Seismic Assessment of Plaridel Bridge

SEISMIC ASSESSMENT OF PLARIDEL BRIDGE USING FRAGILITY CURVE Engr. Michael B. Baylon1 1

Faculty, Civil Engineering Department, Adamson University, Ermita, Manila, Philippines, 1000

Abstract: Seismic assessment started long ago during the Spain colonization in the Philippines, observation of the effects to the structure after an earthquake by naked eye and documentation of each recorded effects has now evolved to different methods that analyses the performance of a building using calculations and software. The bridge was modeled using a computer software package. After the simulations, the researcher obtained set of seismic fragility curves. The research study tackled the Non-linear Static Analysis or the Pushover Analysis, the Non-linear Dynamic Analysis or the Time History Analysis, the ductility factors and then gaining the Fragility curves. Developed seismic fragility curves show the performance of the bridge’s pier at each peak ground acceleration. The Plaridel Bridge can withstand the earthquakes occurring in the Philippines based from the maiden structural plans. Key words: seismic fragility curves, pushover curves, time history analysis, hysteresis.

1. INTRODUCTION Since the Philippines is an island country that is located between two major tectonic plate which is the Eurasian and Pacific plates and near the Pacific ring of fire, it makes the country as one of the many countries in the world that is vulnerable to earthquake (Philippine NDCC, 1990). Based from the Philippine Institute of Volcanology and Seismology or also called as PHIVOLCS, the country is experiencing an average of five earthquakes per day between 1589 to 1990 that results liquefaction, landslides and tsunamis (ADB, 1994). The country experienced numerous major earthquakes that has a magnitude of 7.3 up to 8.3 in the year 1944 to 1993 (Rantucci, 1994). For an island country, bridges are naturally built for an accessible transportation to a different land masses. Bridges, to be less vulnerable once an earthquake strikes, require seismic design which is continually upgrading for modern bridges. Many of constructed bridges that do not attain the requirements of the new level of seismic design are needed to be retrofitted. In addition, bridges can only be retrofitted when it is socially, economically and technically beneficial; those that fail to achieve these requirements are supposed to

be replaced with new bridges (Priestley, Seible and Calvi, 1996). Being built in the late 1990’s The Plaridel bridge in Pangasinan was chosen as the research focus of the study as it was suspected to be vulnerable to damage during an earthquake. Failure to study the effect of an earthquake to a structure may cause not only property lost but also lives of many, due to this matter Seismic assessment is done to prevent or at least reduce the damage. Seismic assessment started long ago during the Spain colonization in the Philippines, observation of the effects to the structure after an earthquake by naked eye and documentation of each recorded effects has now evolved to different methods that analyses the performance of a building using calculations and software. With the present technology and knowledge, assessing a structures response in an earthquake can be done with less uncertainty. One of the most important elements in evaluating the Seismic Assessment of a structure is the so-called fragility curve (Cheng, 2001). The development of the seismic fragility curve takes into account the vulnerability of a structure wherein which for each damage state (slight, moderate, extensive and complete damage); the percentage probability of exceeding a particular damage is plotted with the ground motion intensity (expressed in terms of peak ground

acceleration or PGA) (Karim & Yamazaki, 2001). The research study will yield results of seismic assessment of the Plaridel bridge in Carmen, Pangasinan using fragility curve, that can be used by designers to establish if there is a need for retrofitting of the bridge to comply with the required design of the National Building Code of the Philippines. 2. METHODOLOGY The researcher aim to construct a seismic fragility curve of the Plaridel bridge (Figures 2.1 and 2.2) using Nonlinear Static Analysis and Nonlinear Dynamic Analysis. The researcher went to the Department of Public Works and Highways to obtain the structural plans of the Plaridel bridge. Using the SAP2000 software, the structure was modelled and subjected to ground motions (Figure 2.3). The AutoCAD rendering of Plaridel Bridge can be shown in Figure 2.4. Thereafter, the structure was analysed using pushover analysis and time history analysis. Analysis produced parameter values that was use for the construction of seismic fragility curves.

Figure 2.3. SAP2000 model of Plaridel Bridge Pier 9.

Figure 2.4. AutoCAD 3D Model of Plaridel Bridge deck without the steel truss. This research referred to the method for constructing fragility curve and for the nonlinear static analysis by (Requiso, 2013) and to the method for the nonlinear dynamic analysis by Karim & Yamazaki (2001). Figure 2.1. Before the July 1990 Baguio Earthquake aftermath of Plaridel Bridge. (Source: http://foundationspecialists.com/bridge%20retrofitting%20page%202.ht m)

Figure 2.2. After the retrofitting of Plaridel Bridge. (Source: http://foundationspecialists.com/bridge%20retrofitting%20page%202.ht m)

The Plaridel bridge was symmetrically designed from the length of pier to pier to the reinforcement design of the pier itself, due to its symmetrically designed elements the researcher focused on a pier that is assumed to be more susceptible to failure when subjected to earthquake loads. Pier 9 which has one of the most exposed length has been chosen and was modelled in SAP2000 (Figure 2.3). In creating a model of the Pier 9, the column and the coping beam must be defined in SAP2000.The researcher used section designer to design the column and coping beam. After defining the properties of the pier, the researcher assigned the properties based on the specified length of the plan in a modelled frame. This model will be used for the Pushover analysis and Time history analysis. After creating the model together with the loads, the researcher has performed the simulation

for both nonlinear static and nonlinear dynamic analyses.

will be used to compute for the ductility factors together with the results of the time history analysis.

Figure 2.5. SAP2000 model of the Plaridel Bridge pier column.

Figure 2.7. Research Methodology

Figure 2.6. SAP2000 model of the Plaridel Bridge coping beam. A step by step procedure in conducting the pushover analysis in SAP2000 software was used by the researcher based from the procedure of study of Requiso in 2013. First, the researcher created and defined the model using SAP2000. Second, the researcher then defined the properties for the pushover hinges. These pushover hinges are plastic hinges formed when a section reaches its moment capacity which the SAP2000 will show the yield and max displacement. Third, after defining and assigning the hinges, the researcher defined the load cases for the pushover analysis. The following were examples from pushover analysis at x direction. The researcher ran the simulation per pushover analysis after they defined all the load cases of the model. The SAP2000 generated the pushover curve, then the researcher exported the table coming from SAP2000 to Microsoft Excel to get the exact value of yield displacement and max displacement. This values

The next procedure was the time history analysis using the following step by step procedure of Karim and Yamasaki (2001). First, the researcher defined the time history functions. The researcher input the ground motion data that were acquired in terms of 0.2g to 2.0g. The total number of ground motion data used was 15 for x direction and 15 for y direction. After importing all the ground motion data to SAP2000, the researcher defined the load cases to be used for the nonlinear dynamic analysis or the time history analysis. This was done for both x and y direction. It shows the defined load case for 0.2g excitation of Bohol ground motion data at x direction. Using the previous model from the pushover analysis but removing all the pushover load cases, the researcher ran the simulation by subjecting the model to dead load, live load, and different ground motion data individually. It shows 1 of 30 ground motion data used for the analysis. The SAP2000 then generated the hysteresis model of the structure which was exported to AutoCAD for the computation of its area and determination of maximum displacement. After getting the values needed from both nonlinear static and nonlinear dynamic analysis, the ductility

factors have been obtained by using equations 1, 2, and 3. To come up with seismic fragility curves, these ductility factors are needed (Karim & Yamazaki, 2001). An example of computed Ductility factors from Bohol earthquake is shown in Table 2.1.

𝛿𝑚𝑎𝑥 (𝑑𝑦𝑛𝑎𝑚𝑖𝑐) 𝛿𝑦 𝛿𝑚𝑎𝑥 (𝑠𝑡𝑎𝑡𝑖𝑐) μu = 𝛿𝑦 𝐸ℎ μh = 𝐸𝑒 μd =

(2.1) (2.2)

Table 2.2 Damage index (DI) and damage rank (DR) relationship Source: (Hazus, 2003) Damage index (𝑰𝑫 ) 0.00 < ID ≤ 0.14 0.14 < ID ≤ 0.40 0.40 < ID ≤ 0.60 0.60 < ID ≤ 1.00 1.00 ≤ 𝑰𝑫

Damage rank (DR) D C B A As

Definition No damage Slight damage Moderate damage Extensive damage Complete damage

Table 2.3 Damage Rank classified in Bohol Eq.

(2.3)

where: μu = ultimate Ductility μd = displacement Ductility μh = hysteretic energy ductility 𝛿𝑚𝑎𝑥 (𝑠𝑡𝑎𝑡𝑖𝑐) = displacement at maximum reaction at the push over curve (static) 𝛿𝑚𝑎𝑥 (𝑑𝑦𝑛𝑎𝑚𝑖𝑐) = maximum displacement at the hysteresis model (dynamic) 𝛿𝑦 = yield displacement from the push-over curve (static) 𝐸ℎ = hysteretic energy, i.e., area under the hysteresis model 𝐸𝑒 = yield energy, i.e., area under the push-over curve (static) but until yield point only. Table 2.1. Ductility Factors for Bohol Eq. at x direction

Damage ratio was computed by dividing the number of records to the number of damage rank. The damage ratio was plotted with the ln (PGA) on a lognormal probability paper to obtain the mean and standard deviation for the Probability of Exceedance. After getting the mean and standard deviation, the probability of exceedance (PR) has been computed. Where Φ is the standard normal distribution, X is the peak ground acceleration, λ is the mean and ζ is the standard deviation.

𝑃𝑅 =  (

Damage indices was then computed using equation 4 after ductility factor was obtained. This damage index were used to determine the damage rank.

μd + 𝛽μh 𝐼𝐷 = μu

(2.4)

where 𝛽 is the cyclic loading factor taken as 0.15 for bridges. By using Table 2.2, the damage rank (DR) for each damage index (𝐼𝐷 ) have been identified (Requiso, 2013).

ln(𝑋) − λ ) ξ

(2.5)

Then by plotting the acquired cumulative probability vs the peak ground acceleration (PGA normalized to different excitation), the Seismic fragility curve can be obtained (Karim & Yamazaki, 2001). 3. RESULTS AND DISCUSSION Results from the Pushover analysis from x and y direction are shown Figure 3.1 and Figure 3.2 respectively.

Table 3.4 Partial results of pushover curve at y- dir.

Figure 3.1 Pushover curve x-direction

The result of the pushover curves shows that y direction is the stronger axis as it can withstand a shear force of 8934.519KN at 0.148325m displacement while x direction can only withstand shear force of 5653.095KN at 0.156212m displacement. In Figure 3.5 and 3.6, it shows the relationship of PGA and percentage of damage. The result showed that as the PGA increase from 0.2g to 2.0g the percentage of higher damage state also increases. This is due to the weaken strength of the pier over time.

Figure 3.2 Pushover curve y-direction Table 3.3 Partial results of pushover curve at x direction Figure 3.5 Probability of Occurrence at x direction

Figure 3.6 Probability of Occurrence at x direction

Figure 3.8 and Figure 3.7are the sets of fragility curves due to shear failure of the Plaridel bridge’s pier. From

the obtained fragility curves, it can be observed that as the peak ground acceleration increases the damage rank also increases. It also shows how the performance of the bridge’s pier at each peak ground acceleration varies, it requires high peak ground acceleration for the bridge to show high probability of damage states. At the design requirement of 0.4g PGA of the NSCP, the bridge has 53.02% probability of exceeding Slight damage rank at x direction and 52.07% of probability of exceeding Slight damage rank at y direction which are the highest probability of exceedance among the damage states at that point showing how the bridge meets the minimum requirement design.

Figure 3.7 Seismic Fragility curves in x direction

bridge would collapse in magnitudes equal to or higher than of the said earthquake. 4. CONCLUSION The general objective of this study was to construct fragility curves that will assess the Plaridel bridge’s performance against large magnitude of earthquake. The researcher has met the objective of the study and have made conclusions for this study. Based from the fragility curves due to shear failure, the results showed how vulnerable the structure is to damage when an earthquake occur since at the required design standard of the NSCP of 0.4g peak ground acceleration the Plaridel bridge’s pier already showed probability of complete damage state and at 1.4g to higher peak ground acceleration the bridge’s pier is suspected to collapse already. Although the 1.4g peak ground acceleration was based from Japan’s record, the bridge should still be considered to be retrofitted especially in these days the Philippines is expecting the “Big One” to occur anytime in the future, who knows how strong this earthquake could be but it expected to surpass the 1.4g peak ground acceleration. This study could help all who access the bridge think if one should proceed to pass the bridge in case an earthquake occurs or after an earthquake occurred. ACKNOWLEDGMENT

Figure 3.8 Seismic Fragility curves in y direction

It can also be observed that from earthquakes like Tohoku-Kanto Earthquake with magnitude 9.0 the bridge has a high probability of exceedance for Complete damage state or As which implies that the

This paper will not be accomplished without the help of generous people and institutions alike. Appreciated efforts and support are all extended to the following person and institution that contributed in making this study possible: DPWH for providing structural plans, PHIVOLCS, Kik-Net, and PEER for the ground motion data, my thesis advisees (Arciaga, Alexandria Rose R., Argana, Jayson Mavrick B., Rioveros, Edmund Christian L. and Santos, Arish M) for doing the computer simulations, Adamson University for the financial support, particularly the Civil Engineering Department Chair, Dr. Ma. Cecilia M. Marcos, for the constant motivation in doing research aside from excellence in instructions, Dr. Lessandro Estelito O. Garciano of De La Salle University – Manila as the author’s research mentor in his graduate studies and from whom the author indebted to the field of reliability analysis and fragility analysis.

APPENDICES Computation of Dead Load and Live Load

trailer with 1m space was computed to be (50m) / (4.27m + 9.14m + 1m) = 6.9 rounded off to 7.

Due to the Plaridel Bridge’s symmetrically designed elements, the researcher considered the dead load as half of each span above the Pier 9. The researcher used AutoCAD to model the slab, railings, girders and diaphragm shown in Figure 2.4 and used the AutoCAD’s command massprop to compute for the volume which is then multiplied by 24 kN/m3 to compute for the dead load.

Seven (7) trailers were placed between Pier 8, Pier 9 and Pier 10 and produced a maximum shear force of 1214.175KN at Pier 9 as shown in Figure A.3 and Figure A.4.

Figure A.1 Computation of equivalent load Uniformly Distributed Dead Load =

9972.961kN 11.5m

Uniformly Distributed Dead Load = 867.214kN/m Plaridel Bridge’s live load was based from AASHTO HS20-44 that specified a trailer truck as designated load shown in Figure A.2.

Figure A.3 Autodesk Force effect result

Figure A.2 AASHTO HS20-44 trailer The units were converted by the researchers into SI. 8 kips = 35.59 kN 32 kips = 142.34 kN 14 ft = 4.27m 30 ft = 9.14 m Since each span of the bridge was symmetrical, any pier within the bridge’s span can be considered to produce the maximum shear force when live load is applied. Pier 9, having one of the most exposed height of pier, was considered to be the critical pier. The researcher used Autodesk Force Effect to compute for the maximum shear force produced by the pier upon loading based from AASHTO HS-44. The number of

Figure A.4 Autodesk Force effect result

Table A.1 Autodesk Force effect data tabulation

11.Kobe Takatori January 16, 1995 Magnitude 6.9 12.Kobe Nishi-Akashi January 16, 1995 Magnitude 6.9 13.Kobe Kakogawa January 16, 1995 Magnitude 6.9 14.Kobe KJM January 16, 1995 Magnitude 6.9 15.Kobe HIK January 16, 1995 Magnitude 6.9 Hysteresis In Figure A.5 to Figure A.14, hysteresis models at 0.2g to 2.0g of 1995 Kobe earthquake at x direction at Nishi Akashi station are shown and used in the hysteretic energy, Eh, needed for the ductility factor computations.

The live load for Pier 9 was computed using the formula based from AASHTO HS-44:

Total Live Load,LL = Pier Reaction x no.of lanes x impact factor

Figure A.5. Hysteresis at PGA=0.2g

where: AASHTO Impact factor= 50/(L+125)≤0.3 L is in feet, 100 m = 328 ft AASHTO Impact factor = 50/(164+125) AASHTO Impact factor = 0.1104 or 11.04% Total Live Load,LL = (1214.175)(2)(1+0.1104) Total Live Load, LL = 2696.44kN Total Uniform Live Load =2696.44kN/11.5m Total Uniform Live Load = 234.473kN/m Ground motion data used are limited to the following 1.Tohoku-Kanto-FKS March 11, 2011 Magnitude 9.0. 2.Tohoku-Kanto-AIC March 11, 2011 Magnitude 9.0 3.Tohoku-Kanto-HYG March 11, 2011 Magnitude 9.0 4.Tohoku-SIT March 11, 2011 Magnitude 9.0 5.Bohol October 15, 2013 Magnitude 7.2 6.Mindoro Cainta, Rizal November 15, 1994 Magnitude7.1 7.Mindoro Station Quezon City November 15, 1994 Magnitude 7.1 8.Mindoro Station Marikina City November 15, 1994 Magnitude 7.1 9.Kobe Shin-Osaka January 16, 1995 Magnitude 6.9 10.Kobe Takarazuka January 16, 1995 Magnitude 6.9

Figure A.6. Hysteresis at PGA=0.4g

Figure A.7. Hysteresis at PGA=0.6g

Figure A.8. Hysteresis at PGA=0.8g Figure A.12. Hysteresis at PGA=1.6g

Figure A.9. Hysteresis at PGA=1.0g Figure A.13. Hysteresis at PGA=1.8g

Figure A.10 Hysteresis at PGA=1.2g

Figure A.11. Hysteresis at PGA=1.4g

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