UC Davis

The results of static and dynamic nonlinear analyses of earthen structures are dependent on the implemented numerical methods including the constitutive models, the solution scheme, and the modeling software. Recent significant static failures (e.g., Feijão Dam 1) and past dynamic failures (e.g., 4th Ave. landslide in Anchorage, Alaska) have occurred due to yielding of the plastic soils. These failures were influenced by the strain-softening tendencies of the plastic soils, which highlights the need for continued development of numerical tools to model plastic soils in nonlinear analyses. This dissertation presents the development of a new constitutive model, a relationship that connects element level viscous behavior to field scale analyses, and system level analyses with new solution schemes that incorporate viscous effects and strain- softening in nonlinear analyses.

First, a viscoplastic constitutive model for representing plastic silts and clays in geotechnical static slope stability applications is presented. The PM4SiltR model builds on the stress ratio-controlled, critical state-based, bounding surface plasticity model PM4Silt and is coded as a dynamic link library for use in the finite difference program FLAC 8.1. PM4SiltR incorporates strain rate-dependent shear strength, stress relaxation, and creep using a consistency approach combined with an internal strain rate and auto-decay process. Six parameters are introduced to control the viscous response of PM4SiltR while the parameters controlling the nonviscous portion of the response are the same as for PM4Silt. Single element simulations are presented to illustrate the influence of viscoplasticity on the constitutive response in direct simple shear loading and undrained creep. Single element responses are shown to be consistent with observed experimental results. Simulations of a hypothetical tailings dam of upstream construction are performed to illustrate use of PM4SiltR at the field scale. Results of field scale simulations show PM4SiltR can model undrained creep and progressive failure leading to delayed slope instability after relatively minor changes in loading conditions at.

A numerical study is then presented that shows the effect that viscoplasticity can have on the localization process in sensitive, saturated clays and plastic silts. Numerical simulations of laboratory specimens of sensitive, viscoplastic soil subjected to monotonic, undrained, direct simple shear loading were performed using the PM4SiltR constitutive model. Parametric analyses evaluated the effects of soil sensitivity, post-peak strain-softening rate, and strain rate-dependency, as well as specimen size, mesh discretization, and loading rate. The numerical results showed that the global strain at which a localization forms primarily depends on the strain rate-dependency of the soil's shearing resistance relative to its rate of post-peak strain-softening. A regression model is subsequently presented that relates the global strain at the onset of localization to the soil's strain rate-dependency and post-peak strain-softening rate. The results indicate that the inclusion of reasonable levels of viscoplasticity significantly increases the strain that can develop before a localization develops in clays and plastic silts with modest strain-softening rates. The consistency of the numerical results with available laboratory observations is discussed. Implications for practice and future research needs are discussed.

Next, two-dimensional viscoplastic nonlinear analyses of the 2019 Feijão Dam 1 failure in Brazil are performed using the finite difference program FLAC 8.1 with the user-defined constitutive models PM4SiltR and PM4Sand. A brief history of Feijão Dam 1, its failure, and the conflicting findings from two previous independent failure investigations are summarized. The present study uses the site characterization from those prior studies to develop the dam cross section, define material index properties, and establish groundwater conditions, but uses alternative techniques for characterizing undrained shear strengths. Simulations show that the dam was marginally stable against long-term consolidated, undrained conditions and that modest loading changes were sufficient to trigger failure with deformation patterns consistent with the observed failure. Simulations further show that collapse could have been triggered by a modest wetting event causing an increase in water content and loss of suction above the phreatic surface, by ongoing drilling activities causing a localized loss of shear strength in the tailings, or a combination of both mechanisms. Sensitivity of the results to choices in the calibration process and the numerical solution scheme are discussed. The implications of these results on the interpretation of the Feijão Dam 1 failure and long-term slope stability assessment procedures in practice are discussed.

Finally, two investigations look at the influence of sensitivity and strain-softening on the seismic deformations of a set-back levee. First, nonlinear dynamic analyses are used to investigate how seismic deformations of a 6-m tall levee founded on a deposit of normally consolidated clay may vary with the sensitivity of the clay. The analysis results showed that strain-softening and associated strength loss in the clay layer increased with increasing clay sensitivity, but it did not result in increased levee deformations for the conditions examined. Instead, the results showed that increasing clay sensitivity slightly reduced the levee deformations, which was attributed to the strength loss in the clay also causing a reduction in the accelerations that developed in the levee. Second, the results of nonlinear dynamic analyses (NDAs) of an idealized levee founded on a sensitive clay are compared with simplified procedures that combine limit equilibrium (LE) and Newmark sliding block methods. The tendency for simplified procedures to underestimate or overestimate seismic deformations compared with NDA results is shown to depend on the specific conditions (e.g., soil sensitivity and brittleness, ground motion intensity, margin of safety against instability) and how potential strength loss is accounted for in the simplified methods. Limitations of these findings for practice are discussed.

Overall, the outcomes from this dissertation contribute to an increased understanding on how to account for viscous effects and strain-softening in static and dynamic nonlinear analyses.