Finite Element and Experimental Analysis and Evaluation of Static and Dynamic Responses of Oblique Pre-stressed Concrete Box Girder Bridge

Hashuang bridge is type of prestressed concrete box girder oblique bridge and it is located in Harbin City within Heilongjiang province in the east north of China. The objectives of this study are to investigate the appearance of the bridge structure and identify all the damages in the bridge structural members and to evaluate the structural performance of the bridge structure under dead and live loads. Finite element analysis is used to analyze the static designed internal forces and dynamic responses by adopting SAP200 software Ver. 14.2.0. Static and dynamic load test are adopted to evaluate the structural performance of the bridge structure. The results of field investigation process of the bridge appearance show that the bridge suffers from serious damages. The web of box girder of the second span near pier No.2 (in the quarter of middle span at 39m on the bridge length) suffers from serious shear cracks. The state of abutments, piers and sidewalks is good, but the bearing, drainage holes, steel rail and expansion joints are not good and they suffer from much damage. The steel rail is corroded and the expansion joint loses the material which fills the joint. There are many dusts and debris is collected on the bridge deck in the location near sidewalk. The analysis results of finite element and load tests show that there are high tensile stresses in the quarter of middle span at distance 39 m of the bridge length and the state of the bridge structure is not good and the main problem of the bridge structure in the original design of prestressed tendons. Therefore, this study recommends for repairing and strengthening the bridge structure to increase the stiffness and strength and to improve the bearing capacity of the bridge structural members to increase the service live of the bridge structure.


INTRODUCTION
The prestressed concrete systems can be defined as the preloading of a concrete structure before the application of the service loads to improve the structural performance in specific ways and it is a form of concrete in which internal stresses are introduced by means of high strength pre-strained reinforcement.(Lian, 2008;Arthur, 1987;PCI, 1968) Prestressed concrete box-girder bridges have been widely used as fiscal and visual solutions for the overcrossings, under-crossings of deep valleys to which relatively long spans are required.The most previous researches on box-girder bridges had been conducted by using the finite element method.Prestressed concrete box girder bridge is used in many countries, but they have a crucial limitation compared to steel girders in that a single span length cannot be extended over 50 m due to its relatively heavy self-weight.(Choi et al., 2002;Meyer and Scordelis, 1971;Kwang et al., 2010) The purposes of damages investigation of the bridge components are to sure whether a bridge structure is in safe state or not, identify any maintenance, repair and strengthening which that need to be done, provide a basis of planning for funding of any required maintenance and strengthening and provide information to designers and construction engineers on those features which need maintenance.Depending on its conditions, a bridge structure is inspected every two or more years.The inspection process is also used as a tool to identify the maintenance work required by several bridges.Ensuring safety of the general public consists of identifying those bridges that have an improper probability of failure.(Robert et al., 2005), Washington State Department of Transportation, 2010; Joao and Jorge, 2009;Ali and Wang, 2011a) The main purposes of experimental and theoretical analysis of the bridge structure are to check normal service stage, fatigue and ultimate loads; development of theoretical models to calculate the performance of the bridge structural members; and verifying the analytical results by comparing them with the obtained results from experimental tests.Field load tests of the bridges are an important method to evaluate the structural performance of the bridge structure.They make it possible to compare the theoretical assumptions with the actual behavior of the bridge subjected to the test loads.There are two types of load tests, static load test and dynamic load test.(Aktan et al., 1992;Jiamei et al., 2011;James et al., 2006;Ali and Wang, 2011b) Load tests of bridges in situ are an important procedure for checking the quality of structures.During a static load test, it is necessary to measure the vertical deflections, stresses, strains and bending moment at the points where the maximum effects are expected (in the middle of spans, in the quarter of span).Dynamic load tests are normally applied only after the static load tests were performed and behaved structure within acceptable limits.When the bridges are subjected to dynamic vehicle traffic loads, the bridge will be subjected to vibration state.A moving vehicle on the bridge generates deflections and stresses that are generally greater than those caused by the same vehicle loads applied statically (Fry and Pirner, 2001;Gheorghiţa, 2009;Senthilvasan et al., 2002;Ali and Wang, 2011c).
The main objectives of this study are to investigate the appearance of the bridge structure and identify all the damages in the bridge structural members and to evaluate the structural performance of the bridge structure under dead and live loads.

DESCRIPTION OF THE BRIDGE STRUCTURE
Hashuang bridge is located in Harbin City within Heilongjiang province in the east north of China.This bridge is type of pre-stressed concrete box girder oblique bridge.The total length of the bridge is 95.84 m and has total width is 17m, including two box girders.The width of box girder web is varying from 35cm to 70 cm along the length of the bridge.The arrangement of spans is 28m+40m+28m.The transversal arrangement of the deck is 14.0 m carriageway and 2×1.5 m sidewalk and the deck which is paved by the 8cm waterproof concrete and 8 cm asphalted concrete pavement.The construction process of this bridge adopts the method of cast-in-place span-by-span method (Ali and Wang, 2011a).Figure 1 shows the layout of box girders.

FIELD INVESTIGATION OF THE BRIDGE DAMAGES
Field investigation process is done on the structural members of the bridge structure such as all spans of outside and inside of box girders, piers, abutments, bearings, sidewalks and steel rail.The results of investigation process show that the web of box girder of the second span near pier No.2 (in the quarter of middle span at 39 m on the bridge length) suffers from serious shear cracks.The distance between cracked area and the mid-pier No. 2 is about 10.5 m.These cracks extend from the top to lower flange of box girder.There are two cracks incline 45° to the mid-span direction with widths are 0.5 to 2.0 mm and the widest cracks are found in the middle of web of box girder.Both of the outside web and inside web of box girders have the same crack position.The cracks degree of the box girder's outside web is more serious than the inside web.There are six transverse bending cracks on the bottom of box girder around quartile of middle span.The spacing between these cracks range from 20 cm to 30cm and the width is 0.35 mm.In the span No. 3 near the pier, the web of box girder appears 12 diagonal cracks have width range from 0.1 mm to 0.12 mm. Figure 2 shows the cracks in the box girders.From this figure, it can be noted that the state of the bridge structure is not good because there are serious cracks have large width.
The investigation process of other parts of the bridge structure shows that the state of abutments, piers and sidewalks is good, but the bearing, drainage holes, steel rail and expansion joints are not good and they suffer from much damage.The steel rail is corroded and the expansion joint loses the material which fills the joint.There are many dusts and debris is collected on the bridge deck in the location near sidewalk.

FINITE ELEMENT ANALYSIS OF STATIC DESIGNED INTERNAL FORCES
According to Chinese code (JTJ023-85, 1985), the original design of the Hashuang pre-stressed concrete box girder bridge was carried out.In this analysis, SAP200 software Ver.14.2.0 is used to analyze the internal forces of the bridge structure due to dead load, live load, prestressed load, temperature load and crowded load.

Requirements of analysis:
The following requirements are used in the analysis of the bridge structure.These requirements include:  (Senthilvasan et al., 2002) Table 1: The reduction factor of live load (Senthilvasan et al., 2002) Number • Analysis of vertical deflection: The analysis results of vertical deflection due to static live load shows that the maximum downward vertical deflection is equal to -16mm which occurs in the center of the bridge structure at distance 48 m.
Figure 7 shows the vertical deflection due to static live load.This value is less than the allowable limit value which is equal to 66.6 mm.Therefore, the value meets the requirement: Analysis of internal forces due to load combination I: • Analysis of stress:

FINITE ELEMENT ANALYSIS OF DYNAMIC RESPONSES
Shell element model is used in the dynamic analysis of Hashuang pre-stressed concrete box Girder Bridge.Three joints are selected to determine the dynamic responses which are located in the center of the bridge structure at the area of maximum downward vertical deflection.The first joint has number 2598 which is located in the center of the bridge, the second joint has number 3022 which is located in the left center of the bridge and the third joint has number 2640 which is positioned in the right center of the bridge.Figure 12 shows the location of the selected joints.Linear direct integration time-history type and Hilber-Hughes-Taylor method is used in the dynamic analysis.For modal analysis, Eigen vector modal type is used and the maximum numbers of modes is equal to 20 modes.Six damping ratios are used in this analysis.These damping ratios include 0.0, 0.02, 0.03, 0.05, 0.07 and 0.10. in this analysis, natural frequency and vibration frequency will be analyzed to compare with experimental results of dynamic load test.

Analysis of natural frequency and modal shape:
Table 2 lists the values of natural frequency for modal modes.Figure 13 shows the first five modes of the bridge structures.According to deflection shape of modal mode No.3, the natural frequency of the bridge structure is equal to 4.9635 Hz.According to Table 3, the impact factor (1+µ) of the bridge structure is equal to 1.266.

Analysis of vibration frequency and impact factor:
Ten speeds are used in the analysis of dynamic responses.These speeds are 10k, 20k, 30k, 40, 50k,  3 and vibration frequency, the impact factor of the bridge structure can be calculated.Figure 15 shows the values of impact factor under different speeds.From this figure it can be noted that the most values for the selected joints are near for each others and the maximum value of impact factor is equal to 1.286 which occurs under speeds 20km/h and 80km/h.the average value of impact factor of the bridge structure is equal to 1.104 which is less than the value from natural frequency 1.266, indicating that the vibration state of the bridge structure is good.

STATIC LOAD TEST
The aim of static load test of Hashuang bridge is to measure the vertical deflection, strains, stresses and the development situation of cracks, then compare them with theoretical analysis results to judge synthetically the working state and the bearing capacity of whole bridge structure.According to the inspection results of the bridge structure appearance, the half of middle span (span No.2) is selected as a tested span.
Figure 18 shows the transverse arrangement of deflection measuring points.

DYNAMIC LOAD TEST
When the traffic loads pass on the bridge structure, the bridge suffers from large vibration and the duration of vibration is long.In this test, dynamic responses such as natural frequency, impact factor and dynamic deflection are measured when the bridge is opened to traffic loads to determine the state of the bridge vibration in safe working or not.One vertical 941Bvibration pickup device and transverse 941B-vibration pickup are set on the mid-span of span No.1 (side span of the bridge) and the mid-span of span No.2 (middle span of the bridge) (Ali and Wang, 2011a).length.The value of maximum tensile stress is equal to 3.8 MPa which occurs in the bottom of box girder.This value exceeds and dose not meets the allowable limit values in Code-JTJ023-85 (2.99 MPa) and Code-JTG D62-04 (1.68 MPa).These tensile stresses are related to the position of anchorage of bottom pre-stressed tendons which leads to decrease the effect of prestressed of the section and become not enough and decreased the compression stress.Therefore, the cracks appeared in the sections which have high tensile stresses.Figure 22 shows the arrangement of prestressed tendons in the quarter of middle span at distance 39 m of the bridge length.According to the observation process for the traffic loads, there are serious overloading phenomenon exist universally when vehicles passing the bridge.The maximum vehicles weight more than 150 tons which is two times higher than the weight of live load vehicles in the design code.Serious overloading will cause large main tensile stress in the part of quartiles of middle span which leading to appear the cracks and causes the downward defection in the center of the bridge.According to dynamic load test, when the vehicles pass on the bridge, it suffers from a greater vibration which leading to causes grater dynamic stresses in the bridge structure and then the cracks appeared.Therefore, this study recommends for repairing and strengthening the bridge structure to increase the stiffness and strength and to improve the bearing capacity of the bridge structural members to increase the service live of the bridge structure.

CONCLUSION
The main conclusions of this study are: Therefore, the measured vibration frequency under passing the vehicles on the bridge is equal to 5Hz which is more than the measured natural frequency which is equal to 4.482 Hz. • According to the results of damage investigation process, finite element analysis, static load test and dynamic load test, the main problem of the bridge structure in the original design of prestressed tendons.Therefore, this study recommends for repairing and strengthening the bridge structure to increase the stiffness and strength and to improve the bearing capacity of the bridge structural members to increase the service live of the bridge structure.

Fig. 1 :
Fig. 1: The layout of transverse section of the bridge; (a) Half section of mid-span box girder, (b) Half section of pier box girder (dimension in cm)

Fig. 12 :
Fig. 12: The location of the selected joints

Fig. 16 :Fig
Fig. 16: The selected tested span and longitudinal location of vehicles loading

Fig. 19 :
Fig. 19: The deflection values; (a) Measuring point 1; (b) Measuring point 2 Analysis of static load test results: • Stress results: The results of tensile stress of concrete under static load are listed in Table 6 Figure 20 shows the spectral analysis curve of natural frequency and dynamic acceleration of mid-span No.2 when the bridge is opened to traffic load.From this figure it can be seen that the values of measured natural frequency is equal to 4.482 Hz.The vibration frequency of bridge structure is equal to 5 Hz which is close to the natural frequency 4.482 Hz of the structure.So under the action of vehicles loads, bridge can easily cause a resonant phenomenon, resulting in dynamic acceleration, dynamic strain and dynamic displacement by a big

Fig. 20 :Fig
Fig. 20: The spectral analysis curve of natural frequency and dynamic acceleration of mid-span No. 2

Table 2 :
The values of natural frequency for modal modes Mode No.

Table 4 :
The characteristic parameters of the vehicles

Table 5 :
The arrangement situation of measuring points

Table 6 :
The results of stresses of concrete under static load

Table 7 :
The measuring values of concrete strain (µε)

Table 8 :
The changes in crack width of the box girder web under the action of static load test (mm) Figure19shows the deflection of measuring points 1 and 2. From this Figure it can be noted that the maximum downward deflection is equal to -23.5 mm which locates within half of middle span No.2 under 4 vehicles loads in the measuring point No. 1 and it is less than the allowable limit value which is equal to 66.6m.•Stain results: Table 7 shows the measuring values of concrete strain.• Observation of cracks: Table 8 lists the changes in crack width of the box girder web under the action of static load test.From this table it can be noted that the crack widths of box girder web have been increased by 0.205 mm under the action of load test.After unloading, the cracks are repristination and the residual deformation is 0.01mm.The relative residual deformation is 4.9% which are much less than 20%.It indicates that whole deformation and integrality of structure fit the request of design and have good elasticity working state.

•
Field investigation process of the bridge appearance shown that the bridge suffers from serious damages.The web of box girder of the second span near pier No.2 (in the quarter of middle span at 39 m on the bridge length) suffers from serious shear cracks.These cracks extend from the top to lower flange of box girder.There are two cracks incline 45° to the mid-span direction with widths are 0.5 to 2.0 mm and the widest cracks are found in the middle of web of box girder.Both of the outside web and inside web of box girders have the same crack position.The cracks degree of the box girder's outside web is more serious than the inside web.There are six transverse bending cracks on the bottom of box girder around quartile of middle span.The investigation process of other parts of the bridge structure shows that the state of abutments, piers and sidewalks is good, but the bearing, drainage holes, steel rail and expansion joints are not good and they suffer from much damage.The steel rail is corroded and the expansion joint loses the material which fills the joint.There are many dusts and debris is collected on the bridge deck in the location near sidewalk.•The results of finite element analysis of the bridge structure show that there are high tensile stresses in the quarter of middle span at distance 39 m of the bridge length.The value of maximum tensile stress is equal to 3.8 MPa which occurs in the bottom of box girder.This value exceeds and dose not meets the allowable limit values in Code-JTJ023-85 (2.99 MPa) and Code-JTG D62-04 (1.68 MPa).These tensile stresses are related to the position of anchorage of bottom pre-stressed tendons which leads to decrease the effect of pre-stressed of the section and become not enough and decreased the compression stress.Therefore, the cracks appeared in the sections which have high tensile stresses.• The results of static load test show that the load test values are less than the theoretical values.The values of efficiency coefficient (η) of load test concrete strains ranges from 0.35 to 0.42 which are less than the allowable value of efficiency coefficient (η = 0.90), indicating that the structural strength of the bridge structure meets the design requirements.The values of efficiency coefficient of load test vertical deflection (η) ranges from 0.40 to 1.46.The maximum load test downward deflection in the center of the bridge structure are more than the theoretical value and the values efficiency coefficient of load test (η) is equal to 1.46 which is more than the allowable efficiency coefficient (η ) of load test vertical deflection (η = 1.0).Therefore, the bridge structure dose not meets the design requirements of stiffness and the elastic working state is not good.• The analysis results of dynamic load test show that the value of measured natural frequency is equal to 4.40 Hz which is less than the theoretical natural frequency which is equal to 4.963 Hz.The value of dynamic load test coefficient is equal to 0.88 which is within the fourth level that represents the very poor state, indicating that the bridge structure suffers from long time vibration because of the connection between the two sides of box girders (forward and backward direction) is not good.