Tài liệu Geo risk 2017 reliability based design and code developments

d from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all right GSP 283 Selected Papers from the Proceedings of Geo-Risk 2017 Geo-Risk 2017 Reliability-Based Design and Code Developments Edited by Jinsong Huang, Ph.D. Gordon A. Fenton, Ph.D., P.Eng. Limin Zhang, Ph.D. D. V. Griffiths, Ph.D., P.E., D.GE Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. GEOTECHNICAL SPECIAL PUBLICATION NO. 283 GEO-RISK 2017 RELIABILITY-BASED DESIGN AND CODE DEVELOPMENTS SELECTED PAPERS FROM SESSIONS OF GEO-RISK 2017 June 4–7, 2017 Denver, Colorado SPONSORED BY Geo-Institute of the American Society of Civil Engineers EDITED BY Jinsong Huang, Ph.D. Gordon A. Fenton, Ph.D., P.Eng. Limin Zhang, Ph.D. D. V. Griffiths, Ph.D., P.E., D.GE Published by the American Society of Civil Engineers Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. Published by American Society of Civil Engineers 1801 Alexander Bell Drive Reston, Virginia, 20191-4382 www.asce.org/publications | ascelibrary.org Any statements expressed in these materials are those of the individual authors and do not necessarily represent the views of ASCE, which takes no responsibility for any statement made herein. No reference made in this publication to any specific method, product, process, or service constitutes or implies an endorsement, recommendation, or warranty thereof by ASCE. The materials are for general information only and do not represent a standard of ASCE, nor are they intended as a reference in purchase specifications, contracts, regulations, statutes, or any other legal document. 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Errata: Errata, if any, can be found at https://doi.org/10.1061/9780784480700 Copyright © 2017 by the American Society of Civil Engineers. All Rights Reserved. ISBN 978-0-7844-8070-0 (PDF) Manufactured in the United States of America. Geo-Risk 2017 GSP 283 iii Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. Preface Interest and use of probabilistic methods and risk assessment tools in geotechnical engineering has grown rapidly in recent years. The natural variability of soil and rock properties, combined with a frequent lack of high quality site data, makes a probabilistic approach to geotechnical design a logical and scientific way of managing both technical and economic risk. The burgeoning field of geotechnical risk assessment is evidenced by numerous publications, textbooks, dedicated journals and sessions at general geotechnical conferences. Risk assessments are increasingly becoming a requirement in many large engineering construction projects. Probabilistic methods are also recognized in design codes as a way of delivering reasonable load and resistance factors (LRFD) to target allowable risk levels in geotechnical design. This Geotechnical Special Publication (GSP), coming out of the Geo-Risk 2017 specialty conference held in Denver, Colorado from June 4-7, 2017, presents contributions in sessions: 1) Reliability- and RiskBased Code Developments, 2) Probabilistic Methods and Reliability Analysis, 3) Performance-Based Liquefaction Assessment and Mitigation, 4) Probabilistic Performance and Resilience Assessment, and 5) Load and Resistance Factor Design (LRFD) Developments and Applications. These contributions to the use of reliability based design methodologies and to reliability based code developments in geotechnical practice are very timely, and will provide a valuable and lasting reference for practitioners and academics alike. The editors would like to thank all of the members of ASCE Geo Institute’s Technical Committee on Risk Assessment and Management and the Engineering Practice of Risk Assessment and Management Committee (TC304) of the International Society of Soil Mechanics and Geotechnical Engineering (ISSMGE) for their ongoing support. All the papers in this GSP went through a rigorous review process. The contributions of the reviewers are much appreciated. The Editors Jinsong Huang, Ph.D., M.ASCE, University of Newcastle, NSW, Australia Gordon A. Fenton, Ph.D., P.Eng., FEIC, FCAE, M.ASCE, Dalhousie University, Halifax, Canada Limin Zhang, Ph.D., F.ASCE, Hong Kong University of Science and Technology, PR China D.V. Griffiths, Ph.D., P.E., D.GE, F.ASCE, Colorado School of Mines, Golden, CO, USA © ASCE Geo-Risk 2017 GSP 283 iv Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. Acknowledgments The following individuals deserve special acknowledgment and recognition for their efforts in making this conference a success • • • • • • Conference Chair: D.V. Griffiths, Colorado School of Mines, Golden, Colorado, USA Conference Co-Chair: Gordon A. Fenton, Dalhousie University, Halifax, Canada Technical Program Chair: Jinsong Huang, University of Newcastle, NSW, Australia Short-Courses: Limin Zhang, Hong Kong University of Science and Technology Student Program co-Chairs: Zhe Luo, University of Akron; Jack Montgomery, Auburn University Sponsorships and Exhibits Chair: Armin Stuedlein, Oregon State University The Editors greatly appreciate the work of Ms. Helen Cook, Ms. Leanne Shroeder, Ms. Brandi Steeves, and Mr. Drew Caracciolo of the ASCE Geo-Institute for their administration of many important conference organizational issues, including management of the on-line paper submissions, the conference web site and sponsorship. © ASCE Geo-Risk 2017 GSP 283 v Contents Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. Advances in Geotechnical Reliability-Based Design Calculation of Equivalent Number of Uniform Cycles as Basis for Magnitude Scaling Effects in Liquefaction Risk Models ........................................ 1 Anthony Dombrowski, Lisa Star, and Luis G. Arboleda-Monsalve Effects of Small Variability of Soil Density on the Consequences of Liquefaction ................................................................................. 11 Mohamed A. ElGhoraiby, Majid T. Manzari, and Samer Hamdar Numerical Evaluation of Fragility Curves for Earthquake-Liquefaction-Induced Settlements of an Embankment ................... 21 C. Khalil, I. Rapti, and F. Lopez-Caballero Performance Comparison of Probabilistic and Deterministic Liquefaction Triggering Models for Damage Assessment in 23 Global Earthquakes .............. 31 Brett W. Maurer, Russell A. Green, Sjoerd van Ballegooy, Brendon A. Bradley, and Sneha Upadhyaya Regional Liquefaction Mapping Accounting for Multiscale Spatial Variability of Soil Parameters with Geological Constraints................................. 43 Chaofeng Wang, Qiushi Chen, and C. Hsein Juang Response of Fena Dam to the 1993 Guam Earthquake......................................... 54 Lelio H. Mejia Riverine Levee Upgrades against Liquefaction and Seismic Impact with Double Sheet Pile Walls and Deep Soil Cement Mix Columns ............................ 67 Takefumi Takuma Site Response in Liquefiable Layered Deposits Considering Spatial Variability in Hydraulic Conductivity .................................................................... 76 Raniero Beber and Shideh Dashti A Practical HLRF Algorithm for Slope Reliability Analysis................................ 86 Jian Ji and Jayantha Kodikara Application of Metamodelling Techniques in the Context of Geotechnical Reliability-Based Analysis........................................................................................ 99 Sónia H. Marques © ASCE Geo-Risk 2017 GSP 283 Application of Quasi-Newton Approximation-Based SORM for System Reliability Analysis of a Layered Soil Slope ......................................................... 111 Peng Zeng, Rafael Jimenez, Tianbin Li, Yu Chen, and Xianda Feng Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. Auxiliary Random Finite Element Method for Risk Assessment of 3-D Slope ......................................................................................................................... 120 Te Xiao, Dian-Qing Li, Zi-Jun Cao, Siu-Kui Au, and Xiao-Song Tang Investigating the Influence of Conditional Simulation on Small-Probability Failure Events Using Subset Simulation............................................................... 130 Bram van den Eijnden, Michael A. Hicks, and Philip J. Vardon Methods for Probabilistic Seismic Levee System Reliability Analysis .............. 140 Dong Youp Kwak, Ruben Jongejan, Paolo Zimmaro, Scott J. Brandenberg, and Jonathan P. Stewart Model Uncertainties for the Static Design of Square Foundations on Sand under Axial Compression ............................................................................. 151 Chong Tang, Kok-Kwang Phoon, and Sami O. Akbas Serviceability Limit State Reliability Analysis of Perniö Railway Embankment ........................................................................................................... 161 Monica S. Löfman and Leena K. Korkiala-Tanttu Assessing the Performance of Shield Tunnels Due to Corrosion Using Bayesian MCMC ..................................................................................................... 172 Zhongkai Huang, Dongmei Zhang, and Hongwei Huang Case Study: Excavation Adjacent to High Pressure Natural Gas Transmission Pipelines—A Risk Management Approach .................................. 184 Maria J. Lobo, Scott Newhouse, and Wayne R. Bergstrom Closed Cavity Thin-Wall Components Design for Prefabricated Underground Subway Structures ......................................................................... 194 Xiuren Yang and Yuzhen Han Geotechnical Engineering Challenges in the Path to Resilient Infrastructure .......................................................................................................... 206 Sissy Nikolaou, Nonika Antonaki, Rallis Kourkoulis, Fani Gelagoti, Irene Georgiou, and George Gazetas Interaction of Performance and Construction Risk While Testing Runway Subgrade Using Non-Destructive Methods .......................................................... 216 Kevin Foye and Alvaro Ulloa © ASCE vi Geo-Risk 2017 GSP 283 Parametric Study on Slope Stability Using Recycled Plastic Pin ....................... 226 Mohammad Sadik Khan, Sahadat Hossain, Asif Ahmed, Kelli Greenwood, and Aya Shishani Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. Probabilistic Assessment and Prediction of Shield Tunnel Performance ......... 237 Y. J. Zhang, D. M. Zhang, and H. W. Huang Resilience Analysis of Metro Networks: A Case Study of Shanghai Metro Network ................................................................................................................... 247 Fei Du, Hongwei Huang, Dongming Zhang, and Fan Zhang Selecting Minimum Factors of Safety for 3D Slope Stability Analyses ............. 259 T. D. Stark and D. G. Ruffing Load and Resistance Factor Design (LRFD) Developments and Applications Design of Laterally Loaded Piles—Limits of Limit State Design?..................... 267 Kerstin Lesny Development of Reliability Based Design and Acceptance Protocol for Pile Foundations in Arkansas ................................................................................ 277 Joseph Jabo Evaluation of CALTRANS Design Methods for Steel Pipe Piles ....................... 287 Yujie Hu, Xinbao Yu, and Murad Abu-Farsakh From ASD to Reliability Based LRFD of Geotechnical Structures: Learning from Pioneers and Experts through Videos and Webinars ............... 296 Jiliang Li and Masoud Mojtahed Recent Development of Load and Resistance Factor Design (LRFD) for Driven Piles on Soft Rock....................................................................................... 307 Kam W. Ng and Todd Sullivan Selecting the Right Foundation for Energy Delivery Structures: What Are the Challenges and How Can They Be Overcome? .............................. 317 Haijian Shi and Richard Steeg Site-Specific Geotechnical Resistance Factors for a Large Industrial Project in Canada ................................................................................................... 329 Peter Thomson, Dennis Becker, Gennaro Esposito, and Jim J. Wright Use of Monte Carlo Analysis to Optimize the Calculated Resistance of Driven Micropiles ................................................................................................... 341 Roberto Valentino and Davide Stevanoni © ASCE vii Geo-Risk 2017 GSP 283 viii Reliability- and Risk-Based Code Developments A Simple Reliability-Based Procedure for Seismic Geotechnical Design .......... 352 Vincenzo Pane, Alessia Vecchietti, and Manuela Cecconi Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. An Analytical Approach of Geotechnical Reliability-Based Design and Its Application ......................................................................................................... 364 Wenjun Dong Calibration of Safety Factors for Piping Failure Mechanism in Levees ........... 374 Ana Teixeira, Karolina Wojciechowska, Wouter L. A. ter Horst, and Marcel Bottema Challenges in Applying Fixed Partial Factors to Rock Engineering Design ..... 384 William Bjureland, Johan Spross, Fredrik Johansson, Anders Prästings, and Stefan Larsson Cost-Effective Design of Long Spatially Variable Soil Slopes Using Conditional Simulation .......................................................................................... 394 Yajun Li, Michael A. Hicks, and Philip J. Vardon Design Optimization of Piled-Raft Foundation for Tall Wind Turbine on Clayey Soil ............................................................................................................... 403 Shweta Shrestha, Nadarajah Ravichandran, and Parishad Rahbari Discussion on Imprecise Probabilistic Approaches Applied to the Eurocode 7 Partial Factor Design ......................................................................... 413 Sónia H. Marques Discussion on Robustness in the Context of Eurocode 7 Partial Factor Design ....................................................................................................................... 425 Sónia H. Marques Evaluation of the Uncertainties Related to the Geotechnical Design Method and Its Consideration in Reliability Based Design ................................ 435 Kerstin Lesny, Sami Akbas, Witold Bogusz, Sébastien Burlon, Giovanna Vessia, and Limin Zhang Impact of Resistance Distribution Selection on Foundation Reliability in Consideration of Lower-Bound Limits ................................................................. 445 Seth C. Reddy and Armin W. Stuedlein Insights from Reliability-Based Design in Geotechnical Engineering ............... 459 B. K. Low and K. K. Phoon Probabilistic Design of Slopes in Normally Consolidated Clays ........................ 471 Desheng Zhu, D. V. Griffiths, Jinsong Huang, and Gordon A. Fenton © ASCE Geo-Risk 2017 GSP 283 Reliability Analysis of Foundation Settlement in Nigeria Based on Standard Penetration Test Results........................................................................ 480 Salahudeen A. Bunyamin, Ijimdiya S. Thomas, Eberemu O. Adrian, and Osinubi J. Kolawole Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. Reliability Updating with Survival Information for Dike Slope Stability Using Fragility Curves ........................................................................................... 494 Timo Schweckendiek, Mark G. van der Krogt, Ana Teixeira, Wim Kanning, Rob Brinkman, and Katerina Rippi Reliability-Based Performance Assessment of Bioreactor Landfills Using Coupled Hydro-Bio-Mechanical Framework ...................................................... 504 Girish Kumar and Krishna R. Reddy Revision of “The Technical Standard for Port and Harbor Structures” Based on LRFD ....................................................................................................... 514 Masahiro Takenobu, Masafumi Miyata, Yusuke Honjo, Yu Otake, Takehiko Sato, and Satoshi Nishioka Risk-Based Approach in Geotechnical Design ..................................................... 524 Ramanujachari Kannan Search for the Worst-Case Correlation Length in the Bearing Capacity Probability of Failure Analyses ............................................................................. 534 W. Puła, J. M. Pieczyńska-Kozłowska, and M. Chwała Seismic Earth Pressure Reliability Analysis ........................................................ 545 Robb Eric S. Moss Stochastic Analysis of Levee Stability Subject to Variable Seepage Conditions ................................................................................................................ 554 Robert Lanzafame, Henry Teng, and Nicholas Sitar © ASCE ix Geo-Risk 2017 GSP 283 Calculation of Equivalent Number of Uniform Cycles as Basis for Magnitude Scaling Effects in Liquefaction Risk Models Anthony Dombrowski, S.M.ASCE1; Lisa Star, Ph.D., M.ASCE2; and Luis G. ArboledaMonsalve, Ph.D., M.ASCE3 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. 1 Graduate Research Assistant, Dept. of Civil Engineering and Construction Engineering Management, California State Univ., Long Beach, CA 90840. E-mail: [email protected] 2 Assistant Professor, Dept. of Civil Engineering and Construction Engineering Management, California State Univ., Long Beach, CA 90840. E-mail: [email protected] 3 Assistant Professor, Dept. of Civil Engineering and Construction Engineering Management, California State Univ., Long Beach, CA 90840. E-mail: [email protected] Abstract The seismic demand imposed by a ground motion is related to its amplitude and duration, where greater demand placed on the soil increases the probability that liquefaction is triggered and that its effects will be damaging. Historically, the seismic demand imposed by an arbitrary ground motion was quantified by describing a uniform series of shear stress cycles that caused an equivalent likelihood of liquefaction. The amplitude of the ground motion is usually represented by the Cyclic Stress Ratio (CSR), and the effects of the duration of ground shaking have usually been represented through an equivalent number of uniform amplitude cycles (N) or through the related magnitude scaling factor (MSF). We review methods used to determine N, as well as important factors known to influence the evaluation of N such as: the weight given to cycles of different amplitudes through the cycle sequence, non-zero crossings, multidirectional shaking, and soil and site conditions. Discrepancies between the current cycle counting methods and the known influential factors are identified. A cycle counting routine is proposed, and we apply it to a small suit of records in the NGA-West2 ground motion database with results presented. INTRODUCTION The development of seismic soil liquefaction triggering and consequence models depend on measures of seismic demand. In laboratory testing, quantifying the demand of cyclic loads placed on soils has been achieved through a measure of the amplitude of the loading, the cyclic stress ratio (CSR), and a measure of the number of loading cycles. When evaluating the loading demands from an arbitrary ground motion, the quantification of amplitude and duration becomes necessarily more complicated. Seed et. al (1975) defined the cyclic stress ratio for an arbitrary acceleration record and developed the Cyclic Resistance Ratio (CRR), defined as the CSR required to initiate liquefaction of an earthquake with a Magnitude (M) equal to 7.5. The factor of safety against liquefaction (FSL) is defined as: © ASCE 1 Geo-Risk 2017 GSP 283 2 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. FS = . ∗ (1) where MSF is the magnitude scaling factor, accounting for the decreased resistance to liquefaction for large magnitude earthquakes with large numbers of cycles, and the increased resistance to liquefaction for smaller magnitude, shorter duration, earthquakes. A number of studies have investigated magnitude scaling factors based directly on empirical liquefaction data from case histories. Ambraseys (1988), Andrus and Stokoe (1997), Youd and Noble (1997), and Cetin et al. (2004) assessed case histories where liquefaction was either evident or absent, the latter two using probabilistic methods, in order to regress a relationship between MSF and Mw. An alternative or complimentary way to quantify the duration of an arbitrary seismic load is through the equivalent number of uniform stress cycles (N) concept. Arango (1996) used energy principles to analyze liquefaction triggering at distant sites, and suggested that scaling factors based on N had less scatter than scaling factors based on earthquake magnitude. There have been a large number of procedures proposed to calculate N, and one of the most important factors being how to weigh cycles with different amplitudes. Seed et al. (1975) proposed that N could be evaluated for an arbitrary ground motion using weighting factors based on the Palmgren–Miner (P–M) cumulative damage hypothesis. Magnitude scaling factors proposed and updated by Seed et al. (1975), Seed and Idriss (1982), Idriss (1997), Idriss (1999), Idriss and Boulanger (2008) and Boulanger and Idriss (2014) were based on laboratory derived relationships between scaling factors and number of cycles. N values were correlated with earthquake magnitude to develop the final proposed scaling factors. Idriss and Boulanger (2008) and Boulanger and Idriss (2014) showed that the magnitude scaling factors were dependent not just on magnitude, but also on plasticity and soil conditions, with the relationship between the scaling factor and magnitude being stronger for clean sands compared to clayey soils and stronger for soils with a high penetration resistance compared to low. Liu et al. (2001) used the results of Arango (1996) along with updated laboratory testing results in order to develop updated recommendations for determining N from an arbitrary ground motion. Liu et al. (2001) developed scaling factors, and additionally used random effects regression analysis to develop empirical prediction equations for N, based on magnitude, site distance, site conditions and rupture directivity effects. Hancock and Bommer (2005) reviewed the large number of different procedures that have been proposed for determining N from an arbitrary ground motion, and Stafford and Bommer (2009) presented empirical prediction equations for N, based on magnitude, distance, and site classification. They found that the counting method used to determine N has an effect on both the predicted value and the variance. Cetin and Bilge (2012a) showed that scaling factors are sensitive to the definition of the onset of liquefaction, as well as soil parameters. The objective of this paper is to review methods used to determine the equivalent number of uniform cycles and identify important factors that affect the evaluation. We apply a preliminary cycle counting routine accounting for these influence factors to small suit of records in the NGA-West 2 ground motion database and study the results. © ASCE Geo-Risk 2017 GSP 283 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. WEIGHTING FACTOR CURVES Equivalent uniform cycle counting methods for liquefaction analysis have their basis in material fatigue evaluation and the Palmgren-Miner (P-M) (Pamgren, 1924, and Miner, 1945) cumulative damage hypothesis. P-M damage analysis assumes linear damage accumulation. This allows the development of direct relationships between the damage (or progress towards liquefaction) caused by earthquake cycles of different amplitudes. Weighting factors can be used in order to develop a weighted sum of the cycles in a ground motion. Soil that is subjected to loading with a uniform peak cyclic shear stress amplitude (τcyc),will liquefy after a number of cycles are applied (Nliq). τcyc is found to be normalizable by the vertical effective stress prior to shaking, to provide the cyclic stress ratio, CSR. The test is repeated at different levels of stress with different N values being recorded. The tests are then compiled and a complete CSR-Nliq curve is created. By normalizing CSR by the CSR at a reference level, which is usually taken to be 65% of the CSR where one cycle of loading will cause liquefaction, and normalizing the number of cycles required to liquefy the soil at that reference level by Nliq, CSR-Nliq curves provide the basis for computing weighting factors. The weighting factors used to calculate N for an arbitrary ground motion as developed by Seed et al. (1975) were based on laboratory test results by De Alba et al. (1976). Idriss (1997) developed updated weighting factor curves based on laboratory tests by Yoshimi et al. (1984). Lui et al. (2001) used both laboratory data and field based data from Arango (1996). All assumed that the relationship between CSR-Nliq is linear in log-log space. Green and Terri (2005) proposed an alternative method for determining weighting factors, using energy dissipation of the soil to account for nonlinear stress-strain behavior of soil subjected to larger amplitude shaking. Researchers have found that the shape of the CSR-Nliq curves depended on a number of soil properties and conditions. Relative density was identified as early as De Alba et al (1975) as a factor. CSR-Nliq curves tend to be steeper for soils with high relative density and flatter for soils with low relative density. Lui et al. (2001) accounted for this by using an average curve for the relative density range of most interest for liquefaction studies, to calculate their laboratory based scaling factors. Boulanger and Idriss (2014) use penetration resistance as a proxy for relative density. Soils subjected to loads that induce strains smaller than the threshold shear strain, do not accumulate damage, or progress towards liquefaction. The threshold shear strain thus plays an import role in determining the location of the fatigue limit (or lower boundary) of the CSR-Nliq curves for a given soil. The threshold shear strain depends on soil plasticity, with a higher threshold for clays versus sands. The location of the fatigue limit of the CSR-Nliq curve also depends on the stress-strain relationship of the soil, which is sensitive to the stiffness and density of the soil. Most cycle counting methods do not explicitly account for the threshold shear strain, although some use a low amplitude cut-off based on the relative cycle amplitude. Laboratory testing by Tatsuoka et al (1986) and Mulilis et al. (1977) indicate that soil fabric has an effect on the CSR-Nliq curve, based on testing of soils with different sample preparation techniques. The average behavior of the soil for different sample preparation methods is generally considered. © ASCE 3 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. Geo-Risk 2017 GSP 283 Boulanger and Idriss (2014) reviewed a variety of laboratory testing studies and found that fines content and plasticity do not have consistent effects on the slope or shape of the CSRNliq curves. The onset of liquefaction has sometimes been defined as the time when the excess pore water pressure ratio, ru, at the end of a cycle is equal to 1.0. However, other definitions of liquefaction onset have been proposed including lower thresholds for ru, and single or double amplitude strain based definitions. Cetin and Bilge (2012a) showed that because of the nonlinear accumulation of liquefaction damage at different CSR levels, whether it is measured through pore pressure or strain, the definition of the onset of liquefaction will change the shape of the CSR-Nliq curve. Boulanger and Idriss (2014) using data from Tatsuoka et al. (1986) showed that the CSR-Nliq curves become particularly nonlinear when using large strain definitions of liquefaction onset. NON-LINEAR LOAD DEPENDENT DAMAGE The P-M hypothesis assumes linear damage accumulation. Damage, or progress towards soil liquefaction, is implicitly assumed to increase linearly as the number of cycles approaches Nliq, conveniently allowing us to define a direct relationship between cycles at different stress levels, through the weighting factors. As shown in Figure 1, laboratory testing indicates that there is a non-linear relationship between the number of loading cycles and residual pore pressure accumulation (e.g. Seed et al, 1975, Polito et al., 2008, Cetin and Bilge, 2012b). Polito et al. (2008) and Cetin and Bilge (2012b) showed that the non-linear relationship varies depending on CSR, relative density, nonplastic fines content, and vertical consolidation stress. Laboratory testing of soils using nonuniform cyclic loading has indicated that the order of cycles with different amplitudes may affect the pore pressure generation. No current liquefaction cycle counting methods account for nonlinear damage accumulation, and thus they cannot account for the load-sequence effects. Figure 1: Laboratory data showing range of pore pressure generation curves (from Cetin and Bilge, 2012b) © ASCE 4 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. Geo-Risk 2017 GSP 283 Although this issue has not been addressed in liquefaction analysis, this has been a recognized problem in the field of metal fatigue. Marco and Starkey (1954) proposed the first non-linear damage theory. As shown in Figure 2, they proposed a power relationship between damage and normalized number of cycles, with different damage curves depending on the applied stress level. This means that, unlike when assuming linear damage accumulation, the order in which cycles of different amplitudes are applied is critical for determining progress towards soil liquefaction. It also means that weighting factors are not static throughout the loading sequence. Some cycle counting methods rearrange cycles or portion of cycles before determining cycle amplitudes, so in the following section we review cycle counting methods that preserve the arrangement of counted cycles. Figure 2: Schematic representation of Marco-Starkey theory (from Fatemi and Yang, 1998) CYCLE COUNTING METHODS There are a variety of different cycle counting methods that have been proposed in order to determine the equivalent number of uniform cycles for use in liquefaction or other fatigue studies. Hancock and Bommer (2005) present an extensive review of these methods. We will focus on two methods. All methods use one of two definitions to identify and quantify loading cycles: either the cycle amplitude or the cycle range. The cycle amplitude is determined by measuring from the origin to the peak or valley. Two peaks are required for one full cycle. The cycle range is defined as the distance from the peak to a valley, or vice versa. One full cycle will have an amplitude equal to half of the range. Peak-counting methods have traditionally been used in liquefaction analysis. These methods work by seeking each peak (or valley) in the data and recording the amplitude. © ASCE 5 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. Geo-Risk 2017 GSP 283 Weighting factors can then be applied for each recorded cycle. There have been various recommendations about how to consider non-zero crossing cycles. A non-zero crossing cycle is a cycle that has a reversal before reaching the origin. Some counting cycle methods will define a cycle as whenever a reversal occurs regardless of if the first cycle reaches zero or not, while other cycle counting methods will define a cycle as whenever a reversal occurs after crossing the zero amplitude. The most common range counting method is known as the rainflow-counting method. Half and full cycles are counted based on ranges from the peak to the valley or valley to the peak. Green and Terri (2005) suggest that a range-counting method is preferred because the range is more closely tied to the shape of stress-strain loops. An additional benefit of the rainflow-counting method is that cycles are accounted for, regardless of zero-crossing. MULTIDIRECTIONAL SHAKING Ground motions are measured using three-directional accelerometer data, but cycle counting procedures are based on examining one set of peaks. The three sets include one in the vertical direction and two in the horizontal direction. Because cycle and range counting methods only work on one load cycle record, all cycle counting procedures require some method to combine the information from the original records. Most liquefaction analysis methods disregard the vertical ground motion. Liu et al. (2001) presented several methods of normalizing and combining the two horizontal ground motions. The geometric mean of the time series is calculated as the square root of the product of the two horizontal acceleration values. This measure has the disadvantage that the results are affected by the original orientation of the accelerometers in the field. This could be overcome by using the 50th percentile period dependent rotated geometric mean of the time series (GMrotD50) presented by Boore et al. (2006). Liu et al. (2001) recommended using a second proposed method, the vector sum of the two components, which is calculated as the square root of the sum of the two horizontal acceleration values squared. Both methods have the disadvantage that the absolute sign of the peaks is lost, disallowing the use of range counting methods. Instead of combining the two horizontal ground motions, Seed et al. (1975) treated each component separately. When determining the weighting factors, a decision then needs to be made about whether to calculate the factors relative to the peak acceleration from each record independently or whether to use the largest peak between both records. Laboratory testing by Ishihara and Yamazaki (1980) indicate that fewer loading cycles are required to liquefy soils subjected to multidirectional loading compared to soils with unidirectional shaking. Seed (1976) showed that the ratio of CSR for multidirectional shaking to CSR for unidirectional shaking with the same Nliq, is about 0.9. Green and Terri (2005) also suggested treating each component separately. In order to be consistent with field based estimations of CSR, they recommend calculating the weighting factors based on the peak of the geometric mean of the two ground components, and using one half of the total number of cycles calculated from evaluating both records. © ASCE 6 Geo-Risk 2017 GSP 283 7 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. PROPOSED METHOD FOR CALCULATION OF EQUIVALENT NUMBER OF UNIFORM CYCLES AND PRELIMINARY RESULTS In the following section we propose a preliminary method for calculating the equivalent number of uniform cycles from an arbitrary ground motion. Initial weighting factors are estimated using a similar method to that presented by Green and Terri (2005) with modulus reduction and damping curves by Darendeli (2001). The weighting factors are normalized by the 50th percentile period dependent rotated geometric mean peak horizontal acceleration based on the two horizontal ground motion components. Cycle counts and stress ranges were determined using the rainflow counting procedure. For each cycle counted, the weighting factor is applied, and then the nonlinear damage accumulation is calculated, after the manner of the Marco-Starkey theory, using nonlinear ru-N relationships by Cetin and Bilge (2012b). Five ground motions used in this study were selected from the PEER NGA-West 2 database (http://peer.berkeley.edu/ngawest2/). For each record, the earthquake moment magnitude (Mw), rupture distance (Rup), and shear wave velocity of top 30 m (Vs30) are given in Table 1. Table 1: Ground Motions used in First Sensitivity Testing Moment Magnitude (Mw) Rrup (km) Vs30 (m/s) Northridge-01-Lakewood (Del Amo Blvd) 6.69 56.91 267.35 Northridge-01-Inglewood (Union Oil) 6.69 42.2 316.02 Whittier Narrows-02 Anahiem (Ball Rd.) 5.27 30.42 269.29 Morgan Hill-Fremont (Mission San Jose) 6.19 31.34 367.57 Landers-Big Bear Lake (Civic Center) 7.28 45.48 430.36 Earthquake NameStation Name Figure 3 shows the equivalent number of uniform cycles calculated using the proposed method superimposed against estimates of N as a function of distance and magnitude from Liu et al. (2001), and Seed et al (1975). The results of this small test database indicate that the current predictions of N are within the same range of results indicated by previous studies. Further studies are required to examine bias © ASCE Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. Geo-Risk 2017 GSP 283 Figure 3: Calculate N results superimposed on predictions from Liu et al. (2001) and Seed et al. (1975), for rd = 0.95 and confining pressure = 150 kPa (Modified from Liu et al., 2001) CONCLUSIONS In liquefaction triggering analysis methods, the effects of the duration of ground shaking have usually been represented through an equivalent number of uniform amplitude cycles (N) or through the related magnitude scaling factor (MSF). The process of converting an irregular ground motion into an equivalent number of uniform cycles has been studied by liquefaction researchers. A number of important factors in the determination of the equivalent number of uniform amplitude cycles are identified and the application of these factors in various methods is considered. Weighting factor curves, used to develop a weighted sum of the cycles in a ground motion, have been found to depend on relative density of the soil, and the definition of the onset of liquefaction, and to a lesser extent on soil fabric and fines content. The selection of a cycle counting method and the method of handling of multidirectional ground motion components should account for the relative merits of available methods. Finally, the effect of non-linear progress toward liquefaction, and the effects load-sequence on the evaluation of N has not been directly addressed in liquefaction literature, but material fatigue studies may provide some guidance. Preliminary results from a new cycle counting method accounting for the above factors was applied to a small suite of ground motions and compared in terms of magnitude and distance to past predictions. © ASCE 8 Geo-Risk 2017 GSP 283 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/04/19. Copyright ASCE. For personal use only; all rights reserved. REFERENCES Ambraseys, N. N. (1988). “Engineering seismology.” Earthquake Eng. Struct. Dyn., 17(1), 1– 105. Andrus, R. D., and Stokoe, K. H., II (1997). “Liquefaction resistance based on shear wave velocity.” Proc., NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Nat. Ctr. For Earthquake Engrg. Res., State Univ. of NY, Buffalo, 89–128. Arango, I. (1996). “Magnitude scaling factors for soil liquefaction evaluations.” J. Geotech. Eng., 122(11), 929–936. Boore, D. M., Watson-Lamprey, J., & Abrahmson, N. A. (2006). Orientation-Independent Measures of Ground Motion. Bulletin of the Seismological Society of America, Vol. 96, No. 4A , 1502-1511. Boulanger, R. W., and Idriss, I. M., (2014) “CPT and SPT Based Liquefaction Triggering Procedures”, Report No. UCD/GGM-14/01. Center for Geotechnical Modeling, Department of Civil and Environmental Engineering, University of California. Davis, California Cetin, K. O. and Bilge, H. T. 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