Technical Report Documentation Page Rapid Retrofitting ... · 18/01/2020 · the cumulative damage...

i

Technical Report Documentation Page

1. Report No. 2. Government Accession No. 3. Recipient’s Catalog No.

ABC-UTC-2016-C1-OU02-Final

4. Title and Subtitle 5. Report Date

Rapid Retrofitting Techniques for Induced Earthquakes

January 2020

6. Performing Organization Code

7. Author(s) 8. Performing Organization Report No.

Philip S. Harvey Jr. (https://orcid.org/0000-0002-0565-3102), Kanthasamy K. Muraleetharan (https://orcid.org/0000-0002-4187-4818), Sumangali Sivakumaran

9. Performing Organization Name and Address 10. Work Unit No. (TRAIS)

School of Civil Engineering and Environmental Science University of Oklahoma 202 W. Boyd St., Room 334 Norman, OK 73019-1024

11. Contract or Grant No.

69A3551747121

12. Sponsoring Organization Name and Address 13. Type of Report and Period Covered

Accelerated Bridge Construction University Transportation Center Florida International University 10555 W. Flagler Street, EC 3680 Miami, FL 33174

US Department of Transportation Office of the Assistant Secretary for Research and Technology And Federal Highway Administration 1200 New Jersey Avenue, SE Washington, DC 201590

Final Report (January 2018 to July 2019)

14. Sponsoring Agency Code

15. Supplementary Notes

Visit www.abc-utc.fiu.edu for other ABC reports.

16. Abstract

States such as Oklahoma, Texas, Kansas and Arkansas have historically experienced only one or two tectonic earthquakes annually, but these states are now experiencing earthquakes at an increased rate due to induced seismicity. Consequently, State Departments of Transportation (DOTs) are concerned about how their bridges that were originally designed for low seismic design loads will handle this increased seismic demand. While a bridge collapse is unlikely for an induced earthquake, cumulative effects of large number of small induced earthquakes compounded with an occasional moderate earthquake may lead to damages negatively impacting the safety of the traveling public and the flow of the transportation network. This research addresses the knowledge gap on the effects of low-level frequent earthquakes on the bridges and proposes a framework to assess the cumulative damage on bridges using rainflow counting based on ASTM standard practice for cycle counting in fatigue. In addition, a quantitative measure – Fatigue Damage Index (FDI) – is developed using Miner’s Rule to identify the accumulated damage in the bridge, from which the remaining service life can be estimated. The FDI can also be used to predict when accelerated repairs may be required and to evaluate accelerated retrofit solutions. Further, a “typical” Oklahoma is modeled in a finite element program (OpenSees), and the proposed framework is applied to capture the structural deterioration of the bridge.

17. Key Words 18. Distribution Statement

Induced seismicity, man-made, cumulative damage, fatigue, rainflow counting No restrictions.

19. Security Classification (of this report)

20. Security Classification (of this page) 21. No. of Pages 22. Price

Unclassified. Unclassified. 88

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized

(this page is intentionally left blank)

ii

Rapid Retrofitting Techniques for Induced Earthquakes

Final ReportJanuary 2020

Principal Investigator: P. Scott Harvey Jr.

School of Civil Engineering and Environmental ScienceUniversity of Oklahoma, Norman, OK

Co-Principal Investigator: Kanthasamy K. Muraleetharan

School of Civil Engineering and Environmental ScienceUniversity of Oklahoma, Norman, OK

AuthorsP. S. Harvey Jr., K. K. Muraleetharan, and S. Sivakumaran

Sponsored byAccelerated Bridge Construction University Transportation Center

A report fromSchool of Civil Engineering and Environmental Science

University of Oklahoma202 W. Boyd St., Room 334Norman, OK 73019-1024

iii

DISCLAIMER

The contents of this report reflect the views of the authors, who are responsible for the facts andthe accuracy of the information presented herein. This document is disseminated in the interestof information exchange. The report is funded, partially or entirely, by a grant from the U.S. De-partment of Transportation’s University Transportation Program. However, the U.S. Governmentassumes no liability for the contents or use thereof.

iv

AbstractStates such as Oklahoma, Texas, Kansas and Arkansas have historically experienced only oneor two tectonic earthquakes annually, but these states are now experiencing earthquakes at an in-creased rate due to induced seismicity. Consequently, State Departments of Transportation (DOTs)are concerned about how their bridges that were originally designed for low seismic design loadswill handle this increased seismic demand. While a bridge collapse is unlikely for an inducedearthquake, cumulative effects of large number of small induced earthquakes compounded with anoccasional moderate earthquake may lead to damages negatively impacting the safety of the trav-eling public and the flow of the transportation network. This research addresses the knowledge gapon the effects of low-level frequent earthquakes on the bridges and proposes a framework to assessthe cumulative damage on bridges using rainflow counting based on ASTM standard practice forcycle counting in fatigue. In addition, a quantitative measure – Fatigue Damage Index (FDI) – isdeveloped using Miner’s Rule to identify the accumulated damage in the bridge, from which theremaining service life can be estimated. The FDI can also be used to predict when accelerated re-pairs may be required and to evaluate accelerated retrofit solutions. Further, a “typical” Oklahomabridge is modeled in a finite element program (OpenSees), and the proposed framework is appliedto capture the structural deterioration of the bridge.

v

AcknowledgementsThis project was supported by the Accelerated Bridge Construction University Transportation Cen-ter (ABC-UTC at www.abc-utc.fiu.edu) at Florida International University (FIU) as lead institutionand Iowa State University (ISU), the University of Nevada-Reno (UNR), the University of Okla-homa (OU), and the University of Washington (UW) as partner institutions. The authors wouldlike to acknowledge the ABC-UTC support.

The authors would like to extend special appreciation to the ABC-UTC and the U.S. Depart-ment of Transportation Office of the Assistant Secretary for Research and Technology for fundingthis project.

The authors would like to also thank the project Research Advisory Panel members: WalterPeters and Steve Jacobi from Oklahoma DOT and Gregg Hostetler from CONSOR Engineers(formerly Infrastructure Engineers).

vi

www.abc-utc.fiu.edu

Table of ContentsDisclaimer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Research Approach and Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Description of Research Project Tasks . . . . . . . . . . . . . . . . . . . . . . . . 31.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Induced Ground-Motion Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Ground Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.4 Ground-Motion Intensity Measures . . . . . . . . . . . . . . . . . . . . . . . . . . 72.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Cumulative Seismic Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.3 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.4 Fatigue Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.5 Rainflow Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.6 Cumulative Seismic Demand – Simple Oscillator . . . . . . . . . . . . . . . . . . 12

3.6.1 Pseudo-Acceleration Cycle Counts . . . . . . . . . . . . . . . . . . . . . . 163.6.2 SRSS Cycle Counts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4 Fatigue Damage Index (FDI) Framework . . . . . . . . . . . . . . . . . . . . . . . . 194.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.2 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.3 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.4 Step 1 – Mathematical Model of the Impacted Structure . . . . . . . . . . . . . . . 214.5 Step 2 – Compile Ground-Motion Data . . . . . . . . . . . . . . . . . . . . . . . . 22

vii

4.6 Step 3 – Characterize the Cyclic Seismic Demand . . . . . . . . . . . . . . . . . . 224.7 Step 4 – Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.8 Step 5 – Demand/Capacity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 244.9 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.1 A “Typical” Oklahoma Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.2 Fatigue Damage Index (FDI) Analysis . . . . . . . . . . . . . . . . . . . . . . . . 285.3 Cumulative Seismic Demand – Finite Element Model . . . . . . . . . . . . . . . . 315.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

6 Summary, Conclusions, and Recommendations . . . . . . . . . . . . . . . . . . . . . 34

7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

A Earthquake Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

B Tabulated Cycle Counts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

C Oklahoma Bridge Inventory Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 68C.1 Structure Type Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68C.2 Bridge Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

C.2.1 Prestressed Concrete Girder Bridges . . . . . . . . . . . . . . . . . . . . . 70C.2.2 Steel Girder Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72C.2.3 Continuous Steel Girder Bridges . . . . . . . . . . . . . . . . . . . . . . . 73

C.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

viii

List of Figures1.1 Cumulative number of earthquakes with a magnitude 3.0 or larger in the central

United States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Magnitude 3.0 and larger earthquakes in Oklahoma: (a) 2003–2007 (≈ 12 events),

(b) 2008–2012 (≈ 164 events), and (b) 2013–2017 (≈ 2634 events) . . . . . . . . . 62.2 Seismic stations and earthquakes in the ground-motion data set. . . . . . . . . . . . 72.3 Attenuation of peak ground acceleration (PGA) with epicentral distance from seis-

mic stations (a) OK.U32A and (b) GS.OK005. . . . . . . . . . . . . . . . . . . . . 72.4 Spectral response acceleration Sa (5% damped) measured at seismic stations com-

pared with the design response spectra per the 2009 AASHTO Guide specificationsfor LRFD seismic bridge design: (a) OK.U32A and (b) GS.OK005 . . . . . . . . . 8

2.5 Attenuation of 0.3-sec spectral acceleration (S 0.3) with epicentral distance fromseismic stations (a) OK.U32A and (b) GS.OK005. . . . . . . . . . . . . . . . . . . 9

2.6 Attenuation of 1-sec spectral acceleration (S 1) with epicentral distance from seis-mic stations (a) OK.U32A and (b) GS.OK005. . . . . . . . . . . . . . . . . . . . . 9

3.1 Rainflow counting algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Response of simple harmonic oscillator (T = 0.3 sec, ζ = 5%) subject to the

NS component of the ground-motion acceleration measured at station OK.U32Aduring the M5.8 Pawnee earthquake. . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3 Sequence of peaks and valleys (dots) identified from the response of simple har-monic oscillator (T = 0.3 sec, ζ = 5%) subject to the NS component of the ground-motion acceleration measured at station OK.U32A during the M5.8 Pawnee earth-quake. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.4 Histogram of displacement cycles for the response of simple harmonic oscillator(T = 0.3 sec, ζ = 5%) subject to the NS component of the ground-motion acceler-ation measured at station OK.U32A during the M5.8 Pawnee earthquake. . . . . . 14

3.5 Displacement cycles for the response of simple harmonic oscillator (ζ = 5%) withperiod T = 0.3 sec (left) and 1 sec (right) subject to the EW and NS componentsof all the ground-motion accelerations measured at station OK.U32A in 2016. . . . 15

3.6 Displacement cycles for the response of simple harmonic oscillator (ζ = 5%) withvarying period T subject to the EW (left) and NS (right) components of all theground-motion accelerations measured at station OK.U32A in 2016. . . . . . . . . 15

3.7 Displacement cycles for the response of simple harmonic oscillator (ζ = 5%) withvarying period T subject to the EW (left) and NS (right) components of all theground-motion accelerations measured at station GS.OK005 in 2016. . . . . . . . 15

3.8 Pseudo-acceleration cycles for the response of simple harmonic oscillator (ζ = 5%)with period T = 0.3 s (left) and 1 s (right) subject to the EW and NS componentsof all the ground-motion accelerations measured at station OK.U32A in 2016. . . . 17

3.9 Pseudo-acceleration cycles for the response of simple harmonic oscillator (ζ = 5%)with varying period T subject to the EW (left) and NS (right) components of allthe ground-motion accelerations measured at station OK.U32A in 2016. . . . . . . 17

ix

3.10 Pseudo-acceleration cycles for the response of simple harmonic oscillator (ζ = 5%)with varying period T subject to the EW (left) and NS (right) components of allthe ground-motion accelerations measured at station GS.OK005 in 2016. . . . . . . 17

3.11 Displacement (left) and pseudo-acceleration (right) cycles for the response of sim-ple harmonic oscillator (ζ = 5%) with varying period T ; square root of the sum ofthe squares (SRSS) of the EW and NS counts of all the ground-motion accelera-tions measured at station OK.U32A in 2016. . . . . . . . . . . . . . . . . . . . . . 18

3.12 Displacement (left) and pseudo-acceleration (right) cycles for the response of sim-ple harmonic oscillator (ζ = 5%) with varying period T ; square root of the sum ofthe squares (SRSS) of the EW and NS counts of all the ground-motion accelera-tions measured at station OK.U32A in 2016. . . . . . . . . . . . . . . . . . . . . . 18

4.1 Fatigue damage index (FDI) framework. . . . . . . . . . . . . . . . . . . . . . . . 215.1 Picture of the SH-99 bridge over Tiger Creek. (Image captured March 2016 cour-

tesy of Oklahoma Department of Transportation.) . . . . . . . . . . . . . . . . . . 275.2 Configuration and layout of the SH-99 bridge over Tiger Creek. . . . . . . . . . . . 285.3 Longitudinal (left) and transverse (right) mode shapes of the SH-99 bridge over

Tiger Creek determined using OpenSees. . . . . . . . . . . . . . . . . . . . . . . . 295.4 Displacement cycles for the response of simple harmonic oscillator (ζ = 5%) for

periods corresponding to the longitudinal (left) and transverse (right) directions ofthe SH-99 bridge over Tiger Creek; square root of the sum of the squares (SRSS) ofthe EW and NS counts of all the ground-motion accelerations measured at stationsGS.OK005 in 2016. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.5 Pseudo-acceleration cycles for the response of simple harmonic oscillator (ζ = 5%)for periods corresponding to the longitudinal (left) and transverse (right) directionsof the SH-99 bridge over Tiger Creek; square root of the sum of the squares (SRSS)of the EW and NS counts of all the ground-motion accelerations measured at sta-tions GS.OK005 in 2016. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.6 Pushover analysis—pseudo-acceleration versus stress at the twelve reinforcingbars—in the longitudinal (left) and transverse (right) directions of the SH-99 bridgeover Tiger Creek. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.7 Stress cycles corresponding to equivalent loading in the longitudinal (left) andtransverse (right) directions of the SH-99 bridge over Tiger Creek. . . . . . . . . . 31

5.8 Stress cycles determined from the OpenSees model of the SH-99 bridge over TigerCreek oriented East-West (left) and North-South (right) subject to all the ground-motion accelerations measured at station GS.OK005 in 2016. . . . . . . . . . . . . 32

C.1 Number of spans histogram for Prestressed Concrete Girder bridges. . . . . . . . . 70C.2 Main span length histogram for 3-Span Prestressed Concrete Girder bridges. . . . . 70C.3 Bridge length histogram for 3-Span Prestressed Concrete Girder bridges. . . . . . . 71C.4 Prestressed Concrete Girder Bridges: Three dimensional representation of main

span length and total length histograms. . . . . . . . . . . . . . . . . . . . . . . . 71C.5 Year built histogram for 3-Span Prestressed Concrete Girder bridges. . . . . . . . . 72C.6 Number of spans histogram for Steel Girder bridges. . . . . . . . . . . . . . . . . 72

x

C.7 Main span length histogram for 3-Span Steel Girder bridges. . . . . . . . . . . . . 73C.8 Bridge length histogram for 3-Span Steel Girder bridges. . . . . . . . . . . . . . . 73C.9 Steel Girder Bridges: Three dimensional representation of main span length and

total length histograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74C.10 Year built histogram for 3-Span Steel Girder bridges. . . . . . . . . . . . . . . . . 74C.11 Number of spans histogram for Continuous Steel Girder bridges. . . . . . . . . . . 74C.12 Span length histogram for 3-Span Continuous Steel Girder bridges. . . . . . . . . . 75C.13 Bridge length histogram for 3-Span Continuous Steel Girder bridges. . . . . . . . . 75C.14 Continue Steel Girder Bridges: Three dimensional representation of main span

length and total length histograms. . . . . . . . . . . . . . . . . . . . . . . . . . . 76C.15 Year Built histogram for 3-Span Continuous Steel Girder bridges . . . . . . . . . . 76

xi

List of Tables2.1 Seismic stations composing the ground-motion suite. . . . . . . . . . . . . . . . . 65.1 Fatigue damage index (FDI) for the longitudinal reinforcing bars at the base of the

column in the SH-99 bridge over Tiger Creek for all the ground-motion accelera-tions measured at stations GS.OK005 in 2016. . . . . . . . . . . . . . . . . . . . . 31

5.2 Damage fraction C for the longitudinal reinforcing bars at the base of the columnin the SH-99 bridge over Tiger Creek oriented East-West (EW) for all the ground-motion accelerations measured at stations GS.OK005 in 2016. . . . . . . . . . . . 32

A.1 Earthquake sequence for seismic station OK.U32A in 2016. . . . . . . . . . . . . . 38A.2 Earthquake sequence for seismic station GS.OK005 in 2016. . . . . . . . . . . . . 53B.1 Displacement cycle counts for seismic station OK.U32A in 2016. . . . . . . . . . . 64B.2 Displacement cycle counts for seismic station GS.OK005 in 2016. . . . . . . . . . 66C.1 Design main span for all bridges in the inventory. . . . . . . . . . . . . . . . . . . 68C.2 Bridge classes by construction material. . . . . . . . . . . . . . . . . . . . . . . . 69

xii

1 Introduction1.1 Background

Since 2009, there has been a dramatic increase in the number of earthquakes in the central U.S.(Figure 1.1) (USGS, 2017a). States such as Oklahoma, Texas, Kansas, and Arkansas have nothistorically experienced earthquakes at the rate currently observed, nor of this magnitude (McGarret al., 2015). Studies such as by Keranen et al. (2013) have linked the increased rate of seismicactivity since 2009 to wastewater injection in disposal wells. These induced earthquakes are notlimited to the U.S. but are also experienced in other countries including Canada, China, and theUnited Kingdom (McGarr et al., 2015). The seismicity of places such as California and the NewMadrid seismic zone is well documented and generally thought of when discussing seismic hazardsin the contiguous U.S. Yet the cumulative moment in Oklahoma in 2015 and 2016 (1 January 2015to 31 December 2016) exceeded that of southern California and the New Madrid seismic zones.

The major fault in the central U.S. is the New Madrid fault (Frankel et al., 2009) located alongthe Mississippi River between Tennessee, Arkansas, Missouri, and Kentucky. The only otheridentified source of tectonic earthquakes in this region is the Meer’s fault in southwest Oklahoma,as reflected in the U.S. Geological Survey (USGS) national seismic hazard maps (Petersen et al.,2014) and accordingly the mapped design ground motion data provided by design provisions, suchas the 2009 AASHTO Guide Specifications for LRFD Seismic Bridge Design (AASHTO, 2009). In2016, the USGS made an effort to incorporate non-tectonic earthquakes (or “induced seismicity”)into the national seismic hazard model (Petersen et al., 2016), but these are not reflected in seismicdesign provisions. Accordingly, concern has risen about how civil infrastructure in the central U.S.will handle the increased seismic demand (Harvey et al., 2018a).

A majority of the earthquakes occurring in the central U.S. are small-to-moderate in magni-tude, ranging from magnitude (M) 3.0 to 5.0. Over the last decade, the central U.S. has experi-enced nearly 120 M4.0 and greater earthquakes, with a majority (81) occurring in Oklahoma. At

Figure 1.1: Cumulative number of earthquakes with a magnitude 3.0 or larger in the central United States (USGS,2017a).

1

12:02:44 Coordinated Universal Time (UTC) on 3 September 2016, a M5.8 earthquake struck 15km northwest of Pawnee, Oklahoma. The event was triggered by strike-slip faulting within theinterior of the North America plate (USGS, 2016a), at a focal depth of 5.6 km and is the largestrecorded event in Oklahoma to date. Over the decade prior to this event, the central U.S. expe-rienced two other events larger than M5.0: the 6 November 2011 M5.7 earthquake near Prague,Oklahoma (USGS, 2016b) and the 13 February 2016 M5.1 earthquake near Fairview, Oklahoma(USGS, 2016c). A fourth large event (M5.0) occurred on 7 November 2016 near Cushing, Okla-homa (USGS, 2016d). These M5.0 and larger events were felt in the surrounding states, causeddamage to residential structures, and resulted in minor injuries (Taylor et al., 2017). Slight damageto highway bridges was also reported following the M5.8 Pawnee event, which included spallingof concrete on one bridge (GEER, 2016) and a roller bearing coming dislodged on another (W. L.Peters, pers. comm., 20 October 2016).

While collapse is unlikely for the induced earthquakes currently observed (Harvey et al., 2018b;Chase et al., 2019), the cumulative effects of a large number of small-to-moderate earthquakes onbridges are not fully understood. These cumulative effects compounded with the occasional mod-erate earthquake (M5.0 and larger) may lead to damage requiring rapid repairs to avoid acutetraffic control issues at the affected bridge sites. To reduce impacts to the driving public, ac-celerated bridge construction (ABC) techniques have been developed over recent years (Culmo,2011), but have primarily focused on rapidly constructing new or replacement structures. Anotherbenefit derived from these ABC methods is rapid post-earthquake repair of damaged structures,for example accelerated column repair/replacement with carbon fiber wrapping and steel casings.Post-earthquake accelerated column repair/replacement was identified as a high priority researchneed at a Federal Highway Administration (FHWA) workshop on seismic ABC (FHWA, 2007).While that workshop focused on moderate-to-high seismic zones, the need for additional analysis,new techniques, and associated specifications is also critical for low-to-moderate seismic zones af-fected by induced earthquakes. This research addressed the existing knowledge gap on the effectsof low-level frequent seismic events on bridges.

1.2 Problem Statement

The recent surge in seismic activity in the central U.S. has motivated the need for rapid repairtechniques that leverage ABC methods. The overarching objective of this research was to developanalysis techniques to study the effect of large number of small-to-moderate earthquakes on bridgesand identify appropriate ABC methods for repair of bridges damaged by induced earthquakes.The project considered Oklahoma as a case study and developed techniques and tools that can beapplied to other regions experiencing low-level frequent seismic events. Ultimately, the researchresulted in the following outcomes:

(a) new seismic analysis tools to assess for damage from repeated, small-to-moderate earth-quakes;

(b) guidelines for the appropriate use of these tools.

2

1.3 Research Approach and Method

The overall approach of this resesarch project was organized in two phases: (I) Seismic HazardCharacterization and (II) ABC Repair Guidelines. Phases I and II were to be performed in alinear consecutive fashion, with each phase requiring one year. Phase I, which is the focus of thisreport, involved seismic hazard analysis, numerical modeling, response prediction, and guidelinedevelopment. Oklahoma and the surrounding area—a region experiencing large numbers of small-to-moderate earthquakes—served as the testbed for this project. The following section providesadditional detail on the tasks that were performed to achieve the project objectives in Phase I ofthis project. (Note that Phase II was ultimately not conducted due to funding constraints.)

1.4 Description of Research Project Tasks

The following is a list of conducted tasks, along with the description of each task:

Task 1 – Compile Ground-Motion Data The first task of this research project focused on com-piling ground-motion data for induced earthquakes impacting Oklahoma’s bridges. In addi-tion to the processed ground-motion time histories, key ground-motion intensity measures,such as peak ground acceleration (PGA), peak ground velocity (PGV), and the 5%-dampedspectral acceleration Sa, were compiled. Metadata, such as station longitude/latitude, soilconditions, channels, etc., were curated as well.

Task 2 – Characterize Cumulative Seismic Demand. This task used the ground-motion data ac-quired in Task 1 to quantify the cumulative (or cyclic) seismic demand due to induced earth-quakes. First, simple single-degree-of-freedom oscillators with different natural periodswere considered to generate cycle count spectra. Then, an OpenSees models of a typicalOklahoma bridge was used to run simulations and to determine the number of cycles, andthe amplitude of these cycles, that Oklahoma bridges were subjected to over the period ofhighest seismic activity (2013–2017).

Task 3 – Develop and Evaluate a Fatigue Damage Index. This task used the cumulative seis-mic demands found in Task 2 to develop a fatigue damage index (FDI). The FDI can beused to capture structural deterioration due to accumulated seismic damage by quantifyinghow close a bridge is to its fatigue limit for a given earthquake sequence, from which theremaining service life can be determined.

Task 4 – Prepare Guidelines and Final Report. The research findings from Tasks 1–3 were pre-pared by means of this final report, along with guidelines for the appropriate use of the FDIframework developed in Task 3. The ABC-UTC Guide for Assessing the Effects of Frequent,Low-Level Seismic Events (Harvey and Muraleetharan, 2020) are available on the ABC-UTCwebsite (https://abc-utc.fiu.edu/).

1.5 Outline

The remainder of this report is organized as follows. Section 2 describes the selection procedurefor the induced ground-motion data used in this study, and traditional ground-motion intensitymeasures (PGA and Sa) are compiled and presented. Section 3 provides a background on cycle

3

https://abc-utc.fiu.edu/

counting in general, as well as its use for seismic demands in the context of this project for gen-erating cycle count spectra for induced earthquakes. Section 4 presents the Fatigue Damage Indexframework, which can be used to quantify the cumulative damage in a bridge subject to a sequenceof induced earthquakes. Section 5 demonstrates the use of the FDI framework on a representativebridge located in Oklahoma, validating the framework. Chapter 6 presents a brief summary andconcluding remarks in addition to some recommendations for future research related to this study.

4

2 Induced Ground-Motion Data2.1 Scope

This section describes the selection of ground motions for use in the evaluation of cumulativedamage. Traditional ground-motion intensity measures are presented for a sequence of Oklahomaearthquakes.

2.2 Notation

a1(t; T ) = the 5%-damped acceleration response of a structure with period T subject to groundacceleration ug1(t) in first horizontal direction (m/s2)

a2(t; T ) = the 5%-damped acceleration response of a structure with period T subject to groundacceleration ug2(t) in second horizontal direction (m/s2)

g = gravitational acceleration (m/s2)M = earthquake magnitudePGA = peak ground acceleration (m/s2)Sa(T ) = horizontal response spectral acceleration for a structure with period T (m/s2)S 0.3 = horizontal response spectral acceleration coefficient at 0.3-s period (m/s2)S 1 = horizontal response spectral acceleration coefficient at 1.0-s period (m/s2)T = period of structure (s)t = time (s)ug1(t) = ground acceleration in first horizontal direction (m/s2)ug2(t) = ground acceleration in second horizontal direction (m/s2)Vs30 = average shear wave velocity for the upper 30 m of the soil profile (m/s)

2.3 Ground Motions

This first objective of Task 1 was to identify the time frame, seismic stations, and earthquakesthat would comprise the ground-motion data set. As shown in Figure 1.1, the number of M3 andlarger earthquakes has progressively increased in recent years. Figure 2.1 portrays the temporaland spatial variation in seismic activity over 5-year periods: (a) 2003–2007, (b) 2008–2012, and(c) 2013–2017. Clearly the number of earthquakes skyrocketed after 2008. While the highestnumber of earthquakes with M > 3.0 was recorded in 2015 (nearly 950 in Oklahoma alone), 2016was marked by larger magnitude events: twenty-one earthquakes with M > 4.0, including threeearthquakes with M > 5.0. Therefore, the one-year time frame 1 January 2016 to 31 December2016, which had about 650 earthquakes with M > 3.0, was selected for this study.

The seismicity in Oklahoma has been concentrated in the north-central portion of the state inrecent years (see Figure 2.1(c)). Seismic stations OK.U32A and GS.OK005 were identified asbeing close in proximity to the recent seismic activity, as well as being active the entire year. Table2.1 presents these stations, their locations and soil conditions (Vs30), as well as which horizontalchannels are of interest. OK.U32A is close to Fairview in northwest Oklahoma, and GS.OK005 isnortheast of Oklahoma City, so these stations capture different regions of seismic activity acrossthe state. The ground-motion accelerograms captured by these stations are used to represent theseismic activity a bridge close to these stations would have been exposed to during the one-yearperiod (2016).

5

(a) 2003–2007 (b) 2008–2012

(c) 2013–2017

Figure 2.1: Magnitude 3.0 and larger earthquakes in Oklahoma (USGS, 2017b): (a) 2003–2007 (≈ 12 events), (b)2008–2012 (≈ 164 events), and (b) 2013–2017 (≈ 2634 events).

Table 2.1: Seismic stations composing the ground-motion suite.

V∗s30 ChannelStation Latitude Longitude (m/s) East North

OK.U32A 36.3795 −99.0014 575 BHE BHNGS.OK005 35.6549 −97.1911 518 HNE HNN∗ Vs30 values were taken from USGS (2010)

Ground-motion records were retrieved from Standing Order for Data (SOD) (Owens et al.,2004) for the two stations for all M3.0 and larger earthquakes during the time frame of interest.Bidirectional ground motions are considered, so both the East and North components were re-tained, but the vertical components were not included. The records were processed following thePEER processing procedure (Boore et al., 2012). A total of 614 and 424 earthquakes were pro-cessed for the two stations, respectively. Details of the earthquakes are tabulated in Appendix Aand for stations OK.U32A (Table A.1) and GS.OK005 (Table A.2). Figure 2.2 shows the locationsof these seismic stations with respect to the earthquake activity in 2016. The marker size indicatesthe magnitude of the event, and the marker face color indicates the peak ground acceleration (PGA)measured by the particular station, discussed in Section 2.4.

6

(a) OK.U32A (b) GS.OK005

Figure 2.2: Seismic stations and earthquakes in the ground-motion data set.


Figure 2.3: Attenuation of peak ground acceleration (PGA) with epicentral distance from seismic stations (a)OK.U32A and (b) GS.OK005.

2.4 Ground-Motion Intensity Measures

The second objective of Task 1 was to compile key ground-motion intensity measures (IMs). Ofparticular interest are PGA and spectral acceleration (Sa). The PGA shown in Figure 2.2 is thelargest maximum acceleration regardless of direction (Huang et al., 2008), given by

PGA = maxt

√[ug1(t)]2 + [ug2(t)]2 (2.4.1)

where ug1(t) and ug2(t) are the ground accelerations in two orthogonal horizontal directions, inthis case East and North. Figure 2.3 shows these PGA values versus the epicentral distance toget a sense of ground-motion attenuation with distance from the epicenter. As expected, strongershaking is observed for earthquakes closer to the station. Larger magnitude events tend to producestronger shaking. Notably, the M5.8 Pawnee event produces some of the largest shaking eventhough it occurred farther from the stations than some of the smaller events.

7


Figure 2.4: Spectral response acceleration Sa (5% damped) measured at seismic stations compared with the designresponse spectra per the 2009 AASHTO Guide specifications for LRFD seismic bridge design (AASHTO, 2009): (a)OK.U32A and (b) GS.OK005.

Spectral accelerations are of particular interest to structural engineers. Figure 2.4 shows theresponse spectra for all the earthquakes measured at (a) OK.U32A and (b) GS.OK005. The spec-tral acceleration reported represents the largest maximum response regardless of direction (Huanget al., 2008), which is consistent with mapped spectral accelerations used in design (AASHTO,2009; ASCE, 2017):

Sa(T ) = maxt

√[a1(t; T )]2 + [a2(t; T )]2 (2.4.2)

where a1(t; T ) and a2(t; T ) are the 5%-damped acceleration responses in two orthogonal horizontaldirections for a structure with period T . This is an orientation-independent measure of the spectralacceleration, as opposed to the geometric mean of the response spectra in the two directions (Booreet al., 2006). The largest spectral accelerations are observed at periods between 0.05 and 0.3 sec.There is variation in the response spectra due to magnitude of the event and distance from theepicenter. To illustrate the latter, the measured response spectra in Figure 2.4 are color codedaccording to their epicentral distance. In general the spectral accelerations decrease with increasingepicentral distance (i.e., attenuate). The attenuation of spectral accelerations at 0.3 and 1.0 sec (S 0.3

and S 1, respectively) with epicentral distance is shown in Figures 2.5 and 2.6, respectively.Figure 2.4 also shows the design response spectra per the 2009 AASHTO Guide specifications

for LRFD seismic bridge design (AASHTO, 2009) as a point of comparison for the spectral accel-eration from each station. The design spectra assume site class C based on the shear wave velocitydetermined at the seismic station (Table 2.1). Because the design curves are based on the hazardfrom the Meers fault in southwest Oklahoma, the design spectral accelerations are higher closer tothe fault (GS.OK005) and lower farther from the fault (OK.U32A). However, as shown in Figure2.4, this does not necessarily correspond to the intensity of the ground motions from the recordedearthquakes.

8


Figure 2.5: Attenuation of 0.3-sec spectral acceleration (S 0.3) with epicentral distance from seismic stations (a)OK.U32A and (b) GS.OK005.


Figure 2.6: Attenuation of 1-sec spectral acceleration (S 1) with epicentral distance from seismic stations (a) OK.U32Aand (b) GS.OK005.

2.5 Summary

In summary, two seismic stations (OK.U32A and GS.OK005) were identified for this Oklahomacase study that considered M3.0 and larger earthquakes in 2016. Over 1000 bidirectional ground-motion acceleration records were acquired and processed, extracting intensity measures (PGA andSa) of interest to bridge analysis and design. The ground-motion data collected in Task 1 was thenused in Task 2 (Section 3) to quantify cumulative demand due to induced earthquakes.

9

3 Cumulative Seismic Demand3.1 Scope

This section describes a method of quantifying the cumulative seismic demand from a sequence ofinduced earthquakes, in addition to a background on fatigue analysis and cycle counting in general.

3.2 Notation

A = pseudo-acceleration (m/s2)A = pseudo-acceleration cycle range (m/s2)C = damage fractionD(t) = modal response displacement (m)D = displacement cycle range (m)g = gravitational acceleration (m/s2)M = earthquake magnitudeNk = number of cycles to fatigue failure at stress range S k

nk = number of cycles sustained at stress range S k

nk,EW = number of cycles sustained at displacement cycle range Dk due to east-west compo-nent of horizontal ground motions

nk,NS = number of cycles sustained at displacement cycle range Dk due to north-south com-ponent of horizontal ground motions

nk,SRSS = square root of the sum of the squares (SRSS) of the number of cycles sustained atdisplacement cycle range Dk due to NS and EW components of horizontal groundmotions

PGA = peak ground acceleration (m/s2)Sa = horizontal response spectral acceleration for a structure with period T (m/s2)S k = stress range (MPa)T = period of structure (s)t = time (s)ug(t) = horizontal ground acceleration (m/s2)∆A = pseudo-acceleration bin width (m/s2)∆D = displacement bin width (m)ζ = damping ratio

3.3 General

Peak intensity measures, such as PGA and Sa, are critical when determining the largest loads abridge may experience, but of interest to this project is the number of stress cycles, and fluctuations,Oklahoma bridges have been subjected to in recent years. For the levels of shaking observed, theresponses are expected to primarily remain in the elastic range, but may compromise durabilitydue to fatigue and weaken the structure when subsequently shaken by larger events (M > 5.0earthquakes). In Task 2, first a literature review was performed to determine the state of practicein fatigue analysis, which is described here.

10

3.4 Fatigue Analysis

Fatigue is the weakening of a material caused by repeated applied loads. Fatigue occurs at stressvalues much less than the yield or ultimate strength of the material. Material performance iscommonly characterized by an S –N curve, which represents the number of cycles to failure, N,for a given magnitude of cyclic stress, S . These curves assume repeated cycles at the same cyclicstress magnitude. This assumption is not valid when considering bridges subjected to repeatedseismic loads. That is, the amplitude of cycles will vary considerably during a single event, aswell as under different events of different magnitude located at different distances from the bridge.Therefore, a spectrum of stress magnitudes, S k (k = 1, 2, . . . ,K), is expected, each contributing nk

cycles. Each of these stress magnitudes has a corresponding number of cycles to failure, Nk(S k).The most popular method to account for the spectrum of stresses and number of cycles is Miner’sRule (Miner, 1945):

C =

K∑k=1

nk

Nk(3.4.1)

where the material will fail in fatigue when the damage fraction, C, equals 1. The interpretation ofMiner’s rule is that the proportion of the life consumed at each stress level, nk/Nk (k = 1, 2, . . . ,K),linearly combine with one another. Note that Miner’s rule does not take into account the order inwhich the cyclic loads are applied.

An approach based on Miner’s rule is assumed in this work. This requires counting the numberof cycles a bridge is subjected to when excited by a sequence of earthquakes. The standard practicefor cycle counting in fatigue analysis is rainflow counting (ASTM E1049-85(2017), 2017), orig-inally proposed by Matsuishi and Endo (1968). Rainflow counting is used to quantify the cyclicdemand on bridges and is briefly described in the following section.

3.5 Rainflow Counting

A fatigue cycle is the repeated loading and unloading of an object that accumulates damage inits material. Cycles can be counted on time histories of force, stress, strain, torque, acceleration,deflection, or other loading parameters of interest. One of the most widely used cycle countingalgorithms is rainflow counting, which was included as one of the cycle counting algorithms inASTM E1049-85(2017) (2017). Since Matsuishi and Endo (1968) initially proposed the rainflowcounting algorithm, different types of fatigue cycle counting methods such as level-crossing count-ing, peak counting, simple-range counting, and simplified rainflow counting have been introducedto summarize random or transient load time histories by providing the number of cycles at variousranges (ASTM E1049-85(2017), 2017). The counting algorithm, definitions of cyclic parameters,and the results vary with the type of counting method used. For this work, the rainflow countingalgorithm per ASTM standards was utilized.

The rainflow function in Matlab (Mathworks, Natick, MA) is based on the ASTM standard.A load time history with a sequence of reversals is input into rainflow. Reversals are the localminima and maxima where the first derivative of load time history changes its sign. This rainflowfunction counts cycles by tracking a moving three-point subset of points and a moving referencepoint (say Point Z) explained as follows:

1. The first and second point in the subset are grouped together and are denoted Y .

11

2. The second and third point in the subset are grouped together and are denoted X.

3. In groups X and Y , the points are sorted from earlier to later in time but are not necessarilyconsecutive points in the load time history.

4. The range of X, denoted r(X), is the absolute value of the difference between the amplitudeof the first point and the amplitude of the second point, and r(Y) is the absolute value of thedifference between the amplitude of the second point and the amplitude of the third point.

Figure 3.1 depicts the rainflow counting algorithm. At the end, the rainflow function collects thedifferent cycles and half-cycles and tabulates their ranges (peak to valley), their means, and thepoints at which they start and end. This algorithm is used for all cycle counting in this project.In the following section (Section 3.6), rainflow counting is used to characterize the cumulativeseismic demand considering a simple harmonic oscillator subjected to the sequence of earthquakeground motions acquired in Task 1.

3.6 Cumulative Seismic Demand – Simple Oscillator

In this section, a simple harmonic oscillator is subjected to the sequence of earthquake groundmotions acquired in Task 1. For the purpose of demonstration, a 5%-damped, single-degree-of-freedom oscillator with natural period T = 0.3 sec is analyzed here. To characterize the cumulativedemand, the simple oscillator was subjected to a ground-motion acceleration and the displacementresponse was found. Figure 3.2 shows a representative response of the oscillator when subjectedto the NS accelerogram measured at station OK.U32A during the M5.8 Pawnee earthquake. Thedisplacement cycles were counted using the rainflow counting method implemented in Matlabbased on the ASTM standard procedure (ASTM E1049-85(2017), 2017). The processing proce-dure involves first reducing the displacement time history to a sequence of reversals (i.e., peaksand valleys); see Figure 3.3. Then the rainflow counts are found using the built-in Matlab functionrainflow, which returns the cycle counts. Figure 3.4 shows the histogram of cycles as a functionof cycle average and cycle range for the representative case (Figure 3.2). Similar histograms havebeen generated for all the accelerograms found in Task 1, which are used to portray the cumulativedemand over a one-year time frame.

The cumulative seismic demand from multiple events during a given year can be found bysimply concatenating the cycle counts from all the events in that year. For example, Figure 3.5shows the cycle ranges versus cycle counts for all 2016 events measured at station OK.U32A inthe NS and EW directions for a simple oscillator (ζ = 5%) with period T = 0.3 and 1 sec. Asexpected, there are a larger number of cycles at lower cycle ranges, and few cycles at higher cycleranges. Also from these figures, the effect of the structures period on the cycle range is apparent,i.e., larger cycle ranges for longer period structures. To better illustrate this, Figures 3.6 and 3.7show the cycle range versus cycle counts for all 2016 events measured at stations OK.U32A andGS.OK005, respectively, in the EW and NS directions. These figures portray the cycle counts forvarious natural periods, indicated by the marker color. The periods considered are T = 0.1, 0.2,..., 0.9, 1, 2, ..., and 10 sec. The cycle counts for these cases are tabulated in Appendix B forOK.U32A (Table B.1) and GS.OK005 (Table B.2). Tables B.1 and B.2 list the displacement cyclecounts for seismic stations OK.U32A and GS.OK005, respectively, in 2016 for both the EW and

12

Figure 1. rainflow algorithm

References

1. Matsuishi, M. & Endo, T. (1968) Fatigue of metals subjected to varying stress, Japan Soc. Mech. Engineering.

2. ASTM E1049-85. (Reapproved 2005). "Standard practices for cycle counting in fatigue analysis". ASTM International.

3. Rainflow counts for fatigue analysis - MATLAB rainflow. (2018). URL https://www.mathworks.com/help/signal/ref/rainflow.html

Start

Readthenextreversalpoint

Outofpoints?

<3reversalpoints?

FindXandY,X(2-3)&Y(1-2)

r(X)<r(Y)?

YincludesZ?

1. CountYas1cycle2. DiscardbothpointsinY

1. CountYas1/2cycle2. DiscardthefirstpointofY3. SetZtothesecondpointofY

SetZtothefirstreversalinthehistory

No

No

No

Yes

Yes

Yes

Counteachremaingrangeasa½cycleYes

End

No

Figure 3.1: Rainflow counting algorithm.

13

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-2

-1

0

1

2

Gro

un

d-m

oti

on

ac

ce

lera

tio

n (

%g

)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time (min)

-0.5

-0.25

0

0.25

0.5

SD

OF

re

sp

on

se

dis

pla

ce

me

nt

(mm

)

Figure 3.2: Response of simple harmonic oscillator (T = 0.3 sec, ζ = 5%) subject to the NS component of theground-motion acceleration measured at station OK.U32A during the M5.8 Pawnee earthquake.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-2

-1

0

1

2

Gro

und-

mot

ion

acce

lera

tion

(%g)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2Time (min)

-0.5

-0.25

0

0.25

0.5

SDO

F re

spon

sedi

spla

cem

ent (

mm

)

Figure 3.3: Sequence of peaks and valleys (dots) identified from the response of simple harmonic oscillator (T = 0.3sec, ζ = 5%) subject to the NS component of the ground-motion acceleration measured at station OK.U32A duringthe M5.8 Pawnee earthquake.

00.1

20

0 0.7

40

Num

ber o

f Cyc

les

0.6

Cycle Average (mm)

0.5-0.1

60

0.4

Cycle Range (mm)

0.30.2-0.2 0.10 0

20

40

60

Figure 3.4: Histogram of displacement cycles for the response of simple harmonic oscillator (T = 0.3 sec, ζ = 5%)subject to the NS component of the ground-motion acceleration measured at station OK.U32A during the M5.8 Pawneeearthquake.

14

100

101

102

103

104

105

106

Cycle Counts

0

1

2

3

4

5

Cycle

Ra

ng

e [

mm

]

EW

NS

OK.U32A

2016

T = 0.3 sec

100

101

102

103

104

105

106

Cycle Counts

0

1

2

3

4

5

Cycle

Ra

ng

e [

mm

]

EW

NS

OK.U32A

2016

T = 1 sec

Figure 3.5: Displacement cycles for the response of simple harmonic oscillator (ζ = 5%) with period T = 0.3 sec(left) and 1 sec (right) subject to the EW and NS components of all the ground-motion accelerations measured atstation OK.U32A in 2016.

100

101

102

103

104

105

106

Cycle Counts

0

5

10

15

20

Cycle

Ra

ng

e [

mm

]

0.1

1

10

Period T

[s]

OK.U32A EW 2016

100

101

102

103

104

105

106

Cycle Counts

0

5

10

15

20

Cycle

Ra

ng

e [

mm

]

0.1

1

10

Period T

[s]

OK.U32A NS 2016

Figure 3.6: Displacement cycles for the response of simple harmonic oscillator (ζ = 5%) with varying period T subjectto the EW (left) and NS (right) components of all the ground-motion accelerations measured at station OK.U32A in2016.

100

101

102

103

104

105

106

Cycle Counts

0

10

20

30

40

50

60

Cycle

Ra

ng

e [

mm

]

0.1

1

10

Period T

[s]

GS.OK005 EW 2016

100

101

102

103

104

105

106

Cycle Counts

0

10

20

30

40

50

60

Cycle

Ra

ng

e [

mm

]

0.1

1

10

Period T

[s]

GS.OK005 NS 2016

Figure 3.7: Displacement cycles for the response of simple harmonic oscillator (ζ = 5%) with varying period T subjectto the EW (left) and NS (right) components of all the ground-motion accelerations measured at station GS.OK005 in2016.

15

NS directions. The counts nk (k = 1, 2, . . . , 20) are for cycle ranges Dk = k × ∆D where ∆D is thedisplacement bin width.

3.6.1 Pseudo-Acceleration Cycle Counts

It is important to note that the displacements in Figures 3.2–3.7 are not necessarily real (physical)displacements of a bridge (e.g., drifts), but instead are the normalized modal responses found fromintegrating the following equation:

D(t) + 2ζωD(t) + ω2D(t) = −ug(t) (3.6.1)

where ω = 2π/T . The (normalized) modal response displacements D(t) need to be related toresponse quantities of interest (e.g., physical displacements and stresses in a bridge), as discussedin Section 4.7.

Alternatively, the (normalized modal) displacements can be portrayed as pseudo-accelerations,consistent with spectral accelerations used for design, by the following transformation:

A = ω2 × D (3.6.2)

Doing so, the displacement cycle ranges in Figures 3.5, 3.6, and 3.7 are recast in terms of pseudo-acceleration cycle ranges in Figures 3.8, 3.9, and 3.10, respectively. These pseudo-accelerationscan be treated much like a design spectral response acceleration, Sa, for the determination of loadsand stresses on the structure through an equivalent lateral force (ELF) procedure. From Figure3.8, the effect of the structure period on the pseudo-acceleration cycle range is apparent, i.e., largercycle ranges for shorter period structures; this is consistent with design spectral accelerations ingeneral.

The displacement cycle counts tabulated in Appendix B are directly related to pseudo-acceleration cycle counts. That is, the counts nk (k = 1, 2, . . . , 20) presented in Tables B.1 andB.2 apply for pseudo-acceleration cycle ranges Ak = k × ∆A where the pseudo-acceleration binwidth ∆A = (2π/T )2 × ∆D.

3.6.2 SRSS Cycle Counts

The cumulative seismic demands found in this task are incorporated into the fatigue damage index(FDI) framework developed in Task 4. One aspect of the FDI framework is the combination ofthe cumulative seismic demand in the EW and NS directions. To this end, the square root of thesum of the squares (SRSS) is used (see Section 4.6). Therefore, the NS and EW cycle countsare combined here using their SRSS. Figures 3.11 and 3.12 show the displacement and pseudo-acceleration SRSS cycle counts for simple harmonic oscillators (ζ = 5%) with varying period Tconsidering all the GM accelerations measured at stations OK.U32A and GS.OK005, respectively,in 2016.

The cycle counts nk tabulated in Appendix B are presented separately for the EW and NSdirections. The SRSS cycle counts nk,SRSS are readily found as follows:

nk,SRSS =

√n2

k,EW + n2k,NS (3.6.3)

where nk,EW and nk,NS are the tabulated counts in the EW and NS directions, respectively.

16

100

101

102

103

104

105

106

Cycle Counts

0

1

2

3

4

5C

ycle

Ra

ng

e [

%g

]

EW

NS

OK.U32A

2016

T = 0.3 sec

100

101

102

103

104

105

106

Cycle Counts

0

1

2

3

4

5

Cycle

Ra

ng

e [

%g

]

EW

NS

OK.U32A

2016

T = 1 sec

Figure 3.8: Pseudo-acceleration cycles for the response of simple harmonic oscillator (ζ = 5%) with period T = 0.3 s(left) and 1 s (right) subject to the EW and NS components of all the ground-motion accelerations measured at stationOK.U32A in 2016.

100

101

102

103

104

105

106

Cycle Counts

0

5

10

15

Cycle

Ra

ng

e [

%g

]

0.1

1

10P

eriod T

[s]

OK.U32A EW 2016

100

101

102

103

104

105

106

Cycle Counts

0

5

10

15

Cycle

Ra

ng

e [

%g

]

0.1

1

10

Period T

[s]

OK.U32A NS 2016

Figure 3.9: Pseudo-acceleration cycles for the response of simple harmonic oscillator (ζ = 5%) with varying periodT subject to the EW (left) and NS (right) components of all the ground-motion accelerations measured at stationOK.U32A in 2016.

100

101

102

103

104

105

106

Cycle Counts

0

5

10

15

20

25

30

35

40

45

Cycle

Ra

ng

e [

%g

]

0.1

1

10

Period T

[s]

GS.OK005 EW 2016

100

101

102

103

104

105

106

Cycle Counts

0

5

10

15

20

25

30

35

40

45

Cycle

Ra

ng

e [

%g

]

0.1

1

10

Period T

[s]

GS.OK005 NS 2016

Figure 3.10: Pseudo-acceleration cycles for the response of simple harmonic oscillator (ζ = 5%) with varying periodT subject to the EW (left) and NS (right) components of all the ground-motion accelerations measured at stationGS.OK005 in 2016.

17

100

101

102

103

104

105

106

Cycle Counts

0

5

10

15

20C

ycle

Ra

ng

e [

mm

]

0.1

1

10

Period T

[s]

OK.U32A 2016 - SRSS

100

101

102

103

104

105

106

Cycle Counts

0

5

10

15

Cycle

Ra

ng

e [

%g

]

0.1

1

10

Period T

[s]

OK.U32A 2016 - SRSS

Figure 3.11: Displacement (left) and pseudo-acceleration (right) cycles for the response of simple harmonic oscillator(ζ = 5%) with varying period T ; square root of the sum of the squares (SRSS) of the EW and NS counts of all theground-motion accelerations measured at station OK.U32A in 2016.

100

101

102

103

104

105

106

Cycle Counts

0

10

20

30

40

50

60

Cycle

Ra

ng

e [

mm

]

0.1

1

10

Period T

[s]

GS.OK005 2016 - SRSS

100

101

102

103

104

105

106

Cycle Counts

0

5

10

15

20

25

30

35

40

45

Cycle

Ra

ng

e [

%g

]

0.1

1

10

Period T

[s]


Figure 3.12: Displacement (left) and pseudo-acceleration (right) cycles for the response of simple harmonic oscillator(ζ = 5%) with varying period T ; square root of the sum of the squares (SRSS) of the EW and NS counts of all theground-motion accelerations measured at station OK.U32A in 2016.

3.7 Summary

In this section, a background on fatigue analysis and cycle counting was presented. Displacementand pseudo-acceleration cycle counts were calculated and tabulated for the bidirectional ground-motion acceleration records from two seismic stations (OK.U32A and GS.OK005) during 2016.These cycle counts are used in the fatigue damage index (FDI) framework presented in the follow-ing section (Section 4).

18

4 Fatigue Damage Index (FDI) Framework4.1 Scope

This section describes the proposed fatigue damage index (FDI) and a framework for its applica-tion. The FDI can be used to capture structural deterioration due to accumulated seismic damageby quantifying how close a bridge is to its fatigue limit for a given earthquake sequence, fromwhich the remaining service life can be determined.

4.2 Notation

a(i)NS (t) = ith ground acceleration in the north-south direction (m/s2)

a(i)EW(t) = ith ground acceleration in the east-west direction (m/s2)

C = damping matrix (N-s/m)Cx = damage fraction in “x” directionCy = damage fraction in “y” directionCx = damping matrix in “x” direction (N-s/m)Cy = damping matrix in “y” direction (N-s/m)cx = generalized damping coefficient in “x” direction (N-s/m)cy = generalized damping coefficient in “y” direction (N-s/m)Csm = the dimensionless elastic seismic response coefficientD(i)

NS (t) = displacement response to ith ground acceleration in the north-south direction (m/s2)

D(i)EW(t) = displacement response to ith ground acceleration in the east-west direction (m/s2)

D = displacement cycle range (m)Dk = kth displacement cycle range (m)FDI = fatigue damage indexf(q(t)) = nonlinear restoring force vector (N and N-m)g = acceleration of gravity (m/s2)K = stiffness matrix (N/m)Kx = stiffness matrix in “x” direction (N/m)Ky = stiffness matrix in “y” direction (N/m)kx = generalized stiffness in “x” direction (N/m)ky = generalized stiffness in “y” direction (N/m)M = mass matrix (kg)Mx = mass matrix in “x” direction (kg)My = mass matrix in “y” direction (kg)mx = generalized mass in “x” direction (kg)my = generalized mass in “y” direction (kg)N(s) = number of cycles to fatigue failure at stress range s, found from the material’s S –N

curven(i)

DNS(Dk|ω, ζ) = displacement cycle counts at displacement cycle range Dk for an oscillator with

frequencyω and damping ratio ζ subject to ith ground acceleration in the north-south direction

19

n(i)DEW

(Dk|ω, ζ) = displacement cycle counts at displacement cycle range Dk for an oscillator withfrequency ω and damping ratio ζ subject to ith ground acceleration in the east-west direction

n(i)D (Dk|ω, ζ) = square root of the sum of squares (SRSS) of the EW and NS displacement

cycle counts at displacement cycle range Dk for an oscillator with frequency ωand damping ratio ζ

ns(s) = number of cycles at stress range spe = equivalent uniform static seismic loading per unit length of bridge that is applied to

represent the primary mode of vibration (kip/ft)pe(x) = the intensity of the equivalent static seismic loading that is applied to represent the

primary mode of vibration (kip/ft)q(t) = generalized coordinate vector (in. or rad.)S = ground-motion (GM) sequence comprised of N bidirectional horizontal GMssxk = kth stress cycle range in “x” direction (MPa)syk = kth stress cycle range in “y” direction (MPa)sxk = kth stress cycle amplitude in “x” direction (MPa)syk = kth stress cycle amplitude in “y” direction (MPa)x(t) = generalized displacement in longitudinal direction (m)xg(t) = ground acceleration in “x” direction (m/s2)y(t) = generalized displacement in transverse direction (m)yg(t) = ground acceleration in “y” direction (m/s2)ıx = influence vector in “x” directionıy = influence vector in “y” directionωx = frequency of fundamental mode of vibration in “x” direction (rad/s)ωy = frequency of fundamental mode of vibration in “y” direction (rad/s)Γx = generalized participation factor in “x” directionΓy = generalized participation factor in “y” directionφx j = mode shape vector of jth mode of vibration in “x” direction (rad/s)φy j = mode shape vector of jth mode of vibration in “y” direction (rad/s)ζx = damping ratio of fundamental mode of vibration in “x” directionζy = damping ratio of fundamental mode of vibration in “y” direction

4.3 General

The proposed framework aims to evaluate the potential for cumulative damage (high-cycle fatigue)in structures caused by many small-to-moderate induced earthquakes. To this end, the frameworkcharacterizes the cumulative cyclic demand on a structure for a desired set of ground motion dataand compares the demand against the capacity of the structure to assess the likelihood of fatigue.A new metric, the fatigue damage index (FDI), is used to quantify the proportion of the fatiguelife that is accumulated and can estimate the remaining service life of the structure. The FDIframework is illustrated in Figure 4.1 and is comprised of five steps described here.

20

GM Suite

…

Cyclic Demand

Num

ber o

f Cyc

les

Cycle Average (mm) Cycle Range (mm)

Demand / Capacity

Stre

ss, S

Number of cycles, N

Miner’s Rule

Fatigue DamageIndex (FDI)

Number of cycles, N

DemandS-N Curve (Capacity)

Structural Model Structural Analysis

Stre

ss

Displacement

T

Figure 4.1: Fatigue damage index (FDI) framework.

4.4 Step 1 – Mathematical Model of the Impacted Structure

The first step of the FDI framework is to develop a mathematical model of the impacted bridgeof interest—either a “typical” bridge or a specific bridge. This model is used to determine thenatural modes of vibration for the bridge. Assuming that the bridge has two axes of symmetrysubjected to bidirectional horizontal GM along these axes, then the modal responses in the orthog-onal directions—longitudinal (x) and transverse (y)—can be treated independently. Furthermore,it is assumed that a single (fundamental) mode in each of the orthogonal directions of response issufficient.

The fundamental modes of vibration can be determined by either some approximate methodor modal analysis. To this end, the model may be quite simple or very detailed, depending on theapplication. For example, the former might assume a single-degree-of-freedom (SDOF) model forthe structure in each direction, e.g.,

mx x(t) + cx x(t) + kxx(t) = −mxΓx xg(t) (4.4.1a)

myy(t) + cyy(t) + kyy(t) = −myΓyyg(t) (4.4.1b)

whereas the latter might involve a fully nonlinear three-dimensional finite element (FE) model torepresent the structure, e.g.,

Mq(t) + Cq(t) + f(q(t)) = −Mıx xg(t) −Mıyyg(t) (4.4.2)

where xg(t) and yg(t) are the orthogonal horizontal GMs. In Eq. (4.4.1), x(t) and y(t) are thegeneralized displacements in orthogonal directions (longitudinal and transverse, respectively), withassociated generalized mass m, damping c, stiffness k, and mode participation factor Γ.∗ In Eq.(4.4.2), q(t) is the vector of generalized coordinates, M and C are the mass and damping matrices,

∗Following the notation of Chopra (2017).

21

f(·) is the nonlinear restoring force, and ıx and ıy are the influence vectors for xg(t) and yg(t),respectively. Eq. (4.4.2) can be linearized as follows:

Mq(t) + Cq(t) + Kq(t) = −Mıx xg(t) −Mıyyg(t), (4.4.3)

where K is the stiffness matrix. Under the assumption of plan symmetry about both x and y axes,the responses in the orthogonal directions can be treated independently:

Mxqx(t) + Cxqx(t) + Kxqx(t) = −Mxıx xg(t), (4.4.4a)

Myqy(t) + Cyqy(t) + Kyqy(t) = −Myıyyg(t), (4.4.4b)

where the subscripts x and y are used to distinguish the response in the orthogonal directions.For the simple model given by Eq. (4.4.1), the modal properties are found immediately:

ωx =(kx/mx

)1/2and ωy =

(ky/my

)1/2(4.4.5)

Generally, the damping coefficients cx and cy are not determined directly, but instead values for themodal damping ratios ζx and ζy are assumed. For the linearized FE model given by Eq. (4.4.4), thelowest J natural frequencies (ωx j and ωy j, j = 1, . . . , J) and associated mode shapes (φx j and φy j)of the structure are found by solving the eigenvalue problem, (Kξ−ω

2Mξ)φ = 0 for ξ = x, y. Modaldamping ratios (ζx j and ζy j) are generally assumed or found from classical damping estimates (e.g.,Rayleigh damping).

4.5 Step 2 – Compile Ground-Motion Data

The next step is to compile and organize a sequence of ground motions (GMs) impacting thestructure during the time frame of interest (e.g., one calendar year) and in the desired range ofearthquake magnitudes (e.g., greater than some threshold). The GM sequence is composed of Nbidirectional horizontal GMs, here denoted:

S ={(

a(i)NS (t), a(i)

EW(t))

: i = 1, . . . ,N}

(4.5.1)

where aNS (t) and aEW(t) are the ground accelerations in the north-south and east-west directions,respectively. Because GM measurements are taken at seismic stations that are most likely not colo-cated with the structure of interest, seismic stations should be selected to be roughly representativeof the seismic hazard at the structure’s actual site.

4.6 Step 3 – Characterize the Cyclic Seismic Demand

To quantify the cyclic seismic demand, simple harmonic oscillators representative of the structureare subjected to the sequence S of earthquake ground motions acquired in Step 2. For each oscil-lator, the displacement response is computed independently for the two components of horizontalGM:

D(i)NS (t) + 2ζωD(i)

NS (t) + ω2D(i)NS (t) = −a(i)

NS (t) (4.6.1a)

D(i)EW(t) + 2ζωD(i)

EW(t) + ω2D(i)EW(t) = −a(i)

EW(t) (4.6.1b)

22

for i = 1, . . . ,N. The properties of the SDOF oscillators (i.e., natural frequencies ω = 2π/T anddamping ratios ζ) are based upon the modal properties of the structure found in Step 1. For now,the subscripts “x” and “y” are dropped for brevity. The notation D(i)

NS (t |ω, ζ) and D(i)EW(t |ω, ζ)

will be used hereinafter to denote the displacement response time history of an SDOF oscillator,having properties ω and ζ, in the NS and EW directions, respectively, due to the ith GM. Thecyclic seismic demand is characterized by the displacement cycle ranges and counts based onthese simple oscillators, which are related to physical displacements (and stresses) in the structurein Step 4 (Section 4.7).

As discussed in Section 3, there are many different cycle-counting methods available for use(ASTM E1049-85(2017), 2017). In this study, displacement cycles are counted using rainflowcounting (Matsuishi and Endo, 1968). Rainflow counting is performed independently for eachdisplacement time history, i.e., for each GM (i = 1, . . . ,N) in each orthogonal direction (NS andEW). For each case, the rainflow counting algorithm returns a set of displacement cycle ranges Dwith associated cycle counts (1 or 1/2).† The displacement cycle ranges are then distributed amongK displacement bins

Dk ={D : Dk−1 < D 6 Dk

}, k = 1, 2, . . . ,K (4.6.2)

where D0 = 0, and the cycle counts are summed within each bin. The summed displacementcycle counts in bin Dk are denoted n(i)

DNS(Dk |ω, ζ) and n(i)

DEW(Dk |ω, ζ), which are characterized by

the upper bin edge Dk. The same bins are used for all GMs (i = 1, . . . ,N), and their counts arecombined:

nDNS (Dk |ω, ζ) =

N∑i=1

n(i)DNS

(Dk |ω, ζ) and nDEW (Dk |ω, ζ) =

N∑i=1

n(i)DEW

(Dk |ω, ζ) (4.6.3)

Finally, for each bin, the cycle counts in orthogonal directions are combined by taking the squareroot of the sum of the squares (SRSS):

nD(Dk |ω, ζ) =

√[nDNS (Dk |ω, ζ)]2 + [nDEW (Dk |ω, ζ)]2 (4.6.4)

for k = 1, . . . ,K. Combining the EW and NS counts in this manner accounts for uncertaintyin the orientation of the structure with respect to the cardinal directions, which is analogous tousing the geometric mean of spectral ordinates for uniaxial design spectral accelerations (Beyerand Bommer, 2006; Boore et al., 2006). The displacement cycle ranges Dk found in this step arerepresentative of spectral displacements, and they are mapped to stress cycle ranges in the nextstep. The combination of the modal responses is treated in Step 5.

4.7 Step 4 – Structural Analysis

In this step, the spectral response displacement ranges Dk are related to stresses within the structure.First, consider the simple SDOF structural models given in Eq. (4.4.1). In this case, the spectraldisplacement D is related to the generalized displacements x and y through the mode participationfactor, i.e., x = ΓxD and y = ΓyD. The spectral displacement ranges Dk are mapped to stress ranges

†Here, an over line ( · ) is used to represent a cycle range (peak to valley), which is to be distinguished from acycle amplitude taken to be half the range.

23

sxk and syk of a particular location within the structure (e.g., a weld). To do so, apply equivalentstatic lateral loads

Pxk = mxΓxω2xDk

2and Pyk = myΓyω

2y

Dk

2(4.7.1)

to the structure,‡ and determine the resulting stresses sxk and syk, respectively. The stress rangesare taken to be

sxk = 2 × sxk and syk = 2 × syk (4.7.2)

with corresponding stress cycle counts ns(sxk) ≡ nD(Dk |ωx, ζx) and ns(syk) ≡ nD(Dk |ωy, ζy). Notethat sxk , syk in general.

Next, consider the linearized FE models given in Eq. (4.4.4). As in a response spectrum anal-ysis, stresses within elements of the structure are found by applying equivalent static loads Pξ j

(ξ = x, y) to the structure. These loads are given by

Pξ j(D) = Γξ jMξφξ jω2ξ jD where Γξ j =

φTξ jMξıξ

φTξ jMξφξ j

(4.7.3)

Applying these static loads to the structure at spectral displacements amplitude D =

D1/2, . . . ,DK/2, the corresponding stress amplitudes (denoted s1, . . . , sK) are found. Letting sξ jk

denote the kth stress amplitude in the jth mode ( j = 1, . . . , J) in the ξ direction (ξ = x, y), the stresscycle counts are then given by ns(sξ jk) ≡ nD(Dk |ωξ j, ζξ j) where sξ jk = 2 × sξ jk.

4.8 Step 5 – Demand/Capacity Analysis

In this step, the demand on and capacity of the structure are combined with one another to deter-mine the potential for fatigue. The demand is characterized by the stress cycle counts and rangesdetermined in Step 4. The capacity of the particular structural element of interest is characterizedby the material’s S –N curve. An S –N curve represents number of cycles to failure at each cyclicstress level (range) for a given material and is specific to the test configuration used in fitting thecurve. One must identify appropriate S –N curves for the material based on the in situ loadingconditions.

To compare the demand and capacity, Miner’s rule (Miner, 1945) is used. Expressing Miner’srule (Eq. (3.4.1)) using the notation in this subsection:

Cx =

K∑k=1

ns(sxk)N(sxk)

and Cy =

K∑k=1

ns(syk)N(syk)

(4.8.1)

for the simple SDOF structural models given in Eq. (4.4.1), or

Cx j =

K∑k=1

ns(sx jk)N(sxk)

and Cy j =

K∑k=1

ns(sy jk)N(syk)

, j = 1, . . . , J (4.8.2)

for the linearized FE models given in Eq. (4.4.4). In these equations N(·) represents the number ofcycles to failure at the evaluated stress range, which is evaluated from the material’s S –N curve.Finally, the damage fractions are combined to evaluate the fatigue damage index (FDI), as follows.

‡Note that the 1/2 appearing in Eq. (4.7.1) is to consider the load amplitude, taken to be half of the load range.

24

Fatigue Damage Index. The damage fractions C determined from Eq. (4.8.1) or (4.8.2) representthe damage fraction attributed to individual modes (either fundamental only or multiple) in eachorthogonal horizontal direction. The value for each damage fraction calculated for the variousmodes can be combined using the square root of the sum of the squares (SRSS) method, thecomplete quadratic combination (CQC) method, or an approved equivalent approach. In this study,the SRSS method is assumed in determining the fatigue damage index (FDI):

FDI =

√C2

x + C2y (4.8.3)

for the simple SDOF structural models given in Eq. (4.4.1), or

FDI =

√√√ J∑j=1

(C2x j + C2

y j) (4.8.4)

for the linearized FE models given in Eq. (4.4.4). The material will fail in fatigue when the FDIequals 1.

4.9 Discussion

As indicated in Steps 1 (Section 4.4) and 4 (Section 4.7) and Figure 4.1, the mathematical modelof the impacted structure is critical in the FDI framework. The mathematical model is used todetermine both the fundamental period T1 which is used to determine the cumulative demand (e.g.,from Figure 3.6) and the stress-displacement relationship from a pushover analysis. Typically, themathematical model will be in the form of a finite element (FE) model, using software such asSAP2000 (Computers and Structures, Inc., Walnut Creek, CA). If a FE model is not readily avail-able, alternative methods for determining the fundamental period of the bridge include acceptablemethods in AASHTO LRFD Bridge Design Specifications (AASHTO, 2017), i.e., Eqs. C4.7.4.3.2b-4 or C4.7.4.3.2c-3. Then, an equivalent static seismic load, pe(x) or pe, per unit length of bridgewould be determined based on either Eqs. C4.7.4.3.2b-5 or C4.7.4.3.2c-4, respectively, where thedimensionless elastic seismic response coefficient, Csm, would be taken as

Csm =1g

(2πTm

)2 D2

(4.9.1)

for a given displacement cycle range D, where g is the acceleration of gravity and Tm is the periodof the bridge given by Eqs. C4.7.4.3.2b-4 or C4.7.4.3.2c-3. The equivalent static seismic load-ing would then be applied to the structure to determine the resulting member stress effects, heredenoted sk.

Steps 2 (Section 4.5) and 3 (Section 4.6) of the FDI procedure were demonstrated in Sections2 and 3, respectively, for two seismic stations in Oklahoma during 2016 considering all M3.0 andlarger earthquakes. A similar procedure would be followed for other regions experiencing inducedearthquakes.

4.10 Summary

In this section, a framework was presented for determining how close a bridge member is to itsfatigue life due to repeated seismic loading. The framework comprises five steps, resulting in

25

a quantitative metric (FDI) for the damage fraction. In the following section, the framework isdemonstrated on a “typical” Oklahoma bridge.

26

5 Case StudyIn this section, the fatigue damage index (FDI) framework presented in Section 4 is illustratedthrough a case study. The case study considers a “typical” Oklahoma bridge. To select the Okla-homa bridge that was modeled in this study, it was important to have a detailed understanding ofthe state’s bridge inventory. The Oklahoma Department of Transportation (ODOT) provided datafor 6815 bridges owned and maintained by the state on the ODOT-designated highway system,referred to as “on-system” bridges, which served as the inventory for this study. Note that “off-system” bridges (i.e., bridges owned and maintained by a county, city, or other local or regionalgovernmental unit, and not on the ODOT-designated highway system) were not included.

5.1 A “Typical” Oklahoma Bridge

Appendix C presents a detailed statistical analysis of the ODOT bridge inventory, consideringstructure type, bridge class, main span material, etc. The analysis concluded that 3-span Pre-stressed Concrete (3SPC) Girder bridges represent the most typical Oklahoma bridge. The StateHighway 99 (SH-99) bridge over Tiger Creek was selected for this study because it is representa-tive of the most typical bridge class (3SPC Girder bridge) and complete plans were available. TheSH-99 bridge over Tiger Creek is located northeast of Drumright, Oklahoma. It was built in 1979using guidelines stated in the 1976 Oklahoma Standard Specifications for Highway Constructionand AASHTO Standard Specifications for Highway Bridges (AASHTO, 1973). The bridge is pic-tured in Figure 5.1, and the general layout and configuration is shown in Figure 5.2. The as-builtcharacteristics of SH-99 bridge over Tiger Creek are representative of prestressed concrete bridgesof its design era. This bridge is a prestressed concrete (PC) girder bridge with total length of 46.3m composed of three 15.2-m spans. The width of each span is 13.9 m, and each span is constructedof five pretensioned AASHTO type III girders. The girders for the end spans bear on a seat-typeabutment at one end and a reinforced concrete (RC) bent at the other, and the girders in the mainspan are supported by a bent at each end.

Figure 5.1: Picture of the SH-99 bridge over Tiger Creek. (Image captured March 2016 courtesy of OklahomaDepartment of Transportation.)

27

15.2 m 15.2 m15.2 m

5 - #10 bars5 - #10 bars #4 hoops

@ 305 mm o.c.

76 mm

2.90 m

184 mm

2.74 m

1.37

m3.

20 m

914

mm

1372

mm

A

B - BA - A

A

B B

7.47 m

0.91 m 914 mm

7 - #9 bars 12 - #9 bars6 - #9 bars4 - #4 bars

#5 bars @229 mm o.c.

Figure 5.2: Configuration and layout of the SH-99 bridge over Tiger Creek. Traditional fixed and roller bearings areused in the drawing to represent fixed type and expansion type elastomeric bearings, respectively.

5.2 Fatigue Damage Index (FDI) Analysis

Having selected the impacted bridge of interest, the fatigue damage index (FDI) framework fromSection 4 can be applied. In this section, the step-by-step procedure for assessing the SH-99 bridgeover Tiger Creek is described.

Step 1 – Mathematical Model of the Impacted Structure. A 3D finite element (FE) model ofthe SH-99 bridge over Tiger Creek was developed in OpenSees. Details of the FE model are givenin Kaid Bay Cortez (2016) and Harvey et al. (2018b). For the purpose of this study, a single pierwas analyzed, having tributary mass from the superstructure represented as point masses at the topof the bent beam. An eigenvalue analysis of the pier using OpenSees extracted the fundamentalnatural periods and accompanying mode shapes, shown in Figure 5.3. The period of the pier in thelongitudinal and transverse directions were determined to be 0.314 and 0.127 sec, respectively.

For comparison, the uniform load method (AASHTO, 2017, C4.7.4.3.2c) was also used toestimate the period of the pier. A uniform load was applied to the pier, and the lateral stiffness, K,was estimated as the total applied load divided by the maximum lateral displacement of the pier.Then, the period of the bridge was estimated as Tm = 2π

√W/(gK) where the total weight, W, takes

into account the superstructure, the pier cap, and half the column weights. This method was usedfor both the longitudinal and transverse directions, giving period estimates of 0.326 and 0.155 sec,respectively, which are in good agreement with the eigenanalysis. The period estimates from theuniform load method are used in Step 3 to determine the cyclic seismic demand, assuming 5%damping.

28

Tlong.

= 0.314 sec Ttrans.

= 0.127 sec

Figure 5.3: Longitudinal (left) and transverse (right) mode shapes of the SH-99 bridge over Tiger Creek determinedusing OpenSees.

100

101

102

103

104

105

106

Cycle Counts

0.05

0.1

0.2

0.5

1

2

5

10

20

Cycle

Ra

ng

e [

mm

]

0.314 sec (OpenSees)

0.326 sec (AASHTO C4.7.4.3.2c) 0.3 sec

0.4 sec


100

101

102

103

104

105

106

Cycle Counts

0.05

0.1

0.2

0.5

1

2

5

10

20

Cycle

Ra

ng

e [

mm

]


0.155 sec (AASHTO C4.7.4.3.2c) 0.1 sec

0.2 sec


Figure 5.4: Displacement cycles for the response of simple harmonic oscillator (ζ = 5%) for periods corresponding tothe longitudinal (left) and transverse (right) directions of the SH-99 bridge over Tiger Creek; square root of the sum ofthe squares (SRSS) of the EW and NS counts of all the ground-motion accelerations measured at stations GS.OK005in 2016.

Step 2 – Compile Ground-Motion Data. The ground-motion (GM) data used in this case study iscomprised of the GMs from Section 2. The data consists of bidirectional GMs measured at seismicstation GS.OK005. See Section 2 for more details.

Step 3 – Characterize the Cyclic Seismic Demand. The displacement cycle counts and rangeswere compiled for the periods determined in Step 1. These counts are shown in Figure 5.4 forthe longitudinal and transverse periods estimated using an eigenanalysis (0.314 and 0.127 sec,respectively) and the uniform load method (0.326 and 0.155 sec, respectively). In addition, the twoclosest periods to each modal period are shown as well for reference. There appears to be marginalsensitivity to variations in periods, suggesting that the closest period tabulated in Appendix B couldbe used.

The displacement cycle counts in Figure 5.4 are recast in terms of pseudo-acceleration cyclecounts in Figure 5.5. More dispersion is observed when the various periods are compared, show-ing a slightly greater sensitivity to period. This is especially true for the transverse case [Figure5.5(right)].

29

100

101

102

103

104

105

106

Cycle Counts

0

5

10

15

20

25

30

35

40

45C

ycle

Ra

ng

e [

%g

]0.314 sec (OpenSees)

0.326 sec (AASHTO C4.7.4.3.2c) 0.3 sec

0.4 sec


100

101

102

103

104

105

106

Cycle Counts

0

5

10

15

20

25

30

35

40

45

Cycle

Ra

ng

e [

%g

]


0.155 sec (AASHTO C4.7.4.3.2c) 0.1 sec

0.2 sec


Figure 5.5: Pseudo-acceleration cycles for the response of simple harmonic oscillator (ζ = 5%) for periods corre-sponding to the longitudinal (left) and transverse (right) directions of the SH-99 bridge over Tiger Creek; square rootof the sum of the squares (SRSS) of the EW and NS counts of all the ground-motion accelerations measured at stationsGS.OK005 in 2016.

Step 4 – Structural Analysis. Having established the displacement cycle ranges in Step 3, nowequivalent static earthquake loading is applied to the FE model to determine the resulting memberstress effects. For this case study, the stresses in the reinforcing bars at the base of the columnsare analyzed; all 12 bars are considered. From the pseudo-acceleration cycle ranges reported inFigure 5.5, the maximum cycle ranges in both the longitudinal and transverse directions are aboutA = 40%g. Pushover analyses using equivalent seismic loading up to a spectral acceleration of±20%g were performed in the longitudinal and transverse directions, and the stresses at each of thetwelve reinforcing bars were recorded. The resulting acceleration–stress relationships are shownin Figure 5.6 for each of the recorders located at the reinforcing bars.§ The acceleration–stress re-lationships in Figure 5.6 are then used to map the acceleration cycles in Figure 5.5 to stress cycles.The resulting stress cycle ranges are shown in Figure 5.7 corresponding to the periods calculatedusing the uniform load method (AASHTO, 2017, C4.7.4.3.2c) in the longitudinal and transversedirections. Due to symmetry in the reinforcement layout, there is repetition in the acceleration (andstress) ranges, which are indicated by a single marker in Figure 5.7.

Step 5 – Demand/Capacity Analysis. Finally, the fatigue damage index (FDI) is determined.This requires a representative S –N curve to be selected. For this purpose, the 5%-quantile S –Ncurves from D’Angelo et al. (2014) are used. For the #9 reinforcing bars having diameter greaterthan 20 mm, the S –N curve is given by

ln N = 37.53 − 4.72 ln S (5.2.1)

with a 5%-quantile constant amplitude fatigue limit (CAFL5%) of 134 MPa. The damage fractionin the transverse direction (Ctrans.) is zero because none of the stress cycles are in excess of theCAFL5%; see Figure 5.7 (right). The damage fraction in the longitudinal direction (Clong.) is non-zero because of stress cycles over CAFL5%, and hence FDI ≡ Clong.. The resulting FDI values aregiven in Table 5.1. These values are extremely small, with a maximum value of 13.1(10−3)% for

§Note that these stress are about a compressive stress state induced by the dead load.

30

-150 -100 -50 0 50 100 150 200 250 300

Stress [MPa]

-20

-10

0

10

20

Acce

lera

tio

n [

%g

]

1

2,12

3,11

4,10

5,9

6,8

7

Recorder

No.

-60 -40 -20 0 20 40 60

Stress [MPa]

-20

-10

0

10

20

Acce

lera

tio

n [

%g

]

1,7

2,6

3,5

4

8,12

9,11

10

Recorder

No.

Figure 5.6: Pushover analysis—pseudo-acceleration versus stress at the twelve reinforcing bars—in the longitudinal(left) and transverse (right) directions of the SH-99 bridge over Tiger Creek.

100

101

102

103

104

105

106

Cycle Counts

1

2

5

10

20

50

100

200

400

Cycle

Ra

ng

e [

MP

a] 1,7

2,6,8,12

3,5,9,11

4,10

Recorder

No.GS.OK005 2016 - SRSS

T = 0.326 sec

100

101

102

103

104

105

106

Cycle Counts

1

2

5

10

20

50

100

200

400

Cycle

Ra

ng

e [

MP

a] 1,7

2,6

3,5

4

8,12

9,11

10

Recorder

No.GS.OK005 2016 - SRSS

T = 0.155 sec

Figure 5.7: Stress cycles corresponding to equivalent loading in the longitudinal (left) and transverse (right) directionsof the SH-99 bridge over Tiger Creek.

recorder nos. 1 and 7. For these two cases, an FDI of 1% would occur after about 75 years if thesame levels of induced seismicity were maintained. Therefore, fatigue of the column reinforcingbars in the SH-99 bridge over Tiger Creek is unlikely based on the foregoing analysis, assumingGS.OK005 is representative of the shaking at the bridge site.

5.3 Cumulative Seismic Demand – Finite Element Model

As a means of validating the stress cycles and likelihood of fatigue damage found using FDIframework in the previous section, a comparison can be made with the stresses found directly withthe OpenSees model. That is, the OpenSees model can be subjected to the full series of recorded

Table 5.1: Fatigue damage index (FDI) for the longitudinal reinforcing bars at the base of the column in the SH-99bridge over Tiger Creek for all the ground-motion accelerations measured at stations GS.OK005 in 2016.

Recorder No.1 2 3 4 5 6 7 8 9 10 11 12

FDI (10−3%) 13.1 6.41 0.449 0 0.447 6.39 13.1 6.39 0.447 0 0.449 6.410

31

100

101

102

103

104

105

106

Cycle Counts

1

2

5

10

20

50

100

200

400C

ycle

Ra

ng

e [

MP

a]

1

2

3

4

5

6

7

8

9

10

11

12

Recorder

No.

GS.OK005 2016

SH-99 over Tiger Creek

OpenSees Model -- EW

100

101

102

103

104

105

106

Cycle Counts

1

2

5

10

20

50

100

200

400

Cycle

Ra

ng

e [

MP

a]

1

2

3

4

5

6

7

8

9

10

11

12

Recorder

No.

GS.OK005 2016

SH-99 over Tiger Creek

OpenSees Model -- NS

Figure 5.8: Stress cycles determined from the OpenSees model of the SH-99 bridge over Tiger Creek oriented East-West (left) and North-South (right) subject to all the ground-motion accelerations measured at station GS.OK005 in2016.

ground motions during a given year, and the stress at a point of interest can be monitored. Then,these stress time histories can be processed using rainflow counting to extract the number of stresscycles and their ranges, from which the damage fraction C can be determined using Eq. (3.4.1).

Figure 5.8 shows the stress cycles¶ on the longitudinal reinforcing bars in the columns as deter-mined by the OpenSees model subject to all the ground-motion accelerations measured at stationGS.OK005 in 2016. Two bridge orientations (EW and NS) were considered to assess the influenceof orientation on the stress cycles and damage fraction. Similar stress ranges are observed for theOpenSees model (Figure 5.8) as those determined in the FDI framework (Figure 5.7), with thelatter giving slightly larger stress cycles in the transverse direction.

Finally, the damage fraction can be determined using Miner’s rule in conjunction with the sameS –N curve that was used in the FDI framework (D’Angelo et al., 2014). The stress cycles for theNS-oriented bridge (Figure 5.8 (right)) are below the CAFL5%, so fatigue failure would never becaused. Damage fractions for the EW-oriented bridge are reported in Table 5.2. Again, extremelysmall values are found. Damage fractions found directly with the OpenSees model using a time-history method (Table 5.2) are smaller than the FDI values (Table 5.1), but it is hard to say whetheror no the FDI framework is conservative in general. This is because there was a limited number ofcycles at appreciable stress ranges (> CAFL5%).

¶Note that these stress cycles are about a compresses stress state induced by the dead load.

Table 5.2: Damage fraction C for the longitudinal reinforcing bars at the base of the column in the SH-99 bridge overTiger Creek oriented East-West (EW) for all the ground-motion accelerations measured at stations GS.OK005 in 2016.

Recorder No.1 2 3 4 5 6 7 8 9 10 11 12

C (10−3%) 0.711 0 0.849 0 0.359 0 0.0551 0.467 0.398 0 0 0.388

32

5.4 Summary

This section presented a case study, demonstrating the application of the FDI framework on a“typical” Oklhoma bridge—a 3-span prestressed concrete girder bridges. Results from the FDIframework were compared to those found through a time-history method using a finite elementmodel in OpenSees subjected to the bidirectional GMs measured at seismic station GS.OK005 in2016. The overall conclusion from this case study is that induced earthquakes are unlikely to causefatigue failure in the longitudinal reinforcing bars of the considered “typical” Oklahoma bridgewithin the bridge’s design life. However, there may be other structural members or bridge classesthat may be more susceptible to fatigue failure, and the FDI framework presented here provides astraightforward, step-by-step procedure to perform such an analysis.

33

6 Summary, Conclusions, and RecommendationsBecause of the recent increase in seismic activity in the central U.S. caused by human activities(i.e., induced earthquakes), there has been concern raised over the potential for cumulative dam-aged caused by these frequent, low-level seismic events. The work conducted under this projectwas aimed at developing a method to quantify the cumulative effect of induced earthquakes onABC or conventional bridges.

Through this project, an extensive analysis of induced earthquakes in Oklahoma during 2016—the year with the highest induced seismic activity—was conducted. Through this seismic hazardanalysis, bidirectional ground motions at two seismic stations were compiled, and traditional inten-sity measures—spectral acceleration (Sa) and peak ground acceleration (PGA)—were determined.Additionally, cumulative seismic demand measures were tabulated (Appendix B) for use in thesubsequent analysis by practitioners. The cumulative seismic demands are quantified by the num-ber of cycles at displacement and pseudo-acceleration amplitudes for various periods.

Then, a framework for assessing the potential for cumulative damage was proposed. A metriccalled the fatigue damage index (FDI) is proposed to quantify the percent of a structural element’sfatigue life that remains. The FDI is founded on Miner’s rule for high-cycle fatigue analysis,incorporating the cumulative seismic demand measures. Parallels between the FDI framework andAASHTO-based analysis for earthquake loads are discussed.

The framework was demonstrated for a “typical” Oklahoma bridge. The FDI was calculatedfor a reinforcing bar at the base of a column of a conventional, 3-span, prestressed concrete girderbridge. The resulting FDI indicated that the likelihood of fatigue failure is unlikely during thedesign life of the bridge, for the structural element and bridge considered. Nevertheless, compar-isons with a time-history analysis using a high-fidelity finite element (FE) model of the bridge inOpenSees served to verify the accuracy of the framework for quantifying the stress cycle ranges,stress cycle counts, and remaining fatigue life.

The proposed FDI framework is general enough to be applied to other bridges, conventional orABC, that may be more vulnerable to cumulative damage. The method can be applied for design ofnew bridges or to evaluate the need for repair/replacement of existing bridges. Future work shouldconsider evaluating accelerated (ABC) solutions for rapid repair/retrofit of (potentially) damagedstructures due to induced earthquakes. The viability of accelerated repair solutions for repeated,small-to-moderate earthquakes needs to be assessed. Furthermore, additional verification of theFDI framework is needed; in particular, predictions of fatigue life using the FDI framework shouldbe compared to those found using high-fidelity FE models, experiments, or a combination thereof.

It is worth mentioning that there is one major limitation of the proposed method: the neces-sity of a representative S –N curve for the structural element under consideration. The S –N curveneeds to be representative of the material and configuration considered. Such curves are usuallyavailable for metals (e.g., reinforcing bars, studs, etc.), but for concrete (reinforced or unconfined)are limited. There would be value in maintaining a database of common S –N curves, as well asexperimentally determining curves for materials/configurations not presently available. In partic-ular, S –N curves for accelerated repair materials (e.g., ultra-high performance concrete (UHPC))are needed.

34

7 ReferencesAASHTO, Standard Specifications for Highway Bridges, American Association of State Highway

and Transportation Officials (AASHTO), Washington D.C., 11th edn., 1973.

AASHTO, Guide Specifications for LRFD Seismic Bridge Design, American Association of StateHighway and Transportation Officials (AASHTO), Washington D.C., 2009.

AASHTO, AASHTO LRFD Bridge Design Specifications, American Association of State High-way and Transportation Officials (AASHTO), Washington, D.C., 8th edition edn., 2017.

ASCE, Minimum Design Loads and Associated Criteria for Buildings and Other Structures, Amer-ican Society of Civil Engineers (ASCE), ASCE/SEI 7-16 edn., doi:10.1061/9780784414248,2017.

ASTM E1049-85(2017), Standard Practices for Cycle Counting in Fatigue Analysis, ASTM Inter-national, 2017.

Beyer, K., Bommer, J. J., Relationships between median values and between aleatory variabilitiesfor different definitions of the horizontal component of motion, Bulletin of the SeismologicalSociety of America 96 (2006) 1512–1522, doi:10.1785/0120050210.

Boore, D., Watson-Lamprey, J., Abrahamson, N., Orientation-Independent Measures of GroundMotion, Bulletin of the Seismological Society of America 96 (4A) (2006) 1502–1511, doi:10.1785/0120050209.

Boore, D. M., Azari Sisi, A., Akkar, S., Using pad-stripped acausally filterd strong-motiondata, Bulletin of the Seimological Society of America 102 (2) (2012) 751–760, doi:10.1785/

0120110222.

Chase, R. E., Liel, A. B., Luco, N., Baird, B. W., Seismic loss and damage in light-frame woodbuildings from sequences of induced earthquakes, Earthquake Engineering & Structural Dy-namics 48 (12) (2019) 1365–1383, doi:10.1002/eqe.3189.

Chopra, A. K., Dynamics of Structures: Theory and Applications to Earthquake Engineering,Prentice Hall, Englewood Cliffs, New Jersey, 5th edn., 2017.

Culmo, M. P., Accelerated bridge construction-experience in design, fabrication and erection ofprefabricated bridge elements and systems, Tech. Rep. FHWA-HIF-12-013, Federal HighwayAdministration, Washington, DC, 2011.

D’Angelo, L., Rocha, M., Nussbaumer, A., Bruhwiler, E., S-N-P fatigue curves using maximumlikelihood, in: Proceedings of 7th European Conference on Steel and Composite Structures,ECCS European Convention for Constructional Steelwork, 705–706, 2014.

FHWA, Recording and coding guide for the structure inventory and appraisal of the nation’sbridges, Office of Engineering Bridge Division, Federal Highway Administration, FHWA-PD-96-001 edn., 1995.

FHWA, 2007 FHWA Seismic Accelerated Bridge Construction Workshop Outcomes and Follow-up Activities, Tech. Rep., Federal Highway Administration, San Diego, CA, Final Report from

35

http://dx.doi.org/10.1061/9780784414248

http://dx.doi.org/10.1785/0120050210

http://dx.doi.org/10.1785/0120050209

http://dx.doi.org/10.1785/0120050209

http://dx.doi.org/10.1785/0120110222

http://dx.doi.org/10.1785/0120110222

http://dx.doi.org/10.1002/eqe.3189

the Rapid Bridge Construction: Seismic Connections Moderate-to-High Seismic Zones, 2007.

Frankel, A. D., Applegate, D., Tuttle, M. P., Williams, R. A., Earthquake hazard in the New MadridSeismic Zone remains a concern, U.S. Geological Survey Fact Sheet: 2009-3071, 2 p, 2009.

GEER, The Geotechnical Aspects of the September 3, 2016 M5.8 Pawnee, Oklahoma Earthquake,Tech. Rep., Geotechnical Extreme Events Reconnaissance (GEER), 2016.

Harvey, Jr., P. S., Heinrich, S. K., Muraleetharan, K. K., A Framework for Post-Earthquake Re-sponse Planning in Emerging Seismic Regions: An Oklahoma Case Study, Earthquake Spectra34 (2) (2018a) 503–525, doi:10.1193/053117EQS100M.

Harvey, Jr., P. S., Kaid Bay Cortez, I. A., Heinrich, S. K., Response of a Typical Oklahoma Bridgeto the September 3, 2016, 5.8-Magnitude Earthquake near Pawnee, Oklahoma, Journal of BridgeEngineering 23 (2) (2018b) 04017130, doi:10.1061/(ASCE)BE.1943-5592.0001178.

Harvey, Jr, P. S., Muraleetharan, K. K., ABC-UTC Guide for Assessing the Effects of Frequent,Low-Level Seismic Events, Accelerated Bridge Construction University Transportation Center(ABC-UTC), University of Oklahoma, available at https://abc-utc.fiu.edu/, 2020.

Huang, Y.-N., Whittaker, A. S., Luco, N., Maximum Spectral Demands in the Near-Fault Region,Earthquake Spectra 24 (1) (2008) 319–341, doi:10.1193/1.2830435.

Kaid Bay Cortez, I. A., Effects of Seismic Loading on Oklahoma Highway Bridges, Master’sthesis, University of Oklahoma, 2016.

Keranen, K. M., Savage, H. M., Abers, G. A., Cochran, E. S., Potentially induced earthquakes inOklahoma, USA: Links between wastewater injection and the 2011 Mw 5.7 earthquake, Geology41 (6) (2013) 699–702, doi:10.1130/G34045.1.

Matsuishi, M., Endo, T., Fatigue of Metals Subjected to Varying Stress, in: Japan Society ofMechanical Engineers, 1968.

McGarr, A., Bekins, B., Burkardt, N., Dewey, J., P. Earle, W. E., Ge, S., Hickman, S., Holland,A., E. Majer, J. R., Sheehan, A., Coping with earthquakes induced by fluid injection, Science347 (6224) (2015) 830–831, doi:10.1126/science.aaa0494.

Miner, M. A., Cumulative Fatigue Damage, Journal of Applied Mechanics 12 (1945) A159–A164.

Owens, T. J., Crotwell, H. P., Groves, C., Oliver-Paul, P., SOD: Standing Order for Data, Seismo-logical Research Letters 75 (2004) 515–520, doi:10.1785/gssrl.75.4.515-a.

Petersen, M., Moschetti, M., Powers, P., Mueller, C., Haller, K., Frankel, A., Zeng, Y., Reza-eian, S., Harmsen, S., Boyd, O., Field, N., Chen, R., Rukstales, K., Luco, N., Wheeler, R.,Williams, R., Olsen, A., Documentation for the 2014 update of the United States nationalseismic hazard maps, Tech. Rep. Open-File Report 2014-1091, U. S. Geological Survey, doi:10.3133/ofr20141091, 2014.

Petersen, M. D., Mueller, C. S., Moschetti, M. P., Hoover, S. M., Llenos, A. L., Ellsworth, W. L.,Michael, A. J., Rubinstein, J. L., McGarr, A. F., Rukstales, K. S., 2016 One-Year Seismic HazardForecast for the Central and Eastern United States from Induced and Natural Earthquakes, Open-File Report 2016-1035, U.S. Geological Survey, Reston, Virginia, doi:10.3133/ofr20161035,

36

http://dx.doi.org/10.1193/053117EQS100M

http://dx.doi.org/10.1061/(ASCE)BE.1943-5592.0001178

https://abc-utc.fiu.edu/

http://dx.doi.org/10.1193/1.2830435

http://dx.doi.org/10.1130/G34045.1

http://dx.doi.org/10.1126/science.aaa0494

http://dx.doi.org/10.1785/gssrl.75.4.515-a

http://dx.doi.org/10.3133/ofr20141091



2016.

Sullivan, I., Analytical seismic fragility curves for skewed multi-span steel girder bridges, Master’sthesis, Clemson University, 2010.

Taylor, J., Celebi, M., Greer, A., Jampole, E., Masroor, A., Melton, S., Norton, D., Paul, N.,Wilson, E., Xiao, Y., M5.0 Cushing, Oklahoma, USA earthquake on November 7, 2016, Tech.Rep. Oklahoma-EERI-Recon-Report-2017-02-15-Finalized, EERI, 2017.

USGS, Custom V30s Mapping, URL http://earthquake.usgs.gov/hazards/apps/vs30/custom.php, ac-

cessed June 18, 2015, 2010.

USGS, M 5.0 - 3km W of Cushing, Oklahoma, Earthquake Hazards Program, U. S. Ge-ological Survey, available at http://earthquake.usgs.gov/earthquakes/eventpage/us100075y8#executive, URL http://earthquake.usgs.gov/earthquakes/eventpage/us100075y8#executive, ac-cessed 22 December 2016, 2016d.

USGS, M 5.1 - 31km NW of Fairview, Oklahoma, Earthquake Hazards Program, U. S. Ge-ological Survey, available at http://earthquake.usgs.gov/earthquakes/eventpage/us20004zy8#executive, URL http://earthquake.usgs.gov/earthquakes/eventpage/us20004zy8#executive, ac-cessed 28 November 2016, 2016c.

USGS, M 5.7 - Oklahoma, Earthquake Hazards Program, U. S. Geological Survey, avail-able at http://earthquake.usgs.gov/earthquakes/eventpage/usp000jadn#executive, URL http://earthquake.usgs.gov/earthquakes/eventpage/usp000jadn#executive, accessed 28 November2016, 2016b.

USGS, M 5.8 - 14km NW of Pawnee, Oklahoma, Earthquake Hazards Program, U. S.Geological Survey, available at http://earthquake.usgs.gov/earthquakes/eventpage/us10006jxs#executive, URL http://earthquake.usgs.gov/earthquakes/eventpage/us10006jxs#executive, ac-cessed 28 November 2016, 2016a.

USGS, Induced Earthquakes, Earthquake Hazards Program, U. S. Geological Survey, URL https://earthquake.usgs.gov/research/induced/overview.php, accessed February 17, 2017, 2017a.

USGS, Latest Earthquakes, Online, URL http://earthquake.usgs.gov/earthquakes/map/, accessedDecember 20, 2015, 2017b.

37

http://earthquake.usgs.gov/hazards/apps/vs30/custom.php

http://earthquake.usgs.gov/earthquakes/eventpage/us100075y8#executive



http://earthquake.usgs.gov/earthquakes/eventpage/us20004zy8#executive



http://earthquake.usgs.gov/earthquakes/eventpage/usp000jadn#executive



http://earthquake.usgs.gov/earthquakes/eventpage/us10006jxs#executive



https://earthquake.usgs.gov/research/induced/overview.php

https://earthquake.usgs.gov/research/induced/overview.php

http://earthquake.usgs.gov/earthquakes/map/

A Earthquake Sequences

Table A.1: Earthquake sequence for seismic station OK.U32A in 2016.

Date EpicentralNo. (yyyy/mm/dd) Magnitude Distance (km) Description

1 2016/01/01 3.4 154.0 6 km S of Guthrie, Oklahoma2 2016/01/01 3.0 164.7 7 km ENE of Edmond, Oklahoma3 2016/01/01 3.1 151.9 8 km NNE of Guthrie, Oklahoma4 2016/01/01 3.2 151.0 10 km NNE of Guthrie, Oklahoma5 2016/01/02 3.0 26.5 33 km NW of Fairview, Oklahoma6 2016/01/02 3.0 125.5 2 km NE of Medford, Oklahoma7 2016/01/02 3.1 139.4 15 km W of Perry, Oklahoma8 2016/01/02 3.3 164.1 14 km NE of Edmond, Oklahoma9 2016/01/02 3.3 139.0 15 km W of Perry, Oklahoma10 2016/01/03 3.1 165.1 14 km WSW of Stillwater, Oklahoma11 2016/01/03 3.3 164.3 14 km WSW of Stillwater, Oklahoma12 2016/01/04 3.3 165.3 13 km WSW of Stillwater, Oklahoma13 2016/01/04 3.4 165.1 13 km WSW of Stillwater, Oklahoma14 2016/01/04 3.5 165.3 13 km WSW of Stillwater, Oklahoma15 2016/01/04 3.4 165.4 13 km WSW of Stillwater, Oklahoma16 2016/01/06 3.0 165.7 7 km E of Edmond, Oklahoma17 2016/01/06 4.0 27.0 33 km NW of Fairview, Oklahoma18 2016/01/06 3.2 165.6 8 km E of Edmond, Oklahoma19 2016/01/06 3.2 96.2 26 km WSW of Medford, Oklahoma20 2016/01/06 3.2 163.9 6 km E of Edmond, Oklahoma21 2016/01/06 3.9 27.2 33 km NW of Fairview, Oklahoma22 2016/01/07 3.5 164.2 6 km ENE of Edmond, Oklahoma23 2016/01/07 3.2 27.3 33 km NW of Fairview, Oklahoma24 2016/01/07 4.4 26.2 33 km NW of Fairview, Oklahoma25 2016/01/07 4.7 27.9 33 km NW of Fairview, Oklahoma26 2016/01/07 3.6 25.7 33 km NW of Fairview, Oklahoma27 2016/01/07 3.5 26.3 33 km NW of Fairview, Oklahoma28 2016/01/07 3.1 25.4 33 km NW of Fairview, Oklahoma29 2016/01/07 3.3 31.4 31 km S of Alva, Oklahoma30 2016/01/07 3.6 26.4 33 km NW of Fairview, Oklahoma31 2016/01/07 3.0 164.6 6 km E of Edmond, Oklahoma32 2016/01/07 3.4 28.4 33 km NW of Fairview, Oklahoma33 2016/01/07 3.9 24.5 33 km NW of Fairview, Oklahoma34 2016/01/07 4.4 26.2 32 km NW of Fairview, Oklahoma35 2016/01/07 3.2 25.5 32 km NW of Fairview, Oklahoma36 2016/01/07 3.8 25.2 33 km NW of Fairview, Oklahoma37 2016/01/07 3.7 25.3 33 km NW of Fairview, Oklahoma38 2016/01/07 3.4 24.8 32 km NW of Fairview, Oklahoma39 2016/01/07 3.4 24.5 33 km NW of Fairview, Oklahoma40 2016/01/07 3.7 29.4 33 km S of Alva, Oklahoma

38

Table A.1 (cont.): Earthquake sequence for seismic station OK.U32A in 2016.


41 2016/01/08 3.0 27.9 33 km NW of Fairview, Oklahoma42 2016/01/08 3.0 27.4 33 km NW of Fairview, Oklahoma43 2016/01/08 3.5 127.9 14 km SE of Medford, Oklahoma44 2016/01/08 3.0 211.4 14 km ESE of Pawnee, Oklahoma45 2016/01/08 3.1 96.6 26 km WSW of Medford, Oklahoma46 2016/01/08 3.8 29.4 32 km S of Alva, Oklahoma47 2016/01/08 3.9 29.5 33 km S of Alva, Oklahoma48 2016/01/08 3.0 27.2 33 km NW of Fairview, Oklahoma49 2016/01/08 3.1 58.1 12 km WNW of Helena, Oklahoma50 2016/01/08 3.1 63.0 8 km SW of Cherokee, Oklahoma51 2016/01/08 3.5 29.5 33 km S of Alva, Oklahoma52 2016/01/08 3.5 165.5 7 km E of Edmond, Oklahoma53 2016/01/11 3.4 23.9 34 km NW of Fairview, Oklahoma54 2016/01/11 3.0 26.2 32 km NW of Fairview, Oklahoma55 2016/01/11 3.0 26.5 32 km NW of Fairview, Oklahoma56 2016/01/11 3.0 24.2 33 km NW of Fairview, Oklahoma57 2016/01/11 3.2 24.3 33 km NW of Fairview, Oklahoma58 2016/01/11 3.4 29.9 33 km S of Alva, Oklahoma59 2016/01/13 3.0 165.3 7 km E of Edmond, Oklahoma60 2016/01/13 3.1 152.4 8 km NNE of Guthrie, Oklahoma61 2016/01/13 3.2 131.0 14 km SW of Caldwell, Kansas62 2016/01/13 3.0 122.3 18 km NNW of Medford, Oklahoma63 2016/01/14 3.1 25.3 33 km NW of Fairview, Oklahoma64 2016/01/14 3.2 24.8 34 km NW of Fairview, Oklahoma65 2016/01/14 3.4 118.1 5 km SW of Medford, Oklahoma66 2016/01/14 3.5 124.3 15 km NNW of Medford, Oklahoma67 2016/01/15 3.3 123.9 17 km NNW of Medford, Oklahoma68 2016/01/15 3.1 123.0 17 km NNW of Medford, Oklahoma69 2016/01/15 3.6 193.7 11 km E of Perkins, Oklahoma70 2016/01/15 3.0 80.9 12 km ENE of Helena, Oklahoma71 2016/01/16 3.0 57.2 14 km SW of Helena, Oklahoma72 2016/01/16 3.1 110.6 12 km WSW of Medford, Oklahoma73 2016/01/17 3.5 104.7 24 km WNW of Medford, Oklahoma74 2016/01/17 3.3 165.1 13 km WSW of Stillwater, Oklahoma75 2016/01/18 3.2 163.1 6 km ENE of Edmond, Oklahoma76 2016/01/18 4.1 54.4 6 km E of Fairview, Oklahoma77 2016/01/18 3.0 152.6 8 km NNE of Guthrie, Oklahoma78 2016/01/19 3.0 29.1 33 km NW of Fairview, Oklahoma79 2016/01/19 3.8 29.4 33 km S of Alva, Oklahoma80 2016/01/19 3.3 120.9 3 km NW of Medford, Oklahoma81 2016/01/20 3.0 114.1 14 km ENE of Enid, Oklahoma82 2016/01/20 3.6 164.0 15 km NE of Edmond, Oklahoma83 2016/01/21 3.0 30.9 32 km S of Alva, Oklahoma

39



84 2016/01/21 3.0 110.2 13 km W of Medford, Oklahoma85 2016/01/21 3.0 104.1 22 km W of Medford, Oklahoma86 2016/01/22 3.2 163.0 5 km ENE of Edmond, Oklahoma87 2016/01/22 3.2 32.2 31 km S of Alva, Oklahoma88 2016/01/22 3.1 166.6 5 km S of Langston, Oklahoma89 2016/01/22 3.0 103.7 22 km W of Medford, Oklahoma90 2016/01/22 3.0 27.1 32 km NW of Fairview, Oklahoma91 2016/01/22 3.7 108.0 23 km N of Enid, Oklahoma92 2016/01/22 3.2 94.9 27 km E of Cherokee, Oklahoma93 2016/01/22 3.1 105.2 24 km WNW of Medford, Oklahoma94 2016/01/24 3.0 57.0 14 km SW of Helena, Oklahoma95 2016/01/24 3.5 135.7 11 km SSW of Caldwell, Kansas96 2016/01/24 3.0 26.0 33 km NW of Fairview, Oklahoma97 2016/01/24 3.0 120.0 18 km NW of Medford, Oklahoma98 2016/01/24 3.3 57.4 14 km SW of Cherokee, Oklahoma99 2016/01/25 3.4 160.0 8 km E of Guthrie, Oklahoma100 2016/01/25 3.0 159.7 7 km E of Guthrie, Oklahoma101 2016/01/26 3.2 109.0 25 km WNW of Medford, Oklahoma102 2016/01/28 3.2 93.5 25 km E of Cherokee, Oklahoma103 2016/01/28 3.1 158.1 4 km NNE of Edmond, Oklahoma104 2016/01/28 3.5 173.3 20 km S of McCord, Oklahoma105 2016/01/29 3.4 26.2 33 km NW of Fairview, Oklahoma106 2016/01/29 3.4 24.8 33 km NW of Fairview, Oklahoma107 2016/01/29 3.2 25.7 33 km NW of Fairview, Oklahoma108 2016/01/29 3.6 25.5 33 km NW of Fairview, Oklahoma109 2016/01/30 3.1 245.3 10 km SW of Boley, Oklahoma110 2016/01/30 3.0 26.7 33 km NW of Fairview, Oklahoma111 2016/01/31 3.5 205.0 9 km NE of Pawnee, Oklahoma112 2016/02/01 3.0 176.6 1 km NNW of Stillwater, Oklahoma113 2016/02/02 3.6 25.5 33 km NW of Fairview, Oklahoma114 2016/02/02 3.4 25.7 32 km NW of Fairview, Oklahoma115 2016/02/03 3.2 154.3 9 km NNE of Guthrie, Oklahoma116 2016/02/03 3.5 132.5 9 km E of Medford, Oklahoma117 2016/02/04 3.3 153.0 8 km NNE of Guthrie, Oklahoma118 2016/02/05 3.1 130.1 24 km W of Perry, Oklahoma119 2016/02/05 3.1 158.4 12 km SSE of Perry, Oklahoma120 2016/02/05 3.1 108.5 20 km NNE of Enid, Oklahoma121 2016/02/05 3.5 108.3 20 km NNE of Enid, Oklahoma122 2016/02/06 3.1 169.9 7 km ENE of Langston, Oklahoma123 2016/02/06 3.1 170.2 7 km ENE of Langston, Oklahoma124 2016/02/06 3.4 120.5 4 km WNW of Medford, Oklahoma125 2016/02/06 3.7 170.0 7 km ENE of Langston, Oklahoma126 2016/02/07 3.6 170.0 7 km ENE of Langston, Oklahoma

40



127 2016/02/08 3.5 178.7 3 km SW of Jones, Oklahoma128 2016/02/09 3.4 202.8 10 km SSE of Pawnee, Oklahoma129 2016/02/10 3.1 124.3 16 km SE of Anthony, Kansas130 2016/02/11 3.0 14.6 19 km ENE of Mooreland, Oklahoma131 2016/02/11 3.2 24.9 33 km NW of Fairview, Oklahoma132 2016/02/11 3.1 25.4 33 km NW of Fairview, Oklahoma133 2016/02/13 5.1 28.9 31 km NW of Fairview, Oklahoma134 2016/02/13 4.0 26.1 33 km NW of Fairview, Oklahoma135 2016/02/13 3.1 121.7 9 km NNW of Medford, Oklahoma136 2016/02/13 3.4 28.8 33 km NW of Fairview, Oklahoma137 2016/02/13 3.7 31.0 31 km S of Alva, Oklahoma138 2016/02/13 3.0 23.7 33 km NW of Fairview, Oklahoma139 2016/02/13 3.3 31.2 31 km S of Alva, Oklahoma140 2016/02/13 3.2 140.9 15 km NE of Crescent, Oklahoma141 2016/02/13 3.0 24.0 33 km NW of Fairview, Oklahoma142 2016/02/14 3.7 22.9 32 km NW of Fairview, Oklahoma143 2016/02/14 3.2 23.8 33 km NW of Fairview, Oklahoma144 2016/02/14 3.8 29.9 33 km S of Alva, Oklahoma145 2016/02/14 3.1 24.5 32 km NW of Fairview, Oklahoma146 2016/02/14 3.5 116.4 16 km E of Waukomis, Oklahoma147 2016/02/14 3.4 24.7 33 km NW of Fairview, Oklahoma148 2016/02/15 3.2 26.7 32 km NW of Fairview, Oklahoma149 2016/02/15 3.2 22.9 32 km NW of Fairview, Oklahoma150 2016/02/15 3.2 23.7 33 km NW of Fairview, Oklahoma151 2016/02/15 3.3 148.6 6 km WSW of Perry, Oklahoma152 2016/02/16 3.1 180.9 7 km NNE of Luther, Oklahoma153 2016/02/16 3.3 24.2 31 km NW of Fairview, Oklahoma154 2016/02/17 3.1 23.9 34 km NW of Fairview, Oklahoma155 2016/02/17 3.3 181.0 7 km NNE of Luther, Oklahoma156 2016/02/17 3.0 22.5 33 km NW of Fairview, Oklahoma157 2016/02/17 3.1 23.9 33 km NW of Fairview, Oklahoma158 2016/02/17 3.4 181.0 7 km NNE of Luther, Oklahoma159 2016/02/17 3.0 165.6 8 km E of Edmond, Oklahoma160 2016/02/18 3.5 180.7 7 km NNE of Luther, Oklahoma161 2016/02/19 3.5 32.9 30 km S of Alva, Oklahoma162 2016/02/19 3.2 164.6 7 km E of Edmond, Oklahoma163 2016/02/19 3.1 33.1 30 km S of Alva, Oklahoma164 2016/02/19 3.4 25.6 33 km NW of Fairview, Oklahoma165 2016/02/20 3.0 148.3 7 km WSW of Perry, Oklahoma166 2016/02/21 3.2 180.6 6 km NNE of Luther, Oklahoma167 2016/02/21 3.0 130.9 26 km WNW of Perry, Oklahoma168 2016/02/22 3.1 152.0 3 km NNE of Guthrie, Oklahoma169 2016/02/22 3.4 21.8 33 km NW of Fairview, Oklahoma

41



170 2016/02/22 3.0 181.0 16 km W of Pawnee, Oklahoma171 2016/02/23 3.2 164.6 7 km ENE of Edmond, Oklahoma172 2016/02/23 3.0 165.0 7 km E of Edmond, Oklahoma173 2016/02/23 3.6 164.5 7 km ENE of Edmond, Oklahoma174 2016/02/23 3.7 164.3 6 km E of Edmond, Oklahoma175 2016/02/23 3.0 165.3 7 km E of Edmond, Oklahoma176 2016/02/23 3.0 164.4 6 km ENE of Edmond, Oklahoma177 2016/02/23 3.2 164.9 7 km ENE of Edmond, Oklahoma178 2016/02/23 3.0 165.1 7 km E of Edmond, Oklahoma179 2016/02/24 3.4 162.9 5 km ENE of Edmond, Oklahoma180 2016/02/25 3.0 152.1 12 km SSW of Guthrie, Oklahoma181 2016/02/25 3.6 162.2 9 km SSW of Langston, Oklahoma182 2016/02/25 3.1 16.8 22 km ENE of Mooreland, Oklahoma183 2016/02/26 3.3 163.3 6 km ENE of Edmond, Oklahoma184 2016/02/26 3.4 32.4 17 km NE of Taloga, Oklahoma185 2016/02/27 3.8 133.5 20 km W of Perry, Oklahoma186 2016/02/27 3.5 133.4 20 km W of Perry, Oklahoma187 2016/02/27 3.3 24.9 32 km NW of Fairview, Oklahoma188 2016/02/27 3.5 24.6 33 km NW of Fairview, Oklahoma189 2016/02/27 3.0 117.1 15 km S of Medford, Oklahoma190 2016/02/28 3.0 114.8 14 km ENE of Enid, Oklahoma191 2016/02/29 3.0 165.2 7 km E of Edmond, Oklahoma192 2016/02/29 3.6 16.6 22 km ENE of Mooreland, Oklahoma193 2016/02/29 3.3 16.2 21 km ENE of Mooreland, Oklahoma194 2016/03/01 3.4 180.7 6 km NNE of Luther, Oklahoma195 2016/03/02 3.1 117.3 15 km S of Medford, Oklahoma196 2016/03/02 3.7 23.6 33 km NW of Fairview, Oklahoma197 2016/03/02 3.0 24.0 33 km NW of Fairview, Oklahoma198 2016/03/02 3.9 25.6 32 km NW of Fairview, Oklahoma199 2016/03/03 3.0 117.4 15 km S of Medford, Oklahoma200 2016/03/03 3.9 23.4 33 km NW of Fairview, Oklahoma201 2016/03/03 3.0 154.7 8 km S of Perry, Oklahoma202 2016/03/03 3.1 82.0 15 km NE of Helena, Oklahoma203 2016/03/05 3.0 171.0 9 km SSE of Langston, Oklahoma204 2016/03/07 3.6 24.9 32 km NW of Fairview, Oklahoma205 2016/03/08 3.7 158.1 8 km ENE of Guthrie, Oklahoma206 2016/03/08 3.0 190.1 9 km SE of Luther, Oklahoma207 2016/03/09 3.3 134.1 20 km W of Perry, Oklahoma208 2016/03/09 3.0 178.8 3 km SW of Jones, Oklahoma209 2016/03/10 3.0 114.1 18 km NE of Enid, Oklahoma210 2016/03/10 3.1 134.3 20 km W of Perry, Oklahoma211 2016/03/10 3.1 29.7 32 km S of Alva, Oklahoma212 2016/03/10 3.0 81.8 17 km NNE of Helena, Oklahoma

42



213 2016/03/10 3.1 122.1 22 km E of Waukomis, Oklahoma214 2016/03/10 3.2 122.6 23 km E of Waukomis, Oklahoma215 2016/03/11 3.2 202.3 3 km W of Cushing, Oklahoma216 2016/03/11 3.1 192.8 13 km NW of Chandler, Oklahoma217 2016/03/12 3.4 114.8 14 km E of Enid, Oklahoma218 2016/03/13 3.4 112.9 22 km S of Medford, Oklahoma219 2016/03/14 3.2 24.7 32 km NW of Fairview, Oklahoma220 2016/03/14 3.3 82.5 11 km NE of Cherokee, Oklahoma221 2016/03/15 3.3 206.5 14 km NNE of Chandler, Oklahoma222 2016/03/15 3.1 159.4 5 km ESE of Tonkawa, Oklahoma223 2016/03/16 3.2 82.3 11 km NE of Cherokee, Oklahoma224 2016/03/16 3.3 108.5 25 km WNW of Medford, Oklahoma225 2016/03/16 3.0 80.7 10 km NNE of Cherokee, Oklahoma226 2016/03/17 3.6 81.2 10 km NE of Cherokee, Oklahoma227 2016/03/17 3.1 81.4 10 km NE of Cherokee, Oklahoma228 2016/03/18 3.0 207.8 6 km WSW of Meeker, Oklahoma229 2016/03/19 3.2 49.3 12 km SSE of Alva, Oklahoma230 2016/03/19 3.0 117.7 6 km S of Anthony, Kansas231 2016/03/19 3.4 174.6 8 km WNW of Perkins, Oklahoma232 2016/03/20 3.3 200.6 11 km NW of Yale, Oklahoma233 2016/03/20 3.1 43.9 23 km N of Fairview, Oklahoma234 2016/03/20 3.2 133.2 20 km W of Perry, Oklahoma235 2016/03/21 3.1 49.9 11 km NNE of Fairview, Oklahoma236 2016/03/21 3.0 87.6 18 km NNE of Cherokee, Oklahoma237 2016/03/23 3.1 80.1 12 km N of Cherokee, Oklahoma238 2016/03/24 3.0 15.7 22 km ENE of Mooreland, Oklahoma239 2016/03/25 3.0 180.7 7 km NNE of Luther, Oklahoma240 2016/03/26 3.0 104.5 26 km WNW of Medford, Oklahoma241 2016/03/27 3.3 107.5 22 km N of Enid, Oklahoma242 2016/03/27 3.3 107.2 22 km N of Enid, Oklahoma243 2016/03/27 3.0 159.9 14 km NNW of Blackwell, Oklahoma244 2016/03/27 3.2 120.8 20 km SSE of Medford, Oklahoma245 2016/03/29 4.2 135.2 4 km NNE of Crescent, Oklahoma246 2016/03/29 3.6 135.6 4 km NNE of Crescent, Oklahoma247 2016/03/29 3.3 28.2 27 km NW of Fairview, Oklahoma248 2016/03/29 3.3 24.7 32 km NW of Fairview, Oklahoma249 2016/03/30 3.2 24.7 32 km NW of Fairview, Oklahoma250 2016/03/30 3.4 120.8 20 km SSE of Medford, Oklahoma251 2016/03/31 3.0 182.2 6 km NNE of Luther, Oklahoma252 2016/03/31 3.2 182.2 7 km NNE of Luther, Oklahoma253 2016/03/31 3.2 182.3 7 km NNE of Luther, Oklahoma254 2016/04/02 3.0 182.9 7 km NNE of Perkins, Oklahoma255 2016/04/02 3.1 165.1 8 km ENE of Edmond, Oklahoma

43



256 2016/04/03 3.3 182.1 7 km NNE of Luther, Oklahoma257 2016/04/03 3.2 182.1 7 km NNE of Luther, Oklahoma258 2016/04/04 3.3 85.0 18 km E of Cherokee, Oklahoma259 2016/04/04 3.0 173.5 19 km N of Stillwater, Oklahoma260 2016/04/05 3.0 208.3 5 km SSE of Cushing, Oklahoma261 2016/04/06 3.4 130.5 26 km WSW of Perry, Oklahoma262 2016/04/07 3.3 183.3 2 km E of Luther, Oklahoma263 2016/04/07 3.1 183.5 2 km E of Luther, Oklahoma264 2016/04/07 3.6 183.0 2 km E of Luther, Oklahoma265 2016/04/07 3.7 74.7 16 km SSE of Helena, Oklahoma266 2016/04/07 3.1 74.9 16 km SSE of Helena, Oklahoma267 2016/04/07 3.3 129.8 26 km WSW of Perry, Oklahoma268 2016/04/07 4.2 182.9 1 km E of Luther, Oklahoma269 2016/04/08 3.1 183.1 2 km E of Luther, Oklahoma270 2016/04/08 3.1 163.2 10 km ENE of Perry, Oklahoma271 2016/04/08 3.2 184.0 3 km E of Luther, Oklahoma272 2016/04/08 3.1 183.2 2 km E of Luther, Oklahoma273 2016/04/08 3.0 207.3 5 km S of Cushing, Oklahoma274 2016/04/09 3.1 169.9 7 km N of Spencer, Oklahoma275 2016/04/09 3.0 101.3 25 km W of Medford, Oklahoma276 2016/04/09 3.4 131.7 11 km NNE of Medford, Oklahoma277 2016/04/10 3.4 15.9 22 km ENE of Mooreland, Oklahoma278 2016/04/11 3.5 46.2 21 km WSW of Helena, Oklahoma279 2016/04/12 3.5 133.5 20 km W of Perry, Oklahoma280 2016/04/12 3.3 120.3 20 km S of Medford, Oklahoma281 2016/04/13 3.5 159.0 14 km NNW of Blackwell, Oklahoma282 2016/04/14 3.0 198.7 11 km WNW of Yale, Oklahoma283 2016/04/15 3.0 16.7 31 km E of Mooreland, Oklahoma284 2016/04/15 3.1 17.5 32 km E of Mooreland, Oklahoma285 2016/04/17 3.2 77.4 18 km SE of Helena, Oklahoma286 2016/04/19 3.0 119.5 17 km S of Medford, Oklahoma287 2016/04/20 3.1 22.5 33 km NW of Fairview, Oklahoma288 2016/04/21 3.3 206.1 4 km SW of Yale, Oklahoma289 2016/04/21 3.0 190.0 15 km NNW of Pawnee, Oklahoma290 2016/04/21 3.3 32.8 30 km S of Alva, Oklahoma291 2016/04/23 3.0 15.8 21 km ENE of Mooreland, Oklahoma292 2016/04/23 3.0 250.9 17 km NE of Seminole, Oklahoma293 2016/04/23 3.4 130.2 26 km WSW of Perry, Oklahoma294 2016/04/26 3.0 29.6 27 km NW of Fairview, Oklahoma295 2016/04/26 3.4 25.4 33 km NW of Fairview, Oklahoma296 2016/04/26 3.6 197.1 7 km ENE of Harrah, Oklahoma297 2016/04/26 3.6 180.9 7 km NNE of Luther, Oklahoma298 2016/04/27 3.0 182.7 1 km E of Luther, Oklahoma

44



299 2016/04/27 3.0 196.9 7 km ENE of Harrah, Oklahoma300 2016/04/27 3.7 178.9 9 km N of Luther, Oklahoma301 2016/04/27 3.0 181.0 8 km NNE of Luther, Oklahoma302 2016/04/28 3.0 152.4 9 km SSW of Perry, Oklahoma303 2016/04/29 3.0 104.2 24 km WNW of Medford, Oklahoma304 2016/04/29 3.0 222.2 9 km WNW of Prague, Oklahoma305 2016/04/29 3.4 181.1 8 km NNE of Luther, Oklahoma306 2016/04/29 3.4 180.4 7 km NNE of Luther, Oklahoma307 2016/04/29 3.0 160.7 9 km NNW of Blackwell, Oklahoma308 2016/04/30 3.2 180.5 3 km WNW of Choctaw, Oklahoma309 2016/04/30 3.1 162.9 4 km E of Edmond, Oklahoma310 2016/04/30 3.0 182.7 1 km E of Luther, Oklahoma311 2016/04/30 3.2 92.9 21 km ENE of Cherokee, Oklahoma312 2016/05/01 3.4 135.4 14 km ENE of Anthony, Kansas313 2016/05/01 3.7 24.4 33 km NW of Fairview, Oklahoma314 2016/05/02 3.0 159.2 14 km NNW of Blackwell, Oklahoma315 2016/05/02 3.1 181.1 7 km NNE of Luther, Oklahoma316 2016/05/03 3.7 94.1 22 km NE of Cherokee, Oklahoma317 2016/05/03 3.6 94.3 23 km NE of Cherokee, Oklahoma318 2016/05/03 3.0 117.9 5 km W of Medford, Oklahoma319 2016/05/04 3.3 94.7 23 km NE of Cherokee, Oklahoma320 2016/05/04 3.2 23.2 32 km NW of Fairview, Oklahoma321 2016/05/05 3.0 160.7 9 km NNW of Blackwell, Oklahoma322 2016/05/05 3.5 74.6 11 km SE of Cherokee, Oklahoma323 2016/05/08 3.1 132.9 10 km E of Medford, Oklahoma324 2016/05/08 3.3 128.8 25 km W of Perry, Oklahoma325 2016/05/09 3.4 128.9 25 km W of Perry, Oklahoma326 2016/05/09 3.1 126.3 3 km ENE of Medford, Oklahoma327 2016/05/09 3.0 92.8 21 km ENE of Cherokee, Oklahoma328 2016/05/10 3.1 196.1 4 km SSW of Pawnee, Oklahoma329 2016/05/11 3.1 150.5 12 km NNW of Perry, Oklahoma330 2016/05/12 3.3 133.9 20 km W of Perry, Oklahoma331 2016/05/12 3.0 112.0 22 km SSE of Anthony, Kansas332 2016/05/14 3.1 196.8 12 km SW of Goldsby, Oklahoma333 2016/05/14 3.0 31.7 31 km S of Alva, Oklahoma334 2016/05/15 3.6 115.0 14 km E of Enid, Oklahoma335 2016/05/15 3.4 183.6 2 km E of Luther, Oklahoma336 2016/05/16 3.1 184.3 3 km E of Luther, Oklahoma337 2016/05/19 3.1 152.2 8 km NNE of Guthrie, Oklahoma338 2016/05/19 3.2 170.1 10 km SSE of Langston, Oklahoma339 2016/05/20 3.6 25.2 32 km NW of Fairview, Oklahoma340 2016/05/20 3.0 25.5 33 km NW of Fairview, Oklahoma341 2016/05/21 3.2 174.2 14 km S of McCord, Oklahoma

45



342 2016/05/22 3.2 114.7 14 km E of Enid, Oklahoma343 2016/05/23 3.0 168.0 6 km NE of Langston, Oklahoma344 2016/05/23 3.1 168.1 6 km NE of Langston, Oklahoma345 2016/05/25 3.2 22.8 33 km NW of Fairview, Oklahoma346 2016/05/26 3.3 180.8 7 km NNE of Luther, Oklahoma347 2016/05/27 3.2 23.8 33 km NW of Fairview, Oklahoma348 2016/05/28 3.0 183.9 10 km NE of Stillwater, Oklahoma349 2016/05/29 3.5 155.7 15 km NNW of Langston, Oklahoma350 2016/05/31 3.3 184.9 3 km ESE of Luther, Oklahoma351 2016/06/01 3.2 155.2 13 km NW of Blackwell, Oklahoma352 2016/06/01 3.1 127.6 5 km NE of Anthony, Kansas353 2016/06/02 3.4 114.6 13 km E of Enid, Oklahoma354 2016/06/02 3.2 77.2 18 km SE of Helena, Oklahoma355 2016/06/04 3.2 128.8 25 km W of Perry, Oklahoma356 2016/06/04 3.1 17.6 24 km ENE of Mooreland, Oklahoma357 2016/06/05 3.4 127.4 5 km NE of Anthony, Kansas358 2016/06/06 3.3 178.6 1 km N of Jones, Oklahoma359 2016/06/06 3.2 114.5 13 km E of Enid, Oklahoma360 2016/06/06 3.3 186.9 14 km NW of Pawnee, Oklahoma361 2016/06/06 3.2 201.6 10 km SSE of Pawnee, Oklahoma362 2016/06/06 3.0 117.4 15 km S of Medford, Oklahoma363 2016/06/07 3.2 162.9 4 km ENE of Edmond, Oklahoma364 2016/06/08 3.9 189.7 13 km NNW of Pawnee, Oklahoma365 2016/06/09 3.4 21.3 33 km NW of Fairview, Oklahoma366 2016/06/09 3.3 126.8 25 km SSE of Medford, Oklahoma367 2016/06/09 3.6 134.0 20 km W of Perry, Oklahoma368 2016/06/11 3.5 27.5 32 km NW of Fairview, Oklahoma369 2016/06/11 3.2 145.4 22 km SSW of Conway Springs, Kansas370 2016/06/12 3.1 170.1 10 km SSE of Langston, Oklahoma371 2016/06/12 3.0 169.7 10 km SSE of Langston, Oklahoma372 2016/06/13 3.2 21.4 33 km NW of Fairview, Oklahoma373 2016/06/14 3.0 155.2 7 km S of Perry, Oklahoma374 2016/06/14 3.1 57.9 15 km WNW of Helena, Oklahoma375 2016/06/15 3.0 45.0 10 km SSW of Alva, Oklahoma376 2016/06/15 3.3 45.3 10 km SSW of Alva, Oklahoma377 2016/06/15 3.3 14.5 10 km ENE of Mooreland, Oklahoma378 2016/06/15 3.0 44.9 11 km SSW of Alva, Oklahoma379 2016/06/15 3.1 155.2 7 km S of Perry, Oklahoma380 2016/06/16 3.0 114.9 14 km E of Enid, Oklahoma381 2016/06/17 3.1 163.6 6 km ENE of Edmond, Oklahoma382 2016/07/08 3.4 193.4 9 km SSE of Blanchard, Oklahoma383 2016/07/08 4.2 25.9 32 km NW of Fairview, Oklahoma384 2016/07/08 4.2 25.2 33 km NW of Fairview, Oklahoma

46



385 2016/07/08 3.1 25.9 33 km NW of Fairview, Oklahoma386 2016/07/09 3.1 25.4 33 km NW of Fairview, Oklahoma387 2016/07/09 4.4 23.7 33 km NW of Fairview, Oklahoma388 2016/07/09 3.1 22.4 33 km NW of Fairview, Oklahoma389 2016/07/09 3.4 22.6 33 km NW of Fairview, Oklahoma390 2016/07/09 3.3 22.5 33 km NW of Fairview, Oklahoma391 2016/07/09 3.0 133.7 20 km WNW of Perry, Oklahoma392 2016/07/09 3.0 87.8 22 km ESE of Cherokee, Oklahoma393 2016/07/09 3.6 167.9 6 km NE of Langston, Oklahoma394 2016/07/09 3.0 45.3 10 km SW of Alva, Oklahoma395 2016/07/09 3.4 26.4 32 km NW of Fairview, Oklahoma396 2016/07/09 3.1 170.8 15 km S of Langston, Oklahoma397 2016/07/11 3.1 169.3 7 km ENE of Langston, Oklahoma398 2016/07/13 3.0 34.4 29 km S of Alva, Oklahoma399 2016/07/13 3.0 85.2 14 km NE of Cherokee, Oklahoma400 2016/07/13 3.2 73.6 11 km SE of Cherokee, Oklahoma401 2016/07/14 3.4 179.2 3 km WSW of Nicoma Park, Oklahoma402 2016/07/15 3.0 119.4 19 km ESE of Enid, Oklahoma403 2016/07/16 3.1 157.5 7 km ENE of Guthrie, Oklahoma404 2016/07/16 3.0 160.5 9 km NNW of Blackwell, Oklahoma405 2016/07/17 4.2 134.0 20 km W of Perry, Oklahoma406 2016/07/17 3.5 134.1 20 km W of Perry, Oklahoma407 2016/07/17 3.1 134.7 19 km W of Perry, Oklahoma408 2016/07/18 3.2 139.2 10 km NE of Crescent, Oklahoma409 2016/07/19 3.4 133.4 10 km E of Medford, Oklahoma410 2016/07/19 3.2 134.2 20 km W of Perry, Oklahoma411 2016/07/21 3.6 171.5 19 km ENE of Perry, Oklahoma412 2016/07/22 3.1 138.0 16 km E of Medford, Oklahoma413 2016/07/22 3.4 47.1 24 km SW of Cherokee, Oklahoma414 2016/07/24 3.0 173.3 3 km WNW of Stillwater, Oklahoma415 2016/07/24 3.1 22.1 33 km NW of Fairview, Oklahoma416 2016/07/29 3.6 129.5 26 km WSW of Perry, Oklahoma417 2016/07/31 3.1 194.1 10 km SE of Blanchard, Oklahoma418 2016/08/05 3.4 24.5 32 km NW of Fairview, Oklahoma419 2016/08/05 3.0 93.1 25 km E of Cherokee, Oklahoma420 2016/08/05 3.2 88.0 22 km ESE of Cherokee, Oklahoma421 2016/08/07 3.3 47.0 21 km WSW of Helena, Oklahoma422 2016/08/07 3.0 144.3 16 km SW of Perry, Oklahoma423 2016/08/09 3.1 134.4 19 km W of Perry, Oklahoma424 2016/08/09 3.6 129.5 27 km WSW of Perry, Oklahoma425 2016/08/09 3.9 129.9 26 km WSW of Perry, Oklahoma426 2016/08/09 3.2 130.0 26 km WSW of Perry, Oklahoma427 2016/08/10 3.2 130.9 25 km WSW of Perry, Oklahoma

47



428 2016/08/10 3.6 182.3 1 km E of Luther, Oklahoma429 2016/08/10 3.5 182.3 1 km E of Luther, Oklahoma430 2016/08/12 3.6 87.7 20 km NE of Helena, Oklahoma431 2016/08/12 3.1 147.5 15 km NNW of Perry, Oklahoma432 2016/08/14 3.1 87.6 20 km NE of Helena, Oklahoma433 2016/08/14 3.5 132.6 9 km E of Medford, Oklahoma434 2016/08/15 3.1 147.5 15 km NNW of Perry, Oklahoma435 2016/08/15 3.0 132.3 12 km ESE of Medford, Oklahoma436 2016/08/16 3.3 184.9 3 km E of Luther, Oklahoma437 2016/08/16 3.1 161.0 20 km SSE of Tonkawa, Oklahoma438 2016/08/17 3.3 52.1 3 km SE of Fairview, Oklahoma439 2016/08/17 4.0 189.9 10 km E of Luther, Oklahoma440 2016/08/19 3.5 169.2 7 km SSW of Cheney, Kansas441 2016/08/20 3.2 17.7 24 km ENE of Mooreland, Oklahoma442 2016/08/24 3.3 205.2 6 km SW of Yale, Oklahoma443 2016/08/29 3.6 129.4 27 km WSW of Perry, Oklahoma444 2016/08/29 3.0 130.2 26 km WSW of Perry, Oklahoma445 2016/08/30 3.1 167.9 5 km NE of Langston, Oklahoma446 2016/08/30 3.0 115.6 21 km NW of Medford, Oklahoma447 2016/08/30 3.1 119.6 17 km S of Medford, Oklahoma448 2016/08/31 3.3 101.8 14 km N of Enid, Oklahoma449 2016/09/01 3.1 150.8 6 km ENE of Caldwell, Kansas450 2016/09/01 3.2 37.6 26 km NNW of Fairview, Oklahoma451 2016/09/01 3.0 188.7 14 km NW of Pawnee, Oklahoma452 2016/09/03 3.4 128.0 6 km NNE of Medford, Oklahoma453 2016/09/03 3.4 185.1 4 km E of Luther, Oklahoma454 2016/09/03 5.8 186.0 14 km NW of Pawnee, Oklahoma455 2016/09/03 3.3 192.8 9 km NNW of Pawnee, Oklahoma456 2016/09/03 3.6 187.7 13 km NW of Pawnee, Oklahoma457 2016/09/03 3.3 192.2 9 km NNW of Pawnee, Oklahoma458 2016/09/03 3.4 190.0 11 km NW of Pawnee, Oklahoma459 2016/09/03 3.0 129.7 26 km WSW of Perry, Oklahoma460 2016/09/03 3.0 182.3 15 km W of Pawnee, Oklahoma461 2016/09/03 3.0 192.5 9 km NNW of Pawnee, Oklahoma462 2016/09/04 3.1 190.0 11 km NW of Pawnee, Oklahoma463 2016/09/04 3.2 203.4 6 km N of Cushing, Oklahoma464 2016/09/04 3.2 182.9 14 km W of Pawnee, Oklahoma465 2016/09/04 3.0 189.5 11 km NW of Pawnee, Oklahoma466 2016/09/04 3.0 186.7 14 km NW of Pawnee, Oklahoma467 2016/09/04 3.1 203.2 6 km NNW of Cushing, Oklahoma468 2016/09/05 3.1 140.9 14 km WNW of Perry, Oklahoma469 2016/09/06 3.9 115.4 21 km NW of Medford, Oklahoma470 2016/09/06 3.7 113.0 22 km NW of Medford, Oklahoma

48



471 2016/09/06 3.5 115.8 21 km NW of Medford, Oklahoma472 2016/09/07 3.1 187.9 14 km NW of Pawnee, Oklahoma473 2016/09/07 3.3 116.7 21 km NW of Medford, Oklahoma474 2016/09/08 3.3 134.5 19 km W of Perry, Oklahoma475 2016/09/08 3.2 177.3 5 km N of Stillwater, Oklahoma476 2016/09/08 3.1 177.1 5 km N of Stillwater, Oklahoma477 2016/09/09 3.0 153.1 11 km N of Perry, Oklahoma478 2016/09/09 3.5 173.5 1 km WSW of Spencer, Oklahoma479 2016/09/09 3.7 182.7 14 km W of Pawnee, Oklahoma480 2016/09/09 3.0 66.4 4 km SW of Cherokee, Oklahoma481 2016/09/09 3.1 205.3 4 km WSW of Yale, Oklahoma482 2016/09/10 3.2 178.0 13 km SW of Perkins, Oklahoma483 2016/09/12 3.0 192.7 8 km NNW of Pawnee, Oklahoma484 2016/09/12 3.0 187.8 14 km NW of Pawnee, Oklahoma485 2016/09/13 3.3 51.9 3 km SE of Fairview, Oklahoma486 2016/09/13 3.7 52.0 3 km SE of Fairview, Oklahoma487 2016/09/13 3.0 114.6 8 km WSW of Medford, Oklahoma488 2016/09/13 3.3 135.8 10 km NW of Harper, Kansas489 2016/09/13 3.3 115.0 8 km WSW of Medford, Oklahoma490 2016/09/14 3.7 22.2 32 km NW of Fairview, Oklahoma491 2016/09/14 3.2 164.3 7 km ENE of Edmond, Oklahoma492 2016/09/16 3.0 59.6 9 km ESE of Alva, Oklahoma493 2016/09/16 3.9 23.5 32 km NW of Fairview, Oklahoma494 2016/09/17 3.5 79.7 12 km N of Cherokee, Oklahoma495 2016/09/17 3.0 118.5 11 km S of Medford, Oklahoma496 2016/09/18 3.2 134.2 20 km W of Perry, Oklahoma497 2016/09/20 3.9 115.9 21 km NW of Medford, Oklahoma498 2016/09/20 3.1 115.7 20 km NW of Medford, Oklahoma499 2016/09/21 3.2 169.4 10 km S of Langston, Oklahoma500 2016/09/23 3.0 188.0 12 km NW of Pawnee, Oklahoma501 2016/09/26 3.4 143.6 20 km NE of Crescent, Oklahoma502 2016/09/26 3.8 81.3 10 km NE of Cherokee, Oklahoma503 2016/09/27 3.0 157.2 19 km SSE of Tonkawa, Oklahoma504 2016/09/29 3.1 185.0 12 km WNW of Pawnee, Oklahoma505 2016/09/29 3.1 54.6 6 km E of Fairview, Oklahoma506 2016/09/30 3.3 14.9 14 km ENE of Mooreland, Oklahoma507 2016/10/02 3.2 130.1 26 km WSW of Perry, Oklahoma508 2016/10/04 3.7 185.0 15 km NW of Pawnee, Oklahoma509 2016/10/04 3.3 216.5 12 km N of Stroud, Oklahoma510 2016/10/05 3.0 185.1 14 km WNW of Pawnee, Oklahoma511 2016/10/05 3.0 16.5 5 km ENE of Mooreland, Oklahoma512 2016/10/05 3.3 21.3 33 km NW of Fairview, Oklahoma513 2016/10/05 3.0 216.5 12 km N of Stroud, Oklahoma

49



514 2016/10/05 3.2 20.9 33 km NW of Fairview, Oklahoma515 2016/10/06 3.4 187.0 13 km NW of Pawnee, Oklahoma516 2016/10/06 3.6 139.2 16 km E of Medford, Oklahoma517 2016/10/08 3.3 22.2 33 km NW of Fairview, Oklahoma518 2016/10/09 3.5 189.3 11 km NW of Pawnee, Oklahoma519 2016/10/09 3.0 15.2 14 km ENE of Mooreland, Oklahoma520 2016/10/10 3.0 21.4 33 km NW of Fairview, Oklahoma521 2016/10/13 3.3 75.3 4 km NNE of Cherokee, Oklahoma522 2016/10/15 3.1 115.6 14 km E of Enid, Oklahoma523 2016/10/17 3.0 216.4 13 km N of Stroud, Oklahoma524 2016/10/18 3.0 164.8 7 km E of Edmond, Oklahoma525 2016/10/19 3.1 60.1 8 km WSW of Helena, Oklahoma526 2016/10/19 3.0 191.3 10 km NW of Pawnee, Oklahoma527 2016/10/19 3.1 118.4 5 km SSW of Medford, Oklahoma528 2016/10/19 3.1 21.7 36 km NW of Fairview, Oklahoma529 2016/10/20 3.4 135.9 11 km SSW of Caldwell, Kansas530 2016/10/20 3.0 158.3 6 km SE of Guthrie, Oklahoma531 2016/10/21 3.8 63.3 9 km SSW of Helena, Oklahoma532 2016/10/21 4.0 21.7 33 km NW of Fairview, Oklahoma533 2016/10/21 3.1 21.8 33 km NW of Fairview, Oklahoma534 2016/10/21 3.4 21.2 33 km NW of Fairview, Oklahoma535 2016/10/21 3.0 21.0 33 km NW of Fairview, Oklahoma536 2016/10/21 3.2 20.7 33 km NW of Fairview, Oklahoma537 2016/10/22 3.1 30.8 26 km NNE of Mooreland, Oklahoma538 2016/10/24 3.3 139.0 16 km E of Medford, Oklahoma539 2016/10/24 3.5 136.1 18 km E of Anthony, Kansas540 2016/10/26 3.5 133.1 21 km WNW of Perry, Oklahoma541 2016/10/27 3.6 184.6 3 km E of Luther, Oklahoma542 2016/10/28 3.0 94.3 26 km E of Cherokee, Oklahoma543 2016/10/28 3.1 189.4 13 km NW of Pawnee, Oklahoma544 2016/10/29 3.3 189.9 10 km NW of Pawnee, Oklahoma545 2016/10/29 3.1 146.1 13 km SSW of Tonkawa, Oklahoma546 2016/10/29 3.2 146.7 13 km SSW of Tonkawa, Oklahoma547 2016/10/30 3.4 176.1 21 km N of Stillwater, Oklahoma548 2016/10/30 3.3 160.5 7 km SE of Perry, Oklahoma549 2016/10/31 3.0 187.8 14 km NW of Pawnee, Oklahoma550 2016/10/31 3.4 134.5 19 km W of Perry, Oklahoma551 2016/11/02 3.1 119.5 16 km WNW of El Reno, Oklahoma552 2016/11/02 3.3 119.8 15 km WNW of El Reno, Oklahoma553 2016/11/02 3.0 123.4 22 km ENE of Hennessey, Oklahoma554 2016/11/02 4.4 209.8 12 km ESE of Pawnee, Oklahoma555 2016/11/02 3.1 209.1 12 km ESE of Pawnee, Oklahoma556 2016/11/04 3.3 123.3 21 km ENE of Hennessey, Oklahoma

50



557 2016/11/05 3.3 209.4 12 km ESE of Pawnee, Oklahoma558 2016/11/06 3.4 160.7 7 km SE of Perry, Oklahoma559 2016/11/06 3.0 173.0 21 km ENE of Perry, Oklahoma560 2016/11/07 5.0 202.4 3 km W of Cushing, Oklahoma561 2016/11/07 3.0 205.1 2 km N of Cushing, Oklahoma562 2016/11/07 3.1 157.9 8 km WSW of Conway Springs, Kansas563 2016/11/07 4.1 23.1 32 km NW of Fairview, Oklahoma564 2016/11/07 3.0 181.5 1 km ENE of Nicoma Park, Oklahoma565 2016/11/07 3.3 24.8 33 km NW of Fairview, Oklahoma566 2016/11/08 3.3 148.0 15 km NNW of Perry, Oklahoma567 2016/11/09 3.7 116.9 21 km NW of Medford, Oklahoma568 2016/11/11 3.1 201.9 3 km W of Cushing, Oklahoma569 2016/11/11 3.4 118.5 17 km WNW of El Reno, Oklahoma570 2016/11/11 3.3 117.5 20 km NW of Medford, Oklahoma571 2016/11/11 3.3 190.6 11 km ENE of Luther, Oklahoma572 2016/11/12 3.3 202.1 3 km W of Cushing, Oklahoma573 2016/11/14 3.1 20.4 34 km NW of Fairview, Oklahoma574 2016/11/14 3.3 209.4 12 km ESE of Pawnee, Oklahoma575 2016/11/14 3.0 20.3 34 km NW of Fairview, Oklahoma576 2016/11/15 3.0 208.0 11 km ESE of Pawnee, Oklahoma577 2016/11/19 3.0 20.8 33 km NW of Fairview, Oklahoma578 2016/11/19 3.0 21.3 33 km NW of Fairview, Oklahoma579 2016/11/22 3.5 205.0 2 km N of Cushing, Oklahoma580 2016/11/22 3.0 116.5 9 km WNW of Medford, Oklahoma581 2016/11/24 3.5 182.4 12 km NNE of Stillwater, Oklahoma582 2016/11/24 3.6 202.8 2 km WNW of Cushing, Oklahoma583 2016/11/25 4.0 123.0 4 km NNW of Medford, Oklahoma584 2016/11/27 3.6 132.6 12 km ESE of Medford, Oklahoma585 2016/12/05 3.8 210.2 13 km ESE of Pawnee, Oklahoma586 2016/12/05 3.2 206.7 4 km NNE of Cushing, Oklahoma587 2016/12/05 3.3 138.2 16 km WSW of Perry, Oklahoma588 2016/12/06 3.2 208.6 0 km NNW of Yale, Oklahoma589 2016/12/07 3.0 134.7 19 km W of Perry, Oklahoma590 2016/12/10 3.4 98.8 6 km SSW of Enid, Oklahoma591 2016/12/10 3.2 17.5 23 km ENE of Mooreland, Oklahoma592 2016/12/11 3.2 134.5 19 km W of Perry, Oklahoma593 2016/12/12 3.2 21.9 33 km NW of Fairview, Oklahoma594 2016/12/14 3.2 118.0 15 km S of Medford, Oklahoma595 2016/12/16 3.1 203.2 8 km NE of Pawnee, Oklahoma596 2016/12/17 3.0 139.9 13 km ESE of Harper, Kansas597 2016/12/18 3.3 150.4 12 km NNW of Perry, Oklahoma598 2016/12/18 3.7 164.5 7 km ENE of Edmond, Oklahoma599 2016/12/18 3.0 209.8 12 km ESE of Pawnee, Oklahoma

51



600 2016/12/19 3.1 17.7 24 km ENE of Mooreland, Oklahoma601 2016/12/20 3.5 21.1 33 km NW of Fairview, Oklahoma602 2016/12/20 3.1 319.4 7 km N of Coalgate, Oklahoma603 2016/12/20 3.2 201.8 9 km NW of Yale, Oklahoma604 2016/12/22 3.0 21.6 32 km NW of Fairview, Oklahoma605 2016/12/22 3.3 164.3 7 km ENE of Edmond, Oklahoma606 2016/12/22 3.1 138.2 15 km ESE of Harper, Kansas607 2016/12/23 3.4 17.4 23 km ENE of Mooreland, Oklahoma608 2016/12/23 3.4 17.1 23 km ENE of Mooreland, Oklahoma609 2016/12/24 3.0 16.8 23 km ENE of Mooreland, Oklahoma610 2016/12/24 3.6 189.6 10 km NW of Pawnee, Oklahoma611 2016/12/28 3.4 21.3 33 km NW of Fairview, Oklahoma612 2016/12/29 3.0 164.6 7 km ENE of Edmond, Oklahoma613 2016/12/29 3.2 164.6 7 km ENE of Edmond, Oklahoma614 2016/12/30 3.1 149.2 5 km WSW of Perry, Oklahoma

52

Table A.2: Earthquake sequence for seismic station GS.OK005 in 2016.


1 2016/01/01 4.2 19.6 6 km ENE of Edmond, Oklahoma2 2016/01/01 3.4 28.8 6 km S of Guthrie, Oklahoma3 2016/01/01 3.0 18.9 7 km ENE of Edmond, Oklahoma4 2016/01/01 3.1 38.0 8 km NNE of Guthrie, Oklahoma5 2016/01/02 3.3 17.9 14 km NE of Edmond, Oklahoma6 2016/01/04 3.4 46.4 13 km WSW of Stillwater, Oklahoma7 2016/01/04 3.5 46.4 13 km WSW of Stillwater, Oklahoma8 2016/01/04 3.4 46.4 13 km WSW of Stillwater, Oklahoma9 2016/01/06 3.0 18.1 7 km E of Edmond, Oklahoma10 2016/01/06 4.0 166.8 33 km NW of Fairview, Oklahoma11 2016/01/06 3.2 18.0 8 km E of Edmond, Oklahoma12 2016/01/06 3.2 20.0 6 km E of Edmond, Oklahoma13 2016/01/06 3.9 166.7 33 km NW of Fairview, Oklahoma14 2016/01/07 3.5 19.3 6 km ENE of Edmond, Oklahoma15 2016/01/07 4.4 167.3 33 km NW of Fairview, Oklahoma16 2016/01/07 4.7 166.7 33 km NW of Fairview, Oklahoma17 2016/01/07 3.0 19.5 6 km E of Edmond, Oklahoma18 2016/01/07 3.9 167.7 33 km NW of Fairview, Oklahoma19 2016/01/07 4.4 166.2 32 km NW of Fairview, Oklahoma20 2016/01/07 3.8 167.7 33 km NW of Fairview, Oklahoma21 2016/01/07 3.7 166.1 33 km S of Alva, Oklahoma22 2016/01/08 3.8 167.3 32 km S of Alva, Oklahoma23 2016/01/08 3.9 166.8 33 km S of Alva, Oklahoma24 2016/01/08 3.5 18.2 7 km E of Edmond, Oklahoma25 2016/01/13 3.0 18.3 7 km E of Edmond, Oklahoma26 2016/01/13 3.1 37.6 8 km NNE of Guthrie, Oklahoma27 2016/01/14 3.5 152.5 15 km NNW of Medford, Oklahoma28 2016/01/15 3.6 42.2 11 km E of Perkins, Oklahoma29 2016/01/17 3.3 46.6 13 km WSW of Stillwater, Oklahoma30 2016/01/18 3.2 20.4 6 km ENE of Edmond, Oklahoma31 2016/01/18 4.1 129.7 6 km E of Fairview, Oklahoma32 2016/01/18 3.0 37.6 8 km NNE of Guthrie, Oklahoma33 2016/01/19 3.8 166.6 33 km S of Alva, Oklahoma34 2016/01/20 3.6 18.1 15 km NE of Edmond, Oklahoma35 2016/01/22 3.2 20.5 5 km ENE of Edmond, Oklahoma36 2016/01/24 3.5 147.5 11 km SSW of Caldwell, Kansas37 2016/01/25 3.4 28.2 8 km E of Guthrie, Oklahoma38 2016/01/28 3.5 94.4 20 km S of McCord, Oklahoma39 2016/02/03 3.2 37.0 9 km NNE of Guthrie, Oklahoma40 2016/02/04 3.3 37.2 8 km NNE of Guthrie, Oklahoma41 2016/02/05 3.5 116.2 20 km NNE of Enid, Oklahoma42 2016/02/06 3.1 35.5 7 km ENE of Langston, Oklahoma

53

Table A.2 (cont.): Earthquake sequence for seismic station GS.OK005 in 2016.


43 2016/02/06 3.1 35.4 7 km ENE of Langston, Oklahoma44 2016/02/06 3.4 140.3 4 km WNW of Medford, Oklahoma45 2016/02/06 3.7 35.4 7 km ENE of Langston, Oklahoma46 2016/02/07 3.6 35.5 7 km ENE of Langston, Oklahoma47 2016/02/08 3.5 16.7 3 km SW of Jones, Oklahoma48 2016/02/13 5.1 165.2 31 km NW of Fairview, Oklahoma49 2016/02/13 4.0 166.9 33 km NW of Fairview, Oklahoma50 2016/02/14 3.5 84.0 16 km E of Waukomis, Oklahoma51 2016/02/16 3.1 7.7 7 km NNE of Luther, Oklahoma52 2016/02/17 3.3 7.9 7 km NNE of Luther, Oklahoma53 2016/02/17 3.4 8.0 7 km NNE of Luther, Oklahoma54 2016/02/17 3.0 18.0 8 km E of Edmond, Oklahoma55 2016/02/18 3.5 7.7 7 km NNE of Luther, Oklahoma56 2016/02/19 3.2 19.0 7 km E of Edmond, Oklahoma57 2016/02/21 3.2 7.4 6 km NNE of Luther, Oklahoma58 2016/02/22 3.1 34.5 3 km NNE of Guthrie, Oklahoma59 2016/02/22 3.4 168.2 33 km NW of Fairview, Oklahoma60 2016/02/23 3.2 18.9 7 km ENE of Edmond, Oklahoma61 2016/02/23 3.0 18.7 7 km E of Edmond, Oklahoma62 2016/02/23 3.6 19.2 7 km ENE of Edmond, Oklahoma63 2016/02/23 3.7 19.4 6 km E of Edmond, Oklahoma64 2016/02/23 3.0 18.4 7 km E of Edmond, Oklahoma65 2016/02/23 3.0 19.3 6 km ENE of Edmond, Oklahoma66 2016/02/23 3.2 18.4 7 km ENE of Edmond, Oklahoma67 2016/02/23 3.0 18.4 7 km E of Edmond, Oklahoma68 2016/02/24 3.4 20.6 5 km ENE of Edmond, Oklahoma69 2016/02/25 3.0 29.8 12 km SSW of Guthrie, Oklahoma70 2016/02/25 3.6 26.8 9 km SSW of Langston, Oklahoma71 2016/02/26 3.3 20.2 6 km ENE of Edmond, Oklahoma72 2016/02/27 3.8 76.1 20 km W of Perry, Oklahoma73 2016/02/27 3.5 76.2 20 km W of Perry, Oklahoma74 2016/02/29 3.0 18.4 7 km E of Edmond, Oklahoma75 2016/03/01 3.4 7.5 6 km NNE of Luther, Oklahoma76 2016/03/02 3.7 167.3 33 km NW of Fairview, Oklahoma77 2016/03/02 3.9 166.7 32 km NW of Fairview, Oklahoma78 2016/03/03 3.9 167.4 33 km NW of Fairview, Oklahoma79 2016/03/05 3.0 23.2 9 km SSE of Langston, Oklahoma80 2016/03/07 3.6 167.0 32 km NW of Fairview, Oklahoma81 2016/03/08 3.7 32.2 8 km ENE of Guthrie, Oklahoma82 2016/03/08 3.0 8.5 9 km SE of Luther, Oklahoma83 2016/03/09 3.0 16.6 3 km SW of Jones, Oklahoma84 2016/03/10 3.1 81.2 22 km E of Waukomis, Oklahoma

54



85 2016/03/10 3.2 80.7 23 km E of Waukomis, Oklahoma86 2016/03/11 3.1 23.5 13 km NW of Chandler, Oklahoma87 2016/03/12 3.4 93.0 14 km E of Enid, Oklahoma88 2016/03/13 3.4 117.7 22 km S of Medford, Oklahoma89 2016/03/14 3.2 166.8 32 km NW of Fairview, Oklahoma90 2016/03/15 3.3 38.7 14 km NNE of Chandler, Oklahoma91 2016/03/15 3.1 112.0 5 km ESE of Tonkawa, Oklahoma92 2016/03/16 3.2 163.8 11 km NE of Cherokee, Oklahoma93 2016/03/16 3.3 157.2 25 km WNW of Medford, Oklahoma94 2016/03/17 3.6 162.8 10 km NE of Cherokee, Oklahoma95 2016/03/18 3.0 26.7 6 km WSW of Meeker, Oklahoma96 2016/03/19 3.4 38.2 8 km WNW of Perkins, Oklahoma97 2016/03/20 3.3 70.0 11 km NW of Yale, Oklahoma98 2016/03/20 3.1 150.7 23 km N of Fairview, Oklahoma99 2016/03/20 3.2 76.4 20 km W of Perry, Oklahoma100 2016/03/21 3.1 138.2 11 km NNE of Fairview, Oklahoma101 2016/03/21 3.0 168.6 18 km NNE of Cherokee, Oklahoma102 2016/03/25 3.0 8.0 7 km NNE of Luther, Oklahoma103 2016/03/27 3.3 119.7 22 km N of Enid, Oklahoma104 2016/03/27 3.3 119.7 22 km N of Enid, Oklahoma105 2016/03/27 3.2 116.5 20 km SSE of Medford, Oklahoma106 2016/03/29 4.2 51.0 4 km NNE of Crescent, Oklahoma107 2016/03/29 3.6 50.6 4 km NNE of Crescent, Oklahoma108 2016/03/29 3.3 161.5 27 km NW of Fairview, Oklahoma109 2016/03/29 3.3 167.1 32 km NW of Fairview, Oklahoma110 2016/03/30 3.2 166.9 32 km NW of Fairview, Oklahoma111 2016/03/30 3.4 116.5 20 km SSE of Medford, Oklahoma112 2016/03/31 3.0 7.4 6 km NNE of Luther, Oklahoma113 2016/03/31 3.2 8.1 7 km NNE of Luther, Oklahoma114 2016/03/31 3.2 8.1 7 km NNE of Luther, Oklahoma115 2016/04/02 3.0 46.1 7 km NNE of Perkins, Oklahoma116 2016/04/02 3.1 18.1 8 km ENE of Edmond, Oklahoma117 2016/04/03 3.3 8.3 7 km NNE of Luther, Oklahoma118 2016/04/03 3.2 8.0 7 km NNE of Luther, Oklahoma119 2016/04/04 3.3 147.4 18 km E of Cherokee, Oklahoma120 2016/04/04 3.0 71.5 19 km N of Stillwater, Oklahoma121 2016/04/05 3.0 50.4 5 km SSE of Cushing, Oklahoma122 2016/04/06 3.4 70.5 26 km WSW of Perry, Oklahoma123 2016/04/07 3.3 2.1 2 km E of Luther, Oklahoma124 2016/04/07 3.1 2.2 2 km E of Luther, Oklahoma125 2016/04/07 3.6 1.8 2 km E of Luther, Oklahoma126 2016/04/07 3.7 122.7 16 km SSE of Helena, Oklahoma127 2016/04/07 3.3 70.8 26 km WSW of Perry, Oklahoma

55



128 2016/04/07 4.2 1.7 1 km E of Luther, Oklahoma129 2016/04/08 3.1 2.0 2 km E of Luther, Oklahoma130 2016/04/08 3.2 2.9 3 km E of Luther, Oklahoma131 2016/04/08 3.1 2.0 2 km E of Luther, Oklahoma132 2016/04/09 3.1 19.5 7 km N of Spencer, Oklahoma133 2016/04/09 3.0 149.5 25 km W of Medford, Oklahoma134 2016/04/09 3.4 144.8 11 km NNE of Medford, Oklahoma135 2016/04/10 3.4 187.6 22 km ENE of Mooreland, Oklahoma136 2016/04/11 3.5 150.0 21 km WSW of Helena, Oklahoma137 2016/04/12 3.5 75.8 20 km W of Perry, Oklahoma138 2016/04/12 3.3 116.5 20 km S of Medford, Oklahoma139 2016/04/13 3.5 141.2 14 km NNW of Blackwell, Oklahoma140 2016/04/14 3.0 66.7 11 km WNW of Yale, Oklahoma141 2016/04/15 3.1 173.9 32 km E of Mooreland, Oklahoma142 2016/04/17 3.2 120.2 18 km SE of Helena, Oklahoma143 2016/04/19 3.0 119.8 17 km S of Medford, Oklahoma144 2016/04/20 3.1 168.0 33 km NW of Fairview, Oklahoma145 2016/04/21 3.3 63.4 4 km SW of Yale, Oklahoma146 2016/04/21 3.0 93.2 15 km NNW of Pawnee, Oklahoma147 2016/04/21 3.3 166.2 30 km S of Alva, Oklahoma148 2016/04/23 3.0 69.1 17 km NE of Seminole, Oklahoma149 2016/04/23 3.4 70.9 26 km WSW of Perry, Oklahoma150 2016/04/26 3.0 161.4 27 km NW of Fairview, Oklahoma151 2016/04/26 3.4 167.0 33 km NW of Fairview, Oklahoma152 2016/04/26 3.6 17.5 7 km ENE of Harrah, Oklahoma153 2016/04/26 3.6 8.5 7 km NNE of Luther, Oklahoma154 2016/05/26 3.3 8.2 7 km NNE of Luther, Oklahoma155 2016/05/28 3.0 61.8 10 km NE of Stillwater, Oklahoma156 2016/05/29 3.5 48.5 15 km NNW of Langston, Oklahoma157 2016/05/31 3.3 3.3 3 km ESE of Luther, Oklahoma158 2016/06/01 3.2 138.3 13 km NW of Blackwell, Oklahoma159 2016/06/01 3.1 184.9 5 km NE of Anthony, Kansas160 2016/06/02 3.4 93.3 13 km E of Enid, Oklahoma161 2016/06/02 3.2 120.4 18 km SE of Helena, Oklahoma162 2016/06/04 3.2 76.3 25 km W of Perry, Oklahoma163 2016/06/04 3.1 187.2 24 km ENE of Mooreland, Oklahoma164 2016/06/05 3.4 184.8 5 km NE of Anthony, Kansas165 2016/06/06 3.3 12.1 1 km N of Jones, Oklahoma166 2016/06/06 3.2 93.2 13 km E of Enid, Oklahoma167 2016/06/06 3.3 89.1 14 km NW of Pawnee, Oklahoma168 2016/06/06 3.2 76.9 10 km SSE of Pawnee, Oklahoma169 2016/06/07 3.2 21.1 4 km ENE of Edmond, Oklahoma170 2016/06/08 3.9 91.6 13 km NNW of Pawnee, Oklahoma

56



171 2016/06/09 3.4 168.1 33 km NW of Fairview, Oklahoma172 2016/06/09 3.3 111.9 25 km SSE of Medford, Oklahoma173 2016/06/09 3.6 75.9 20 km W of Perry, Oklahoma174 2016/06/11 3.5 166.4 32 km NW of Fairview, Oklahoma175 2016/06/11 3.2 178.7 22 km SSW of Conway Springs, Kansas176 2016/06/12 3.1 22.7 10 km SSE of Langston, Oklahoma177 2016/06/12 3.0 22.5 10 km SSE of Langston, Oklahoma178 2016/06/13 3.2 168.4 33 km NW of Fairview, Oklahoma179 2016/06/14 3.0 63.2 7 km S of Perry, Oklahoma180 2016/06/15 3.3 182.2 10 km SSW of Alva, Oklahoma181 2016/06/15 3.1 63.1 7 km S of Perry, Oklahoma182 2016/06/16 3.0 93.1 14 km E of Enid, Oklahoma183 2016/06/17 3.1 19.8 6 km ENE of Edmond, Oklahoma184 2016/06/18 3.2 17.2 15 km S of Langston, Oklahoma185 2016/06/18 3.6 15.4 6 km NE of Harrah, Oklahoma186 2016/06/19 3.3 159.5 24 km SW of Cherokee, Oklahoma187 2016/06/19 3.0 136.7 9 km NNW of Blackwell, Oklahoma188 2016/06/20 3.4 167.5 33 km NW of Fairview, Oklahoma189 2016/06/21 3.3 167.5 33 km NW of Fairview, Oklahoma190 2016/06/21 3.5 149.7 19 km WSW of Helena, Oklahoma191 2016/06/23 3.0 187.1 23 km ENE of Mooreland, Oklahoma192 2016/06/25 3.3 70.6 26 km WSW of Perry, Oklahoma193 2016/06/25 3.4 192.5 15 km ENE of Mooreland, Oklahoma194 2016/06/25 3.1 154.0 4 km ESE of Caldwell, Kansas195 2016/06/26 3.4 209.2 17 km WNW of Harper, Kansas196 2016/06/26 3.0 64.8 16 km NNW of Crescent, Oklahoma197 2016/06/28 3.4 175.9 11 km S of Alva, Oklahoma198 2016/06/28 3.6 22.6 10 km SSE of Langston, Oklahoma199 2016/06/29 3.3 75.6 20 km W of Perry, Oklahoma200 2016/06/29 3.0 90.3 13 km ESE of Chickasha, Oklahoma201 2016/06/30 3.5 166.8 32 km NW of Fairview, Oklahoma202 2016/07/01 3.3 75.4 20 km W of Perry, Oklahoma203 2016/07/02 3.2 134.7 10 km E of Medford, Oklahoma204 2016/07/02 3.3 204.1 9 km N of Harper, Kansas205 2016/07/02 3.4 134.6 10 km E of Medford, Oklahoma206 2016/07/03 3.4 69.4 6 km NNW of Yale, Oklahoma207 2016/07/04 3.0 22.1 10 km SSE of Langston, Oklahoma208 2016/07/05 3.0 22.1 10 km S of Langston, Oklahoma209 2016/07/05 3.2 76.5 25 km W of Perry, Oklahoma210 2016/07/05 3.5 209.0 16 km WNW of Harper, Kansas211 2016/07/08 3.4 76.1 9 km SSE of Blanchard, Oklahoma212 2016/07/08 4.2 166.6 32 km NW of Fairview, Oklahoma213 2016/07/08 4.2 167.0 33 km NW of Fairview, Oklahoma

57



214 2016/07/08 3.1 167.4 33 km NW of Fairview, Oklahoma215 2016/07/09 4.4 167.3 33 km NW of Fairview, Oklahoma216 2016/07/09 3.0 80.1 20 km WNW of Perry, Oklahoma217 2016/07/09 3.6 35.9 6 km NE of Langston, Oklahoma218 2016/07/09 3.0 184.2 10 km SW of Alva, Oklahoma219 2016/07/09 3.4 166.5 32 km NW of Fairview, Oklahoma220 2016/07/09 3.1 17.2 15 km S of Langston, Oklahoma221 2016/07/11 3.1 35.7 7 km ENE of Langston, Oklahoma222 2016/07/13 3.0 165.7 29 km S of Alva, Oklahoma223 2016/07/13 3.2 149.0 11 km SE of Cherokee, Oklahoma224 2016/07/14 3.4 24.7 3 km WSW of Nicoma Park, Oklahoma225 2016/07/15 3.0 87.8 19 km ESE of Enid, Oklahoma226 2016/07/16 3.1 32.0 7 km ENE of Guthrie, Oklahoma227 2016/07/17 4.2 75.6 20 km W of Perry, Oklahoma228 2016/07/17 3.1 75.6 19 km W of Perry, Oklahoma229 2016/07/18 3.2 50.4 10 km NE of Crescent, Oklahoma230 2016/07/19 3.4 134.9 10 km E of Medford, Oklahoma231 2016/07/19 3.2 75.9 20 km W of Perry, Oklahoma232 2016/07/21 3.6 78.2 19 km ENE of Perry, Oklahoma233 2016/07/22 3.1 130.2 16 km E of Medford, Oklahoma234 2016/07/22 3.4 159.7 24 km SW of Cherokee, Oklahoma235 2016/07/24 3.0 53.2 3 km WNW of Stillwater, Oklahoma236 2016/07/24 3.1 167.6 33 km NW of Fairview, Oklahoma237 2016/07/29 3.6 71.3 26 km WSW of Perry, Oklahoma238 2016/07/31 3.1 73.0 10 km SE of Blanchard, Oklahoma239 2016/08/05 3.4 167.0 32 km NW of Fairview, Oklahoma240 2016/08/05 3.0 146.1 25 km E of Cherokee, Oklahoma241 2016/08/05 3.2 143.3 22 km ESE of Cherokee, Oklahoma242 2016/08/07 3.3 149.4 21 km WSW of Helena, Oklahoma243 2016/08/07 3.0 61.4 16 km SW of Perry, Oklahoma244 2016/08/09 3.1 75.5 19 km W of Perry, Oklahoma245 2016/08/09 3.6 70.8 27 km WSW of Perry, Oklahoma246 2016/08/09 3.9 70.5 26 km WSW of Perry, Oklahoma247 2016/08/09 3.2 70.8 26 km WSW of Perry, Oklahoma248 2016/08/10 3.2 70.3 25 km WSW of Perry, Oklahoma249 2016/08/10 3.6 1.2 1 km E of Luther, Oklahoma250 2016/08/10 3.5 1.1 1 km E of Luther, Oklahoma251 2016/08/12 3.6 137.6 20 km NE of Helena, Oklahoma252 2016/08/14 3.5 134.6 9 km E of Medford, Oklahoma253 2016/08/15 3.1 85.9 15 km NNW of Perry, Oklahoma254 2016/08/15 3.0 128.6 12 km ESE of Medford, Oklahoma255 2016/08/16 3.3 3.5 3 km E of Luther, Oklahoma256 2016/08/16 3.1 95.3 20 km SSE of Tonkawa, Oklahoma

58



257 2016/08/17 3.3 130.9 3 km SE of Fairview, Oklahoma258 2016/08/17 4.0 10.4 10 km E of Luther, Oklahoma259 2016/08/19 3.5 219.3 7 km SSW of Cheney, Kansas260 2016/08/20 3.2 186.8 24 km ENE of Mooreland, Oklahoma261 2016/08/24 3.3 60.9 6 km SW of Yale, Oklahoma262 2016/08/27 3.6 93.1 14 km E of Enid, Oklahoma263 2016/08/29 3.6 71.1 27 km WSW of Perry, Oklahoma264 2016/08/29 3.0 70.8 26 km WSW of Perry, Oklahoma265 2016/08/30 3.1 35.8 5 km NE of Langston, Oklahoma266 2016/08/30 3.0 156.4 21 km NW of Medford, Oklahoma267 2016/08/30 3.1 119.9 17 km S of Medford, Oklahoma268 2016/08/31 3.3 114.9 14 km N of Enid, Oklahoma269 2016/09/01 3.1 158.5 6 km ENE of Caldwell, Kansas270 2016/09/01 3.2 157.0 26 km NNW of Fairview, Oklahoma271 2016/09/01 3.0 91.0 14 km NW of Pawnee, Oklahoma272 2016/09/03 3.4 140.4 6 km NNE of Medford, Oklahoma273 2016/09/03 3.4 3.6 4 km E of Luther, Oklahoma274 2016/09/03 5.8 88.7 14 km NW of Pawnee, Oklahoma275 2016/09/03 3.3 89.7 9 km NNW of Pawnee, Oklahoma276 2016/09/03 3.6 89.0 13 km NW of Pawnee, Oklahoma277 2016/09/03 3.3 89.4 9 km NNW of Pawnee, Oklahoma278 2016/09/03 3.4 89.2 11 km NW of Pawnee, Oklahoma279 2016/09/03 3.0 70.9 26 km WSW of Perry, Oklahoma280 2016/09/03 3.0 75.5 15 km W of Pawnee, Oklahoma281 2016/09/03 3.0 89.6 9 km NNW of Pawnee, Oklahoma282 2016/09/04 3.1 88.8 11 km NW of Pawnee, Oklahoma283 2016/09/04 3.2 56.6 6 km N of Cushing, Oklahoma284 2016/09/04 3.2 76.5 14 km W of Pawnee, Oklahoma285 2016/09/04 3.0 88.4 11 km NW of Pawnee, Oklahoma286 2016/09/04 3.0 89.4 14 km NW of Pawnee, Oklahoma287 2016/09/04 3.1 56.4 6 km NNW of Cushing, Oklahoma288 2016/09/05 3.1 80.7 14 km WNW of Perry, Oklahoma289 2016/09/06 3.9 156.4 21 km NW of Medford, Oklahoma290 2016/09/06 3.7 155.9 22 km NW of Medford, Oklahoma291 2016/09/06 3.5 156.1 21 km NW of Medford, Oklahoma292 2016/09/07 3.1 90.0 14 km NW of Pawnee, Oklahoma293 2016/09/07 3.3 156.6 21 km NW of Medford, Oklahoma294 2016/09/08 3.3 75.6 19 km W of Perry, Oklahoma295 2016/09/08 3.2 58.4 5 km N of Stillwater, Oklahoma296 2016/09/08 3.1 58.4 5 km N of Stillwater, Oklahoma297 2016/09/09 3.0 82.7 11 km N of Perry, Oklahoma298 2016/09/09 3.5 24.2 1 km WSW of Spencer, Oklahoma299 2016/09/09 3.7 76.1 14 km W of Pawnee, Oklahoma

59



300 2016/09/09 3.0 160.3 4 km SW of Cherokee, Oklahoma301 2016/09/09 3.1 63.3 4 km WSW of Yale, Oklahoma302 2016/09/10 3.2 25.7 13 km SW of Perkins, Oklahoma303 2016/09/12 3.0 88.8 8 km NNW of Pawnee, Oklahoma304 2016/09/12 3.0 89.9 14 km NW of Pawnee, Oklahoma305 2016/09/13 3.3 130.9 3 km SE of Fairview, Oklahoma306 2016/09/13 3.7 130.9 3 km SE of Fairview, Oklahoma307 2016/09/13 3.0 137.0 8 km WSW of Medford, Oklahoma308 2016/09/13 3.3 206.1 10 km NW of Harper, Kansas309 2016/09/13 3.3 137.2 8 km WSW of Medford, Oklahoma310 2016/09/14 3.7 167.5 32 km NW of Fairview, Oklahoma311 2016/09/14 3.2 19.2 7 km ENE of Edmond, Oklahoma312 2016/09/16 3.0 175.6 9 km ESE of Alva, Oklahoma313 2016/09/16 3.9 167.1 32 km NW of Fairview, Oklahoma314 2016/09/17 3.5 170.0 12 km N of Cherokee, Oklahoma315 2016/09/17 3.0 126.2 11 km S of Medford, Oklahoma316 2016/09/18 3.2 75.2 20 km W of Perry, Oklahoma317 2016/09/20 3.9 156.1 21 km NW of Medford, Oklahoma318 2016/09/20 3.1 155.8 20 km NW of Medford, Oklahoma319 2016/09/21 3.2 22.3 10 km S of Langston, Oklahoma320 2016/09/23 3.0 88.7 12 km NW of Pawnee, Oklahoma321 2016/09/24 3.3 36.1 6 km NE of Langston, Oklahoma322 2016/09/26 3.4 53.5 20 km NE of Crescent, Oklahoma323 2016/09/26 3.8 161.5 10 km NE of Cherokee, Oklahoma324 2016/09/27 3.0 95.0 19 km SSE of Tonkawa, Oklahoma325 2016/09/29 3.1 83.2 12 km WNW of Pawnee, Oklahoma326 2016/09/29 3.1 129.6 6 km E of Fairview, Oklahoma327 2016/09/30 3.3 193.2 14 km ENE of Mooreland, Oklahoma328 2016/10/02 3.2 70.7 26 km WSW of Perry, Oklahoma329 2016/10/04 3.7 88.7 15 km NW of Pawnee, Oklahoma330 2016/10/04 3.3 51.5 12 km N of Stroud, Oklahoma331 2016/10/05 3.3 167.7 33 km NW of Fairview, Oklahoma332 2016/10/05 3.0 51.5 12 km N of Stroud, Oklahoma333 2016/10/05 3.2 168.1 33 km NW of Fairview, Oklahoma334 2016/10/06 3.4 88.4 13 km NW of Pawnee, Oklahoma335 2016/10/06 3.6 133.3 16 km E of Medford, Oklahoma336 2016/10/08 3.3 167.5 33 km NW of Fairview, Oklahoma337 2016/10/09 3.5 88.8 11 km NW of Pawnee, Oklahoma338 2016/10/09 3.0 193.5 14 km ENE of Mooreland, Oklahoma339 2016/10/10 3.0 167.9 33 km NW of Fairview, Oklahoma340 2016/10/10 3.2 90.5 14 km NW of Pawnee, Oklahoma341 2016/10/10 3.0 120.4 18 km SE of Helena, Oklahoma342 2016/10/13 3.3 162.6 4 km NNE of Cherokee, Oklahoma

60



343 2016/10/14 3.2 193.8 14 km ENE of Mooreland, Oklahoma344 2016/10/15 3.1 92.7 14 km E of Enid, Oklahoma345 2016/10/17 3.0 51.7 13 km N of Stroud, Oklahoma346 2016/10/18 3.0 18.9 7 km E of Edmond, Oklahoma347 2016/10/19 3.0 89.1 10 km NW of Pawnee, Oklahoma348 2016/10/19 3.1 133.6 5 km SSW of Medford, Oklahoma349 2016/10/20 3.4 147.2 11 km SSW of Caldwell, Kansas350 2016/10/20 3.0 26.7 6 km SE of Guthrie, Oklahoma351 2016/10/21 3.8 134.6 9 km SSW of Helena, Oklahoma352 2016/10/21 4.0 167.8 33 km NW of Fairview, Oklahoma353 2016/10/21 3.4 167.8 33 km NW of Fairview, Oklahoma354 2016/10/21 3.0 167.9 33 km NW of Fairview, Oklahoma355 2016/10/21 3.2 168.1 33 km NW of Fairview, Oklahoma356 2016/10/24 3.3 132.9 16 km E of Medford, Oklahoma357 2016/10/24 3.5 176.2 18 km E of Anthony, Kansas358 2016/10/26 3.5 80.7 21 km WNW of Perry, Oklahoma359 2016/10/27 3.6 3.2 3 km E of Luther, Oklahoma360 2016/10/28 3.0 145.2 26 km E of Cherokee, Oklahoma361 2016/10/28 3.1 91.1 13 km NW of Pawnee, Oklahoma362 2016/10/29 3.3 87.2 10 km NW of Pawnee, Oklahoma363 2016/10/29 3.1 103.2 13 km SSW of Tonkawa, Oklahoma364 2016/10/29 3.2 103.2 13 km SSW of Tonkawa, Oklahoma365 2016/10/30 3.4 74.2 21 km N of Stillwater, Oklahoma366 2016/10/30 3.3 66.2 7 km SE of Perry, Oklahoma367 2016/10/31 3.0 90.0 14 km NW of Pawnee, Oklahoma368 2016/10/31 3.4 75.6 19 km W of Perry, Oklahoma369 2016/11/02 3.1 85.5 16 km WNW of El Reno, Oklahoma370 2016/11/02 3.3 85.3 15 km WNW of El Reno, Oklahoma371 2016/11/02 3.0 69.0 22 km ENE of Hennessey, Oklahoma372 2016/11/02 4.4 86.3 12 km ESE of Pawnee, Oklahoma373 2016/11/02 3.1 85.4 12 km ESE of Pawnee, Oklahoma374 2016/11/04 3.3 69.3 21 km ENE of Hennessey, Oklahoma375 2016/11/05 3.3 85.9 12 km ESE of Pawnee, Oklahoma376 2016/11/06 3.4 66.1 7 km SE of Perry, Oklahoma377 2016/11/06 3.0 79.7 21 km ENE of Perry, Oklahoma378 2016/11/07 5.0 51.2 3 km W of Cushing, Oklahoma379 2016/11/07 3.0 54.6 2 km N of Cushing, Oklahoma380 2016/11/07 4.1 167.2 32 km NW of Fairview, Oklahoma381 2016/11/07 3.0 20.5 1 km ENE of Nicoma Park, Oklahoma382 2016/11/07 3.3 167.2 33 km NW of Fairview, Oklahoma383 2016/11/08 3.3 85.7 15 km NNW of Perry, Oklahoma384 2016/11/09 3.7 156.5 21 km NW of Medford, Oklahoma385 2016/11/11 3.1 50.4 3 km W of Cushing, Oklahoma

61



386 2016/11/11 3.4 86.4 17 km WNW of El Reno, Oklahoma387 2016/11/11 3.3 156.5 20 km NW of Medford, Oklahoma388 2016/11/11 3.3 11.5 11 km ENE of Luther, Oklahoma389 2016/11/12 3.3 50.8 3 km W of Cushing, Oklahoma390 2016/11/14 3.3 85.8 12 km ESE of Pawnee, Oklahoma391 2016/11/15 3.0 84.2 11 km ESE of Pawnee, Oklahoma392 2016/11/19 3.0 167.8 33 km NW of Fairview, Oklahoma393 2016/11/22 3.5 54.6 2 km N of Cushing, Oklahoma394 2016/11/22 3.0 144.0 9 km WNW of Medford, Oklahoma395 2016/11/24 3.5 64.9 12 km NNE of Stillwater, Oklahoma396 2016/11/24 3.6 51.7 2 km WNW of Cushing, Oklahoma397 2016/11/25 4.0 141.2 4 km NNW of Medford, Oklahoma398 2016/11/27 3.6 128.6 12 km ESE of Medford, Oklahoma399 2016/12/05 3.8 86.8 13 km ESE of Pawnee, Oklahoma400 2016/12/05 3.2 57.1 4 km NNE of Cushing, Oklahoma401 2016/12/05 3.3 71.4 16 km WSW of Perry, Oklahoma402 2016/12/06 3.2 67.9 0 km NNW of Yale, Oklahoma403 2016/12/10 3.4 99.5 6 km SSW of Enid, Oklahoma404 2016/12/10 3.2 187.8 23 km ENE of Mooreland, Oklahoma405 2016/12/11 3.2 75.4 19 km W of Perry, Oklahoma406 2016/12/12 3.2 167.8 33 km NW of Fairview, Oklahoma407 2016/12/14 3.2 122.9 15 km S of Medford, Oklahoma408 2016/12/16 3.1 91.2 8 km NE of Pawnee, Oklahoma409 2016/12/18 3.3 83.1 12 km NNW of Perry, Oklahoma410 2016/12/18 3.7 18.8 7 km ENE of Edmond, Oklahoma411 2016/12/18 3.0 86.3 12 km ESE of Pawnee, Oklahoma412 2016/12/19 3.1 187.3 24 km ENE of Mooreland, Oklahoma413 2016/12/20 3.5 167.9 33 km NW of Fairview, Oklahoma414 2016/12/20 3.1 145.8 7 km N of Coalgate, Oklahoma415 2016/12/20 3.2 68.8 9 km NW of Yale, Oklahoma416 2016/12/22 3.3 19.1 7 km ENE of Edmond, Oklahoma417 2016/12/23 3.4 187.3 23 km ENE of Mooreland, Oklahoma418 2016/12/23 3.4 187.2 23 km ENE of Mooreland, Oklahoma419 2016/12/24 3.0 187.3 23 km ENE of Mooreland, Oklahoma420 2016/12/24 3.6 87.0 10 km NW of Pawnee, Oklahoma421 2016/12/28 3.4 167.6 33 km NW of Fairview, Oklahoma422 2016/12/29 3.0 18.8 7 km ENE of Edmond, Oklahoma423 2016/12/29 3.2 18.7 7 km ENE of Edmond, Oklahoma424 2016/12/30 3.1 69.3 5 km WSW of Perry, Oklahoma

62

B Tabulated Cycle CountsTables B.1 and B.2 give the displacement cycle counts for seismic stations OK.U32A andGS.OK005, respectively, in 2016 for both the EW and NS directions. The counts nk (k =

1, 2, ..., 20) are for cycle ranges Dk = k × ∆D where ∆D is the bin width. Moreover, the counts nk

(k = 1, 2, ..., 20) presented in Tables B.1 and B.2 also apply for pseudo-acceleration cycle rangesAk = k × ∆A where the pseudo-acceleration bin width ∆A = (2π/T )2 × ∆D.

The cycle counts nk in Tables B.1 and B.2 are presented separately for the EW and NS direc-tions. The SRSS cycle counts nk,SRSS are readily found as follows:

nk,SRSS =

√n2

k,EW + n2k,NS (B.0.1)

where nk,EW and nk,NS are the tabulated counts in the EW and NS directions, respectively.

63

Tabl

eB

.1:D

ispl

acem

entc

ycle

coun

tsfo

rsei

smic

stat

ion

OK

.U32

Ain

2016

.

T∆

DC

ycle

coun

tnk

atdi

spla

cem

entc

ycle

rang

eD

k=

k×

∆D

inE

Wdi

rect

ion

(s)

(mm

)n 1

n 2n 3

n 4n 5

n 6n 7

n 8n 9

n 10

n 11

n 12

n 13

n 14

n 15

n 16

n 17

n 18

n 19

n 20

0.1

0.01

877

1027

.514

9338

015

785

2914

.520

8.5

55

20.

50.

51

0.5

10.

50

0.5

0.2

0.04

748

2483

.559

9.5

175

60.5

44.5

23.5

97

1.5

12

0.5

2.5

0.5

11.

52

00.

51

0.3

0.05

140

9149

.555

6.5

136.

568

53.5

31.5

2311

.512

.54.

54.

52

20.

53

2.5

0.5

1.5

0.5

10.

40.

102

4030

1522

8.5

6133

.517

.59.

57.

55.

52

0.5

3.5

0.5

2.5

0.5

0.5

00

01

0.5

0.5

0.12

939

6843

209

7132

179.

54

32

23

32

0.5

0.5

02

0.5

0.5

0.5

0.6

0.14

640

7494

177

6125

.513

.57

25

0.5

20

0.5

00

10

0.5

0.5

00

0.7

0.18

240

2302

.514

2.5

4921

.57.

54

12

1.5

01

1.5

1.5

0.5

00

00

00

0.8

0.15

839

5300

.516

172

.546

.521

83

2.5

3.5

12.

53

10

11

0.5

0.5

00

0.9

0.15

641

2375

142

86.5

34.5

14.5

107

22

4.5

10.

50.

50

1.5

1.5

00

00

10.

210

4252

92.5

117.

559

27.5

13.5

4.5

11

1.5

21.

52.

52.

52

1.5

00

00

02

0.54

044

2738

4313

7.5

41.

52

10.

50.

50.

50.

51

00

00

00

03

0.49

040

4837

20.5

6.5

7.5

23

43.

54

00

00

00

00

00

04

0.76

036

7180

.517

7.5

41.

51

11.

50

00

00

00

00

00

05

0.88

034

2472

12.5

7.5

21

1.5

00

00

00

00

00

00

00

60.

790

3519

9011

3.5

2.5

11

00

00

00

00

00

00

00

70.

740

3625

5212

.55

21

00

00

00

00

00

00

00

08

0.69

038

0673

106

20.

50

00

00

00

00

00

00

00

90.

640

4053

21.5

142.

54

10

00

00

00

00

00

00

00

100.

560

4267

5414

25.

51

0.5

00

00

00

00

00

00

00

64

Tabl

eB

.1(c

ont.)

:Dis

plac

emen

tcyc

leco

unts

fors

eism

icst

atio

nO

K.U

32A

in20

16.

T∆

DC

ycle

coun

tnk

atdi

spla

cem

entc

ycle

rang

eD

k=

k×

∆D

inN

Sdi

rect

ion

(s)

(mm

)n 1

n 2n 3

n 4n 5

n 6n 7

n 8n 9

n 10

n 11

n 12

n 13

n 14

n 15

n 16

n 17

n 18

n 19

n 20

0.1

0.01

879

8590

.513

6143

5.5

161

8028

20.5

75.

53.

53.

52.

53

41.

50

0.5

1.5

01

0.2

0.04

746

8637

.565

0.5

151.

558

3813

116.

57

3.5

12.

51.

51.

50.

50.

50.

50

00

0.3

0.05

139

8689

573

155.

569

.546

2015

.59.

58

74.

51.

52

1.5

21

0.5

00

00.

40.

102

3893

8519

869

.538

.514

.510

67

44

2.5

1.5

1.5

21.

50

00

00

0.5

0.12

939

9027

157.

552

2817

103.

54

1.5

50.

50.

50.

51

00

00

00

0.6

0.14

639

3887

.517

749

.522

.515

66

4.5

22

1.5

23

11.

51.

50.

50.

50.

50.

50.

70.

182

3677

1317

957

3515

6.5

66

32.

53.

53.

53.

52.

51.

53.

51

2.5

1.5

1.5

0.8

0.15

836

4935

.520

580

.531

.514

.512

6.5

54.

52

62.

52.

52.

50.

50.

52.

53

22.

50.

90.

156

3821

68.5

205.

575

.528

.516

.58

7.5

4.5

1.5

40.

50

12

31

11.

50.

50.

51

0.21

040

2197

117.

546

14.5

145

4.5

20.

51

1.5

10.

51.

50

10.

50

00.

52

0.54

042

0303

328

5.5

53

1.5

00.

50

21.

50

0.5

00.

50.

50

01

30.

490

3806

3120

.59

48

6.5

2.5

0.5

3.5

11.

53

20

00.

50

10.

51

40.

760

3355

6713

.59

45

33

0.5

20

0.5

10

0.5

01

00.

50.

51.

55

0.88

031

5378

13.5

6.5

53

1.5

1.5

30

0.5

01

00

01

00.

50.

51

60.

790

3294

29.5

14.5

6.5

4.5

1.5

31

1.5

1.5

0.5

00

10

00

0.5

0.5

01

70.

740

3408

5215

65

0.5

0.5

30.

52

00

01

00

00

10

0.5

80.

690

3585

4112

55

1.5

01.

51

10

0.5

01.

50

00.

50

00.

50.

59

0.64

038

4001

.512

6.5

32

11

0.5

01

0.5

00.

50.

50.

50

00.

50

0.5

100.

560

4038

619.

57.

52

21.

50

10.

50.

50

0.5

10.

50

0.5

00

01

65

Tabl

eB

.2:D

ispl

acem

entc

ycle

coun

tsfo

rsei

smic

stat

ion

GS.

OK

005

in20

16.

T∆

DC

ycle

coun

tnk

atdi

spla

cem

entc

ycle

rang

eD

k=

k×

∆D

inE

Wdi

rect

ion

(s)

(mm

)n 1

n 2n 3

n 4n 5

n 6n 7

n 8n 9

n 10

n 11

n 12

n 13

n 14

n 15

n 16

n 17

n 18

n 19

n 20

0.1

0.05

157

0603

215

5438

2111

94

4.5

41.

53.

51

21

10.

50.

50

00.

20.

148

3170

30.5

146.

532

217

06

2.5

1.5

0.5

00.

50

0.5

00

01

11

0.3

0.41

024

5474

.538

114.

54

1.5

12

00.

50.

50

0.5

0.5

1.5

01

00

0.5

0.4

0.80

020

5814

.514

.53.

54

0.5

33

1.5

0.5

10.

51

11

00

0.5

00

10.

50.

930

1767

19.5

144

2.5

2.5

01

11.

50.

50.

51.

50

0.5

10

1.5

00

10.

61.

1515

8010

.521

.58

0.5

02

0.5

11.

50.

51

10.

50.

50.

50

0.5

0.5

0.5

0.5

0.7

1.16

1472

3226

9.5

12.

51.

50

0.5

00.

50.

50

01.

50

0.5

10

0.5

1.5

0.8

1.00

1364

7929

72

1.5

12.

52.

50.

52

1.5

1.5

1.5

00.

50

0.5

00

10.

91.

1312

7232

30.5

9.5

12.

52

0.5

0.5

1.5

12

00.

50

11

11

11

11.

2412

0729

.529

.56

82.

54

0.5

0.5

01.

50

0.5

10

01.

51

00

12

1.90

7667

511

6.5

5.5

01.

50

0.5

0.5

10

00

0.5

0.5

00

01

0.5

31.

6456

806.

57

3.5

3.5

12

1.5

1.5

31

0.5

0.5

0.5

0.5

0.5

00.

51

0.5

1.5

42.

8044

894.

57

1.5

31

1.5

20

10

0.5

00.

50.

50

01

00.

51

52.

6038

444.

57

3.5

1.5

10

11.

50

0.5

00.

50.

50

00

10

01

62.

3034

348

52.

52.

50.

50

10.

50.

50

1.5

00

01

00

00.

50.

57

1.89

3093

0.5

8.5

2.5

1.5

10.

50

10

01.

50

0.5

00

0.5

00

0.5

0.5

81.

6427

967

8.5

41.

51.

51

0.5

0.5

00

01

00.

50

0.5

00.

50

0.5

91.

4324

925.

512

.54

31.

51.

50.

50.

50

0.5

00

0.5

00

10

00.

50.

510

1.42

2357

119

.53.

51.

51

1.5

1.5

00.

50

01

00

00.

50.

50

00.

5

66

Tabl

eB

.2(c

ont.)

:Dis

plac

emen

tcyc

leco

unts

fors

eism

icst

atio

nG

S.O

K00

5in

2016

.

T∆

DC

ycle

coun

tnk

atdi

spla

cem

entc

ycle

rang

eD

k=

k×

∆D

inN

Sdi

rect

ion

(s)

(mm

)n 1

n 2n 3

n 4n 5

n 6n 7

n 8n 9

n 10

n 11

n 12

n 13

n 14

n 15

n 16

n 17

n 18

n 19

n 20

0.1

0.05

156

0216

191.

558

25.5

145

5.5

31

20

11.

50

0.5

10

10

20.

20.

148

3066

6617

749

.522

.58.

58.

54

2.5

00

00

00

00

00

00

0.3

0.41

023

4464

64.5

146

1.5

1.5

20

00

00

00

00

00

00

0.4

0.80

019

1527

.540

62

10

00

00

00

00

00

00

00

0.5

0.93

016

2224

25.5

65.

55.

51

00

00

00

00

00

00

00

0.6

1.15

1456

99.5

39.5

43

11

00

00

00

00

00

00

00

0.7

1.16

1331

2222

.512

.52.

51.

50.

51

00

00

00

00

00

00

00.

81.

0012

1825

4011

.56

41

0.5

00

00

00

00

00

00

00.

91.

1311

2542

319

3.5

21.

51

00

00

00

00

00

00

01

1.24

1068

1627

9.5

31.

51

00

00

00

00

00

00

00

21.

9066

240

13.5

3.5

30

00

00

00

00

00

00

00

03

1.64

4898

612

.58

22.

52

00

00

00

00

00

00

00

42.

8038

429

7.5

21

20.

50

00

00

00

00

00

00

05

2.60

3270

6.5

51

1.5

1.5

00

00

00

00

00

00

00

06

2.30

2763

64.

52

1.5

10

00

00

00

00

00

00

00

71.

8924

933

6.5

2.5

0.5

10

00

00

00

00

00

00

00

81.

6422

764

211

1.5

0.5

0.5

00

00

00

00

00

00

00

91.

4320

466.

588

.53

11.

50

00

00

00

00

00

00

00

101.

4218

357.

518

29.

52

0.5

0.5

00

00

00

00

00

00

00

67

C Oklahoma Bridge Inventory AnalysisTo select the Oklahoma bridge that was modeled in this study, it was important to have a de-tailed understanding of the state’s bridge inventory. The Oklahoma Department of Transporta-tion (ODOT) provided data for 6815 bridges owned and maintained by the state on the ODOT-designated highway system, referred to as “on-system” bridges, which will serve as the inventoryfor this study. Note that “off-system” bridges (i.e., bridges owned and maintained by a county, city,or other local or regional governmental unit, and not on the ODOT-designated highway system)were not included.

C.1 Structure Type Statistics

For analyzing the bridge inventory, it is convenient to focus on typical structure types. This willmake the amount of data and time to process it more manageable. To proceed systematicallyand in an organized way, it is essential to identify different structure types and the characteristicsspecific to each structure type. Based on the National Bridge Inventory (NBI) database (FHWA,1995), each structure type is organized by design type and material type (NBI Item 43). TableC.1 presents the bridge distribution by design type. Culvert bridges constitute over 44% of theinventory, and, because culvert bridges are assumed to represent a different type of system, theyare not taken into account in this study. Girder bridges are the dominant design type with 44% ofthe inventory. The remaining bridge design types represent less than 12% of the inventory and willnot be considered further in this study because they are not characteristic of a typical Oklahomabridge.

Next, the girder bridges were categorized based on kind of material (NBI segment 43A). TableC.2 lists the defined material types, as well as the proportion of the 3002 girder bridges that fallinto the respective material types. The biggest percentage is concentrated in Prestressed Concrete

Table C.1: Design main span for all bridges in the inventory.

Design type Number Percentage (%)

Culvert 3042 44.63Girder 3002 44.05Slab 508 7.45Floorbeam 58 0.85Frame 48 0.70Box Beam – Multiple 45 0.66Tee Beam 29 0.43Arch – Deck 9 0.13Box Beam – Single 7 0.10Segmental 6 0.08Truss – Deck 2 0.02Other 1 0.01

Total 6815 100.00

68

Girder bridges (47%), followed by Steel Girder (28%) and Continuous Steel Girder bridges (22%).The remaining bridge structure types represented less than 3% of the girders bridges and will not beconsidered further in this study because they are not representative of a typical Oklahoma bridge.

After identifying the bridge structure types, the most typical values for number of spans, dimen-sions such as main span length and bridge length, as well as the year built were obtained. Thena condensed list of bridges for the bridge structure types was generated. In areas of the UnitedStates that are not seismically active, seismic design in bridges was mainly considered after the1990s. Because of this, the year that a bridge was constructed is an important indicator of the typeof bridge design and seismic considerations. Furthermore, the year shows how long the bridge hasbeen exposed to environmental or structural hazards, indicating the bridge deterioration over theyears.

The skew angle is a common bridge parameter, but it is not the focus of this study. Sullivan(2010) specified that higher skew angles lead to fragile bridge systems, while skew angles less than30 degrees do not alter the bridge susceptibility. The critical skew angle, below which skew doesnot play a critical role in fragility, was then considered to be 30 degrees. From the girder bridgeinventory data (3002 bridges), 39% of the bridges are skewed. Of these skewed bridges, 5.2% havevariable skew and only 33% have (constant) skew greater than 30 degrees. When skew angle issmall, it is more feasible to consider simplifying assumptions for modelling. Because the numberof bridges that have zero skew and that have skew angles less than 30 degrees is significant, skewangle will not be discussed in the following sections describing the selection of typical bridgeclasses but will be considered for the final selection.

C.2 Bridge Class

The following subsections focus on filtering bridge characteristics such as number of spans, mainspan length, bridge length (total length) and year built for each of the major structure types: Pre-stressed Concrete Girder bridges, Steel Girder bridges and Continuous Steel Girder bridges. Thebridge characteristics are characterized using histograms and key statistics (e.g., percentiles andmode).

Table C.2: Bridge classes by construction material.

Name Number Percentage (%)

Prestressed Concrete Girder 1423 47.40Steel Girder 849 28.28Continuous Steel Girder 660 21.99Concrete Girder 61 2.03Prestressed Continuous Concrete Girder 8 0.27Others 1 0.03

Total 3002 100.00

69

Figure C.1: Number of spans histogram for Prestressed Concrete Girder bridges.

Figure C.2: Main span length histogram for 3-Span Prestressed Concrete Girder bridges.

C.2.1 Prestressed Concrete Girder Bridges

Fig. C.1 shows the histogram for number of main spans for the Prestressed Concrete Girder bridges.Examination of the graph indicates that the majority of the bridges possess one to five spans.Single-span bridges constitute 14.8% of the inventory, and multi-span bridges constitute the re-maining 85.2% of the inventory. Moreover, it is observed that 48% of the bridges are representedby three spans. As such, this study focuses on 3-span Prestressed Concrete Girder bridges, here-inafter denoted 3SPC bridges.

Histograms for main span length and bridge length are presented in Figs. C.2 and C.3, respec-tively. The main span length and total length data are binned in 1.5 m (5 ft) and 4.5 m (15 ft)increments, respectively. Although the data shows variation, there are some trends to highlight forthe main span length and bridge length histograms.

For instance, the largest groupings of main span length are concentrated at 15.25 m (50 ft) and30.5 m (100 ft), while the predominant bridge lengths are concentrated at 45.72 m (150 ft) and91.44 m (300 ft). Upon closer inspection of the predominant main span lengths and bridge length,the bridge length is three times larger than the main span length, which for a 3-span bridge wouldindicate equal span lengths.

70

Figure C.3: Bridge length histogram for 3-Span Prestressed Concrete Girder bridges.

Figure C.4: Prestressed Concrete Girder Bridges: (left) Three dimensional representation of main span length andtotal length histograms. (right) Aerial view of relationship between main span length and total length. The black lineindicates a bridge length three times the main span length.

The relationship between main span length and the bridge length with the number of bridges isrepresented in Fig. C.4 (left). It is evident from Fig. C.4 (right) that the bridge length is commonlyequal to three times the main span length, as indicated by the black line. Because the majorityof the bridges falls on the black line, 3SPC bridges with a total length three times the main spanlength will be considered candidates for the modeling portion of this study. In particular, we willconsider 3SPC bridges with (a) 15-m main span length with 45-m total length and (b) 30-m mainspan length with 90-m total length, as these two combinations constitute roughly 18% of the 6903SPC bridges.

A histogram of the year built for 3SPC bridges is shown in Fig. C.5. Fig. C.5 shows thatthe 3SPC bridge construction is concentrated from the 1970s to the 2010s. In these five decades,the average is approximately 130 bridges, whereas the other decade have less than 10 bridges.This demonstrates that the use of 3SPC bridges in Oklahoma has been utilized widely over recentdecades.

71

Figure C.5: Year built histogram for 3-Span Prestressed Concrete Girder bridges.

Figure C.6: Number of spans histogram for Steel Girder bridges.

C.2.2 Steel Girder Bridges

The number of main spans for Steel Girder bridges is shown in Fig. C.6. Inspection of the graphindicates that the majority of the bridges possess one to five spans. Single-span bridges consti-tute 12% of the inventory, and multi-span bridges constitute the remaining 88% of the inventory.Moreover, it is observed that 56% of the bridges are represented by three spans. As such, this studyfocuses on 3-span Steel Girder bridges, hereinafter denoted 3SS bridges.

Figs. C.7 and C.8 display histograms of the main span length and bridge length, respectively.The main span length and total length data are binned in 1.5 m (5 ft) and 4.5 m (15 ft) increments,respectively. Although the data shows variation, there are some trends to highlight for the mainspan length and bridge length histograms.

For example, the largest groupings of main span length are concentrated at 12.2 m (40 ft) and15.25 m (50 ft), while the predominant bridge lengths are concentrated at 36.58 m (120 ft) and45.72 m (150 ft). Upon closer inspection of the predominant main span lengths and bridge lengths,the bridge lengths are three times larger than the main span length, which for a 3-span bridge wouldindicate equal span lengths.

The relationship between main span length and the bridge length with the number of bridges isrepresented in Fig. C.9 (left). It is evident from Fig. C.9 (right) that the bridge length is commonly

72

Figure C.7: Main span length histogram for 3-Span Steel Girder bridges.

Figure C.8: Bridge length histogram for 3-Span Steel Girder bridges.

equal to three times the main span length, as indicated by the black line. Because the majority ofthe bridges falls on the black line, 3SS bridges with a total length three times the main span lengthwill be considered candidates for the modeling portion of this study. In particular, we will consider3SS bridges with (a) 12-m main span length with 36-m total length and (b) 15-m main span lengthwith 45-m total length, as these two combinations constitute nearly 20% of the 481 3SS bridges.

Fig. C.10 represents a histogram of the year built for 3SS bridges. 3SS bridge construction isconcentrated between the 1930s and 1980s. In these six decades, the average looks to be around90 bridges, whereas the other decades have less than 10 bridges. The number of bridges increasesdramatically from the 1930s to 1940s, which marks the beginning of using 3SS bridges in highwaysystems. The histogram possesses noticeable peaks around 1940s and 1970s. However, the graphshows that the use of 3SS Girder bridges in Oklahoma has substantially decreased over the lastthree decades.

C.2.3 Continuous Steel Girder Bridges

The number of main spans for Continuous Steel Girder bridges is shown in Fig. C.11. Assessmentof the graph reveals that the majority of the bridges possess two to eight spans. Single-span bridgesconstitute 0.3% of the inventory, and multi-span bridges constitute the remaining 99.7% of theinventory. Moreover, it is observed that 40% of the bridges are represented by 3-spans, while twospans represent 30.6%. As such, this study focuses on 3-span Continuous Steel Girder bridges,hereinafter denoted 3SCS bridges.

73

Figure C.9: Steel Girder Bridges: (left) Three dimensional representation of main span length and total length his-tograms. (right) Aerial view of relationship between main span length and total length. The black line indicates abridge length three times the main span length.

Figure C.10: Year built histogram for 3-Span Steel Girder bridges.

Figure C.11: Number of spans histogram for Continuous Steel Girder bridges.

Histograms for main span length and bridge length are showed in Figs. C.12 and C.13, respec-tively. As the same for the previous two bridge structure types, the main span length and total

74

Figure C.12: Span length histogram for 3-Span Continuous Steel Girder bridges.

Figure C.13: Bridge length histogram for 3-Span Continuous Steel Girder bridges.

length data are binned in 1.5 m (5 ft) and 4.5 m (15 ft) increments, respectively. Although themain-span and bridge-length data display variation, there are still some trends to point out. Forexample, main span length is concentrated at 24.4 m (80 ft), while the predominant bridge lengthis concentrated at 64.0 m (210 ft). Upon closer inspection of the predominant main span lengthsand bridge lengths, the bridge lengths are three times larger than the main span length, which for a3-span bridge would indicate equal span lengths.

The correlation between main span length and the bridge length with the number of bridgesis represented in Fig. C.14 (left). It is evident from Fig. C.14 (right) that the bridge length iscommonly equal to three times the main span length, as indicated by the black line. 3SCS bridgeswith a total length three times the main span length will be considered candidates for the modellingportion of this study. In particular, we will consider 3SCS bridges with 24-m main span length with64-m total length, as this combination constitutes roughly 14% of the 274 3SCS bridges.

Fig. C.15 shows a histogram of the year built for 3SCC bridges. 3SCS bridge constructionis concentrated between the 1960s and 1980s. In these three decades, the average is around 200bridges, whereas other decades have less than 50 bridges. For this bridge structure type, the shapeof the histogram increases promptly from the 1960s to 1970s and then decreases in the 1980s. Thegraph shows that the employment of 3SCS Girder bridges in Oklahoma has substantially decreasedover the last three decades.

75

Figure C.14: Continue Steel Girder Bridges: (left) Three dimensional representation of main span length and totallength histograms. (right) Aerial view of relationship between main span length and total length. The black lineindicates a bridge length three times the main span length.

Figure C.15: Year Built histogram for 3-Span Continuous Steel Girder bridges

C.3 Summary

After establishing the different series for main span length, bridge length and year built for eachbridge structure type, three major bridge classes were found: 3-Span Prestressed Concrete Girderbridges, 3-Span Steel Girder bridges and 3-Span Continuous Steel Girder bridges. The precedingbridge inventory analysis presented key statistics on main structure type, skew, number of spans,and lengths of spans, establishing 3-span girder bridges to be predominant. Of the 3-span girderbridges, Prestressed Concrete was the most represented material in the state of Oklahoma. There-fore, 3-span Prestressed Concrete Girder bridges represent the most typical Oklahoma bridge. TheState Highway 99 (SH-99) bridge over Tiger Creek was selected for this study because it is repre-sentative of the most typical bridge class (3SPC Girder bridge) and complete plans were available.The mathematical modeling is described in Kaid Bay Cortez (2016) and Harvey et al. (2018b).

76

Date post:	27-Jul-2020
Category:	Documents
Upload:	others
View:	4 times
Download:	0 times

Technical Report Documentation Page Rapid Retrofitting ... · 18/01/2020 · the cumulative damage...

Documents