Tài liệu Geotechnical earthquake engineering and soil dynamics v numerical modeling and soil structure interaction

Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Geotechnical Earthquake Engineering and Soil Dynamics V Numerical Modeling and Soil Structure Interaction GSP 292 Papers from Sessions of Geotechnical Earthquake Engineering and Soil Dynamics V EDITED BY Austin, Texas June 10–13, 2018 Scott J. Brandenberg, Ph.D., P.E. Majid T. Manzari, Ph.D. Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. GEOTECHNICAL SPECIAL PUBLICATION NO. 292 GEOTECHNICAL EARTHQUAKE ENGINEERING AND SOIL DYNAMICS V NUMERICAL MODELING AND SOIL STRUCTURE INTERACTION SELECTED PAPERS FROM SESSIONS OF GEOTECHNICAL EARTHQUAKE ENGINEERING AND SOIL DYNAMICS V June 10–13, 2018 Austin, Texas SPONSORED BY Geo-Institute of the American Society of Civil Engineers EDITED BY Scott J. Brandenberg, Ph.D., P.E. Majid T. Manzari, Ph.D. Published by the American Society of Civil Engineers Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. 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/10.1061/9780784481479 Copyright © 2018 by the American Society of Civil Engineers. All Rights Reserved. ISBN 978-0-7844-8147-9 (PDF) Manufactured in the United States of America. Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 Preface Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. This volume is one of four Geotechnical Special Publications (GSPs) containing papers from the Fifth Geotechnical Earthquake Engineering and Soil Dynamics Conference: (GEESDV) held in Austin, Texas during June 10–13, 2018. The GEESDV is the latest event in a series of highly successful conferences held in Sacramento CA (2008), Seattle WA (1998), Park City UT (1988), and Pasadena CA (1978). The conference is organized by the Earthquake Engineering and Soil Dynamics Technical Committee of the Geo-Institute (G-I) of the American Society of Civil Engineers (ASCE) and brings together practicing geo-professionals, researchers, and students from around the world to share the latest advances, engineering applications, and pedagogical approaches in this discipline. This Geotechnical Special Publication is the outcome of two years of concerted efforts by the conference lead organizers and the members of the “technical program” and “proceedings” committees. All submitted papers were reviewed and accepted by at least two independent peer-reviewers. The final accepted technical papers are organized in the following special publications:     Volume 1: Liquefaction Triggering, Consequences, and Mitigation Volume 2: Seismic Hazard Analysis, Earthquake Ground Motions, and RegionalScale Assessment Volume 3: Numerical Modeling and Soil Structure Interaction Volume 4: Slope Stability and Landslides, Laboratory Testing, and In Situ Testing The Editors would like to express their sincere appreciation to the members of the technical program and proceedings committees as well as the session chairs and reviewers. The Editors, Scott J. Brandenberg, Ph.D., P.E., M.ASCE Majid T. Manzari, Ph.D., M.ASCE Acknowledgments The organizing committee would like to thank the authors, reviewers, session chairs, ASCE staff, and OmniPress staff, without whom this publication would not be possible. GEESDV Conference Program Committee Conference Chair Ellen M. Rathje, Ph.D., P.E., F.ASCE, University of Texas at Austin © ASCE iii Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 Conference Co-Chair Adrian Rodriguez-Marek, Ph.D., M.ASCE, Virginia Tech Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Technical Program Chair Scott J. Brandenberg, Ph.D., P.E., M.ASCE, University of California Los Angeles Proceedings Chair Majid T. Manzari, Ph.D., M.ASCE, George Washington University Technical Program Committee Shideh Dashti, Ph.D, AM.ASCE, University of Colorado at Boulder Ramin Motamed, Ph.D., P.E., M.ASCE, University of Nevada, Reno Scott M. Olson, Ph.D., P.E., M.ASCE, University of Illinois Brady R. Cox, Ph.D., P.E., A.M.ASCE, University of Texas Proceedings Committee Tong Qiu, Ph.D., P.E., M.ASCE, Pennsylvania State University Namasivayam (Sathi) Sathialingam, Ph.D, P.E., G.E., D.GE., F.ASCE, Fugro Consultants, Inc. Mahdi Taiebat, Ph.D., P.E., M.ASCE, University of British Columbia Short Course / Student Programs Co-Chairs Dimitrios Zekkos, Ph.D., P.E., M.ASCE, University of Michigan Christopher E. Hunt, Ph.D., P.E., G.E., M.ASCE, Geosyntec Consultants Student and Younger Member Activities Chair Menzer Pehlivan, Ph.D., P.E., M.ASCE, CH2M Sponsorships and Exhibits Chair Thaleia Travasarou, Ph.D., P.E., G.E., M.ASCE, Consultant GEESDV Topics and Session Chairs Liquefaction Triggering, Consequences, and Mitigation Katerina Ziotopoulou, Ph.D., A.M.ASCE, University of California, Davis Shideh Dashti, Ph.D., A.M.ASCE, University of Colorado at Boulder Brett Maurer, Ph.D., A.M.ASCE, University of Washington Mourad Zeghal, Ph.D., A.M.ASCE, Rensselaer Polytechnic Institute Laurie G. Baise, Ph.D., M.ASCE, Tufts University Kevin W. Franke, Ph.D., P.E., M.ASCE, Brigham Young University Arash Khosravifar, Ph.D., P.E., M.ASCE, Portland State University © ASCE iv Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 Soil Structure Interaction Anne Lemnitzer, Ph.D., A,M.ASCE, University of California, Irvine Armin W. Stuedlein, Ph.D., P.E., M.ASCE, Oregon State University Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Ground Motion and Site Response Dong Youp Kwak, Ph.D., RMS James Kaklamanos, Ph.D., A.M.ASCE, Merrimack College Albert R. Kottke, Ph.D., P.E., M.ASCE, Pacific Gas and Electric Ramin Motamed, Ph.D., P.E., M.ASCE, University of Nevada, Reno Regional Scale Assessment of GeoHazards Qiushi Chen, Ph.D., A.M.ASCE, Clemson University Seismic Hazard Assessment Sebastiano Foti, Ph.D., Politecnico di Torino Recent Advances In Situ Site Characterization Thaleia Travasarou, Ph.D., G.E., M.ASCE, Fugro Consultants, Inc. Seismic Slope Stability and Landslides Jennifer Donahue, Ph.D., P.E., M.ASCE, JL Donahue Engineering, Inc. Jack Montgomery, Ph.D., A.M.ASCE, Auburn University Recent Advances in Numerical Modeling Giuseppe Buscarnera, Ph.D., Aff.M.ASCE, Northwestern University Mahdi Taiebat, Ph.D., P.Eng, M.ASCE, University of British Columbia Majid T. Manzari, Ph.D., M.ASCE, The George Washington University Usama S. El Shamy, Ph.D., P.E., M.ASCE, Southern Methodist University Recent Advances in Laboratory Testing Inthuorn Sasanakul, Ph.D., P.E., M.ASCE, University of South Carolina Brad P. Wham, Ph.D., A.M.ASCE, University of Colorado Scott M. Olson, Ph.D., P.E., M.ASCE, University of Illinois, Urbana Mark Stringer, Ph.D., M.ASCE, University of Canterbury © ASCE v Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 Contents Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Plenary Topics On the Modeling of Soils after the Onset of Liquefaction ....................................................... 1 Pedro Arduino Numerical Modeling A Constitutive Model Controlling Damping for 2D and 3D Site Response .......................... 17 Samuel Yniesta and Scott J. Brandenberg A Modified Uniaxial Bouc-Wen Model for the Simulation of Transverse Lateral Pipe-Cohesionless Soil Interaction ............................................................................ 25 Kien T. Nguyen and Domniki Asimaki A Practical 3D Bounding Surface Plastic Sand Model for Geotechnical Earthquake Engineering Application..................................................................................... 37 Zhao Cheng Analysis of the Contractive Behavior of Soil Deposits Subjected to Biaxial Excitation................................................................................................................................. 48 Vicente Mercado, Mourad Zeghal, and Omar El-Shafee Assessment of Soil-Structure-Fluid Interaction of a Digester Tank Complex in Liquefiable Soils under Earthquake Loadings .................................................................. 57 Deepak Rayamajhi, Dario Rosidi, Michele McHenry, and Nathan M. Wallace Assessment of Vulnerability Curves of Pircas over Slopes by the Discrete Element Method (DEM)—A Case Study in Carabayllo, Peru .............................................. 66 Criss Zanelli, Sandra Santa Cruz, Noelia Valderrama, and Dominique Daudon Capabilities and Limitations of Different Numerical Tools in Capturing Seismic Site Performance in a Layered Liquefiable Site ....................................................... 79 Jenny Ramirez, Andres R. Barrero, Long Chen, Alborz Ghofrani, Shideh Dashti, Mahdi Taiebat, and Pedro Arduino Cyclic Multi-Directional Response of Clay Deposits: Evaluating a Constitutive Model .................................................................................................................. 89 H. Nouri, C. Rutherford, and G. Biscontin Cyclic Shearing Response of Granular Material in the Semi-Fluidized Regime ................................................................................................................................... 100 Andres R. Barrero, William Oquendo, Mahdi Taiebat, and Arcesio Lizcano © ASCE vi Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 Data Analytics Applied to a Microscale Simulation Model of Soil Liquefaction........................................................................................................................... 108 Usama El Shamy and Michael Hahsler Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Discrepancy Metrics and Sensitivity Analysis of Dynamic Soil Response .......................... 115 Mourad Zeghal, Nithyagopal Goswami, Majid Manzari, and Bruce Kutter Discrete Element Simulation of Soil Liquefaction: Fabric Evolution, Large Deformation, and Multi-Directional Loading ........................................................... 123 Gang Wang, Duruo Huang, and Jiangtao Wei Effectiveness of Ground Improvement in Sands upon Seismic Loading Using Non-Linear Soil Model ............................................................................................... 133 Sparsha Nagula and Jürgen Grabe Energy Dissipation in Soil Structure Interaction System .................................................... 142 Han Yang, Yuan Feng, Sumeet K. Sinha, Hexiang Wang, and Boris Jeremić Evaluation of Liquefaction Case Histories from the 2010–2011 Canterbury Earthquakes Using Advanced Effective Stress Analysis ..................................................... 152 Nikolaos Ntritsos, Misko Cubrinovski, and Aimee Rhodes Evaluation of the ISA-Hypoplasticity Constitutive Model for the LEAP-2017 Project ............................................................................................................... 165 William Fuentes, Vicente Mercado, and Carlos Lascarro Fragility Assessment of Transportation Infrastructure Systems Subjected to Earthquakes .......................................................................................................................... 174 Sotiris Argyroudis, Stergios Mitoulis, Amir M. Kaynia, and Mike G. Winter Fragility Based Seismic Performance Assessment of Buried Structures ............................ 184 Wenyang Zhang, Abdoul R Ghotbi, Elnaz E. Seylabi, Payman K. Tehrani, Alp Karakoc, Richard Gash, and Ertugrul Taciroglu General Equation and Simplified Model to Predict Damping Properties of Clays Using Soil Plasticity ..................................................................................................... 193 Behzad Amir-Faryar and M. Sherif Aggour Implementation, Validation, and Application of PM4Sand Model in PLAXIS .................. 200 Gregor Vilhar, Anita Laera, Federico Foria, Abhishek Gupta, and Ronald B. J. Brinkgreve Modeling Delayed Flow Liquefaction Initiation after Cyclic Loading ................................ 212 Zhenhao Shi, Ferdinando Marinelli, and Giuseppe Buscarnera Numerical Simulation of the Seismic Response of Gravity Retaining Walls ...................... 221 Usama El Shamy and Aliaksei Patsevich © ASCE vii Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Partially Saturated Soil: Formulation through Generalized Fluid Vector and Validation with Leaking Test ........................................................................................ 228 S. Iai Prediction of Three-Dimensional Dynamic Soil-Pile Group Interaction in Layered Soil by Boundary Element Analysis and Seismic Cone Penetration Tests ....................................................................................................................................... 237 Zhiyan Jiang and Jeramy C. Ashlock Selective Filtering of Numerical Noise in Liquefiable Site Response Analyses................... 248 Yannis Z. Tsiapas and George D. Bouckovalas Simplified Method for Nonlinear Soil-Pile Interactions in Two Dimensional Effective Stress Analysis ....................................................................................................... 258 Y. Tamari, O. Ozutsumi, K. Ichii, and S. Iai Simplified Soil-Pile Interaction Modeling under Impact Loading ...................................... 269 Mojdeh Asadollahi Pajouh, Jennifer Schmidt, Robert W. Bielenberg, John D. Reid, and Ronald K. Faller SSI versus SSSI for Adjacent Pump Stations in San Francisco .......................................... 281 Kirk C. Ellison, Armin Masroor, Sue Chen, William Liang, Tina Kwan, Bessie Tam, and Martin Walker Soil Structure Interaction A Nonlinear Model Inversion to Estimate Dynamic Soil Stiffness of Building Structures ............................................................................................................... 293 Hamed Ebrahimian, S. Farid Ghahari, Domniki Asimaki, and Ertugrul Taciroglu A Quasi-Static Displacement-Based Approximation of Seismic Earth Pressures on Rigid Walls ...................................................................................................... 300 Joaquin Garcia-Suarez and Domniki Asimaki Calibration of a New Pressure Sensor and Application to a Dynamic Soil Structure Interaction Study .................................................................................................. 312 Anne Lemnitzer and Lohrasb Keykhosropour Centrifuge Modeling to Evaluate Kinematic Soil-Foundation-Structure Interaction ............................................................................................................................. 321 Amin Borghei and Majid Ghayoomi Comparison of Experimental and Computational Snap-Back Responses of Driven Steel Tube Piles in Stiff Clay .................................................................................... 330 M. J. Pender, L. S. Hogan, and L. M. Wotherspoon © ASCE viii Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 Comparison of Pseudo-Static Limit Equilibrium and Elastic Wave Equation Analyses of Dynamic Earth Pressures on Retaining Structures ......................................... 340 Nathaniel Wagner and Nicholas Sitar Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Dynamic Stresses in Foundation Soils beneath Strip Footings ............................................ 351 Bahareh Heidarzadeh, Jonathan P. Stewart, and George Mylonakis Evaluation of the Influence of Frequency Characteristics of Input Earthquake on Seismic Coefficient for Gravity Quay Wall via Dynamic Centrifuge Tests..................................................................................................... 361 Moon-Gyo Lee, Jeong-Gon Ha, Heon-Joon Park, and Dong-Soo Kim Factors Affecting the Torsional Response of Deep Foundations ......................................... 368 Qiang Li and Armin W. Stuedlein Field Experiment of Rocking Shallow Foundation on Cohesive Soil Subjected to Lateral Cyclic Loads ........................................................................................ 379 Keshab Sharma and Lijun Deng Inertial and Liquefaction-Induced Kinematic Demands on a Pile-Supported Wharf: Physical Modeling .......................................................................... 388 Milad Souri, Arash Khosravifar, Stephen E. Dickenson, Scott Schlechter, and Nason McCullough Interactive Web Application for Computing Seismic Earth Pressure ................................ 398 Nikolaos P. Machairas, Magued G. Iskander, and Mehdi Omidvar Investigating Implications of Induced Seismicity on Wind Turbine Foundations ........................................................................................................................... 407 Eric Ntambakwa, Ian Prowell, and Carlos Guzman Investigation of Rocking Mechanism of Shallow Foundation via Centrifuge Tests .................................................................................................................... 416 Kil-Wan Ko, Jeong-Gon Ha, Heon-Joon Park, and Dong-Soo Kim Key Parameters for Predicting Residual Tilt of Shallow-Founded Structures Due to Liquefaction............................................................................................. 425 Zach Bullock, Zana Karimi, Shideh Dashti, Abbie Liel, and Keith Porter Pile Driving Vibration Attenuation Relationships: Overview and Calibration Using Field Measurements ................................................................................ 435 Athina Grizi, Adda Athanasopoulos-Zekkos, and Richard D. Woods Response of Hybrid Monopile-Friction Wheel Foundation under Earthquake Loading Using Centrifuge Modelling .............................................................. 445 Xuefei Wang, Xiangwu Zeng, and Xinyao Li © ASCE ix Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Seismic Bearing Capacity of a Strip Footing Situated on Soil Slope Using a Non-Associated Flow Rule in Lower Bound Limit Analysis .................................. 454 K. Halder, D. Chakraborty, and S. K. Dash Uplift Analysis of an Underground Structure in a Liquefiable Soil Subjected to Dynamic Loading ............................................................................................. 464 Priya Beena Sudevan, A. Boominathan, and Subhadeep Banerjee Winkler Stiffness Intensity for Flexible Walls Retaining Inhomogeneous Soil ......................................................................................................................................... 473 Maria Giovanna Durante, Scott J. Brandenberg, Jonathan P. Stewart, and George Mylonakis © ASCE x Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 On the Modeling of Soils after the Onset of Liquefaction Pedro Arduino, Ph.D., M.ASCE1 1 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Dept. of Civil and Environmental Engineering, Univ. of Washington, Seattle, WA 98005. E-mail: [email protected] ABSTRACT Catastrophic infrastructure failures frequently are frequently caused by the dynamic interaction of soil and water. Earthquake induced liquefaction, high-water induced levee failures, bridge scour, and rainstorm-induced slides are all examples of such phenomena involving various time and space scales. In many cases, engineering techniques for predicting onset of failures are available and widely used in practice, but there is a dearth of tools available for more general consideration of post-failure behavior. Modeling behavior up to and beyond the point of failure is complicated by the fact that the overall material response involves complex interactions between solid and liquid phases and transitions from solid behavior to sediment transport. Frameworks designed for use in either solid-only or fluid-only contexts are not capable of tracking the significant phenomena throughout a given event history. The early work of Biot, and subsequent adoption of mixture theories, facilitated the development of coupled finite element applications capable of representing the response of saturated and partially saturated soils. This together with the development of constitutive models capable of representing the contractive and dilative response of soils enhanced the predictive capabilities of liquefaction and lateral spreading in the context of a deforming soil/water domain. However, these advancements are limited to moderately small deformations and situations where the fluid and solid domains coexist in a smeared domain. Advances in experimental work at multiple scales create an opportunity to revisit and expand existing constitutive models to incorporate fabric information at the micro-scale and provide physical data to validate computational models at the macro-scale. Meshless techniques like SPH and MPM help mitigate mesh distortion at large deformation providing suitable techniques for lateral spreading and other phenomena like debris flow where mixing and separation is relevant. This paper reviews a few of these aspects indicating trends, opportunities and challenges, and ventures into the prospects of future liquefaction simulation. THE MULTIPHASE NATURE OF SOILS Geomaterials, in particular soils, consist of assemblages of particles with different sizes and shapes which form a skeleton (porous matrix) whose voids are filled with water or other liquids and air or gas. The word “soil”, therefore, implies a mixture of assorted mineral grains with various fluids (i.e. a multi-phase material). The study of this type of material is of great importance in applied civil engineering, particularly in geotechnical engineering. The design of foundations for vibrating machines, the study of propagating earthquake impulses in geologic materials, and the catastrophic loss of strength of a soil associated with the increase of pore water pressure known as ``liquefaction'' are examples of geotechnical problems where the analysis of the response of multi-phase materials (i.e. soils or porous media) becomes important. The importance of this subject has been recognized since the early 1940's, when the apprehension of the colossal devastation caused by major earthquakes created the need to better understand its possible effects in order to mitigate higher losses that could be avoided by adequate engineering design. © ASCE 1 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 During the last four decades significant progress has been made in understanding the behavior of a porous matrix interacting with one or more fluids. In the area of geotechnical engineering three approaches are identified: (1) field observations prior, during, and after earthquakes, (2) laboratory experimentation, and (3) theoretical/numerical studies. Among the last group three different philosophies have emerged: decoupled methods (or total stress approach), indirectly coupled methods (quasi-effective stress approach), and fully coupled methods (or effective stress approach). This paper focuses on the use of fully coupled methods of analysis, which are based on the theory of mixtures. The premise of these theories is that a mixture may be viewed as a superposition of ``n'' individual continua, each following its own motion. In the light of these theories, the behavior of porous media cannot be described directly, since, in general, it is not possible to know a priori which spatial position will be occupied by which particular constituent. For this reason, substitute continuum models must be used to replace the particulate structure, where a single material (component) is assumed to occupy the total region. The use of volume fraction theories constitutes the necessary connection between global bulk average quantities and the local effective quantities. Figure 1 shows a schematic of a typical Representative Elementary Volume (REV) for a porous media where volume fractions n(s) = n and n(f) = 1-n are defined using Equations (1) (where n = porosity) (Arduino & Macari 2001). Figure 1: Typical Representative Elementary Volume (REV) V ( ) ;  n( )  1 V (1) V(f) V (s) V  V ( f ) (f) (s) n   n; n    1 n V V V Within this framework the problem generally leads to geometrical and physical nonlinear relations. In order to obtain a simple and practical theory, further simplifications must be introduced. For this reason a mixture composed of only two constituents, i.e., the porous matrix and a saturating fluid, is considered. The different components are assumed to share a common temperature with a vanishing temperature gradient. Furthermore, the compressibility of the solid particles is assumed to be much smaller than the compressibility of the body as a whole and the deviator stress in the media fluid is assumed to be negligible in comparison to that in the solid's skeleton. Finally, the development of the constitutive equations is many times restricted to the case of small strains. n( )  GOVERNING EQUATIONS OF A SOIL-FLUID MIXTURE When considering a mixture of a solid interacting with a fluid the continuum balance equations are: © ASCE 2 Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 3 Equation of motion - Solid phase   (1  n)s xi( s )  (1  n)s xi(,sj) x (js )  (1  n)s bi( s )  n 2f (k sf )ij1 ( x (js )  x (j f ) )   ij'(,sj)  (1  n) p,i  0 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Equation of motion - Fluid phase   nf xi( s )  nf xi(, fj ) x (j f )  nf bi( s )  (2) n 2f (k sf )ij1 ( x (js )  x (j f ) )  np,i  0 Equation of motion - Mixture n p  (1  n) xi(,si )  nxi(,if )  0 Kf In these equations the balance of mass for the mixture results from the combination of the balance of mass for the solid and fluid phases and assumes the fluid is compressible, with bulk modulus Kf. The resulting set of equations is equivalent to Biot’s field equations for an inert mixture composed of a porous solid skeleton and a saturating Newtonian fluid and includes interaction forces and convective terms for the solid and fluid motions. Biot established these equations years before the theory of mixture was postulated by Truesdell in 1960. Solution of this system of differential equations may be obtained using approximate methods of analysis. Among these, the Finite Element (FE) method is most frequently used in the literature. Proceeding along standard FE lines a weak formulation associated with the governing field equations for a saturated porous media may be obtained, (Arduino & Macari 2001 a and b). A solution for the weak formulation can be obtained using a spatial semi-discretization of the domain W into non-overlapping finite element followed by an appropriate time stepping process applicable to the discretized set of equations. In 1984 Zienkiewickz et al. proposed two and three field finite element formulations of the generalized Biot equations, (Zienkiewicz 1984).These have become to be known as the u-U, u-p, and u-p-U formulations, depending on the independent variables chosen in the approximation scheme, and constitute the basic skeleton of most commercial and open-source FE numerical platforms used in today’s geotechnical engineering practice. As an example the open-source numerical platform OpenSees includes 2D and 3D coupled elements formulated based on the u-p approximation (Opensees 2007). A critical component in these platforms is the constitutive model used to resolve the nonlinear stress-strain response of the solid fraction. CONSTITUTIVE MODELS Material (constitutive) models play a vital role in the solution of the differential equations discussed above. As such, an enormous amount of research has gone into their development and application. While the complexity of these models varies significantly, the primary goal of each is the same: to capture and replicate material response observed in the field and in the laboratory. Quite often this boils down to identifying key components that are decisive or fundamental in predicting a material’s behavior when subjected to a given loading. The present state of constitutive modeling in soil plasticity is quite advanced. The first fundamental advances towards developing this field were made in the fifties and early sixties, and consist of the Drucker-Prager generalization of the Coulomb frictional criterion for soils, and the Critical State Soil Mechanics (CSSM) framework and associated Cam-Clay type of models. © ASCE Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 With the increased requirement of earthquake resisting design it became imperative to capture the soil response under cyclic loading conditions. This requirement is basically accounted for by the fundamental property of plasticity to be able to simulate the reverse loading response after pre-loading in one direction. This demand prompted the development of new, more advanced, soil plasticity models, such as nested surfaces models, kinematic hardening models, bounding surface models and many others, all of them addressing mainly the cyclic loading response. Unfortunately, the mathematical sophistication/complexity of advanced soil plasticity models resulted in the need of calibrating large number of parameters many of them with no direct physical meaning or parameters difficult to measure using conventional sensors in experimental (or field) settings. Moreover, since most of today’s advanced models are 3D in nature they require validation and verification using experimental results that follow general stress paths. Figure 2 shows experimental results from a 3D cubic device using a variety of stress paths intended to stimulate material response that could be used to develop (and/or improve) model functionality and help calibrate model parameters. Figure 2: Useful experimental stress paths: (a) Undrained constant total mean stress, p, (b) cyclic simple shear, (c) constant deviatoric q while reducing total mean stress p, and (d)circular path with constant deviatoric q and constant total mean stress p In the context of liquefiable soils several models for cyclic loads have been extended to account for contraction and dilation and the phase transformation phenomena observed during cyclic loads at small mean effective stresses. A complete description of all these models is beyond the scope of this paper. Here as an example only the Manzari-Dafalias (MD) model (Dafalias et al. 2004) is described. The MD model is a bounding surface model capable of producing stress-strain relationships for both denser-than-critical and looser-than critical sands. It is also capable of capturing critical state conditions where shear strains accumulate at constant volume. Its kinematic hardening evolution law is based on basic bounding surface principles as © ASCE 4 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 postulated by Dafalias and others (Dafalias 1982). An important feature of the MD model is the dependence of the deviatoric strain direction on the Lode angle which makes the model capable of capturing sand behavior under stress paths other than those of conventional triaxial compression or extension. Figure 3 shows schematics of the MD dilation, critical and bounding surfaces in deviatoric and principal stress spaces, as well as, experimental cubic triaxial results showing recorded plastic flow directions at different Load angles that validate the shape of the MD surfaces. Figure 3, (a) Manzari Dafalias surfaces in deviatoric and principal stress spaces, (b) Experimental results validating shape of yield and bounding surface. Figure 4: Manzari Dafalias simulations at different densities and drained and undrained conditions. The MD constitutive model is made compatible with critical state soil mechanics through dependence of the bounding surface and phase transformation surfaces on the value of effective volumetric stress (p) and void ratio (e) at the current state of the material (see Figure 4). For this purpose the so called state parameter, defined as ψ = e−ec by Been and Jefferies (Been 1985), is used to represent the state of the material relative to the critical state line. To account for softening of denser-than-critical sands and continuous accumulation of deviatoric strain at constant volumetric strain at critical state, the so called bounding and dilatancy surfaces are tied to the critical state surface through the state parameter. This proves to be very effective in simulating the behavior of sands with different densities and under different effective confining pressures using a single set of material parameters. Finally the behavior of sands during load reversals and cyclic loading is tied to a fabric tensor that evolves during loading and reloading. © ASCE 5 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 For a detailed description of the MD material model, the reader is referred to (Dafalias et al. 2004). The MD model has been used in multiple contexts. In recent years researchers have attempted to modify the MD formulation to improve different aspects of the model. For example, Pisanò and Jeremić tried to add viscous damping to compensate for the lack of low strain damping in the original formulation (Pisano et al. 2014). Recently, Boulanger and Ziotopoulou modified the model to better capture the general behavior of sands and improve the calibration process by reducing the number of parameters that needs to be calibrated. They also improved some of fundamental features, namely the evolution of the fabric tensor (Boulanger et al. 2013). This model is referred as PM4Sand in the literature. Figure 5 (a) and (b) show comparisons between PM4Sand simulations and cyclic stress experimental results for an Ottawa-F65 sand. Figure5(c) shows good agreement between simulated and recorded number of cycles to liquefaction for different relative densities and cyclic stress ratios. Figure 5: Comparison between PM4Sand simulations and experimental results: (a) stress path, (b) stress-strain curves and (c) numerical vs experimental number of cycles to liquefaction. Although very useful the MD model, as well as all models for liquefiable soils, suffer from the inherent limitation they have to transition from solid to fluid behavior and back. During liquefaction the soil matrix collapses and the solid particles become suspended in water. Under this condition the solid-water mixture begins to behave like a viscous fluid. Mathematical models obviously must account for the “metamorphosed” soil behavior – i.e. solid-like during the preliquefaction stage, and liquid-like during the liquefaction stage. Modeling of such phenomena is not straightforward, and some researchers propose one might switch to particulate mechanics, or discrete element modeling to account for such disparate behaviors. In general, however, switching a solution from continuum model to a micromechanical model is awkward and cumbersome. A logical approach is to use continuum models all the way and utilize the particulate mechanics approach only to determine the overall properties of soils in the liquefied stage. In here the role of soil micromechanics, in addition to providing a fundamental insight into the particulate nature of soils, is to provide overall effective properties of the granular assembly as well (e.g., overall moduli, viscosity, etc.) for use with continuum-based models. In this regard great progress has been made in recent years using advanced DEM techniques to represent solid particles and the help of CT scanning images on samples subjected to monotonic and cyclic loads (see Andrade et al. 2012). © ASCE 6 Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. FINITE ELEMENT SIMULATION Although useful to understand basic behavior, the end goal of constitutive models is to be implemented in general numerical platforms for the solution of boundary value problems. For example the current OpenSees platform distribution includes the Manzari-Dafalias model, multiyield models for pressure independent and pressure dependent granular materials (PIMY, and PDMY) (see Elgamal et al. 2003), the recently proposed PM4Sand, and several versions of the bounding surface model proposed by Borja and Aimes (1994). As an example of a the use of an advanced constitutive model and robust finite element platform a few results from the Liquefaction Experiments and Analysis Projects (LEAP) effort are discussed. LEAP is aimed at producing high quality experimental data sets and undertakes a systematic validation of existing computational models of the dynamic response and liquefaction of saturated granular soils (Manzari et al. 2014). Within this context, LEAP-GWU 2015 was a first validation effort using centrifuge tests of a benchmark sloping soil deposit. The centrifuge experiment was designed to be readily repeatable at multiple centrifuge facilities (Manzari et al. 2014). Specifically, the tests were conducted using “rigid-wall” containers to avoid the complexity of boundary conditions of laminar boxes. The rigid-walls provide analogous conditions at different centrifuge facilities, are simpler to simulate in a numerical model, and, hence, are more appropriate for validation purposes than articulated laminar boxes. The adopted centrifuge model corresponds to a prototype of a submerged uniform sand deposit with a length of 20 m and a height decreasing from 4.875 m to 3.125 m (or a 5o sloping surface, Figure 6). A ramped (up and down) sinusoidal input base motion was prescribed as a target for all the conducted tests. The same Ottawa F-65 sand was used at all centrifuge facilities and an extensive set of material and element tests were conducted to characterize this soil and provide data necessary for constitutive model calibration (see Figure 4). Figure 6: LEAP Finite Element mesh and location of recorded pore water pressures (P), accelerations (AH) and displacements (D). Input motion shown at bottom (sinusoidal f = 2Hz) To assess the capabilities of a few prominent constitutive models and numerical modeling techniques for soil liquefaction analysis, a series of blind predictions were undertaken by researchers and practitioners in the USA and Japan. Figure 7 shows comparisons of experimental results and numerical simulations obtained using OpenSees and the Manzari-Dafalias model (Ghofrani and Arduino 2016). Figure 7(a) shows acceleration response spectra at locations AH1, AH3, AH5, AH7, and AH9 and Figure 7(b) excess pore pressure time histories at locations P1, © ASCE 7 Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. P3, P5, P7, and P9. Overall, the predicted response is in good agreement with the observed response in the centrifuge. Figure 7: LEAP predictions results for RPI centrifuge experiment: (a) acceleration response spectra (5% damping) and (b) excess pore water pressures (see Figure 6 for location of sensors) Figure 8: LEAP predictions for centrifuge experiments: (a) surface horizontal displacement near the middle of the specimen, (b) surface vertical displacements at three locations along the surface (see Figure 6 for location of sensors). Figure 8 shows ultimate horizontal and vertical displacements at the surface recorded in the centrifuge (color dots on the right axis) along with the evolution of the corresponding predicted displacements for two experiments. Although the simulated results are in the range of displacements observed in the centrifuge, the predicted values represent poorly the large deformation phenomenon that results after liquefaction. Besides obvious inconsistencies in the centrifuge tests, other reasons can be enumerated to justify these differences, including changes © ASCE 8 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Geotechnical Earthquake Engineering and Soil Dynamics V GSP 292 in hydraulic conductivity and void ratio redistribution affecting critical aspects of the constitutive model and finite element response. However, they also expose other difficulties that become notorious after the onset of liquefaction; namely the problem of using small deformation theories at the constitutive level and mesh distortion at the finite element level. Once liquefaction is triggered, or during liquefaction incursions at small mean stresses, the soil deformations are large and therefore the small strain approximation (i.e., the norm of displacement gradient is small when compared to unity) is not valid anymore. This requires alternative finite deformation measures based on finite deformation theories, which unlike small deformation theory, can be formulated in either the initial or deformed configuration. As such, there are typically additional complexities associated with constitutive laws and care must be taken to ensure frame indifference and objectivity e.g., Truesdell and Noll (1965); Marsden and Hughes (1983). Although there are ways to extend small strain implementations into the finite deformations regime, most of the existing models for liquefaction are structured using small strain theory simplifications difficult to modify. Among all possible deformation measures the left Cauchy-Green deformation tensor provides the basis for a return mapping algorithm that is remarkably similar to frameworks commonly used for small deformation measures. THE PROBLEM OF LARGE DEFORMATIONS Possible Numerical Strategies - Meshless Techniques Even when using well defined constitutive models that account for large deformations, the ensuing finite element simulations may still suffer from exaggerated mesh distortion that limit their applicability in practice. This is a well know problem difficult to resolve using conventional finite element techniques. To alleviate this problem several alternative methodologies can be used including Arbitrary Lagrangian-Eulerian (ALE) methods, both Lagrangian and Eulerian Finite Element Methods (FEM), meshless or meshfree methods including the Material Point Method (MPM) and Smooth Particle Hydrodynamics (SPH), and select Finite Difference (FD) techniques. A thorough literature review would include a detailed comparison of all these numerical methods. However, this is beyond the scope of this work. Therefore, in this paper we limit to a brief comparison between MPM and SPH and discuss MPM more in detail; in part due to the experience of the author on the use of this method. The Material Point Method The Material Point Method (MPM) is a numerical technique that is best suited for modeling history dependent materials in a dynamic, large deformation setting. The formulation tracks moving points relative to stationary nodes, and can be used to capture the behavior of both fluids and solids in a unified framework. The standard, or traditional, implementation solves the governing equation of motion at fixed nodes that collectively form a grid. Each body or phase in the analysis is represented by a collection of discrete points known as material points or particles (Sulsky et al. 1995). This general concept is shown in Figure 9 (a). In MPM each body in the analysis is represented by a series of discrete points known as material points or particles. The different components that make up a simulation are classified as either Body- or Domain/GridBased. The Body-Based group is comprised of the continuum body itself and the computational points that collectively describe the object. Each particle represents a portion of the total mass, and thus carries an implied volume as well as state variables that depend on the application. In geotechnical applications each material point is assigned a position, velocity, stress, strain, and © ASCE 9