Early history of soil–structure interaction

Soil–structure interaction is an interdisciplinary field of endeavor which lies at the intersection of soil and structural mechanics, soil and structural dynamics, earthquake engineering, geophysics and geomechanics, material science, computational and numerical methods, and diverse other technical disciplines. Its origins trace back to the late 19th century, evolved and matured gradually in the ensuing decades and during the first half of the 20th century, and progressed rapidly in the second half stimulated mainly by the needs of the nuclear power and offshore industries, by the debut of powerful computers and simulation tools such as finite elements, and by the needs for improvements in seismic safety. The pages that follow provide a concise review of some of the leading developments that paved the way for the state of the art as it is known today. Inasmuch as static foundation stiffnesses are also widely used in engineering analyses and code formulas for SSI effects, this work includes a brief survey of such static solutions.     

Structure–soil–structure interaction: Literature review

The concept of structure–soil–structure dynamic interaction was introduced, and the research methods were discussed. Based on several documents, a systematic summary of the history and status of the structure–soil–structure dynamic interaction research that considers adjacent structures was proposed as a reference for researchers. This study is in the initial stage, given its complexity and excessive simplification of the model for soil and structures, and should be carried forward for its significance. An attempt was made to summarize the common major computer programs in this area of study. Furthermore, the advantages, disadvantages, and applicability of such programs were discussed. The existing problems and the future research trend in this field were also examined.     

Dynamic response of structures subjected to pounding and structure–soil–structure interaction

During strong earthquakes, adjacent structures with non-sufficient clear distances collide with each other. In addition to such a pounding, cross interaction of adjacent structures through soil can exchange the vibration energy between buildings and make the problem even more complex. In this paper, effects of both of the mentioned phenomena on the inelastic response of selected steel structures are studied. Number of stories varied between 3 and 12 and different clear distances up to the seismic codes prescribed value are considered. The pounding element is modeled within Opensees. A coupled model of springs and dashpots is utilized for through-the-soil interaction of the adjacent structures, for two types of soft soils. The pounding force, relative displacements of stories, story shears, and plastic hinge rotations are compared for different conditions as the maximum responses averaged between seven consistent earthquakes. As a result, simultaneous effects of pounding and structure–soil–structure interaction are discussed.     

Real-time dynamic hybrid testing for soil–structure interaction analysis

Simulating dynamic soil–structure interaction (SSI) problems is a challenge when using a shaking table because of the semi-infinity of soil foundations. This paper develops real-time dynamic hybrid testing (RTDHT) for SSI problems in order to consider the radiation damping effect of the semi-infinite soil foundation using a shaking table. Based on the substructure concept, the superstructure is physically tested and the semi-infinite foundation is numerically simulated. Thus, the response of the entire system considering the dynamic SSI is obtained by coupling the numerical calculation of the soil and the physical test of the superstructure. A two-story shear frame on a rigid foundation was first tested to verify the developed RTDHT system, in which the top story was modeled as the physical substructure and the bottom story was the numerical substructure. The RTDHT for a two-story structure mounted on soil foundation was then carried out on a shaking table while the foundation was numerically simulated using a lumped parameter model. The dynamic responses, including acceleration and shear force, were obtained under soft and hard soil conditions. The results show that the soil–structure interaction should be reasonably taken into account in the shaking table testing for structures.     

Real-time dynamic hybrid testing for soil–structure interaction analysis

Simulating dynamic soil–structure interaction (SSI) problems is a challenge when using a shaking table because of the semi-infinity of soil foundations. This paper develops real-time dynamic hybrid testing (RTDHT) for SSI problems in order to consider the radiation damping effect of the semi-infinite soil foundation using a shaking table. Based on the substructure concept, the superstructure is physically tested and the semi-infinite foundation is numerically simulated. Thus, the response of the entire system considering the dynamic SSI is obtained by coupling the numerical calculation of the soil and the physical test of the superstructure. A two-story shear frame on a rigid foundation was first tested to verify the developed RTDHT system, in which the top story was modeled as the physical substructure and the bottom story was the numerical substructure. The RTDHT for a two-story structure mounted on soil foundation was then carried out on a shaking table while the foundation was numerically simulated using a lumped parameter model. The dynamic responses, including acceleration and shear force, were obtained under soft and hard soil conditions. The results show that the soil–structure interaction should be reasonably taken into account in the shaking table testing for structures.     

Effects of soil–structure interaction on seismic base isolation

The effects of soil–structure interaction on the performance of a nonlinear seismic base isolation system for a simple elastic structure are examined. The steady-state response of the system to harmonic excitation is obtained by use of the equivalent linearization method. Simple analytical expressions for the deformation of the base isolation system and of the superstructure at resonance are obtained in terms of an effective replacement oscillator characterized by amplitude-dependent frequency, damping ratio, and excitation. Numerical results suggest that the seismic response of a structure resting on an inelastic base isolation system may be larger when the flexibility of the soil is considered than the corresponding response obtained by ignoring the effects of soil–structure interaction. It is shown that, in the undamped case and in the absence of soil–structure interaction effects, a critical harmonic excitation exists beyond which the steady-state resonant response of the isolators and structure become unbounded.     

Seismic response of base-isolated buildings including soil–structure interaction

This study investigates the effect of soil–structure interaction (SSI) on the response of base-isolated buildings. The equations of motion are formulated in the frequency domain, assuming frequency-independent soil stiffness and damping constants. An equivalent fixed-base system is developed that accounts for soil compliance and damping characteristics of the base-isolated building. Closed-form expressions are derived, followed by a thorough parametric study involving the pertinent system parameters. For preliminary design, the methodology can serve as a means to assess effective use of base isolation on building structures accounting for SSI. This study concludes that the effects of SSI are more pronounced on the modal properties of the system, especially for the case of squat and stiff base-isolated structures.     

Dynamic soil–structure interaction of monopile supported wind turbines in cohesive soil

Offshore wind turbines supported on monopile foundations are dynamically sensitive because the overall natural frequencies of these structures are close to the different forcing frequencies imposed upon them. The structures are designed for an intended life of 25 to 30 years, but little is known about their long term behaviour. To study their long term behaviour, a series of laboratory tests were conducted in which a scaled model wind turbine supported on a monopile in kaolin clay was subjected to between 32,000 and 172,000 cycles of horizontal loading and the changes in natural frequency and damping of the model were monitored. The experimental results are presented using a non-dimensional framework based on an interpretation of the governing mechanics. The change in natural frequency was found to be strongly dependent on the shear strain level in the soil next to the pile. Practical guidance for choosing the diameter of monopile is suggested based on element test results using the concept of volumetric threshold shear strain.     

Influence of plasticity on the seismic soil–micropiles–structure interaction

This paper includes an analysis of the influence of soil plasticity on the seismic response of micropiles. Analysis is carried out using a global three-dimensional modeling in the time domain. The soil behavior is described using the non-associated Mohr–Coulomb criterion. Both the micropiles and the superstructure are modeled as three-dimensional beam elements. Proper boundary conditions are used to ensure waves transmission through the lateral boundaries of the soil mass. Analyses are first conducted for harmonic loadings and then for real earthquake records. They show that plasticity could have a significant influence on the seismic response of the soil–micropiles–structure systems. This influence depends on the amplitude of the seismic loading and the dominant frequencies of both the input motion and the soil–piles–structure system.     

Active control of irregular buildings considering soil–structure interaction effects

This paper analyzes the soil–structure interaction (SSI) effect on vibration control effectiveness of active tendon systems for an irregular building, modeled as a torsionally coupled (TC) structure, subjected to base excitations such as those induced by earthquakes. An H_∞ direct output feedback control algorithm through minimizing the entropy, a performance index measuring the trade-off between H_∞ optimality and H₂ optimality, is implemented to reduce the seismic responses of TC structures. The control forces are calculated directly from the multiplication of the output measurements by a pre-calculated frequency-independent and time-invariant feedback gain matrix, which is obtained based on a fixed-base model. Numerical simulation results show that the required numbers of sensors, controllers and their installation locations depend highly on the degree of floor eccentricity. For a large two-way eccentric building, a one-way active tendon system placed in one of two frames farthest away from the center of resistance (C.R.) can reduce both translational and torsional responses. The SSI effect is governed by the slenderness ratio of superstructure and by the stiffness ratio of soil to superstructure. When the SSI effect is significant, the proposed control system can still reduce the structural responses, however, with less effectiveness than that of the assumed fixed-base model. Therefore, the TC and SSI effects should be considered in the design of active control devices, especially for high-rise buildings located on soft site.     

Experimental validation of soil–structure interaction of offshore wind turbines

Estimating the natural frequencies of a wind turbine system consisting rotor, nacelle, tower, foundation and surrounding soil is one of the important design considerations. This paper experimentally investigates the behaviour of a model wind turbine supported on a particular type of foundation called a monopile. Monopile is a single large diameter (2.5–4 m) long slender column inserted deep into the ground. This can be thought of as an extension of the wind turbine tower. In particular, the role of soil/foundation in the dynamics of wind turbines has been investigated. Analytical methods are developed incorporating the rotational and translation flexibility of the foundation. Novel experimental techniques have been developed to obtain the parameters necessary for the analytical model. The analytical model is validated using a finite element approach and experimental measurements. In total, results from 17 test cases is reported in the paper. Experimental results show that the natural frequencies and the damping factors of the wind turbine tower change significantly with the type of soil/foundation. Analytical results for the natural frequencies agree reasonably well to the experimental results and finite element results.     

Conversion factors for design spectral accelerations including soil–structure interaction

In this paper maximum response of a single degree of freedom system resting on a flexible base is determined under consistent earthquakes and the results are presented as acceleration spectra including soil–structure interaction (SSI). Flexibility of base is modeled using frequency-dependent springs and dampers. The spring–damper coefficients are calculated for the desired natural mode of vibration of a multi-degree-of-freedom system. Consistency of earthquakes is maintained considering their magnitude, distance, local soil type, and return period. The latter parameter is accounted for by the use of earthquake categories identified by their similar spectral values. Ratio of spectral acceleration modification factors with SSI from this study to those calculated using the ASCE 7-10 procedure are determined for each case. Examination of the resulting curves shows that the mentioned code is conservative/non-conservative in estimation of spectral responses with SSI in certain cases for the lower/higher modes of vibration. The code’s procedure is modified using the developed curves for a conversion factor.     

Determination of scoured bridge natural frequencies with soil–structure interaction

This study developed a finite element method with the effect of soil–fluid–structure interaction to calculate bridge natural frequencies. The finite element model includes bridge girders, piers, foundations, soil, and water. The effective mass above the soil surface was then used to find the first natural frequency in each direction. A field experiment was performed to validate that the natural frequencies calculated using the proposed finite element method had acceptable accuracy. The calculated natural frequencies with the fluid–structure interaction effect are always smaller than those without this effect. However, the frequency change due to the fluid effect is not obvious, so using the soil–structure interaction model is accurate enough in the bridge natural frequency analysis. The trend of the frequency decreases with the increase of the scour depth, but the curve is not smooth because of non-uniform foundation sections and layered soils. However, when the scour depth is such that pile cap is exposed, the changes in natural frequency with the scour depth are more obvious, and this is useful for measurement of the depth using bridge natural frequencies.     

Energy dissipation by nonlinear soil strains during soil–structure interaction excited by SH pulse

Three variants of a two-dimensional (2-D) model of a building supported by a rectangular, flexible foundation embedded in nonlinear soil are analyzed. The building, the foundation, and soil have different physical properties. The building is assumed to be linear, but the foundation and the soil can experience nonlinear deformations. It is shown that the work spent for the development of nonlinear strains in the soil can consume a significant part of the input wave energy, and thus less energy is available for excitation of the building. The results help explain why the damage, during the 1994 Northridge earthquake in California, to residential buildings in the areas that experienced large strains in the soil was absent or reduced.     

Seismic soil–pile interaction in liquefiable soil

Numerical analysis of seismic soil–pile interaction was considered in order to investigate the influence of flow mechanisms. Two models were employed—a simplified model, where the pore pressure at any depth is that of the free field, and a more complete model in which the pore pressure is associated with three-dimensional flow. The soil behavior was modeled by a nonlinear, quasi-hysteretic constitutive relation. A parametric study was carried out, varying the superstructure mass and soil permeability. It was found that there is a pore pressure threshold below which both models yield similar results, but that this threshold cannot be quantified a priori, as it depends strongly on soil–pile interaction.     

A parallel finite–infinite element model for two-dimensional soil–structure interaction problems

A parallel soil–structure interaction (SSI) model is presented for applications on distributed computer systems. Substructring method is applied to the SSI system and a coupled finite–infinite element based parallel computer program is developed. In the SSI system, infinite elements are used to represent the soil which extends to infinity. In this case, a large finite element mesh is required to define the near field for reliable predictions. The resulting large-scale problems are solved on distributed computer systems in this study. The domain is represented by separated substructures and an interface. The number of substructures are determined by the available processors in the parallel platform. To avoid the formation of large interface equations, smaller interface equations are distributed to processors while substructure contributions are performed. This saves a lot of memory storage and computational effort. Direct solution techniques are used for the solution of interface and substructure equation systems. The program is investigated through some example problems. The example problems exposed the need for solving large-scale problems in order to reach better results. The results of the example problems demonstrated the benefits of the parallel SSI algorithm.     

Dynamic structure–soil–structure interaction between nearby piled buildings under seismic excitation by BEM–FEM model

The dynamic through–soil interaction between nearby pile supported structures in a viscoelastic half-space, under incident S and Rayleigh waves, is numerically studied. To this end, a three-dimensional viscoelastic BEM–FEM formulation for the dynamic analysis of piles and pile groups in the frequency domain is used, where soil is modelled by BEM and piles are simulated by one-dimensional finite elements as Bernoulli beams. This formulation has been enhanced to include the presence of linear superstructures founded on pile groups, so that structure–soil–structure interaction (SSSI) can be investigated making use of a direct methodology with an affordable number of degrees of freedom. The influence of SSSI on lateral spectral deformation, vertical and rotational response, and shear forces at pile heads, for several configurations of shear one-storey buildings, is addressed. Maximum response spectra are also presented. SSSI effects on groups of structures with similar dynamic characteristics have been found to be important. The system response can be either amplified or attenuated according to the distance between adjacent buildings, which has been related to dynamic properties of the overall system.     

Seismic soil–pile–structure kinematic and inertial interaction—A new beam approach

The main purpose of this study is to investigate the accuracy of an advanced beam model for the soil–pile–structure kinematic and inertial interaction and demonstrate its efficiency and advantages compared to other commonly used beam or solid models. Within this context, a Beam on Nonlinear Winkler Foundation model is adopted based on the Boundary Element Method (BEM), accounting for the effects induced by geometrical nonlinearity, rotary inertia and shear deformation, employing the concept of shear deformation coefficients. The soil nonlinearity is taken into consideration by means of a hybrid spring configuration consisting of a nonlinear (p–y) spring connected in series to an elastic spring–damper model. The nonlinear spring captures the near-field plastification of the soil while the spring–damper system (Kelvin–Voigt element) represents the far-field viscoelastic character of the soil. An extensive case study is carried out on a pile-column–deck system of a bridge, found in two cohesive layers of sharply different stiffness and subjected to various earthquake excitations, providing insight to several phenomena. The results of the proposed model are compared with those obtained from a Beam-FE solution as well as from a rigorous fully three-dimensional (3-D) continuum FE scheme.     

The effect of soil–structure interaction on the seismic risk to buildings

This paper studies the effect of soil–structure interaction (SSI) on the seismic risk estimates of buildings. Risk, in this context, denotes the probability distribution of seismic monetary loss due to structural and nonstructural damage. The risk analysis here uncovers the probability that SSI is beneficial, detrimental, or uninfluential on seismic losses. The analyses are conducted for a wide range of buildings with different structural systems, numbers of stories, and foundation sizes on various soil types. A probabilistic approach is employed to account for prevailing sources of uncertainty, i.e., those in ground motion and in the properties of the soil–structure system. In this approach, probabilistic models are employed to predict the response, damage, and repair cost of buildings. To properly account for the ground motion uncertainty, a suite of nearly 7000 accelerograms recorded on soil is employed. It is concluded that structures on very soft soils are extremely likely to incur smaller losses due to SSI, which is in line with the common belief that SSI is a favorable effect for such systems. However, the results for buildings on moderately soft soils reveal a considerable probability, up to 0.4, that SSI has an adverse effect on the structure and increases the seismic losses.