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Earthquake-induced liquefaction poses grave safety risks to the underground structures. In this study, 1-g shaking table tests were conducted to investigate the uplift behaviors and soil-structure interaction (SSI) of a two-part tunnel located in liquefiable soils, with special attention paid to the influence of structural surface roughness. Two parallel tests, including a free-field test and a soil-tunnel test, were carried out to investigate the field responses and the effect of SSI during liquefaction induced by various input motions. The test results indicate that the ground partially liquefied during the first shaking event, and then experienced full liquefaction in the subsequent events with higher loading amplitude and longer loading duration. The excess pore pressure and horizontal acceleration responses around the tunnel were significantly altered due to the presence of the tunnel, which also led to different patterns of acceleration amplification and strain development in its vicinity. While structural surface roughness influenced the aforementioned responses to some extent, it played a more dominant role in the uplift behavior of the tunnel. The segment with lower surface roughness experienced significantly greater uplift compared to the rougher counterpart. Furthermore, it was found that the structural uplift behavior can be divided into distinct stages that feature different patterns of pore pressure development, and such behavior was notably different under varied loading conditions. The findings in this research emphasize the importance of incorporating the considerations of surface roughness in future numerical or experimental studies so that the structural uplift can be better captured. • The characteristics of earthquake motions have significant impacts on the triggering and development of field liquefaction. • The field dynamic responses in the vicinity of the tunnel were notably changed due to the soil-structure interaction. • Structural surface roughness had a remarkable influence on the structural uplifts. • The structural uplifting behavior was notably different under earthquakes with varied loading amplitudes and durations. [ABSTRACT FROM AUTHOR]

This paper presents the development of a large-scale tunnel model using an innovative loading device, which is then subjected to longitudinal seismic response analysis through a shaking table test. The loading device, designed to support the tunnel with springs, applies seismic loads from the shaking table and simulates the soil-structure interaction. Initially, the rationality and accuracy of the loading device were validated through numerical and analytical methods. Experimental results reveal that, under various seismic excitations, the acceleration response is significantly lower at the tunnel ends compared to the middle. The tensile strain response at the arch waist exhibits a U-shaped deformation along the longitudinal axis, while the compressive strain response exhibits a bending deformation with multiple inflection points. Furthermore, both tensile and compressive strain responses at the arch bottom show more pronounced bending deformations along the longitudinal direction. The findings indicate that the peak value of the input seismic excitation does not alter the deformation pattern of the tunnel. Within the longitudinal length L of the tunnel, the tensile zone reaches a maximum strain value ε max , whereas the compressive zone reaches a minimum strain value ε min. These experimental insights offer valuable references for the seismic design of tunnels. • An innovative loading device was designed and developed based on shaking table. • The large-scale model can more accurately capture the seismic response of the tunnel. • The test results reveal the deformation patterns of a large-scale tunnel model. • The loading device and experimental method can be applied to underground structures. [ABSTRACT FROM AUTHOR]

The paper proposes a methodology for assessing the seismic soil-foundation-abutment response in the spirit of the sub-structure approach. The methodology is suitable for conventional bridge abutments characterized by massive structural components and accommodates for various structural and soil configurations, from both stratigraphic and topographic perspectives. The abutment is assumed to be rigid, which is a generally acceptable hypothesis given the typical geometry of conventional bridge abutments with walls, orthogonal wingwalls, and a concrete deep or strip foundation. The methodology aligns with codes, which foresees a linear behaviour for the abutments and suggest a low behaviour factor to account for dissipative capabilities due to the backfills and the radiation phenomena in the soil. The soil is assumed to perform elastically, but the overall soil nonlinearity induced by seismic wave propagation can be incorporated into the method using a linear equivalent representation of soil properties. The methodology is applied to a real case study in order to demonstrate its effectiveness in addressing the soil-structure interaction problem and to provide practical suggestions for the method implementation, including possible simplifications. • Methodology for seismic response of conventional bridges with massive abutments. • Advanced modelling for bridges with complex abutments and multi-level foundations. • Soil-abutment interaction method for various foundations and soil conditions. • A case study provides insights and recommendations for the methodology implementation. • Importance of soil-abutment interaction effect in seismic risk assessment of bridges. [ABSTRACT FROM AUTHOR]

Soil-structure interaction (SSI) will change structural characteristics of a tall building, while parameters of the passive tuned mass damper (TMD) should be specifically optimized in this case. However, the structural model and soil parameters are full of uncertainties, and the seismic response mitigation of passive TMD suffers from the frequency and damping detuning. To improve its seismic performance, the semi-active TMD (STMD) is presented in this study, which can adjust frequency and damping ratio simultaneously. It can not only add or remove its mass to retune the frequency, but the eddy current damping ratio can also be adjusted in real time by reset the air gap, according to a developed output signals based solely combined algorithm. To verify its seismic mitigation performance preliminarily, a SDOF main structure is investigated, while it is found that when the frequency detuning occurs on the STMD with variable damping solely, a significant performance degradation is detected; while STMD with variable frequency and damping ratio always has the best control performance. Then, a 40-story benchmark high-rise building with different SSI types is presented as the case study. Numerical results show that STMD can reduce structural displacement responses effectively and has a better control performance than optimal passive TMD for each model. Meanwhile, frequency detuning of passive TMD is discussed and degradation of robustness is found in the passive TMD with ±15 % stiffness detuning. It can be known that proposed STMD has the best control robustness as well, because it is always tuned. • The proposed STMD can vary its mass and frequency according to the wavelet transform based algorithm. • STMD can adjust its damping ratio according to a switching algorithm based on relative velocity and acceleration. • The seismic mitigation of STMD is verified through a SDOF main system and tall building with SSI. • Results show that STMD always has the best seismic mitigation effect in each SSI model. [ABSTRACT FROM AUTHOR]

In conventional designs, the pile and pile cap are typically considered rigid connections. However, this type of connection experiences a concentrated force during earthquakes, leading to frequent damage at the pile heads. To mitigate pile head damage, semirigid pile‒pile cap connections are proposed. Centrifuge shaking table tests were conducted to investigate the seismic response of the superstructure‒pile foundation system. Two layers of Toyoura sand, including a moderately dense upper layer and a denser bottom layer, were used as the foundation soil. The superstructure was simplified as lumped masses and columns with two different heights and periods. The foundation consisted of a 3 × 3 group of piles. Rigid and semirigid pile‒pile cap connections were evaluated. The experiments investigated the effect of connection type on the distribution of bending moments in the piles and analyzed the acceleration and displacement responses of the superstructure under different pile‒pile cap connections. According to the results, semirigid connections reduced the peak bending moment at the pile head by 50–70 %, especially for low-rise superstructure cases. The influence depth of the connection type on the pile bending moment reaches approximately 10 times the pile diameter. For low-rise superstructure cases, semirigid connections slightly reduced the natural frequency of the superstructure, leading to a decrease in the superstructure acceleration during earthquakes with a short dominant period. The semi-rigid connections reduce the rotation of foundations but promote the translational displacement of foundations. For the mid-rise superstructure cases, semirigid connections reduce the translational displacement and increase the rotational displacement of the foundation. These experiments provide insights into the seismic performance of superstructure‒pile foundation systems with different pile‒pile cap connections and can serve as a reference for seismic design in similar engineering practices. • A series of centrifuge shaking table tests are conducted to study the dynamic behavior of the superstructure-pile foundation system with different types of pile-pile cap connection; • The influence of pile-pile cap connection on the seismic responses of the superstructure with different height and period are evaluated and discussed; • The influence of pile-pile cap connection on the dynamic bending moment of piles are assessed. [ABSTRACT FROM AUTHOR]

Seismic safety of highway bridges is one of the critical issues for the functionality of transportation lifelines after severe earthquakes. Skewed highway bridges are found to be more vulnerable due to the irregular distribution of seismic demands on the bridge components. Moreover, scour induced loss of soil material and hence reduction in lateral support around the foundation piles can amplify the seismic effects on the structural components of water crossing bridges. A numerical study was conducted to investigate the seismic performance of skewed and straight highway bridges with varying scour depths and two different scouring types around the bridge piles. Analytical models of straight (0°) and 45° skewed bridges were created using the OpenSees program and a series of nonlinear response history analysis was carried out under the effect of recorded strong ground motions. In the first scouring type which was called as Case-1, scour depth was assumed the same around all piles and varied uniformly. In Case 2, two different non-uniform scouring types with linearly varying scour depth around the piles were investigated. The uncertainty in the earthquake ground motion excitation direction of the two horizontal components was also studied by considering the variable incidence angle of ground motion pairs. The maximum seismic demands of the members at different ground motion incidence angles were evaluated and compared to the demands obtained for the critical ground motion incidence angles suggested by Caltrans. Superstructure displacement, curvature demands of bridge column and shear force demands of pile elements are the seismic demand parameters examined within the scope of the study and were compared for each scour condition for both straight (0°) and 45° skewed bridge. • Comparison of uniform and non-uniform scour cases for skewed bridges. • The effect of ground motion incidence angle on the seismic demands of bridge members. • Comparison of engineering demand parameters according to regulations given in Caltrans. [ABSTRACT FROM AUTHOR]

Many grain silos in earthquake intensity areas are at significant risk of post-seismic damage, which compromise their functionality and pose an enormous challenge to post-disaster rescue and social stability. However, the current specifications based on fixed-base foundations are not fit for the seismic design of silos in soft soil areas. Therefore, it is of great practical significance to study the seismic disaster prevention of siloes considering soil-structure interaction (SSI) for food security and post-disaster supply. In this research, a column-bearing silo in a soft soil area is taken as the research object. The relative displacement response, elastic-plastic development and storage lateral pressure of the structure under different ground motions are studied in detail when the state of filling storage material is empty, half-filled and fully filled. Compared with the fixed-base model, the mechanism of the ground motion response and the influence of the SSI effects on the dynamic characteristics of the column-bearing silo structure under different storage conditions are revealed. In addition, structural vulnerability analysis is carried out with the incremental dynamic analysis (IDA) method. Finally, the structural damage probability with and without SSI effects under different storage conditions is further discussed. The results demonstrate that the SSI effects have a certain damping effect on the column-bearing silo. The amount of storage material changes the failure probability of the structure. Moreover, full-silo is the most dangerous condition, indicating that the filling state of storage material affects the stiffness degradation. This study provides theoretical insight to the influence of the SSI effect on the seismic resilience of structures. • The influence of SSI on the structural dynamic characteristics and the material lateral pressure are investigated. • The elastic-plastic development coefficient of displacement is proposed to evaluate the safety of the structure. • The vulnerability assessment of the silo with or without SSI effects under different storage conditions is discussed. • The influence of storage material on the failure probability of the structure is evaluated. [ABSTRACT FROM AUTHOR]

This study investigates dynamic earth pressure on basement walls by considering soil-structure interaction, a factor that is often overlooked by conventional methods like Mononobe-Okabe, Seed and Whitman, and Wood. Superstructure, basement, and soil were numerically simulated in a single model to evaluate the inertial and kinematic effects of buildings on dynamic earth pressure on the basement walls. The numerical model was validated using data from a centrifuge test and an instrumented building. Then, a parametric study was performed, with the height, width, and basement depth of the building varied with six input motions. The results showed that the inertia of the building increased dynamic thrust. Furthermore, the dynamic thrust showed a similar trend with the displacement response spectrum curve of the ground surface acceleration as the building height increased, while the distribution shape transitioned from triangular to inverted triangular. Additionally, wider buildings had increased dynamic earth pressure, while deeper buildings exhibited smaller normalized dynamic thrust. • Dynamic earth pressure on basement walls was investigated using numerical simulation. • Building inertia increased dynamic earth pressure on basement walls. • Dynamic thrust exhibited a similar trend to displacement response spectrum curve. • Increase of basement depth decreased normalized dynamic thrust. • With presence of buildings, conventional methods underesmitated dynamic earth pressure. [ABSTRACT FROM AUTHOR]

Tuned mass damper (TMD) has been applied in civil engineering fields to reduce the seismic response. However, few TMDs are used in the nuclear structure due to the huge additional mass of the traditional TMD device on the nuclear structure. In this paper, the PCS water tank of a nuclear structure is reconstructed into a TMD system to reduce the seismic response of the nuclear structure. The proposed novel water tank-TMD device can use its characteristics of large mass to achieve the tuned shock absorption effectively while maintaining the original function of the water tank. Moreover, more and more nuclear power structures are being built on non-bedrock sites, and the effects of soil-structure interaction (SSI) on the seismic response and seismic migration performance of nuclear power structures need to be reasonably considered. The effects of SSI and auxiliary plants on the seismic response of the nuclear containment plants equipped with PCS water tanks are first investigated. Subsequently, the performance of the water tank-TMD system in reducing the seismic responses of nuclear containment plants is analyzed in detail by considering the effect of SSI, design frequency of TMD, and design criteria of TMD. The research results show that the proposed water tank-TMD system can effectively reduce the seismic response of nuclear containment plants. Besides, it is necessary to consider the influence of SSI on the dynamic characteristics of the structure in the design of TMD when the SSI effect is strong. The water tank-TMD system designed according to the TMD criteria proposed by Sadek et al., and Salvi and Rizzi has better reduction performance compared with that designed by other design criteria. • The PCS water tank of a nuclear structure is reconstructed to a tuned mass damper (TMD) system. • The seismic performance of the nuclear structure equipped with TMD considering the SSI effect is investigated. • The water tank-TMD system design methods considering the SSI effects are investigated. [ABSTRACT FROM AUTHOR]

This paper presents an analytical solution for evaluating kinematic response in piles subjected to shear waves. The proposed model treats the pile as a Timoshenko beam supported by a two parameter Winkler foundation, capturing both transverse and rotational ground reactions. Validation against both analytical and numerical solutions from the literature, particularly 3D finite element models, shows very good agreement. The proposed model generalizes different solutions currently applied in practice, covering various pile slenderness ratios and ground conditions. This approach addresses limitations in existing Euler-Bernoulli beam resting on Winkler or Vlasov-Pasternak foundation models, by incorporating shear distortions in the structure and ground friction at the interface. Shear stresses induced by the rotational springs are found to significantly influence the kinematic factors, as well as bending and, particularly, shear forces. Finally, simplified expressions for kinematic interaction factors and forces are provided for expedited analyses of practical engineering problems. • An improved model based on Timoshenko beam on two parameter foundation is proposed. • Model includes transverse and rotation springs, and shear distortion in the beam. • Relevant differences with Euler-Bernoulli beam on Winkler foundation are found. • Simplified solutions for long piles are proposed. • The model overcomes limitations of existent analytical solutions in literature. [ABSTRACT FROM AUTHOR]

Monopiles are the most widely adopted foundation type for Offshore Wind Turbines (OWTs) in shallow waters. With the expansion of the construction of OWT, the number of OWT farms in seismic regions increases globally including the coastal areas of Japan and China. It is necessary to evaluate the impact of earthquakes including the vibration and soil liquefaction on the OWTs supported by the monopile foundation, while the effects of liquefaction on offshore structures, especially for OWTs with monopiles, have not been sufficiently studied. This study investigates the seismic response of the monopile-supported OWTs with the use of an advanced soil model. A three-dimensional numerical model is built, and dynamic analyses are carried out using the OpenSees framework. The pressure-dependent multi-yield (PDMY03) constitutive model is used to simulate the dynamic soil behavior. The applicability of the large-diameter pile modeling method for proper soil-pile interaction modeling in this numerical analysis is first validated through centrifuge tests on monopiles subjected to lateral loading. The dynamic analyses are then carried out to demonstrate the seismic response of the entire OWT system. The numerical results indicate that the contribution of higher modes of vibration is becoming of increased importance for large wind turbines and soil-structure interaction plays a significant role in the dynamic response. Moreover, the monopile-supported OWT in dense sand deposits experiences substantial lateral displacement and rotation under the combined action of wind and earthquake loads when liquefaction occurs. • Seismic response of offshore wind turbines on monopile is analyzed by 3D FE analysis. • Modeling is validated through the simulation of laterally loaded monopiles. • Impacts of liquefaction and wind load on the monopile response are demonstrated. [ABSTRACT FROM AUTHOR]

One of the most effective systems for reducing dynamic responses of the structures subjected to earthquake excitations is tuned mass dampers (TMDs). In the traditional design theory of TMDs, the structures are assumed to be rigidly connected to the ground. Using this approach, known as the fixed foundation approach, may lead to deterioration of the performance of the TMD in cases where soil-structure interaction (SSI) is significant. Therefore, it is crucial to consider the SSI effects to obtain the optimum parameters of the TMDs. Unlike previous studies, two key parameters (i.e., structure-to-soil stiffness ratio and aspect ratio of the structure) are considered, which define the principal SSI effects on the effectiveness of TMD. For the aspect ratio of the structure, three different values (i.e., λ = 1, 2, and 4) are considered, these values correspond to the squat, ordinary, and slender structures representing traditional buildings, respectively. Four different values (i.e., a 0 = 0, 0.5, 1, and 2) are also considered for the structure-soil stiffness ratio. This ratio being equal to 0 corresponds to the fixed foundation approach. This also demonstrates that the structure is constructed on hard rock. The optimum parameters of the TMD are obtained using the Jaya algorithm (JA). The proposed methodology is applied to three different buildings (i.e., 3-story, 6-story, and 12-story), and the optimum parameters of the TMD are verified using a total of 72 ground motions corresponding to NEHRP site classes C, D, and E. Numerical results show that the effectiveness of TMD is significantly affected by the basic parameters that define the principal SSI. In addition, the efficiency of the TMD is significantly related to the characteristics of the ground motions. It has been observed that TMD does not perform adequately in reducing vibrations in low-rise buildings (i.e., λ = 1) constructed on low-stiffness soils (i.e., a 0 = 2). • The effect of the basic parameters defining principal SSI on the optimization of TMD using the Jaya Algorithm is investigated. • The effectiveness of TMD in reducing seismic responses in structures with different slenderness ratios is investigated considering the SSI. • The effect of the relationship between the structure's stiffness and the soil's stiffness on the TMD's seismic performance is investigated. • To clearly demonstrate the SSI effect, the selected ground motions are grouped according to NEHRP site classes. [ABSTRACT FROM AUTHOR]

This study established a numerical model for soil-structure interaction (SSI) to examine the effects of the spatial incidence angle of SV waves and soil nonlinearity, utilizing viscoelastic artificial boundaries (VAB) and equivalent nodal force (ENF) method. Both the foundation's and superstructure's torsion and rocking responses were then analyzed. The findings indicate that subjected to spatially oblique incident SV waves, the rectangular foundation primarily has the rocking response while the torsional response is negligible. Furthermore, the maximum torsional and rocking angles about the x-axis at each frame floor are significantly enlarged by comparison with the perpendicular incident case. Moreover, the soil nonlinearity could increase the foundation's rocking angle and enlarge the maximum torsion and rocking responses of the structure's floors. Consequently, structural seismic damage assessment requires considering both the soil nonlinearity and incident seismic wave angles. • The nonlinear behavior of 3D soil under spatial oblique incident SV waves is simulated using the revised Davidenkov model. • The torsion and rocking response of foundations and frameworks under spatial oblique incident SV waves is investigated. • The incident angle of SV waves and soil nonlinearity influence the dynamic responses of the superstructure and foundation. [ABSTRACT FROM AUTHOR]

The adverse conditions of the soil such as soft soil can have seismic consequences that may either amplify seismic response or render the structure vulnerable. On one hand, the design and construction of asymmetric structures have become prevalent due to aesthetic considerations and structural space limitations. Studies indicate that structures with geometric irregularities are susceptible to seismic forces, leading to non-uniform distribution of floor drifts, excessive torsional behavior, and more, depending on the degree of irregularity. In this research, the main goal was to investigate the effect of soil and structure interaction on the torsion of asymmetric Mid-Rise Structures. To achieve this goal two asymmetric Steel moment frame system 15-story structures aim to address the effect of interaction between soil and structure on the seismic performance, one with a rigid base and the other with a flexible base, one with a rigid base and the other with a flexible base. To mitigate the settlement of soil-associated structures, a pile-raft system is employed, considering the softness of the soil. Additionally, to study the torsional behavior of these structures, their planes are asymmetrically designed in L-shape and C-shape configurations, subjected to four ground motion excitations in both far and near-field scenarios. Three-dimensional finite element numerical simulations are performed using Abaqus software. Various configurations of the pile-raft system for the asymmetric C-shape structure are examined to assess the effects of pile diameter and length on the torsional irregularity coefficient. The results show that the soil-structure interaction increases the maximum floor rotation angle, placing these structures in critical conditions concerning torsional irregularity under near-field and far-field seismic excitations. • Importance of studying the phenomenon of interaction in asymmetric structures, even with low-frequency content. • Soil-structure interaction results in increased rotation angles and changes in lateral displacement behavior. • The difference in rotation angles between SSI and non-SSI models is more pronounced in far-field earthquake. • Importance of considering the impact of pile characteristics on the seismic response of asymmetric structures. • Increasing the length of piles reduces the torsional irregularity coefficient on the lower floors [ABSTRACT FROM AUTHOR]

The soil-structure interaction (SSI) effects are typically ignored in modeling and analyses of the seismic response of tall buildings. This paper presents an in-depth investigation of the SSI effects on the response of a 50-story skyscraper, with a basement and on piles, as a function of the soil shear wave velocity, V S , varied between 50 and 800 m/s. A detailed three-dimensional finite element model of the structure and soil was developed in OpenSees, which was excited by vertically incident plane SV-, SH- and P-waves. The three translational and three rotational components of the response were analyzed. The SSI effects on its apparent dynamic properties (frequencies of vibration and damping ratios), floor translations and rotations, effective input base translations and rotations, interstory drifts, floor and base reaction forces and floor and base reaction moments were analyzed in the linear domain. It was concluded that the SSI effects for such a tall building are not negligible and ignoring them does not produce conservative estimates of the response. • In-depth study of soil-piles-basemnt-structure interaction for a 50-story skyscraper. • A detailed 3D finite element model of structure, basement, piles and soil was developed in OpenSees. • Apparent frequencies and damping, translational and rotational responses, etc. Are investigated. • The SSI effects for this building are not negligible. • Ignoring the SSI effects may lead to nonconservative estimates of the response. [ABSTRACT FROM AUTHOR]

This investigation examines the structure-soil-structure interaction (SSSI) problem between a tunnel and nearby aboveground building, considering the impact of the stiffness of tunnel and building's foundation. A two-dimensional (2D) model is utilized, which includes a flexible circular tunnel and a three-story building anchored by a flexible semi-circular foundation embedded in a homogeneous half-space. The response of the system to incident plane SH-wave excitation is solved analytically using the wave function expansion method. The analysis focuses on how the system response is affected by the stiffness of the tunnel and the building's foundation. Tunnel stiffness plays a leading role in tunnel response analysis. The model with a rigid tunnel and rigid foundation can offer a reasonable system response overall, but it fails to accurately represent tunnel deformation and stress distribution. Depending on the stiffness of the building's foundation, the maximum value of the inter-story displacement of the first floor can be overestimated by around 70 %, with even greater overestimations for higher floors. The results help understand observed seismic behaviors and provide insight into the effects of foundation and tunnel stiffness on the tunnel-building interaction system. • Analytical solution for dynamic 2D structure-soil-structure interaction (SSSI). • SSSI problem considering the relative stiffness of tunnel and building foundation to surrounding soil. • Results show rigid tunnel model cannot accurately reflect tunnel response. • For building close to tunnel, 70% amplification of inter-story response due to SSSI. [ABSTRACT FROM AUTHOR]

The soil-structure interaction (SSI) is an integral part of the seismic response of structures. The knowledge about its effects is based largely on numerical simulations involving simplified models. In this paper, we examine the consequence of several assumptions in SSI models of buildings, with emphasis on the rigid foundation assumption. To this end, we analyze several variants of a linear three-dimensional finite element model of the structure and soil corresponding to a uniquely instrumented 50-story skyscraper, with a basement on a pile foundation, located in southwest China. The models are excited by triaxial motion due to a vertically incident plane wave. The most realistic model (with basement and piles, both with bond contact with the soil), predicted an 8 % reduction of the apparent frequency and a 30 %–50 % increase in the apparent damping ratio of the 1st mode of vibration, relative to the model with fixed basement. The model with a rigid foundation (basement) embedded in the soil underestimated the reduction in apparent frequency by a factor of two. The SSI effects were the most pronounced for the model with flexible basement and no piles (16 %–19 % reduction in apparent frequency and 73 %–86 % increase in apparent damping ratio). The basement-structure interaction reduced the apparent frequency by 5 %–8 % depending on the direction. It is concluded that, for such a building, a detailed model of the structure and its foundation is needed to predict reliably the SSI effects. • Study of role of the foundation flexibility of real buildings in their response during earthquakes. • The consequence of several assumption in modeling soil-structure systems are examined for tall buildings. • The case study is a uniquely instrumented 50-story skyscraper, with a basement and on a pile foundation. • Variants of a 3D finite element model are analyzed for vertically incident 3—component waves. • The concept of basement-structure interaction is introduced and its effects are measured. [ABSTRACT FROM AUTHOR]

Periodic structures may be designed as periodic foundations to reduce the seismic response of engineering structures. The periodic foundation is more suitable for the seismic mitigation of nuclear power structures because of its wide attenuation domain. Based on the dispersion relationship of infinite periodic structures, this research constructs a one-dimensional layered periodic foundation using rubber and concrete materials, determines the attenuation domain frequency band gap that meets the seismic design requirements of nuclear power structures, and optimizes the raft design of nuclear power structures. At the same time, with the scarcity of bedrock sites, the site selection of nuclear power structures is inevitably shifted to soft rock sites. Therefore, this paper also considers the influence of the soil-structure interaction (SSI) on the seismic response of nuclear power structures. A three-dimensional finite element model of the nuclear power structure-periodic foundation-site system was established, and a detailed parameter analysis of the seismic performance of the periodic foundation of nuclear power structures considering the SSI effect was carried out. The results show that the seismic response of nuclear power structures can be significantly reduced by designing the attenuation domain of the periodic foundation. • Application of one-dimensional periodic structure to earthquake-resistant method of nuclear power structure. • Based on the dispersion equation in the infinite period attenuation domain, periodic foundation design is proposed, which is suitable for the seismic design requirements of the nuclear power project. • The seismic performance of the periodic foundations for nuclear power structures is analysed and investigated in detail by considering the SSI effect. • The seismic damping effect of the periodic foundation in nuclear power projects is correctly evaluated. [ABSTRACT FROM AUTHOR]

In active earthquake zones, it is very likely that the structures would experience multiple shakings in major seismic events. For underground structures, the soil-structure interactions and the resultant dynamic responses could vary significantly according to the characteristics of the shakings. In this paper, the scenario of a shallow tunnel in liquefiable ground subject to multiple shakings is studied. The OpenSees platform and the PM4Sand constitutive model are employed to construct a plane-strain numerical model, where a rectangular tunnel is buried in saturated Hostun sand. Its validity is verified by the data from a centrifuge test of four consecutive shakings. The numerical soil-structure system is then configured for further investigation on the subject matter. Firstly, the liquefaction-induced uplift is identified as the main threat to the integrity of the tunnel in a seismic event of multiple shakings. Then, the pertinent soil-structure interactions are intensely discussed in a parametric analysis considering the influences of the permeability coefficient, the tunnel self-weight, and the shaking sequence. • A centrifuge test on tunnel in liquefiable soil under multiple shakings is numerically modelled. • Liquefaction-induced uplift is identified as the main threat to the tunnel in such occasion. • The uplift under multiple shakings is intensely discussed in a parametric analysis. [ABSTRACT FROM AUTHOR]

The seismic damage assessment for structures is an essential investigation to guarantee the seismic performance-based design. However, the seismic responses and damage development process of underground structures are now unclear due to the complicated soil-structure interaction, which results in a lack of the seismic damage assessment for underground structures. In this paper, the seismic damage mechanism and seismic failure path of the underground large-scale frame structure (ULSFS) are investigated, and a novel seismic damage assessment is proposed for the ULSFS based on the structural characteristics and seismic action distributions. During earthquakes with different seismic intensities, the seismic responses of the ULSFS are investigated. The vulnerable structural components are clarified and the seismic damage mechanisms are revealed. Focusing on the representative times, the seismic failure path of the ULSFS is studied throughout the whole seismic history. Based on the damage distribution characteristics and seismic failure mechanism, the entire ULSFS is divided to be outside damage region and inside damage region, respectively. According to the modal frequency response analysis, the seismic damage coefficients of columns and beams in different damage regions are determined. Based on the stiffness variations of damage components, an analysis method is proposed to achieve the seismic damage weights of columns and beams on different stories. Associating the seismic damage coefficients with seismic damage weights, the seismic damage assessment for the ULSFS is developed. The results show that: the outside damage region of ULSFS where the soil-structure interaction is considerable undergoes more considerable seismic damage than that of the inside damage region (roughly 30 % on average), and the seismic failure path would develop from outside to inside and from bottom to top in the ULSFS; the proposed seismic damage assessment is credible with the consideration of damage distribution characteristics and seismic failure paths of the ULSFS; during small earthquakes, middle earthquakes and great earthquakes, the seismic damage of the ULSFS is quantified to be approximately 0.05, 0.40 and 0.75, which indicates the ULSFS suffers the rare damage, medium damage and severe damage respectively. This paper can provide the necessary supplements and theoretical references for the seismic performance evaluation of large underground structures. • The seismic failure path of the underground large-scale frame structure (ULSFS) is revealed. • ULSFS is divided into outside and inside damage regions based on damage distribution characteristics and failure mechanism. • Seismic damage coefficients of components on the same story are developed by modal frequency responses. • Seismic damage weights of components on different stories are proposed corresponding to the stiffness variation. • A seismic damage assessment for the ULSFS based on damage distribution characteristics and seismic failure path. [ABSTRACT FROM AUTHOR]

The conventional seismic analysis and design of transmission tower-insulator-line systems usually ignore the effects of soil-structure interaction (SSI) and the randomness of ground motions, which might lead to an unreasonable estimation of the system's seismic performance. In addressing this issue, this paper proposes two effective simplified models of coupled transmission tower-insulator-line systems considering soil-structure interaction (CTILSs-SSI), for stochastic seismic dynamic response analysis. In these models, the foundation and tower are simulated by single and multiple degree of freedom models, respectively; meanwhile, the insulator is simulated by a single pendulum model, and the effect of SSI is considered using the swing-rocking (S-R) model. Specifically, for the in-plane vibration, the transmission line is simulated by a multiple degree of freedom rigid-bar assemblage with lumped masses; for the out-of-plane vibration, the transmission line is simulated by a multiple pendulum model. On this basis, the equations of motion for CTILSs-SSI under both in-plane and out-of-plane vibrations are derived utilizing the Euler-Lagrange equation. Subsequently, a non-stationary stochastic seismic dynamic response analysis framework for CTILSs-SSI is proposed by incorporating the proposed simplified models with the probability density evolution method (PDEM). An ultra-high voltage (UHV) transmission tower-insulator-line system is taken as an example. The simplified models of this exemplar system are established and validated using ANSYS software. In addition, the deterministic and stochastic seismic dynamic response analyses of this exemplar system are conducted. The analysis results demonstrate that the dynamic response amplitudes of the tower top and the tower's natural periods increase considering the effect of SSI, and the impact of SSI increases as the subsoil softens. Furthermore, the probability density function (PDF) of the tower top displacement of the CTILS-SSI exhibits distinct shapes at various moments. The mean value of the tower top displacement of the CTILS-SSI fluctuates around zero over time, while the standard deviation increases within approximately 0s–10s and then decreases. • Two effective simplified models of CTILSs-SSI are derived. • A stochastic seismic response analysis framework for CTILSs-SSI is proposed. • The effect of SSI on the seismic response of tower-line systems is explored. • The stochastic character of the seismic response of CTILSs-SSI is investigated. [ABSTRACT FROM AUTHOR]

The LEAP (Liquefaction Experiment and Analysis Project) is a continuing international collaboration to produce a reliable databank of high-quality experimental results for the validation of numerical tools. LEAP-2020, investigates the problem of a floating rigid sheet-pile quay wall embedded in dense sand layer. This paper discusses two experiments conducted at Rensselaer Polytechnic Institute (RPI) and investigates: (1) the repeatability potential of centrifuge testing in the presence of Soil-Structure Interaction (SSI), and (2) the effects of soil-structure Interaction on the system response during liquefaction. • Investigation of the response for a liquefiable sand deposit supported by a sheet-pile quay wall, using two centrifuge tests. • The two tests showed high repeatability in the soil and sheet-pile response. • The mechanism of excess pore water pressure generation is coupled with the sheet-pile response. [ABSTRACT FROM AUTHOR]

Recent advancements in geotechnical physical modeling have enabled visualization and analysis of deformation mechanisms in soil sections through the integration of Particle Image Velocimetry (PIV) in dynamic centrifuge modeling. PIV requires a rigid wall container. In this paper, we summarize the design considerations that enable reliable measurement and visualization of soil deformation mechanisms at the University of Colorado (CU) Boulder's 400 g-ton, 5.5 m radius centrifuge facility. The primary objective of this system is to investigate the response of complex and stratigraphically variable, saturated granular soil deposits beneath shallow-founded structures, though it can also be used for other configurations that benefit from advanced visualization in the centrifuge. The setup aims to enable quantification and visualization of different deformation mechanisms, including shear, volumetric, and soil ejecta formation, near and away from structures. The paper provides detailed design considerations for the system components, including a rigid container with a transparent Perspex wall and duct seal inclusions, a linear-elastic single-degree of freedom (SDOF) structure, soil texture, a potential ground improvement technique, and a high-speed camera system. Through fully-coupled, three-dimensional (3D) nonlinear finite element analyses, we investigate the influence of container type, domain size, and duct seal geometry on boundary effects, with consideration of nonlinearities within various soil profile configurations with and without the presence of a building model. The findings highlight the critical impact of proximity to lateral boundaries of the container on accelerations, excess pore pressures, foundation settlement, tilt, and shear strains, as well as the benefits of duct seal in reducing those boundary effects. The results also show that the extent of boundary effects on key performance measures depends on the properties of the container, soil layers, and ground motion. The simulations also show that surface ejecta potential within stratigraphic soil profiles is highly sensitive to the depth of the groundwater table and variations in soil permeability, which must be considered in designing experimental programs that investigate the development of soil ejecta. • We summarize considerations for reliable scaled simulation of soil deformation mechanisms. • Prior dynamic centrifuge models did not consider major stratigraphic variations in soil. • We present design of rigid transparent box with duct seal and PIV to measure and visualize. • The analyses investigate the influence of domain size and duct seal on boundary effects. • Boundary effects are sensitive to container size, type, duct seal geometry, and soil type. [ABSTRACT FROM AUTHOR]

In this study, the effect of dynamic soil-structure modelling assumptions on the calculated seismic response of railway bridges with single column piers resting on shallow foundations is investigated. For this purpose, 10 structural models of a typical railway bridge are built in decreasing levels of complexity, starting from the most complicated model with nonlinear elements to accurately simulate dynamic soil-structure interaction. Then, the structural model is gradually simplified to a level where the effects of foundation-soil and abutment-backfill interactions are totally eliminated. Nonlinear time history analyses of the structural models are conducted with a set of ground motions with various intensities representing small, medium and large intensity earthquakes. Analyses results revealed that removing the abutments from the structural model results in significant discrepancies in the longitudinal direction response of the bridge but has negligible effect in the transverse direction. Furthermore, analyses results show good correlation between the complex and simplified models in deck displacement and bearing displacement but notable differences are observed in substructure responses when the soil-structure interaction is neglected. Therefore, at least linear soil-structure interaction modeling should be considered in the analyses for correct estimation of the substructure responses. • Effect of soil-structure modelling assumptions on the seismic response of bridges resting on shallow foundations is outlined. • Effect of including and excluding the abutments from the structural model on the seismic response of bridges is outlined. • The effect of radiation damping and equivalent hysteretic damping on the seismic response ofbridges is presented. • Information on structural modeling of bridges for seismic analyses is provided. [ABSTRACT FROM AUTHOR]

To control the seismic response of the core-frame (CF) structure and attenuate the stress level of the core tube, a novel core-damper-frame (CDF) system is proposed by decoupling the perimeter frame and the central core with flexible damper connectors. In this way, the large inertia force of the perimeter frame cannot be fully transmitted to the core, and the stress of the core is mitigated. In the meantime, the damper connectors would absorb a considerable amount of seismic energy, protecting the perimeter frame as the relative displacement between the two subsystems (perimeter frame and core tube) occurs. By incorporating the soil-structure-interaction (SSI) and the filtered Gaussian white-noise excitation model, the "excitation-soil-core-damper-frame" augmented system is established. Combing the augmented system and the genetic algorithm, a stochastic optimization procedure of the CDF considering the SSI effect is proposed. The optimization aims to minimize a series of performance objectives including displacement, acceleration, shear force, and overturning moment of the CDF system. The conflicting relationships between the multiple objectives are discussed; the influence of the SSI effect and the excitation parameters are evaluated. From an illustrative 40-story CDF structural example, the system shows great superiority in controlling the higher mode vibrations, and could significantly reduce the peak core acceleration (by 54.44 %), frame acceleration (by 56.48 %), core drift (by 28.83 %), frame drift (by 39.28 %), core shear (by 83.67 %), and frame moment (by 22.41 %), as compared to its conventional CF counterpart. In special, over 50 % of the input seismic energy is dissipated by the damper connectors in the CDF system. • Decoupling core tube and perimeter frame with damper connectors. • Optimizing core-damper-frame system considering soil-structure-interaction. • Recognizing the conflicting relationship between optimal objectives. • Highlighting the superiority in controlling acceleration and core stress. • Analyzing energy distribution between core, frame, connector, and soil. [ABSTRACT FROM AUTHOR]

This paper introduces a straightforward traction-based approach for implementing transmitting boundaries in time-domain nonlinear seismic soil–structure interaction (SSI) analyses. The primary objective is to simplify the challenges associated with integrating appropriate boundaries into finite-element analysis software. The proposed method conceptualizes an SSI model as a free body extracted from its original domain and determines the boundary traction (i.e., stress boundary conditions in the engineering sense) at the cutting surface. This determination is based on the current velocity, free-field dynamic responses, and static equilibrium stresses. In scenarios employing the classic viscous boundary, traction is solely dependent on the free-field dynamic responses and static equilibrium stresses, facilitating predetermined calculations. Detailed implementation guidelines for Abaqus are provided to illustrate the practicality of the proposed technique. The efficacy of this technique was validated by its ability to accurately reproduce both linear and nonlinear one-dimensional shear waves in three-dimensional models. Furthermore, the nonlinear responses of the SSI models with varying soil dimensions underscored the effectiveness of the approach for domain reduction. • A simple, traction-based approach is presented for transmitting boundaries in time-domain nonlinear seismic SSI analyses. • The primary objective is to simplify the implementation of appropriate soil boundaries in finite element analysis software. • The traction can be predefined with freefield and static equilibrium responses when employing the classic viscous boundary. • The traction-based approach provides greater flexibility in selecting soil geometries and sources of free-field responses. • Implementation instructions for Abaqus, a commercial finite element analysis software, are provided as a demonstration. [ABSTRACT FROM AUTHOR]

In this paper, a novel two-step nonlinear ground acceleration feedback mechanism is proposed for vibration mitigation of building structures considering soil-structure interaction. Hence, an observer based receding horizon control (RHC) scheme is presented for active control of the structures. Afterward, a nonlinear two-step auto-regressive framework is appended to the RHC formulations to consider the adaptive seismic term in the resulted control law. Soil-structure interaction (SSI) is also considered in the controller structure regarding soft, medium, and dense soil conditions. A data-driven approach is then introduced for lessening the complexity of the proposed framework for practical applications. A forty-story building equipped with active mass damper (AMD) subjected to earthquake excitations is selected as the numerical study. The superiority of the proposed method is evaluated compared to other control strategies including conventional RHC, ideal RHC, and linear version of the proposed controllers. The outcomes indicate the remarkable accuracy of the proposed method against mentioned control approaches. • Nonlinear ground acceleration tracking mechanism is proposed for seismic control of high-rise buildings considering soil-structure interaction. • A nonlinear two-step AR equation is synthesized as the earthquake dynamics to be appended to the control process. • The flexibility of the supported soil is included to consider the soil-structure interaction. • A data-driven controller is presented to include all the proposed exclusive features in an uncomplicated manner. [ABSTRACT FROM AUTHOR]

Soil-structure interaction is a key aspect when calculating the dynamic response of nuclear structures in front of ground motions induced by earthquakes. However, modelling the seismic response in the time-domain using FEM-based models to represent the soil volume is computationally expensive because of the large number of elements involved. For this reason, it is a common practice to employ 1-D models, which allows an explicit solution of the dynamic response of the system in a fraction of time. Yet, due to the importance of nuclear structures, sometimes it is mandatory to employ 3D FEM-based models. In addition, based on probabilistic estimations of the seismic hazard at a site, it is generally necessary that the seismic response of the model comply with the spectral ordinates of the input action at the surface level. In doing so, specific accelerograms acting at the bedrock should be developed. If these signals are obtained by deconvolution using the 1D model, and then applied to the 3D one, the response calculated at the surface level will always be somewhat different from the target free field motion (the one considered in the deconvolution process at the surface level). There are several sources, like the Poisson effect in the 3D model, explaining this difference. Therefore, it is necessary to modify the input signal so that the dynamic response obtained with the FEM model fit the target spectrum. This article presents an innovative approach to achieve this goal, developing an enhanced transfer function stemming from the 1D and 3D models. Two seismic scenarios and a specific soil profile have been used as benchmark. Results show that this approach provides an adequate solution for the studied problem. • Soil-structure interaction is a key aspect when calculating the seismic response of nuclear structures. • Modelling this response in the time-domain using FEM models to represent the soil volume is computationally expensive. • The seismic response of the model must comply with specific spectral ordinates related to the hazard of the site. • This article presents an innovative approach to achieve this goal, using an enhanced transfer function from 1D and 3D models. • Two seismic scenarios and a specific soil profile have been used as benchmark. • Results show that this approach provides an adequate solution for the studied problem. [ABSTRACT FROM AUTHOR]

We present the outcomes derived from controlled laboratory experiments on utilizing gravel rubber mixtures (GRM) as a geotechnical seismic isolation (GSI) stratum beneath the foundational structure of the EuroProteas prototype. The study encompassed three distinct GRM compositions characterized by varying rubber proportions relative to the total mixture weight (0%, 10%, and 30%) employed as the foundation soil. These GSI-structure systems were subjected to external harmonic forces applied atop the structure of EuroProteas across a broad spectrum of frequencies and force magnitudes. Preceding the commencement of field experiments, resonant column and cyclic triaxial compression assessments were conducted on specimens featuring identical rubber fractions and mean grain size ratios. Our laboratory tests revealed that an increase in rubber content resulted in a reduction of the shear modulus (G o) and an augmentation of the damping ratio (D o) while concurrently inducing a more linear character in the G/G o -log γ -D profiles. The findings derived from the laboratory examinations align closely with those ascertained from field investigations. Expressly, it was confirmed that a GSI layer with a thickness of 0.50 meters, composed of a GRM incorporating 30% rubber content, exhibited a discernible reduction in the overall stiffness of the GSI-structure system, accompanied by a corresponding alteration in its fundamental vibrational frequency. The enhanced damping within the system manifested through observable reductions in acceleration recordings and diminished strain development at the base of the GRM layer with 30% rubber content, encompassing a wide range of frequencies. • Controlled laboratory tests on GRM having different percentiles of rubber • Large field tests GRM to investigate their geotechnical seismic isolation capacity • Increase rubber content to reduce the shear modulus and increase damping of the GRM • Findings from the laboratory tests align closely with those obtained from field tests • A GRM layer 0.5 m thick having 30% rubber per weight offers seismic isolation [ABSTRACT FROM AUTHOR]

This study aims to advance knowledge on multi-hazard damage to shallow foundation bridges subjected to simultaneous scour, earthquake, and vehicular loads. While most water-crossing bridges have deep foundations, still, a significant number of water-crossing bridges have shallow foundations. In addition, there is limited research focusing on damage assessment of bridges with shallow foundations under multi-hazard scenarios. Therefore, this study proposes a probabilistic multi-hazard damage assessment framework for bridges with shallow foundations exposed to seismic, scour, and vehicular loadings. The proposed framework includes steps for hazard modeling, multi-hazard finite element modeling, non-linear time history analysis, and multi-hazard fragility modeling, and it was showcased on Chemin des Dalles Bridge, which is a typical bridge located in the Province of Quebec in Canada. Demand and fragility models parameterized on hazard and soil parameters were developed for the bridge components and a system fragility model was also developed using a series system assumption. The results from the analysis of these damage and fragility models indicated that scour notably increases component- and bridge-level response in typical shallow foundation bridges. However, until the scour depth is lower than the foundation height, the increased damage does not impose a significant threat to the bridge's safety. It was observed that earthquakes had the highest influence on the bridge components' response followed by scour and vehicular loads. Overall, the proposed framework can be used to facilitate policy-making toward informed bridge maintenance and retrofitting to aid in disaster mitigation planning and emergency response. • Novel framework for multi-hazard damage assessment of shallow foundation bridges. • Uniform scour around foundation had little impact on shallow foundation bridges. • Influence of hazards, high to low, was Earthquake, Scour, Vehicular load. • Soil quality's effect was greater than scour depth on shallow foundation bridge's response. • 3D Finite-element modeling of scoured shallow foundation bridges was presented. [ABSTRACT FROM AUTHOR]

Three-sided underpass culverts are structural systems used to provide passing vehicle or pedestrian. It is of great importance that such infrastructure systems remain useable, especially after disasters such as earthquakes that can cause great destruction, in order to ensure that infrastructure services can be maintained continuously. In this context, the aim of this study is to investigate using finite element method (FEM) the dynamic responses of three-sided underpass culvert system under near-fault ground motions with velocity pulse and far-fault ground motions. For this aim, the modal analysis of the soil-underpass culvert interaction system has been realized using proposed soil-structure interaction (SSI) model. The frequencies of the interaction system obtained from the finite element model developed using proposed approaches have been verified comparing with the results obtained from the literature and the site periods. After showing that the modes of the interaction system can be obtained with the help of the proposed numerical model, the full transient dynamic analyses have been performed in the time history using five near-fault and far-fault records, considering four different soil systems. The comparisons shows that the variations of the soil systems and the ground motion type can significantly affect the top peak relative displacements and the dynamic stresses of the three-sided underpass culvert. • Verification of 2-D finite element model proposed with a 2-D FE-PML model proposed in literature. • Soil-structure interaction effects on the three-sided underpass culvert dynamic behaviors are evaluated. • Effects of near-fault and far-fault ground motions on the three-sided underpass culvert dynamic behaviors are evaluated. • Soil-structure interaction may importantly affect the dynamic behaviors of the three-sided underpass culvert. • The dynamic behaviors of the culvert system can be significantly affected by near-fault ground motions. [ABSTRACT FROM AUTHOR]

Soil-structure interaction (SSI) is crucial to the dynamic response of nuclear power plants (NPPs), and should be properly considered when analysing the seismic isolation performance of base-isolated NPPs. In this study, a three-dimensional numerical simulation program is developed for the time-domain dynamic analysis of base-isolated NPPs considering SSI effects. The seismic input is realised using the method of external source wave motion, and the nonlinear behavior of isolators is fully considered. Using this program, the SSI effects of the base-isolated nuclear island building under different sites are analysed and compared, including the acceleration, displacement, and floor response spectra. The numerical results show that the SSI effects change the spectral characteristics of the actual seismic input. When the shear wave velocity of the site is relatively large, the SSI effects can increase the dynamic response of base-isolated NPPs. Additionally, the isolation performance of the base-isolated NPPs is weakened when SSI effects are considered, and with a decrease in the shear wave velocity of the site, the isolation capacity is further reduced. The influence of the SSI effects should be fully considered in the base isolation design of NPPs. • The seismic input was realised based on the theory of external source wave motion. • A numerical procedure for the time-domain dynamic analysis of base-isolated NPPs considering SSI effects was proposed. • The coupled effects between the base isolation and SSI of NPPs was investigated. • An important influence of SSI on the seismic response and isolation performance of base-isolated NPPs was fully determined. [ABSTRACT FROM AUTHOR]

Dynamic soil-structure interaction is typically decomposed in kinematic and inertial effects. Inertial interaction generally results in an increase in the fundamental period and damping of the system, which, for slender structures, corresponds to a decrease of the inertial forces transmitted to the superstructure. Relations to estimate the period increase are mainly available in the literature for shallow foundations. In this paper, the fundamental period of bridge piers on compliant caisson foundations was obtained from dynamic centrifuge tests. A rigid and a flexible bridge pier were subjected to trains of sinusoidal waves and real ground motions. The interpretation of the experimental results permitted to (i) evaluate the increase of period with respect to fixed-base conditions; (ii) assess the dependency of the compliant-base period on the motion intensity. The second aspect sheds light on the role played by non-linearity of soil behaviour and emphasises the importance of performing preliminary soil response analyses. • Inertial interaction results in an increase of the system fundamental period. • Dynamic centrifuge tests of bridge piers on caisson foundations were performed. • The increase of the fundamental period with respect to the fixed-base was evaluated. • The dependency of the fundamental period on the earthquake intensity was assessed. • The results emphasises the need of performing preliminary soil response analyses. [ABSTRACT FROM AUTHOR]

A significant amount of damage and casualties induced by several strong-motion earthquakes which recently stroke South-East Mediterranean area is due to the major seismic vulnerability of residential buildings. In small villages and mid-size towns, those buildings very often consist of two- to four-story, unreinforced masonry (URM) structures not designed for earthquake resistance, with direct foundations usually corresponding to an in-depth extension of load-bearing walls. For such structures, especially when founded on soft soils, site amplification and soil-foundation-structure interaction (SFSI) can significantly affect the seismic performance; conversely, such phenomena should be investigated through methods that allow a trade-off between accuracy and computational effort, hence encouraging their implementation in engineering practice. This paper provides a comprehensive updated description of the studies carried out in the last years by the authors, which are based on both linear and nonlinear, parametric, dynamic analyses of complete soil-foundation-structure (SFS) models representative of existing residential building configurations on different soils. Specifically, the parametric study investigated SFS models with different masonry types, aspect ratios, and code-conforming homogeneous and heterogeneous soil profiles. The methodology and analysis results allowed for reaching the following objectives: (i) predicting the elongation of the fundamental period and the variation of equivalent damping of the SFS system with respect to fixed-base conditions, through a simplified approach based on an equivalent simple oscillator; and (ii) estimating the probability of exceeding increasing damage levels associated with out-of-plane overturning of URM walls, through fragility functions that take into account SFS interaction. The effectiveness of these simplified tools was successfully validated against well-documented case studies, at the scales of both single instrumented buildings and urban area. • Significance of soil-foundation-structure interaction for masonry buildings. • Updated approach for estimating the elongation of the period for masonry buildings. • Development of fragility curves accounting for soil-foundation-structure interaction. • Validation of the above simplified procedures on well-documented case studies. [ABSTRACT FROM AUTHOR]

A complex multiple-support response spectrum (CMSRS) method with a concise and universal expression is required to estimate the seismic responses of soil–structure interaction (SSI) systems under non-uniform seismic excitations to replace existing complex methods. This paper introduces and defines a new concept called equivalent acceleration of boundary load (EABL) that converts widely used equivalent loads into equivalent accelerations, and further develops an efficient CMSRS-EABL method for the seismic analysis of the SSI system. First, EABL offers three main benefits: it simplifies the expressions without sacrificing precision, extends the applicable scope of viscous-spring artificial boundary (VSAB) to all stress-type artificial boundaries, and presents dynamic equations in a familiar form. Subsequently, the CMSRS–EABL formula was successfully deduced based on the equivalent simplified dynamic equations. This formula significantly simplifies the traditional method by reducing the effective modal participation factors, mean-square-roots, and cross-correlation coefficients by 4, 5 and 15 items, respectively. Finally, a rectangular construction surrounded by a VSAB–soil combination was used as an example to illustrate the convenience of the developed CMSRS–EABL method and verify its precision. The results indicate that the proposed method is characterized by greater simplicity and ingenuity, and it is capable of high precision similar to that of the conventional methods. We believe this method will be of significant benefit in evaluating the anti-seismic performance of deeply buried and long-standing structures. • A new concept called "EABL" is introduced for simpler and more universal seismic analysis of SSI systems with stress-type artificial boundaries. • The CMSRS-EABL formula is deduced based on the equivalent simplified dynamic equations, simplifying the traditional CMSRS method. • The proposed complex non-uniform response spectrum method is verified to be capable of enough accuracy and reliability. [ABSTRACT FROM AUTHOR]

Interest in renewable and clean energy over the past decade has motivated immense research on wind energy. The main issues in design of offshore wind turbines in regions of recent development have been aero- and hydro-dynamic loads; however, earthquake is a design concern in seismic areas such as East Asia and Western United states. This paper reviews the state of practice in seismic design of offshore wind turbines. It is demonstrated that wind turbines are in particular vulnerable to vertical earthquake excitation due to their rather high natural frequencies in vertical direction; however, inclusion of the radiation damping could contribute considerably reduce the earthquake loads. Moreover, it is demonstrated how soil nonlinearity could lead to settlement and permanent tilting of offshore wind turbines on caisson foundations or tripods. Using these cases, the paper demonstrates that the design of offshore wind turbines for earthquake loading is driven by performance-based considerations. • Effect of combined environmental and earthquake loads on offshore wind turbines, highlighting the issue of permanent tilt. • Nonlinear foundation springs with reduced/controlled hysteretic damping for soil-structure interaction analysis. • Rigorous modelling of radiation damping and its role in reduction of vertical seismic response of wind turbines. • Harmonization of earthquake hazard requirements in design of wind turbines. • Review of key issues in earthquake design of offshore wind turbines. [ABSTRACT FROM AUTHOR]

The interconnectedness of current urban life with infrastructures urges the decision-makers to consider the resilience of urban lifeline systems as a priority. This motivates the research presented here, where the performance of a complex urban gas distribution system in a city with more than 12 million resident population is evaluated under the effects of seismic-induced liquefaction. The paper reviews the liquefaction potential in the Greater Tehran Area, and identifies the inputs for the analysis of soil-pipe interactions. The performance assessment is carried out using both numerical (finite elements analysis) and small scaled experimental assessments, for validation of the numerical models. The experimental results indicate that the numerical models are adequate for the performance evaluation of buried pipelines. The assessment shows that the buried pipelines perform well in most areas of the city, however, structural damage is expected in areas with higher seismic demands. In such areas, hands-on countermeasures are proposed to mitigate the risk of liquefaction-induced damage on the buried pipelines system. The results, methodology and procedures can be used as a framework the similar urban infrastructure risk analysis and mitigation studies. • Liquefaction potential methodologies in urban areas are reviewed, along with the past studies in the studied region in the Greater Tehran Area. • The main inputs in soil-pipe analysis, such as characteristics of the pipe, surrounding soil and the permanent ground displacements (PGDs) are gathered. • Effects of the liquefaction-induced PGDs on the buried gas pipelines are analysed using finite element analysis (FEA) verified against experimental studies in shaking table test facilities. • The risk assessment and risk mitigation counter-measures are presented to improve the response of the buried pipeline systems in the area. • Methodology, results and procedures can be very useful in the similar research and case-studies. [ABSTRACT FROM AUTHOR]

Contemporary analysis–design methods against faulting can significantly improve life-safety, but the problem of permanent deformation persists. This paper proposes a novel mitigation technique, addressing post-seismic serviceability. A "smart" barrier is employed to divert the fault rupture, introducing a minimum energy path. The "smart" barrier consists of two sheet-pile walls, connected with rows of sacrificial members. The latter are steel rings, whose performance is a function of geometry. The proposed system can be produced in the form of prefabricated panels, and its performance is largely insensitive to site conditions or workmanship. The barrier is compressed, absorbing tectonic deformation with minimum disturbance to the protected structure. The problem is analyzed employing the FE-method, using a thoroughly validated soil constitutive model with strain softening, confirming the efficiency of the mitigation concept. Further analyses demonstrate the use of sacrificial rings to protect continuous bridge decks, being installed between the deck and the bearings. • A "smart" barrier is proposed to protect critical infrastructure by diverting the fault rupture. • It consists of two sheet-pile walls, connected to each other with rows of sacrificial members. • The sacrificial members are steel rings, the ultimate capacity of which is a function of geometry. • The proposed "smart" barrier can be produced in the form of prefabricated panels. • The sacrificial rings can also be used to protect continuous bridge decks. [ABSTRACT FROM AUTHOR]

The seismic actions transmitted to a structure can be limited by inserting a frictional system between the foundation and the underlying soil. This allows a controlled sliding when the seismic forces reach a given critical value, that should be chosen to provide a desired seismic performance of the structure. Although this type of dissipative foundation has recently been adopted for the towers of two long-span bridges, its design still requires the development of a clear and robust design approach. In this view, the present paper studies the response of dissipative foundations, developing a generalised non-dimensional formulation that can be useful for design. The dynamic response of the foundation is analysed using a Newmark rigid block model, that is modified to account for the multi-directionality of the ground motion and to include a simplified description of the dynamic response of the superstructure. The main factors affecting the dynamic response of the dissipative system are highlighted through an extensive parametric study, leading to the definition of an optimised design approach of the dissipative foundation. • The paper studies the response of friction dissipative foundations of the type adopted in two recent long-span bridges. • A modified dynamic sliding-block model is developed to carry out an extensive parametric study. • The model results are expressed in a rigorous non-dimensional form. • The results show that the seismic performance of the system depends on the features of the entire soil-structure system. • A design approach is proposed to maximise the seismic efficiency of the dissipative foundation. [ABSTRACT FROM AUTHOR]

Modes of vibration play a dominant role in the design of WTG (Wind Turbine Generator) support structures. It is necessary to choose the overall system frequency such that the modes of vibration do not coincide with the rotor frequencies as well as the wave frequencies. WTG supported on multiple foundations (such as jackets or seabed frames) may exhibit rocking modes of vibration if the vertical stiffness of the foundation is not large enough which in turn may have serious implications on the fatigue performance of the overall structure. From the O&M (Operation and Maintenance) point of view, it is necessary to design the overall system to have sway-bending as the dominant mode of vibration. This paper develops a formulation for obtaining foundation (for both piles and shallow suction caissons) sizes and spacing such that rocking vibrations are prevented and sway-bending vibrations are achieved. Expressions for the minimum vertical stiffness of foundations are proposed for different configurations: square base, symmetrical (equilateral) triangle, or asymmetrical (isosceles) triangle. Verification of the method is carried out through finite element analysis and a step-by-step solved example is taken to show the application of the formulation. It is hoped that the formulation will assist designers to optimize the foundation arrangement and provide preliminary sizing for tender design. • Establishing criteria for different modes of vibrations for jackets supporting wind turbines. • Formulations for the minimum vertical stiffness of foundation to avoid rocking. • Example showing the applicability of the formulation. • Effects of foundation configuration (symmetric or symmetric) and spacing on modes of vibration. [ABSTRACT FROM AUTHOR]

More and more underground infrastructures have been built in special soil in recent years, especially in the loess area of western China. The loess, as a special soft soil, can have particular influence on the seismic characteristics of underground structures. Therefore, the seismic performance and safety evaluation of underground structures in loess area should be concerned. A series of large-scale shaking table tests were performed to investigate the damage mechanisms of a frame-type subway station structure in a loess site. The test results showed that the model soil softening and the stiffness degradation of the soil-structure system were more serious under stronger input motions. The acceleration response of the soil-structure interaction system in a loess site was more like that of a free-field when input PGA is lower. However, the soil-structure interaction phenomenon was more remarkable both in horizontal and vertical direction when higher PGA was input. The dominant frequency of the input motion had an inverse effect on the lateral soil deformation. The direct-force action mode of the dynamic earth pressure acting on underground structures presents a trumpet-type distribution. Meanwhile, the soil-structure interaction exhibited complex mechanical behavior, and slipping or gapping in test cases with higher PGA may occur. The strain measured in the center pillar and middle slab of the subway station was larger than that in other components. The results provide an insight into how strong ground motion might induce the influence and a possible way to describe quantitatively the damage of subway structure in loess ground. •A series of shaking table tests of subway model structure in a loess soil were conducted. • The dynamic characteristics of the loess soil under different ground motions were analyzed. • The seismic behavior of the subway station structure was obtained and analyzed through the test. [ABSTRACT FROM AUTHOR]

The September 19th, 2017 Mw 7.1 Puebla-Mexico City earthquake lead to strong ground shaking in the densely populated Mexico City basin, and surrounding country areas in central Mexico. As a result, 38 mid-rise buildings collapsed and several hundred more were damaged in Mexico City, and extensive damage was observed in the states of Puebla and Morelos. This special edition synthesizes observations related to structural and foundation performance, and the corresponding damage patterns, carried out by two UNAM-GEER engineering reconnaissance teams sent to investigate the geotechnical earthquake engineering aspects of this event. Articles were solicited of researchers that were in the field that investigated: the characteristics of the event, the demand and damage distribution across Mexico City and surrounding regions, the seismic performance of buildings, lifelines, and other critical infrastructure, considering the site response and soil-structure interaction effects in the observed damage distribution. Special attention was paid to the impact of regional ground subsidence, in the seismic-soil structure interaction exhibited by the affected building. Advanced non-intrusive survey methods were used to map damage patterns in a regional level. Comparisons were made between the observed building damage patterns following the September 19th, 1985 Michoacan earthquake, and the 2017 Puebla-Mexico City earthquake, and the distinct differences in the damage distribution between the two earthquakes were revised. Overall, building and foundation performance were observed to be quite good during the 2017 event, especially when compared to the 1985 event. Structures that were observed to be heavily damaged or collapsed were all built prior to 1985, and incorporated poor structural design and/or construction, which resonated with the soil column on which they were constructed, and/or were built upon very soft soils that contributed to significant foundation deformations. Detailed building damage pattern maps of specific neighborhoods that were investigated are provided, and lessons learned from this event are summarized in each research paper include in this special issue. • UNAM-GEER reconnaissance teams investigated the geotechnical aspects of the earthquake. • This special issue included seismology, site response and soil-structure interaction studies. • Damage distribution across Mexico City and surrounding regions was established. • Performance of buildings, lifelines, and other critical infrastructure was assessed. • Detailed building damage pattern maps of specific neighborhoods were prepared. [ABSTRACT FROM AUTHOR]

Structural or foundation rocking are effective ways to prevent the development of large force demands in building systems experiencing ground shaking. In practice, structural rocking may result in large displacements and therefore is often accompanied with dampers, while residual and differential settlements are sometimes a barrier for utilisation of foundation rocking. This paper presents a novel approach to test simultaneously in a centrifuge the performances of a building model rocking above its foundation level (structural rocking) and of a dynamically equivalent building rocking below its foundation level (foundation rocking). These tests are used to explore the role of the foundation and soil response when considering the relative trade-offs between the two building types. In the experiments, dry sand was used in both dense and loose states and a series of earthquake excitations were applied. Results demonstrate that the rocking motion of the buildings is evident in the soil response beneath the structures, and foundation rocking causes larger dynamic differential settlements than structural rocking for a given rocking amplitude. However, these differential settlements may still be small enough to be tolerated from a serviceability limit state point of view. • A centrifuge methodology to compare structural and foundation rocking. • Direct comparison of soil behaviour beneath structural and foundation rocking. • Wavelet transforms used to identify time-dependent soil-structure interaction. • Foundation rocking caused larger settlements than structural rocking. • Soil below a building with structural rocking remained practically linear. [ABSTRACT FROM AUTHOR]

The dynamic response of structures in contact with soil is receiving increasing interest and there is a growing need for more accurate models capable of simulating the behaviour of these systems. This is particularly important in the field of offshore wind turbines, where accurate estimates of system frequency are needed to avoid resonance, and in the structural health monitoring fields, where accurate reference damage models are used. Previous work has shown that there is significant uncertainty in how to specify mobilised soil stiffness for dynamic soil-pile interaction modelling. Moreover, the contribution of soil mass in dynamic motion is often ignored. This paper applies a finite-element iterative model updating approach previously developed by the authors to two experimental piles to ascertain the mobilised soil stiffness and mass profiles from impact test data. The method works by obtaining a frequency response function (FRF) from an impact test performed on a test pile, developing a numerical model of this system, applying initial estimates of soil mass and stiffness, and updating these properties to match the experimental FRF with that generated in the numerical model. A range of elements are investigated including multiple runs of the approach to test repeatability, the influence of different starting estimates for stiffness, the effect of variability in experimental test data, and the influence of the pile length over which masses are distributed. Moreover, potential sources of error are discussed. The method provides reasonably consistent estimates of the soil stiffness and mass acting in the lateral dynamic motion of a given pile tested in this paper. The approach may be useful in the continued improvement of Soil-Structure Interaction (SSI) modelling for dynamic applications. • Paper investigates FE model updating approach applied to two test piles. • Soil stiffness is initially estimated using subgrade reaction approaches. • FRFs are developed from the test piles using impact testing. • FRFs are used in the FE updating approach to estimate acting stiffness and mass. • Sources of error are investigated and discussed. [ABSTRACT FROM AUTHOR]

The spatial seismic excitations affected by water-saturated soil, a double-phase medium, and overlying water are desirable to be considered for evaluating the seismic response of some typical structures such as large-span cross-sea bridges considering soil-structure interaction. This paper focuses on the study of a theoretical method and numerical simulation of multi-support seismic underground excitations in saturated soil with overlying water for obliquely incident SV waves that can produce P 1, P 2 and SV waves in saturated soil. First, the reflection coefficients (results are different from the case for P waves incidence) of three kinds of waves (P 1, P 2, SV) at the interface between saturated soil and overlying water are derived. Based on the reflection coefficients and the boundary conditions at the elastic solid-saturated soil interface, the transfer functions of soil layers with arbitrary depths are proposed to calculate the key elements (i.e., the underground power spectral density, response spectrum function and underground coherency function) for generating the multi-support seismic underground motions. Second, these three key elements are used to establish the underground power spectral matrix, and then the underground motions are generated by decomposing the matrix. Finally, the method is verified by numerical examples and the influences of overlying water depth and incident angle on ground motions are investigated. The effect of incident angle on transfer functions show great difference between the small-angle and large-angle case. Moreover, the phenomenon that is diffrent from P-waves incidence case is investigated,found and emphasized, and the reasons are given. • Reflection coefficients at the interface between saturated soil and water are derived. • Transfer functions of soil layers with arbitrary depths are deduced to further calculate the key elements for establishing the underground PSD matrix. • PSD matrix is established for simulating the spatially variable seismic underground motions of saturated soil with overlying water. • Parameter sensitivity of the predicted seismic motions to the soil thickness, incident angle and water depth is investigated. • The difference of phenomenon from that under P-waves incidence case is found and the reason is given. [ABSTRACT FROM AUTHOR]

The innovative concept of geotechnical seismic isolation (GSI) system with the use of a continuous layer of low-modulus materials, such as rubber-soil mixtures (RSM), surrounding the foundation of structure has attracted considerable research interest on its performance at both system and material levels, since it was first proposed over a decade ago. The performance of the GSI system has been studied through a number of numerical, physical and hybrid modeling techniques; but due to the complexity of the problem, the isolation mechanism has not been thoroughly investigated. Hence, this article aims at initiating this aspect of development. A simple and efficient lumped-parameter analytical model is developed for analyzing the dynamic soil-foundation-structure interaction (SFSI) of the GSI system. Considering the importance of various nonlinearities involved, a theoretical approach for estimating effective shear strain is derived for capturing the nonlinearity of subsurface materials by the equivalent-linear method. The effectiveness of the analytical model is then demonstrated through a representative case study, based on which the main features of the isolation mechanism are investigated. The seismic isolation capability of the GSI system is founded on the reduced lateral stiffness of the RSM layer and the lower modulus of RSM that reduces the rocking stiffness. The proposed system could take advantage of the rocking isolation mechanism with reversible foundation deformations due to the higher elasticity of the RSM material. • First lumped-parameter analytical model for geotechnical seismic isolation system. • Nonlinearity of subsurface material incorporated in soil-foundation-structure model. • New theoretical approach for estimating effective shear strain in equivalent-linear method. • Demonstrated and explained the mechanism of GSI system through case study. [ABSTRACT FROM AUTHOR]

The buckling of steel pipe piles during installation is numerically studied. Generally, numerical simulation of installation processes is challenging due to large soil deformations. However, by using advanced numerical approaches like Multi-Material Arbitrary Lagrangian-Eulerian (MMALE), such difficulties are mitigated. The Mohr-Coulomb and an elastic-perfectly plastic material model is used for the soil and pile respectively. The pile buckling behavior is verified using analytical solutions. Furthermore, the model is validated by an experiment where a pipe pile is driven into sand using vibratory loading. Several case scenarios, including the effects of heterogeneity in the soil and three imperfection modes (ovality, out-of-straightness, flatness) on the pile buckling are investigated. The numerical model agrees well with the experimental measurements. As a conclusion, when buckling starts, the penetration rate of the pile decreases compared to the non-buckled pile since less energy is dedicated to pile penetration given that it is spent mainly on buckling. • An advanced numerical method, MMALE, is used to study pile buckling during the installation process. • By use of an efficient soil-structure interaction scheme, some of the simplifications used in previous studies are omitted. • The effects of initial imperfections in the pile, and heterogeneities in the soil on early buckling are studied. • The driving energy is spent on other phenomena such as pile buckling and lateral displacement, resulting in less penetration. • The study points out the MMALE method as a cost-effective evaluation tool for the pile design considering complex conditions. [ABSTRACT FROM AUTHOR]

In this paper, a simplified discrete model for calculating the modal parameters of the fundamental vertical mode of a simple beam on viscoelastic supports is proposed. Exact closed-form expressions for the fundamental natural frequency and modal damping ratio of the aforementioned coupled system are derived, as a function of the beam geometry and the foundation impedances. Using this model, the effect of the dynamic stiffness and dissipation capacity of the foundation-soil system on the modal characteristics of the fundamental vertical mode of the railway beam bridges is investigated and discussed. The proposed closed-form expressions, in combination with the impedance functions of different foundation-soil systems, can clarify the main features of dynamic SSI analysis of the railway beam bridges and lead to review the recommended modal damping ratios in the code provisions and design manuals. • Develop a discrete model for SSI analysis of simple beams on viscoelastic supports. • Derivate exact closed-form expressions for estimating fundamental frequency and damping of bridges on impedance functions. • Perform an extensive parametric study considering different beam geometries and soil configurations. • Identify the key parameters governing the dynamic response of short-span railway bridges, considering dynamic SSI. [ABSTRACT FROM AUTHOR]

The current study investigated the extent to which the choice of the soil constitutive models can impact the predicted seismic performance of a 20-story reinforced concrete moment-resisting building with a mat foundation considering the Seismic Soil-Structure Interaction (SSSI). Since the soil, in general, is the weakest material, involved in the commonplace geotechnical engineering projects, a soil constitutive model would be able to rule the dynamic response of the system. In this research, the hardening plasticity-based soil constitutive model, named "hyperbolic hardening with hysteretic damping", in conjunction with the two simple, conventional soil models, namely, the isotropic elastic with hysteretic damping model, and elastic-perfectly plastic Mohr-Coulomb with hysteretic damping model, were invoked in the three-dimensional coupled soil-structure numerical simulations using FLAC3D software. The direct method of analysis was used for analyzing the soil-foundation-structure system in one single step without a need to separately analyze each part of the domain. The cherry-picked earthquake excitations, viz, the 1999 Chi-Chi (Taiwan), and 2011 Kohriyama (Japan), were scaled by means of the widely-used response spectrum matching method as per the design response spectrum of a strong rock. The plastic moment concept was employed so as to assign the elastic-perfectly plastic model to the superstructure and its foundation. Additionally, the strain-compatible shear modulus and damping dependency on the cyclic shear strain were considered via the programmed hysteretic damping algorithm. The numerical predictions included the response spectra at the seismic bedrock and ground surface, base shear forces, shear force distributions along the building height, maximum and permanent foundation displacements, and foundation rocking, plus the flooring lateral deflections and inter-story drifts. The life safety limits for the transient and residual total inter-story drift ratios were not met whilst considering the soil pre-failure plasticity. The concluded remarks herein on the significant effects of the soil hardening plasticity on the seismic performance of the adopted 20-story moment-resisting frame would be applicable to the other structures on a mat foundation, potentially experiencing the foundation rocking amidst the earthquakes. Schematic of numerical model concomitant with seismic analysis of soil-foundation-superstructure system, having adopted soil constitutive models, viz, isotropic Elastic with Hysteretic Damping (E-HD), elastic-perfectly plastic Mohr-Coulomb with Hysteretic Damping (MC-HD), and Hyperbolic Hardening with Hysteretic Damping (H2-HD), conducted in FLAC3D, subjected to scaled 1999 Chi-Chi earthquake and scaled 2011 Kohriyama earthquake, so as to investigate effects of soil pre-failure hardening plasticity on seismic performance of 20-story reinforced concrete moment-resisting building frame, supported on mat foundation, experiencing foundation rocking, using soil-structure interaction approach: fx1 • Hyperbolic hardening with hysteretic damping model was adopted for the Seismic Soil-Structure Interaction (SSSI) analysis. • Adopted soil model possessed the shear strain hardening, dilation hardening, and pressure-dependent stiffness. • Soil hardening plasticity dislocated the predicted seismic performance level of the adopted 20-story moment-resisting frame. • Excluding the soil plasticity would result in the life-threatening seismic design of a building with significant rocking. [ABSTRACT FROM AUTHOR]

The paper presents simple formulas to evaluate parameters of a lumped system reproducing the frequency-dependent dynamic stiffness of end-bearing pile foundations. The model can be implemented in commercial finite element software and allows performing inertial soil-structure interaction analyses of structures considering the coupled roto-translational, vertical and torsional behaviour of the soil-foundation system. Pile groups arranged in a square layout are considered; the soil profile is constituted by a homogeneous deformable soil layer overlying a bedrock where piles are socked for a fixed length. Formulas are calibrated with a nonlinear least square procedure, based on data provided by an extensive non-dimensional parametric analysis of the soil-foundation systems, performed with a Winkler's type model, previously developed by the authors, which assumes soil and piles to behave linearly. Firstly, the suitability of the adopted numerical tools in capturing the dynamic stiffness of end-bearing foundations is proven. Then, capabilities of the proposed formulas in estimating parameters of the best lumped systems are shown, and, for some case studies, comparisons of non-null terms of the impedance matrix obtained through the best lumped system, the one computed through the formulas, and the impedances resulting from the dynamic analyses, are presented. Finally, some applications of the proposed formulas in the framework of the seismic soil-structure interaction analysis of bridges are shown to demonstrate the capability of the adopted lumped system and the formula efficiency in assuring a reliable evaluation of the superstructure seismic response, with respect to that obtained from a more rigorous approach. • Formulas for estimating an efficient LPM for pile group foundations are proposed. • A physical LPM reproducing impedances of end-bearing pile groups is adopted. • Translational, rotational, and coupled behaviours of foundations are considered. • The LPM can be implemented in commercial software for structural analyses. • Formulas can be adopted to perform inertial soil-structure interaction analyses. [ABSTRACT FROM AUTHOR]