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.     

Seismic Simulation of Inelastic Soils via Frequency-Dependent Moduli and Damping

Although soils are known to exhibit nonlinear behavior even at small strains, evaluations of the response of sedimentary basins to strong seismic motions are almost always based on linear, elastic solutions incorporating frequency-independent damping. The principal reasons for this relate to the robustness of the linear algorithm and the ease with which the required parameters can be determined experimentally in engineering practice. Most often, but not always, attempts are made in these analyses to compensate for the inelastic behavior by adjusting the material parameters for the representative levels of strain by means of an iterative method. However, both the standard iterative method and the direct linear solution without iterations suffer from two important shortcomings. First, they do not account for the effect of high confining pressures on inelastic behavior. However, it is known from experiments with sands subjected to cyclic shearing strains under confining pressures of up to 5 Mpa, that in highly confined samples, the material remains nearly elastic for a larger range of strains than do those samples subjected to a lesser pressure. Second, the amplification analyses disregard the fact that small-amplitude, high-frequency components of deformation involve hysteresis loops with little modulus degradation or damping (i.e., nearly elastic secondary loops). Thus, motions computed at the surface of the basin with the standard method usually exhibit unrealistically low amplitudes at high frequencies. This article presents the results obtained with a series of “true” nonlinear numerical analyses with inelastic (Masing-type) soils and layered profiles subjected to broadband earthquake motions, taking into account the effect of the confining pressure. These show that it is possible to simulate closely the actual inelastic behavior of rate-independent soils by means of linear analyses in which the soil moduli and damping change with frequency. It is emphasized that the variation in the linear model of the material parameters with frequency arises solely because the strains have broad frequency content, and not because the materials exhibit any rate dependence when tested cyclically. The proposed new model is successfully applied to a 1-km-deep model for the Mississippi embayment near Memphis, Tenn. The seismograms computed at the surface not only satisfy causality (which cannot be taken for granted when using frequency-dependent parameters), but their spectra contain the full band of frequencies expected.     

1D Time-Domain Solution for Seismic Ground Motion Prediction

A full time-domain solution for predicting earthquake ground motion based on the 1D viscoelastic shear-wave equation is presented. The derivation results in a time-domain equation in the form of an infinite impulse response filter. A solution in the time domain has several advantages including causality, direct modeling of impulsive and transient processes, and ease of inclusion of nonlinear soil behavior. The method is applicable to any arbitrarily layered silhouette presented as SH-wave velocity, damping coefficient, and mass density profiles for designated soil intervals. For nonlinear evaluations, an equivalent-linear formulation is incorporated and the standard modulus and damping degradation curves become part of the input set. Input motion can be either rock-outcrop or body-wave motions measured or estimated at the bottom of the geologic profile, and the output is the estimated ground motion time history. Application of the method to vertical array strong motion records from Garner Valley, and Wildlife Site, Calif., shows that predicted surface (and interval) ground motion is virtually identical to that measured. The differences between the results of linear and nonlinear analyses are negligible for most cases. A comparison of the time-domain model with SHAKE shows that SHAKE fails to accurately predict time histories in some situations, whereas the time-domain solution always yields satisfactory predicted surface ground motions.     

Small-Strain Behavior of Granular Soils. II: Seismic Response Analyses and Model Evaluation

Using the recorded response at two vertical array sites, the SimSoil model presented in the companion paper is evaluated. The SimSoil model, which describes the small strain nonlinear behavior of granular materials, is implemented as a material model in AMPLE2000, a nonlinear, one-dimensional site response analysis code. Shear wave velocity profiles and laboratory test data available for both the La Cienega site, which was instrumented over 250?m, and the Lotung site, which was instrumented over 47?m, were used to determine SimSoil model parameters. Predictions from AMPLE2000 are compared with the measured response at several elevations for earthquakes that resulted in both nonlinear and nearly linear soil behavior. Using the available laboratory data and known input motions, the predictions of the response at these sites matched the recorded response well for varied magnitudes of shaking with a single set of parameters for each site.     

Soil Isolation for Seismic Protection Using a Smooth Synthetic Liner

A synthetic liner consisting of a nonwoven geotextile over an ultrahigh molecular weight polyethylene, geotextile/UHMWPE, placed within a soil profile can dissipate seismic energy transmitted to the overlying soil layer and structure. This concept of soil isolation can be an effective and inexpensive way of reducing seismic ground motions through slip displacements. Shaking table tests on soil layers isolated using cylindrical and tub-shaped liners were conducted using harmonic and earthquake base excitations. The results show that an isolation liner can significantly reduce the accelerations at the surface of the isolated soil mass. Accompanying such a reduction in accelerations are slip displacements that manifest around the perimeter of the isolated soil. Because of the curved nature of the liner, permanent slips are minimized by the restoring effect of the gravitational forces of the isolated soil mass. Analytical results under field scale conditions indicate that a soil isolation liner can dramatically reduce the peak and spectral accelerations of a vertically propagating shear wave. Such a reduction can provide seismic protection to a structure founded on soil-isolated ground.     

Optimal Control of Earthquake Response Using Semiactive Isolation

The responses of two, low-rise, 2-degree-of-freedom base isolated structures with different isolation periods to a set of near-field earthquake ground motions are investigated under passive linear and nonlinear viscous damping, two pseudoskyhook semiactive control methods, and optimal semiactive control. The structures are isolated with a low damping elastic isolation system in parallel with a controllable damper. The optimal semiactive control strategy minimizes an integral norm of superstructure absolute accelerations subject to the constraint that the nonlinear equations of motion are satisfied and is determined through a numerical solution to the Euler–Lagrange equations. The optimal closed-loop performance is evaluated for a controllable damper and is compared to passive viscous damping and causal pseudoskyhook control rules. Results obtained from eight different earthquake records illustrate the type of ground motions and structures for which semiactive damping is most promising.     

Parametric Studies on the Behavior of Reinforced Soil Retaining Walls under Earthquake Loading

The finite element procedures are extremely useful in gaining insights into the behavior of reinforced soil retaining walls. In this study, a validated finite element procedure was used for conducting a series of parametric studies on the behavior of reinforced soil walls under construction and subject to earthquake loading. The procedure utilized a nonlinear numerical algorithms that incorporated a generalized plasticity soil model and a bounding surface geosynthetic model. The reinforcement layouts, soil properties under monotonic and cyclic loadings, block interaction properties, and earthquake motions were among major variables of investigation. The performance of the wall was presented for the facing deformation and crest surface settlement, lateral earth pressure, tensile force in the reinforcement layers, and acceleration amplification. The effects of soil properties, earthquake motions, and reinforcement layouts are issues of major design concern under earthquake loading. The deformation, reinforcement force, and earth pressure increased drastically under earthquake loading compared to end of construction.     

Influence of Input Motion and Site Property Variabilities on Seismic Site Response Analysis

Seismic site response analysis evaluates the influence of local soil conditions on earthquake ground shaking. There are multiple sources of potential uncertainty in this analysis; the most significant pertaining to the specification of the input motions and to the characterization of the soil properties. The influence of the selection of input ground motions on equivalent-linear site response analysis is evaluated through analyses performed with multiple suites of input motions selected to fit the same target acceleration response spectrum. The results indicate that a stable median surface response spectrum (i.e., within ±20% of any other suite) can be obtained with as few as five motions, if the motions fit the input target spectrum well. The stability of the median is improved to ±5 to 10% when 10 or 20 input motions are used. If the standard deviation of the surface response spectra is required, at least 10 motions (and preferably 20) are required to adequately model the standard deviation. The influence of soil characterization uncertainty is assessed through Monte Carlo simulations, where variations in the shear-wave velocity profile and nonlinear soil properties are considered. Modeling shear-wave velocity variability generally reduces the predicted median surface motions and amplification factors, most significantly at periods less than the site period. Modeling the variability in nonlinear properties has a similar, although slightly smaller, effect. Finally, including the variability in soil properties significantly increases the standard deviation of the amplification factors but has a lesser effect on the standard deviation of the surface motions.     

Three-Dimensional Linear and Simplified Nonlinear Soil Response Methods Based on an Input Wave Field

We propose three-dimensional linear and simplified nonlinear soil response methods based on an input seismic wave field. An input wave field is employed to treat seismic surface waves excited by a deep structure in a shallow soil model. First, the linear method is applied to a hard- and a soft-soil site located in Mexico City, and soil responses excited by S-, surface-, and whole-wave fields reproduce the input waves fields well. Then, the linear method is applied to estimate soil responses for three large earthquakes at two soft-soil sites located in the reclaimed zone of Tokyo Bay, and again it works well. Finally, we attempt to perform nonlinear and liquefaction soil response analyses in the reclaimed zone, on the basis of an input wave field modified according to varied soil properties. The nonlinear method seems to provide reasonable nonlinear and liquefaction soil responses.     

Nonlinear Coupled Seismic Sliding Analysis of Earth Structures

Earthquake-induced sliding displacements of earth structures are generally evaluated using simplified sliding block analyses that do not accurately model the seismic response of the sliding mass nor the seismic forces along the slide plane. The decoupled approximation introduced to capture each of these effects separately is generally believed to be conservative. However, recent studies using linear viscoelastic sliding mass models have revealed instances where the decoupled approximation is unconservative. In this paper, a coupled analytical model that captures simultaneously the fully nonlinear response of the sliding mass (necessary for intense motions) and the nonlinear stick-slip sliding response along the slide plane is presented. The proposed sliding model is validated against shaking table experiments of deformable soil columns sliding down an inclined plane. The effect of sliding on the response of earth structures is evaluated, and comparisons are made between sliding displacements calculated using coupled and decoupled analytical procedures with linear and nonlinear material properties. Nonlinearity resulting from stick-slip episodes is often the dominant source of nonlinearity in this problem. The decoupled approximation was unconservative primarily for intense ground motions for systems with low values of ky, larger values of ky∕kmax, and high period ratios (Ts∕Tm). Results indicate that a decoupled analysis is adequate for earth structures that are not expected to experience intense, near-fault motions. However, for projects undergoing intense, near-fault ground motions, a fully nonlinear, coupled stick-slip analysis is recommended.     

Centrifugal Modeling of Seismic Behavior of Large-Diameter Pipe in Liquefiable Soil

This study focused on the behavior of a large-diameter burial pipe with special reference to its stability against flotation subject to soil liquefaction. Centrifugal modeling technique was used where the results are presented for a total of eight shaking table tests conducted on the burial pipe in a laminar box under 30g gravitational field. The ground was prepared with Nevada sand at a relative density of 38% and shaken with a sinusoidal wave at an amplitude of 0.5g. The use of a viscous fluid in a saturated soil deposit satisfied the time scaling relationships of both dynamic and dissipation phenomena. The centrifugal modeling technique simulated flotation of pipeline as the soil liquefied. A technique that used gravels and geosynthetic material was used to mitigate flotation. The response of the soil deposit, in terms of acceleration and excess pore pressure, was investigated. The uplifting of the pipe, earth pressure response and ground surface deformation were also presented. Based on the test results, a design procedure was proposed for the burial pipe in resisting flotation due to soil liquefaction. The deadweight and stiffness of the gravel unit, which was confined by geosynthetic, were important items in design.     

Site Response at Treasure and Yerba Buena Islands, California

A variety of methods are utilized to reinvestigate the physical relationship between the seismic response of Treasure Island (TI) and Yerba Buena Island (YBI) in California. These islands are a soil (TI) and rock (YBI) site pair separated by 2 km. The site pair has been used previously by researchers to identify soil response to earthquake shaking. Linear regime ground motions (MW4.0–MW4.6 and PGA: 0.014–0.017 g) recorded in the TI vertical array indicate a coherent wavefield in the sediments and an incoherence between the rock and sediments. Our analyses show that the greatest change in the wavefield occurred between the rock and soil layers, corresponding to a significant impedance contrast. The waveforms change very little as they propagate through the sediments, indicating that the site response is a cumulative effect of the entire soil structure and not a result of wave propagation within individual soil layers. In order to highlight the complexity of the site response, correlation analysis was used to demonstrate that the rock and soil ground motions were not highly coherent between the two sites. YBI was, therefore, shown to be an inappropriate reference site for TI. One-dimensional (1D) vertical wave propagation and inverse techniques were used to differentiate between 1D site response and more complex site behavior. Both 1D methods (vertical wave propagation and inverse transfer functions) proved incapable of capturing the site response at TI beyond the initial four seconds of motion. Finite difference waveform modeling, based on a two-dimensional velocity structure of the northern San Francisco Bay was needed to explain the linear site response at TI as horizontally propagating surface waves trapped in the bay sediments. A simplified velocity structure for the San Francisco Bay including a single 100 m basin layer (constant shear-wave velocity of 400 m/s) over a 1.5 km/s layer of Franciscan bedrock was able to trap energy in the basin and produce surface waveform ringing similar to that observed in the TI data. Due to surface waves propagating in the San Francisco Bay sediments, any 1D model will not fully characterize site response at TI. All 1D models will fail to produce the late arriving energy observed in the ground motions.     

Micromechanics-Based Predictions on the Overall Stress-Strain Relations of Cement-Matrix Composites

A micromechanics-based model is proposed to determine the nonlinear stress-strain relations of cement-matrix composites at different concentrations of inclusions (aggregates). We first conducted some experiments to uncover the stress-strain behavior of the cement paste with a water-to-cement ratio of 0.45, and those of the mortar with the same cement paste but at three different volume concentrations of aggregates. The behavior of the cement paste is then simulated by Burgers’ rheological model. In the development of the composite model, we extend the linear elastic response to the nonlinear one through the replacement of elastic moduli by the corresponding secant moduli. The nonlinear stress-strain curves of the cement-matrix composite are then determined from those of the cement paste and inclusions. It is shown that the predicted stress-strain curves of the mortar are in close agreement with the experimental curves up to an aggregate volume fraction of 49% or 60?wt?%.     

Inelastic Analysis of Pile–Soil Interaction

In this paper, inelastic pile–soil interaction is analyzed by using a hybrid type of numerical method. Piles are modeled as linear finite elements and the soil half-space is modeled using boundary elements. Inelastic modeling of the soil media is introduced by a rational approximation to a continuum with nonlinear interface springs along the piles. For this purpose, a modified ?zdemir’s nonlinear model is implemented and systems of equations are coupled for piles and pile groups at interacting nodes. To verify the proposed algorithm, three experimental results from previously conducted tests on piles under static axial and lateral loads are compared with those obtained from the present analysis.     

Dynamic Soil Stiffnesses at Side of Embedded Structures with Rectangular Base

Soil behavior at the side of an embedded structure with rectangular base area is formulated. The soil medium is idealized as a stack of horizontal sheets interconnected by distributed vertical springs. Each sheet is made of a previously proposed column-spring system. The computed results indicate that, at frequencies higher than the fundamental natural frequency of the soil medium, the vertical springs can be eliminated and each sheet can be treated as an independent sheet in the plane strain condition. This approximation and Galerkin’s method for weighted residuals lead to very simple expressions for the soil stiffnesses per depth at the side of a structure with rectangular cross section. The formulations developed are computationally very convenient and confirmed to produce results close to those computed by a far more rigorous method. The dynamic soil stiffnesses at the side of a structure are computed for various cases. The dynamic response analyses of partially embedded structures are presented to demonstrate the application of the approach and formulations developed.     

Fully Nonhydrostatic Modeling of Surface Waves

A fully nonhydrostatic model is tested by simulating a range of surface-wave motions, including linear dispersive waves, nonlinear Stokes waves, wave propagation over bottom topographies, and wave–current interaction. The model uses an efficient implicit method to solve the unsteady, three-dimensional, Navier-Stokes equations and the fully nonlinear free-surface boundary conditions. A new top-layer pressure treatment is incorporated to fully include the nonhydrostatic pressure effect. The model results are verified against either analytical solutions or experimental data. It is found that the model using a small number of vertical layers is capable of accurately simulating both the free-surface elevation and vertical flow structure. By further examining the model’s performance of resolving wave dispersion and nonlinearity, the model’s efficiency and accuracy are demonstrated.     

Nonlinear Soil–Abutment–Bridge Structure Interaction for Seismic Performance-Based Design

Current seismic design of bridges is based on a displacement performance philosophy using nonlinear static pushover analysis. This type of bridge design necessitates that the geotechnical engineer predict the resistance of the abutment backfill soils, which is inherently nonlinear with respect to the displacement between soil backfill and the bridge structure. This paper employs limit-equilibrium methods using mobilized logarithmic-spiral failure surfaces coupled with a modified hyperbolic soil stress–strain behavior (LSH model) to estimate abutment nonlinear force-displacement capacity as a function of wall displacement and soil backfill properties. The calculated force-displacement capacity is validated against the results from eight field experiments conducted on various typical structure backfills. Using LSH and experimental data, a simple hyperbolic force-displacement (HFD) equation is developed that can provide the same results using only the backfill soil stiffness and ultimate soil capacity. HFD is compatible with current CALTRANS practice in regard to the seismic design of bridge abutments. The LSH and HFD models are powerful and effective tools for practicing engineers to produce realistic bridge response for performance-based bridge design.     

Nonlinear Aeroelastic Simulation of a Full-Span Aircraft with Oscillating Control Surfaces

In this paper, the transonic and low-supersonic aeroelastic behavior of the generic fighter model was investigated in the time domain. The simulation of flutter flight test using forced harmonic motion of control surfaces including inertial coupling effects was conducted at the various conditions. The detailed dynamic aeroelastic responses are computed using a coupled time-marching method based on the effective computational structural dynamic and computational fluid dynamics techniques. The nonlinear aerodynamic effects due to an existing shock wave on the lifting surfaces were considered using a transonic small disturbance equation. A modal model obtained by a free vibration analysis was used for the structural model. The relations between the computed flutter boundary and the simulation results of the responses using the harmonic motions of control surfaces at various conditions were investigated.     

Learning of Dynamic Soil Behavior from Downhole Arrays

An increasing number of downhole arrays are deployed to measure motions at the ground surface and within the soil profile. Measurements from these arrays provide an opportunity to improve site response models and to better understand underlying dynamic soil behavior. Parametric inverse analysis approaches have been used to identify constitutive model parameters to achieve a better match with field observations. However, they are limited by the selected material model. Nonparametric inverse analysis approaches identify averaged soil behavior between measurement locations. A novel inverse analysis framework, self-learning simulations (SelfSim), is employed to reproduce the measured downhole array response while extracting the underlying soil behavior of individual soil layers unconstrained by prior assumptions of soil behavior. SelfSim is successfully applied to recordings from Lotung and La Cienega. The extracted soil behavior from few events can be used to reliably predict the measured response for other events. The field extracted soil behavior shows dependencies of shear modulus and damping on cyclic shear strain level, number of loading cycles, and strain rate that are similar qualitatively to those reported from laboratory studies but differ quantitatively.