed pose a significant design issue for OWTs in some regions.
... The modeling of nonlinearity in soil-pile foundation systems, attempted by authors such as El Ganainy and El Naggar (2009) and Chatzigogos et al. (2009), deals with the yielding of soil, but it lacks consideration of the frequency-dependent characteristics of these soil-pile foundation systems. Recently, Lesgidis et al. (2018) expanded a modeling approach to account for both the frequency and the amplitude dependence of the soil-pile system within the framework of nonlinear SSI using a lumped parameter model (Saitoh, 2007) and employing a dynamic trait extraction approach. They considered the nonlinearity in their work to approximately simulate the FEM results of simplified soil foundation systems. ...
Article
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This paper investigates the frequency-dependent pile-head impedance characteristics of a model soil-pile foundation system under large amplitude loads, inducing soil yielding. Testing was conducted on a scaled single pile embedded in sand under a 1g condition. A laminar shear box mounted on a unidirectional shaking table was used to house the soil-pile foundation system. Quasi-static loads and dynamic loads were applied to obtain the force–displacement relationships and pile-head impedance functions, respectively, through the pile head connected to a loading actuator providing fixity to the pile head in all directions, except horizontal. In the quasi-static case, loads with three different velocities were applied to study the rate-dependent characteristics of the lateral bearing capacity of the pile. The Stereo-PIV system was employed to measure the surface soil displacement around the pile. The lateral bearing capacity changed with the loading velocity, but the soil near the pile showed a consistent failure pattern despite a significant change in velocity. Lateral pile-head dynamic impedance functions were obtained for low-to-high amplitude harmonic loading for a wide range of frequencies. The dynamic stiffness was seen to converge to that of the secant static stiffness with an increase in the amplitude of the dynamic loading for all the excitation frequencies.
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The gradual extension of performance-based design in geotechnical engineering has focused the attention on the seismic performance of foundations, typically, in terms of settlement, tilt and bearing capacity degradation. The aim of the present paper is to explore the role of superstructure inertia on the performance of shallow foundations through a series of non-linear numerical analyses of structure-foundation-soil systems, performed with the Finite Difference Code FLAC3D. The NTUA-Sand constitutive model is used to simulate the nonlinear cyclic soil response. The parametric analyses focus upon the effect of key soil-structure interaction parameters, such as the frequency characteristics of the structure – foundation (SFS) system and that of the free-field soil profile, as well as, the structural and excitation properties. Initially, the nonlinear fundamental period of vibration of the SFS system is correlated to the above key parameters of the system and the seismic excitation. In the sequel, to isolate the SSI effects, settlements of SFS systems are compared with the respective settlements of equivalent foundation-soil systems (FS). Simplified relations are finally developed for the analytical calculation of SSI effects on foundation settlements, based on a multi-variable statistical analysis of the available numerical predictions.
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The present study explores the effect of soil–structure interaction (SSI) on the foundation motion as recorded at accelerometric stations located at the basement of buildings through a large dataset employed from sites where both foundation and free-field ground motion recordings are available. The significance of such instrumentation is highlighted, in terms of assessing the high frequency filtering that occurs at the foundation level and its potential implication on ground motion prediction models (GMPMs) that are produced with these datasets. Based on the recorded data, analytical expressions relating foundation, and free-field motion intensity measures, which have been produced in a previous work, are verified. A sub-structure analysis procedure is extended to include the site and building characteristics of the recorded data. Nonlinear regression analyses are performed, utilizing numerous analysis results, to derive improved, robust analytical expressions, as well as, to include building characteristics. Residual analysis is performed to assess possible bias due to other variables, as well. The produced analytical expressions are validated against the recorded data and compared to the existing expressions in terms of prediction errors. The produced analytical expressions can be utilized for correcting motions recorded at the basement level of buildings to obtain estimates of free-field ground motions. The latter being “building-free” is most appropriate for the development of new generation GMPMs that are not biased by the influence of kinematic and inertial interaction. The impact of correcting ground motion data through the proposed analytical expressions is discussed through their implementation on recently published strong motion dataset.
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Substructure method is widely used to evaluate the seismic performance of caisson foundations supporting bridge piers subjected to strong ground motions, mainly because of its simplicity. However, the strongly‐simplifying assumption of linear viscous‐elastic behaviour for the foundation soil limits its applicability to flexible systems subjected to low‐intensity earthquakes, for which irreversible strains and pore water pressure build‐up are not anticipated. Furthermore, lumped‐parameter models are typically adopted in calculations in which soil‐foundation compliance is reproduced via dynamic impedance functions, whose dependency on frequency of excitation is often neglected. Modification of free‐field motion leading to foundation input motion (FIM), due to the presence of caisson embedment, is also mostly ignored. The influence of these simplifying assumptions on the seismic performance of bridge piers on caisson foundations is assessed in this paper through a parametric study, where soil‐caisson‐bridge pier‐deck systems differing in geometric and mechanical properties are subjected to real seismic records. Dynamic analyses were carried out in the time domain with the finite element method, using a 3D continuum and a lumped‐parameter model for the foundation soil. In the 3D model both the linear viscous‐elastic and the nonlinear soil behaviour were assumed, while linear viscous‐elastic behaviour was assumed in the lumped‐parameter model. The influence of inelastic soil behaviour was assessed by comparing the seismic performance of the systems obtained with the 3D model, while the role of FIM was evaluated by comparing the results of the dynamic analyses computed assimilating the soil to a linear elastic medium.
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Bridge performance under earthquake loading can be significantly influenced by the interaction between the structure and the supporting soil. Even though the frequency dependence of the interaction mentioned in this study has long been documented, the simplifying assumption that the dynamic stiffness is dominated by the mean or predominant excitation frequency is still commonly made, primarily as a result of the associated numerical difficulties when the analysis has to be performed in the time domain. This study makes use of the advanced lumped parameter models recently developed in order to quantify the impact of the assumption on the predicted fragility of bridges mentioned in this study. This is achieved by comparing the predicted vulnerability for the case of a reference, well studied, actual bridge using both conventional, frequency-independent, Kelvin-Voigt models and the aforementioned lumped parameter formulation. Analysis results demonstrate that the more refined consideration of frequency dependence of soil-structure interaction at the piers and the abutments of a bridge not only leads to different probabilities of failure for given intensity measures but also leads to different hierarchy and distribution of damage within the structure for the same set of earthquake ground motions even if the overall probability of exceeding a given damage state is the same. The paper concludes with the comparative assessment of the effect for different soil conditions, foundation configurations, and ground motion characteristics mentioned in this study along with the relevant analysis and design recommendations.
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This paper presents a novel macroelement for single vertical piles in sand developed within the hypo-plasticity theory, where the incremental nonlinear constitutive equations are defined in terms of generalized forces, displacements and rotations. Inspired from the macroelement for shallow foundations of Salciarini and Tamagnini (Acta Geotech, 4(3):163–176, 2009), the new element adopts the “intergranular displacement” mutuated from Niemunis and Herle (Mech Cohes Frict Mater, 2:279–299, 1997) to reproduce the behavior under cyclic loading. Analytical and numerical strategies are provided to calibrate the macroelement’s parameters. Comparisons with experimental results show the performance of the macroelement that while being simple and computational fast is suitable for finite element calculations and engineering design.
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This study presents a methodology to make a simple equivalent model of frequency-dependent impedance functions of soil-structure interactions using a frequency-independent spring and dashpot, together with a proposed element called "gyro-mass". The gyro-mass is frequency-independent and is defined as a unit system that generates a reaction force due to the relative acceleration of the nodes between which the gyro-mass is placed. It is found that a model consisting of a spring, dashpot and gyro-mass may generate various types of frequency-dependent impedance characteristics. This study proposes two types of simple models that express typical frequency-independent impedance functions of soil-structure interactions by using the gyro-mass. The advantage of these models is that the frequency-dependent characteristics can easily be expressed by a small number of elements and degrees of freedom. Moreover, they can be applied directly to conventional time-history analyses, even beyond the elastic region of the structural members. An example in which a simple model is applied to the time-history analysis of a soil-pile-superstructure system with an inelastic structural member when subjected to an earthquake wave is illustrated.
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A new nonlinear soil-structure interaction macroelement is presented. It models the dynamic behaviour of a shallow strip foundation under seismic action. Based on sub-structured methods, it takes into account the dynamic elastic effect of the infinite far field, and the material and geometrical nonlinear behaviour produced in the near field of the foundation. Effects of soil yielding below the foundation as well as uplift at the interface are considered. Through the concept of macro-element, the overall elastic and plastic behaviour in the soil and at the interface is reduced to its action on the foundation. The macro-element consists of a non linear joint element, expressed in the three degrees of freedom of the strip foundation, reflecting the limited bearing capacity of the foundation. This model provides a practical and efficient tool to study the seismic response of a structure in interaction with the surrounding soil medium. Applications to a bridge pier show the potentialities of this kind of model.
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It is highlighted in the past that the soil–structure interaction phenomenon can produce a significant alteration on the response of a bridge structure. A variety of approaches has been developed in the past, which is capable of tackling the soil–structure interaction problem from different perspectives. The popular approach of a discretized truncated finite element model of the soil domain is not always a numerically viable solution, especially for computationally demanding simulations such as the probabilistic fragility analysis of a bridge structure or the real time hybrid simulation. This paper aims to develop a complete modeling procedure that is capable of coping with the soil–structure interaction problem of inelastic bridge structures through the use of a frequency dependent lumped parameter assembly. The proposed procedure encounters accuracy and global stability issues observed on past methods while maintaining the broad applicability of the method by any commercial FEM software. A case study of an overpass bridge structure under earthquake excitations is illustrated in order to verify the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.
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Lumped parameter models with a so called “gyro‐mass” element (GLPMs) have been proposed recently in response to a strong demand for efficiently and accurately representing frequency‐dependent impedance functions of soil–foundation systems. Although GLPMs are considered to be powerful tools for practical applications in earthquake engineering, some problems remain. For instance, although GLPMs show fairly close agreement with the target impedance functions, the accuracy of the transfer functions and the time‐histories of dynamic responses in structural systems comprising GLPMs have never been verified. Furthermore, no assessment has been performed on how much difference appears in the accuracy of dynamic responses obtained from GLPMs and those from conventional Kelvin–Voigt models comprising a spring and a dashpot arranged in parallel with various frequency‐independent constants. Therefore, in this paper, these problems are examined using an example of 2×4 pile groups embedded in a layered soil medium, supporting a single‐degree‐of‐freedom system subjected to ground motions. The results suggest that GLPMs are a new option for highly accurate computations in evaluating the dynamic response of structural systems comprising typical pile groups, rather than conventional Kelvin–Voigt models. Copyright © 2011 John Wiley & Sons, Ltd.
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Performance-based earthquake engineering (PBEE) assessment studies on highway bridges can only address post-earthquake repair fully when considering the response of the bridge-foundation-ground and the consequences of damage and repair to all system components. In this paper, nonlinear time history analysis of coupled bridge-foundation-ground systems is coupled with a PBEE framework to investigate a typical highway overpass bridge founded on different soil profiles. The prototype bridges are typical reinforced concrete highway overpass bridges with single-column bents founded on four sites of varying stiffness and strength profiles ranging from rigid rock to weak upper soil strata. Probabilistic repair cost and time response quantities are used to contrast performance of the four scenarios. Intensity-dependent repairs, repair hazard curves, and repairs disaggregated by performance groups indicate contributions to system repair for each scenario. A sensitivity study is presented that demonstrates the most important parameters to be the damage state and repair quantities related to the foundations and abutments.