Currently there is no consistent, widely accepted procedure for discretizing levee systems subjected to seismic load for probabilistic analysis. Further, statistical independence of performance between levee sections is often assumed without verification. This stems from the difficulty in: quantifying the spatial autocorrelation structure of random variables used to predict performance and, implementing autocorrelation structure into probabilistic levee analysis. In this research we use First Order Reliability Method (FORM), Second Order Reliability Method (SORM), Sequential Important Conditional Sampling (SCIS) and Directional Important Sampling (DIRS) in an attempt to define a robust methodology for discretizing a levee system for probabilistic analysis and to show that assuming independence of performance between individual levee sections is not valid.

We chose to use the levee that protects Sherman Island, CA as our case study. Sherman Island is located in the California Bay Delta, which is the terminus of the Sacramento and San Joaquin rivers and a strategically vital hub of infrastructure for the region and the State of California. To use the reliability tools we have selected it was necessary for us to define compatible levee performance models. Compatible models must be continuous functions of random variables that are differentiable and the random variables must be continuous and described by a joint probability distribution. Rather than develop our own models we adopted levee performance models developed in the Delta Risk Management Strategy (DRMS) Phase 1 Report (URS 2009). This report was a comprehensive risk analysis of the California Bay Delta. The seismic performance models developed within were not fully compatible with or reliability tools. Therefore we made appropriate and technically sound adjustments to the models.

To ensure that our seismic levee performance models were producing reasonable results we used them to calculate point estimates of failure probability at Sherman Island for past seismic events: M≈7.9 1906 Great San Francisco Event, M=5.8 1980 Livermore Event, M=6.19 1984 Morgan Hill Event and M=6.9 1989 Loma Prieta Event. There were no documented seismic failure for the three most recent events and our failure probability estimates agree well with this.

As mentioned above, quantifying the spatial autocorrelation structure of random variables used to predict levee performance is a non-trivial task. As part of this study we investigated the spatial autocorrelation structure of ground motion intensity measures. Specifically we characterized the spatial autocorrelation structure of single-station intra-event residuals and site terms. We did this for three different sets of ground motion data: a Californian dataset (Chiou et al., 2010), a Taiwanese dataset (Lin et al., 2011) and a Japanese dataset (Rodriguez-Marek et al., 2011). Single-station intra-event residuals come from single-station sigma ground motion prediction equations, which are models that have removed repeatable site effects from the standard deviation. We show that the spatial autocorrelation structure of single-station intra-event residuals and site terms are region dependent and sensitive to the period of pseudo spectral acceleration. Further we show that single-station intra-event residuals stay autocorrelated for greater distances than intra-event residuals. We implemented our characterization of ground motion autocorrelation into our levee reliability analysis.

There was not sufficient data for us to quantify the spatial autocorrelation structure of the random variables that describe material properties of the levee. There are studies on spatial autocorrelation of material properties in the literature however; none of studies are at an applicable scale for our analysis. Additionally, there is little guidance on whether or not model error terms are autocorrelated. We test a range of assumptions on the spatial autocorrelation of the material properties and model error terms in our analysis.

The results of our analysis suggest that: A robust methodology for discretization of levee systems under seismic load is dependent on the scale of the potential failure mechanisms and, the assumption of statistical independence of performance between levee sections is not appropriate. Though we were unable to develop a specific methodology for the discretization of a levee system we provide a relationship for adjusting failure probability estimates of a levee based on its length and assumptions about the scale of potential failure mechanisms and the amount of autocorrelation present in random variables used for prediction.

The Standard Penetration Test (SPT) has been a staple of geotechnical engineering practice for more than 70 years. Empirical correlations based on in situ SPT data provide an important basis for assessment of a broad range of engineering parameters, and for empirically based analysis and design methods spanning a significant number of areas of geotechnical practice. Despite this longstanding record of usage, the test itself is relatively poorly standardized with regard to the allowable variability of specific details of equipment and procedures, and this requires a number of adjustments or corrections to further standardize this "standard" test. In addition, for many engineering purposes, it is also useful or necessary to "normalize" the penetration resistance measured by SPT in order to account for the influence of effective vertical effective overburden stress at the depth where an individual SPT is performed.

This research addressed two of corrections and adjustments that can be applied to SPT: (1) normalization of measured penetration resistances to account for effective overburden stress, and (2) corrections of SPT data for the effects of variations in hammer energy successfully transferred into the rods during driving due to "short rod" effects.

The development of procedures and relationships for normalization of SPT penetration data for effects of effective overburden stress dates back more than 60 years, and a number of top geotechnical experts of the past six decades have weighed in on this issue. Despite this long history, current normalization relationships are not based on very extensive data sets, and they are based largely on data for clean sands only (SW and SP) and so do not necessarily represent a suitable basis for overburden normalization of SPT for silty soils (SP-SM, SP-SC, SM and ML) which can be of significant interest in a number of problem areas including, but not limited to, soil liquefaction engineering. The approach taken here was to first re-evaluate the important data developed by Marcuson and Bieganousky (1977) based on large-scale laboratory calibration chamber tests of SPT performed on three clean sands. Then the resulting overburden normalization relationships developed were further examined by cross-comparison with several additional sets of field (in situ) SPT data.To extend these types of relationships to silty soils, data were next gathered for six silty foundation soil strata beneath major dams, where the overlying (largely trapezoidal) earthen dam embankments provided the needed broad ranges of effective overburden stresses within foundation strata that were judged to be suitably laterally geologically continuous as to provide a basis for development of these types of relationships. In the end, it was found that the new relationships developed for "silty" soils, with suitable fines adjustments (similar to the fines adjustments currently employed in widely used SPT-based liquefaction triggering correlations), match relatively well with the newly developed relationships for overburden stress normalization of SPT data for cleaner sands.

The issue of short rod effects has a shorter history, having first been broached by Schmertmann and his colleagues in the early 1970's. Considerable additional work has followed, and with ongoing advances in both the availability of improved instrumentation (especially high frequency accelerometers) and of analytical methods, it has become clear that earlier measurement and analytical methods developed prior to about the mid-1980's overestimated to some extent the reduction in hammer energy delivery for conditions wherein rods were "short" (less than about 45 feet in length). With improved modern accelerometers, we are now able to fully track the very high frequency accelerations produced by steel to steel hammer/anvil impacts, and as a result it is now no longer necessary to make simplifying assumptions that had been intrinsic in pre-1986 measurements and analyses. It is now possible to trace hammer energy (and wave travel) up and down the rods for multiple cycles of wave travel and to account for additional hammer energy transferred into and out from the rods until the entire "event" had been concluded. Debate has ensued as to the magnitude of actual hammer energy correction that is appropriate now that this improved measurement data is becoming available. The approach taken here was to gather instrumented hammer energy data from SPT performed, under closely controlled conditions, for purposes of "calibration" of automatic (mechanical) hammers. The resulting data show that short rods effects are indeed somewhat less significant then had previously been postulated, but that this reduction in short rods effects is less pronounced that has been postulated by a number of recent papers. An additional finding, also of engineering significance, is that "common practice" with regard to performing of SPT for purposes of calibration of automatic hammers often does not properly account for short rod effects, and that this can produce a conservative bias in SPT data when these hammers are subsequently used for actual engineering investigations. Recommendations are presented for (a) new short rod corrections, and (b) for hammer energy calibration testing of automatic SPT hammer systems.

Abstract

Evaluation of the State of Practice Regarding Nonlinear

Seismic Deformation Analyses of Embankment Dams

Subject to Soil Liquefaction Based on Case Histories

By

Khaled Hossain Chowdhury

Doctor of Philosophy – Civil and Environmental Engineering

University of California, Berkeley

Professor Raymond B. Seed, Chair

Nonlinear seismic deformation analysis (NDA) is an important analytical tool used to (1) evaluate seismic safety of existing dams, (2) to design seismic mitigation of dams, (3) to evaluate and implement reservoir restrictions and other interim safety measures while seismic mitigation design and implementation are pending, and (4) for design of new embankment dams to ensure the seismic safety of dams that serve important purposes such as flood control, water supply, power generation, and tailings impoundments, especially with regard to risk exposures of downstream populations and facilities.

Nonlinear seismic deformation analyses of embankment dams are complex. They require (1) proper site characterization, (2) development of ground motions considering the recent State of Knowledge protocols, (3) liquefaction triggering relationships, (4) post-liquefaction strength relationships, (4) modeling of behaviors of non-liquefiable soils, (5) constitutive models, (6) accounting for volumetric recompression settlement, and (7) engineering evaluation of analysis results. These inter-dependent aspects of seismic deformation analyses, when applied through nonlinear analytical tools such as FLAC, may not always provide correct predictive answers if the concepts, relationships, and models are not implemented properly.

Evaluation of different aspects of the current State of Practice in seismic deformation analyses was performed in these current studies. The approach taken was to apply suites of combinations of (1) four different analytical or constitutive models, (2) three liquefaction triggering relationships, (3) three post-liquefaction residual strength (Sr) relationships, and (4) various additional analysis protocols to back-analyses of a series of three well-documented seismic performance field case histories.

The three field performance case histories were (1) seismic site response and performance of the Port Island vertical strong motion array in the 1995 Kobe, Japan earthquake, (2) the performance of the Lower San Fernando Dam during the 1971 San Fernando earthquake (a large deformations or flow failure case history), and (3) the performance of the Upper San Fernando dam (a moderate deformations case history) during the 1971 San Fernando earthquake.

Approaches and implementation protocols for the current studies included (1) evaluating different modeling schemes, (2) performing seismic deformation analyses with different numerical modeling schemes, (3) identifying the accuracy and reliability of different modeling schemes, and their advantages and limitations, based on three well documented case histories, (4) identifying advantages and limitations of continuum-based numerical modeling schemes in predicting deformations in embankment dams, and (5) developing improved analytical approaches to improve performance of seismic deformation modeling for forward analyses.

The lessons learned from the NDA are important. A careful implementation of the different concepts, relationships, and models successfully predicted the performance of both the moderate deformations observed in the Upper San Fernando Dam, and the large deformations or flow failure observed in the Lower San Fernando Dam in the 1971 San Fernando earthquake. Six out of nine NDA performed for the USFD successfully predicted magnitudes and principal mechanisms of this moderate deformations case history. Four out of six NDA performed for the LSFD successfully predicted magnitudes and mechanisms of this large deformations or flow failure case history.

Lessons learned from evaluation of the current State of Practice regarding seismic deformation analyses of embankment dams subject to liquefaction are important. These lessons were developed based on insights from different NDA performed in the current studies and also considering the current State of Practice guidance and protocols.

The back-analyses in the current studies demonstrated an ability to produce very good engineering “predictions” of both observed mechanisms of displacements and distress, as well as magnitudes of deformations and displacements.

Accomplishing this appears to require the following:

1. Suitable analytical or constitutive models.

2. Calibration of these models with respect to cyclic (seismic) pore pressure generation with suitable liquefaction triggering relationships, including both Kα and Kσ relationships.

3. Use of suitable post-liquefaction residual strength (Sr) relationships.

4. Suitable procedures and protocols for transition to Sr behaviors in potentially liquefiable soils.

5. Suitable treatment of potential cyclic softening, and strain softening, behaviors in sensitive clayey soils.

6. Suitable characterization of geometry and stratigraphy, and suitable evaluation of material properties and behaviors.

7. Suitable development and application of appropriate seismic “input” motions.

8. Appropriate evaluation and interpretation of the analysis results, with an understanding of the models and relationships employed, and also the intrinsic limitations of the continuum analysis methods employed with regard to accurate analyses of very large deformations and displacements.

9. And engineering judgment.

Recent improvements in seismological source modeling, analysis of travel path effects, and characterization of local site effects on strong shaking have led to significant advances in both code-based and more advanced procedures for evaluating seismic demand for structural design. A missing link, however, has been an improved and empirically verified treatment of soil-structure interaction (SSI) effects on both the strong motions transmitted to structures and the structural response to these motions. This paper describes analysis procedures and system identification techniques for evaluating inertial SSI effects on seismic structural response. The analysis procedures are similar to provisions in some building codes but incorporate more rationally the influence of site conditions and the foundation embedment, flexibility, and shape on foundation impedance. Implementation of analysis procedures and system identification techniques is illustrated using a building shaken during the 1994 Northridge earthquake. The analysis procedures predict the observed SSI effects accurately. A companion paper applies these analyses to empirically evaluate SSI effects using available strong motion data from a broad range of sites and then develops general conclusions regarding SSI effects on seismic structural excitation and response.

System identification analyses are used to evaluate soil-structure interaction effects for 77 strong motion data sets at 57 building sites that encompass a wide range of structural and geotechnical conditions. Kinematic interaction effects on the "input" motion at the bases of structures are found to be relatively modest in many cases, whereas inertial interaction effects on the structural response to these motions can be significant. To quantify inertial interaction effects, fixed- and flexible-base modal vibration parameters are used to evaluate first-mode period lengthening ratios T-tilde /T and foundation damping factors zeta-tilde0. The response of some structures is dominated by inertial interaction (e.g., T-tilde /T [approximate] 4, zeta-tilde0 [approximate] 30%), whereas others undergo negligible soil-structure interaction (e.g., T-tilde /T [approximate] 1, zeta-tilde0 [approximate] 0). Simplified analytical formulations described in the companion paper by Stewart et al. are used to predict inertial interaction effects. The predictions are found to be reasonably accurate relative to empirical results, with some limitations for deeply embedded and long-period structures. A collective examination of the empirical and predicted results reveals a pronounced influence of structure-to-soil stiffness ratio on inertial interaction, as well as secondary influences from structure aspect ratio and foundation embedment, type, shape, and flexibility.

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.

This paper presents a complete methodology for both probabilistic and deterministic assessment of seismic soil liquefaction triggering potential based on the cone penetration test (CPT). A comprehensive worldwide set of CPT-based liquefaction field case histories were compiled and back analyzed, and the data then used to develop probabilistic triggering correlations. Issues investigated in this study include improved normalization of CPT resistance measurements for the influence of effective overburden stress, and adjustment to CPT tip resistance for the potential influence of "thin" liquefiable layers. The effects of soil type and soil character (i.e., "fines" adjustment) for the new correlations are based on a combination of CPT tip and sleeve resistance. To quantify probability for performance-based engineering applications, Bayesian "regression" methods were used, and the uncertainties of all variables comprising both the seismic demand and the liquefaction resistance were estimated and included in the analysis. The resulting correlations were developed using a Bayesian framework and are presented in both probabilistic and deterministic formats. The results are compared to previous probabilistic and deterministic correlations.