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Twenty-four centrifuge model tests have been conducted at nine different geotechnical centrifuge facilities around the world as part of the international LEAP effort (liquefaction experiments and analysis projects). All of the centrifuge models represent a 4 m deep 5 degree sloping submerged sand deposit. The mean effective PGA of the input motion for all of the experiments was approximately 0.15 g and the mean relative density was approximately 65%, but the effective PGA's varied between about 0.07 g and 0.3 g, and the relative densities varied between about 40% and 75%. The test matrix was designed to enable experimental quantification of not only the median response but also the trend and sensitivity of the model response to density and shaking intensity. Quantification of the sensitivity of the response to initial conditions is a prerequisite for objective evaluation of the quality of the model test data. In other words, a discrepancy between two experiments should be evaluated after accounting for the uncertainty in the initial conditions and the sensitivity of the response to initial conditions. For the first time, a sufficient number of experiments has been performed on a similar problem to provide meaningful quantitative evaluation of the trend between PGA, density, and displacement. The sensitivity is quantified by the gradient of the trend and the uncertainty of the trend is quantified from the residuals between the fitting data and the trend.

Several centrifuge model tests have been conducted using the NEES facility at UC Davis to study the dynamic behavior of rocking shallow foundations and the interaction with highway bridges or building systems. The results suggest that rocking should be encouraged as one mechanism for absorbing energy and thereby reducing ductility demand on the structure. During these tests, the interactions between researchers and practictioners has been valuable (a) as a technology transfer mechanism, (b) to figure out the direction of research to convince practitioners that results are definitive, and (c) for academics and practitioners to collaborate in appropriate changes in national standards such as ASCE/SEI-41 (ASCE standard for Seismic Rehabilitation of Existing Buildings). This paper provides examples to illustrate the roles and influences of physical modeling in the evolution of practice related to rocking foundations for bridges and buildings.

Past studies have revealed that the different characteristics of near- fault pulse-like and far-field broadband motions have varying effects on the response of structures. In this paper, a suite of pulse-like and broadband motions are utilized to investigate the response of rocking-foundation and hinging column bridges including large deformation effects. Incremental Dynamic Analyses were carried out on simplified models of which the following parameters were varied: the rocking strength, the column height, and the fundamental period. Results show that, in a probabilistic sense, rocking systems are more susceptible to tip-over in pulse-like motions than in broadband motions. The re-centering effect of rocking systems makes them relatively immune to damage in motions that consist of many small inelastic pulses. Elastic-perfectly plastic hinging systems have less re-centering capability and hence they are more susceptible to accumulated deformation and eventual collapse in many small cycles that might occur in long duration broadband motions.

Structures located in densely populated, seismically active urban areas are treated as isolated structures in normal design practice. The influence of neighboring structures on the response of a soil-foundation-superstructure system, which is known as structure-soil-structure interaction (SSSI), is not accounted for in current design procedures, largely because of a lack of understanding and analytical tools. The objective of this study is to develop a simple analytical model that may be used to evaluate SSSI effects while accounting for the influence of loading frequency, footing size, footing spacing, and wave attenuation. In particular, the special case of interacting surface footings within a single structure, footing-soil-footing interaction (FSFI), is considered. In-phase and out-of-phase FSFI effects are examined through a series of parametric studies and the amplification (or reduction) of response due to FSFI is evaluated. For a system composed of vertically vibrating footings arranged in a 2 x 2 grid, results indicate that for most realistic geometric and loading conditions, FSFI will only have minor effects on footing motions. Additionally, it is shown that the amount of radiation damping at a footing results in two competing phenomena: (1) decreased soil-structure system response, and (2) increased FSFI effects.

The rocking foundation mechanism has proven to be an effective means to dissipate seismic energy, and thereby reduce the seismic demand on the superstructure. Its use has been broadly applied in both the building and bridge domains. Nonetheless, a common concern remains regarding its global behavior in a building system. Specifically designers must understand how the rocking foundation dynamically interacts with other inelastic components, particularly those designed into the structural components. To advance understanding, this paper presents and compares the seismic response of two extreme structural configurations, namely, a structural hinging-dominated (SHD) system and a foundation rocking-dominated (FRD) system. These two structural systems were recently tested in a 9-m-radius centrifuge-based shake table at UC Davis. Results indicate that the SHD system is more prone to localize the seismic energy at the structural fuse element, with relatively little energy transferred to the rocking footing. As a result, the structural fuses have a fairly large demand, which in turn cause significant transient and residual deformation in the superstructure. The FRD system, on the other hand, with broad moment-rotation hysteretic response of the foundation effectively minimizes the superstructure seismic demands in terms of roof drift and base shear, while the structural fuse element remains linear-elastic, even under intense base shaking.

Current research has shown the capabilities and improved seismic performance of rocking shallow foundations for bridges, and much work has been done for implementation of such a mechanism in industry. By properly reducing the size of the footing, rocking behavior due to seismic loading can occur about the footing base. It has been shown experimentally that rocking foundations on competent soils can reduce seismic ductility demand on bridge columns and improve bridge performance. One concern of rocking systems is the potential for significant settlement accumulation in poor soil conditions. This research explores soil, footing, and structural response of similar bridge structures on poor, liquefiable, and saturated soil conditions in addition to the effectiveness and practicality of using unconnected piles as a potential settlement mitigation technique. A centrifuge test series showed rocking foundations in saturated sand over a liquefiable soil layer not only experience the traditional deformations from liquefaction, but are also susceptible to additional deformations such as suction and erosion around the footing.

Rocking foundations have shown performance advantages that may benefit the seismic performance of structures. Previous centrifuge tests have well characterized the behavior of rectangular rocking foundations on sand, but few results are available for clayey ground. In this study a series of centrifuge model tests of shear walls and single-degree-of-freedom (SDOF) structures with rocking foundations supported on clay of medium strength are conducted. Vertical bearing failure, slow cyclic loading, and dynamic shaking tests were performed at three different levels of centrifugal acceleration. The moment capacity, settlement, and rotation of each loaded model were tracked and then compared to previous published results. The measured moment capacity is found to match the theoretical values. The settlement vs. rotation behavior was characterized, and it is found that settlement is somewhat smaller than previous results for similar models tested on sand.

Preliminary results from a study to develop innovative bridge foundations to optimize bridge performance under earthquake events are presented. Numerical models of bridges with both flexible and stiff footings are compared to demonstrate the potential importance of soil-footing stiffness on the performance of a soil-footing-column-deck-abutment system. Detailed numerical models were developed to capture the inelastic behavior of soil-footing systems. This article summarizes two types of foundation models developed using the OpenSees computational platform. One model uses a contact interface model, soilFootingSection2D, to simulate the foundation and has been proven to be effective in analyzing the cyclic response and displacement of soil-foundation-bridge system. The other uses 2-D nonlinear Winkler foundation consisting of various constitutive springs. Although the former model is more detailed and fundamentally sound in modeling the footings, in its current state it is limited to 2-D use only. The latter model, once verified via comparison to experimental data, can be extended to 3-D. Future work will use the 3-D nonlinear footing models to more accurately simulate the 3-D response of a bridge system to 3-D ground motions.

This paper addresses the development of an electrical resistivity needle probe to be deployed during centrifuge model testing to assess with high -resolution the spatial variability of soil electrical resistivity. The probe is able to detect thin layers and accurately resolve interfaces between soil layers. The prototype probes are made from thin, stainless steel needles, with an insulated wire inserted into the needle, and bonded to it with epoxy resin, to form a coaxial probe (Cho et al. 2004). Different tip shapes including single -wedge, double-wedge and cone have been developed to optimize the spatial resolution of porosity, soil interfaces and layering. The calibration and testing of the needle probe has been conducted both at Georgia Tech and UC Davis. This paper presents results of resistance versus depth and porosity versus depth, and compares the porosity based on measurement of mass and

Nonlinear dynamic analyses using the finite element (FE) method are compared to the results of dynamic centrifuge model tests of pile-supported structures in liquefying sand profiles. The FE models utilized soil spring elements that connect pile elements to one- or two-dimensional meshes of a soil profile. Development and implementation of the soil spring materials models in the OpenSees FE platform are described. Single element examples are used to illustrate the behavior of the soil and soil spring material models. Comparisons of FE analysis to centrifuge test data of pile-supported structures in liquefying sand profiles suggest that these FE methods can reasonably approximate the essential features of soil and structural response.