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Open Access Publications from the University of California

Lumped Macroelement Modeling of Earth-Retaining Structures under Seismic Loading for Nonlinear Time-History Analyses

  • Author(s): Dasmeh, Arastoo
  • Advisor(s): Taciroglu, Ertugrul
  • et al.

This dissertation addresses various engineering problems involving the seismic re- sponse modeling of earth-retaining structures. These are namely, (i) lateral pas- sive seismic behavior of ordinary skew-angled bridge abutments, (ii) lateral pas- sive seismic behavior of high-speed rail transition abutments (with no skew), and finally (iii) active and passive seismic behavior of (cantilevered) earth-retaining walls. The approach adopted for each problems is the same, which is to devise a macroelement model with physics-based parameters (e.g., soil density, shear strength, wall height, etc.) that captures salient response features. These models are able to predict the lateral capacity of the retained soil and residual displace- ments with a modest computational effort—as compared to, for example, predic- tive simulations carried out with three-dimensional finite element models—, which renders them to be amenable for repeated nonlinear time-history analyses required for performance-based seismic assessment and design. The three aforementioned problems are briefly described below:

I. Presence of skew-angled abutments complicates the seismic behavior of or- dinary bridges, primary driver of which is the passive lateral resistance of the engineered backfill behind the abutment. The eccentricity of the soil reaction


relative to the bridge’s center of stiffness or mass causes a skew bridge to rotate under seismic excitations, and a nonuniform soil pressure distribution develops behind the abutment backwall. A distributed nonlinear spring model is devised here to represent the lateral passive reaction of the backfill soil. To that end, a modification factor is devised so that Log-Spiral Hyperbolic (LSH) backbone curves –which had been developed in prior research and were validated for back- fills of straight abutment–can be used to generate the backbone curves of the said springs. This new modeling approach is verified against three-dimensional finite element model simulations and is validated with data from large-scale experiments conducted at Brigham Young University that had produced direct measurements of load-deformation backbone curves for several skew angles. In the final step, the validated modified-LSH model is used in parametric studies to devise a simple bilinear load-deformation relationship that is parameterized with respect to the backwall height, abutment skew angle, and the backfill soil properties. This sim- ple relationship is intended for routine use in the capacity-based seismic design and analysis of skew bridges.

II. California’s High-Speed Rail (HSR) System is slated to traverse nearly the entire length of the state, and thus it will be exposed seismic risks from almost every known major tectonic fault there. The present study deals with the seismic responses of bridge-abutment transition backfills (BATBs), which are essential components of HSR bridges. BATBs provide a gradual variation of vertical stiff- ness between the bridge deck and the engineered backfill zone, enabling smooth operations for trains traveling at high speeds. All prior investigations focused on this vertical stiffness in order to better characterize the localized vertical dif- ferential movements around BATBs under periodic high axial loads from train sets. Lateral behavior of BATBs, which are important under seismic loads, have not been previously investigated. The present study offers a parametric nonlin- ear lateral force-displacement backbone curve for BATBs that is verified against


three-dimensional finite element models and validated against data from large- scale tests conducted at Brigham Young University. The parametric curve takes backwall height as well as abutment skew angle into account.

III. Performance-based seismic assessment (PBSA) of earth retaining struc- tures requires the use of accurate yet computationally efficient analysis models. To date, limit equilibrium models offered the most computationally efficient re- sults, but they only produce estimates of peak lateral seismic forces and cannot be used in nonlinear time-history analyses. While detailed finite element models can possibly fill this need, they are not amenable for repeated simulations required for quantifying the uncertainties associated with estimated ground motions within the PBSA framework. A novel Lumped Impedance Model (LIM) is developed in this study that generates as accurate solutions as detailed FE models, with trivial computational effort. The model is able to also reproduce lateral passive load-deformation backbone curves as predicted by a state-of-the art limit equi- librium model, by its design. The computational saving offered by LIM is due to lumping of mass and stiffness of the retained soil, and the strategic placement of elastoplastic macroelements along pre-calculated active and passive failure hy- perplanes. LIM is verified against analytical solutions in frequency-domain for linear response regimes—wherein it is shown that LIM can accurately capture the frequency-dependent responses of the retained soil—as well as other previous studies for inelastic conditions. LIM is also verified against detailed FEM sim- ulations of cantilevered retaining wall subjected to both narrow- and broadband excitations, and it is shown that both elastic and inelastic responses of the retained soil (including residual wall displacements and rotations) are adequately captured. Finally, a framework for PBSA of earth-retaining structures using LIM as the pre- dictive model is proposed and its use is demonstrated through an example seismic assessment application wherein a fragility curve is computed.


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