Luận án tiến sĩ triết học reduced order model for dynamic soil pipe interaction

Reduced-order model for dynamic soil-pipe interaction analysis Thesis by Kien Trung Nguyen In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2020 Defended May 15th, 2020 ii © 2020 Kien Trung Nguyen ORCID: 0000-0001-5761-3156 All rights reserved iii Acknowledgements First and foremost, I would like to express my deepest appreciation to my advisor, Professor Domniki Asimaki, for her support through my Caltech graduate journey. Domniki has given me the motivation and the freedom to pursue my research. Her guidance has signifi- cantly deepened my experience into the field of site response and geotechnical earthquake engineering. The problem-solving skills that I learn from her will absolutely benefit my future careers.

I am also thankful for the excellent exemplar of a successful professor that she has provided. Next, I would like to thank Professor José Andrade, Professor John Hall, and Professor Chiara Daraio for serving on my thesis committee, for generously offering their time and support throughout the review of this thesis, and for their insightful comments. I would like to acknowledge Dr. Craig Davis, previously at the Los Angeles Department of Water and Power role, in motivating this work.

I would also like to acknowledge the postdoctoral researchers and PhD students in my research group, for good advice as well as collaboration and friendships. Apart from my own group, I have also learned a lot from other PhD students and professors at Caltech during my coursework, which have provided me with a solid background necessary to conduct my research. For this, I very much appreciate. Thanks should also go to the administrative staff at the Mechanical and Civil Engineering Department, International Student Programs, and Graduate Studies Office for always being so helpful and friendly.

To my roommates, friends, and V-League group, thank you for spending time with me, offering me advice, and helping me during my time at Caltech. Lastly, I am deeply indebted to my family and in-laws for all their love and encouragement, despite the long distance between us. And I would like to thank, with love, my wife Phuong for her understanding, constant support, and unconditional love. iv Abstract Pipelines are very vulnerable infrastructure components to geohazard-induced ground de- formation and failure.

How soil transmits loads on pipelines and vice versa, known as soil-pipe interaction (SPI), thus is very important for the assessment and design of resilient pipeline systems. In the first part, this work proposes a simplified macroelement designed to capture SPI in cohesionless soils subjected to arbitrary loading normal to the pipeline axis. We present the development of a uniaxial hysteresis model that can capture the smooth nonlinear reaction force-relative displacement curves (FDCs) of SPI problems. Using the unscented Kalman filter, we derived the model parameter 𝜅 that controls the smoothness of the transition zone from linear to plastic using published experimental data.

We extended this uniaxial model to biaxial loading effects and showed that the macroelement can capture effects such as pinching and shear-dilation coupling. The model input parameters were calibrated using finite element (FE) analyses validated by experiments. The FDCs of the biaxial model were verified by comparison with FE and smoothed-particle hydrodynamic (SPH) simulations for different loading patterns: cyclic uniaxial, 0-shaped, 8-shaped, and transient loading. Accounting for smooth nonlinearity, hysteresis, pinching, and coupling effects, the proposed biaxial macroelement shows good agreement with FE and SPH analyses, while maintain- ing the computational efficiency and simplicity of beam-on-nonlinear-Winkler foundation models, as well as a small number of input parameters.

Next, this work presents analytical solutions for computing frequency-domain axial and in- plane soil impedance functions (SIFs) for an infinitely long rigid circular structure buried horizontally in homogeneous elastic half-space. Using Hankel– and Bessel–Fourier series expansion, we solved a mixed-boundary-value problem considering a harmonic displace- ment at the structure boundary and traction-free boundary condition at the half-space free surface. We then verified our analytical solutions using results obtained from FE simula- tions. The SIFs of a buried structure in a homogeneous elastic half-space calculated by these two approaches are in perfect agreement with each other.

In addition, we used analytical solutions and FE simulations to comprehensively investigate factors that affect the SIFs in homogeneous and two-layered half-spaces, respectively. The parametric study shows that SIFs of buried structures in elastic half-space primarily depend on frequency of excitation, shear modulus and Poisson’s ratio of the half-space, burial depth and radius of the structure. In a two-layered soil domain, SIFs depend also on material contrast and the distance from the structure location to the interface between soil layers. v Lastly, it demonstrates how the SIFs obtained previously can be incorporated into a reduced- order model to analyze SPI problems, specifically a straight pipe subjected to Rayleigh surface wave propagating through homogeneous and heterogeneous elastic half-spaces.

Calculated displacement time histories at the control points are shown to agree well with those computed by direct two-dimensional FE analyses. vi Published Content and Contributions Asimaki, D. Seylabi (2019), Next generation reduced order models for soil-structure interaction, in Earthquake Geotech- nical Engineering for Protection and Development of Environment and Constructions, vol. 138–152, CRC Press, London, doi: 10.N participated in the conception of the project, solved and analyzed the pipeline structures, and wrote Section 4 of the manuscript.

Asimaki (2018), A modified uniaxial Bouc–Wen model for the simula- tion of transverse lateral pipe-cohesionless soil interaction, in Geotechnical Earthquake Engineering and Soil Dynamics V, pp. 25–36, American Society of Civil Engineers, Texas, doi:10.N performed all data analysis, model development, numerical simulations, produced all figures, and wrote most of the manuscript.N performed all data analysis, model development, numerical simulations, produced all figures, and wrote most of the manuscript. vii Table of Contents Acknowledgements. iv Published Content and Contributions.

vi Table of Contents. vi List of Illustrations. ix List of Tables. xiv Chapter 1: Introduction .1 Pipelines and seismic actions .2 Methods for soil-pipe interaction analysis .1 Model neglecting soil-pipe interaction .2 Beam-on-Winkler-foundation model considering soil-pipe interaction 4 1.3 Full three-dimensional model considering soil-pipe interaction .3 Challenges in soil-pipe interaction analysis .4 Organization of the text.

9 Chapter 2: Smooth nonlinear hysteresis model for coupled biaxial soil-pipe interaction in sandy soils .2 Uniaxial hysteresis model .3 Biaxial hysteresis model .1 Finite element method .2 Smoothed-particle hydrodynamics .3 Validation of the FEM and SPH models .4 Parameter calibration for BMBW model .5 Uniaxial cyclic loading .9 Suggestions for input parameters. 37 Chapter 3: Dynamic axial soil impedance function for rigid circular structures buried in elastic half-space .2 Review of axial soil impedance function .3 Analytical solution for soil impedance function of homogeneous half-space .4 Finite element analysis for soil impedance functions of homogeneous and two-layered half-spaces .1 Numerical computation of impedance function .2 Finite element models .6 Homogeneous half-space .7 Two-layered half-space .1 Effect of material contrast .2 Effect of structure location. 62 Chapter 4: Dynamic in-plane soil impedance functions for rigid circular struc- tures buried in elastic half-space .2 Review of in-plane soil impedance functions .3 Analytical solution for soil impedance functions of homogeneous half-space 67 4.4 Traction-free condition at 𝑦 = 0 .5 Dirichlet boundary condition at cylinder interface .6 Calculation of in-plane soil impedance functions .8 Direct evaluation of the integral .4 Finite element analysis for soil impedance functions of homogeneous and two-layered half-spaces .1 Numerical computation of in-plane soil impedance functions .2 Finite element models .6 Homogeneous half-space .1 Effect of burial depth .2 Effect of Poisson’s ratio .7 Two-layered half-space .1 Effect of material contrast .2 Effect of structure location. 95 Chapter 5: Application: Reduced-order modeling of buried pipe subjected to the propagation of Rayleigh surface wave .2 Models for soil-pipe interaction analysis .1 Model neglecting soil-pipe interaction .2 Model considering soil-pipe interaction with free-field input .3 Models based on substructure and finite element methods .3 Results and comparisons .1 Summary of previous chapters.

115 Appendix A: Asymptotic method for computing high oscillatory integrals. 124 x List of Illustrations Number Page 1.1 Pipe damage by: (a) landslide; (b) lateral spreading; and (c) P-wave propa- gation. (Adapted from Highland et al.2 Methods for SPI analysis.3 Beam-on-Winkler-foundation model based on Winkler’s hypothesis.1 Pinching effect observed from vertical cyclic pipe loading.2 Smoothness of FDC depending on 𝜅. (Reprinted from Nguyen and Asimaki 2018, © ASCE.3 Estimating 𝜅 by UKF method: (a) FDC and MBW (data from Robert et al.4 𝜅 for loose sand 𝐼 𝐷 = 0–35%, medium sand 𝐼 𝐷 = 35%–65%, dense sand 𝐼 𝐷 = 65%–100% for lateral and uplift pipe movement.5 Incremental reaction force as a function of nonlinearity: (a) d𝑢 ® k 𝜁; ® and (b) ® ∦ 𝜁.

d𝑢 ® (Adapted from Varun and Assimaki 2012.6 Transformation from local to global coordinate system. (Adapted from Varun and Assimaki 2012.7 Hysteresis spring in series with slip-lock element.8 Initial stiffness in different parts of FDC.9 Values of 𝜒 for variation of 𝜃 𝑑𝑢 .10 Schematic illustration of continuum and proposed reduced model.11 Geometry of the numerical models (not to scale): (a) FEM model; and (b) SPH model.12 Validation of FEM and SPH models.13 Calibration from numerical results: (a) lateral loading; (b) upward vertical loading; (c) downward vertical loading; and (d) pipe trajectory in lateral loading for 𝜒0 .14 𝐹𝑥 - 𝑢 𝑥 for small pipe displacement 𝑢 𝑛 /𝐷 = 0.15 𝐹𝑦 - 𝑢 𝑦 for small pipe displacement 𝑢 𝑛 /𝐷 = 0.16 𝐹𝑥 - 𝑢 𝑥 for large pipe displacement 𝑢 𝑛 /𝐷 = 0.17 𝐹𝑦 - 𝑢 𝑦 for large pipe displacement 𝑢 𝑛 /𝐷 = 0.18 Lateral uplift failure envelope.19 Cyclic displacement loading patterns: (a) 0-shape loading; and (b) 8-shape loading.20 𝐹𝑥 - 𝑢 𝑥 and 𝐹𝑦 - 𝑢 𝑦 for 0-shape loading and small pipe displacement 𝑢 𝑛 /𝐷 = 0.21 𝐹𝑥 - 𝑢 𝑥 and 𝐹𝑦 - 𝑢 𝑦 for 0-shape loading and large pipe displacement 𝑢 𝑛 /𝐷 = 0.22 𝐹𝑥 - 𝑢 𝑥 and 𝐹𝑦 - 𝑢 𝑦 for 8-shape loading and small pipe displacement 𝑢 𝑛 /𝐷 = 0.23 𝐹𝑥 - 𝑢 𝑥 and 𝐹𝑦 - 𝑢 𝑦 for 8-shape loading and large pipe displacement 𝑢 𝑛 /𝐷 = 0.24 Kobe earthquake signal.25 𝐹𝑥 - 𝑡 and 𝐹𝑦 - 𝑡 from BMBW, SPH, and ASCE model for Kobe earthquake.26 𝐹𝑥 - 𝑢 𝑥 and 𝐹𝑦 - 𝑢 𝑦 from BMBW, SPH, and ASCE model for Kobe earthquake.27 𝜒0 for various embedment ratios 𝐻/𝐷 and sand types.28 𝛿 𝑠 and 𝜎 for various embedment ratios 𝐻/𝐷 and sand types.1 Schematics of: (a) strip foundation; (b) embedded foundation; (c) pile foun- dation; and (d) buried structure.2 Geometry to compute SIF of a cross section: (a) full-space for pile founda- tion; and (b) half-space for buried structure.3 The rigid axial displacement.4 The problem geometry.5 Geometry of Graf’s addition theorem.6 Convergence of series truncation: (a) real part; and (b) imaginary part.7 Rate of convergence.8 Numerical model for the estimation of SIF: (a) infinite half-space FE model; and (b) truncated half-space FE model using perfectly matched layer (PML) elements.9 The applied force in time and frequency domain.10 Displacement signal for ℎ/𝑎 = 16 in: (a) time domain; and (b) frequency domain.12 SIFs for ℎ/𝑎 = 5: (a) real part; and (b) imaginary part.13 SIFs for different cases of burial depth: (a) real part; and (b) imaginary part.14 Geometry of two-layered half-space.15 SIFs for ℎ1 /𝑎 = 4 and ℎ2 /𝑎 = 2 depending on material contrast ratio: (a) real part; and (b) imaginary part.16 SIFs for ℎ1 /𝑎 = 4 and ℎ2 /𝑎 = 4 depending on material contrast ratio: (a) real part; and (b) imaginary part.17 SIFs for ℎ1 /𝑎 = 4 in two-layered domain (𝜇1 /𝜇2 = 0.25) and homogeneous half-space (𝜇1 /𝜇2 = 1.18 SIFs for ℎ1 /𝑎 = 8 in two-layered domain (𝜇1 /𝜇2 = 0.25) and homogeneous half-space (𝜇1 /𝜇2 = 1.1 Rigid cylinder kinematics for the definition of SIFs.2 The problem configuration.3 The branch cuts and the integration contour.4 The integration components.