Normal Fault Rupture Interaction with Strip Foundations

Observations after earthquakes where surface fault ruptures crossed engineering facilities reveal that some structures survived the rupture almost unscathed. In some cases, the rupture path appears to divert, “avoiding” the structure. Such observations point to an interaction between the propagating rupture, the soil, and the foundation. This paper (i) develops a two-step nonlinear finite-element methodology to study rupture propagation and its interaction with strip foundations; (ii) provides validation through successful Class “A” predictions of centrifuge model tests; and (iii) conducts a parameter study on the interaction of strip foundations with normal fault ruptures. It is shown that a heavily loaded foundation can substantially divert the rupture path, which may avoid outcropping underneath the foundation. The latter undergoes rigid body rotation, often detaching from the soil. Its distress arises mainly from the ensuing loss of support that takes place either at the edges or around its center. The average pressure q on the foundation largely dictates the width of such unsupported spans. Increasing q decreases the unsupported width, reducing foundation distress. The role of q is dual: (1) it compresses the soil, “flattening” fault-induced surface “anomalies”; and (2) it changes the stress field underneath the foundation, facilitating rupture diversion. However, even if the rupture is diverted, the foundation may undergo significant stressing, depending on its position relative to the fault outcrop.     

Dynamic Response of Rigid Foundations of Arbitrary Shape Using Half-Space Green’s Function

This paper deals with the dynamic steady-state force-displacement relationships (impedance) for rigid foundations of arbitrary shape resting on a semi-infinite medium consisting of homogeneous, isotropic, linear elastic materials using the boundary element method (BEM). An elaborate numerical technique is used to calculate Green’s function, yielding a highly accurate numeric approximation in an explicit form. By using a BEM formulation for triangular elements (linear and infinite shape function) compliance of rigid massless surface foundations was obtained. The use of triangular elements causes stress continuity between elements to be satisfied. Meanwhile, the tendency for foundation edge stresses toward infinity can be modeled by using these triangular infinite stress elements. As a result of this, computations are more accurate but less time-consuming. This procedure is used to evaluate the vertical rocking compliance functions for rigid rectangular, circular, and square foundations with internal holes. Finally, comparisons are made between the results obtained from the proposed approach and those from other methods.     

Stochastic Finite-Element Analysis of Seismic Soil–Structure Interaction

A procedure is presented for the probabilistic analysis of the seismic soil-structure interaction problem. The procedure accounts for uncertainty in both the free-field input motion as well as in local site conditions, and structural parameters. Uncertain parameters are modeled using a probabilistic framework as stochastic processes. The site amplification effects are accounted for via a randomized relationship between the soil shear modulus and damping on the one hand, and the shear strain of the subgrade on the other hand, as well as by modeling the shear modulus at low strain level as randomly fluctuating with depth. The various random processes are represented by their respective Karhunen-Loève expansions, and the solution processes, consisting of the accelerations and generalized forces in the structure, are represented by their coordinates with respect to the polynomial chaos basis. These coordinates are then evaluated by a combination of weighted residuals and stratified sampling schemes. The expansion can be used to carry out very efficiently, extensive Monte Carlo simulations. The procedure is applied to the seismic analysis of a nuclear reactor facility.     

Numerical Modeling of Seismic Response of Rigid Foundation on Soft Soil

A numerical model was developed to simulate the response of two instrumented, centrifuge model tests on soft clay and to investigate the factors that affect the seismic ground response. The centrifuge tests simulated the behavior of a rectangular building on 30?m uniform and layered soft soils. Each test model was subjected to several earthquakelike shaking events at a centrifugal acceleration level of 80g. The applied loading involved scaled versions of an artificial western Canada earthquake and the Port Island ground motion recorded during the 1995 Kobe Earthquake. The centrifuge model was simulated with the three-dimensional finite-difference-based fast Lagrangian analysis of continua program. The results predicted with the use of nonlinear elastic–plastic model for the soil are shown to be in good agreement with measured acceleration, soil response, and structural behavior. The validated model was used to study the effect of soil layering, depth, soil–structure interaction, and embedment effects on foundation motion.     

Effect of Near-Fault Vertical Ground Motions on Seismic Response of Highway Overcrossings

Results of comprehensive nonlinear response history analyses on a range of configurations representing typical highway overcrossings subjected to combined effects of vertical and horizontal components of near-fault ground motions are reported. Current seismic design guidelines in California neglect the vertical components of ground motions for peak ground accelerations less than 0.6?g and provide rather simplistic measures to account for vertical effects when they need to be incorporated in the design. Results from the numerical simulations show that the vertical components of ground motions cause significant amplification in the axial force demand in the columns and moment demands in the girder at both the midspan and at the face of the bent cap. Axial capacity of the columns and moment capacity of the girder at the face of the bent cap were generally found to be sufficient to resist the amplification in the respective demands due to vertical effects. However, midspan moments in negative bending due to vertical motions are found to exceed the capacity of the girder. The amplified midspan moments lead to yielding of the top reinforcement resulting in average peak strains on the order of 1%. It is concluded that seismic demand analysis of ordinary highway bridges in general and overcrossings in particular should incorporate provisions for considering the adverse vertical effects of near-fault ground motions.     

Nonlinear Response of Deep Immersed Tunnel to Strong Seismic Shaking

Critical for the seismic safety of immersed tunnels is the magnitude of deformations developing in the segment joints, as a result of the combined longitudinal and lateral vibrations. Analysis and design against such vibrations is the main focus of this paper, with reference to a proposed 70?m-deep immersed tunnel in a highly seismic region, in Greece. The multisegment tunnel is modeled as a beam connected to the ground through properly calibrated interaction springs, dashpots, and sliders. Actual records of significant directivity-affected ground motions, downscaled to 0.24 g peak acceleration, form the basis of the basement excitation. Free-field acceleration time histories are computed from these records through one-dimensional wave propagation equivalent-linear and nonlinear analyses of parametrically different soil profiles along the tunnel; they are then applied as excitation at the support of the springs, with a suitable time lag to conservatively approximate wave passage effects. The joints between the tunnel segments are modeled realistically with special nonlinear hyperelastic elements, while their longitudinal prestressing due to the great (7?bar) water pressure is also considered. Nonlinear dynamic transient analysis of the tunnel is performed without ignoring the inertia of the thick-walled tunnel, and the influence of segment length and joint properties is investigated parametrically. It is shown that despite ground excitation with acceleration levels exceeding 0.50 g and velocity of about 80?cm/s at the base of the tunnel, net tension and excessive compression between the segments can be avoided with a suitable design of joint gaskets and a selection of relatively small segment lengths. Although this research was prompted by the needs of a specific project, the dynamic analysis methods, the proposed design concepts, and many of the conclusions of the study are sufficiently general and may apply in other immersed tunneling projects.     

Effects of Space Distribution of Excitation on Seismic Response of Arch Dams

The effects of the ground motion spatial variation and of the canyon geometry on the dynamic response of arch dams during the event of an earthquake is studied in this paper. The seismic response of a dam subject to time harmonic longitudinal, shear, and Rayleigh waves impinging the dam site from different directions is analyzed. Several canyon and reservoir geometries are considered. A three-dimensional boundary element model which allows for the rigorous representation of the dynamic interaction between the dam, the foundation rock, and the water is used. The foundation rock is modeled as a uniform viscoelastic boundless domain where the incident traveling wave field is defined by its analytical expression, which may include any spatial variation. The obtained results show the importance of three-dimensional effects which are many times neglected.     

Effect of Nonlinear Soil Behavior on Inelastic Seismic Response of a Structure

The characteristics of the earthquake motions at the base of a structure are affected by the properties of the underlying soil through the soil amplification and soil–structure interaction phenomena. In this paper the effect of nonlinear soil behavior on the elastic and inelastic response spectra of the motions that would be recorded at the free surface of a soft soil deposit or at the base of each structure is investigated. The analyses are conducted for a soil layer by itself and for a complete soil structure system using a finite element discretization of the soil in cylindrical coordinates and an approximate linear iterative procedure to simulate nonlinear behavior. Studies are conducted for structures, with a constant base and variable height modeled as equivalent linear or nonlinear single degree of freedom systems and an input motion at the base of the soil deposit representative of rock outcrop motions. Both mat and pile foundations are considered. The results illustrate clearly the importance of the nonlinear soil behavior.     

Combined Finite- and Boundary-Element Analysis of the Effects of Tunneling on Single Piles

An efficient and practical method of analysis to predict the effects of tunneling on existing single pile foundations is described. The method involves a combination of the finite- and boundary-element (FAB) methods, with free-field ground movements predicted by the finite-element method and the response of an embedded pile to these ground movements predicted by the boundary-element method. The method allows prediction of the full three-dimensional (3D) response of the pile as tunnel excavation proceeds towards the pile and away from it. Very good agreement is obtained between predictions of the pile response obtained by the FAB method and a 3D finite-element analysis which specifically includes the pile in the finite-element mesh. The vastly superior computational efficiency of the FAB method over the full 3D finite element approach is also illustrated.     

Response Spectrum Analysis of Suspension Bridges for Random Ground Motion

The response spectrum method of analysis for suspension bridges subjected to multicomponent, partially correlated stationary ground motion is presented. The analysis is based on the relationship between the power spectral density function and the response spectrum of the input ground motion and fundamentals of the frequency domain spectral analysis. The analysis duly takes into account the spatial correlation of ground motions between the supports, the quasi-static component of the response, and the modal correlation between different modes of vibration. A suspension bridge is analyzed under a set of important parametric variations in order to (1) compare between the responses obtained by the response spectrum method of analysis and the frequency domain spectral analysis; and (2) investigate the behavior of suspension bridges under seismic excitation. The parameters include the spatial correlation of ground motion, the angle of incidence of the earthquake, the ratio between the three components of ground motion, the number and nature of modes considered in the analysis, and the nature of the power spectral density function of ground motion. It is shown that the response spectrum method of analysis provides a fair estimate of responses under parametric variations considered in the study.     

Use of Exact Solutions of Wave Propagation Problems to Guide Implementation of Nonlinear Seismic Ground Response Analysis Procedures

One-dimensional nonlinear ground response analyses provide a more accurate characterization of the true nonlinear soil behavior than equivalent-linear procedures, but the application of nonlinear codes in practice has been limited, which results in part from poorly documented and unclear parameter selection and code usage protocols. In this article, exact (linear frequency-domain) solutions for body wave propagation through an elastic medium are used to establish guidelines for two issues that have long been a source of confusion for users of nonlinear codes. The first issue concerns the specification of input motion as “outcropping” (i.e., equivalent free-surface motions) versus “within” (i.e., motions occurring at depth within a site profile). When the input motion is recorded at the ground surface (e.g., at a rock site), the full outcropping (rock) motion should be used along with an elastic base having a stiffness appropriate for the underlying rock. The second issue concerns the specification of viscous damping (used in most nonlinear codes) or small-strain hysteretic damping (used by one code considered herein), either of which is needed for a stable solution at small strains. For a viscous damping formulation, critical issues include the target value of the viscous damping ratio and the frequencies for which the viscous damping produced by the model matches the target. For codes that allow the use of “full” Rayleigh damping (which has two target frequencies), the target damping ratio should be the small-strain material damping, and the target frequencies should be established through a process by which linear time domain and frequency domain solutions are matched. As a first approximation, the first-mode site frequency and five times that frequency can be used. For codes with different damping models, alternative recommendations are developed.     

Time-Harmonic Analysis of Wave Propagation in Unbounded Layered Strata with Zigzag Boundaries

A frequency-domain consistent absorbing boundary for horizontally layered strata is derived for the cases of antiplane shear and plane strain. The boundary can be composed of nonvertical as well as vertical segments, thus enabling efficient modeling of unbounded media. While the nonvertical boundary, as long as not horizontal, can be inclined at an arbitrary angle, numerical instability is encountered as the boundary becomes nearly horizontal, leading to erroneous results. A modification of the formulation based on selective reduced integration is proposed to make the new boundary condition more robust. Application problems in foundation dynamics and dam–foundation–reservoir interaction are considered to demonstrate the computational efficiency provided by the new boundary.     

Analysis of Dynamic Response of Architectural Glazing Subject to Blast Loading

The effect of blast loading on civilian structures has received much attention over the past several years. The behavior of architectural glazing is of particular interest owing to the disproportionate amount of damage often associated with the failure of this component in a blast situation. This paper presents the development of a simple yet accurate finite element-based tool for the analysis of architectural glazing subjected to blast loading. This has been achieved through the creation of a user-friendly computer program employing the explicit finite-element method to solve for the displacements and stresses in a pane of glass. Both monolithic and laminated panes have been considered, in single and insulated unit configurations, and employing several types of glass. In all cases, the pane of glass has been modeled as a plate supported by an array of boundary conditions that include spring supports, and two failure criteria are employed. Furthermore, the program is designed to predict the hazard level, given a particular glazing configuration and blast load.     

Three-Dimensional Analysis of Lateral Pile Response using Two-Dimensional Explicit Numerical Scheme

A procedure for exploiting a two-dimensional (2D) explicit, numerical computer code for the 3D formulation of dynamic lateral soil-pile interactions is considered. The procedure is applied to two models using simultaneous computation of a series of plane strain boundary value problems, each of which represents a horizontal layer of soil. The first model disregards the shear forces developed between the horizontal layers, and may be considered as a generalized Winkler model. The second model takes account of these forces by coupling the behavior of the horizontal layers. Several verification problems for a single pile and pile groups in a homogeneous soil layer modeled as a viscoelastic material were solved and compared to known solutions in order to assess the reliability of the models. Excellent agreement was observed between results of the present analyses and existing solutions.     

Handling of Constraints in Finite-Element Response Sensitivity Analysis

In this paper, the direct differentiation method (DDM) for finite-element (FE) response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints (MPCs). The analytical developments are provided for three different constraint handling methods, namely: (1) the transformation equation method; (2) the Lagrange multiplier method; and (3) the penalty function method. Two nonlinear benchmark applications are presented: (1) a two-dimensional soil-foundation-structure interaction system and (2) a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDM-based response sensitivity results are compared with corresponding forward finite difference analysis results, thus validating the formulation presented and its computer implementation. The developments presented in this paper close an important gap between FE response-only analysis and FE response sensitivity analysis through the DDM, extending the latter to applications requiring response sensitivities of FE models with MPCs. These applications include structural optimization, structural reliability analysis, and finite-element model updating.     

Hilbert-Huang Transform Analysis of Dynamic and Earthquake Motion Recordings

This study examines the rationale of Hilbert-Huang transform (HHT) for analyzing dynamic and earthquake motion recordings in studies of seismology and engineering. In particular, this paper first provides the fundamentals of the HHT method, which consist of the empirical mode decomposition (EMD) and the Hilbert spectral analysis. It then uses the HHT to analyze recordings of hypothetical and real wave motion, the results of which are compared with the results obtained by the Fourier data processing technique. The analysis of the two recordings indicates that the HHT method is able to extract some motion characteristics useful in studies of seismology and engineering, which might not be exposed effectively and efficiently by Fourier data processing technique. Specifically, the study indicates that the decomposed components in EMD of HHT, namely, the intrinsic mode function (IMF) components, contain observable, physical information inherent to the original data. It also shows that the grouped IMF components, namely, the EMD-based low- and high-frequency components, can faithfully capture low-frequency pulse-like as well as high-frequency wave signals. Finally, the study illustrates that the HHT-based Hilbert spectra are able to reveal the temporal-frequency energy distribution for motion recordings precisely and clearly.     

Ground Response in Lotung: Total Stress Analyses and Parametric Studies

Previous papers have reported on the performance of a recently developed nonlinear ground response analysis code, SPECTRA, with reference to the prediction of the free-field response at a Large-Scale Seismic Test site in Lotung, Taiwan during the M6.5 earthquake of May 20, 1986. Two more major earthquakes of different characteristics shook this test site later that same year, a M6.2 earthquake that occurred on July 30 and a M7.0 earthquake that occurred on November 15. The present article analyzes the free-field responses recorded by a downhole array from these latter two events using the code SPECTRA and a widely used equivalent linear analysis code SHAKE. The studies focus on the relative accuracy and sensitivity of the two codes with respect to the variations of the input material parameters, using time histories, acceleration response spectra, Fourier acceleration amplitude spectra, and Arias intensities as criteria for the comparison. The two codes captured the general wave form of the acceleration histories well, but there was a general tendency for both codes (particularly SHAKE) to underpredict the Arias intensities of the earthquakes.     

Behavior of Rigid Footings on Gravel under Axial Load and Moment

A laboratory testing program was conducted to study the settlement and rotation response of rigid square footings under combined axial load and moment. A total of 17 tests were performed in which the size of the footing, footing embedment, axial load, and load eccentricity were changed. The test soil consisted of a fine and well-graded gravel contained in a box with dimensions: 1.52×1.52?m (5×5?ft) cross section and 0.91?m (3?ft) deep. The soil was compacted in layers 150?mm (6?in.) thick to an approximate relative density of 84%. In each test, the axial load, moment, settlement at the center of the footing, and footing rotation were measured. Concentrically loaded footings with different sizes exhibited a similar behavior in terms of the applied stress-normalized settlement (settlement divided by size of footing) response. The analytical model proposed was based on such normalized response as an input, and it was calibrated to account for the change in soil stiffness with confinement. The formulation captures the inherent nonlinear deformations of the soil with load and the coupled nature of settlements and rotations of footings under axial load and moment. The model was tested by comparing calculated values with laboratory measurements from tests not included in its calibration. The comparisons showed a satisfactory agreement between calculations and measurements, bringing confidence in the analytical formulation proposed and the methodology used.     

Development of Finite-Element Modeling Approach for Lateral Load Analysis of Dry-Glazed Curtain Walls

This paper presents a finite-element modeling option to provide an analytical approach for a seismic analysis of dry-glazed curtain-wall systems. In this modeling approach, Ansys finite-element software was used to model the glass panel, aluminum glazing frame, perimeter rubber gaskets, rubber setting and side blocks, glass-to-frame clearances, and glass-to-frame contact once the clearance was overcome by in-plane drift. The results of the finite-element modeling of the curtain-wall system were compared with full-scale laboratory test results. The effect of some of the parameters such as gasket friction and aspect ratio were evaluated. The study showed that finite-element modeling is a viable approach for analytical evaluation of curtain walls. The modeling can function to predict the drift associated with glass-panel cracking. Further refinement of the modeling approach developed can increase the accuracy of the prediction.     

Effect of Asynchronous Earthquake Motion on Complex Bridges. II: Results and Implications on Assessment

Nonuniform seismic excitation has been shown through previous analytical studies to adversely affect the response of long-span bridge structures. To further understand this phenomenon, this study investigates the response of complex straight and curved long-span bridges under the effect of parametrically varying asynchronous motion. The generation process and modeling procedures are presented in a companion paper. A wide-ranging parametric study is performed aimed at isolating the effect of both bridge curvature and the two main sources of asynchronous strong motion: geometric incoherence and the wave-passage effect. Results from this study indicate that response for the 344?m study structure is amplified significantly by nonsynchronous excitation, with displacement amplification factors between 1.6 and 3.4 for all levels of incoherence. This amplification was not constant or easily predicable, demonstrating the importance of inelastic dynamic analysis using asynchronous motion for assessment and design of this class of structure. Additionally, deck stiffness is shown to significantly affect response amplification, through response comparison between the curved and an equivalent straight bridge. Study results are used to suggest an appropriate domain for consideration of asynchronous excitation, as well as an efficient methodology for analysis.