*Project # NCTRSB*

### Research Team

- Scott J. Brandenberg (PI), Assistant Professor, University of California, Los Angeles
- Jian Zhang (co-PI), Assistant Professor, University of California, Los Angeles
- Yili Huo, Graduate Student, University of California, Los Angeles
- Minxing Zhao, Graduate Student, University of California, Los Angeles

### Research Abstract

Liquefaction has damaged many bridges during past earthquakes and is an important issue for bridge owners, particularly state departments of transportation. Recent research has clarified many aspects of interaction between bridges and liquefied soils, and clearly demonstrated that liquefaction is a dynamic process involving a complex combination of low-frequency kinematic interaction and higher frequency inertia interaction. Yet liquefaction is most often addressed using static analysis methods that can at best merely approximate the dynamic features of response. A particularly relevant reason for this is that dynamic three-dimensional analysis using constitutive models capable of capturing the salient features of liquefaction is quite simply too computationally demanding to utilize for anything other than high-end research in computational mechanics. This research seeks to bridge this gap by performing dynamic global analysis of bridges in liquefiable ground using the following sequence of steps: (1) perform a one-dimensional nonlinear site response analysis accounting for the effects of liquefaction, (2) construct a global dynamic bridge model, distributing soil-structure interaction elements along embedded components, and (3) impose the boundary conditions from the site response analysis on the free-ends of the soil-structure interaction elements. The motivation for developing this approach is to include important dynamic features of response in a less computationally demanding framework that could be readily transitioned to practice for analysis of important bridges, and to observe several important features of dynamic response that have not yet been studied in adequate detail, such as phasing between kinematic and inertia loads.

### Research Outcomes

**Site Response in Liquefied Ground**

A suite of one-dimensional nonlinear site response studies have been performed to observe the influence of liquefaction on ground surface motion. The liquefiable sand layers were modeled using the PressureDependMultiYield02 constitutive model implemented in OpenSees, and analyses were performed using both drained and undrained loading conditions. Both fault normal and fault parallel motions were input to the base of the one-dimensional soil columns, which was modeled using three-dimensional brick elements. Response spectra were computed for the ground surface motion for both undrained and drained conditions, and ratios of the spectra were defined as C_{liq} = (S_{a})_{undrained} / (S_{a})_{drained }(see Fig. 1). As anticipated, liquefaction tends to reduce short period spectral acceleration, and increase long period spectral acceleration. However, the reduction in peak ground acceleration is only moderate (i.e., the median reduction in PGA is only about 31%). This conclusion does not align with the common understanding of liquefied sand being a base-isolation layer that significantly reduces ground motion to the point that kinematic demands and inertia demands can be treated as separate events. Dilatancy behavior of liquefied sand was observed to be an important factor in propagating large waves through liquefiable sands.

**Three-Dimensional Bridge Analysis**

The one-dimensional site response simulations were utilized as inputs to global three-dimensional bridge models. Soil-structure interaction was modeled using PyLiq2 materials in OpenSees that allow input of free-field mean effective stress from a text file, but are otherwise identical to PyLiq1 materials. This modification saves significant time because the PyLiq1 materials require the zeroLength elements to be connected to a computationally costly soil mesh. Two p-y elements are oriented in orthogonal horizontal directions and the free-ends of the elements are excited with the ground motions from the one-dimensional site response analysis. A schematic of the approach is shown in Fig. 2. Simulations were performed for a range of different structural configurations using a set of 40 ground motions developed for the PEER Transportation Systems Research Program (Baker et al. 201x). Site response simulations with and without liquefaction were imposed on the bridge models. Results from the simulations are post-processed to observe the overall failure mechanisms, and phasing of kinematic and inertia loads to obtain a better understanding of how to analyze the bridges using simpler methodologies. Example results are shown in Figs. 3 and 4. The direction of lateral spreading is largely in the longitudinal direction (i.e., toward a water body running under the bridge. As a result, the longitudinal pile cap displacements are larger than the transverse displacements. The bridge presented in Figs. 3 and 4 had a continuous superstructure that limited longitudinal deformations of the tops of the pier columns, and the drift experienced by the pier column is largely caused by pile cap displacement induced by lateral spreading. Liquefaction also increases the transverse response of the bridge relative to the nonliquefied soil profiles. Transient ground lurch during liquefaction can cause large transient and permanent deformations in the abutments, pile caps and pier columns.

**Interpretation of Boundary Conditions for Local Static Analysis**

The 3-D global analyses are simpler than comparable analyses that utilize a three-dimensional soil mesh, but still too complicated for routine application for ordinary bridges. Hence, a valuable contribution of the global dynamic analyses is characterization of boundary conditions that are appropriate to impose on the top of the pier column for static analysis of a local subsystem (e.g., a pile group and pier column). Fig. 5 shows the ratio of the global displacement at the top of the pier column with liquefaction to that without liquefaction (C_{Δ}) for various cases that correspond to different bridge configurations. The figure clearly shows that liquefaction tends to reduce the global displacement of the superstructure for all but cases 3 and 4. Cases 3 and 4 correspond to bridges with simply-supported spans that rest atop the pier columns, whereas the other cases consist of a continuous superstructure with moment-resisting connections between the pier columns and superstructure. This finding is important because we have methods for estimating superstructure displacement demands in the absence of liquefaction, and the results in Fig. 5 explain how this displacement should be modified to account for the effects of liquefaction. Local static analyses were conducted using the median value of C_{Δ} from Fig. 5, and the predicted structural demands agree reasonably well with the more complicated global dynamic simulation results.

**Simplified Method to Predict Ratio of EDPs With and Without Liquefaction**

Utilizing the developed global dynamic analysis procedure, an extensive sensitivity analysis has been conducted to evaluate the effects of various structural, foundation, and soil parameters on the structural response quantities, such as the pier drift ratio, abutment and pile cap displacement and rotation etc. Both liquefaction and non-liquefaction cases have been considered for soil layers with varying non-liquefied crust layer thickness, liquefied layer thickness, and pile sizes etc. Based on these global dynamic analysis results, we are deriving the simplified response ratio *C _{EDP}*, which relates the EDPs of the bridges on liquefiable ground to that of the non-liquefiable cases. Since the responses of bridges under ground shaking without liquefaction can be obtained fairly easy in practice, the responses of bridges under liquefaction induced lateral spreading can be obtained by

*EDP*for bridges that have similar structural configurations and soil conditions to those analyzed in our study. Figure 6 plots the response ratio

_{liq}= C_{EDP}(EDP_{non-liq})*C*of pier drift ratio as function of the cumulative absolute displacement, CAD, of the ground level motion corresponding to the non-liquefied cases for (a) bridges founded on different pile sizes; (b) embankment with different slope inclination angles; (c) different thickness of non-liquefiable crust layer; and (d) different pier column design. A regressive equation for

_{EDP}*C*is being developed and will be validated further.

_{EDP}### Research Impact

The primary impacts of this research are (1) documentation and validation of a new method for global dynamic analysis of bridges in liquefied soil that is not too complex to use for evaluation of important bridges (3-D dynamic analyses with continuum soil mesh remain essentially a research tool), (2) a suite of global dynamic analyses that are useful for learning about phasing of kinematic and inertia loads, (3) a set of site response studies on soil profiles with and without liquefaction, (4) guidance for imposing displacement boundary conditions at the top of pier columns in local static analyses to account for the effects of liquefaction, and (5) simplified response ratio to derive the EDPs of bridges with liquefaction for given bridge responses under non-liquefiable cases using global dynamic analysis. This research will improve both the analysis and design tools for quantifying the impact of liquefaction on bridge responses.