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A frequency-and intensity-dependent macroelement for reduced order seismic analysis of soil-structure interacting systems
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.
... As an example, Fig. 9 b and 9 c show the standard deviation range and mean of ∕ max and the damping ratio curves for the mean effective confining stress value ′ = 360 KPa and PI = 0. The soil-structure interaction phenomenon was incorporated into the numerical models through the use of a lumped parameter (LP) modeling method in the time domain according to [49] , and [71] . The implementation of SSI in the probabilistic assessment procedure is directly achieved by matching each building realization and earthquake ground motion pair with a different lumped parameter model generated according to the previously discussed soil profile variability models. ...
... The semi-coupled substructuring method is the most common method to collect kinematic and inertial responses of bridges (Carbonari et al. 2017, González et al. 2020, Lesgidis et al. 2018. It separates the bridge system into two subsystems including the superstructure and the substructure. ...
The coupled soil-pile-structure seismic response is recently in the spotlight of researchers because of its extensive applications in the different fields of engineering such as bridges, offshore platforms, wind turbines, and buildings. In this paper, a simple analytical model is developed to evaluate the dynamic performance of seismically isolated bridges considering triple interactions of soil, piles, and bridges simultaneously. Novel expressions are proposed to present the dynamic behavior of pile groups in inhomogeneous soils with various shear modulus along with depth. Both cohesive and cohesionless soil deposits can be simulated by this analytical model with a generalized function of varied shear modulus along the soil depth belonging to an inhomogeneous stratum. The methodology is discussed in detail and validated by rigorous dynamic solution of 3D continuum modeling, and time history analysis of centrifuge tests. The proposed analytical model accuracy is guaranteed by the acceptable agreement between the experimental/numerical and analytical results. A comparison of the proposed linear model results with nonlinear centrifuge tests showed that during moderate (frequent) earthquakes the relative differences in responses of the superstructure and the pile cap can be ignored. However, during strong excitations, the response calculated in the linear time history analysis is always lower than the real conditions with the nonlinear behavior of the soil-pile-bridge system. The current simple and efficient method provides the accuracy and the least computational costs in comparison to the full three-dimensional analyses.
... Previous attempts to analyze the soil-pile system, considering the nonlinearity in the soil, have been made by Chatzigogos et al. (2009) andEl Ganainy andEl Naggar (2009), but these studies overlooked the frequencydependent characteristics of the soil-foundation system. In a recent work by Lesgidis et al. (2018), a modeling approach was proposed that considers both frequency and amplitude dependencies within the framework of nonlinear SSI. This approach utilizes a lumped parameter model (Saitoh, 2007) and a dynamic trait extraction method. ...
The frequency-dependent horizontal impedance functions of a model floating 2 × 2 pile group, embedded in cohesionless sand under a 1g condition, were investigated experimentally. The tests were conducted using large amplitude loads inducing soil yielding. The soil-pile system was housed in a laminar shear box fastened to the top of a unidirectional shaking table. Quasi-static and dynamic loads were applied in a lateral direction under the fixed pile-head condition to evaluate the force–displacement relationship and the horizontal impedance functions, respectively. The results of the quasi-static loading exhibited rate-dependent behavior for the lateral load-bearing capacity of the piles. Notably, the analysis of the soil surface near the piles, using a stereo-PIV calibration, demonstrated a consistent failure pattern despite the significant variation in velocity. Furthermore, an important observation was the convergence of the horizontal dynamic impedance functions towards the secant static stiffness as the amplitude of dynamic loading increased.
... The macroelements for deep foundations developed to date have several limitations that do not allow reproducing (at least in a direct way) the response of a pile group under seismic loading. A newly established frequency-dependent macroelement technique is capable of reproducing the dynamic attributes of the system at multiple levels of increasing ground shaking [107]. ...
Seismic excitation causes the soil to begin acting nonlinearly at higher strain. Hence, the nonlinearity of the soil, foundation, and structure should be appropriately considered. This can be achieved by proper modelling of soil-structure-foundation interaction (SSI). The continuum, Winkler-based, and Macroelement models are the major modelling techniques for considering SSI. The continuum method involves determining absorbing boundaries, the size of the soil domain, soil element size, constitutive soil model, and soil structure interface. In contrast, the Winkler-based model uses nonlinear spring and dashpot to represent inelastic behaviour and energy dissipation properties of soil, respectively. Macroelement replaces the entire soil foundation arrangement with one element at the bottom of the superstructure. The trade-off between the advantageous effects of the SSI model, particularly in terms of energy dissipation, and its unfavourable effects, such as settling or tilting, should also be optimised during the analysis and design phases. The present paper aims to provide a concise review and comparative analysis of the several methodologies proposed by the researchers that consider the nonlinearity in soil-foundation-structure interaction (SSI). The importance of the study lies in the adoption of an approach that reduces computational effort and time. Moreover, the experimental works are also reviewed with regard to the soil structure interaction. It can be inferred from the current study that various approaches have some benefits and drawbacks; thus, these approaches can opt accordingly.
... For seismically isolated bridges and bridge foundations with limited rotational rigidity around their transverse axes, consideration of SSI effects was also found to be significant. Moreover, the significance of the SSI consideration is related to the ratio between the time of the structure and the predominant period at the site and duration of earthquake ground motion, as well as to its (Boulanger et al. 1999) frequency content (Lesgidis et al. , 2018Rahmani et al. 2018;Lim and Jeong 2018). ...
Bridges are among the most important transportation elements that may be damaged by earthquakes. An integral abutment bridge (IAB) is a bridge linking the superstructure directly to the substructure. As soil piles, abutments, and superstructures act as a combined system to resist lateral loading on the bridge, soil stiffness has a major impact on load distribution. This research attempts to determine how the structure and soil parameters affect the IABs. The parametric study consists of four variables, namely bridge span (short, medium, and large spans were 18.3, 35.4, and 64.5 m, respectively), backfill height/ pressure (3.1, 4.6, and 6.1 m, respectively), stiffness of soil mixture backfills (high, intermediate, and low), and soil density around the piles (high, intermediate, and low). Because of the small width-length ratio of the bridge, a 2D model of an IAB with soil springs around the piles and abutments was developed with finite element software. Findings show that the value of the backfill pressure affects girder axial forces and girder bending moments at the IAB. Also, the stiffness of soil mixture backfills is an important factor to change lateral displacements, while less movement is related to high stiffness of soil mixture backfills with intermediate clay around the pile. It is clear that the maximum axial girder moments at the superstructure generally decrease when the stiffness of the soil mixture behind the abutments and around piles increases, similar to pile deflection and abutment displacements. In addition to maximum abutment, the head moment decreases when abutment backfill is dense and increases when piles are located in hard clay, similar to pile moments. Lastly, dense sand backfill behind abutments is recommended since it decreases pile deflections, pile lateral forces, abutment displacements, abutment head moments, and particularly pile bending moments.
... 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. ...
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.
... Under these circumstances, the performance of soil-foundationstructure (SFS) systems, assuming nonlinear soil response, has received wide attention by researchers in both experimental [6][7][8][9][10] and numerical studies. The conducted numerical research has followed various approaches, such as the Finite Element discretization of the continuous soil medium [11][12][13][14][15], as well as, the use of macro-elements to simulate the soil-foundation interface [16][17][18] or beam on Winkler foundation models [19]. Overall, these studies recognize that energy dissipation during shaking, associated with nonlinear soil response, leads to the reduction of seismic demands for the superstructure. ...
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.
... 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. ...
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 spatial distribution of horizontally buried structures makes them more susceptible to seismic hazards. This naturally requires a reliable and effective method to analyze soil-buried structure interaction (SbSI) problems, in which the reduced-order model is widely-used thanks to its robustness and computational efficiency. However, for buried structures, no reduced-order model was capable of simultaneously capturing the frequency-dependent characteristics and the true nonlinear nature of the interaction forces. Accordingly, we proposed a dual frequency- and deformation-dependent macroelement model to investigate dynamic axial SbSI problems in the time domain. Novel uniaxial material models, such as Modified Bouc-Wen and Gyromass, were also implemented in OpenSees for the macroelement model development. Results of the proposed approach show good agreement with those of published experiments and finite element analyses. Finally, we present an illustrative example of a buried pipe subjected to spatially varying seismic ground motions. To highlight the importance of frequency- and deformation-dependent characteristics, we compared the results obtained from the proposed approach with those from a frequency-independent Kelvin-Voigt model. It is noticed that ignoring the frequency-dependency can lead to an underestimate of the axial strain envelope, e.g. up to 30% in the case of seismic excitation with a central frequency of 6 Hz.
The response of a two-storey RC school building in the town of Argostoli, Cephalonia Island, Greece, during the seismic sequence of January and February 2014, is examined. The structure was built following an older generation of seismic codes dating from the 1950s, which provide limited strength and ductility against lateral loads. Despite the severity of ground shaking, the building suffered relatively minor damage, like most of the RC buildings in the town. Following a short presentation of some basic seismological, structural and geotechnical aspects of the seismic sequence, the paper focuses on the seismic performance of the structure at hand. To this end, a series of detailed non-linear static and time-history dynamic analyses are reported, which highlight the interplay of soil, foundation and superstructure in modifying the seismic demand. It is demonstrated that SSI had an unexpectedly important (detrimental) role in the behavior of the structure, increasing its natural period by about 25% and aggravating ductility demand in almost all columns, despite the moderately soft soil conditions (VS=180m/s). The results shed light on the seismic performance of the building and help drawing conclusions on the engineering effects of the 2014 Cephalonia earthquake sequence.
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.
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.
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.
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.
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.
This paper presents a novel framework with which the inelastic behavior and the frequency-dependent dynamic characteristics of soil-foundation system can be represented with a computationally efficient numerical model. The inelastic behavior of soil in the vicinity of a shallow foundation is represented with a macro-element which is based on the classical plasticity theory. The frequency-dependent property of soil-foundation system is represented with a recursive parameter model. The framework allows integration of both models such that both the inelastic behavior and the frequency-dependent characteristics can be captured. The proposed method is verified against FE analysis of a shallow foundation in the two dimensional parametric space of frequency and inelasticity. The verification shows that the model using the proposed framework can fully represent the inelastic cyclic behavior at low frequency excitation and the dynamic response at high frequency excitation. The method provides an approximate solution for the cases in-between, e.g. a foundation subjected large amplitude high-frequency excitation. As an application example, the method is applied to an analysis of a bridge pier subjected to earthquake loading.
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.
A systematic procedure to develop a consistent lumped-parameter model with real frequency-independent coefficients to represent the unbounded soil is developed. Each (modelled) dynamic-stiffness coefficient in the frequency domain is approximated as a ratio of two polynomials, which is then formulated as a partial-fraction expansion. Each of these terms is represented by a discrete model, which is the building block of the lumped-parameter model. A second-order term, for example, leads to a discrete model with springs and dampers with two internal degrees of freedom, corresponding to two first-order differential equations, or, alternatively, results in a discrete model with springs, dampers and a mass with one internal degree of freedom, corresponding to one second-order differential equation.
The lumped-parameter model can easily be incorporated in a general-purpose structural dynamics program working in the time domain, whereby the structure can even be non-linear. A thorough evaluation shows that highly accurate results are achieved, even for dynamic systems with a cutoff frequency.
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.