nonlinear earthquake engineering simulation using ...

NONLINEAR EARTHQUAKE ENGINEERING SIMULATION USING PARALLEL COMPUTING SYSTEM

A thesis submitted in partial fulfillment of the requirements for the degree of MASTER IN EVALUATION CONTROL AND REDUCTION OF ENVIRONMENTAL SEISMIC RISK (MECRES)

IN DEPARTMENT OF STRUCTURAL AND GEOTECHNICAL ENGINEERING SAPIENZA UNIVERSITY OF ROME

BY, KHALED MASHFIQ SUPERVISOR

-

PROF. ROSARIO GIGLIOTTI SAPIENZA UNIVERSITY OF ROME

CO-SUPERVISORS -

DR. MARCO FAGGELLA, SAPIENZA UNIVERSITY OF ROME PROF. ANDRE BARBOSA, OREGON STATE UNIVERSITY

DECEMBER, 2012 ROME, ITALY

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ACKNOWLEDGEMENTS

My first vote of thanks goes to my parents without their support it would be really impossible for me to study abroad. They have given me a great deal of courage which helped throughout my stay in Rome.

I would like to thank my supervisor Prof. Rosario Gigliotti. Without him, this thesis would not have been possible. I thank him for his patience, flexibility and encouragement that carried me through many difficult times, and for his mentorship and insights that helped to shape my research skills and personal attitude.

I am extremely grateful to my co-supervisor Dr. Marco Faggella. He was instrumental in his vision and guidance in the matter of parallel computing, ground motion selection and also with nonlinear analysis. He has supported me through my difficult period giving me guidance 24/7.

I would take the chance to thank my co-supervisor Prof. Andre Barbosa, for his valuable time he spend on explaining the tricks and trades of cloud computing and parallelization with condor. Furthermore, his ideas shaped up my research extent.

My sincere gratitude goes to Dr. Frank McKenna, Developer of OpenSees. Without his help it would be quite impossible to setup a parallel computing system for earthquake engineering simulation in Sapienza University of Rome I would also thank Giulia Sellitto, Masters Student in Sapienza University of Rome, The models used for this study were primarily developed by her. She supported me with timely guidance to finish the nonlinear simulation. I would also like to thank Pietro Maioli for his valuable time on Information Technology issues, also my dear friend SM Iftekharul Alam, Phd Student, Purdue University for his guidance on linux operating systems.

Finally, I would like to thank EU-NICE and MECRES team to give me this wonderful opportunity to learn specially Prof. Giogio Monti.

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Table of Contents 1.

CHAPTER 01: Earthquake Engineering Simulation Using Parallel Computing Systems 1 1.1

Introduction ................................................................................................................. 1

1.2

OpenSees Software Framework .................................................................................. 1

1.3

Parallel Computing Systems ........................................................................................ 2

1.3.1

Available OpenSees parallel interpreters: ............................................................ 4

1.4 Building the OpenSees Interpreters and Parallel Computation Platform in Linux Machines ................................................................................................................................ 6 1.4.1

Setting up MPICH2 Platform ............................................................................... 6

1.4.2

Compilation and installation of Mathematical Libraries ...................................... 7

1.4.3

Installation of TCL framework ............................................................................ 8

1.4.4

Compilation of OpenSees Parallel ....................................................................... 8

1.4.5

Example of Parallelization for Parameter study ................................................... 8

1.5

Parallel computation with OpenSees sequential and condor ..................................... 10

1.6

Parallel Model Results ............................................................................................... 12

2. CHAPTER 02: Ground Motion Selection And Scaling For Probabilistic Response Analysis Of Strucutres ............................................................................................................. 13

3.

2.1

Introduction ............................................................................................................... 13

2.2

Record Selection Using REXEL 3.4: ........................................................................ 13

2.3

Ground motion selection approach: ........................................................................... 14

2.3.1

Seismic hazard disaggregation for the site ......................................................... 15

2.3.2

Selected Ground Motions ................................................................................... 16

2.3.3

Ground Motion Scaling for Incremental Dynamic Analysis ............................. 18

CHAPTER 03: Nonlinear Incremental Dynamic Simulation And Response Analysis ... 21 3.1

Introduction ............................................................................................................... 21

3.2

Description of the structural models .......................................................................... 21

3.2.1

Model 1 .............................................................................................................. 21

3.2.2

Model 2 .............................................................................................................. 24

3.3

Parallel Simulation of Incremental Dynamic Analysis ............................................. 26

3.4

Response Analysis ..................................................................................................... 26

3.5

Limitations ................................................................................................................. 33

3.6

Conclusion ................................................................................................................. 33

3.7

References ................................................................................................................. 35

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List of Figures: Figure 1.1: General schematics of Parallel Computing, source: https://computing.llnl.gov/tutorials/parallel_comp/ .................................................................. 2 Figure 1.2: Graph demonstrating Amdahl’s Law....................................................................... 4 Figure 1.3: Domain decomposition schematics using OpenSeesSP, source: http://opensees.berkeley.edu/ ..................................................................................................... 5 Figure 1.4: Parameter study script spawning on different processor, http://opensees.berkeley.edu/ ..................................................................................................... 6 Figure 1.5: Parameter number setup & Simple parameter parallelization algorithm ................. 8 Figure 1.6: Example Parallel script for Incremental Dynamic Analysis for multiple ground motion, Source: McKenna F., OpenSees Parallel Workshop, 2008 .......................................... 9 Figure 1.7: Total Analysis Time plotted against assigned number of processors assigned to the task (test case linear dynamic, 6 Storied building, 60 ground motion) ...................................... 9 Figure 1.8: Condor Computing System, source: condor user manual .................................... 10 Figure 1.9: Typical Condor submit script, Courtesy: Andre Barbosa, 2012 ........................... 11 Figure 2.1: Uniform Hazard Spectra Vs NTC Spectrum for 10% and 63% probability of exceedance in 50 years ............................................................................................................. 15 Figure 2.2: Seismic hazard disaggregation for events with 10% Probability of Exceedance in 50 years .................................................................................................................................... 15 Figure 2.3: Seismic hazard disaggregation for events with 63% Probability of Exceedance in 50 years .................................................................................................................................... 16 Figure 2.4: Spectrum matching plot for ground motion selection for probability of exceedance 10% in 50 Years, Site - Mormanno, Calabria, (7 Ground Motion Record) ............................. 17 Figure 2.5: Spectrum matching plot for ground motion selection for probability of exceedance 63% in 50 Years, Site - Mormanno, Calabria, (7 Ground Motion Record) .......... 18 Figure 2.6: Logarithmic interpolation of intermediate hazard levels ....................................... 19 Figure 2.7: SaT1 at different levels of hazard .......................................................................... 20 Figure 3.1: Model 1 Structural configuration........................................................................... 21 Figure 3.2: Typical Hysteretic Stress-Strain Relation for Kent and Park concrete material model ........................................................................................................................................ 23 Figure 3.3: Steel Material Hysteretic Behavior of Model with or without Isotropic Hardening .................................................................................................................................................. 23 Figure 3.4: Schematics of beam with hinges element .............................................................. 23

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Figure 3.5: Fibre modelling of a reinforced concrete section .................................................. 24 Figure 3.6: Model 2 Structural configuration........................................................................... 24 Figure 3.7: Steel Material - Hysteretic Behavior of Model w/o Isotropic Hardening ............. 26 Figure 3.8: Peak Interstorey Drift Ratio Vs PGA of Hazard Level, Model1 ........................... 27 Figure 3.9: Maximum Curvature at floor level Vs PGA of Hazard Level,Model1 ................. 28 Figure 3.10: Absolute Peak Floor Acceleration Vs Peak Ground Acceleration of Hazard Level at each storey, Model1 ............................................................................................................. 29 Figure 3.11: Peak Interstorey Drift Ratio Vs PGA of Hazard Level, Model 2 ........................ 30 Figure 3.12: Maximum Curvature at floor level Vs PGA of Hazard Level, Model2 .............. 31 Figure 3.13: Absolute Peak Floor Acceleration vs Peak Ground Acceleration of Hazard Level at each storey, Model2 ............................................................................................................. 32

List of Tables:

Table 1.1: Some Parallel computing system and their processing mechanism .......................... 3 Table 1.2: Mathematical libraries used by OpenSees ................................................................ 7 Table 2.1: Criteria for ground motion selection ....................................................................... 16 Table 2.2: Selected Ground Motion for probability of exceedance 10% in 50 Years ............. 17 Table 2.3: Selected Ground Motion for probability of exceedance 63% in 50 Years ............. 17 Table 2.4: Different target hazard level for IDA analysis ........................................................ 18 Table 3.1: Section configuration of model 1 ............................................................................ 22 Table 3.2: Section configuration of model 2 ............................................................................ 25

List of Equations:

Equation 1.1 ............................................................................................................................... 3 Equation 1.2 ............................................................................................................................... 3 Equation 2.1 ............................................................................................................................. 14

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LIST OF ABBREVIATIONS

CDF

Cumulative Distribution Function

CPU

Central Processing Unit

DOF

Degree Of Freedom

EC6

Eurocode 6

EC8

Eurocode 8

EDP

Engineering Demand Parameter

ELS

Elastic Limit State

FE

Finite-Element

FEMA

Federal Emergency Management Agency

GPU

Graphics Processing Unit

HTC

High Throughput Computing

IDA

Incremental Dynamic Analysis

IDR

Interstorey Drift Ratio

IM

Intensity Measure

INGV

Italian National Institute of Geophysics and Volcanology

MDOF

Multi-Degree-Of-Freedom

MPI

Message Passing Interface

PBD

Performance-Based Design

PBEE

Performance-Based Earthquake Engineering

PDF

Probability Density Function

PFA

Peak Floor Acceleration

PGA

Peak Ground Acceleration

PGD

Peak Ground Displacement

PGV

Peak Ground Velocity

PSHA

Probabilistic Seismic Hazard Analysis

RC

Reinforced Concrete

ReLUIS

Rete dei Laboratori Universitari di Ingegneria Sismica

SDOF

Single-Degree-Of-Freedom

SLC

Stato Limite di prevenzione del Collasso (Limit State of Collapse Prevention)

SLD

Stato Limite di Danno (Damage Limit State)

SLO

Stato Limite di immediata Operatività (Limit State of immediate occupancy)

SLV

Stato Limite di salvaguardia della Vita (Limit State Life Safety)

UHS

Uniform Hazard Spectra

ULS

Ultimate Limit State

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1. CHAPTER 01 EARTHQUAKE ENGINEERING SIMULATION USING PARALLEL COMPUTING SYSTEMS 1.1

Introduction

In general, most of the earthquake engineering simulations require a lot of computing power for conducting realistic earthquake simulations of structural and also geotechnical systems. Inclusion of nonlinear behaviour, time history analysis or probabilistic response analysis just multiplies the computing demand. Some of the probabilistic simulations are so computation intensive, it might take years to run on a conventional desktop machine [Barbosa A., 2011]. That is why parallel computing is becoming a necessary part of earthquake engineering simulations. In principle, parallel computer can run multiple jobs or small parts of big job simultaneously utilizing all the resources available to it. In recent years computing systems have experienced a drastic improvement in raw processing power and also in the number of processing units. Even the desktop computers and laptop computers are equipped with multicore processors nowadays. To harness this raw power given to us by this powerful machines we need to improve the methods how we are utilizing the resources. For example, if we are running a sequential program (one process will wait for other processes to finish) in multicore machines we are going to loose a lot of processing power. The objective of this chapter is to explore and implement different parallelization options available for earthquake engineering simulation. The software framework selected for study is OpenSees as it has a good inbuilt parallelization mechanism. OpenSees has become very popular to many researchers all over the world because of its wide array of choice for material models, elements, solution algorithm etc.

1.2

OpenSees Software Framework

OpenSees [McKenna, F., 1997] is an object-oriented software framework for creating nonlinear finite element applications. The framework provides classes for modelling structural and geotechnical systems, classes to perform nonlinear analysis on the model, and classes to monitor the response of the model during the analysis. The framework is primarily

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written in C++ and provides classes for building finite element applications that can be run on both sequential and parallel computers.

1.3

Parallel Computing Systems

Parallel computing system is a form of computer in which many calculations are carried out simultaneously with the help of multiple processing elements such as CPU (Central Processing Unit), GPU (Graphics Processing Unit), Desktop Computers on a grid. It can either operate in the form of shared memory or message passing. Parallel computers come in many different forms, such as parallel supercomputer with many thousands of processors, local networks of workstations with tens to hundreds of processors, and even single multicore processor personal computers with a few processors.

Figure 1.1: General schematics of Parallel Computing, source: https://computing.llnl.gov/tutorials/parallel_comp/

Parallel computing systems can be categorized based on their processing mechanism, memory access and also the manner of communication between the processors. Following is a classification of some parallel computing system – i.

Scalar Computers (single processor system with pipelining, eg. Pentium4)

ii.

Parallel Vector Computers

iii.

Shared Memory Multiprocessor

iv.

Distributed Memory a. Distributed Memory MPPs (Massively Parallel System) b. Distributed Memory SMPs (Shared-memory multiprocessors) - Hybrid Systems

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v.

Cluster Systems

vi.

Grid

Shared Memory Multiprocessor - Processors operate independently but all access the same memory.

Distributed Memory MPPs (Massively Parallel System) - Processors operate independently - Processors are allowed to have their own memory - Data shared through communication network. Shared-memory multiprocessors - More than 1 scalar processor that share the same memory and memory bus.

Cluster computers Distributed memory computers can also be built from scratch using mass produced PCs and workstations Table 1.1: Some Parallel computing system and their processing mechanism

But one important aspect of the parallel computer has to be kept in mind “it is as fast as the slowest link in the system”. Usually the slowest links are communication between memory and process, sequential portion of the program. This phenomenon can be well explained by famous Amdahl’s [Amdahl 1967] law-

- - - Equation 1.1 - - - Equation 1.2

Where, Time(1) = Time taken by 1 processor to complete the operation Time(p) = Time taken by p processors to complete the same operation

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n = Total number of Processor and α = Portion of sequential Operation

Amdahl's Law 20 18 16 Speedup

14 Sequential Portion α =5%

12 10

α =10%

8

α =50%

6

α =90%

4 2 0 1

8

64

512

4096

32768

Number of Processor (n) Figure 1.2: Graph demonstrating Amdahl’s Law

From the graphs it is clear that even for a program with 95% parallel operation the maximum speed up is 20 times .There is no significant increase in speed after increasing the processor number beyond 512 processors for a program with 10% sequential portion.

1.3.1 Available OpenSees parallel interpreters:

The OpenSees parallel version of the framework uses Message Passing Interface (MPI) for interfacing. For parallel machines with this library, two interpreters can be built from the OpenSees source code distribution: OpenSeesSP and OpenSeesMP.

1.3.1.1

OpenSeesSP

Name of this interpreter is elaborated as 'OpenSees Single Parallel Interpreter'. This interpreter can be utilized for solving large problem with the help of Domain Decomposition techniques. Domain decomposition methods are used to solve a large boundary value problem by splitting it into smaller boundary value problems on subdomains, coordinating solutions between adjacent domains through iteration. No special scripts are needed for domain decomposition. The process is done through MUMPS (aMUltifrontal Massively Parallel

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sparse direct Solver), PETSC (Portable, Extensible Toolkit for Scientific Computation), SuperLU (general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations) and other parallel libraries. The intension of developer for creating the interpreter was to provide researchers a usable parallel system with minimal or no change to the script. Scripting for this interpreter require minimal or no learning.

Figure 1.3: Domain decomposition schematics using OpenSeesSP, source: http://opensees.berkeley.edu/

But speedup is largely dependent on the sequential portion of the program which is splitting and merging of subdomains.

1.3.1.2

OpenSeesMP:

“OpenSeeMP” the name comes from OpenSees “Multiple Parallel” Interpreter's application. It can be used for Performing parameter studies or analysis of large models with user defined partitions. This interpreter is more powerful as it gives more control to the users but requires knowledge about parallel processing.

When the job is submitted in OpenSeesMP each

processor is spawned with same script but with two extra variable ‘np’ (total number of process spawned), ‘pid’ (process id). The user can script in such a way that every processor gets a different job simultaneously. Processor load balancing can also be implemented through sending and receiving processors current status of workload.

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Figure 1.4: Parameter study script spawning on different processor, http://opensees.berkeley.edu/

1.4

Building the OpenSees Interpreters and Parallel Computation Platform in Linux Machines

To compile and use OpenSeesSP or OpenSeesMP in a parallel computing system requires several steps. A summary of the whole compilation process will be presented in this chapter. A more detailed step by step procedure is included in the Appendix-A. Most important part of a parallel computing system is MPI (Massage Passing Interface). Message Passing Interface (MPI) is a standardized and portable message-passing system designed by a group of researchers from academia and industry to function on a wide variety of parallel computers. Latest version of OpenSeesMP/SP utilizes MPICH2. MPICH is a freely available, portable implementation of MPI for distributed-memory applications used in parallel computing.

1.4.1 Setting up MPICH2 Platform

During compilation and installation of MPICH2 extra care should be taken to ensure the compatibility with OpenSees version. Installation of MPICH2 is done through ‘make’ command and customising the installation path to fit user needs. For example, system folders cannot be accessed by normal users, for that situation user has to provide a folder path inside his user home. After installation, the executable path should be incorporated in the environment variable path of linux. This will make sure MPICH2 is always running when the user logs in.

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1.4.2 Compilation and installation of Mathematical Libraries

For its mathematical calculation OpenSees utilizes various open-source algebra packages, matrix solvers, parallel matrix solvers. All the required libraries and their functions are summarized in the table below -

Package Name

Overview

BLAS

Basic Linear Algebra Subprograms

MPIBLACS

Basic Linear Algebra Communication Subprograms - MPI optimized LAPACK — Linear Algebra PACKage LAPACK is written in Fortran

LAPACK

90 and provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. ScaLAPACK is a library of high-performance linear algebra routines

ScaLAPACK

for parallel distributed memory machines. ScaLAPACK solves dense and banded linear systems, least squares problems, eigenvalue problems, and singular value problems.

METIS

METIS is a C program which can partition a graph, partition a finite element mesh, or reorder a sparse matrix.

ParMetis

Parallel version of METIS

MUMPS

MUMPS a MUltifrontal Massively Parallel sparse direct Solver

Table 1.2: Mathematical libraries used by OpenSees

All of these packages have to be compiled separate using make functionality for Linux machines. During compilation output location has to be noted. These output location are used in OpenSees compilation as the source libraries.

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1.4.3 Installation of TCL framework

This step requires administrative privileges. OpenSees uses Tcl/Tk, a general purpose scripting language that has been extended with commands for OpenSees. It is necessary install a proper version compatible with OpenSees Version. TCL provides an easy automatic installation mechanism through “install.sh”.

1.4.4 Compilation of OpenSees Parallel

After Installation and compilation of all the required packages the makefile.def of OpenSees source code has to be edited with proper location path of source libraries. A detailed description of this step is included in Appendix –A.

1.4.5 Example of Parallelization for Parameter study

When a job is submitted in OpenSees parallel version two extra variables are obtained pid = identification number of the process, np = total number of process. Using these two variables a simple algorithm for parallel lopping can be performed where no two processors will process the same job. A schematic of such algorithm is given below where total number of process is 4 and monitored process is pid =0 R = Remainder of (Parameter Set Number / Total Number of Process) If R == pid then parameter set is run Result: No two processors get the same job Job Selection by processor 0

Figure 1.5: Parameter number setup & Simple parameter parallelization algorithm

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set pid [getPID] set np [getNP] set count 0; source ReadRecord.tcl set g 386.4 foreach scaleFactor {0.5 0.75 1.0 1.5 2.0} { foreach gMotion [glob -nocomplain -directory ./ *.AT2] { if {[expr $count % $np] == $pid} {

####PARALLEL PORTION ENSURE UNIQUE JOB TO UNIQUE pid

source model.tcl source analysis.tcl set ok [doGravity] loadConst -time 0.0 if {$ok == 0} { set gMotionName [string range $gMotion 0 end-4] ReadRecord $gMotion $gMotionName$scaleFactor.dat dT nPts timeSeries Path 1 -filePath $gMotionName$scaleFactor.dat -dT $dT -factor [expr $g*$scaleFactor] recorder EnvelopeNode -file $gMotionName$scaleFactor.out -node 100 -dof 1 doDynamic $dT $nPts file delete $gMotionName$scaleFactor.dat } } incr count 1 } }

Figure 1.6: Example Parallel script for Incremental Dynamic Analysis for multiple ground motion, Source: McKenna F., OpenSees Parallel Workshop, 2008

But this script does not ensure load balancing for processor for larger problems load balancing procedures should be incorporated. For testing the developed parallel platform a 6 storied, 3 span linear elastic structure was subjected to 60 ground motions with different processor number. As expected the speedup slows down with increment of processor number.

Figure 1.7: Total Analysis Time plotted against assigned number of processors assigned to the task (test case linear dynamic, 6 Storied building, 60 ground motion)

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1.5

Parallel computation with OpenSees sequential and condor

Another option for parallel computing is with OpenSees sequential through the use of Condor. Condor is a specialized batch system for managing compute-intensive jobs. Like most other batch systems, Condor provides a queuing mechanism, scheduling policy, priority scheme, and resource classifications. Users submit their compute jobs to Condor; Condor puts the jobs in a queue, runs them, and then informs the user as to the result.

Figure 1.8: Condor Computing System, source: condor user manual

A Condor pool [Condor 7.9.1 Manual, 2012] is comprised of a single machine which serves as the central manager, and an arbitrary number of other machines that have joined the pool. Conceptually, the pool is a collection of resources (machines) and resource requests (jobs). The role of Condor is to match waiting re-quests with available resources. Every part of Condor sends periodic updates to the central manager, the centralized repository of information about the state of the pool. Periodically, the central man-ager assesses the current state of the pool and tries to match pending requests with the appropriate resources.

To use OpenSees sequential with Condor, first condor pool has to be setup with a central manager which will control the full parallelization workflow. Following are the building blocks of condor

Central manager - The central manager collects information about the resources available

to the pool, and negotiates between a machine that is submitting a job and the machine that will execute the job. Only one machine in a pool can play this role.

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

Execute machine - Any machine (including the central manager) configured to execute

jobs submitted to the pool. 

Submit machine - Any machine (including the central manager) configure to submit jobs

to the pool. 

Checkpoint server - Any one machine in the pool can act as a backup machine for the

jobs running on the pool. Setting one up is optional, and for our basic pool, we are going to ignore it.

After Setup of condor pool, multiple instances of OpenSees Sequential job can be run at the same time using “condor_submit” daemon.

Following is an example of condor_submit script################################################ # Submit description file for goExampleCondor.tcl ####### ################################################ Executable = opensees_2.exe Universe = vanilla Input = goExampleCondor.tcl Arguments = goExampleCondor.tcl $(Process) $(Process) Error = err.$(Process) Output = out.$(Process) log = log.$(Process) # transfer_input_files = file1.tcl, file2.tcl, otherFile.tcl # should_transfer_files = YES #### these two lines above are needed if there are more input files to be transfered to "execute node" for analysis when_to_transfer_output = ON_EXIT # Initialdir = run$(Process) #### if input files and results of each run are to go to a different output folder queue 10 #### this last digit corresponds to the number of runs.. condor starts numbering $(Process) at 0 and not 1!

Figure 1.9: Typical Condor submit script, Courtesy: Andre Barbosa, 2012

This submit script will spawn multiple instances of OpenSees sequential program with model file “goExampleCondor.tcl” in every node but with two extra parameter one is process identification number another is total number of process. Using these extra two parameter parallelization can be implemented in a similar manner like OpenSeesMP.

Adding the following lines inside OpenSees model will get two parameters pid (process id) and np (total number of process) –

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set pid [lindex $argv 0]; set np [lindex $argv1]; ########################################### # START PARALLEL MODULE BASED ON np AND pid # ###########################################

1.6

Parallel Model Results

For this specific study two nonlinear 2D model of a 3 storied 3 spans and 6 storied 3 spans reinforced concrete building were selected. These two buildings were subjected to 14 ground motion record scaled to 18 hazard levels to observe the EDP (Engineering Demand Parameter) at different level. For the first model, one time history analysis of the model takes approximately 5 minutes in an average to complete when run on a single processor. Which implies 14 X 18 = 252 time history analysis will require 252X10 =1260 minutes or 21 hours. For the second model single ground motion run takes 10 minutes, which will result in 42 hours of sequential simulation. For two models average required time for sequential analysis would be 63 hours. In real situation the model has to be run more than once for the purpose of debugging and troubleshooting. Using the parallel computing system developed in Local cluster of Department of Structural Engineering, Sapienza University of Rome one complete run of both models together took about two hours utilizing 24+24 = 48 processors only. One run of full set of time history generates about 3GB of data which was compressed and transferred to the post processing machine using a FTP (File Transfer Protocol) client. The compiled version of OpenSeesMP was very stable during the whole process of debugging and final run.

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2. CHAPTER 02 GROUND

MOTION

SELECTION

AND

SCALING

FOR

PROBABILISTIC

RESPONSE ANALYSIS OF STRUCUTRES

2.1

Introduction

Researchers have found that the uncertainties in the structural response related to the application of different records can vary significantly depending upon both on the chosen ground motion intensity measure and on the type of structure in relation to its level of nonlinearity [Cantagallo C., 2011].

The record selection used in this study was based on Probabilistic Seismic Hazard Analysis (PSHA) derived from Italian study carried out between 2004 and 2006 by the National Institute of Geophysics and Volcanology (INGV) and the Department of Civil Protection (DPC). This work [http://ess1.mi.ingv.it/] provides the seismic hazard analysis and the disaggregation for each point of a regular grid made of approximately 16 852 nodes analyzing the entire Italian territory.

2.2

Record Selection Using REXEL 3.4:

REXEL 3.4 beta [Iervolino I., 2009], available on the internet on the website of the Italian consortium of earthquake engineering laboratories: Rete dei Laboratori Universitari di Ingegneria Sismica – ReLUIS (http://www.reluis.it/), allows to define the design spectra according to the Eurocode 8 (EC8 – CEN, 2003), the new Italian Building Code (NIBC – CS.LL.PP., 2008), ASCE Standard ASCE/SEI 7-05 (ASCE, 2006) or completely userdefined.

The datasets included in REXEL are the European Strong-motion Database (ESD) (last updated on July 2007), whose URL is http://www.isesd.cv.ic.ac.uk, the Italian Accelerometric Archive (ITACA) (last updated on October 2010) by Istituto Nazionale di Geofisica e Vulcanologia (INGV), whose URL is http://itaca.mi.ingv.it and the database with Selected Input Motions for displacement-Based Assessment and Design (SIMBAD v 2.0) (last updated on November 2011) developed by Smerzini and Paolucci (2011) in the framework of the

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ReLUIS 2010-2013 project (http://www.reluis.it/), in the task referring to Displacement Based Approaches for Seismic Assessment of Structures.

REXEL can search 7 1-component accelerograms whose average matches the reference spectrum in the specified range of periods and with the provided upper- and lower-bound tolerances. The found combinations can be applied in one direction for plane analysis of structures. Large individual variability may affect the accuracy of the estimation of the structural performance if a set of limited number of records (e.g., 7) is employed (Cornell 2004). REXEL enables to have individual records in the combination with a spectral shape as much as possible similar to that of the target spectrum.

REXEL also gives the option to measure how much the spectrum of an individual record deviates from the spectrum of the code. Following is the equation of deviation calculation,

√ ∑

.

...

Equation 2.1

In Equation 2.1, Saj(Ti) is the pseudo-acceleration ordinate of the real spectrum j corresponding to the period Ti, while Satarget(Ti) is the value of the spectral ordinate of the code spectrum at the same period, and N is the number of values within the considered range of periods. This is a good indicative parameter for selecting a ground motion set with low deviation values.

2.3

Ground motion selection approach:

To study the probabilistic response of structure two different sets of ground motion were selected, each of the ground motions sets having seven ground motion records from different events. One set was selected matching with SLV spectrum of NTC -08 with a probability of exceedance of 10% in 50 years. On the other hand, the second set selected based on SLD spectrum of NTC-08 with a probability of exceedance 63% in 50 years. The study site was selected Mormanno, Calabria in Italy. Long – 15.966, Lat – 39.907 coordinate location was used in REXEL to obtain the NTC-08 spectra. To generate site specific the spectra site class –A, Usage Category Cu – II, topographic category – T1 and

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nominal life Vn was taken as 50 years. After obtaining the target NTC-08 spectra it was compared to the Uniform Hazard Spectra (UHS) from Instituto Nazionale di Geofisica e Vulcanologia (INGV) probabilistic seismic hazard analysis (PSHA) (http://esse1gis.mi.ingv.it/s1_en.php). Both of the UHS had a good match with the target NTC-08 spectra.

Figure 2.1: Uniform Hazard Spectra Vs NTC Spectrum for 10% and 63% probability of exceedance in 50 years

2.3.1 Seismic hazard disaggregation for the site

Seismic hazard disaggregation is an important aspect of PSHA. It can give a greater insight to different hazard scenario by extracting the parameter like Moment magnitude, Distance to source for most likely earthquakes having the largest contribution to the hazard level in consideration. INGV provides PGA based disaggregation for the whole Italian region. Seismic hazard disaggregation for two different levels of hazard are given below -

Figure 2.2: Seismic hazard disaggregation for events with 10% Probability of Exceedance in 50 years

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Figure 2.3: Seismic hazard disaggregation for events with 63% Probability of Exceedance in 50 years

From the disaggregation plot two suitable range of M-R were selected for 10% POE and 63% POE hazard levels given in the table below – Set1 – 10 % POE in 50 Years

Set1 – 63 % POE in 50 Years

M Range (Moment Magnitude)

4.0 - 7.5

4.0 - 7.5

R Range (Distance to Site)

0 - 30

0 - 40

Table 2.1: Criteria for ground motion selection

2.3.2 Selected Ground Motions

For searching ground motion upper bound and lower bound of average spectrum from the ground motion was set to 90% and 130 % respectively. The selection parameters and thresholds were defined in REXEL. With automatic matching REXEL presents different combination of records. Using unscaled record selection option 100,000 set of ground motion was generated. A set was selected from those combinations which had a low value of deviation for individual record to target and also mean spectrum to target, presented in the tables below -

16

Waveform ID

Earthquake ID

Station ID

Earthquake Name

Date

Mw

Fault Mechanism

Epicentral Distance [km]

EC8 Site class

198

93

ST64

Montenegro

15/04/1979

6.9

thrust

21

A

147

65

ST28

Friuli (aftershock)

15/09/1976

6

thrust

14

B

7142

2309

ST539

Bingol

01/05/2003

6.3

strike slip

14

A

6093

2050

ST1372

Kozani (aftershock)

19/05/1995

5.2

normal

16

B

4677

1635

ST2562

South Iceland

17/06/2000

6.5

strike slip

21

B

414

192

ST163

Kalamata

13/09/1986

5.9

normal

11

B

333

157

ST121

Alkion

24/02/1981

6.6

normal

20

C

Table 2.2: Selected Ground Motion for probability of exceedance 10% in 50 Years Waveform ID

Earthquake ID

Station ID

Earthquake Name

Date

Mw

Fault Mechanism

Epicentral Distance [km]

EC8 Site class

1926

258

ST1330

Mataranga

30/05/1992

5.2

?

34

B

368

175

ST143

Lazio Abruzzo

07/05/1984

5.9

normal

22

A

292

146

ST98

Campano Lucano

23/11/1980

6.9

normal

25

A

366

175

ST141

Lazio Abruzzo

07/05/1984

5.9

normal

36

B

599

290

ST223

Umbria Marche

26/09/1997

5.7

normal

25

C

435

210

ST159

Kyllini

16/10/1988

5.9

strike slip

36

B

1243

473

ST575

Izmit (aftershock)

13/09/1999

5.8

oblique

15

A

Table 2.3: Selected Ground Motion for probability of exceedance 63% in 50 Years

Ground Motion Selection for Probability of Exceedence 10% in 50 Years Site - Mormanno, Calabria, (7 Ground Motion Record Set)

Sa (g)

1.00

000198x

0.90

000147y

0.80

007142y

0.70

006093y

0.60

004677y

0.50

000414x 000333y

0.40

Target Set1

0.30

Target90%

0.20

Target130%

0.10

AVG

0.00

SaT1

0.0

0.5

1.0

1.5

T (sec)

2.0

2.5

T= 0.15s T= 2.0s

Figure 2.4: Spectrum matching plot for ground motion selection for probability of exceedance 10% in 50 Years, Site - Mormanno, Calabria, (7 Ground Motion Record)

17

Ground Motion Selection for Probability of Exceedence 63% in 50 Years Site - Mormanno, Calabria, (7 Ground Motion Record Set) 0.35

001926x 000368x

0.30

000292x

Sa(g)

0.25

000366x 000599y

0.20

000435x

0.15

001243x Target Set2

0.10

Target90%

Target130%

0.05

Series11

0.00

SaT1

0.0

0.5

1.0

1.5

2.0

T (sec)

2.5

T= 0.15s T= 2.0s

Figure 2.5: Spectrum matching plot for ground motion selection for probability of exceedance 63% in 50 Years, Site - Mormanno, Calabria, (7 Ground Motion Record)

2.3.3 Ground Motion Scaling for Incremental Dynamic Analysis

For the purpose of getting a smooth IDA curve 9 extra Hazard Level were interpolated logarithmically from the hazard curve distributed uniformly mostly in the higher range of PGA. The blue rows in the following table indicate original levels of hazard and grey rows represent interpolated levels of hazard. POE 50 Years

AFOE

PGA

ln AFOE

ln PGA

2.0% 2.5% 3.2% 4.0% 5.0% 6.0% 7.1% 8.4% 10.0% 12.2% 14.9% 18.2% 22.0% 30.0% 39.0% 50.0% 63.0% 81.0%

0.000404 0.000510 0.000644 0.000813 0.001026 0.001228 0.001470 0.001760 0.002107 0.002611 0.003236 0.004010 0.004969 0.007133 0.009886 0.013863 0.019885 0.033215

0.479 0.440 0.404 0.371 0.341 0.315 0.292 0.270 0.250 0.225 0.203 0.182 0.164 0.134 0.114 0.094 0.076 0.056

-7.81396 -7.58103 -7.34809 -7.11515 -6.88222 -6.70226 -6.52230 -6.34235 -6.16239 -5.94792 -5.73344 -5.51897 -5.30449 -4.94295 -4.61664 -4.27854 -3.91779 -3.40477

-0.73626 -0.82153 -0.90680 -0.99207 -1.07734 -1.15418 -1.23102 -1.30786 -1.3847 -1.49080 -1.59690 -1.70301 -1.80911 -2.00842 -2.17595 -2.36234 -2.57571 -2.88419

Table 2.4: Different target hazard level for IDA analysis

18

Hazard Curve (Red Dots Represent Logarithmically Interpolated PGA values)

Peak Ground Aceeleration (g)

1.00

0.10

0.01 0.01%

0.10%

1.00%

10.00%

Annual Frequency of Exceedence (%)

Figure 2.6: Logarithmic interpolation of intermediate hazard levels

Scaling to above mentioned 18 hazard levels was done based on “PGA of target hazard level” to “PGA of original hazard level” ratio.

Where, = Scale factor for scaling the ground motion to target hazard level = Peak Ground Acceleration for the target hazard level = Peak Ground Acceleration for original hazard level

After scaling the ground motion, PGA of each ground motion was plotted against Annual frequency of Exceedance to observe the variability of PGA with the hazard curve,

19

PGA of All Ground Motion For Different Hazard Level 1.000 gm01 gm02

Peak Ground Acceleration (g)

gm03 gm04 gm05 gm06

0.100

gm07 gm08 gm09 gm10 gm11 gm12 gm13

0.010 0.01%

0.10%

1.00%

10.00%

Annual Frequency of Exceedance(%)

gm14 PGA HL

Figure 2.7: SaT1 at different levels of hazard

Here black line indicates the original hazard curve obtained from INGV website. (http://esse1-gis.mi.ingv.it/s1_en.php)

The basic objective of this exercise was to find ground motion sets, which has good compliance with spectral shape of the target spectrum, within code provisions. The ground motions were not scaled based on one single spectral ordinate (i.e. SaT1/PGA) rather the whole set of ground motion were scaled to the target hazard level.

20

3. CHAPTER 03 NONLINEAR

INCREMENTAL

DYNAMIC

SIMULATION

AND

RESPONSE

ANALYSIS

3.1

Introduction

In earthquake engineering nonlinear time history analysis is of great importance. Nonlinear time history analysis has the capacity to predict behavior and responses of structures more accurately than linear methods [Spacone, 2007]. Nonlinear methods are gaining more and more user-base as modern design codes are supporting this kind of analysis. Nonlinear static methods are not sufficient to study the realistic dynamic variation of responses. For this study two 2D nonlinear panel was designed and modeled with nonlinear material models and force based elements for the site Mormanno, Calabria, Italy. The models were subjected to 14 ground motions with 18 scaled level of Intensity to observe the response and Engineering Demand Parameters (EDP).

3.2

Description of the structural models

3.2.1 Model 1

The Model building is a 3 storied reinforced concrete structure with 3 spans in x direction and 2 spans in the y direction.

3000

3000

Y 2850 X

3000

3000 Y Z

2850

X

Y

Z

Figure 3.1: Model 1 Structural configuration

21

The design was carried out in accordance with NTC-08 provision. Following are the different sections used for different elements-

Column 1:300x300

Beam Section 1: 300x500

Beam Section 2-3 : 300x500

Beam Section 4 : 300x500

Beam Section 5 : 300x500

Beam Section 6 : 300x500

Table 3.1: Section configuration of model 1

X-Y plane panel was selected for analysis. For the study 3 types of concrete were modelled with the Kent and Park model for concrete [Kent DC, 1971] i) unconfined concrete: fpc (concrete

compressive strength at 28 days) = -20.75 MPa, εc0 (concrete strain at maximum

strength) = -0.002 , fpcu (concrete crushing strength)= -4.15 MPa and εcu(concrete strain at crushing strength) = 0.0165, ii) confined concrete column: fpc = -21.759 MPa, εc0 = 0.002097, fpcu = -4.352 MPa and εcu = -0.011, confined concrete beam: fpc = -21.1 MPa, εc0 = 0.002, fpcu = -4.220 MPa and εcu = -0.008. iii) “Uniaxial bilinear steel material object with kinematic hardening and optional isotropic hardening” was selected as the steel material model with fy (yield strength) = 340MPa, E (initial elastic tangent)= 210 GPa and b (strainhardening ratio) = 0.

22

Figure 3.2: Typical Hysteretic Stress-Strain Relation for Kent and Park concrete material model

Figure 3.3: Steel Material Hysteretic Behavior of Model with or without Isotropic Hardening

In order to account for the real structural behavior of frames, gravity loads were applied statically before the earthquake excitation was applied dynamically. Eigen Analysis was performed before applying gravity loading. Beam and column elements were modeled with Beam With Hinges Element [Scott, M.H et al. 2006]

Fiber Section

Figure 3.4: Schematics of beam with hinges element

23

Figure 3.5: Fibre modelling of a reinforced concrete section

There are many advantages to this formulation over the standard “forceBeamColumn” element, such as Nonlinear behavior is confined to the integration points at the element ends, Represents linear curvature distributions exactly.

3.2.2 Model 2

This Model building has identical configuration to first model but it has 6 stories and the column sections are changed after every two stories.

Y

X

Figure 3.6: Model 2 Structural configuration

24

The design was carried out in accordance with NTC-08 provision. Following are the different sections used for different elements-

Stirrups f6 @15mm

Stirrups f6 @15mm

Column 1:300x300

Column 2:300x400

Column 3:300x500

Storey Level – 1,2

Storey Level – 3,4

Storey Level – 5,6

Beam Section 1: 300x500

Beam Section 2-3 : 300x500

Beam Section 5 : 300x500

Beam Section 6 : 300x500

Beam Section 4 : 300x500

Table 3.2: Section configuration of model 2

For the second model Kent Park concrete model was used for confined and unconfined concrete. Steel material was modeled with Giuffre-Menegotto-Pinto steel material model with fy = 340MPa, E = 210 GPa and R0 (transition parameter from elastic to plastic) =18.5.

25

Figure 3.7: Steel Material - Hysteretic Behavior of Model w/o Isotropic Hardening

3.3

Parallel Simulation of Incremental Dynamic Analysis

For performing the dynamic analysis a parallel simulation model was setup in such a way that post processing the output becomes easier and can be performed with looping and single command. The model was run in the parallel computing platform developed in Structural Engineering Department of Sapienza university of Rome. There are total 14 ground motions and 18 scaling level. So after the simulation total 252 sets of individual records were generated for each model. Total runtime for a successful simulation was around 50 minutes for model 1 and 120 minutes for model 2 using 20 processing units each model. About 3 gigabyte of data was generated, which was transferred using file transfer protocol to the post processing machine. A directory structure GMxx\HLxx was created to save individual set of outputs from recorders, and post processed using looping algorithm.

3.4

Response Analysis

Maximum drift ratio from all storey level and individual storey level were plotted against peak ground acceleration of all hazard level to compare, which stories are experiencing more drift and contributing to the global drift demand. Inspecting the figure it is evident that first storey has the largest contribution to drift demand. Plotting section curvature at the base of the column against peak ground acceleration shows the same pattern of curvature.

26

Model1: 3 Storied Building Level-3 02% POE in 50 years

0.4 0.3 10% POE in 50 years

0.2 0.1 0

63% POE in 50 years

0

0.5

1

1.5

2

2.5

1.5

2

2.5

1 1.5 IDRmax-X(%)

2

2.5

Level-2

PGA(g)

0.4 0.3 0.2 0.1 0

0

0.5

1 Level-1

0.4 0.3 0.2 0.1 0

0

0.5

Figure 3.8: Peak Interstorey Drift Ratio Vs PGA of Hazard Level, Model1

Another important observation can be made from the IDA (Incremental Dynamic Analysis) curve of maximum interstorey drift ratio is that up to 63% POE (Probability of Exceedance) in 50 years behaviour of the structure is mostly linear. But those linear curves are different for different ground motion, which shows the effect of variability of ground motion on responses. For 63% to 10% POE in 50 years range structure starts showing some nonlinear behaviour and from 10% to 2% POE in 50 years behaviour is predominantly nonlinear with some collapse cases.

27

Level-3 02% POE in 50 years

0.4 0.3 10% POE in 50 years

0.2 0.1 0

63% POE in 50 years

0

10

20

30

40

50

30

40

50

40

50

Level-2

PGA(g)

0.4 0.3 0.2 0.1 0

0

10

20 Level-1

0.4 0.3 0.2 0.1 0

0

10

20 30 Kmax-X(micro-radian/mm)

Figure 3.9: Maximum Curvature at floor level Vs PGA of Hazard Level,Model1

From the figure it can be concluded that the first storey column base experiences most of the curvature demand.

28

Level-3 0.4 0.2 0

0

0.2

0.4

0.6

0.8

1

1.2

Level-2 02% POE in 50 years

0.4 10% POE in 50 years

0.2 PGA(g)

63% POE in 50 years

0

0

0.2

0.4

0.6

0.8

1

1.2

0.8

1

1.2

0.6 0.8 PFAmax-X(g)

1

1.2

Level-1 0.4 0.2 0

0

0.2

0.4

0.6 Level-0

0.4 0.2 0

0

0.2

0.4

Figure 3.10: Absolute Peak Floor Acceleration Vs Peak Ground Acceleration of Hazard Level at each storey, Model1

From peak floor acceleration IDA curve it can be seen that third floor experiences the maximum floor acceleration, while level 1 and 2 experiences similar acceleration.

29

Model 2: 6 storied building

Level-6 0.5

02% POE in 50 years 10% POE in 50 years 63% POE in 50 years

0

0

0.5

1

1.5 Level-5

2

2.5

0

0.5

1

1.5 Level-4

2

2.5

0

0.5

1

1.5 Level-3

2

2.5

0

0.5

1

1.5 Level-2

2

2.5

0

0.5

1

1.5 Level-1

2

2.5

0

0.5

1 1.5 IDRmax-X(%)

2

2.5

0.5

0

PGA(g)

0.5

0 0.5

0 0.5

0 0.5

0

Figure 3.11: Peak Interstorey Drift Ratio Vs PGA of Hazard Level, Model 2

For the second model maximum IDR demand is at level1and level -2/4 has similar demands, failures mostly occurring between 10% POE in 50 Years to 63% POE in 50 Years floor level 1to 4. Top Floor has the lowest drift demand.

30

Level-6 0.5

02% POE in 50 years 10% POE in 50 years 63% POE in 50 years

0

0

10

20 30 Level-5

40

50

0

10

20 30 Level-4

40

50

0

10

20 30 Level-3

40

50

0

10

20 30 Level-2

40

50

0

10

20 30 Level-1

40

50

0

10 20 30 40 Kmax-X(micro-radian/mm)

50

0.5

0

PGA(g)

0.5

0 0.5

0 0.5

0 0.5

0

Figure 3.12: Maximum Curvature at floor level Vs PGA of Hazard Level, Model2

31

Level-6 0.5 0

0

0.2

0.4

0.6 Level-5

0.5 0

0.8

1

1.2

02% POE in 50 years 10% POE in 50 years 63% POE in 50 years

0

0.2

0.4

0.6 Level-4

0.8

1

1.2

0

0.2

0.4

0.6 Level-3

0.8

1

1.2

0

0.2

0.4

0.6 Level-2

0.8

1

1.2

0

0.2

0.4

0.6 Level-1

0.8

1

1.2

0

0.2

0.4

0.6 Level-0

0.8

1

1.2

0

0.2

0.4 0.6 0.8 PFAmax-X(g)

1

1.2

0.5

PGA(g)

0 0.5 0 0.5 0 0.5 0 0.5 0

Figure 3.13: Absolute Peak Floor Acceleration vs Peak Ground Acceleration of Hazard Level at each storey, Model2

From the figure above it is visible that level -1 and level – 2 experiences higher peak floor acceleration demands.

32

3.5

Limitations

There were some limitations in this study. Variation of input parameters was not considered for the model, model was simulated using a median value of material strength and other parameter. Only PGA based hazard disaggregation was utilized which readily available from INGV, Sa based disaggregation was not used. Floor diaphragm action was modeled with rigid constraint, which can induce unrealistic axial force and possibly change bending moments in the beam and shear forces in the columns modeled with force based beam column [Terzic V. , 2011].

3.6

Conclusion

Use of parallel computing system for earthquake engineering simulation is really necessary when the models are really big or requires numerous number of run for the purpose of probabilistic study. The parallel incremental dynamic analysis in this study showed that proper utilization of time can be done by researchers without having to wait for a long time to get the output files. But the main challenge is to develop a parallel computing system which can utilize all the resources available. Through the experience of developing OpenSeesMP platform in Sapienza University cluster a developer manual “Compilation Guideline of OpenSeeMP on Linux Machines” was produced for future reference of researchers, which can be found in OpenSees wiki website (Appendix-A). But special care should be taken on job management aspects of parallelization. Processor load balancing mechanism has to be incorporated inside the parallelization scheme as some analysis will finish before others due to the size of ground motion, convergence issues. An effective processor load balancing mechanism will ensure the full use of all the resources and complete analysis on shortest possible time.

For ground motion selection the approach was to match the spectral shape to the target spectrum shape. Deviation was calculated from the target spectrum to the natural ground motion spectrum, then based on the minimal deviation record sets were selected. The findings from different researches states that Sa(T1) alone as the IM is not optimal (e.g. not efficient nor sufficient) in characterizing the ground motion intensity [2-D analysis: Baker and Cornell 2005; 3-D analysis Faggella et al., 2011]. This process ensures spectral shape matching rather than a single value of intensity measure.

33

From the plots of incremental dynamic analysis it is evident that structural behavior gets really complex in the nonlinear range. Even for ground motion with similar spectral shape results in large variability in EDP largely due to higher mode response and nonlinearity. Damping parameter largely affects the overall stability of the model. For this study damping matrix was updated at every step, from dynamic stiffness matrix as it shows good resemblance to real damping behavior. This kind of study with different a set of natural ground motions can give us the idea of realistic variation of structural responses due to ground motion variability even with same intensity measures.

It is shown in this study; with the help of parallelization it is really quick and efficient to study response variation due to variability of input parameters (Ground Motion), which can be used for performance based design. Researchers can build their own parallel computing system with minimum effort, otherwise it is possible to use free cloud computing resources available like NEEShub (https://nees.org/tools/openseeslab/).

34

3.7

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