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User Manual - PEER - University of California, Berkeley

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1. Column below Grade Diameter Youngs Modulus 30000000 Deck Deck Length Deck Width Deck Depth Deck Properties fao m fi 1 9 m fi 83 m Shamsabadi s HFD Model 0 0254 m Longitudinal Gap Skew Angle 1 83 m Wall Height Deck Depth C Clay C User Defined Max Displacement ymax 0 091 5 m K50 Ultimate Pressure Fult 263 34 kPa Re Calculated Constants C amp D 54521 967212 10220776152 Calculated Curve Constants Constant C Constant D fo degree View Parameters for HFD Model 28700 kN m m Fa Embankment Embankment Length 25 m 0 5 m 30000 kN Depth of Embankment Foundation Total Weight of Embankment Activate Abutment Pile Abutment Pile Pile Length m Diameter F Pioperies Sane Step 1 select HFD Abutment Abutment Model Number of Bearings Bearing Height Number of Shear Keys Fan eee SANDY SOIL 14D Yax 0 0511 a s C Keg t i Ym COHESIVE SOIL G al Ke a Ymax O LOH x s ki i ull 2 rR O Ysp ylin Fivaz Shamsabadi et al 2007 PRACTICAL ABUTMENT MODEL 5 5ksf ui five Par min OO kaf Foree Kips a 5500k in fi Kou 25 0k int fi ylin Cancel b Fig 33 Steps to define a HFD abutment model a choosing HFD model at the bridge model window b HFD model window 33 Analysis Options Unit System Soil Mate
2. Fig 100 Total repair time CWD Crew Working Day as a function of intensity 95 MM PREE Analysis Output a Ed Pas Contribution to expected repair time CWD from each repair quantity File RTsens _E txt Jf ereere Fig 101 Contribution to expected repair time CWD from each repair quantity 7 2 2 Hazard Curves Based on the local site Seismic Hazard specified losses are estimated and displayed graphically as e The defined local site hazard curve as a mean annual frequency v of exceedance ground motion Fig 102 e Return period against total repair cost ratio Fig 103 e Mean annual frequency MAF of exceedance loss against total repair cost ratio RCR Fig 104 e Return period against total repair time RT Fig 105 e Mean annual frequency MAF of exceedance loss against total repair time Fig 106 The median ground motion hazard curve is assumed to have a power law form with two unknown parameters k ko in Eq 4 in the range of the ground motion intensities bracketed by the 2 and 10 probability of exceedance IM values im The two parameter fit linear in log 96 space to the nonlinear in log space hazard curve tends to overpredict frequencies of exceedance for IM extremes both above and below the range of intensities considered Therefore care should be taken when extrapolating any resultant hazard curves to extremely low or high frequencies of exceedance Using a least squares fit in log spa
3. 4 Temporary support abutment 5 Structural concrete bridge 6 Structural concrete footing 7 Structural concrete approach slab 8 Aggregate base approach slab 9 Bar reinforcing steel bridge 10 Bar reinforcing steel footing retaining wall 11 Epoxy inject cracks 12 Repair minor spalls 13 Column steel casing 14 Joint seal assembly 15 Elastomeric bearings 16 Drill and bond dowel 17 Furnish steel pipe pile 18 Drive steel pipe pile 19 Drive abutment pipe pile 20 Asphalt concrete 21 Mud jacking 22 Bridge removal column 23 Bridge removal portion 24 Approach slab removal 25 Clean deck for methacrylate 26 Furnish methacrylate 27 Treat bridge deck 28 Barrier rail 29 Re center column 6 5 3 Compute Hazard Curves The user is also able to specify a Seismic Hazard for a particular geographic location of this bridge system in terms of specified values for any IM e g derived from USGS seismicity maps The user interface provides default values for site hazard specific to a location in Northern California The hazard values are provided at each of the 2 5 and 10 probability of exceedance in 50 years only for PGA and PGV The user should input hazard values specific to the site being studied as well as the intensity measure selected for analysis If an IM other than PGA or PGV is selected the user interface will leave the three hazard level input boxes blank for user input as there are no readily available hazard ma
4. C Gro BRAE Model D Bridg Mes C MyDoc _PBEE CalTrans sim E B fR File Edit view X Convert P Select Bounda B C TitleText Beare XLabel Displacement m 7 YLabel Elevation m STEP 2 Marks dots 6 71000e 000 5 72234e 011 5 15890e 010 5 29000e 000 Fig 120 Cantilever beam simulation using BridgePBEE 2 Fixed end Beam with Point Load This is a case where the column base is fixed at rigid rock and there is zero rotation at the column top This case can be obtained by making the bridge deck very stiff and also applying the Roller abutment model The Fiber section with Elastic material is used to simulate the column In this case the equivalent flexural stiffness EI 3375450 kN m as reported by the user interface when Elastic properties are selected in Fig 10 Load P 40 kN half load 20 kN is used in the user interface Length L 13 42 m half length 6 71 m 1s used in the user interface The end displacement w PL 12EI 1 492 E 04 m BridgePBEE gives 1 496E 04 m Fig 121 114 OpenSeesPBEE FixedEndBeam pbe Sele File Execute Display Help Model Input x Gi Finite Element Mesh STEP 1 PEEK M ES Response profile of Displacement in Longitudinal direction Print Displacement Profile File pdispProf txt Kes I fo 52 C MyDoc _PBEE CalTrans sim fa File Edit View x Convert P Select TitleText ALabel Displacement Y
5. Moment of Inertia Transverse Axis RaO O m4 oe a Moment of Inertia Yertical Axis 53 3 m4 Column Fropertie Column below Grade Step 2 click Deck Properties Deck Deck Length Abutment Model Deck idth Number of bearings Deck Depth Bearing Height Step 3 define deck Z Deck Properties D Mumber of Shear h properties Step 1 define deck length width and depth Cancel Fig 16 Steps to define the deck geometrical configuration and material properties 17 Table 4 Default Values for Bridge Deck Parameter Value Deck length m 90 0 Deck width m 11 9 Deck depth m 1 83 Table 5 Default Values for Deck Material Properties Parameter Value Elastic modulus MPa 28 000 Shear modulus MPa 11 500 Cross section area m 5 72 Moment of inertia transverse axis m Moment of inertia vertical i 4 53 9 axis m Weight per unit length kN m 130 3 2 81 3 3 Embankment Parameters The geometric configuration of the embankments is shown in Fig 2 by the triangular shapes to the right and left of the bridge deck These geometric triangular configurations are simply represented by relatively rigid beam column elements This simple idealization of the embankment allows for Fig 7 representation of the distributed self weight of soil embankment if present and a depth of embankment abutment foundation into the soil mesh The user will specify the embankment length in the longitudinal bridge di
6. Right Abutment File abutForceDispRL txt Fig 45 Abutment response time histories 5 2 4 Deformed Mesh 7 Deformed Mesh Sele Owe to pushover F z disp contour M 3D view Play Animation Due to gravity soil only Due to gravity bridge included Due to pushover Unit m 4 320e 005 3 685e 005 3 449e 005 3 014e 005 2 578e 005 Deformed mesh 2 143e 005 ee contour fill 1 707 e 005 1 27 20 005 l 8 360e 006 2 disp contour 4 005e 006 3 500e 007 2D z 10 m 4 705e 006 9 060e 006 1 341e 005 1 777e 005 2 212e 005 2 646e 005 3 083e 005 3 519e 005 3 954e 005 4 390e 005 Step No eo a gt Tim po Animation Delay millisecond Scale Factor 51 72 larger value ss slower fi 0 Vv Endless Playing J Bridge Only Fig 46 Deformed mesh and contour fill 42 5 3 Eigenvalue Analysis To conduct an Eigenvalue analysis please follow the steps shown in Fig 47 and then click Save Model amp Run Analysis Fig 48 shows the output window for an Eigenvalue analysis which can be accessed by clicking menu Display Fig 3 and then choosing Deformed Mesh EF BodgePbtl defaultlase phe File Execute Display Help id Model Input PR a Pein ement Mesh STEP 1 DEFINE Analysis Type PBEE Analysis C Ground Shaking Step A specify yearn Number of Modes Bridge Parameters Soil Parameters Mesh Parameters Analysis Options Boundary Conditions B C Type
7. j GrideePREE defauttCase pbe Fm Execute Comey Hep 2 Matel Input ea La Finite Element Hash STEP 1 DEFINE MODEL rae ny Seow OA Enea Anahi Type M Pushover Step 1 Click Ground Shaking Model Detraion Bridge Parameters Step 2 Click PBEE Motions _ Mesh Parameters apr a Boundary Conditions BC Type Shen Bean e r Bedrock Type Fad Esme STEP 2 EXECUTE FE ANALYSIS Save Model amp Run Analysis STEP 3 COMPUTE REPAIR COST PHEE Analysis Fig 50 Steps to define PBEE motions 51 PBEE Input Motions PBEE Input Motion Folder Browse CAMyDoc POEE detaultCase_plitiles detaultCase EU Inout Motions 10 Records in Total 1 Records Selected Display Intensity Measures Timestep Sec Duration Sec BORREGOA ELC 40 0000 LOMAFIA E 34 9600 LOMAPLAP 34 4600 NORTHRICNF 25 0000 COALINGASH PYE 34 4600 NOR TAHRISCS 40 0000 BORREGO B ELC 40 0000 COALINGA H LO5 40 0000 IMP ALLA CAL 34 5400 LIVERMORIA KOD 20 4500 Randomly Choose i Records tor Each Bin Double click on any record to wiew its characteristics including response spectra scale Factor Longitudinal i Transverse i Vertical i f Compute Response to Entire Record Length Free vibration Duration 5 seconds l Compute Response for seconds Time Step 002 seconds OK Cancel Fig 51 PBEE input motions widow 32 E Motion H CAL _ Intensity Measures Longitudinal Transverse Horizontal SRSS Vertical PGA g 0 128176 0 0
8. step 2 click Define OK ICE Fig 32 Steps to define an EPP Gap abutment model 31 3 4 8 HFD Model As suggested by Shamsabadi et al 2007 2010 a Hyperbolic Force Displacement HFD relationship is employed to represent abutment resistance to bridge displacement in the longitudinal direction Fig 33 In this HFD model resistance appears after a user specified gap is traversed Fig 33b and the bridge thereafter gradually mobilizes the abutment s passive earth pressure strength Herein this strength is specified according to Shamsabadi et al 2007 2010 at 265 kPa for a nominal 1 7 m bridge deck height with full resistance occurring at a passive lateral displacement of 0 09 m the sand structural backfill scenario Similarly abutment resistance to the transverse bridge displacement is derived from the longitudinal hyperbolic force displacement relationship according to the procedure outlined in Aviram et al 2008 To define an HFD abutment model please follow the steps shown in Fig 33 4 Soil Parameters First some important master control options are defined by clicking Analysis Options as shown in Fig 6 This will display the interface shown in Fig 34 below The following modifications can be made in this window 1 Select to keep the soil properties as defined by their linear properties or opt to conduct nonlinear soil computations note that the default is Linear 2 Select from among a number of
9. 2006 including sophisticated longitudinal transverse and vertical nonlinear abutment response as well as a participating mass corresponding to the concrete abutment and mobilized embankment soil A system of zero length elements is distributed along two rigid elements oriented in the transverse bridge direction The discrete zero length elements represent each component of the abutment that contributes to the combined behavior and allow for differential response in each element as the superstructure rotates about the vertical bridge axis A general scheme of this abutment model is presented in Fig 27 The bearing pads create a series system between the two transverse rigid elements Rigid element 1 and 2 in Fig 27 Rigid element 1 is connected to the deck end by a rigid joint The longitudinal elastomeric bearing pad response and gap closure behavior are illustrated by L1 in Fig 27 The number and distribution of the bearing pads is defined according to the number and location of the girders in the box with plan and thickness dimensions according to plans or specifications The longitudinal backfill back wall and pile system response are accounted for by the two zero length elements at the extreme locations of rigid element 2 designated as L2 Longitudinal response The longitudinal response is based on the system response of the elastomeric bearing pads gap abutment back wall abutment piles and soil backfill material Prior to impact or g
10. 30 Fig 31 Steps to define a SDC 2010 Clay abutment model cc ccccsssssssseeseseeeeeeeeeees 31 Fig 32 Steps to define an EPP Gap abutment model icici ciesesacdvnceenciievdewtodvernadergae dvedeenabdewdeds 31 Fig 33 Steps to define a HFD abutment model a choosing HFD model at the bridge model window b HED Model WiIndOW sacesesssssssaccscncescsoscavadeadsianaonsssavdeaaswcedesossauiudes E 33 il PE SAGA Y SISO DUONG a E E E E 34 Fig 35 Beam column element types available for column 2 0 0 0 ccceceeeeeeeeeseeeeeeeeeeeeeeeeeeeeeeees 34 Fig 36 Rayleigh damping coefNoreniSennestisienie rio n S a E 35 Kie 3 7 SOUS CAVA CTT ILO Meria a e ccd dunia bd vic a e a le 35 Frs 30 gt User deimed clay material Ue Clay 2 xfs cccutcetst cates E etter aerveenebes 36 Fig 39 Steps to define a load pattern for pushover analysis cccccccccccscsssssesssssseseeeeeeeeeeeees 37 Fig 40 Load pattern for pushover analySis cccccccseseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeees 38 Fig 41 Steps to define a user defined load pattern U Push 0000000oooooonnnnnnnnnnnnnssssssssssseesseee 39 Fig 42 Example of user defined pushover load pattern U Push ic eeeesssesseeeeeeeeeeeeeeees 40 Fig 43 Response time histories and profiles for column and pile shaft 00 0 0 eeeeeeceeeeees 41 Fig 44 Response relationships for column and pile shaft cccccssssssssssssseseeeeeeeeeeeeees 4 Fig 45 Abutme
11. 5656 3 10 2594 4631 52 10 2594 ies Fig 59 Repair quantities window Unit Costs UC Structure aeua structure backfill Temporary suppor superstructure Temporary suppor abutment Structural concrete bridge Structural concrete footing structural concrete approach slap Aggregate base approach slab Bar reinforcing steel bridge Bar reinforcing steel footing retaining w Epoxy inject cracks Repair minor spalls Column steel casing Joint seal assembly Elastomeric bearings Drill and bond dowel Furnish steel pipe pile Drive steel pipe pile Drive abutment pipe pile Asphalt concrete Mug jacking Bridge removal column Bridge removal portion Approach slab removal Clean deck for methacrylate Furnish methacrylate Treat bridge deck Barrier rail Re center column oqure Foot agure Foot Cubic ard Cubic ard Cubic ard Found LB Pound LB Linear Foot LF oqure Foot SF Found LB Linear Foot LF Each EA Linear Foot LF Linear Foot LF Each EA Each EA TON Cubic ard Ly Cubic ard ly Cubic ard Cy Cubic ard ly oqure Foot SF Gallon GAL oqure Foot SF Linear Foot LF Each EA Fig 60 Unit Costs window 57 E Production Rates PR ER PR std dev structure excavation structure backfill Temporary support superstructure Temporary support abutment structural concrete bridge structural concrete footing structural concrete approa
12. Cover Concrete Young s Modulus Concrete Compressive Strength Concrete Strain at Maximum Strength Concrete Crushing Strength Concrete Strain at Crushing Strength 0 006 Ratio between Unloading Slope 01 Tensile Strength 3864 kPa Tensile Softening Stifness l q30000 kPa Fig 10 Fiber Section window Fig 11 Column fiber section based on PEER best modeling practices report Berry and Eberhard 2007 Table 1 Default Values for Column Reinforced Concrete RC Section Properties Parameter Value Longitudinal bar size US 10 Longitudinal steel 2 Transverse bar size US 7 Transverse steel 1 6 Steel unit weight kN m 77 Steel yield strength kPa 460 000 Concrete unit weight kN m 22 8 Concrete unconfined strength kPa 27 600 Table 2 Default Values for Steel02 Material Properties Parameter Value Typical range Steel yield strength kPa 460 000 345 000 470 000 Young s modulus MPa 200 000 Strain hardening ratio 0 01 0 005 0 025 Controlling parameter RO 15 10 20 Controlling parameter cR1 0 925 Controlling parameter cR2 0 15 The strain hardening ratio is the ratio between the post yield stiffness and the initial elastic stiffness The constants RO cR1 and cR2 are parameters to control the transition from elastic to plastic branches Table 3 Default values for Concrete02 Material Properties Parameter Core Cover Elastic modulus MPa 25 312 25 312 Compressive stre
13. FEA model is not changing the time history analyses do not need to be repeated These are the most time and resources intensive portions of the complete analyses Once the time history results are computed the user may perform what if scenarios by changing any of the parameters of the intermediate damage loss and hazard models The PBEE portions of the analysis do not require recomputing the time history results unless the model is changed or a new selection of ground motions 1s made Finite element computations are conducted using OpenSees http opensees berkeley edu Mazzoni et al 2009 an open source framework developed by the Pacific Earthquake Engineering Research PEER Center The current version of the interface is limited to ordinary bridge overpasses with two spans and a single column bent The analysis options available in BridgePBEE include e Pushover Analysis e Modal Analysis e Single 3D Base Input Acceleration Analysis e Full Performance Based Earthquake Engineering PBEE Analysis This document describes how to conduct the above analyses in BridgePBEE For information on how to download and install BridgePBEE please visit the BridgePBEE website http peer berkeley edu bridgepbee The coordinate system employed in BridgePBEE is shown in Fig 1 The origin is located at the column base the ground surface 1 2 System Requirements BridgePBEE runs on PC compatible systems using Windows NT V4 0 2000 XP Vista o
14. RCR between the cost of repair and the cost of replacement cost does not include demolition It is shown in and it can range between 0 and some number higher than 100 there is no reason why it is bounded by replacement cost this 1s purely an owner operator decision This ratio is useful for comparing the performance of different bridge design options for new construction For the evaluation of existing structures the RCR including demolition costs might be more useful Constructing a new bridge on the same site after an earthquake would require both demolition of the damaged bridge and construction of its replacement The costs of new construction used in the interface come from Caltrans bridge cost estimates used for planning purposes They are based on the deck and type of construction providing a range of cost SF of deck area circa 2007 to be consistent with the repair data used 47 Repair time for the bridge can be expressed either as an approximation of repair duration or repair effort The repair effort represents the total number of crew workdays CWD required to complete the task This 1s different from repair duration which counts the total duration of the repair project The repair duration includes the effect of scheduling concurrent on site construction processes while the repair effort does not The repair duration can vary based on the amount and type of concurrent construction processes schedule dependencies availability
15. ShearBeom F Bedrock Type STEP 2 EXECUTE FE ANALYSIS Save Model amp Run Analysis STEP 3 COMPUTE REPAIR COST PBEE Analysis Fig 47 Steps to perform an Eigenvalue analysis 43 Mode Shapes KE Mode shape gt Z disp contour Evie Zoom In Zoom Out Zoom Frame W ee me 30 gt Up Dn nit m 3 627 e 002 3 421 e 002 3 015e 002 2 608e 002 2 202e 002 1 796e 002 a09e 002 9 832e 003 5 769e 003 1 706e 003 2 356e 003 6 419e 005 046e 002 455e 002 661e 002 2 246 e 002 2 67 32 002 3 080e 002 3 406e 002 3 094e 002 4 2998 002 Mode Mo i 4 E _______ Frequency Hz 1 21414 Scale Factor fi J0 fa Bt esis ts E E EN i 0 M Endless Pla l Bridge Only Mode Shapes Mode shape r Z disp contour ID wiew Zoom In Zoom Out Zoom Frame ae vz me 3D lt gt Up Dn 3 015e 002 2 606e 002 2 202e 002 1 796 00 1 389e 002 2 356e 003 6 419e 005 046e 002 455e 002 1 561 e 002 2 26 e 002 2 67 32 0072 3 080e 002 3 406e 002 3 094e 002 42996 002 Made No f3 l Frequency Hz 1 97372 scale Factor Hoo Unit m 3 627 e O02 3 421e 002 Fig 48 Sample output for an Eigenvalue analysis 44 6 PBEE Analysis Ground Shaking To conduct a single earthquake analysis or a full PBEE analysis the Ground Shaking option under Analysis Type Fig 2 is used For that purpose
16. a ee 111 Fig 119 Mesh refinement example 3 a Change meshing controlling parameters in the horizontal direction b the resulting mesh ee eeeeesesssseeeeccecceeeeeeeeaeaeaeeeeeeeeeseeeeeeeeeeeeeeeaaaas 112 Fig 120 Cantilever beam simulation using BridgePBEE ccccccccecceeeeeeeeeeeeeeeeeeeeeeeeeeeees 114 Fig 121 Fixed end beam simulation using BridgePBEE cc cccccscssesseeesssseeeeeeeeeeeeees 115 Fig 122 Deck deformation under gravity the maximum displacement is 0 0372 m 116 Fig 123 Fixed end roller beam analytical solution from efunda cOm cccccceeeeeeeeeeeees 116 Fis 124 Longitudinal PUSDOVET anosmio secede te eniaa wae aman taumeuntautennnuniants 117 Fig DD Transverse US MON CL tones siielnds hiaaatec abound ueaalend ol ctese eeaba deena tuietsieaueeesiote ete aeaateeronutecsaeaas 117 Fig 126 Choosing PBEE MONON Sl cde eee tiotee ee Oe ie Retina 119 Fig 127 Directory structure of PBEE Moun Selassie erat panintiednenildeieineitie 120 oi Coe ee Fares 0 8 oom MO Ul a treme eran erent at taretntr ty einen erin er Neats ra ener tee 120 Fis 129 Sample atal Tle moraii wee ania a a A 121 Fig 130 Example of user defined motion cccccccccccssssssssssseseeecececeeceeeeeeeeeaussseeeesseeeeeeeeeeseeees 121 Fis 31 Visual Stdio Tile PBEE SLN neronen a a E E 128 Piei Modiin Me PBEE GPP x sxcscasent isazathacacenteanstoden O T O 129 Fig 133 Building PBEE DLL in Visu
17. available Brick elements in OpenSees 3 Conduct more than one earthquake simulation at a time when performing a PBEE multi earthquake record analysis 4 Apply own weight of the soil using a global lateral stress coefficient and a single value of Young s modulus that is user defined this will reduce initial shear stresses in the mesh due to own weight application but generally may have minimal impact on the subsequent earthquake computations anyway 5 by clicking on Change OpenSees Options Fig 35 you can change the beam column element type advanced feature please exercise with care and 6 by clicking on Change Rayleigh Damping Fig 36 you can change the viscous damping characteristics of the model The soil parameters section Fig 37 below is activated by clicking Soil Parameters in Fig 6 Here the horizontally stratified soil profile can be defined layer by layer as many as 10 layers as shown in Fig 37 below Currently only the cohesive soils are available to select e g by clicking on the U Clay2 section in Fig 37 and then selecting any of the available soil types stiff medium and soft clay or U Clay2 in Fig 38 32 Bridge Model Column C Rectangular C Oblong 1 22 m 12 21 m 6 71 m Column Properties F Linear Column M Use Different Properties for Column below Grade e2 Im kPa Circular Diameter Total Column Length Column Length above Grade
18. b displacement below the inflection point divided by the length of this distance This takes care of rotation at the base different boundary conditions etc so that the results are consistent when computing damage The Square Root of Sum of Squares SRSS values of the 2 horizontal components are used The tangential drift ratios are combined separately at each time step to obtain SRSS PGI Max tangential drift ratio SRSS is the maximum of the SRSS values of all time steps PG2 Residual tangential drift ratio SRSS is the SRSS value at the last time step The tangential drift ratio is in percentage To calculate the tangential drift ratio the following 2 lines were added into the tcl file recorder Hlement fLile A ELG dit time ele ScolumnEle tangentDrret recorder Element file A ELC ifp time ele S columnEle inflectionPoint 8 1 where columnEle 1s the element of the column Only one forced based beam column element nonlinearBeamColumn is used for the column In the dft file there will be 5 columns of data for each time step and the first column is time In the ifp file there will be 3 columns for each time step and the first column is also time Subsequently the tangential drift ratio is calculated using the code snippet shown in Fig 87 For the tangential drift ratio in the longitudinal direction X direction or bridge longitudinal direction the tdx1 and tdx2 variables are the second and third column the first
19. b menu File c menu Execute d menu Display and e menu Help BridgePBEE s main features are organized into the following menus e File Controls reading writing and printing of model definition parameters and exiting BridgePBEE e Execute Controls running analyses e Display Controls displaying of the analysis results e Help Visit the BridgePBEE website and display the copyright Disclaimer message Fig 4 About BridgePBEE EE BridgePBEE Ver 1 0 October 2011 BridqePBEE is developed by Drs Jinchi Lu UC San Diego Kevin Mackie U Central Florida and Ahmed Elgamal UC San Diego Acknowledgement This research was funded by Pacific Earthquake Engineering Research PEER Center Qpensees currently ver 2 1 0 is employed is a software framework for developing applications to simulate the performance of structural and geotechnical systems subjected to earthquakes For more information visit http opensees berkeley edu The Opensees geotechnical simulation capabilities were developed by Dr Zhaohui Yang and Dr Ahmed Elgamal For more information please visit http cyclic ucsd edufopensees The implemented PGEE analytical framework is provided by Dr Kevin Mackie LI Central Florida For questions or remarks please send email to Dr Jinchi Lu Ginlu tucsd edu Dr Kevin Mackie Kevin Mackiet uctedu or Dr Ahmed Elgamal felgamal ucsd edu Copyright 2 2011 The Regents of the University of California All Rights Reserve
20. computational modeling in geomechanics Alexandria Egypt October 3 5 4 1YGEC 09 4th International Young Geotechnical Engineers Conference 2 6 October ISSMGE Elgamal A 2010 Calibrated 3D computational modeling of soil structure systems and liquefaction scenarios Proc Fifth Intl Conf on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics May 24 29 San Diego CA Lu J 2006 Parallel finite element modeling of earthquake site response and liquefaction PhD Thesis Department of Structural Engineering University of California San Diego La Jolla CA Mackie K R and Stojadinovic B 2005 Fragility basis for California highway overpass bridge seismic decision making PEER Report No 2005 02 Pacific Earthquake Engineering Research Center University of California Berkeley Mackie K and Stojadinovi B 2006 Seismic Vulnerability of Typical Multi span California Highway Bridges Proceedings of the Fifth National Seismic Conference on Bridges and highways September 18 20 San Francisco Mackie K R Wong J M and Stojadinovic B 2008 Integrated probabilistic performance based evaluation of benchmark reinforced concrete bridges PEER Report No 2007 09 Pacific Earthquake Engineering Research Center University of California Berkeley 132 Mackie K R Wong J M and Stojadinovic B 2010 Post earthquake bridge repair cost and repair time estimation methodology Earthquake Engin
21. e End Element Output the response values for both nodes top node bottom node of every element this line is discontinuous e Max the response profile at a certain step when the maximum absolute value occurs Pressure is the difference of the shear forces at the both ends of each element divided by the element length If Response Summary is selected the Middle Dropdown List see Fig 67 response profiles of displacement bending moment shear force and pressure will be plotted in one window Fig 69 To convert all the plots in the current window to a PDF file Adobe PDF or similar has to be available or send to a printer click Print located near the top left corner of the window this feature is available in all figure windows in BridgePBEE To view the data of each plot this feature is also available in all plots in BridgePBEBE click the filename e g click momProf txt in Fig 68 and an Internet Explorer window will pop up and display the momProf txt data file 2 Column Response Time Histories 65 The column response time history will be displayed if Response Time Histories in the Left Dropdown List Fig 67 is selected Fig 70 shows the window for displaying the column longitudinal displacement time histories The top plot in the window Fig 70a is the response profiles for at specific load steps while the remaining plots are the response time histories at different depths Fig 70b In the plot for the Response Prof
22. height above grade Deck length Spence ey eee E Se eee ee ee Zz ay e e a Total column height Embankment length Depth of embankment Embankment length foundation Side view Embankment length Deck length Embankment length width Plan view Fig 111 Schematic view of an idealized single bent bridge system Step 1 In the user interface click Bridge Parameters With reference to Fig 111 define the following parameters according to your preference Diameter This is the bridge column outer diameter which is currently also the pile diameter Integral column foundation scenario Total Column Length Starting from the bridge deck all the way to the pile tip Column Length above Surface from bridge deck to mud line Embankment Length in plan view longitudinally from bridge edge to street level away from bridge 104 Depth of Embankment Foundation Height of approach embankment at bridge edge from the ground surface to the base of the approach embankment foundation Fig 111 Deck Length Length of bridge in the longitudinal direction Soil Parameters make sure at least the total Thickness of soil layers is defined This is the total thickness of the ground stratum from the ground surface all the way down to the base of the soil mesh Make sure that the column pile base tip is within the defined soil domain depth Note Earthquake input motion is imparted along the base of the soil mesh This base is assumed to repre
23. large pile group as a large single column If this option is selected Fig 7 the column below grade will have linear properties as specified by its diameter and Young s Modulus 125 3 All the equations presented in this Appendix are based on the Mander model for spiral reinforced circular concrete columns The user may want to use their own constitutive model or parameters In this case the values of these parameter can be defined directly in Fig 10 126 12 Appendix E Customization of PBEE Quantities Users can customize PBEE quantities through updating a file named PBEE DLL which 1s located at the installation folder C Program Files BridgePBEE or C Program Files x86 BridgePBEE on a 64bit PC Please follow the steps below to build an updated PBEE DLL file and then replace the one at the installation folder Step 1 Download PBEE ZIP Please go to the BridgePBEE website to download a source code project file filename PBEE zip for Visual Studio We ll use this one to build the PBEE DLL file Step 2 Open PBEE SLN File Unzip PBEE zip to a certain location and then use Visual Studio 2005 version preferred to open a Visual Studio Solution file named PBEE SLN Fig 131 Open the file named PBEE CPP and make appropriate changes Fig 132 Step 3 Build PBEE DLL File Under Visual Studio 2005 click menu Build and then Build Solution to build an updated PBEE DLL file Fig 133 Step 4 Replace PBEE DLL File Mak
24. major components required for this calibration were damage scenarios that describe particular instances of earthquake damage schematic design of bridge repairs to address the state of damage in the scenarios and the link between repair design methods and procedures and subsequent quantities There is a direct link between damage scenarios and the repair 1 e there is a single repair procedure for a single state of damage The repair quantity results were parameterized in terms of basic bridge geometry and properties so that they can be used to extrapolate loss modeling for other bridges in the same class such as those that can be built within the user interface Data for time and monetary repair costs were obtained by estimating the costs of the damage and loss scenarios using published Caltrans construction estimation data case studies from previous earthquakes and interviews with Caltrans bridge engineers Monetary costs were adjusted to 2007 values based on Caltrans cost index data Repair costs are estimated for each damage scenario based on quantities of each repair item Cost estimates accounted for variations in unit cost and the details involved in estimating a combination of repairs together The benefit of separating the Qs from costs is that the unit cost model is easily updated for new years of data local economic conditions site accessibility and incentives Normalized costs of repair are obtained by using the repair cost ratio
25. motion set 53 E Intensity Measures Intensity Measures Longitudinal direction Record om in ta Ba i Bee mo w jo D io th PGA w oin g PGV Transverse direction Record Jom inh wh e FGA b o M b e je in g PGV 4NA RANANe NNT cm sec 30069000e 001 T0558000e 001 28519000e 001 55790000e 001 7T9623000e 001 12467000e 001 82817000e 002 46518000e 001 28176000e 001 54459000e 001 H w to d e ha H e e cm sec 66580000e 002 38501000e 001 43293000e 001 2028 7000e 001 85231000e 001 97237000e 001 1 PED 62889658e 001 37122023e 001 49998773e 001 2 0668323e 001 2388472424001 L7T384072e 002 87896621e 000 OTTOS8O5e 001 2S861251e 001 87948980e 001 PGD 32037153e 001 15274818e14001 92047198e 001 O06627983e 001 907T637T32e 001 02166526e 002 cm cm mae j je in om i iD w je D 5 95 22231035e 001 89163715e 000 12410005e 000 10940729e 000 42181514e 000 42637996e 001 275048 76e 000 96151696e 000 909517910e 001 L12557582e 000 D 5 95 91173142e 001 64336429e 000 48788021e 000 02601795e 001 2 SS6G5223e 000 91310633e 001 4051 AT AsSesAnn sec 3 15300000e 001 60300000eE 001 15000000eE 001 61700000e4 001 67650000e4 001 78150000e 001 15800000e 001 20200000e 001 61000000e 001 sec g 3 S 2 a a 4 CAW 27200000e 001 CAV TRAAAAAAS
26. the bin folder and rename to your earthquake name e g Quake1 Step 4 create a folder under the earthquake name and rename to your input motion name e g MOTION 1 Step 5 create the 6 files 3 INFO files and 3 DATA files for this input motion Fig 130 Note If you download the input motion files from the PEER NGA Database there is no need to re format the data into one column as shown in Fig 129 Just copy the data points into the corresponding DATA files And then make the INFO files containing the number of data points and the sampling period DT 2 lines according to the header information PBEE Input Motions PBEE Input Motion Folder Browse l Motion set name CAMyDoc PBEE PREEMOotonSetl m Input Motions i Records in Jisai bie cc ec acto aay intensity Measures Pecord Bin iid id Duration Sec LM Ey El Choose a folder 40 0000 a LMLR L 39 9500 J LMLR 39 7450 4 LMLR C PBEEMotions 44 9500 5 LMLR 5 amp aaa 34 9500 f LMLR Faure _ 39 5750 f LMILE E E LMSR 34 9900 uE LMLR E Near 39 7900 4 LiMILF E C SMLR 29 9900 i 10 LhILF SMSR 35 3600 11 LMLR PBEEMotionseti_SNotions 40 0000 IM12 LLR PEEEMotionseti_10MNtions 34 3300 De select All C PBEEMotionSet1_i6mottns He for Each Bin Double click T gt FBEEMotionSeti Max50Sas Double click on any record to E PREEMotionSet1 MaxPGAs Scale Factor Longitudin C PBEEMotionSet1Smallset fal h C Compute Response to Enti M
27. the input earthquake excitation s must be specified Input files at http peer berkeley edu bridgepbee that exercise this option include Examples 2 5 If only one earthquake record 1s selected out of a specified ensemble suite of input motions then a conventional single earthquake analysis will be performed 6 1 Theory and Implementation of PBEE Analysis In the user interface an implementation of the Pacific Earthquake Engineering Research PEER Center s performance based earthquake engineering framework Cornell and Krawinkler 2000 is used to generate probabilistic estimates of repair cost and repair time The PEER PBEE framework utilizes the total probability theorem to compute the desired probability distributions by disaggregating the task into several intermediate probabilistic models with different sources of randomness and uncertainty The hazard model uses earthquake ground motion data to determine an intensity measure IM The demand model uses response from dynamic analysis to determine an engineering demand parameter EDP The damage model connects the EDP to a damage measure DM Then the DM is linked to consequences that are termed the decision variables DV Repair cost and repair time can be thought of as two possible decision variable DV outcomes characterized probabilistically by the framework The complete analysis is accomplished using the local linearization repair cost and time methodology LLRCAT described by
28. xogan ot Jagd g Jaag Ee please update the following 2 lines only double Mean 29 double StdDev 29 y for int i OF i lt 29 itt dbPBEEProductionRates Mean i Mean i dbPBEEProductionRates StdDev i StdDev i E FBEE_ API void PBEEUnitCosts double dbPBEEUnitCosts Mei Repair Item Names Structure excavation Fornrucnire harktilil iiil Fig 132 Modifying file PBEE CPP 129 7S PBEE Microsoft Visual Studio File Edit View Project Build Debug Tools VMware Window Community Help Rebuild Solution Ctrl Alt F 7 Clean Solution Build Solution for Intel Static Security Analysis FE Rebuild Solution for Intel Static Security Analysis ed Solution PBEE 1 project Build PBEE I E ohana Rebuild PBEE tl Header Files Resource Files Clean PBEE o La Source Files Project Only G PBEE cpp cH stdafk cpp Profile Guided Optimization xogan at Jaod g Jaras Eh Batch Build Configuration Manager Compile Ctrl F f please update the following lines only double Mean 23 1 2 2 2 34 2 33 2 10 10 2 1 2 double StdDev 29 0 2 0 5 3 8 3 8 0 7 0 7 0 3 for int i OF i lt 29 itt i dbPBEEProductionRates Mean i Mean i dbPBEEProductionRates StdDev il StdDev il E PBEE API void PBEEUnitCosts double dbPBEEUnitCosts Me Repair Item Names Structure excavation Structure harkfill LT Fig 133 Building PBEE DLL in Visual S
29. 2 m by default The default value is for the gross moment of inertia it can be reduced as desired by the user to better capture cracked column properties e Moment of Inertia Longitudinal Axis calculation for the default value is the same as the above e Cross Section Area the default value 0 7854 m is calculated based on the circular cross section with a diameter of 1 22 m e Mass Density the mass density of the column The default value is 2 4 ton m Elastic beam column elements elasticBeamColumn Mazzoni et al 2009 are used for the column in this case Step 2 Click Column Step 1 check Linear Properties Column B mw Gepth of Embankment Foundation Os o o0 m Total Weg Step 3 Define values in Activate Abutrey Column Properties i Linear Column Abutment File W Linear Material Properties of Column this window Use Different Properties for Column below Grade Youngs Modulus SQ000000 Diameter Moment of Inertia Transverse Axis 0 108745 Tpunige Wie ul Moment of Inertia t Longitucianl Axis 0 108745 m4 Cross Section Area 0 7854 m Deck Deck Length Mass Density 2 4 ton m3 Deck idth Deck Depth Cancel Deck Properties Number of Shear Keys Cancel kPa md Fig 8 Steps to define the elastic properties of the column 11 3 1 2 Nonlinear Fiber Section To define the nonlinear Fiber section for the column follow the steps shown in Fig 9 The window to define the Fiber
30. 3576014E Beta corce Fig 58 Damage states window W TTT 56 E Repair item itemName 0 Unit ColMax DS1__ Col Max DS2__ Col Max DS3__ ColMax DS4 oon on b wr Structure excavation Structure backfill Temporary support superstructure Temporary support abutment Structural concrete bridge Structural concrete footing Structural concrete approach slab Aggregate base approach slab Bar reinforcing steel bridge Bar reinforcing steel footing retaining w Epoxy inject cracks Repair minor spalls Column steel casing Joint seal assembly Elastomeric bearings Drill and bond dowel Furnish steel pipe pile Drive steel pipe pile Drive abutment pipe pile Asphalt concrete Mud jacking Bridge removal column Bridge removal portion Approach slab removal Clean deck for methacrylate Furnish methacrylate Treat bridge deck Barrier rail Re center column Cubic Yard CY Cubic Yard CY Squre Foot SF Squre Foot SF Cubic Yard CY Cubic Yard CY Cubic Yard CY Cubic Yard CY Pound LB Pound LB Linear Foot LF 44 0289 86 0577 Squre Foot SF 27 6623 69 2058 Pound LB Linear Foot LF Each EA Linear Foot LF Linear Foot LF Each EA Each EA TON Cubic Yard CY Cubic Yard CY Cubic Yard CY Cubic Yard CY Squre Foot SF Gallon GAL Squre Foot SF Linear Foot LF Each EA 12 5719 12 5719 5656 3 10 2594 4631 52 10 2594 12 5719 12 5719
31. 41 0 656 0 664 Free field PA 0 386 2 181 0 380 0 349 0 370 0 344 0 375 0 374 0 855 0 851 Free field PV 0 259 132 0 297 0 271 0 273 0 259 0 449 0 451 0 682 0 713 Free field PD 0 326 167 0 368 0 337 0 349 0 327 0 528 0 534 0 885 0 933 Free field D 5 95 0 518 232 0 605 0 579 0 585 0 568 0 799 0 799 1 551 1 552 Free field CAV 0 396 175 0 365 0 341 0 358 0 342 0 341 0 337 1 047 1 045 Free field Arias Intensity Free field SA Period 1 sec Free field SV Period 1 sec Free field SD Period 1 sec Free field PSA Period 1 sec Free field PSV Period 1 sec N UJ N 0 360 164 0 296 0 273 0 293 0 274 0 140 0 138 0 867 0 880 0 388 168 0 368 0 347 0 364 0 352 0 413 0 410 0 882 0 946 0 419 195 0 439 0 405 0 426 0 408 0 549 0 542 1 130 1 197 0 388 168 0 368 0 347 0 364 0 352 0 413 0 410 0 882 0 946 0 388 168 0 368 0 347 0 364 0 352 0 413 0 409 0 881 0 946 0 388 168 0 368 0 347 0 364 0 352 0 413 0 409 0 881 0 946 E One sigma Values Beta Values for PG1 File PG1Beta txt Blee b Fig 91 Lognormal standard deviations beta values for each PG a table format b bar graph format 87 7 1 7 Bridge Peak Accelerations for All Motions The bridge peak accelerations for all input motions can be accessed by clicking menu Display Fig 3 and then Bridge Peak Accelerations for All Motions Fig 92 The window to display the bridge peak accelerations for all motions is shown in Fig 93 The responses are available
32. 78436 0 136192 0 055177 PGv cm sec 15 386125 13 294415 18 303170 8 918327 PGD cm 10 951791 6 175585 11 657001 2 756336 D 5 95 sec __32 020000 _ _31 985000 _ 32 010000 _ 35 715000 _ CAV cm sec 391 374865 334 268962 565 656903 216 962519 Arias Intensity cm sec ___13 978722 23 417409 4 607266 9 461872 _ Acceleration Time Histories and Pseudo Spectral Acceleration PSA Longitudinal Acceleration g Motion File H CAL225 AT2 data Longitudinal Pseudo Spectral Acceleration g File File motionX txt spectralAccx txt BRE Transverse Acceleration g Motion File H CAL315 AT2 data Transverse Pseudo Spectral Acceleration g File File motionY txt spectralAccY txt kes fr fot Ea fei We fot ES Fig 52 Intensity measures time histories and response spectra of individual record W Histogram for Intensity Measures Bix Please choose Histogram for PGA PG PGD D 5 95 CAV amp Arias Intensity View Intensity Measure Values z Histogram for PGA PGY PGD D 5 95 CAV amp Arias Intensi Fx Print Histogram for PSA PSV amp SD Period 1 sec E Peak Ground Acceleration PGA Longitudinal PGA Histogram File hPGAX txt Longitudinal PGA Cumulative Distribution File cPGAX txt BRAE Transverse PGA Histogram File hPGAY txt Transverse PGA Cumulative Distribution File cPGAY txt Bie Fig 53 Histogram and cumulative distribution for the whole input
33. 80 There are 3 dropdown lists available for users to choose The contents of the 3 lists are as follows Left Dropdown List e Due to gravity soil only e Due to gravity bridge included e Due to pushover or Due to base shaking Middle Dropdown List Deformed mesh Disp contour fill X Disp contour Y Disp contour Z Disp contour The Right Dropdown List includes options of 3D view as well as 2D views for a number of pre defined planes To view the bridge structure only check Bridge Only in the bottom right corner of the window Fig 80 BridgePBEE defaultCase pbe File Execute f S TA Help Model PG Quantities for All Motions Ove Bridge amp Ground Peak Accelerations for All Motions m Maximum Column amp Abutment Forces for All Motions Bridge Only Zoomin Out Frame STEP 1 Detailed Output Please Select Input Motion Current A ELC Analysis sain eh uns Motion A ELC Column Response Time Histories amp Profiles Motion A ELC Column Response Relationships Motion A ELC Abutment Responses Motion A ELC Analysis Summary PBEE Analysis Ground Shaking PBEE Motions Model Definition Bridge Parameters Soil Parameters Mesh Paremeters Analysis Options Boundary Conditions B C Type r E Bedrock Type STEP 2 EXECUTE FE ANALYSIS Save Model amp Run Analysis STEP 3 COMPUTE REPAIR COST PBEE Analysis Display the deformed mesh and play animation F
34. 9 Motion Set 3 These motions 80 in total are labeled Broadband _ separated into the two bins Broadband rock and Broadband soil as developed by Dr Jack Baker for PEER Additional information about these motions 1s available at the website http peer berkeley edu transportation projects ground motion studies for transportation systems Motion Set 4 These motions 260 in total include the above Motion Set 2 and Motion Set 3 as well as the additional bin v near fault motions of Motion Set 1 All of the above 4 ground motion data sets were resampled to a sampling frequency of 50 Hz regardless of whether initial sampling frequency was 100 or 200 Hz due to the computational demands of running full ground structure analyses for an ensemble of motions Standard interpolation methods were used to resample the time domain signals so that the signal shape 1s preserved The resampled records were then baselined to remove any permanent velocity and displacement offsets Baselining was accomplished using a third order polynomial fitted to the displacement record 6 3 2 Specifications of PBEE Input Motions To conduct a PBEE analysis input motions must be defined please follow the steps shown in Fig 50 The window to define PBEE input motions is shown in Fig 51 To unselect all motions click De select All To see all motions click Select All same button as De select All The dropdown list of Randomly Choose Records for Each Bin w
35. 9029E 04 B a Pi j Col 14 Sel UNIX Fig 129 Sample data file MOTION File Edit wiew Favorites Tools Help O Back gt wi pe Search amp Folders Hab Address S D _ PBEE MotionSet1 bind uakel MOTION 4 Go Folders Mame gt Size Type Date Modified j MotionSeti A S MOTIONI UP AT2 data 53K6 DATA Fie 2 7 2009 3 56 PM SB bint MOTION UP AT2 info LKB INFOFie 2 7 2009 3 56 PM Sl Quakes MOTIONIO00 AT2 data 53KE DATAFie 2 7 2009 3 56 PM F MoTIONt MOTIONIO00 AT2 inFo LKB INFO File 2 7 2009 3 56 PM E PBEEMotionSseti MOTIONIO90 AT2 data 53KE DATAFie 2 7 2009 3 56 PM E PBEEMotionsetia 3 MOTION1090 4T2 inFo INFO File 2 7 2009 3 56 PM co fs omoecre aceuie cein E Tii lt 6 objects Disk Free space 9 62 GB F My Computer Fig 130 Example of user defined motion 121 11 Appendix D Calculation of Steel and Concrete Material Properties Steel Bars By default the Steel02 material is used to simulate steel bars The format of the Steel02 command is as follows Mazzoni et al 2009 uniaxialMaterial Steel02 matTag fy EO b RO cR1 cR2 Where fy is the steel yield strength Table 2 EO is Young s modulus of steel and b is the strain hardening ratio ratio between post yield tangent and initial elastic tangent RO cR1 and cR2 are parameters to control the transition from elastic to plastic branches The number of longitudinal bars 1s calculated a
36. ANALYSIS Save Model amp Run Analysis STEP 3 COMPUTE REPAIR COST L PERE ANB Fig 63 Post processing capabilities menu options available in a base shaking analysis 62 Analysis Options i Unit System 4 soil Materials solid Element Optian Cy c Units Cc ajil lode Brick Elemerit oe Enolish Units C Nonlinear Node Standard Brick Element s C Node Bhar Brick Element Mesh Display i if Show Axes Show Intermediate Modes for 20 ode Element Advanced Options F Output Data FP Analysis with no gravity weight applied Include Column Response Protiles amp Wot good for sressure dependent structural or soil materials and Relationships alsa not good tor inclined model orinclined ground surface i Include Soil Displacement Use Global Elastic Material for Application of Own Weight Gisele ete Initial Lateral vertical Confinement Ratio 0 1 0 9 Include Sail Stress Strain Young s Modulus und Sutace Inclination Angle 0 30 oeg f Display Deformed Mesh for Final Step Pia ie bees CY ee aean Aea Doo Dnk Recommended for Large Models Abutment Rigid Link Stifness x Pile Stifness i OOUOOO0000 BOAO Cancel Change Opensees Options Change Rayleigh Damping Fig 64 Analysis options in BridgePBEE BridgePBEE defaultCase pbe TAR File Execute ai s vm Help PG Quantities for All Motions EF Model In Bridge amp Ground Peak Accelerations for All Mo
37. BridgePBEE OpenSees 3D Pushover and Earthquake Analysis of Single Column 2 span Bridges User Manual Beta 1 0 http peer berkeley edu bridgepbee Jinchi Lu Kevin Mackie and Ahmed Elgamal December 201 1 l U Table of Contents ETOJN Oeren E T E re eer eee neers eae l E OVVIO W eee E ET T E teat ee ees l E Dy CREGUT me Sea T O eee eae ae 2 L3 AACKMO WICC CIICIIS skeerne E EEE E EE OAE T EA ETAO 3 bas 8 0h eea a R a A A R 4 Geine Stained uei a E E 5 2 Dar 0 reinen e a E E E E 5 A2 ANECO aa E E E E E N 5 22N MU BaT oea a E A E EE a E ATA eas 6 Dae Model TMU WndoWesssswe den 7 Doo Pinte Eiement Mesh Window otnenea n e acta cee Aeon toca 8 Bidee Mode Meare me een mene te mee tree oer ce ee te meme are Cer Cer tree ne Beene ane eee eee ne 9 Sel Couma Tare ssi ci ated O atten Meant ta E EA 10 ILL Column Linear Material Properes pueraria iE RE AA 11 zE2 Nonlinear Fiber SE CUOM eenia E O 12 SL Colin Delow Grade oroe E E g e e 17 S22 Bad2e Deck Paramete Seinri E E A a 17 29 Embankment Pardel Seige nE a a A 18 Se AUMEN Parametrs eee a a a E ee ea ee 19 JAF BSC AA DUI ONE geese es siisinnis vcone ducts aston bcs er ee ene a O aiae n EEA OE a OE A ai 19 Dee RONE Mode leran RN 21 343 lt Simpliited Model SDC 2004 arein a E E den 22 DAA SPME Mode leenen a lgecuruvieteoyltoutueudatetwa vice lwounsbeteo nite 26 SPs amet gt Oo 2081 0 ire cin 10 Brame ee Rr Ree ne Roun ne ten ts PRE enone ere
38. Cer Se ERC ea eee eee 30 DAO DDC O10 Cay oa E E ae ence ee E 30 FP EPR OR 8 0 oC ee en ee em ee 30 SO HPO Mode lera e ean utente on ee ee 32 SOLPI A UG err tat cna te asiars Senses ence E sree sta aie Stasis tea tee Degas ore ETA 32 Pushover Ge FICE VAIS Analyses osso or A T esate 37 SA Load PACT nyien e ee en eae emer 37 5 1 1 Pushover by User Defined Load Pattern U Push ccc cccccccceceeeeeeeeeeeeees 38 2 Outputior Pushover Analysis cssceiseiet adams tueeian AN 40 5 2 1 Column Response Time Histories and Profiles ccccccessssseecccceeeeeeeseeeeeeeees 41 5 2 2 Column Response Relationships eo00ssoeeeennnssssssseeresssssssseeressssssseeereesssssssrerees 4 5 2 3 Abutment Force Displacement and Response Time Histories 42 SLAS MDS LOTIS IVS SI aod cece iceninbastic des wositciussbesnalnncneaiseniavastecenwod OE E uosiauaeete 42 Ded Eigenvalue AMIAIY S16 sis x6 step ce ansteoh det ara es A a cease teaciees 43 PBEE Analysis Ground Shaking 335i tecotaleibaveavoatatehsdauesenahdooussoutuadeenesenoraaatous 45 6 1 Theory and Implementation of PBEE Analysis c cece ccececcceccccececeeeeeeeeeaaeseeeeeeeeeeees 45 6 2 Input Necessary for User defined PBEE Quantities ccccccccccccccceceeceeaeeeeeeseeeeeees 48 6 3 Definition specification of PBEE input motion ensemble suite eeeeccecceeeeeeees 49 63 4 Available Ground MOODS xii ccsasaeaieissassivaascasieactuhcnchl edeivisiaibiv
39. E REPAIR COST PBEE Analysis Fig 39 Steps to define a load pattern for pushover analysis 5 1 Load Pattern The pushover options include monotonic pushover as well as pushover by a user defined loading pattern U Push Please see the next section for how to define a U Push file Two methods of pushover are available Fig 40 force based and displacement based If Force Based Method is chosen please enter the parameters of force increment per step Longitudinal X Force Transverse Y Force Vertical Z Force Moment X Moment Y and Moment Z 37 If Displacement Based Method is chosen please enter the displacement increment parameters per step Longitudinal Displacement Transverse Displacement Vertical Displacement Rotation around X Rotation around Y and Rotation around Z The pushover load displacement linearly increases with step in a monotonic pushover mode The load displacement is applied at the column top Pushover Define UPish Force Increment Per Step Logitudinal Force 1 kN Transverse Mri Force oO kM Vertical z Force 0 kN O Eker Oo Ne Esra f L Push Moment of Moment ofr Moment of z Applied Location Column Head pmu L Method Force Based Method C DisplacementBased Method Displacement Increment Per Step Longitudinal Displacement Transverse Displacement vertical Displacement Rotation around Rotation around r Rota
40. EE Analysis For Help press F1 Unit S1 Fig 56 OpenSees analysis in progress 6 5 PBEE Analysis Once the FE analysis of all motions in the ensemble is complete click PBEE Analysis Fig 2 to display PBEE Analysis PBEE Analysis Damage States Repair Unit Costs Production Rates Compute Repair Cost Intensity Measure SRSS PGY F Compute Repair Time Display Results as a Function of Intensity Measure Yv Intensity Measure S5R55 PGY Hazard Level for 2 of Probability of Exceedance 160 cm sec Hazard Lewel for 5 of Probability of Exceedance feo cm sec Display Mazari Cuvee Hazard Level for 10 of Probability of Exceedance fi 0 cm sec Interval in Year 50 Year Click Here for EPS Version of All PBEE Figures Display Disaggregation Intensity Measure SRSS PGY Intensity Measure Value f 0 cm sec Fig 57 PBEE analysis window 55 6 5 1 PBEE Quantities In the figure above Fig 57 only Damage States can be currently modified by the user directly within the user interface however this is an advanced feature that should be exercised with care or just left as is Under Damage States Fig 58 Lambda 1s the median EDP that defines onset of the damage state and is one parameter of the assumed lognormal distribution of damage when conditioned in EDP It has the same units as the EDP for the selected PG Beta is the lognormal standard deviation and is the s
41. Fig 73 Column response output options 71 Column Response Relationships Motion SCS Load displacement at 6 71 m column Top in Longitudinal direction Load Displacement Curve 6 71 m above ground surface column top File load dispX 6 71m txt Fig 74 Load displacement curve at column top Column Response Relationships Motion SCS Moment curvature at 6 71 m column Top in Longitudinal direction Moment Curvature Curve 6 71 m above ground surface column top File curvX 6 71m txt Fig 75 Moment curvature curve at column top 12 7 1 3 Abutment Responses Time Histories The abutment responses can be accessed by clicking menu Display and then Abutment Responses Fig 76 The abutment responses window includes the following options Fig 77 e Force Displacement Relationships e Relative Deck end Abutment Displacement Time Histories e Resisting Force Time Histories e Pile Cap Displacement Time Histories where Pile Cap refers to the embankment base right below the deck end please see Fig 86 in Section 7 1 6 Three directions longitudinal transverse and vertical directions of the above responses for both left and right abutments are all displayed Fig 78 shows the abutment response time histories The force refers to the resisting force acting on deck end and the displacement refers to the relative deck end abutment displacement BridgePBEE defaultCase pbe ER File Execute Es EV H
42. File txt Fig 14 Stress strain curve of Concrete02 material for the cover concrete default values employed C represents compression and T represents tension Axial Load Negative is Compression h1 915 kN Maximum Curvature joz rad m Number of Analysis Increments to Max Curvature 00 Unloading Steps Re calculate amp Wew MomentCurvature Curse Close vyindow Moment Curvature Relationship Moment Curvature Response File mcFile txt Fig 15 Moment curvature response for the column with default steel and concrete parameters and the deck weight 11 915 kN applied at the column top 16 3 1 3 Column below Grade If Use Different Properties for Column below Grade is checked Fig 7 the column below grade can be different from the portion above grade In this case the column below grade is assumed to be elastic only The column diameter and the Young s Modulus are required to define Fig 7 the properties of this elastic column below grade 3 2 Bridge Deck Parameters To define the deck please follow the steps shown in Fig 16 The default values are listed in Tables 4 and 5 below The default values were obtained from a two cell reinforced concrete box girder deck configuration Bridge Model Column Embankment tf Circular E Deck Properties Diameter Total Colurin Length fs Modulus 2a000000 KPa Column Length above Grad hear Modulus 11500000 KPa Cross Section Area 57200 mz
43. Help I Bridge Only Zoomin xY yz xz 3D lt gt Up Dn BridgePBEE For Help press F1 b Fig 118 Mesh refinement example 2 a Change Number of Mesh Layers in the vertical direction b the resulting mesh 111 General Definition ip Horizontal Meshing Horizontal Meshing Vertical Meshing M Minimize Number of Elements in Horizontal Direction Mesh Layer Length From Col Center rn 1 Col Radius JE Uniform Ratio of Element Meshing Length over Next x Tos ToT es 22 195 3 22 195 eo BE I 4 Embankment Pa TTT x aaqa Mesh Adjustment beside Embankment P Activate Adjusting Mesh beside Embankment size of 1st Layer Factor of Deck Width Ratio of Element Size over Next 1 means Uniform BridgePBEE Finite Element Mesh EF File Execute Display Help i i T Bridge Only Zoomin xY yz xz 3D lt gt Up Dn BridgePBEE For Help press F1 b Fig 119 Mesh refinement example 3 a Change meshing controlling parameters 1n the horizontal direction b the resulting mesh 112 9 Appendix B Simple Pushover Examples Bridge on Rigid Ground Steps to build a bridge model on a fixed base In BridgePBEE a very stiff ground mesh 1s currently used to simulate a fixed base scenario Simplest Approach Start with Example 1 at http peer berkeley edu bridgepbee and modify the bridge model to match your specifications Alternative Approach To mak
44. Label Elevation m Marks dots DataSet End 1 49572e 004 71000e 000 ve doloe 90000e 000 2 43401e 010 i 00000e 001 2 20660e 010 9 29000e7000 For Help press Fi Unit SI Z Fig 121 Fixed end beam simulation using BridgePBEE 3 Bridge self weight with rigid Column amp roller abutment model The distributed load of deck p 130 3 kN m Half of the bridge length L 45 m Elastic modulus of deck 28 000 000 kPa Moment of Inertia 2 81 m Fig 122 displays the deformation of bridge deck under gravity The maximum is 0 0372 m Fig 122 The close form solution gives 0 0368 m Fig 123 115 Deformed Mesh Due to gravity bridge include z disp contour 3D view 7 tiot Zoom In Zoom Out Zoom Frame xY YZ xZ 3D gt Up Dn Unit m 6 007 e 011 1 662e 003 3 724e 003 5 586e 003 7 448e 003 9 309e 003 1 117e 002 1 303e 002 1 490e 002 1 676e 002 1 662e 002 2 048e 002 2 234e 002 2 420e 002 2 607 e 002 2 793e 002 2 979e 002 3 165e 002 3 351 e 002 3 538e 002 3 724e 002 Scale Factor epo ARE i iy main I v Endless Play V Bridge Only Displacement H L 5 o p Lan gar id 48 EI Ww W SEa 64 as Krp 0 0368 m ee leg 6 EI Fig 123 Fixed end roller beam analytical solution from efunda com 116 4 Nonlinear Column Bridge Pushover a Longitudinal Pushover Fig 124 EELS Response Relationships Load displacement at 6 71 m column To
45. Mackie et al 2010 and depicted conceptually in Fig 49 In the LLRCAT methodology each bridge system is disaggregated into independent structural or non structural components or subassemblies defined as performance groups PGs that are damaged assessed and repaired together using a specific combination of different repair methods Demands on the bridge system and components are determined using 3D nonlinear time history analysis under multiple component earthquake excitation The damage in each of the PGs is characterized according to several discrete damage states DSs that are defined by distributions of critical EDPs A feature of the LLRCAT implementation used is the introduction of a repair model between the original PEER abstraction of DM and DV Jumping directly from DMs to repair costs 1s difficult to accomplish because it skips over the details of repair design and the variability of cost and time estimating Creating these two additional models makes it easier to implement a step by step procedure for defining the models The repair model and cost model are created through the process of schematic design of repairs and estimating the costs of those designs Different repair methods are employed for the various damage states of each PG or bridge component The repair methods for each PG require a combination of several repair quantities Qs Repair quantities for all PGs are then combined with due consideration of the correlation betwee
46. W Harzard Curves Return Period File ReturnPd RT txt Fig 105 Return period against total repair time W Harzard Curves Mean Annual Frequency of Exceedance Loss File HazardDV_RT txt Mean Annual Total Repair Time 0 668341 CWD Fig 106 Mean annual frequency of exceedance loss against total repair time 99 7 2 3 Disaggregation Figs 107 109 display the disaggregation Fig 57 of expected cost by performance group the disaggregation of expected cost by repair quantities and the disaggregation of expected time by repair quantities respectively In thie figures below the disaggregation 1s performed at an intensity of 100 cm s PGV for all three figures a user IM and value as shown in Fig 57 This IM and its value are shown in the plot titles E PBEE Analysis Output Disaggregation of Expected Cost by Performance Group PGW 100 cm sec File Disagg txt Max tangential drift ratio SRSS col Residual tangential drift ratio SRSS col Max long relative deck end abut disp left Max long relative deck end abut disp right Max absolute bearing disp left abut Max absolute bearing disp right abut Residual vertical disp left abut Residual vertical disp fright abut Residual pile cap disp SRSS left abut PG10 Residual pile cap disp SASS right abut PG11 Residual pile cap disp SRSS col Fig 107 Disaggregation of expected cost by performance group 100 MM PBEE Analy
47. Y OF CALIFORNIA HAS NWO OBLIGATIONS TO PROVIDE MAINTENANCE SUPPORT UPDATES ENHANCEMENTS OR MODIFICATIONS Fig 4 BridgePBEE copyright and disclaimer window 2 2 2 Model Input Window The model input window controls definitions of the model and analysis options which are organized into three regions Fig 2 e Step 1 Define Model Controls analysis types pushover analysis eigenvalue analysis or ground shaking and analysis options also controls definitions of bridge and soil strata including material properties Meshing parameters are also defined e Step 2 Execute FE Analysis Controls execution of the finite element analysis and display the progress bar e Step 3 Compute Repair Cost Controls the PBEE analysis 2 2 0 Finite Element Mesh Window The finite element mesh window Fig 2 displays the generated mesh In this window the mesh can be rotated by dragging the mouse moved in 4 directions by pressing keys of LEFT ARROW RIGHT ARROW UP ARROW or DOWN ARROW respectively The view can be zoomed in by pressing key F9 out by pressing key F10 or frame by pressing key F11 To display a 2D view press key F2 for Plane XY where X is the longitudinal direction Y the transverse direction F3 for Plane YZ where Z is the vertical direction or F4 for Plane XZ An isometric view of the mesh can be achieved by pressing key F5 Alternatively users can use the corresponding b
48. ableriaeacdeeacne deste 49 6 3 2 Specifications of PBEE Input Motions cc ecccccccccccccccessseeeccceeeeesaaeeseeeeeeees 50 7 10 11 13 OA Save Mode knd RUM AMAL SI rrano e E E EO E OTEO OE 54 09 PBEEADAYS S eo E a O a 55 Codd PEBER 1011 0115 18 en N 56 6 5 2 Compute Repair C OSTA TINE ai a e a aenaeelecdien 58 O5 5 gt Compie Hazard Curves canan ae E E 59 OGSA Compute DISA oregoni e T A A 60 Time History and PBEE OUMU ro E E 61 Tal Tne Hisor Output ONNE S xst2t a escas TE T 6l 7 1 1 Column Response Time Histories and Profiles cccccssseseeecccceeeceaeeeseeeeeees 64 A12 Column Response RelanonshiPSissnssirine a Aa 70 7 1 3 Abutment Responses Time HIStoies iissinsdeieisiseceaustidvaniehadicacssadtiuivnedsausideanaaieess 73 Ped Delorned Mosher irenesnen eien er E a 76 kko SolResponse Time Hist rie S scianca an a e ce LEE PBEE Output Quante Siora ns S E E E EEN 81 7 1 7 Bridge Peak Accelerations for All MOtions ccccesssssseeeeeeeececeeeeeeeeeeeeasaeeeeesees 88 7 1 8 Maximum Column amp Abutment Forces for All Motions ccccccccccccccssseeeeeeeees 90 ke PBEE OCON S oh sharing tS date attested caren Rea edt Pecado eee caste deeacaen eis ates 93 Tet REDIT COS Ce MINS oracles dete ete candela adeno tia oe aoe anesadne ea eeaata 93 B2 Hazard CV CS pater ch eee ace tne alas ch eo scent nie leash ae ced cated 96 Pity Disagree aO soson E E O OO 100 Ta BPS Verro All PREP TIOUN Sc
49. abutment shown in Fig 86 relative to the deck end node e g Node C for the right abutment shown in Fig 86 The residual value is used value at the final time step PG9 Residual pile cap displacement SRSS left abutment PG10 Residual pile cap displacement SRSS right abutment These PGs address possible damage below grade due to lateral translation of the piles and pile caps While not a direct measure pile cap displacement was selected as it would not require knowledge or observations of piles below grade The EDP is defined by calculating the SRSS value of the 2 horizontal displacements of the abutment pile cap node e g Node D for the right abutment shown in Fig 86 The residual is obtained from the value at the final time step PG11 Residual pile cap displacement SRSS column This quantity is analogous to the two previous PG but is representative of response and damage at the abutment foundations The EDP 1s obtained by calculating the SRSS value of the 2 horizontal displacements of the column pile cap node e g Node O shown in Fig 86 and taking the value at the final time step The PG Performance Group quantities for all input motions can be accessed by clicking menu Display Fig 3 and then PG Quantities for All Motion Fig 88 The window to display PG quantities is shown in Fig 89 The PG quantities are displayed against any of the 22 intensity measures including 11 for the input acceleration and the other 11
50. ackie U Central Florida For questions or remarks please send email to Dr Jinchi Lu jinlu ucsd edu Dr Kevin Mackie Kevin Mackie ucf edu or Dr Ahmed Elgamal elgamal ucsd edu BridgePBEE is written in Microsoft Visual C 2005 with Microsoft Foundation Class MFC Library version 8 0 The Java Applet package used to display graphical results in BridgePBEE is obtained from the website http ptolemy eecs berkeley edu GIF images are generated with GNUPLOT for MS Windows 32 bit Version 3 7 available at http www gnuplot org 1 4 Units The SI unit system is used throughout the user interface For conversion between SI and English Units please check http www unit conversion info Some commonly used quantities can be converted as follows e 1kPa 0 14503789 psi e lpsi 6 89475 kPa e lm 39 37 in e lin 0 0254 m 2 Getting Started 2 1 Start Up On Windows start BridgePBEE from the Start button or from an icon on your desktop To Start BridgePBEE from the Start button 1 Click Start and then select Programs 2 Select the BridgePBEE folder 3 Click on BridgePBEE The BridgePBEE main window is shown in Fig 2 BridgePBEE Untitled File Execute Display Help Model Input x Finite Element Mesh Re Generate Bridge Only Zoom In Frame STEP 1 DEFINE MODEL Serene Out Frame Analysis Type C Pushover C Eigenvalue PBEE Analysis PBEE Motions Model Definition Bridge Parameter
51. ake New Folder a cate seconds Compute Response for f Time Step 0 02 seconds There are 5 bins in this motion set Fig 126 Choosing PBEE motion set 119 Earthquake name Vertical component fi A ELC Sele File Edit View Favgrites Tools Help ae Motion Address c MyDoc _gBEE PEEEMotionSet1 LMLR BORREGO A Go set name Psigers A Name Size Type Date Modified AOA PBEEMotionSet1 E A ELC UP AT2 info 1KB INFOFile 2 7 2009 3 56 PM SMR FS A ELC UP AT2 data 53KB DATAFie 2 7 2009 3 56 PM Bin name El BORREGO A ELC270 AT2 info 1KB INFOFile 2 7 2009 3 56 PM O atic A ELC270 AT2 data 53KB DATAFie 2 7 2009 3 56 PM amp E omar A ELC180 AT2 info 1KB INFOFile 2 7 2009 3 56PM E E NORTHR A ELC180 AT2 data 53KB DATAFie 2 7 2009 3 56 PM C MSR 2 C Near G SMR i SMSR MT Motion name Horizontal components Fig 127 Directory structure of PBEE motion set C MyDoc _PBEE PBEEMotionSet1 LMLR BOR O File Edit Search View Encoding Language Settings Macro Run TextFX Plugins Window x cH ABS aise sD aC me A ELC180 AT2 info Data points NPTS 4000 Sampling period DI sec 0 0100 ay gt Fa 3 lt i Ln 3 Col 1 Sel UNIX Fig 128 Sample info file 120 B C MyDoc _PBEE PBEEMotionSet 1 LMLR BORR Sel File Edit Search View Encoding Language Settings Macro Run TextFx Plugins Window SAH Ss isa ses Doc ms A ELC180 AT 2 data 0 118107E 02 0 136645E 02 0 900667E 03 0 64
52. al Studio 2005 00 00 ccccccccceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeseeeeees 130 Fig 134 Replacing file PBEE DLL under the installation folder ceccccceeeeeeeeeeeeeeeees 131 vi List of Tables Table 1 Default Values for Column RC Section Properties 2 0 eccccccccccececcessseeeecceeeeeeeaneeees 14 Table 2 Default Values for Steel02 Material Properties cc ceseececcccceceeeeeeeeeeecceeeeeaaeeeees 14 Table 3 Default values for ConcreteO2 Material Properties 0 c cc ecccccccccceeccessseeeeceeeeeeeaaeeeees 14 Tibe A Deria Values tor Side DeCK acs eees ts eat eee ee 18 Table 5 Default Values for Deck Material Properties 2 0 0 0 ccccccseeseseeccceeeecceeeeeeeeecceeeeeaaeeeees 18 Table 6 Geometric and Material Properties of a Bearing Pad cc cccccssssseseseeeeeeeeeeeeeeeeees 27 Table 7 Spring Abutment Model Properties seiss tieniti nana E O E A 28 Table g Abument C OMMGUTALION S eiei a a E ele 28 Tabe OC lay Materials POP E Se ea E E E 36 Table WO PEE R par Qaim eS oreren inn nade I a E E O E TNE 59 Table 11 PBEE Performance Groups i sieisssdvedicesioneinsonvslasaiaededviodvedideniosneasawhelehelgsiodasiuestehonyelavss 8l Vil 1 Introduction 1 1 Overview BridgePBEE is a PC based graphical pre and post processor user interface for conducting Performance Based Earthquake Engineering PBEE studies for bridge ground systems The user interface allows for e Management of ground motions Simplified struct
53. ance groups are not necessarily the same as load resisting structural components For example non structural components may also form a performance group since they also suffer damage and contribute to repair costs The notion of a performance group also allows grouping several components together for related repair work For example it is difficult to separate all of the individual structural components that comprise a seat type abutment shear key back wall bearings approach slab etc as they all interact during seismic excitation and their associated repair methods are coupled Therefore the abutment repair group incorporates the fact that repairs to the back wall require excavation of the approach slab Performance groups also address the issue of potentially double counting related repair items Some repair items require the same preparation work such as soil excavation For example both back wall repair and enlargement of an abutment foundation require at least 4 ft of excavation behind the back wall If these repair items were in different PGs then double counting the excavation would be a problem Bundling these related repair methods within a PG allows for independent consideration of each PG The correlation between repair items from the PGs is handled at the demand model level in the methodology A total of 11 PGs are considered PGI Max column drift ratio PG2 Residual column drift ratio PG3 Max relative deck end abutment displacem
54. ap closure the superstructure forces are transmitted through the elastomeric bearing pads to the stem wall and subsequently to the piles and backfill in a series system After gap closure the superstructure bears directly on the abutment back wall and mobilizes the full passive backfill pressure Transverse Response The transverse response is based on the system response of the elastomeric bearing pads exterior concrete shear keys abutment piles wing walls and backfill material The bearing pad model discussed above is used with uncoupled behavior with respect to the longitudinal direction The constitutive model of the exterior shear keys is derived from experimental tests Megally et al 2003 The parallel system of transverse bearing pads and shear keys are labeled T1 in Fig 27 Vertical Response The vertical response of the abutment model includes the vertical stiffness of the bearing pads V1 in series with the vertical stiffness of the trapezoidal embankment V2 The user can modify the vertical tensile force factor for the bearing pads multiplier on the vertical bearing strength The embankment stiffness per unit length of embankment was obtained from Zhang and Makris 2000 and modified using the critical length to obtain a lumped stiffness Model Characteristics Each bearing pad has a height A of 0 0508 m 2 in and a side length square of 0 508 m 20 in The properties of a bearing pad are listed in Table 6 The abu
55. arch Center University of California Berkeley California Kotsoglu A and Pantazopoulou S 2006 Modeling of Embankment Flexibility and Soil structure Interaction in Integral Bridges Proceedings of First European Conference on Earthquake Engineering and Seismology September 3 8 Geneva Switzerland Caltrans SDC 2004 Caltrans Seismic Design Criteria Version 1 3 California Department of Transportation Sacramento California Caltrans SDC 2010 Caltrans Seismic Design Criteria Version 1 6 California Department of Transportation Sacramento California Elgamal A Yang Z Parra E and Ragheb A 2003 Modeling of cyclic mobility in saturated cohesionless soils International Journal of Plasticity 19 6 883 905 Elgamal A and Lu J 2009 A Framework for 3D finite element analysis of lateral pile system response Proceedings of the 2009 International Foundation Congress and Equipment Expo Contemporary Topics in In Situ Testing Analysis and Reliability of Foundations ASCE GSP 186 M Iskander D F Laefer and M H Hussein Editors Orlando Florida March 15 19 pp 616 623 Elgamal A Jinchi Lu J and Forcellini D 2009a Mitigation of liquefaction induced lateral deformation in a sloping stratum 3D numerical simulation Journal of geotechnical and geoenvironmental engineering ASCE Vol 135 No 11 November 1672 1682 Elgamal A Lu J Yang Z and Shantz T 2009b Scenario focused three dimensional
56. below Grade Giarmeler pungs Mogulus Deck parameters Abutme tp S Deck Width 11 4 im Number of E Deck Depth 1 83 ml Jeck Froperies Cancel Fig 7 Bridge Model window 3 1 Column Parameters Parameters to define the geometrical configurations of the column include refer to Fig 7 e Circular column cross section type Currently only circular cross section is available e Diameter column diameter which is 1 22 m by default e Total Column Length the total length of the column including the pile shaft below grade The default value is 12 m e Column Length above Grade the length of the column above grade The default value is 6 71 m To define the material properties of the column click Column Properties There are 2 scenarios in this case 1 Linear material properties will be defined if Linear Column is checked 2 Nonlinear Fiber Section will be defined if Linear Column is unchecked Please see next section for detailed information 10 3 1 1 Column Linear Material Properties To define the linear material properties of the column follow the steps shown in Fig 8 Parameters to define a linear column include Fig 8 e Young s Modulus Young s Modulus of the column The default value is 3 x 10 kPa e Moment of Inertia Transverse Axis the default value I 1D 64 0 108745 m where D column diameter D 1 2
57. cccceccceeeeeeeeeeceeeeeeeeeeeeeeeeeees 11 Fi 9 Steps todefinea nonlinear Fiber Section s 3 i00i decdicuonicoics niies a i e 12 Fi SEO TADS SC CU ON WACO Waa teat insctuasdeee ante ito caueta uae ineivehe eanuee cates aidedaeateenneheles 13 Fig 11 Column fiber section based on PEER best modeling practices report Berry and B 0Xe 6 075 6 ae 0 LS EEA ee oe ne eee anne ee re AAE E mT eee ee eon ne ae T E eee 13 Fig 12 Stress strain curve for Steel02 material default values employed C represents compression and T represents tension surrat oriens neg teehee sonnneianee 15 Fig 13 Stress strain curve of Concrete02 material for the core concrete default values employed C represents compression and T represents tension cccsseseeseeseeeeeeeeeeeeeeeees 15 Fig 14 Stress strain curve of Concrete02 material for the cover concrete default values employed C represents compression and T represents tension ccccseesseseeeeeeeeeeeeeeeeeeees 16 Fig 15 Moment curvature response for the column with default steel and concrete parameters and the deck weight 11 915 kN applied at the column top 000nnnnnnnnnnnnnnsssssssssoeeeeenesnnsssssssssse 16 Fig 16 Steps to define the deck geometrical configuration and material properties 17 Fig 17 Elastic abutment model csreeceiieni nenea aa a aa 19 Fig 18 Steps to define Elastic abutment model ccccccceecceeeeeeeeeeeeeeeeeeee
58. cccceceeseeeseeeccceeecaeaeeeeeeeceeseaaeneees 70 Fig 72 Menu items to access the column response relationshipS cccccccssssessesessseeeeeeeeeeeeees 71 Fig 73 Column response Output OPTIONS steieren o E aE ET ETN TEE Aia 71 Fig 74 Load displacement Curve at COlUIMM LOD serienn e i a T2 Fig 75 Moment curvature curve at column top eeeesseooessosesrrrrrrrrrrrerrrrrrrerrrrerrererrrrrrerrrrerees 12 1V Fig 76 Menu items to access the abutment reSPOMNSeS ccccceeesesseessseeseeeeeeeeeeeeeeeeeeeeeeeeeees 73 Fig 77 Menu items to access the abutment reSPOMNe cccccesesesseesesseeeeeeeeeeeeeeeeeeeeeeeeeeeees 74 Fig 78 Abutment response time histories scroll down to see all directions a abutment force displacement relationships b relative deck end abutment displacement time histories c resisting force time histories and d abutment pile cap time histories cceeeeseeeeeeeeeeeeeeees 75 Fig 79 Menu items to access the deformed MOS havi sisicsecsasvcssasesesssucsiorerdecveuaseseneescetesteheteioeeadens 76 Fia SO DelOmned MeS porisee e a a a e a 77 Fig Sl Menu Items to access the soil TESPORSCS 4 asa ae ee eee 78 Fig 82 Response options for soil time histories cc eeeeeeeeessseeeeccceceeeeecessaaeeeesssseeeeeeeeeeeeeees 79 Fig 83 Planes for locations of the soil response time histories cccccseeseseseeeeeeeeeeeeeeeeeees 79 Fig 84 Locations o
59. ce the unknown parameters can be determined numerically from the three values input by the user 2 5 and 10 probability of exceedance in 50 years On the site hazard curves plotted in the interface both the data points and the fitted curve are shown Fig 102 Vim im k im 4 The power law fit to the hazard data is used to compute the loss hazards The loss model probability of exceeding RCR or RT conditioned on intensity levels is integrated with the absolute value of the derivative of this IM hazard to obtain the loss hazard curve MAF of exceeding either RCR or RT Details of the numerical integration are presented in Mackie et al 2008 and other sources The loss hazard curves both for repair cost and repair time are further integrated over intensity to yield mean annual loss For example in Fig 104 the mean annual repair cost ratio expected for the bridge at the given site is 0 05 of the replacement cost MS Harzard Curves Mean Annual Frequency of Exceedance Ground Motion File HazardIM txt Fig 102 Mean annual frequency of exceedance ground motion 97 MS Harzard Curves Return Period File ReturnPd txt Fig 103 Return period against total repair cost ratio W Harzard Curves Mean Annual Frequency of Exceedance Loss File HazardDV txt Mean Annual Total Repair Cost Ratio 0 047664 Fig 104 Mean annual frequency of exceedance loss against total repair cost ratio 98
60. ch slab Aggregate base approach slab Bar reinforcing steel bridge Bar reinforcing steel footing retaining wv Epoxy inject cracks Repair minor spalls Column steel casing Joint seal assembly Elastomeric bearings Drill and bond dowel Furnish steel pipe pile Drive steel pipe pile Drive abutment pipe pile Asphalt concrete Mud jacking Bridge removal column Bridge removal portion Approach slab removal Clean deck for methacrylate Furnish methacrylate Treat bridge deck Barrier rall Re center column Unit CAD Crew Working Day am Oo d Oo 1 ts tu Pa Fig 61 Production Rates window 6 5 2 Compute Repair Cost amp Time Now you can select any of the Intensity Measures e g PGV above and then click Compute Repair Cost or Compute Repair Time in Fig 57 to display the probabilistic repair cost and Crew Working time in Days CWD along with Standard Deviation displayed for each PG eleven of them and each repair quantity 29 of them see Table 10 as shown below See Section 7 2 1 for the detailed output To convert all PBEE figures to the EPS format click Click Here for EPS Version of All PBEE Figures A MS Word window with the EPS figures included in the document will pop up once the converting is done please see Section 7 2 4 for the detailed output 58 Table 10 PBEE Repair Quantities Item Item name l Structure excavation 2 Structure backfill 3 Temporary support superstructure
61. column is time respectively of the tangential drift recorder file e g A ELC dft The taxi variable is the second column the first column is time of the inflection point recorder file e g A ELC ifp For the transverse tangential drift ratio the tdx1 and tdx2 variables are the fourth and fifth column of the dft file and the taxi variable is the third column of the ifp file Fig 86 Finite element mesh in BridgePBEE Node O Column base node at ground surface Node A Column top node Node B Deck end node Node C Abutment top node having the same coordinates as Node B Nodes B are C are connected by an abutment model Node D Abutment pile cap node 82 tdxl amp tdx2 the tangent drift recorder file at time step i tdxi the inflection point recorder at time step i tdx tangential drift ratio if fabs tdxi lt l1e 20 4 tdx tdx2 H tdxi else if fabs H tdxi lt le 20 tdx tdx1 tdxi else tdx _ max fabs tdx1 tdxi fabs tdx2 H tdxi tdx tdx sgn tdx2 H tdxi if fabs tdx2 H tdxi lt le 20 tdx 0 else if tdx2 H tdxi gt 0 tdx tdx return tdx Fig 87 Code snippet to calculate the tangential drift ratio of column PG3 Maximum longitudinal relative deck end abutment displacement left PG4 Maximum longitudinal relative deck end abutment displacement right These two PGs are intended to address the issue o
62. cy of exceedance loss against total repair time ccce 99 Fig 107 Disaggregation of expected cost by performance group ccceeeeeseeeeeessssseeesseeeeens 100 Fig 108 Disaggregation of expected repair cost by repair QuaNntitieS cccseesseessseeeseeseeees 101 Fig 109 Disaggregation of expected repair time by repair quantities ccceccceeeeeeeeeeeeeeeeees 102 Fig 10 Converting all PBEE figur s to EPS formatis es cistieveseitiee a 103 Fig 111 Schematic view of an idealized single bent bridge system cccseeessseeeeeeeeeeeeees 104 Fig 112 General meshing controlling parameters default values cc eesessessssseeeeeeeeeeeees 105 Fig 113 Meshing controlling parameters for horizontal direction default values 106 Fig 114 Adjusting mesh near embankment a before adjusting b after adjusting 107 Fig 115 Meshing controlling parameters for vertical direction default values 0008 108 Fig 116 Finite element mesh created with default values cccccceeeeesseesseeseeeeeeceeeeeeeeeeeees 109 Fig 117 Mesh refinement example 1 a Change Num of Slices to 32 b the resulting mesh essai ee sea ast sa ha se abe E A ovine acted Monica atten ca AE one ta TE oe agua tena o faa 110 Fig 118 Mesh refinement example 2 a Change Number of Mesh Layers in the vertical direcHOn DB THE TESUIMIN SIME SIMs neenaiea a a
63. d The Regents grants permission without fee and without a written license agreement for a use of this software and tts documentation by educational research and non profit entities for noncommercial purposes only and b use reproduction and modification of this software by other entities for internal purposes only Permission to incorporate this software into commercial products may be obtained by contacting the University of California This sofware program and documentation are copyrighted by The Regents of the University of California The software program and documentation are supplied as is without any accompanying services from The Regents The Regents does not warrant that the operation of the program will be uninterrupted or errartree The end user understands that the program was developed for research purposes and is advised notto rely exclusively on the program for any reason IN WO EVENT SHALL THE UNIVERSITY OF CALIFORNIA BE LIABLE TO ANY PARTY FOR DIRECT INDIRECT SPECIAL INCIDENTAL OR CONSEQUENTIAL DAMAGES INCLUDING LOST PROFITS ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION EVEN IF THE UNIVERSITY OF CALIFORNIA HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGE THE UNIVERSITY OF CALIFORNIA SPECIFICALLY DISCLAIMS ANY WARBAM TIES INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE THE SOFTWARE PROVIDED HEREUNDER IS ON AN AS IS BASIS AND THE UNIVERSIT
64. duction Rates WING OW sarerea a a a a Ghee aitoti eueaeeieals 58 Fig 62 Post processing capabilities menu options available in a pushover analysis 62 Fig 63 Post processing capabilities menu options available in a base shaking analysis 62 Fig 64 Analysis options in BridgePBEE cccccceseeesssesesseeeeseeeseeseeeeseeeeeeeeeeeeeeeeeeeeeeeeeeeeees 63 Fig 65 Steps to display output for a different input motion a click menu Display Fig 3 b SC PEC am APU NOLO Aisecsesmaceranceeceasuncsdu aus ceesicausseete aches gauge es E or easmaunse T 64 Fig 66 Menu items to access the column response time histories and response profiles 66 Fig 67 Response time histories and profiles for column and pile shaft displacement is shown at the nodes only one element is used above ground ccccceseseeecccceeeeeeeeeeeeaseeeesseseeeeeeeeees 67 Fig 68 Bending moment profile in the longitudinal plane eceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeens 67 Fis 69 Response SUMIMIALY wird sisi hie cians Aina tata Ws ead Hu ew leas lees 68 Fig 70 Column longitudinal displacement response time histories a response profiles at specific load steps b response time histories at different elevations cccccceeeeeeeeeeeeeeeeeees 69 Fig 71 Column longitudinal acceleration response time histories at different elevations free field and input accelerations are also inCluded cc ceeeseeecc
65. dvanced Options Use KU for Elastic Own Weight Sound s Modulus for Elastic Own Weight Fig 38 User defined clay material U Clay2 The properties of the cohesive stiff medium and soft clay models are shown in Table 9 below Table 9 Clay material properties Soft Clay Medium Clay Stiff Clay Mass density ton m 1 3 1 5 1 8 Reference shear 4 4 5 modulus dea 1 3x10 6 0x10 1 5x10 Reference bulk 4 5 5 iodului 6 5x10 kPa 3 0x10 kPa 7 5x10 Cohesion kPa 18 37 75 Peak shear strain 0 1 0 1 0 1 Friction angle degree i i Pressure dependent 0 0 0 coefficient The above mentioned soil models are based on earlier research Elgamal et al 2003 Elgamal and Lu 2009 Elgamal et al 2009 Elgamal et al 2009b Elgamal 2010 Lu 2006 Yang et al 2003 Finally the soil meshing procedures are discussed in Appendix A 36 5 Pushover amp Eigenvalue Analyses To conduct a pushover analysis a load pattern must be defined please follow the steps shown in Fig 39 The load pattern window is shown in Fig 40 Please see Appendix B for pushover examples EF Bridget BEE defaultlase pbe Fle Execute Depay Help C Eigenvalue z PBEE Analysis Step 2 click GroundShekng Define Pattern Model Definition Bridge Parameters soi Parameters Mesh Paremeters Analysis Options Boundary Conditions B C Type r p Bedrock Type STEP 2 EXECUTE FE ANALYSIS Save Model amp Run Analysis STEP 3 COMPUT
66. e there is no accounting for shear flexibility or shear degradation directly Additional relevant details on the parameters used in both the Cover and Core Concrete are included in Appendix D below Cover concrete The Concrete02 material is used to simulate the concrete for both cover and core The format of the Concrete02 command is as follows uniaxialMaterial Concrete02 matTag fpc epsc0 fpcu epsu lambda ft Ets Where fpc is the concrete compressive strength epsc0 is the concrete strain at maximum strength fpcu is the concrete crushing strength epsu is the concrete strain at crushing strength all of the above values are entered as negative lambda is the ratio between unloading slope at epsu and initial slope ft is the tensile strength and Ets is tension softening stiffness absolute value slope of the linear tension softening branch For cover concrete fpc is equal to the concrete unconfined strength in Table 1 epsc0 0 002 fpcu 0 0 epscu 0 006 lambda 0 1 ft 0 14 fpc and Ets ft epsc0 Core concrete 1 For core concrete of circular column cross sections according to the Mander model the procedure to calculate the confined concrete strength fpc f is as follows 123 foo f 1 254 2 254 f 7942 af 9 Where f f is the unconfined compressive strength and f can be obtained from the following equation F KP 10 Where f is the steel yield strength
67. e models are required for each performance group PG PGs represent a collection of structural components that act as a global level indicator of structural performance and that contribute significantly to repair level decisions Performance groups are not necessarily the same as load resisting structural components The complete analysis is accomplished using the local linearization repair cost and time methodology LLRCAT detailed more in Chapter 6 The interface handles all of the above mentioned intermediate models and provides default data for the case of reinforced concrete box girder bridges The decision variables that can be generated as output are the repair cost ratio RCR or the ratio of repair cost to replacement cost and the repair time RT or repair effort measured in terms of crew working days CWD These outcomes are presented graphically as loss models conditioned on earthquake intensity In addition site specific ground motion hazard can be specified and the user interface will then also generate loss hazard curves mean annual frequencies of exceeding different loss levels The loss hazard curves are presented graphically as mean annual frequencies or return periods An important feature of the interface is that the PBEE analysis can be executed sequentially ground motion selection time history analysis loss modeling hazard and visualization However once a final selection of geometry and materials has been made the
68. e sure that BridgeBEEE is not running and then copy the new PBEE DLL file to the installation folder and overwrite the old one Fig 134 Step 5 Run BridgePBEE Start BridgePBEE the program is now running with the updated PBEE quantities 127 Y PBEE Microsoft Visual Studio Edit View Project Build Debug Tools VMware Window Community Help e es Ga om p Release x Win32 Ri oral m Peel res ae Start Page Fad Solution REE 1 project exe ____h PBEE cpp Defines the entry point _ _ _______ the DLL app aa PBEE if i J Header Files l ma include stdafx h isl Loy Source Files tinclude PBEE h c stdafx cpp xogo 4 seuojds g Jaag g ifdef MANAGED L pragma managed push off endif BOOL APIENTRY DliMain HMODULE hModule DWORD ul reason for call LPVOID lpReserved switch ul reason for call DLL PROCESS ATTACH DLL THREAD ATTACH DLL THREAD DETACH DLL PROCESS DETACH break H return TRUE Fig 131 Visual Studio file PBEE SLN 128 3 PBEE Microsoft Visual Studio Global Scope lod Solution PBEE 1 project El 24 PBEE a D Header Files ij Resource Files Gi E Source Files Asphalt concrete Mud jacking Bridge removal Bridge removal Approach slab removal column portion G PBEE cpp 2 C stdafx cop ReadMe tet Clean deck for methacrylate Furnish methacrylate Treat bridge deck Barrier rail Re center column
69. e the soil very stiff please follow the steps below Step 1 In the main page of the interface Fig 2 click File then New Model and Yes to create a new model Step 2 Click Soil Parameters in the main window Step 3 Click 22 U Clay2 from Soil Type dropdown list Step 4 Enter a large number for the Shear Wave Velocity e g 10 000 m sec and click OK to close U Clay2 window Step 5 Click OK to close Soil Strata window Step 6 Click File and then Save Model to save the model Simple Verification Linear column properties 1 Cantilever Beam with Longitudinal Load at Free End This case can be obtained by making the bridge deck very flexible e g use a very small value for the elastic modulus The Roller abutment model is employed The Fiber section with Elastic Material is used to simulate the column In this case the equivalent flexural stiffness is EI 3375450 kN m as reported back by the user interface see Fig 10 when Elastic is selected Load P 20 kN Length L 6 71 m The end displacement w PL 3EI 5 97 E 04 m BridgePBEE gives 6 1E 04 m Fig 120 113 OpenSeesPBEE Cantilever pbe SEE File Execute Display Help H Model Input X Finite Element Mesh Sel is SS ee a eel STEP 1 PEEKE M Response Sele Analyst 9 nalys s Response profile hg Displacement in Longitudinal direction Pus C Eig Print e Be EA Displacement Profile File pdispProf txt
70. e tield Py Free teld FO Freecield D 5 95 Free teld CAW Freecield Arias Intensity Free teld 5A Period 1 sec Free field SW Period 1 sec Freetield SD Period 1 sec Freetield PSA Period 1 sec Free teld FSW Period 1 sec R f i i a v a i b w T 2 s Case2BMesh4 PGs doc Read Only Microsoft Word 2 Home p Fage Layout Refere H Case BMesh4 1 Drift Ratio Ko Fig 1 PG1 Max tangential drift ratio SRSS col lill Pagel of6 Words 103 English U 5 100 Fig 90 Converting figures to EPS format 86 E One sigma Values Beta Values Numbers in bold are the smallest for each PG PG1 PG2 PG3 PG4 PGS PG6 PG7 PG8 PG9 PG10 PGA 0 339 251 0 320 0 285 0 305 0 279 0 330 0 331 0 698 0 677 PGV 0 274 37 0 317 0 289 0 290 0 274 0 460 0 464 0 698 0 717 PGD 0 377 199 0 426 0 400 0 409 0 390 0 586 0 592 1 016 1 059 D S 95 0 519 0 608 0 584 0 588 0 572 0 804 0 805 1 556 1 559 CAV 0 350 179 0 304 0 270 0 296 0 271 0 272 0 273 0 854 0 847 Arias Intensity 0 321 157 0 263 0 234 0 254 0 233 0 214 0 216 0 693 0 699 SA Period 1sec 0 313 155 0 304 0 269 0 287 0 262 0 335 0 341 0 656 0 664 SV Period 1 sec 0 328 2 172 0 334 0 301 0 316 0 294 0 386 0 393 0 797 0 800 SD Period 1 sec 0 313 E 0 304 0 269 0 287 0 262 0 335 0 341 0 656 0 664 PSA Period 1 sec 0 313 155 0 304 0 269 0 287 0 262 0 335 0 341 0 656 0 664 PSV Period 1sec 0 313 155 0 304 0 269 0 287 0 262 0 335 0 3
71. econd parameter of the assumed lognormal distribution Hence beta is dimensionless and has a typical range between 0 and 1 although it is not bounded by 1 This parameter is closely related to the coefficient of variation standard deviation normalized by the mean under certain conditions small beta values The Repairs Unit Costs and Production Rates are displayed in Figs 59 61 respectively Users can customize these PBEE quantities through updating a file named PBEE DLL which is located at the installation folder C Program Files BridgePBEE or C Program Files x86 BridgePBEE on a 64bit PC Please follow the steps described in Appendix E to build an updated PRBEE DLL file and then replace the one in the installation folder Damage States D5 Column OS SEE Max Tangent Drt SASS 7 0S1 Cracking Lambda O 2405b72762 73 DSe2 Spalling Lambda i54 1 657467 701 Da Bar Buckling Lambdaf s 6 0 351b405 2 DOS4 Failure Lambda fs J96001599 Abutment DS ERE Max Relative Deck Lef Abutment Long Disp fri 0S1 Cleaning 0S2 Assembly 0S3 Back Vall Spalling D4 Back Wall Failure Approach DS ERE Let 4oproach Residual Vertical Displacement E 0S1 Pavement Lambda im 0 073152 Beta Dae AC Regrade Lambdafm 0 146304 Beta Doss Rebuilding Lambda im 0 3048 Beta Foundation OS EDP Left Abutment Foundation 0S1 Add File Threshold Lambda gim 0 062062434L Beta Dse Enlarge and Add Piles Lambdafm 0 10
72. ed Mesh In addition for PBEE analysis scenarios Intensity Measures IMs and response spectra for each input motion are calculated and are available for display in Table and Figure formats Performance Group PG Quantities and Bridge peak accelerations for all employed shaking motions are also available for display against any of the computed IMs The post processing capabilities can be accessed from Menu Display Fig 3 Fig 62 and Fig 63 show the post processing capabilities available in a pushover analysis and a base shaking analysis respectively Fig 64 shows the Analysis Options window Depending on the selection of the Output Data options Fig 64 the menu items shown in Fig 62 and Fig 63 may be enabled or disabled For example In order to view column response profiles and response relationships Include Column Response Profiles amp Relationships Fig 64 has to be checked before analysis in this case menu items of Column Response Time Histories amp Profiles as well as Column Response Relationships shown in Fig 62 and Fig 63 will be enabled To view the deformed mesh and animation both Output Data options of Include Column Response Profiles amp Relationships and Include Soil Displacement Fig 64 must be checked If the user wants to view the deformed mesh for the final step only check Display Deformed Mesh for Final Step Only Recommended for Large Models Fig 64 The option is particularly useful when the outpu
73. edrock Type Rigid Bedrock STEP 2 EXECUTE FE ANALYSIS STEP 3 COMPUTE REPAIR COST PBEE Analysis BridgePBEE Display response time histories for the soil domain Unit SI Fig 81 Menu items to access the soil responses 78 Response Time Histories Motion A ELC Longitudinal acceleration time histories at 0 0 m column center al in Longitudinal plane crossing column cent Longitudinal acceleration time histories Longitudinal displacement rel to base histories Transvers acceleration time histories Transverse displacement frel to base histories Vertical acceleration time histories Vertical displacement time histories al Acceleration Time Histories m s s Excess pore pressure time histories ground surface File laccHis Om txt shear stress zx vs strain amp eff confinement shear stress yz vs strain amp eff confinement Longitudinal normal stress time histories Transverse normal stress time histories shear stress zx time histories shear stress yz time histories Depth 0 5m File laccHis_0 5m txt Fig 82 Response options for soil time histories Response Time Histories Motion A ELC Sele Longitudinal displacement rel to base histories at 0 0 m column center in Longitudinal plane crossing column cent Longitudinal plane crossing column center Transverse plane crossing column center Longitudinal Displacement Time Histories m Dep
74. eeeeeeeeeeeeeeeeeeeeeeeeees 20 Fig 19 Longitudinal force displacement relationship for the Elastic abutment model 20 Pig 20 ROMer abutment mode leei a e ues caseubidet eae E E 21 Fig 21 Steps to define a Roller abutment model cc ccccccceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeees 21 Fig 22 Longitudinal force displacement relationship for the Roller abutment model 22 Fig 23 General scheme of the Simplified abutment model Aviram et al 2008 0008 22 Fig 24 Longitudinal backbone curve force displacement relationship two on each end of the padgee Caltrans SDC 2004 anren A a R 23 Fig 25 Steps to define the Simplified abutment model cece eeeeeeseeeeseeeeeeeeeeeseseeeeeeeeeeeees 24 Fig 26 Longitudinal force displacement relationship for the Simplified abutment model a longitudinal direction b transverse direction c cc cccccsssssesessseeeeeccceceeeeeeeeeeaaaaessssseeeseeeeeeeeeees 25 Fig 27 General scheme of the Spring abutment model Aviram et al 2008 cc eeeecceeeees 2J Fig 28 Steps to define a Spring abutment mode lrini ass veasidev a EA E 28 Fig 29 Force displacement relationship for the Spring abutment model a longitudinal direction THLE Ver eEG ON sf tei shactsane its ire caste tis onc camna naa niet bec eosnae tuoi saad saauaesusoneab N 29 Fig 30 Steps to define a SDC 2010 Sand abutment model 0 ec eeeeeeeeeessesseeeessssseseeseeeens
75. eering and Structural Dynamics 39 3 281 301 Mackie K R Wong J M and Stojadinovic B 2011 Bridge damage and loss scenarios calibrated by schematic design and cost estimation of repairs Earthquake Spectra 27 1127 1145 Maroney B H and Chai Y H 1994 Seismic Design and Retrofitting of Reinforced Concrete Bridges Proceedings of 2nd International Workshop Earthquake Commission of New Zealand Queenstown New Zealand Mander J B Priestley M J N and Park R 1988 Theoretical Stress Strain Model for Confined Concrete Journal of the Structural Division ASCE 114 pp 1804 1826 Mazzoni S McKenna F Scott M H Fenves G L et al 2009 Open System for Earthquake Engineering Simulation User Command Language Manual Pacific Earthquake Engineering Research Center University of California Berkeley OpenSees version 2 0 May Megally S H Seible F Bozorgzadeh A Restrepo J and Silva P F 2003 Response of Sacrificial Shear Keys in Bridge Abutments to Seismic Loading Proceedings of the FIB Symposium on Concrete Structures in Seismic Regions May 6 9 Athens Greece Shamsabadi A Rollins K M and Kapuskar M 2007 Nonlinear Soil Abutment Bridge Structure Interaction for Seismic Performance Based Design Journal of Geotechnical and Geoenvironmental Engineering 133 6 707 720 June Shamsabadi A Khalili Tehrani P Stewart J P and Taciroglu E 2010 Validated Simulation Models fo
76. elp PG Quantities for All Motions A Model Bridge amp Ground Peak Accelerations for All Motions t Mesh iaj x Maximum Column amp Abutment Forces for All Motions Bridge Only Zoom in Out Frame xY YZ XZ 3D lt gt UpiDn STEP 1 ed Out Frame x2 30 Up Dn Detailed Output Please Select Input Motion Current A ELC Analysis Deformed Mesh Motion A ELC Column Response Time Histories amp Profiles Motion A ELC Column Response Relationships Motion A ELC Eid Abutment Responses Motion A ELC Analysis Summary PBEE Analysis Ground Shaking PBEE Motions Model Definition Bridge Parameters Soil Parameters Mesh Paremeters Analysis Options Boundary Conditions B C Type fiz Bedrock Type z STEP 2 EXECUTE FE ANALYSIS Save Model amp Run Analysis STEP 3 COMPUTE REPAIR COST PBEE Analysis Fig 76 Menu items to access the abutment responses 73 M Abutmert Responses A xz Fonce Cisplace ment Relationships jPorce Displacement Raletionships jisplacement Relationship n Preepiler abi lied Ralahnenhi ii brce noting on decker Aelatve Deck end Abumer Disp acement Time H stones k end atutment duplacement Searing Force Time Histonss Sile Cap Diiplacemeni Time Histories Right Abutmest EVAL ee ET ae rile d Kos Fig 77 Menu items to access the abutment responses Abutment Responses Force Displacemen
77. ement Mesh Display V Show Axes M Show Int PBEE Options Number of records to be run atthe same time 4 Output Data Include Column Response Profiles amp Relationships Advanced Options fit f PUSS ASCh Cet ENaren En is a V Include Soil Displacement M Use Global Elastic Material for Application of Own Weight Initial Lateral Vertical Confinement ba Ratio 0 1 0 9 Young s Modulus fe J000 kPa Abutment Rigid Link Stiffness x Pile Stiffness fi oo00000000 l Include Soil Acceleration M Include Soil Stress Strain Display Deformed Mesh for Final Step Only Recommended for Large Models Cancel Change OpenSees Options Change Rayleigh Damping Fig 55 Options to change number of records to be run at the same time 54 BridgePBEE defaultCase pbe File Execute Display Help Model Input x Finite Element Mesh STEP 1 DEFINE MODEL Analysis Type Pushover C Eigenvalue Bas z gt J 4 10 Motions PBEE Analysis Ground Shaki Current Motion 1 1 A ELC Run4of4 Base shaking Finished 0 92 45 00 seconds Model Definition Current Motion 2 2 A2E Run4of4 Base shaking Finished 0 66 44 96 seconds Bridge Paramet Current Motion 3 3 CAP Run 4 of 4 Base shaking Finished 0 78 44 96 seconds B C Type Current Motion 4 4 CNP Run 4 of 4 Base shaking Finished 0 76 30 00 seconds Boundary Conditio Bedrock Type STEP 3 COMPUTE REPAIR COST PB
78. ement in Longit dinal direction Response profile Displacement Longitudinal direction Response histories F Displacement g Longitudinal direction i i Vertical direction d Bending Moment a d fg Shear Force Pressure Response Summa Fig 67 Response time histories and profiles for column and pile shaft displacement is shown at the nodes only one element is used above ground 7 Column Response Response profile of Bending Moment in Longitudinal direction Displacement Print Acceleration rin Rotation Bending Moment i SS Profile File momProf txt ressure Response Summa Fig 68 Bending moment profile in the longitudinal plane 67 Column Response Motion T01 Response profile of Response Summary in Longitudinal direction Displacement TEA Rotation Bending Moment shear Force Pressure Response summary Fig 69 Response summary 68 Column Response Motion T01 Response histories of Displacement in Longitudinal direction Print Displacement Bending Moment Shear Force Pressure Profiles for All Steps ile ProfHist txt 7 Column Response Motion T01 Response histories of Displacement in Longitudinal direction 3 Displacement Bending Moment ent Time Histories 6 71 m ab slate cas column top File pdispHis 6 7i1m txt 0 m ground surface File pdispHis Om txt 5 m below ground surface F
79. ent left PG4 Max relative deck end abutment displacement right PGS Max bridge abutment bearing displacement left PG6 Max bridge abutment bearing displacement right PG7 Approach residual vertical displacement left PG8 Approach residual vertical displacement right PG9 Abutment residual pile cap displacement left PG10 Abutment 46 residual pile top displacement right PG11 Column residual pile displacement at ground surface Discrete DSs are defined for each PG Damage states are numbered sequentially in order of increasing severity The DSO damage state corresponds to the onset of damage when repair costs begin to accumulate An upper limit to the quantities and costs is called DS because it corresponds to the most severe possible damage state for the elements in a PG DS usually corresponds to complete failure and replacement of all the elements in the entire PG The DSs are connected to structural demands obtained from finite element analysis results by way of an EDP specific to each PG The repair quantities associated with each DS are developed more fully in the definition of the damage scenarios All the PGs and DSs are linked to a single EDP in this implementation Based on previous work the methodology was calibrated for defining post earthquake performance of select bridges that fall within the class of ordinary post tensioned box girder reinforced concrete highway overpasses Mackie et al 2011 The three
80. erial properties of the Fiber section are listed in Table 2 for Steel02 and Table 3 for Concrete02 core and cover The Concrete02 material parameters were obtained from the Mander 1988 constitutive relationships for confined and unconfined concrete More details on the derivation of the default values and the OpenSees uniaxialMaterial definitions used for each material are shown in Appendix D 12 Column Material Properties RC Section Properties Longitudinal Bar Size Longitudinal Steel s Transverse Bar Sizet Transverse Steel steel Unit vveight Steel Yield Strength Concrete Unit Weight Concrete Uncontined Strength Steel foung s Modulus otrain hardening Ratio Core Concrete foung s Modulus Concrete Compressive strength Concrete strain at Maximum Strength Concrete Crushing Strength Concrete Strain at Crushing Strength Ratio between Unloading Slope Tensile Strength Tensile Softening Stifness mm WT 460000 29 8 27600 mm t 46 457 187 0 00367 44979 3651 0 036 TARE 6504 006 1771820 801 l kN m3 kPa kM m3 kFa kPa kPa kPa Rt Materials Cancel lew Moment Curvature Response Steel Material Steel02 View Stress Strain Core Concrete Material Concrete0 View Stress Strain Cover Concrete Material Concretell2 lew Stress Stiain Controlling Parameter RO Controlling Parameter cR Controlling Parameter cRe
81. f abutment impact into the backwall so they are defined as only the motion of the deck into the abutment Maximum absolute values in the longitudinal direction are used For example for the right abutment shown in Fig 86 it is the relative longitudinal displacement of node B deck end node in the direction of node C abutment top node A zero value is used for the times during which the deck end node moves away from the abutment top node PGS Maximum absolute bearing displacement left abutment PG6 Maximum absolute bearing displacement right abutment These two PGs are intended to address bearing damage whether or not an explicit representation of the bearings is included in the user selected abutment model Therefore the EDP for the PG is based on the relative displacements of the deck end node e g Node B for the right abutment shown in Fig 86 to the abutment top node e g Node C for right abutment shown in Fig 86 The SRSS values of the resulting two relative horizontal displacements is used and both motion into the backwall and away from the backwall are considered PG7 Residual vertical displacement left abutment PGS8 Residual vertical displacement right abutment 83 This PG is used to gage immediate repairs for rideability and 1s not a measure of the permanent slumping of the embankment for example Therefore the EDP is calculated as the vertical displacement of the abutment top node e g Node B for the right
82. f soil response time hiStOTies cccceeeesseeeseeeeeeeeeseeeeseeeeeeeeseesseeeeeseeeeens 80 Fig 85 Soil settlement time histories under abutment ccccsssessssesseseeeeeececeeeeeeeeeeeeeeeeeees 80 Fig 86 Finite element mesh in BridgePBEE Node O Column base node at ground surface Node A Column top node Node B Deck end node Node C Abutment top node having the same coordinates as Node B Nodes B are C are connected by an abutment model Node D DULIMEME PUE Cap MOUS erene ee oie saatcascsee a ee aac N A E 82 Fig 87 Code snippet to calculate the tangential drift ratio of COLUMIN ccc eeececceeeeeeeeeeeeeeees 83 Fig 88 Menu items to access the PG quantities for all MOTIONS ccccceeeeeeeeeeeeeeeeeeeeeeeeees 85 Fig 89 PG quantities for all motions scroll down to see all 11 PGS eeccceeeeeeeeeeeeeeees 86 Fig 90 Converting fizures tO EPS TOPmMal sisscvaissacveadssasasnsnendownesssntvasesauenndessietniaashawedsyeetaalsawendess 86 Fig 91 Lognormal standard deviations beta values for each PG a table format b bar graph NOTH lt c 3655 sso sc abtusanicadom aie sanaanm sense E anos cante enema nies ncaa te caumeatenycdateusousacces caaseuens 87 Fig 92 Menu items to access bridge peak accelerations for all MOTIONS ccccceceeeeeeeeeeeees 88 Fig 93 Bridge peak accelerations for all motions a maximum bridge accelerations b maximum column base accele
83. f the bridge that may be displayed through a pushover analysis To define a Roller abutment model please follow the steps shown in Fig 21 The typical force displacement curve for the Roller abutment model is shown in Fig 22 Abutment Model Roller ongitudinal Gap Only Used m tor PBEE Repair Cost Estimation Step 3 enter parameters for Roller i gt 3000 kN Abutment File m rn shutment Mocel Deck Length 90 m Deck Width 113 rn Number of Bearings Deck Depth 1 83 mm Bearing Height Deck Properties Number of Shear Keys step 2 click Define Fig 21 Steps to define a Roller abutment model 21 Longitudinal Force Displacement Relationship Force resisting force acting on deck end displacement relative deck end abutment displacement Left Abutment Right Abutment File abutForceDispLL txt File abutForceDispRL txt Fig 22 Longitudinal force displacement relationship for the Roller abutment model 3 4 3 Simplified Model SDC 2004 The simplified model of the embankment abutment system provides several nonlinear springs to better represent abutment bridge interaction that is neglected with the elastic or roller abutment models The general scheme of the simplified model is presented in Fig 23 It consists of a rigid element of length d superstructure width connected through a rigid joint to the superstructure centerline with defined long
84. fined pushover load pattern U Push 5 2 Output for Pushover Analysis Output windows for a pushover analysis include e Response time histories and profiles for column and pile shaft under grade e Response relationships force displacement as well as moment curvature for column and pile shaft under grade e Abutment response time histories e Deformed mesh contour fill and animations 40 5 2 1 Column Response Time Histories and Profiles EEKE M Response Re ponse profile of Disp acement in Longit dinal direction Response profile Displacement Longitudinal direction Displacement Longitudinal direction Rotation e Vertical direction 7 Bending Moment fed IO fo JES Shear Force Pressure Response Summa Fig 43 Response time histories and profiles for column and pile shaft 5 2 2 Column Response Relationships Column Response Relationships Longitudinal direction Load displacement Longitudinal direction htac bo fmn top Fie Fig 44 Response relationships for column and pile shaft 4 5 2 3 Abutment Force Displacement and Response Time Histories 7 Abutment Responses Force Displagement Relationships i Force Displacement Relationships Force Displacement Relationships Relative Deck end Abutment Displacement Time Histories Resisting Force Time Histories isplacement Time Histories Displacement Relationship gprce acting on deck end ack end abutment displacement
85. for the free field response The PG quantities for each input motion are displayed by bin of the motion see legend in Fig 89 When an IM is paired with an EDP and all the individual realizations are plotted the result is typically termed a demand model or probabilistic seismic demand model PSDM Previous research has demonstrated that the central values of PSDMs are often well described using a power law relationship between EDP and IM The parameters of such a power law fit can be obtained using least squares analysis on the data Therefore when plotted in log log space as is shown in Fig 89 the best fit or mean relationship is linear The mean in log log space is shown along with the standard deviation also in log log space of the power law fit If it is assumed that the EDP responses are lognormally distributed when conditioned on IM then these curves can be interpreted as being defined by the two parameters of a lognormal distribution the median can be related to the mean of the logarithm of the data and the lognormal standard deviation is as shown 84 To convert all figures currently displayed in the window click Convert Figures to EPS Format A MS Word window with the EPS figures included in the document will pop up once the converting is done Fig 90 To view lognormal standard deviations for each PG Fig 91 click View Beta Values in Fig 89 The information is tabulated with values in bold indicating the lowest log
86. hAnI cm sec 4 6 1 1 g 2 4 a 3 cm sec 25500000e 001 O08450000e 001 60650000e 001 15400000e 001 62550000eE7001 68150000E 001 ai 5 1 1 8 1 2 79868212e 003 14867413e 003 59 7816204e 002 O3826578e 003 91413446e 002 6 o2347853e 002 91374865e 002 24758229e 002 03169465e 002 O8981512e 002 37204128e 003 o27T64641e 003 91509909e 002 62616813e 003 STAPOOANeE LATS AriasBracketed 78451763e 002 16701389e 002 2 cm 003347223 4 01901392 AriasBracketed 1 2 2 2 o 5 G 15473555 85808333 49228081 54139287 01592393 46347522 39787222 00367926 cm 17039209 T95532297 25352607 65611272 04834179 01793673 gayaspnan E ariga gATe ANANN Fig 54 Intensity Measures IM table for the whole input motion set 6 4 Save Model and Run Analysis After defining the finite element model click on Save model and run analysis The finite element computations will start for several earthquakes at a time as specified in the Analysis Options Fig 55 window below You can select as many as 8 records to be run at the same time in order to reduce the overall run time for dual core machines or better Fig 56 shows the analysis progress for each record Analysis Options Unit System Soil Materials Solid Element Option SI Units E 2 Brick Elemen Benoa Una C Nonlinear 8 Node Standard Brick Element C 8 Node Bhar Brick El
87. he moment curvature curve at the column top The vertical axis is the bending moment and the horizontal 70 axis is the curvature To view the data for the plot click the txt filename e g click curvX_6 71m txt in Fig 75 BridgePBEE defaultCase pbe Seles File Execute ei sFvm Help PG Quantities for All Motions x o Model Bridge amp Ground Peak Accelerations for All Motions t Mesh iz x STER T Maximum Column amp Abutment Forces for All Motions l Bridge Only Zoomin xY lt gt Up Dn Detailed Output Please Select Input Motion Current A ELC pAnalysis Deformed Mesh Motion A ELC Column Response Time Histories amp Profiles Motion A ELC Column Response Relationships Motion A ELC Abutment Responses Motion A ELC Analysis Summary PBEE Analysis Ground Shaking PBEE Motions Model Definition Bridge Parameters Soil Parameters Mesh Paremeters Analysis Options Boundary Conditions B C Type Shear Beam M Fixed Vert Bedrock Type Pigid Bedrock STEP 2 EXECUTE FE ANALYSIS Save Model amp Run Analysis STEP 3 COMPUTE REPAIR COST PBEE Analysis BridgePBEE Display response time histories and profiles for pile Unit SI Fig 72 Menu items to access the column response relationships 1 E TETE Fie rec Fiche e mrad prs al en m qolann Top jlongtdmaldypcion i a y Lergasina direction TOOMET
88. hing controlling parameters for vertical direction default values The finite element mesh created with the above default values is shown in Fig 116 Examples of mesh generation are shown in Figs 117 119 108 BridgePBEE Finite Element Mesh EF File Execute Display Help l Bridge Only Zoomin Out Frame xY Eaka Ba lt gt Up Dn BridgePBEE For Help press F1 Fig 116 Finite element mesh created with default values 109 general Definition Horizontal Meshing Vertical Meshing General Definition Mesh Scale Ful mesh Column Num of Slices 64 Please choose 16 or larger Number of Beam Column Elements above Ground Surface Flease enter 1 if fiber element is used Bridge Deck Number of Beam Column Elements for Deck Even Number fo x e BridgePBEE Finite Element Mesh Def EF Fie Execute Display Help ol x i l Bridge Only Zoom In xY yz xz 3D gt Up Dn BridgePBEE For Help press F1 b Fig 117 Mesh refinement example 1 a Change Num of Slices to 32 b the resulting mesh 110 General Definition Vertical Meshing Horizontal Meshing ertical Meshing Mesh Layer Height Mumberof Ratio of Top From m Mesh Uniform Element Height Topdown Layers Meshing over Bottom Ji A x Te TnT q x q q 1909490 4 e s f f z 0 i Cancel Apply BridgePBEE Finite Element Mesh Execute Display
89. hquake BORREGO A ELC see Fig 127 Each motion is composed of 3 perpendicular acceleration time history components 2 laterals and one vertical As shown in Fig 127 each motion folder contains 6 files categorized into 2 file types the DATA files contain the time history acceleration unit in g of a component and the INFO files contain the characteristics of the corresponding component Fig 128 and Fig 129 displays sample INFO amp DATA files Naming of these files has to follow the format below Input motion name angle or UP or DWN for vertical component AT2 data or info Note that the filenames with the smaller angle will be used for the longitudinal direction and the other one with the larger angle will be used for the transverse direction The first 2 lines of each INFO file must follow the style of the example below Data points NPTS 4000 Sampling period DT sec 0 01 Where 4000 and 0 01 are the number of data points and the time step respectively of an input motion component 2 Steps to Create an Input Motion Based on the above description for the directory structure of a PBEE motion set one can easily create an input motion Fig 130 Step 1 create a folder and rename to your PBEE motion set name e g MotionSet1 see Fig 130 118 Step 2 create a folder under the motion set folder and rename to your bin name e g bin1 Step 3 create a folder under
90. ig 79 Menu items to access the deformed mesh 76 Deformed Mesh Motion A ELC Seles Due to seismic excitation disp contour 3D VEW Play Animation ar YZ Wad SD lt gt Lp Due to gravity soil only Due to gravity bridge included Due to pushover Writ m 3 310e 007 5512 006 g 3 432e 006 _ j 5 314e 006 195e 006 Deformed mesh nnd 9 077 e 006 Disp contour fill 1 096e 005 1 264e 005 1 47 2 005 1 660e 005 1 546e 005 2 037 e 005 2 2 256 005 2 41 3e 005 2 601 e 005 2 7 096 005 2 97 7 e 005 3 166e 005 3 354e 005 3 542e 005 3 7 30e 005 Step Mo 4 Time second D Animation Delay millisecond l scale Factor 0 larger value means slower 0 Endless Playing Bridge Only Fig 80 Deformed mesh 7 1 5 Soil Response Time Histories The soil response time histories can be accessed by clicking menu Display Fig 3 and then Soil Response Histories Fig 81 The soil response window is shown in Fig 82 There are 3 dropdown lists available for users to choose The contents of the 3 lists are as follows Left Dropdown List Fig 82 Longitudinal acceleration time histories Longitudinal displacement rel to base histories Transverse acceleration time histories Transverse displacement rel to base histories Vertical acceleration time histories Vertical displacement time histories Excess pore pressure time histories Shear stress zx vs
91. ign and geometric parameters making it possible to solve for a variety of bridges within class 48 However any changes beyond these configurations would require numerical values for all the repair quantities to be input It is assumed that the repair quantity estimates for each PG and DS are also random quantities and can be described by a mean or median value and a coefficient of variation or lognormal standard deviation In the interface beta has been set as 0 4 but could be modified by the user in the future if so desired The repair quantities may then be handed over to a cost estimator who would have the ability to access historical pricing and bid information In addition the type and magnitude of each repair quantity would correspond to standard DOT estimates and specifications procedures Each repair quantity can then be bid or an estimation of cost and effort time production rate made These unit costs and production rates are also random quantities and can be described by a mean or median value and a coefficient of variation or lognormal standard deviation The values currently in the interface all have a beta of 0 2 but could again be set by the user 1f desired See more details about PERT criteria for the production rates in Mackie et al 2008 Modifying the default PBEE quantities repair quantities unit costs and production rates is detailed in Appendix E 6 3 Definition specification of PBEE input motion ensemble s
92. ile pdispHis 5m txt Fig 70 Column longitudinal displacement response time histories a response profiles at specific load steps b response time histories at different elevations 69 EF Column Response Motion T01 Response histories of Acceleration in Longitudinal direction Acceleration Rotation Hon Time Histories 6 71 m aljBending Moment column top File paccHis 6 71m txt Shear Force Pressure Free field Acceleration File FreefieldAcc txt Input Acceleration File InputAcc txt b Fig 71 Column longitudinal acceleration response time histories at different elevations free field and input accelerations are also included 7 1 2 Column Response Relationships The column response relationships can be accessed by clicking menu Display Fig 3 and then Column Response Relationships Fig 72 The column response relationships window is shown in Fig 73 There are 3 dropdown lists available for users to choose from The contents of the 3 lists are as follows Left Dropdown List e Load displacement e Moment curvature Right Dropdown List e Longitudinal Direction e Transverse Direction The Middle Dropdown List includes all elevations starting from column top Again zero elevation refers to the ground surface Fig 74 shows the longitudinal load displacement curve at the column top The load refers to the shear force of the beam column element at the specified elevation Fig 75 shows t
93. iles for All Steps Fig 70a only 20 steps including the initial state Step 0 the first step and the final step are shown if more than 20 steps are simulated Step 0 refers to the initial state after application of own weight and before the dynamic run i e pushover or earthquake shaking If Acceleration is selected the free field acceleration response time history and the input acceleration time history are also plotted Fig 71 The free field location is shown in Fig 66 at the ground surface along the diagonal line of the mesh near the edge corner node Tj BridgePBEE defaultCase pbe Seles PG Quantities for Al Motions Bridge amp Ground Peak Accelerations for Al Motions it Mesh i m l fox Maximum Column amp Abutment Forces for All Motions C Bridge Oniy Zoomin Out Frame XY v2 Z 3D gt up Dn Detaled Output Please Select Input Motion Current A ELC Column Response Time Histories amp Profiles 1 Column Response Relationships Abutment Responses PBEE Motions Model Definition Bridge Paraneters Soil Parameters Mesh Par meters Analysis Options Boundary Conditions B C Type i Bedrock Type Ea STEP 2 EXECUTE FE ANALYSIS Save Model amp Run Anahysis STEP 3 COMPUTE REPAIR COST Free field location PBEE Analysis Fig 66 Menu items to access the column response time histories and response profiles 66 Column Response Re ponse profile of Displac
94. ill randomly select a certain number of input motions from each bin the input motions are categorized by bin Double click any record to view its intensity measures and response spectra Fig 52 SRSS stands for Square Root of Sum of Squares of the 2 horizontal components Click Display Intensity Measures Fig 51 to view the histogram and cumulative distribution plots for whole input motion set Fig 53 The intensity measures include e PGA Peak Ground Acceleration PGV Peak Ground Velocity PGD Peak Ground Displacement Ds 95 Strong Motion Duration CAV Cumulative Absolute Velocity Arias Intensity SA Spectral Acceleration assuming 1 second period SV Spectral Velocity SD Spectral Displacement PSA Pseudo spectral Acceleration PSV Pseudo spectral Velocity The strong motion duration Ds 95 is defined according to the time domain bounded by the 5 and 95 cumulative Arias intensity of the record All of the spectral intensity measures are defined at an effective viscous damping of 5 unless otherwise noted 50 In the histogram window Fig 53 click Display Intensity Measures Values to view the intensity measures listed in text format Fig 54 The user can copy and paste to her his favorite text editor such as MS Excel in Fig 54 right click and then click Select All to highlight and then right click and then click Copy to copy to the clipboard To incorporate user defined input motions please see Appendix C
95. in the longitudinal and transverse directions as well as for the SRSS of the 2 horizontal directions Fig 93 The figures in this window include The free field location is defined in Fig 66 Maximum bridge acceleration Maximum column base acceleration Maximum free field acceleration Maximum input acceleration Bridge peak acceleration column base peak acceleration Column base peak acceleration input peak acceleration Free field peak acceleration input peak acceleration Bridge peak acceleration input peak acceleration BridgePBEE defaultCase pbe Sele File Execute ESEIA Help PG Quantities for All Motions nt ay Model Bridge amp Ground Peak Accelerations for All Motions t m ot a a Maximum Column amp Abutment Forces for All Motions l Bridge Only Zoom in O OYZ lt gt STEP 1 Detailed Output Please Select Input Motion Current A ELC Analysis Deformed Mesh Motion A ELC Column Response Time Histories amp Profiles Motion A ELC Column Response Relationships Motion A ELC Abutment Responses Motion A ELC Analysis Summary PBEE Analysis f Ground Shaking PBEE Motions Model Definition Bridge Parameters Soil Parameters Mesh Paremeters Analysis Options Boundary Conditions B C Type 7 ji Bedrock Type STEP 2 EXECUTE FE ANALYSIS Save Model amp Run Analysis STEP 3 COMPUTE REPAIR COST PBEE Analysis Fig 92 Menu items to access bridge pea
96. itudinal transverse and vertical nonlinear response at each end Transverse Modified SDC 2004 curve Maroney and Chai 1994 Longitudinal SDC 2004 backbone curve with gap Elastic superstructure Boundary conditions Rigid joint Rigid element d Superstructure width Vertical Elastic spring for bearing pads k Fig 23 General scheme of the Simplified abutment model Aviram et al 2008 ZZ The longitudinal response defined for the simplified model accounts only for the gap and the embankment fill response where passive pressures are produced by the abutment back wall Fig 23 The shear resistance of bearing pads connecting the bridge to the abutment wall is ignored In the longitudinal direction Fig 23 a gap element is assigned an elastic perfectly plastic EPP backbone curve after gap closure with abutment stiffness K and ultimate strength P p obtained from section 7 8 1 of the Caltrans SDC 2004 see Fig 24 There is no stiffness in the longitudinal direction when the deck pulls away from the abutment The stiffness and strength are calculated using the SDC equations K 11500 00 1 P 239 00i E 2 Where w is the width of the back wall unit m and Ais the height of the back wall unit m In the current implementation the width of the back wall is taken as the bridge deck width minus twice of the bridge deck depth The units of K and P are kN m and kN respectivel
97. k accelerations for all motions 88 Bridge amp Ground Peak Acceleartions Response in Longitudinal direction with respect ta Ej fo S Period 1 sec ov Period 1 sec SD Period 1 sec FSA Period 1 sec PS Period 1 sec Free field FA Free field PW Free field PD Free field 05 45 Free field CAW Free field Arias Intensity Freeield 5A Period 1 sec Freeteld SW Period 1 sec Freetield SD Period 1 sec Freeield PSA Period 1 sec Free ield FSW Period 1 sec Bridge amp Ground Peak Acceleartions Response in Longitudinal direction with respectto Maximum Column Base Acceleration g File MaxColBaseAcc txt Kes I fo 5 89 Bridge amp Ground Peak Acceleartions Response in Longitudinal direction with respect to POY Maximum Free field Acceleration g File MaxFreefieldAcc txt Fig 93 Bridge peak accelerations for all motions a maximum bridge accelerations b maximum column base accelerations and c maximum free field accelerations 7 1 8 Maximum Column amp Abutment Forces for All Motions The maximum column amp abutment forces for all input motions can be accessed by clicking menu Display Fig 3 and then Maximum Column amp Abutment Forces for All Motions Fig 94 The window to display the maximum column amp abutment forces for all motions is shown in Fig 95 The responses are available in the longitudinal and transverse directions as well a
98. m Left Abutment Force kN File MaxLAbutForce txt c Fig 95 Maximum column amp abutment forces for all motions a maximum column shear forces b maximum column bending moments and c maximum abutment forces 92 7 2 PBEE Outcomes 7 2 1 Repair Cost amp Time The final PBEE results will be displayed against any intensity measure e g PGV in terms of Contribution to expected repair cost from each performance group Fig 96 Total repair cost ratio Fig 97 Contribution to expected repair cost from each repair quantity Fig 98 Contribution to repair cost standard deviation from each repair quantity Fig 99 Total repair time CWD where CWD stands for Crew Working Day Fig 100 Contribution to expected repair time CWD from each repair quantity Fig 101 E PBEE Analysis Output Print Contribution to expected repair cost from each performance group File PGsens_ E txt Fig 96 Contribution to expected repair cost from each performance group 93 E PBEE Analysis Output Total repair cost ratio File RCR Model txt Fig 97 Total repair cost ratio as a function of intensity E PBEE Analysis Output Fig 98 Contribution to expected repair cost from each repair quantity 94 E PBEE Analysis Output Fig 99 Contribution to repair cost standard deviation from each repair quantity E PBEE Analysis Output Total repair time CWD File RT Model txt
99. n Transverse Axis kN rmrad Rotation Vertical Axis kIs tmiraci Note on each end of the bridge two springs connect the bridge to the abutment The properties above are for each of these 2 springs Abutment Madel Deck Length Deck Width Number of Bearings Deck Depth Bearing Height Deck Properties Number of Shear keys Step 2 click Define Fig 18 Steps to define Elastic abutment model Longitudinal Force Displacement Relationship Force resisting force acting on deck end displacement relative deck end abutment displacement Left Abutment Right Abutment File abutForceDispLL txt File abutForceDispRL txt Fig 19 Longitudinal force displacement relationship for the Elastic abutment model 20 3 4 2 Roller Model The roller abutment model Fig 20 consists of rollers in the transverse and longitudinal directions and a simple boundary condition module that applies single point constraints against displacement in the vertical direction 1 e bridge and abutment are rigidly connected in the vertical direction These vertical restraints also provide a boundary that prevents rotation of the deck about its axis torsion Elastic superstructure Boundary conditions fa Rigid joint amp nd Rigid element d Superstructure lt lt width Fig 20 Roller abutment model This model can be used to provide a lower bound estimate of the longitudinal and transverse resistance o
100. n components Repair costs RC are obtained through a unit cost UC Repair times RT are obtained through a production rate PR The PRs are in terms of crew working days CWD representing one working day for a normal sized crew and can be combined later by construction management experts to obtain total site construction times 45 Repair cost A RC gt re G ue qdm dG dmledp dG edplim aim imanedp Repair tine ART gt rt ClprjamydG amedp dctedyim Aim mailed Repair Cost Loss Analysis G uc q dm Seismic in jamage tepai RC repar cost decision variable Hazard Analys Analysi Estimates UC unit repair cost Analysis Glg dm Repair Time Loss Analysis IM intensity R meast quantity A im RT repair tme decision variable LPR labor production rate Fig 49 Schematic procedure of the LLRCAT methodology for a single bridge component The characterization and visualization of the ground motion suites using different choices of IMs will be discussed in Section 6 3 The FEM parameter selection analysis options and outcomes that generated EDPs were similarly covered in Section 3 The bridge is then broken down into performance groups PGs for each major bridge superstructure substructure and foundation component Each performance group represents a collection of structural components that act as a global level indicator of structural performance and that contribute significantly to repair level decisions Perform
101. ngth kPa 46 457 27 600 Strain at maximum strength 0 00367 0 002 Crushing strength kPa 44 979 0 Strain at crushing strength 0 036 0 006 Ratio between unloading slope 0 1 0 1 Tensile strength kPa 6504 3864 Tensile softening stiffness kPa 1 771 820 1 932 000 Figs 12 14 show the stress strain curves for the steel core and cover concrete materials respectively These plots can be obtained for updated material properties directly from the interface by clicking on the corresponding View Stress Strain buttons in the Column Material Properties window Fig 10 The moment curvature response for the column is shown in Fig 15 generated with consideration of the overall deck weight 11 915 kN applied at the column top 14 MS Stress Strain Curve for Steel Material Stress Strain Curve File ssFile txt Fig 12 Stress strain curve for Steel02 material default values employed C represents compression and T represents tension E Stress Strain Curve for Core Concrete Material Siress Strain Curve File ssFile txt Fig 13 Stress strain curve of Concrete02 material for the core concrete default values employed C represents compression and T represents tension Important note The above displayed graphics applet allows for mouse driven zoom capability To zoom just left click and drag at the desired location 15 E Stress Strain Curve for Cover Concrete Material Stress Strain Curve File ss
102. normal standard deviation for all the computed IMs in a given PG The same information is shown graphically as a bar chart separate bar chart for each PG Such a figure is useful for determining the selection of optimal IM for a given EDP or PG BridgePBEE defaultCase pbe File Execute iss Evm Help TPG Quantites forAlMotons a Model Bridge amp Ground Peak Accelerations for All Motions t h Maximum Column amp Abutment Forces for All Motions l Bridge Only Zoomin STEP 1 Detailed Output Please Select Input Motion Current A ELC Analysis Deformed Mesh Motion A ELC C Pus Column Response Time Histories amp Profiles Motion A ELC 1 Column Response Relationships Motion A ELC Abutment Responses Motion A ELC Analysis Summary PBEE Analysis Ground Shaking PBEE Motions Model Definition Bridge Parameters Soil Parameters Mesh Paremeters Analysis Options Boundary Conditions B C Type ear i f Fixe Bedrock Type fi i STEP 2 EXECUTE FE ANALYSIS STEP 3 COMPUTE REPAIR COST PBEE Analysis Fig 88 Menu items to access the PG quantities for all motions 85 PG Quantities DAR Responses with respectto SRSS of Poy Conver Figures to EFS Format View Beta Values i IEE EEE EC f a A lrift ratio SRSS col IDriftRatioSRSS txt SA Period 1 sec ow Period 1 sec sO Period 1 sec PSA Period 1 sec FSW Period 1 sec Free tield FA Fre
103. nt response time hIstOries cccccceseesssseseesseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeees 42 Pig 40 Delormed mesh and contour Tirassa a E aasaes 42 Fig 47 Steps to perform an Eigenvalue analysis cccccscssseceecccccceceeeeeeecaaeeeessssseseeeeeeeeeeeeees 43 Fig 48 Sample output for an Eigenvalue analySiS cccccccccccccccceeeeeeaeeseeeeseseeceeeeeeseeeeeeaaaaas 44 Fig 49 Schematic procedure of the LLRCAT methodology for a single bridge component 46 Pe 50s Seps tode Nne PBEE MO MONS 55 vases easicaderataspiairsaeniace e a 51 Fig 51 PBEE imputmouons WdOW sinensis E aie ahsies aver uiaaiea ea diswiedeaveays 52 Fig 52 Intensity measures time histories and response spectra of individual record 53 Fig 53 Histogram and cumulative distribution for the whole input motion Set eee 53 Fig 54 Intensity Measures IM table for the whole input motion Set ccccseseeeeeeeeeeeeeees 54 Fig 55 Options to change number of records to be run at the same time cc eeeeeeeeeseeeeeeees 54 Fig 56 OPen Ses analysis In Procress x teteuiicndv er decteedesaicsleeagieeadiansa pe eases awe 55 FeS PBBE analysis windOw aside alent eid eileen ie ea 55 Fig 56 Damage states WINDOW Je haessescsasan ieie ened aniani i A ona aa neieiet aea Oe Aosa 56 Pig 50 Repar guantes WiIMUOW crcregen ranri a T E aguas caries 57 Fio 00 UME OSS WOW ce a a ana thane creeeabetawie 57 Fia 0l Pro
104. of labor and whether or not contract incentives are provided in order to decrease duration Repair times are also computed on the basis of each repair quantity Q For any repair item a probability of 50 that Q gt 0 indicates that the associated repair time should be added to the total repair time for the project 6 2 Input Necessary for User defined PBEE Quantities If the user is interested in providing user or project specific information in a PBEE analysis the following paragraphs describe the data needed by the interface to execute the PBEE analysis and post process the results Performance groups need to be defined for each important component or subassembly of the system that has potential repair consequences Performance groups are defined in terms of a single EDP that characterizes the response of this PG Once this EDP metric has been defined and time history analysis performed to obtain a distribution of EDP realizations for different ground motions the PBEE methodology can be implemented The PBEE methodology requires definition by the user of discrete damage states for each PG a repair method with associated repair quantities for each discrete DS for each PG and the corresponding costs and times required to execute the repair method The damage states are discrete and supplied in the form of what is commonly called a fragility curve This is a misnomer however because the information required 1s the value of the EDP not IM req
105. p in Longitudinal direction Print Load Displacement Curve 6 71 m above ground surface column top File load _dispX_6 71m txt Fig 124 Longitudinal pushover b Transverse Pushover Fig 125 Column Response Relationships Load displacement at 6 71 m column Top in Transverse direction Load Displacement Curve 6 71 m above ground surface column top File load _dispY_6 71m txt Kes ft ES Fig 125 Transverse pushover 117 10 Appendix C How to Incorporate User defined Motions 1 Directory Structure of a PBEE Motion Set To conduct a PBEE analysis input motions must be defined please follow the steps shown in Fig 50 The window to define PBEE input motions is shown in Fig 51 Click Browse to select a PBEE motion set Fig 126 Click on the motion set name e g PBEEMotionSet1 and then click on OK to choose this motion set Fig 126 In BridgeBPEE the input motions are organized in a format that the program can read Specially the input ground motions are sorted into bins Fig 127 shows the directory structure of a PBEE motion set named PBEEMotionSet1 The second level directories are bins e g LMLR LMSR Near SMLR SMSR see Fig 126 and Fig 127 The third level directories are earthquake names e g there are 3 earthquakes under bin LMLR BORREGO LOMAP NORTHR see Fig 127 And the fourth level directories are the input motion names e g there is 1 input motion under eart
106. p is the transverse steel percentage and K can be t obtained from the following equation for spirally confined circular columns 1 2 K 11 2 Where Pp A ce o A 12 An assumed value of the area of the confined core is used for default values This area should be modified based on the expected compressive block in the column during lateral loading 2 A alde 13 4 ad SS 14 Pde Where dy is the transverse bar diameter do D 26 0 15 Where c is the clear cover c 1 5 11 epscO Zi epscQ p E 16 C 124 Where Ec 0 043w J f Where w is the concrete unit weight unit kg m ili epsu epscu epscu 0 004 2p C Where 1s the ultimate steel strain 0 12 iv fpcu f epsc epscr l ji LPSCH enser epsc Where Te Ja epsc epsc0 1 5 1 E epscr _ E Ta epsc Notes 17 18 19 20 21 1 The information above is specific to the Steel02 and Concrete02 models of the Fiber section Other options include Fig 10 Steel01 and Concrete01 for more information please see the OpenSees documentation and Elastic properties for the fibers These options can be activated by clicking on the default Steel02 or Concrete02 sections Fig 10 and changing these options 2 A different property may be specified for the Column below grade for instance to roughly represent a
107. pile and soil might contribute this is an advanced feature and should be exercised with care 34 Damping Coefficients E Damping Curve Soil Strata 1 Sat cohesionless very loose silt permeability 2 Sat cohesionless very loose sand permeability 3 Sat cohesionless very loose gravel permeability 4 Sat cohesionless loose silt permeability Sat cohesionless loose sand permeability l Sat cohesionless loose gravel permeability 7 Sat cohesionless medium silt permeability id Sat cohesionless medium sand permeability I Sat cohesionless medium gravel permeability 10 Sat cohesionless medium dense silt permeability 11 Sat cohesionless medium dense sand permeabilif 12 Sat cohesionless medium dense gravel permeabi 3 Sat cohesionless dense silt permeability 4 Sat cohesionless dense sand permeability j15 Sat cohesionless dense gravel permeability 6 Cohesive soft 7 Cohesive medium 8 Cohesive stiff M Activate Column Zone Ma 9 U Sand j20 U Sandz Activate Column sail Intel ak U Cla Lar Saturated Soil Analysis aver hickness x aver hiCKHeSsS gt area ay z Kee i ARUGI nange Fig 37 Soil strata definition 35 U Clay2 for Soil Layer 1 Mass Density 2 ton m3 shear Wawe Velocity 430 ms Poisson s Ratio Cohesion C multiplied by fsqrtsiy2 180 kPa Cancel Feak shear strain Gamma multiplied by sarte s rom 0 001 20 Number of ield Surfaces 0 30 A
108. ps or conversions from PGA for an arbitrary IM The default PGA hazard values were obtained from USGS hazard maps These PGA values were converted to PGV values using the firm ground conversion of 48 1n sec g It 1s 59 not meant to imply that switching between PGA and PGV or any other IM will yield equal hazard Once a desired local site seismicity 1s defined users can click Display Hazard Curves Fig 57 to display the mean annual frequency of exceedance and return period Please see Section 7 2 2 for the detailed output 6 5 4 Compute Disaggregation Users can also click Display Disaggregation Fig 57 to display the disaggregation by performance groups and repair quantities Please see Section 7 2 3 for the detailed output Only the disaggregation of the expected repair cost time by performance group is possible due to the LLRCAT formulation However both expected and variance disaggregation plots are available when disaggregating by repair quantity The user can select the intensity measure and value on which to disaggregate The default value 1s a PGV value equal to the 10 probability of exceedance in 50 years specified in the previous section 60 7 Time History and PBEE Output 7 1 Time History Output Quantities At the end of the FE analysis phase time histories and bridge responses will be available of the form e Column Response Time Histories and Profiles e Column Response Relationships e Abutment Responses e Deform
109. r Windows 7 The system should have a minimum hardware configuration appropriate to the particular operating system Internet Explorer 3 0 or above or compatible Browser with Java Applet enabled is needed to view the graphic results For best results your system s video should be set to 1024 by 768 or higher Transverse axis Y Vertical axis Z Longitudinal axis X Fig 1 Coordinate system in BridgePBEE 1 3 Acknowledgments This research was funded in part by the Pacific Earthquake Engineering Research PEER Center Transportation Program Dr Stephen Mahin Director and Dr Yousef Bozorgnia Executive Director Dr Steven Kramer U of Washington Seattle coordinated a review process of BridgePBEE Feedback and suggestions provided by Dr Kramer and the anonymous reviewers are greatly appreciated OpenSees currently ver 2 1 0 is employed is a software framework Mazzoni et al 2009 for developing applications to simulate the performance of structural and geotechnical systems subjected to earthquakes for more information visit http opensees berkeley edu Throughout Dr Frank McKenna was always generous and gracious with his assistance in matters related to OpenSees The employed OpenSees geotechnical simulation capabilities were developed by Dr Zhaohui Yang and Dr Ahmed Elgamal For more information please visit http cyclic ucsd edu opensees The implemented PBEE analytical framework is provided by Dr Kevin M
110. r Lateral Response of Bridge Abutments with Typical Backfills J Bridge Eng 15 3 302 311 May Werner S D 1994 Study of Caltrans Seismic Evaluation Procedures for Short Bridges Proceedings of the 3rd Annual Seismic Research Workshop Sacramento California Yang Z Elgamal A and Parra E 2003 A computational model for cyclic mobility and associated shear deformation Journal of Geotechnical and Geoenvironmental Engineering 129 12 1119 1127 Zhang J and Makris N 2002 Kinematic Response Functions and Dynamic Stiffnesses of Bridge Embankments Earthquake Engineering amp Structural Dynamics 31 11 pp 1933 1966 133
111. r Wave Velocity Embankment Slope Yerical Horizontal Step 1 select SDC 2010 Sand Abutment Model amp Deck Length Deck width Number of Bearings Deck Depth Bearing Height Deck Properties Number of Shear Keys step 2 click Define Fig 30 Steps to define a SDC 2010 Sand abutment model 3 4 7 EPP Gap Model This model is similar to the Simplified SDC 2004 abutment model but employs user defined parameters for the stiffness maximum resistance and gap size between bridge deck and back wall To define an EPP Gap abutment model please follow the steps shown in Fig 32 30 Abutment Model SDC 2010 Clay Pea Gap 0 0254 m Step 3 enter parameters Initial Stiffness 114350 kN mm for SDC 2010 Clay Maximum Passive Pressure cad kPa abutment model skew Angle degree Soil Mass Density kg m3 soil shear Wave velocity ms Embankment Slope Verical Horizontall step 1 select SDC 2010 Clay Deck Length Deck Vviclth Number of Bearings Deck Depth 1 Bearing Height Deck Properties Number of Shear Keys Abutment Model EPP Gap cues Gap 0 0254 m Step 3 enter parameters Initial Stifness 28700 kimm for EPP Gap abutment Maximum Passive Pressure 239 kPa skew Angle degree Soil Mass Density kgm 3 soil shear Wave Velocity ms Embankment Slope Yertical Horzantal Deck Length Deck Wrictth Number of Bearings Deck Depth Bearing Height Deck Properties Number of Shear Keys
112. r wave velocity of the embankment soil respectively parameters in window see Fig 25 To define a Simplified abutment model please specify the parameters shown in Fig 25 The typical force displacement curve for the Simplified abutment model is shown in Fig 26 Abutment Model Simplified foe Gap step 3 enter parameters Initial Stiffness for Simplified abutment Maximum Passive Pressure model Skew Angle Soll Mass Density soll Shear Wawe Velocity Embankment Slope Verical Horizontal Wis Abutment Magde Deck Length Deck Width Number of Bearings Deck Depth 1 Rearing Height Deck Properties Number of Shear Keys step 2 click Define Fig 25 Steps to define the Simplified abutment model 24 Longitudinal Force Displacement Relationship Force resisting force acting on deck end displacement relative deck end abutment displacement Left Abutment Right Abutment File abutForceDispLL txt File abutForceDispRL txt BRAE E Transverse Force Displacement Relationship Force resisting force acting on deck end displacement relative deck end abutment displacement Left Abutment Right Abutment File abutForceDispLT txt File abutForceDispRT txt E E Fig 26 Longitudinal force displacement relationship for the Simplified abutment model a longitudinal direction b transverse direction 25 3 4 4 Spring Model A more complex abutment model was developed by Mackie and Stojadinovic
113. rations and c maximum free field accelerations 0006 90 Fig 94 Menu items to access maximum column amp abutment forces for all motions 9 Fig 95 Maximum column amp abutment forces for all motions a maximum column shear forces b maximum column bending moments and c maximum abutment fOFces eeeeeeeeeeeeeeeees 92 Fig 96 Contribution to expected repair cost from each performance group 0 cccecees 93 Fig 97 Total repair cost ratio as a function Of intensity ccccscssseeeeseeeeeeeeeeeeeeeeees 94 Fig 98 Contribution to expected repair cost from each repair quantity ccceeeeesseeeeeeee 94 Fig 99 Contribution to repair cost standard deviation from each repair quantity 95 Fig 100 Total repair time CWD Crew Working Day as a function of intensity 95 Fig 101 Contribution to expected repair time CWD from each repair quantity 96 Fig 102 Mean annual frequency of exceedance ground MOTION cccccccessesseeeseeeeeeeeeeeeeees 97 Fig 103 Return period against total repair cost PatiO cece eccccccecccccccceeeeeeeccaaeesesesseseeeeeeeeeeeeess 98 Fig 104 Mean annual frequency of exceedance loss against total repair cost ratio 6 98 Fig 105 Return period against total repair time ce ceeeeeeeeesseeecccceceeeeeeceaaaeeesssseeeeeeeeeeeeeeeees 99 Fig 106 Mean annual frequen
114. rection depth of the embankment below grade and total weight of the embankment the user must calculate this parameter to match the mass of the actual soil embankment The embankment parameters will have no effect in the rigid ground simulation cases but will contribute when the bridge is supported on soil mesh In addition a single pile represented only by beam column elements 1 e cross sectional geometry of the pile is not represented may be included by the user Fig 7 to further support the embankment abutment The single pile 1s positioned below the embankment geometric configuration closest to the bridge and aligned with the bridge longitudinal axis This option is activated by selecting the checkbox Activate Abutment Pile Length of this additional pile can be specified as well as its diameter The material properties of this pile can be the same as the bridge s central column or can be defined independently by clicking Define as shown in Fig 7 Upon clicking define a window similar to that of Fig 10 will open and the user can follow the procedures associated with Fig 10 as described earlier 18 3 4 Abutment Parameters Abutment behavior soil structure interaction and embankment flexibility have been found by post earthquake reconnaissance reports to significantly influence the response of the entire bridge system under moderate to strong intensity ground motions Specifically for Ordinary Standard bridge structure
115. rials Solid Element Option Sl Units mk SU jeee Eula Eleran E Enait Unk Nonlinear Mode Standard Brick Element C Mode Bhar Brick Element Mesh Display PBEE Options lf Show Axes Number of records to be ja Show Intermediate Modes for 20 Node Element run atthe same time Advanced Options Output Data Analy Include Column Response Profiles amp Relationships not gos Cine minj NEIME grounna SUMECE W Include Soil Displacement M Use Global Elastic Material for Application of Own eight Initial Lateral erical Confinement Ratio 0 1 0 9 Include Soil stress Strain Young s Modulus 600 M include F Include Soil Acceleration Display Deformed Mesh for Final step Only Recommended for Large Models Abutment Rigid Link Stifness x Pile Stiffness i OOOOoo0000 Cancel Change Opensees Options Change Rayleigh Damping Fig 34 Analysis options OpenSees Options Column Nonlinear Element Type nonlinearBeamColumn Number of Intergration Points 5 Pile Below Grade Nonlinear Element Type nonlinearBeamColumn Number of Intergration Points 3 Cancel Fig 35 Beam column element types available for column If you select Activate Tension Cutoff for Cohesive Soil as shown in Fig 37 the soil shear strength will become negligible when volumetric stress is tensile allowing for instance the pile to pull away without resistance from the adjacent clay on the side where tension between the
116. rs is 2 or larger To obtain a refinement near the embankment Fig 114 check Activate Adjusting Mesh beside Embankment this option is only valid if Num of Slices is 32 or larger Then define the size of the 1 layer as a factor of Deck Width Fig 114 shows an example of using this option To minimize the number of elements in the horizontal direction check Minimize Number of Elements in Horizontal Direction As a result all other options defined for the horizontal meshing will be ignored This checkbox option 1s particularly useful when a rigid ground case 1s needed Horizontal Meshing Vertical Meshing M Minimize Number of Elements in Horizontal Direction Mesh Layer Length From Col Center m 1 Col Radius Uniform Patio of Elernent Meshing Length over Next G 2 ch x 4 Embankment p al 4 1 TTT f E B 4 4 4 10 ToT fot m z _ _ Mesh Adjustment beside Embankment Activate Adjusting Mesh beside Embankment Size of 1st Layer Factor of Deck width Ratio of Element Size over Next 1 means Uniform cme sey Fig 113 Meshing controlling parameters for horizontal direction default values 106 SS N ne H N pee a i SA ea i Ine inca f oi PAAS 107 Fig 114 Adjusting mesh near embankment a before adjusting b after adjusting vertical direction starting from the ground surface downwards looking at the side vie
117. s Soil Parameters Mesh Paremeters Analysis Options Boundary Conditions B C Type hear Bea FE Bedrock Type STEP 2 EXECUTE FE ANALYSIS Save Model amp Run Analysis STEP 3 COMPUTE REPAIR COST PBEE Analysis lgePBEE For Help press F1 Fig 2 BridgePBEE main window 2 2 Interface There are 3 main regions in the BridgePBEE window menu bar the model input window and the finite element mesh window 2 2 1 Menu Bar The menu bar shown in Fig 3 offers rapid access to most BridgePBEE main features BridgePBEE Untitled BridgePBEE Untitled Fie Execute Ip Open Model i Close Model Save Model Save Model As Model Summary b BridgePBEE Untitled pbe Model PG Quantities for All Motions Seen Bridge amp Ground Peak Accelerations for All Motions Maximum Column amp Abutment Forces for All Motions STEP 1 Detailed Output Please Select Input Motion Current A ELC Analysis Deformed Mesh Motion A ELC Column Response Time Histories amp Profiles Motion A ELC C Pus Column Response Relationships Motion A ELC Fic Abutment Responses Motion A ELC Soil Response Histories Analysis Summary BridgePBEE Untitled File Execute Display Help idgePBEE Website nt x Finite Element Mesh About BridgePBEE STEP 1 DEFINE MODEL Model Input e Fig 3 BridgePBEE s menu and submenu bars a menu bar
118. s follows A bars amp 5 b Where p is the longitudinal steel percentage Table 1 A the column cross section area Ap 1s the cross section area of the steel bar If the number of longitudinal bars is known the longitudinal steel percentage reinforcement ratio can be calculated A a 6 C Where A is the area of longitudinal steel which is equal to the area of each bar times the number of bars For example the diameter of a 18 bar is 2 257 inches so area is 4 in If there are 10 bars in a 36 inch diameter circular column then 104 039 S 36 4 or 3 9 The transverse steel percentage reinforcement ratio for a spirally confined circular column currently the only type of column supported in the interface 1s 122 p u w da Where dp 1s the diameter of the transverse spiral always smaller than the diameter of the longitudinal bars The spacing between transverse bars is s The diameter of the confined core is des which is the gross diameter minus twice the cover and minus the diameter of the transverse bars see Eq 10 So for a 5 spiral spaced at 3 inches on center in the same column mentioned above r pamm 8 386 22 7 or 1 3 Currently the transverse reinforcement does affect the shear response through changes in the uniaxial constitutive model for the concrete core However the columns are modeled considering only flexurally dominated response 1
119. s for the SRSS of the 2 horizontal directions Fig 95 The figures in this window include Maximum column shear forces Maximum column bending moments Maximum abutment forces left abutment Maximum abutment forces right abutment 90 BridgePBEE defaultCase pbe PG Quantities for All Motions Model Inia l l Bridge amp Ground Peak Accelerations for All Motions Maximum Column amp Abutment Forces for All Motions Detailed Output Please Select Input Motion Current A ELC Analysis Deformed Mesh Column Response Time Histories amp Profiles Py Column Response Relationships C Eig Abutment Responses STEP i1 Motion A ELC Motion A ELC Motion A ELC Motion A ELC Ba Analysis Summary PBEE Analysis Ground Shaking PBEE Motions Model Definition Bridge Parameters Mesh Paremeters Soil Parameters Analysis Options Boundary Conditions B C Type Shear Beam Bedrock Type Pigi Bedrock STEP 2 EXECUTE FE ANALYSIS Save Model amp Run Analysis STEP 3 COMPUTE REPAIR COST Maximum Forces Response in Longitudinal direction with respect to Pay Maximum Column Shear Force kN File MaxColForce txt Kei We ts 9 Maximum Forces Eek Response in Longitudinal direction with respect to FG Maximum Column Bending Moment kN m File MaxColBendingMoment txt Maximum Forces Maximu
120. s in California with short spans and relatively high superstructure stiffness the embankment mobilization and the inelastic behavior of the soil material under high shear deformation levels dominate the response of the bridge and the intermediate column bents Kotsoglu and Pantazopoulou 2006 and Shamsabadi et al 2007 2010 Seven abutment models are implemented in BridgePBEE The abutment models are defined as Elastic Roller Simplified SDC 2004 Spring SDC 2004 SDC 2010 Sand SDC 2010 Clay and EPP Gap abutment models 3 4 1 Elastic Abutment The elastic abutment model Fig 17 consists of a simple set of 6 translational elastic springs at each end of the bridge see schematic below 2 longitudinal 2 transverse and 2 vertical springs By default no additional rotational springs are specified but can be added by the user Rigid joint w gt d Superstructure As w a width Fig 17 Elastic abutment model Bridge amp Rigid element To define an Elastic abutment model please follow the steps shown in Fig 18 The typical force displacement curve for the Elastic abutment model is shown in Fig 19 19 Abutment Model Elastic Poe Longitudinal Gap Only Used i tor PGEE Repair Cost Estimation Step 3 enter parameters kN m for Elastic abutment Longitudinal Stifness E Pe Transverse Stiffness kM mn 0000 Vertical Stiffness kim Rotation Longitudinal Axis k m rad Rotatio
121. se of soil mesh for earthquake excitation scenarios Acceleration Absolute or Total Rotation Bending Moment Shear Force Pressure e Response Summary Right Dropdown List e Longitudinal Direction 64 e Transverse Direction e Vertical Direction Please note that the above Middle Dropdown List is only valid for the longitudinal and transverse directions If the Vertical Direction in the Right Dropdown List is selected the Middle Dropdown List will become the displacement refers to the one relative to the model base e Displacement Acceleration Rotation Torsional Moment Torque Axial Force 1 Column Response Profiles The column response profile will be displayed if Response Profiles in the Left Dropdown List Fig 67 1s selected For example Fig 68 shows the bending moment in the longitudinal plane The horizontal axis of the plot is the response name e g displacement bending moment etc and the vertical axis is the elevation of the column and the pile shaft below grade Zero elevation means the ground surface For Displacement Acceleration and Rotation two lines are plotted for the response profile selected these lines are continuous e End the response profile at the final step e Max the response profile at a certain step when the maximum absolute value occurs In the cases of Bending Moment Shear Force and Pressure three lines are plotted e End Envelope Envelope of the response values at the final step
122. section is shown in Fig 10 Nonlinear beam column elements with fiber section Fig 11 are used to simulate the column pile shaft in this case Forced based beam column elements nonlinearBeamColumn Mazzoni et al 2009 are used for the column 1 element number of integration points 5 as well as the pile shaft below grade number of integration points 3 The default values for the material properties of the column pile shaft are shown in Tables 1 3 Bridge Model Step 2 Click Column Step 1 make sure Linear Properties Column is unchecked Ezo l ir a Embankment Foundation 05 rm i im otal eight of Embankment 30000 k 671 Activate Abutment Pile Abutment Pile Pile Length m Use Diferent Properties for Column below Grade Diameter rm Column below Grade Ri Diameter m i Youngs Modulus kPa Abutment Deck Abutment Mocel Spring Define Deck Length Deck Width Number of Bearings 3 Deck Depth i Bearing Height 0 051 m Deck Properties Number of Shear Keys Cancel Fig 9 Steps to define a nonlinear Fiber Section By default the Steel02 material in OpenSees Mazzoni et al 2009 is employed to simulate the steel bars and Concrete02 material is used for the concrete core and cover Steel02 is a uniaxial Giuffr Menegotto Pinto material that allows for isotropic strain hardening Concrete02 is a uniaxial material with linear tension softening The default values for the mat
123. sent rigid bedrock As such this input earthquake excitation constitutes total motion imparted at this Bedrock level Step 2 Click Mesh Parameters to define additional meshing parameters Tab General Definition Fig 112 Make sure Mesh Scale is Full mesh and Number of Slices is 16 or larger This parameter refines the mesh by creating additional elements in horizontal plane of the soil mesh Horizontal Meshing Vertical Meshing Mesh Scale E Column Mum of Slices 32 Please choose 16 or larger Humber of Bearm Column Elements above Ground Surface Please enter ifiber element is used Bridge Deck Number of Beam Column Elements for Deck Even Number 10 Fig 112 General meshing controlling parameters default values Tab Horizontal Meshing Fig 113 This section controls mesh refinement along the horizontal direction Length of each soil horizontal layer is defined in the left column Number 105 of mesh elements in each defined is specified in the column Number of Mesh Layers Note that the first mesh layer is starting from the center of the mesh when the column is located and the length of the first mesh layer is equal to the column radius The fourth mesh layer is for the embankment Ratio of Element Length over Next is used to obtain a gradually changing element size within a layer if Uniform Meshing is unchecked obviously this option is only valid if the of mesh laye
124. si a E EA 102 Appendix A How to Define the Soil Finite Element Mesh no000nonnnnnnnnnnnnnnnnsssssssssseee 104 Appendix B Simple Pushover Examples Bridge on Rigid Ground cccccceceeeeees 113 Appendix C How to Incorporate User defined Motions cccccccesccccccceeeeeeseeeeeeeeeeeeaas 118 Appendix D Calculation of Steel and Concrete Material Properties cccececccceeeeeees 122 Appendix E Customization of PBEE Quantities 2 0 0 cccccccccccccccccssssseeececceeeeesaeseeeeceeeeeaas 127 RGlCTON Cesena aes a aac cae ieee 132 il List of Figures Fig l Coordimate system in Bridger BEE ssactctcsnacesialstcana ie cantadandietaaetieriesieienaieeaantele 3 PG 2 PO CP PBEE mani Wy TIN OW cies atsencae ahah onsdoeen see eemeansantesseMeshchanedo essere stncsie usa scenes tatanstas 5 Fig 3 BridgePBEE s menu and submenu bars a menu bar b menu File c menu Execute d MEn DISplay and eJ memi FU es faa ai tne tess saad te ona a a a 6 Fig 4 BridgePBEE copyright and disclaimer WIndOW c cseeeessseeeeeseeeeeeeeeeeeeeeeeeeeeeeeeeeeeees 7 Fig 5 Buttons available in the Finite Element Mesh window ccccsesseseeeeeseeeseeeeeeeeeeeeeeeees 8 Fig 6 BridgePBEE main window defining a bridge model ccccccceccceeeeeeeeeeeeeeeeeeeeeeeeeeeeees 9 Fig Ja Brde Model Wdowiec a Gites veal awn Rie 10 Fig 8 Steps to define the elastic properties of the column cccc
125. sis Output Disaggregation of Expected Cost by Repair Quantity PGV 100 cm sec File DisaggCost txt Structure excavation Structure backfill Temporary support superstructure lt Temporary support abutment Structural concrete bridge Structural concrete footing Structural concrete approach slab Aggregate base approach slab Bar reinforcing steel bridge Bar reinforcing steel footing retaining wall Epoxy inject cracks Repair minor spalls Column steel casing Joint seal assembly Elastomeric bearings Drill and bond dowel Furnish steel pipe pile Drive steel pipe pile Drive abutment pipe pile Asphalt concrete Mud jacking Bridge removal column Bridge removal portion Approach slab removal Clean deck for methacrylate Furnish methacrylate Treat bridge deck Barrier rail Re center column Fig 108 Disaggregation of expected repair cost by repair quantities 101 MM PBEE Analysis Output Disaggregation of Expected Time by Repair Quantity PGV 100 cm sec File DisaggTime txt Structure excavation Structure backfill Temporary support superstructure lt Temporary support abutment Structural concrete bridge Structural concrete footing Structural concrete approach slab Aggregate base approach slab Bar reinforcing steel bridge Bar reinforcing steel footing retaining wall Epoxy inject cracks Repair minor spalls Col
126. strain amp eff confinement Shear stress yz vs strain amp eff confinement Longitudinal normal stress time histories Transverse normal stress time histories 11 e Shear stress zx time histories e Shear stress yz time histories Right Dropdown List Fig 83 e Longitudinal plane crossing column center e Transverse plane crossing column center Distances away from the column center are calculated to match the corresponding soil nodes and are listed in the Middle Dropdown List Fig 84 Fig 85 1s the sample output of the soil settlement time histories under the left abutment BridgePBEE defaultCase pbe Sele File Execute esky Help PG Quantities for All Motions x aA Model In Bridge amp Ground Peak Accelerations for All Motions t Mesh Ox STER T Maximum Column amp Abutment Forces for All Motions l Bridge Only Zoom in Out Frame xY t gt Up Dn Detailed Output Please Select Input Motion Current A ELC Analysis Deformed Mesh Motion A ELC Column Response Time Histories amp Profiles Motion A ELC C Pu Column Response Relationships Motion A ELC an Abutment Responses Motion A ELC Soil Response Histories Motion A ELC C Ba Analysis Summary PBEE Analysis Ground Shaking PBEE Motions Model Definition Bridge Parameters Soil Parameters Mesh Paremeters Analysis Options Boundary Conditions B C Type Shear Beam M Fixed Vert B
127. t Relationships Longitudinal Force Displacement Relationship Force resisting force acting on deck end displacement relative deck end abutment displacement Left Abutment Right Abutment File abutForceDispLL txt File abutForceDispRL txt Kes ft 5S 7 Abutment Responses Relative Deck end Abutment Displacement Time Historie v Relative Deck end Abutment Longitudinal Displacement Left Abutment File abutDispHistLL txt Relative Deck end Abutment Transverse Displacement Left Abutment File abutDispHistLT txt Abutment Responses Resisting Force Time Histories Longitudinal Resisting Force Left Abutment File abutForceHistLL txt Kes fh fot Transverse Resisting Force Left Abutment File abutForceHistLT txt Abutment Responses lt ee PEK Pile Cap Displacement Time Histories Pile Cap Longitudinal Displacement Left Abutment File abutPilecapDispHistLL txt Pile Cap Transverse Displacement Left Abutment File abutPilecapDispHistLT txt Fig 78 Abutment response time histories scroll down to see all directions a abutment force displacement relationships b relative deck end abutment displacement time histories c resisting force time histories and d abutment pile cap time histories 75 7 1 4 Deformed Mesh The deformed mesh can be accessed by clicking menu Display Fig 3 and then Deformed Mesh Fig 79 The deformed mesh window is shown in Fig
128. t data is large and all output cannot be loaded into memory To display output for a different input motion please follow steps shown in Fig 65 The name of the selected input motion will also appear on the menu items Fig 63 6l EF Bndgef BEE defaultiase1 pbe EF a a eos ee x 1 Fintte Element Mesh Maximum Column amp Abutment Forces for All Motons a l Bridge Only Zoomin Out Frame aor Deformed Mesh Column Response Time Hetories amp Profiles Column Response Relatonshis Abutment Responses PBEE i LEJER C Ground Shaking Model Definition Bridge Parameters Soil Parameters Mesh Parameters Analysis Options Boundary Conditions B C Type Bedrock Type Sigd Pedro STEP 2 EXECUTE FE ANALYSIS Save Model amp Run Analysis STEP 3 COMPUTE REPAIR COST Hi BridpePBEF defanitCase nha r PG Quantities for All Motions 3 f t Mesh Bridge amp Ground Peak Accelerations for All Moons Mandmum Column amp Abutment Forces for Al Motions l Bridge Only Zoom In Out Frame Detaled Output Please Select Input Motion Curent A ELC Deformed Mesh Column Response Time Hetories amp Profes Column Response Relabonships Abutment Responses PBEE Analysis Ground Shaking PBEE Motions Model Definition Bridge Parameters Soil Parameters Mesh Faremeters Analysis Options Boundary Conditions B C Type Bedrock Type STEP 2 EXECUTE FE
129. th Om ground surface File ldispHis Om txt Depth 0 5m File IldispHis_ 0 5m txt Fig 83 Planes for locations of the soil response time histories 79 Response Time Histories Motion A ELC Longitudinal acceleration time histories at 0 0 m column center in Longitudinal plane crossing column cent 0 0 m fcolurin center Print 0 61 mi from column center 11 1234 mi from column center 22 005 mi from column center as 34 9114 m from column center oe Longitudinal A 45 mi from column center j m s s Depth Om grq57 5 m from column center is Om txt T m from column center be 5 m from column center 95 rm from column center 0 61 m from column center 11 1234 m from column center 22 005 m from column center 34 9114 m from column center 45 m from column center 57 5 m from column center 70 m from column center 02 5 m from column center 95 m from column center Depth 0 5m Fle laccHis 0 5m Fig 84 Locations of soil response time histories Response Time Histories Motion A ELC Vertical displacement time histories at 45 m from column center in Longitudinal plane crossing column cent Vertical Displacement Time Histories m Depth Om ground surface File vdispHis Om txt a Depth 0 5m File vdispHis_ 0 5m txt a Fig 85 Soil settlement time histories under abutment 80 7 1 6 PBEE Output Quantities At the end of the finite element analysis phase
130. the following output performance group quantities for each earthquake record are used in the next phase of PBEE analysis Table 11 PBEE Performance Groups Pet ormance Performance group names PG Maximum column drift ratio Residual column drift ratio Maximum relative deck end abutment displacement left Maximum relative deck end abutment displacement right Maximum bridge abutment bearing displacement left Maximum bridge abutment bearing displacement right Approach residual vertical displacement left Approach residual vertical displacement right Abutment residual pile cap displacement left Abutment residual pile top displacement right Column residual pile displacement at ground surface Oo AOANMABWN e o In addition Intensity Measures for the computed Free Field ground surface acceleration records are computed so that outcomes can be either shown against the input base shaking IMs or the computed ground surface IMs noted as Free Field in the user interface The sections below detail how the response quantities are obtained for each PG Refer to Fig 86 for the annotated model that is used to describe the location of sampling points during time history analysis PG1 Maximum tangential drift ratio SRSS column PG2 Residual tangential drift ratio SRSS column The tangential drift ratio is defined as the maximum of a displacement above the inflection point divided by the length of this distance and
131. tion around 2 Time Total Number of Steps oo Cancel Fig 40 Load pattern for pushover analysis 5 1 1 Pushover by User Defined Load Pattern U Push To define your own load pattern U Push please follow the steps shown in Fig 41 The U Push window is shown in Fig 42 Click Select Change Pushover File to change file The user defined pushover file should contain single column data 38 Pushover Type Step 1 click U Push C Monotonic Puy Force Based Method oie Pus TTE Sin Mizi C Displacement Based Method E EE Displacement Increment Fer step Logitudinal tj Fore Step 2 click Define U Push Transverse ri Fo Transverse Displacement Longitudinal Displacement Vertical 2 Force Vertical Displacement Moment ot Rotation around x Moment ot Rotation around Moment ot Z Rotation around Z Time Total Number of steps Applied Location Column Head AOE OGE Pied ange ig To Fig 41 Steps to define a user defined load pattern U Push 39 Current W Push File CAProgram Files BridqePBEE motions upush tet select Change Pushover File CAProgram Files BridqePBEE motions upush 1 tet UF ish Cet _ View Pushover Loading Histor Number of steps Value starting Point 0 Ending Point 4 207 10e 007 Max Yalue Point 1 25999 Min Walue Point axis Step Vertical axis None BRE Fig 42 Example of user de
132. tions it Mesh E Maximum Column amp Abutment Forces for All Motions l Bridge Only Zoomin Frame gt Up Dn STEP 1 Detailed Output Please Select Input Motion Current A ELC Analysis Deformed Mesh Motion Column Response Time Histories amp Profiles Motion Column Response Relationships Motion Abutment Responses Motion Analysis Summary PBEE Analysis f Ground Shaking PBEE Motions Model Definition Bridge Parameters Soil Parameters Mesh Paremeters Analysis Options Boundary Conditions B C Type ShearBeam i Bedrock Type Bigid Bedrock STEP 2 EXECUTE FE ANALYSIS Save Model amp Run Analysis STEP 3 COMPUTE REPAIR COST PBEE Analysis 63 E PBEE Motions Flease choose a motion 100 records in total PGASRSSig PGVSRSSim s Mex Drift Ratio 0 601 b Fig 65 Steps to display output for a different input motion a click menu Display Fig 3 b select an input motion 7 1 1 Column Response Time Histories and Profiles The column response time histories and response profiles can be accessed by clicking menu Display Fig 3 and then Column Response Time Histories and Profiles Fig 66 The column response window is shown in Fig 67 There are 3 dropdown lists available for users to choose The contents of the 3 lists are as follows Left Dropdown List e Response Histories e Response Profiles Middle Dropdown List Displacement relative to ba
133. tment is assumed to have a nominal mass proportional to the superstructure dead load at the abutment including a contribution from structural concrete as well as the participating soil 26 mass An average of the embankment lengths obtained from Zhang and Makris 2002 and Werner 1994 is included in the calculation of the participating mass due to the embankment of the abutment The user can modify the lumped mass through the soil mass Rigid element 1 Flastic superstructure Rigid element 2 Rigid joint 2 Web 3 spacing Elastomeric bearmg pads BP As many BPs as webs of box girder BP response L ILP Participating mass Zhang and Makris 2002 Wi Embankment NO 2002 Werner 1994 nonlinear springs 4 7 J bk cae Bearing pads response Longitudinal BP shear resistance and backwall gap contact element in parallel Transverse J BP shear resistance and brittle shear keys Embankment response Longitudinal L SDC 2004 backbone curve Transverse T Modified SDC 2004 backbone curve Vertical F Embankment vertical stiffness extreme BPs only in parallel Vertical F BP vertical stiffness and contact element for stem wall in parallel Fig 27 General scheme of the Spring abutment model Aviram et al 2008 Table 6 Geometric and Material Properties of a Bearing Pad Shear Modulus G 1034 2 kPa 0 15 ksi Young s Modulus E 34473 8 kPa 5 ksi Yield Displacement 150 shear s
134. train A Lateral Stiffness where A is the cross section area and A is the height EA Vertical Stiffness Pi Vertical Tearing Stress 15513 2 kPa 2 25 ksi To define a Spring abutment model please follow the steps shown in Fig 28 The default values for the Spring abutment model are shown in Tables 7 amp 8 The typical force displacement curve for the Spring abutment model is shown in Fig 29 21 Abutment Model Spring z x fLongitudinal Gap 0 1016 m Initial Stiffness i 1500 kN mm Maximum Passive Pressure 1239 kFa step 3 enter parameters for Spring abutment model 30000 kN Skew Angle Soil Mass Step 1 select Spring soil Mass Density Soil Shear Wave velocity Embankment Slope Verical Horizontal 0 5 Vertical Tensile Force Factor i for Bearing Fad i ms Step 2 click Define O AButmentModel Grring SDC 2004 Deck Length 90 m pring L Deck Width 119 m Number of Bearings Deck Depth 1 83 m Bearing Height Deck Properties Number of Shear keys step 4 enter of bearings and the bearing height Fig 28 Steps to define a Spring abutment model Table 7 Spring Abutment Model Properties Parameter Value Soil mass Mg 150 Skew angle degree 0 Soil shear wave velocity m s 150 Embankment slope 2 Soil mass density kg m 1 760 Longitudinal gap m 0 1016 Table 8 Abutment Configurations Parameter Val
135. tudio 2005 130 BridgePBEE Edit View Favorites Tools Help acl Bs Ey a p Search Folders fF 7 Name ize Type File and Folder Tasks A ed wanuol 37 eve Application 3 A EE FUE is eene Aprin 11 21 2011 ee unins000 dat 3 DAT File 11 21 2011 6 K Sai this folder to the README txt Text Document 9 29 2011 4 E Share this folder ar File Confirm File Replace x sion al OTOEMY olotannle HOR iL1IA 108E i anle Q 23 2011 2 G Program Files 7 a 8 6 2010 11 B hy Documents Would you like to replace the existing fle 11 21 20116 gt Shared Documents 8 50 KB 11 21 2011 6 modified Monday September 26 2011 12 34 10 AM 9 6 2011 11 3 W My Computer a My Network Places with this one A 9 00 KB H modified Today December 14 2011 4 17 19 PM Other Places Me This folder already contains a file named PBEE dll 11 9 2011 3 11 21 20116 Details BridgeP File Folder Date Modified Monday November 21 2011 6 40 PM 15 0 MB E My Computer Fig 134 Replacing file PBEE DLL under the installation folder 131 13 References Aviram A Mackie K R and Stojadinovic B 2008 Effect of Abutment Modeling on the Seismic Response of Bridge Structures Earthquake Engineering and Engineering Vibration 7 4 395 402 Berry M P and Eberhard M O 2007 Performance Modeling Strategies for Modern Reinforced Concrete Bridge Columns Report No 2007 07 Pacific Earthquake Engineering Rese
136. ue Number of bearings 3 Bearing height m 0 051 Number of shear keys 2 Shear key height m 1 83 28 Longitudinal Force Displacement Relationship Force resisting force acting on deck end displacement relative deck end abutment displacement Left Abutment Right Abutment File abutForceDispLL txt File abutForceDispRL txt es lt ot Kes ls et Transverse Force Displacement Relationship Force resisting force acting on deck end displacement relative deck end abutment displacement Left Abutment Right Abutment File abutForceDispLT txt File abutForceDispRT txt es I fet Ke i fet Fig 29 Force displacement relationship for the Spring abutment model a longitudinal direction b transverse direction 29 3 4 5 SDC 2010 Sand This model is similar to the Simplified SDC 2004 abutment model but employs the parameters of the most recent SDC 2010 for a sand backfill Embankment To define a SDC 2010 Sand abutment model please follow the steps shown in Fig 30 3 4 6 SDC 2010 Clay This model is similar to the Simplified SDC 2004 abutment model but employs the parameters of the most recent SDC 2010 for a Clay backfill Embankment To define a SDC 2010 Clay abutment model please follow the steps shown in Fig 31 Abutment Model SDC 2010 Sand Mae Gap Step 3 enter parameters Initial Stiffness for SDC 2010 Sand Maximum Passive Pressure abutment model skew Angle soll Mass Density soll shea
137. uired to trigger different probabilities of exceeding the given discrete DS It is often assumed that said curves are well described by the lognormal probability distribution and therefore the only parameters required are the two lognormal distribution parameters lambda and beta Lambda is the median and beta is the lognormal standard deviation A PG can have as many discrete DS as are required to cover the full range of possible responses experienced by the PG These should be input as is shown in Section 6 5 1 below Once the different states of damage have been established damage scenarios need to be generated that show different possible snapshots of damage that the structure may be in after an earthquake event Once these scenarios have been generated note the scenarios need to be detailed and include exact descriptions of the extent and depth of damage they can be used to decide what repair method would be appropriate for each PG or group of PGs Such information is specific to the type of structure the discrete DSs and the PGs It is really only obtainable from experts with past experience designing repair procedures given a damage scenario or snapshot Once the repair methods have determined specific details about the repair quantities specific meaning square footage of deck cubic yards of concrete etc can be specified The current data employed in the interface has repair quantities parameterized in terms of the common bridge des
138. uite 6 3 1 Available Ground Motions Four ground motion data sets are available Motion Set 1 This PBEE motion ensemble were obtained from the PEER NGA database http peer berkeley edu nga and consist of 100 3D input ground motions triplets sorted into 5 bins Each motion is composed of 3 perpendicular acceleration time history components 2 lateral and one vertical These motions were selected through earlier efforts Gupta and Krawinkler 2000 Mackie et al 2007 to be representative of seismicity in typical regions of California The motions are divided into 5 bins of 20 motions each with characteristics 1 moment magnitude Mw 6 5 7 2 and closest distance R 15 30 km 11 Mw 6 5 7 2 and R 30 60 km 111 Mw 5 8 6 5 and R 15 30 km iv Mw 5 8 6 5 and R 30 60 km and v Mw 5 8 7 2 and R 0 15 km The engineering characteristics IMs and time histories of each motion and of the ensemble overall may be viewed directly within BridgePBEE Motion Set 2 These motions 160 in total are developed by Dr Mackie from the 80 motions of Motion Set 1 excluding the 20 motions in bin v above to account for the more accurate site classifications NEHRP C and NEHRP D in NGA The magnitude distance and spectral shape were intended to be similar to the previous bins and indeed all of the previous motions appear in either the NEHRP C or NEHRP D bins now As such these motions are divided into 8 bins compared to the 4 bins of Motion Set 1 4
139. umn steel casing Joint seal assembly Elastomeric bearings Drill and bond dowel Furnish steel pipe pile Drive steel pipe pile Drive abutment pipe pile Asphalt concrete Mud jacking Bridge removal column Bridge removal portion Approach slab removal Clean deck for methacrylate Furnish methacrylate Treat bridge deck Barrier rail Re center column Fig 109 Disaggregation of expected repair time by repair quantities 7 2 4 EPS Version of All PBEE Figures A MS Word file contained all PBEE figures in the EPS format can be created as shown below 102 Case2BMesh4 RepairCost doc Read Only Microsoft Word o E amp 8 Home Insert Page Layout References Mailings Review View Add Ins g r r 1 r I F l r eae dam 2 8 2 E L ea E 5 M I y 1 i ne ee oe i ow k ee bibeeded dues r Is ee i ee a a a A Fig 1 Contribution to expected repair cost 5 from each performance group r Page 1 of 8 Words 118 English U 5 Fig 110 Converting all PBEE figures to EPS format 103 8 Appendix A How to Define the Soil Finite Element Mesh A bridge and approach embankments supported on a ground strata will be defined The bridge configuration is shown below Fig 111 In this simple configuration the approach embankments are idealized by a rigid triangular configuration employed to exert the self weight of these embankments on the supporting ground Column
140. ure and soil mesh generation Simplified assignment of material properties for both the soil and structure Time history and PBEE analyses Visualization of output data The interface is unique because it enables complete PBEE studies in a single GUI driven package The PBEE implementation employed is based on Pacific Earthquake Engineering Research PEER Center s performance based earthquake engineering framework Cornell and Krawinkler 2000 The framework includes several building blocks intermediate probabilistic models that allow the user to generate probabilistic estimates of repair cost and repair time consequences or decision variables directly These results are obtained seamlessly in the interface alongside more traditional outputs such as displacements strains etc The intermediate models require e Hazard model that uses earthquake ground motion data to determine an intensity measure IM e Demand model uses response from dynamic analysis to determine an engineering demand parameter EDP e Damage model connects the EDP to a damage measure DM or discrete set of damage states DS e Repair model describes repair methods and repair quantities Q necessary to return the DSs to original functionality e Loss model links Qs to consequences that are termed the decision variables DV Repair cost and repair time can be thought of as two possible decision variable DV outcomes characterized probabilistically by the framework Th
141. uttons shown in Fig 5 Finite Element Mesh Fig 5 Buttons available in the Finite Element Mesh window 3 Bridge Model To define a bridge model click Bridge Parameters in the Model Input window Fig 6 Fig 7 displays the Bridge Model window For a single bent bridge essentially four parts are needed to define column deck embankment and abutment EF Bridge BEE defaultlase pbe Fie Execute Deplsy Help Hi Model Input x Lid Finite Element Mesh Re G I Bridge Only Zoomin Fra STEP 1 DEFINE MODEL Liei ridge Only Zoomin Out Frame Analysis Type C Pushover C Eigenvalue To define a bridge model cicco Click Bridge Parameters PBEE Analysis f Ground Shaking Model Definition Bridge Parameters ool Parameters Mesh Paremeters Analysis Options Boundary Conditions B C Type s Fre Bedrock Type STEP 2 EXECUTE FE ANALYSIS Seve Model amp Run Analysis STEP 3 COMPUTE REPAIR COST PBEE Analysis Fig 6 BridgePBEE main window defining a bridge model Bridge Model Colur npankmern Qolumn parameters Er mbankment parar lepih of Embankment Foundation Ciameter f o Total seign of Embankment Total Column Length 1 Colurin Length above Grade E71 0 Civote Abutment Fie Anutrnen Pile File Length Column Properties Linear Coluran se Different Properties for Column below Grade Column
142. w from the Tab Vertical Meshing Fig 115 This section defines the soil profile layering along the top downwards Height thickness of each soil layer is defined in the left column Number of mesh elements in each defined is specified in the column Number of Mesh Layers at least equal to 1 to define a soil profile consisting of a single type of soil Height thickness of this layer must be equal to the entire soil stratum height Note that the number of mesh layers in the upper zone where the pile foundation is embedded will automatically define the number of beam column elements of this pile below ground surface As such it is generally advisable to select an adequate number of mesh layers in this zone Note If there 1s any error during mesh generation please follow the error message instructions to adjust the controlling parameters and then try again Note Element size is a parameter that affects frequency content of the ground response Smaller size elements particularly along the soil domain height will permit higher frequencies if present in the input motion to propagate to the ground surface with more fidelity General Definition Horizontal Meshing Vertical Meshing Mesh Layer Height Number of Ratio of Top From m Mesh Uniform Element Height Topdown Layers Meshing ower Bottom 1 H xl 5 mo lt TTT TTT TIITII qQ 4 qQ qI Fig 115 Mes
143. y abut abut Forme P shut Kelative displacement Nett bridge abutment A butments Fig 24 Longitudinal backbone curve force displacement relationship two on each end of the bridge Caltrans SDC 2004 In the transverse direction a zero length element is defined at each end of the rigid link with an assigned Elastic perfectly plastic EPP backbone curve representing the wing wall and pile resistance similar to the longitudinal backbone The transverse backbone is obtained by multiplying the longitudinal backbone by Cz 2 3 and Cw 4 3 and is mobilized immediately there is no gap in the transverse direction The resistance of the brittle shear keys and distributed bearing pads is ignored in this model for simplicity Skew changes the orientation of the rigid link at the end of the deck segment 25 In the vertical direction an elastic spring is defined at each end of the rigid link with a stiffness corresponding to the vertical stiffness of the embankment soil mass The embankment is assumed to have a trapezoidal shape and based on the effective length formulas from Zhang and Makris 2002 the vertical stiffness K unit 1 m can be calculated from Zhang and Makris 2002 v fas z nf 3 Lo Where H is the embankment height d is the deck width z 0 5d S S is the embankment slope parameter in window see Fig 20 E 2 8G G pV p and V are the mass densit g sl P s P S y and the shea

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