The dynamic behavior of three different bridge vehicle models was investigated using the proposed semi-analytical method to study the effect of different bridge vehicle parameters on the bridge response statistics and the dynamic amplification factor. The identification of the vehicle parameters of three models with the help of simulated results is presented.
LIST OF TABLES
Fig.7.22 Progressive estimate of stiffness of rear suspension kv2 from acceleration data at different locations. Fig.7.52 Progressive estimation of front left vehicle suspension stiffness kv21 from acceleration data at different locations.
NOMENCLATURES
M] Mass matrix of the coupled vehicle-bridge system Mvk Generalized mass of the vehicle body in flexure. Mvk Generalized mass of the vehicle body in bending n Magnitudes of the matrix of the coupled vehicle-bridge system.
INTRODUCTION
Overview
The traditional way to control overloading on highway bridges is to measure the gross weight of the vehicle in a static state. This is usually achieved by a "uteh-bridge" system installed on the sides of highways and also in factories to monitor the load on the highway pavement and bridge.
Literature Review
- Vehicle Parameter Identification
- Vehicle Bridge Interaction
The governing equation of the bridge idealized as a beam model was established by finite element analysis. In the modeling, the effect of the inertia of the strips and the arch together with the deck is taken into account.
Gaps in Literature
Bridge dynamic test results were used by Brownjohn (2003) for assessment of highway bridge upgrading and finite element model updating. Brencich and Sabia (2007) studied efficiency of masonry bridge element from measured bridge dynamic response. 2013) used full-scale dynamic test for damage detection and to observe dynamic properties of post-tensioned concrete bridge. Furthermore, full-scale bridge test result was used for the assessment of induced dynamic force on the bridge and to determine dynamic load allowance factor (Szurgott el when investigating actual contribution of bridge surface condition in the bridge dynamic response subjected to moving vehicle.
The parameters of vehicles driving on the bridge were identified by Deng and Cai (2009) based on the dynamic test result of the bridge.
Scope and Objective of the Present Work
The researchers found that the particle filtering technique is computationally expensive, as it requires a large number of response samples to obtain convergent results. Although the particle filter technique can take care of the inaccuracies of the model, the forward solution of the mathematical model of the dynamic system by iterative or numerical schemes requires more computational time. Given this fact, it would be useful to develop an idealized but fairly accurate physical model that would allow the connection of closed-form solutions to the iterative process of the particle filtering technique.
To perform field dynamic testing on an existing bridge under controlled movement of a loaded truck and to update the finite element model of the test bridge.
Organization of Thesis
VEHICLE PARAMETER IDENTIFICATION
- Overview
- Methods of Moving Load Identification
- Direct Inverse Method
- Indirect Inverse Method
- General Theory of Particle Filtering Method
- Bayesian Inference to Dynamic State Estimation
- Monte Carlo Integration and Importance Sampling
- Bootstrap Particle Filtering
- Application of Bootstrap Particle Filtering Method for Vehicle Parameter Identification
- Closure
Where [A(ω)] is the system matrix in the frequency domain, {f(ω)} is the frequency change of the moving force and {b(ω)} is the frequency domain function of the measured response of the bridge at the selected station. The mean estimate of the integral g( ) ( ) d using the Monte Carlo integration method can be written as Due to the similarity of the probability densities ( ) and f( ), each integral of the form g( ) ( ) d can be written as
Since the state of the system depends on system parameters { }, the observation equation can be rewritten as.
BRIDGE-VEHICLE INTERACTION MODELS
- General
- Idealization of bridge
- Deck roughness
- Mean surface profile
- Random unevenness
- Coupled System Equations
- Bridge-vehicle equations of motion for Model-1
- Bridge-vehicle equations of motion for Model-2
- Closure
In the present study, we include pre-cambering of bridge decks in the form of shallow parabolas (Fig.3.1), whose equation with reference to the origin at the left support is given by. The governing differential equations for motion of the two lumped masses can be written as 0. The governing differential equation for motion of the bridge in bending and torsion can be expressed as.
The governing differential equation of motion of the vehicle's vertical deflection can be expressed as.
DEVELOPMENT OF A SEMI-ANALYTICAL METHOD IN FORWARD SCHEME
- Overview
- Discretization of Partial Differential Equations
- Discretization of flexible vehicle equation of motions
- Discretization of bridge equations of motions .1 Bending Vibration of bridge
- Response Statistics
- Dynamic Amplification Factor
- Closure
Using the properties of the Dirac delta function, the generalized force Qvk(t) in the kth mode of transverse oscillation of the vehicle body can be expressed as,. Substituting equation (4.1) and equation (4.7) into equation (4.14) and performing the integration in the bridge domain, the generalized mass can be expressed as Other parameters have already been introduced in the formulation of the equation of motion of Model-2.
When the vehicle is at the exit point, then t=L/V where L is the span of the bridge.
FIELD TESTING AND FINITE ELEMENT MODEL UPDATING
- Overview
- Test Bridge
- Test Vehicle
- Deck Roughness Measurement
- Instrumentation of Tested Bridge
- Finite Element Modeling of the Bridge
- Finite Element Model Updating
- Response Surface Method (RSM)
- Genetic Algorithm
- Procedure of Response Surface based FE model updating of Test Bridge
- Closure
Before performing the dynamic test with a moving vehicle, the longitudinal profile of the bridge frame was recorded using the "Total Station". The three-factor CCD adopted by Mayers et.al (1989) is shown in Figure 5.15 and their corresponding values are given in Table 5.3, which was used in the current update of the finite element model of the tested bridge. In this chapter, the field test procedure of the bridge under dynamic load was discussed with details of the test bridge, the vehicle and the instruments on the bridge.
FE model of the bridge was created in SAP2000 commercial software which is later used as one of the preferred models in forward solution in the identification scheme.
RESULT AND DISCUSSION- PART-I: DYNAMIC BEHAVIOUR OF THEORETICAL MODEL
Overview
System Parameters
- Bridge parameters
- Vehicle parameters
As mentioned in 6.1, a combination of deterministic variable mean and random surface roughness was considered in the present study. According to ISO proposal, roughness shape coefficient m was taken as 2, lower cutoff frequency. The data of a long and heavy commercial vehicle type TATA 3516C-EX was selected for the case studies.
In Half Car Model, vehicle body is idealized as Euler-Bernoulli beam, which includes bending flexibility in the model.
Response Statistics for Model-1
- Vehicle Response
- Bridge Response
Further, it is seen that the peak of the responses shifts to the left as the vehicle speed increases, indicating that the temporal frequency of the pavement excitation has increased. The effect of speed, vehicle path eccentricity, approach plate placement on the mean and standard deviation of the midspan response quantities was studied. The magnitude of velocity and acceleration is also found to increase with forward vehicle speed.
The contribution of torsional motion to mid-span bridge bending was studied by varying the location of the wheel from the centerline of the bridge deck.
Dynamic Amplification Factor for Model-1
- Effect of bridge surface roughness and vehicle speed
- Effect of bridge span and velocity
The combined effect of bridge span and vehicle speed on DAF is not fully known. The contour diagram can be helpful in selecting the possible bridge span range and a satisfactory speed limit. The result shows that when the bridge span increases from 15 m to 35 m, the dynamic amplification factor decreases by an amount of 12% to 15% regardless of the increase in vehicle speed.
Dynamic amplification factor with change of bridge span and vehicle speed 6.4.3 Effect of vehicle mass and approach alignment.
Response Statistics for Model-2
- Vehicle Response
- Bridge Response
The mean and standard deviation of the front wheel displacement, velocity and acceleration time histories were shown in Figures 6.19 to 6.21 and those for the rear wheel in Figures 6.22 to 6.24. A comparison of the mean and standard deviation of the bridge in mid-span bending with different values of vehicle bending stiffness is shown in Figure 6.30. A comparison of the mean and standard deviation of the interaction force caused by the front and rear wheels was presented in Fig. 6.31 and fig.
The contribution of a significant number of structural vehicles to the bridge response has been examined in a bar chart shown in Figure 6.33 (a) and Figure 2.
Dynamic Amplification Factor for Model-2
- Effect of bridge surface roughness and vehicle speed
- Effect of bridge span and velocity
- Effect of vehicle axle spacing and approach settlement on DAF
Hossain and Amanat, 2011) have investigated the combined effect of bridge span and speed on Dynamic Amplification Factor, their study ignored vehicle flexibility. The sections of the plot along the tension direction indicate that in a span of 15m to 35m, dynamic amplification factors decrease by an amount of 5.4% to 8.1%, while the sections along the speed axis show that the increase in speed from 40 km/h to 80 km /t results in 10% to 16%. The effect of the vehicle wheelbase as well as the settlement of the approach road on the dynamic amplification factor (DAF) is shown in Fig.
Dynamic amplification factor for different wheelbase and approach settlement 6.6.4 Effect of vehicle mass and approach settlement.
Response Statistics for Model-3
- Vehicle Response
The mean and standard deviation of displacement, velocity and acceleration at the center of the vehicle body are shown in Fig. The standard deviation of the mean displacement at the center of the vehicle body shows a high peak when the vehicle is closer to the midspan of the bridge. The mean and standard deviation of the time history of displacement, velocity and acceleration for each of the four continuous measures are shown in Fig.6.44 to Fig.6.55.
The mean and standard deviation of the wheel responses are found to be lower compared to the model where vehicle body roll is ignored.
Dynamic Amplification Factor for Model-3
- Effect of bridge surface roughness and vehicle speed
- Effect of bridge span and velocity
- Effect of vehicle mass and approach settlement on DAF
The combined effect of surface roughness and vehicle speed on the dynamic gain factor is shown in Figure 6.62. Dynamic gain factor with vehicle speed and bridge span 6.8.3 Effect of vehicle wheelbase and approach alignment on DAF. The effect of the vehicle wheelbase on the dynamic amplification factor (DAF) in the presence of different settlements on the approach road is shown in Figure 1.
It was found that up to a certain level of access road DAF decreases with increasing vehicle mass.
Comparison of Different Models Behaviour
- Bridge response with pre-cambered profile
Time histories of bridge midspan deflection with different vehicle models are given in Figs. Appearance of high-frequency components in displacement averages indicates that higher modes of the bridge are excited as the flexible body moves over a sudden change in road level. In addition to this, sudden changes in pavement height also excite the higher mode of flexible vehicle which increases the frequency of the dynamic load induced in the bridge.
The higher frequency dynamic band power in turn excites the higher modes of bridge, which can then become significant in building up the response.
Closure
In order to investigate the effect of different vehicle models on bridge response, an approach settlement of size 40 mm was considered. The result shows that the bridge dynamic response of Model-3 is increased by an amount of 17% in the presence of approach settlement. The adequacy of the number of bending and torsional modes of the vehicle models was investigated.
In addition, a pre-rounded median profile and approach settlement along with random bumps were included to compare the dynamic response of the bridge against three different vehicle models.
RESULT AND DISCUSSION- PART-II: VEHICLE PARAMETER IDENTIFICATION FROM SIMULATED BRIDGE RESPONSE
Comparison of Vehicle Load Estimation with Published Results
- Comparison with the results of numerical study
- Comparison with the results of experimental study
Further, the gross axle force time history has been reconstructed from the estimated vehicle parameters by considering the same bridge surface condition and vehicle speed as assumed by (Law et. al, 2004) in their study. It can be seen that high fluctuations of moving force around the reference load have been produced at the end of the time history of front axle pressure and at the beginning of rear axle pressure in the results obtained by (Law et. al, 2004). The second comparative study has been carried out using experimental data provided by Law et al.
The 3/4 span acceleration record obtained experimentally in the reference (Law et al., 1997) was used as measurement data in the Particle Filter Method for estimating the mass of the model car.
Influence of Various Factors on Vehicle Parameters Identification in Model-1
- Effect of artificial noise level
- Effect of initial range of vehicle parameters for construction of prior PDF p( 0 ) In the absence of any information about the unknown parameters, it is assumed that the initial
Bridge acceleration at mid-span and quarter-span for vehicle speed 60 km/h 7.3.1 Effect of bridge reaction measurement location. The bridge acceleration measurement at different locations along the span was used as input to the particle filter algorithm. The result shows that measurement different from the center span takes a longer iteration to reach convergence.
Overall, the result reveals that measuring bridge response at mid span gives about 2 to 7 percent error, while measurements other than mid span lead to 4 to 7 percent error.
