Abstract
Engineering Evaluation of Post-Liquefaction Strength
by
Joseph Patrick Weber
Doctor of Philosophy in Engineering – Civil and Environmental Engineering
University of California, Berkeley
Professor Raymond B. Seed, Chair
Over the past three decades, engineers working in the area of soil liquefaction engineering have been called upon to develop increasingly well-refined evaluations of expected performance of structures and of critical infrastructure in the event of potential soil liquefaction. A critical element in such evaluations is the engineering assessment of post-liquefaction strengths of in situ materials. Prior to the past three decades, it was common practice to ascribe assumed negligible strengths and stiffnesses to liquefied soils for engineering analyses. Today, increasingly higher-order analyses are performed involving either simplified seismic deformation or seismic displacement analysis methods, or fully nonlinear analyses implemented in a finite element or finite difference framework. In all of these analyses, the evaluation and modeling of post-liquefaction strengths is typically a critical issue.
This has led to a surge of interest, and to a significant amount of research involving laboratory, centrifuge, and analytical studies. The focus for engineering analysis and design efforts for actual projects is often on the use of empirical relationships for engineering evaluation of in situ post-liquefaction strengths. This is due, in large part, to complications and challenges inherent in the use of laboratory-scale physical testing for development of estimates of post-liquefaction strengths at full field scale. These challenges are generally well understood, but some of them (e.g. localized void redistribution under globally “undrained” shearing) continue to confound reliable assessment by means of laboratory testing for most projects. As a result, empirical relationships, established based on back-analyses of full-scale field liquefaction failure case histories, are the common approach for most projects. These current efforts have been focused on this approach.
These current studies began with a technical review of previous efforts. That proved to be a valuable exercise. Evaluation of previous work, and recommendations, with emphasis on strengths and drawbacks of prior efforts, led to some important insights. It turns out that a number of previous efforts had developed important lessons, and in some cases important pieces of the overall puzzle. They also served to provide ideas and to inspire elements of these current studies, and they provided lessons with regard to mistakes to avoid.
A suite of full-scale liquefaction failure case histories were then reviewed, vetted and selected for back-analyses. New methods were developed for performing these back-analyses, including methods that more accurately and reliably deal with momentum effects in liquefaction failures that experience large displacements. A suite of additional empirical relationships were developed specifically for cross-comparison of the results of back-analyses of large deformation liquefaction failures. In the end, a suite of back-analysis results of unprecedented reliability were developed, based on (1) improved back-analysis procedures, (2) internal cross-checking within the framework of the empirical relationships developed, and (3) external cross-checking against the results obtained by previous investigations, with an informed understanding of the strengths and drawbacks of the back-analysis methods and assumptions employed in those previous studies.
The resulting hard-earned back-analysis case history database was then used, in the context of probabilistic regressions that incorporated the best obtainable evaluations of uncertainties, to perform probabilistic regressions by the maximum likelihood method in order to develop new predictive relationships for engineering evaluation of post-liquefaction strength as a function of both (1) corrected SPT penetration resistance, and (2) initial in situ effective vertical stress.
These new relationships were then compared with previous relationships and recommendations. Here, again, with understanding of the strengths and drawbacks of the procedures by which the previous relationships were developed, and of the back-analyses that often provided the parameters for the earlier efforts, a coherent overall pattern emerged and the relative juxtaposition of values of post-liquefaction strengths provided by different relationships can now be better understood.
The new predictive relationships developed in these current studies agree surprisingly well with the recent recommendations of Wang (2003) and Kramer (2008) who executed a similar overall effort, but with significant differences in approaches, and judgments, at essentially every step of the way. This level of agreement occurs when adjustments are made for apparent errors in development of a number of their model input parameters, and so the work to develop better understandings of strengths and weaknesses of various case history back-analysis approaches was particularly important here. Similarly, the results and recommendations from these current studies can also be shown to provide fairly good agreement with earlier recommendations of (1) Seed and Harder (1990), (2) Olson and Stark (2002) and (3) Idriss and Boulanger (2008), but only over specific ranges of (1) initial in situ effective vertical stress, and (2) corrected SPT penetration resistance. In other ranges, these previous relationships can now be shown to be either conservative, or unconservative, and the reasons for this can now be understood.
The new predictive relationships for engineering evaluation of post-liquefaction strength are presented in a fully probabilistic form, and can be used for probabilistic risk studies and design of high-level projects. They are then recast in a simplified deterministic relationship likely to be more widely applicable to more routine projects.
These new relationships offer potentially significant advantages over previously available recommendations and relationships. They are based on back-analyses, and regressions, which provide insight into the underlying forms of the relationships between post-liquefaction strengths and both (1) penetration resistance and (2) effective vertical stress, over the ranges of conditions well-represented in the 30 full-scale field liquefaction case histories back-analyzed. Because they provide insight as to the underlying forms of these relationships, they provide a better basis for extrapolation to higher ranges of penetration resistance, and to higher ranges of effective stress, than do previous recommendations. The back-analyzed field case history database provides fair to good coverage for values of N1,60,CS up to approximately 14 blows/ft, and for representative effective overburden stresses of up to approximately 4 atmospheres. The range of principal engineering interest is usually N1,60,CS ≈ 10 to 22 blows/ft., however, as it is over that range that field behavior, and project performance, often transitions from unacceptable to acceptable. Similarly, for major earth and rockfill dams (and their foundations), ranges of effective overburden stress considerably larger than 4 atmospheres are often of critical importance.
In addition to the development of improved relationships for engineering evaluation of post-liquefactions strengths, the suite of new empirical relationships developed for use in cross-checking of back-analyses of liquefaction failure case histories will likely also have applications with regard to checking of engineering analyses of expected performance for forward analyses of actual engineering projects, including high-level analyses involving fully nonlinear finite element or finite difference analyses for critical and/or high risk projects.
