Seismic soil-structure interaction by the superposition method

The superposition technique is a simple yet powerful method for soil-structure seismic interaction problems. The method essentially consists of obtaining total motions by superposing free field motions and interaction motions, both previously calculated in separate analyses. Although this method is strictly applicable only to linear systems, the equivalent linear method is easily incorporated in order to approximate soil non-linearities. The superposition technique is valid for 3-D geometries, and allows for a seismic environment consisting of any kind of body or surface waves, or combinations thereof. The method is explained in detail, and three case studies are also summarized as an illustration of the flexibility of the method.     

Vertical soil-structure interaction of nuclear power plants subjected to seismic excitation

The vertical soil-structure interaction problem is investigated by coupling an N-mass lumped mass structure to a two-dimensional elastic half space. This problem is formulated as an integral equation of the Volterra type. Numerical results are obtained by iteration for an idealized threemass two-mode model of a nuclear power plant containment structure. The effects of interaction are evaluated by comparing free-field acceleration spectrum response curves with similar curves determined from foundation motion.     

Special topics on soil-structure interaction

In the design of nuclear power plants, the topic of soil-structure interaction has traditionally been one of great theoretical and practical controversy for several reasons. In the beginning of the era of nuclear power, the science of soil-structure interaction was in its infancy and very little theory or observational data were available to the engineering profession. At the same time, the state of the art of structural dynamics, however, was already developed and engineers had a considerable amount of data on actual dynamic performance of structures, so that a great amount of confidence in the ability to perform a dynamic structural analysis was already in existence. It was only natural to extend the basic fundamentals of dynamic structural modeling to soil-structure interaction. Consequently, many ‘approaches’ and ‘theories’ of how to account for soil-structure interaction were erroneously developed without providing real consideration of basic fundamentals of interaction of a foundation with an elastic continuum, commonly referred to as elastic half-space or continuum solutions. At the same time, while great confusion was developing on how to apply elastic half-space theory to earthquake analysis problems, the dynamic finite element approach was born and was thought by many to be the final panacea to the problem of soil-structure interaction. Of course, as is usually the case, there is no perfect or single best approach to any problem and the end result is that each of the many approaches to account for soil-structure interaction, has its strong and weak points depending on site or structural conditions. This paper is intended to discuss some of the important details of soil-structure interaction theory to provide a common means of comparison and to introduce some new approaches to simplify the solutions of deeply embedded foundations.A review of recent literature on soil-structure interaction reveals several important facts. First, conflicting comparisons between the lumped parameter and finite element solutions apparently exist. In some cases, both approaches give similar results while for others the results vary widely essentially because different models are used for comparison of both methods. Secondly, fundamental errors are committed on finite element mesh size parameters and boundary conditions. Thirdly, misunderstandings on soil mass and foundation or structural modal damping lead to gross errors in the lumped parameter approach. Finally, the limitations of the various approaches are not always understood. It is noted that both the finite element and lumped parameter approaches should yield similar results if they are appropriately used to solve the same problems. A summary of the advantages and limitations of both approaches are presented and discussed with a short presentation regarding the state of the art in the determination of soil stiffness and material damping characteristics.Furthermore, the paper will illustrate one type of analysis technique which uses a hybrid approach of both finite element results and lumped parameter solutions. Such an approach is developed to account more accurately for the influence of embedment. Results using both pure finite element solutions and lumped parameter models show that the influence of embedment can be accurately considered even for deeply embedded structures (depth to width ratio equal to 1.0). The key to the approach lies in establishing the coupling between horizontal and rocking modes of foundation vibration. Once the coupling parameter is accounted for, it is then possible to develop a lumped parameter models that account for the variation of soil motions below the ground sufrace. Previous lumped parameter models have not accounted for these variations from the surface to the depth of the foundation.Details of the lumped parameter approach for embedded foundations and an illustration with numerical examples are provided. Recommendations are then presented on a procedure for soil-structure interaction of deeply embedded foundations. The primary advantages are that: (1) the model is more easily generated than a finite element model, (2) the model is less susceptible to modeling errors, such as mesh size, model size, and boundary influences, (3) parametric studies may be easily conducted since parameters such as damping may be more directly controlled, and (4) the computer costs for analysis are significantly reduced.     

Multi-scattering and boundary effects in soil-structure interaction

This paper presents two applications of a coupled finite element and boundary element method (FEBEM) to two-dimensional, transient problems of scattering of elastic SH waves. One application concerns multi-scattering: examples are shown for scattering from two semi-cylindrical inclusions embedded in a half-plane and separated by a small distance. Responses of one inclusion in the time and frequency domains are compared with those associated with a single inclusion. The other application concerns the effect of the size of the finite element mesh and boundary on accuracy. Response of the flat foundation with rectangular shape and seated on a half-plane is analyzed. It is shown that while simple silent boundaries are quite effective for large models, Rayleigh damping cannot model radiation damping effectively.     

The use of frequency-independent soil-structure interaction parameters

The validity of approximating frequency-independent foundation impedance functions by constant parameters was evaluated for nuclear power plant structures. The soil-structure interaction system with the frequency-dependent impedances was analyzed using the Foss method to uncouple the equations of motion; this closely follows the method developed by Jennings and Bielak. The interaction system with the constant impedances was approximately analyzed by the normal mode method using equivalent modal damping values computed according to a procedure developed by Tsai. The above two methods were applied to simplified containment structural models founded on an idealized elastic half-space, the shear wave velocities being taken to be 600, 1150, 2000 and 10 000 ft/sec. The results such as frequencies, damping, and in-structure response spectra were then compared. It was concluded that frequency-independent foundation impedances can be adequately used for plant sites having relatively deep and uniform overburdens.     

Seismic soil-structure interaction: Analysis and centrifuge model studies

A method for nonlinear dynamic effective stress analysis applicable to soil-structure interaction problems is introduced. Full interaction including slip between structure and foundation is taken into account and the major factors that must be considered when computing dynamic soil response are included.An experimental investigation using simulated earthquake tests on centrifuged geotechnical models was conducted to obtain prototype response data of foundation soils carrying both surface and embedded structures and to validate the dynamic effective stress analysis. The centrifuge tests were conducted in the Geotechnical Centrifuge at Cambridge University, England. Horizontal and vertical accelerations were measured at various points on structures and in the sand foundation. Seismically induced pore water pressure changes were also measured at various locations in the foundation. Computer plots of the data were obtained while the centrifuge was in flight and representative samples are presented. The results clearly show the pronounced effect of increasing pore water pressures on dynamic response.It is demonstrated that a coherent picture of dynamic response of soil-structure systems is provided by dynamic effective stress nonlinear analysis. On the basis of preliminary results, it appears that the effects of pore water pressure can be predicted.     

Effects of horizontally travelling waves in soil-structure interaction

Phenomena related to horizontally travelling waves are normally not considered in soil-structure interaction. Only vertically incident S- and P-waves are commonly assumed. To determine the influence of this very basic assumption, the responses of a massless basemat, of a massless structure, of a basemat with mass and of a mass-spring system connected to a basemat with mass are parametrically analysed for harmonic and transient excitations for all wave forms (SH-, P-, SV- and Rayleigh waves). Comparisons of the results of the same structures, calculated for the standard vertically incident body waves of the same amplitudes are made. Various possibilities of combining P- and SV-waves to create specified horizontal and vertical free-field motions are examined. By way of illustration, a reactor building and the through-soil coupling of a reactor and a reactor auxiliary building are examined in detail, using the J-145 record of the 1971 San Fernando earthquake as a travelling wave. The effect of a flexible basemat on the structural response is discussed.     

Two-dimensional approximations to the three-dimensional soil-structure interaction problem

The feasibility of representing a three-dimensional soil-structure interaction problem by a plane strain model, and the errors involved in such representation, were studied. By comparing the rocking and translational force-displacement relationships for a rigid circular foundation placed on an elastic half-space and the corresponding relationships for a strip footing placed on an elastic half-plane it was found that it is not possible to obtain a two-dimensional representation that will approximate both the dynamic stiffness and radiation damping over a reasonable range of frequencies. Several two-dimensional models were considered and a measure of the errors involved is presented. In general, the two-dimensional models overestimate the radiation damping associated with the three-dimensional problem. To study the effects that the use of a two-dimensional plane strain model may introduce in the solution of the soil-structure interaction problem for typical nuclear power plants, a comparison was made between the system frequencies and modal dampings obtained for three and two-dimensional models. The corresponding response at the top of the containment shell, top of the internal structure, and base slab for a particular earthquake were also compared. It was found that by properly selecting the two-dimensional model it was possible to obtain close approximations to the system frequencies. However, since the dampings associated with the low frequency modes are overestimated, the earthquake response of the structure, as obtained by the two-dimensional model, is underestimated to a significant degree.     

A mixed implicit/explicit procedure for soil-structure interaction

This paper describes an efficient method for the solution of dynamic soil-structure interaction problems. The method which combines implicit and explicit time integration procedures is ideally suited to problems in which the structure is considered linear and the soil non-linear. The equations relating to the linear structures are integrated using an unconditionally stable implicit scheme while the non-linear soil is treated explicitly. The explicit method is ideally suited to non-linear calculations as there is no need for iterative techniques. The structural equations can also be integrated explicitly, but this generally requires a time step that is much smaller than that for the soil. By using an unconditionally stable implicit algorithm for the structure, the complete analysis can be performed using the time step for the soil. The proposed procedure leads to economical solutions with the soil non-linearities handled accurately and efficiently.     

Simplified soil-structure interaction analysis with strain dependent soil properties

Recent work regarding the response of above-ground soil structures, such as dams, has indicated the need to use strain dependent soil properties. Unlike other building materials soil stiffness and damping properties are highly strain dependent. The application of these concepts to problems in soil-structure interaction has also been suggested. Without commenting on the appropriateness of this extension to soil-structure interaction problems, it is suggested that answers similar to those given by the strain dependent solution of finite element models can be obtained more simply by the use of lumped-parameter impedance functions. To establish this equivalence, it is imperative that all other variables in the problem be made equal for both models; that is, the strain dependency problem must be isolated if the comparison of the two approaches is to be meaningful. The proposed method uses a damping value equal to the average strain dependent soil profile damping. The strain dependent soil profile damping values are obtained by the use of a much simpler model using one-dimensional wave propagation theory. From this same one-dimensional model, the strain dependent soil stiffness corresponding to the average top layer of soil with and without an overburden to approximate the superstructure is used in the equivalent simplified model. Several case comparisons indicate the validity of the proposed method.     

Effect on non-linear soil-structure interaction due to base slab uplift on the seismic response of a high-temperature gas-cooled reactor (HTGR)

In high seismic regions it has often been the practice to use oversized base slabs for the major nuclear power plant structures in order to prevent, or at least minimize, the amount of dynamic base slab uplift which will result from the overturning moments developed during seismic ground motion. Two major reasons have been expressed as to why dynamic base slab uplift should be minimized: (1) As nuclear power plants are normally designed for seismic loadings based upon linear analysis, and since soil-structure interaction becomes nonlinear when only a portion of the base slab is in contact with the soil, linear elastic analysis may be unacceptable if base slab uplift occurs (as the resultant design loads may be incorrect), and (2) substantial uplift could cause excessive toe pressures in the supporting soil and significant impact forces when the slab recontacts the soil.The primary purpose of this paper is to evaluate the importance of the nonlinear soil-structure interaction effects resulting from substantial base slab uplift occurring during a seismic excitation. The structure considered for this investigation consisted of the containment building and prestressed concrete reactor vessel (PCRV) for a typical HTGR plant. A simplified dynamic mathematical model was utilized consisting of a conventional lumped mass structure with soil-structure interaction accounted for by translational and rotational springs whose properties are determined by elastic half space theory. Three different site soil conditions (a rock site, a moderately stiff soil, and a soft soil site) and two levels of horizontal ground motion (0.3 and 0.5 g earthquakes) were considered.Based upon the parametric cases analyzed in this investigation, it may be concluded that linear analysis (which ignores the nonlinear soil-structure interaction effects of base slab uplift) can be used to conservatively estimate the important behavior of the base slab even under conditions of substantial base slab uplift. For all cases investigated here, linear analysis resulted in higher base overturning moments, greater toe pressures, and greater heel uplift distances than nonlinear analyses. It may also be concluded that the nonlinear effect of uplift does not result in any significant lengthening of the fundamental period of the structure. Also, except in the short period region (period less than half of the fundamental period) only negligible differences exist between in-structure response spectra based on linear analysis and those based on nonlinear analysis.Finally, it may be concluded that for sites in which soil-structure interaction is not significant, as for the rock site, the peak structural response (shears and moments) at all locations above the base mat are not significantly influenced by the nonlinear effects of base slab uplift. However, for the two soil sites the peak shears and moments are, in a few instances, significantly different between linear and nonlinear analyses. As a result, linear analysis may be used to determine all structural response for rock sites even when there is substantial base slab uplift. However, for soil sites, nonlinear analyses are necessary if substantial base slab uplift occurs.     

Deflection-based method for seismic response analysis of concrete walls: Benchmarking of CAMUS experiment

A number of shake table tests had been conducted on the scaled down model of a concrete wall as part of CAMUS experiment. The experiments were conducted between 1996 and 1998 in the CEA facilities in Saclay, France. Benchmarking of CAMUS experiments was undertaken as a part of the coordinated research program on ‘Safety Significance of Near-Field Earthquakes’ organised by International Atomic Energy Agency (IAEA). Technique of deflection-based method was adopted for benchmarking exercise. Non-linear static procedure of deflection-based method has two basic steps: pushover analysis, and determination of target displacement or performance point. Pushover analysis is an analytical procedure to assess the capacity to withstand seismic loading effect that a structural system can offer considering the redundancies and inelastic deformation. Outcome of a pushover analysis is the plot of force–displacement (base shear–top/roof displacement) curve of the structure. This is obtained by step-by-step non-linear static analysis of the structure with increasing value of load. The second step is to determine target displacement, which is also known as performance point. The target displacement is the likely maximum displacement of the structure due to a specified seismic input motion. Established procedures, FEMA-273 and ATC-40, are available to determine this maximum deflection. The responses of CAMUS test specimen are determined by deflection-based method and analytically calculated values compare well with the test results.     

The use of boundary elements to represent the far field in soil-structure interaction

To solve soil-structure interaction problems, the modelling is mostly restricted to a two-dimensional representation of the reality. It is only recently that three-dimensional soil-structure interaction problems are attacked. The solution of these problems by using a straight forward finite element representation is very expensive.This paper describes the combination of finite elements and boundary elements for static computations of foundations. The advantages and disadvantages are given. Afterwards, the developments for dynamic analysis using boundary elements are also described.     

Recent tendency of the practice of soil-structure interaction design analysis in Japan and its theoretical background

Many methods of soil-structure interaction analysis for design calculations of nuclear power plants are available. The validity of methods has often been examined by their application to simulation analysis of shaker tests or seismic observations of nuclear power plant buildings, and forced vibration tests of large-scale foundation blocks. In this paper, such simulation analyses performed in Japan are reviewed and discussed for their practical applications.     

A review of soil-structure interaction effects in the seimic analysis of nuclear power plants

A survey of investigations of soil-structure interaction in the seismic analysis of nuclear power plants is presented. After a discussion of various methods that have been applied to calculate interaction effects, results of various investigations are discussed. Differences in system response associated with various analytical models are pointed out. Conclusions and recommendations for additional studies are made.     

用于ICF实验的大型数据库系统的开发

讨论了ICF实验数据采集处理和管理系统中数据库系统的设计，从物理实验的基本需求出发，对数据库系统运行的软硬件环境，数据库系统平台的选择，特殊的录入方法和功能，数据库的结构和应用开发以及当今相关技术状况进行了分析，最后给出了一个实用的集中式实验数据库系统和它在实验中的应用情况。     

Thermal interaction in crusted melt jets with large-scale structures

The objective of the present study is to experimentally observe thermal interaction, which is capable of triggering, due to water entrained, or entrapped within crusted melt jets with ‘large-scale structures’. The present experiment was carried out by dropping molten zinc and molten tin of 100 g. These were sufficient to generate large-scale structures of melt jets. The results showed that the entrapment-type thermal interaction occurs in molten-zinc jets with rare probability, and the entrainment-type thermal interaction occurs in molten tin jets with high probability. The difference in thermal interaction between the molten zinc and molten tin is considered to be mainly due to a difference in kinematic viscosity between them.     

Centrifuge modelling of seismic soil structure interaction effects

Proper understanding of the role of unbounded soil in the evaluation of dynamic soil structure interaction (SSI) problem is very important for structures used in the nuclear industry. In this paper, the results from a series of dynamic centrifuge tests are reported. These tests were performed on different types of soil stratifications supporting a rigid containment structure. Test results indicate that accelerations transmitted to the structure's base are dependent on the stiffness degradation in the supporting soil. Steady build up of excess pore pressure leads to softening of the soil, which decreases the shear modulus and shear strength and subsequently changes the dynamic responses. It is also shown that the presence of the structure reduces the translational component of the input base motion and induces rocking of the structure. The test results are compared with some standard formulae used for evaluating interaction in the various building codes. It was concluded that the dynamic shear modulus values used should be representative of the site conditions and can vary dramatically due to softening. Damping values used are still very uncertain and contain many factors, which cannot be accounted in the experiments. It is emphasized that simplified design processes are important to gain an insight into the behaviour of the physical mechanism but for a complete understanding of the SSI effects sophisticated methods are necessary to account for non-linear behaviour of the soil material.     

Seismic response analysis of soil-structure interactive system using a coupled three-dimensional FE-IE method

This paper proposes a slightly new three-dimensional radial-shaped dynamic infinite elements fully coupled to finite elements for an analysis of soil-structure interaction system in a horizontally layered medium. We then deal with a seismic analysis technique for a three-dimensional soil-structure interactive system, based on the coupled finite-infinite method in frequency domain. The dynamic infinite elements are simulated for the unbounded domain with wave functions propagating multi-generated wave components. The accuracy of the dynamic infinite element and effectiveness of the seismic analysis technique may be demonstrated through a typical compliance analysis of square surface footing, an L-shaped mat concrete footing on layered soil medium and two kinds of practical seismic analysis tests. The practical analyses are (1) a site response analysis of the well-known Hualien site excited by all travelling wave components (primary, shear, Rayleigh waves) and (2) a generation of a floor response spectrum of a nuclear power plant. The obtained dynamic results show good agreement compared with the measured response data and numerical values of other soil-structure interaction analysis package.