Vehicle Axle Load Research Articles

Evaluation of dynamic vehicle axle loads on bridges with different surface conditions

Vehicles generate moving dynamic loads on bridges. In most studies and current practice, the actions of vehicles are modelled as moving static loads with a dynamic increase factor, which are obtained mainly from field measurements. In this study, an evolutionary spectral method is presented to evaluate the dynamic vehicle loads on bridges due to the passage of a vehicle along a rough bridge surface at a constant speed. The vehicle–bridge interaction problem is modelled in two parts: the deterministic moving dynamic force induced by the vehicle weight, and the random interaction force induced by the road pavement roughness. Each part is calculated separately using the Runge–Kutta method and the total moving dynamic load is obtained by adding the forces from these two parts. Two different types of vehicle models are used in the numerical analysis. The effects of the road surface roughness, bridge length, vehicle speed and axle space on the dynamic vehicle loads on bridges are studied. The results show that the road surface roughness has a significant influence on the dynamic vehicle–bridge interaction. The dynamic amplification factor (DAF) and dynamic load coefficient (DLC) depend on the road surface roughness condition.

Effectiveness of Vehicle Weight Estimation from Bridge Weigh-in-Motion

The effectiveness of vehicle weight estimations from bridge weigh-in-motion system is studied. The measured bending moments of the instrumented bridge under a passage of vehicle are numerically simulated and are used as the input for the vehicle weight estimations. Two weight estimation methods assuming constant magnitudes and time-varying magnitudes of vehicle axle loads are investigated. The appropriate number of bridge elements and sampling frequency are considered. The effectiveness in term of the estimation accuracy is evaluated and compared under various parameters of vehicle-bridge system. The effects of vehicle speed, vehicle configuration, vehicle weight and bridge surface roughness on the accuracy of the estimated vehicle weights are intensively investigated. Based on the obtained results, vehicle speed, surface roughness level and measurement error seem to have stronger effects on the weight estimation accuracy than other parameters. In general, both methods can provide quite accurate weight estimation of the vehicle. Comparing between them, although the weight estimation method assuming constant magnitudes of axle loads is faster, the method assuming time-varying magnitudes of axle loads can provide axle load histories and exhibits more accurate weight estimations of the vehicle for almost of the considered cases.

Calculation of dynamic impact loads for railway bridges using a direct integration method

This paper introduces railway bridge assessment in the UK and the concept of dynamic impact loads. The dynamic impact loads demonstrated in the codes of practice in several other countries have been reviewed and have been found to be significantly different in the different codes. A technique for calculating dynamic impact load using a direct integration method has been developed. In many cases, the mass of the train may be similar to the mass of the bridge in heavy railway bridges but the mass of the vehicle is normally neglected in an analysis due to complexities in computation. Time-varying non-linear mass models are employed to reflect the effect of moving vehicle mass. An existing prototype bridge has been selected to compare results from the codes of practice and the technique developed in this study. The correlation between vehicle speed, axle load, and dynamic impact load has been investigated.

Multiple vehicle axle load identification from continuous bridge bending moment response

The identification of multiple vehicle dynamic axle loads on multi-span continuous bridge is presented. The objective of the present study was to develop a practical technique to determine dynamic axle loads of multiple vehicles based on the measured bridge response. Based on the inverse problem of turning bridge responses into time-varying point loads, the solution can be determined using least squares regularization optimization. The updated static component (USC) technique is adopted to improve the accuracy and eliminate the difficulty of an optimal regularization selection. The computer simulation and experimental studies were conducted to investigate the effectiveness of the proposed method. A scaled model of a three-span, continuous bridge and two scaled 2-axle vehicles were designed, constructed and fabricated in the laboratory. Various moving schemes of multiple vehicle travel including following, overtaking and side-by-side movements were considered. The actual dynamic axle loads of the model vehicles during the travel were directly monitored and used in accuracy evaluation. From the obtained results, it is observed that the USC technique effectively improved the accuracy and robustness of the problem, particularly in correction of the absence of identified axle loads around the internal bridge supports. The method is robust and accurately identifies every dynamic axle load for all moving schemes of vehicles. No conflict of the identified axle loads during axle overlapping and passing the bridge support is observed because the axle loads are identified independently and controlled by static influence lines from the USC algorithm. The comparison between the measured and reconstructed bending moments indicates that the approach is correct. The accuracy of identified dynamic axle loads for all cases of study is within a relative percentage error of 13%.

Experimental study on the identification of dynamic axle loads of moving vehicles from the bending moments of bridges

The identification of the dynamic axle loads of moving vehicles from the bending moments of a bridge is experimentally studied. The main purpose is to develop a practical technique to estimate the dynamic axle loads of vehicles during their motions. Although previous numerical investigations have revealed the potential application of certain load identification techniques, their experimental or actual field test investigations are very limited. In addition, the results from existing experimental or actual field test investigations could not lead to any conclusive information, since the actual dynamic axle loads were not directly measured, but only the weights or static axle loads of vehicles were used for their comparisons. In this paper, the dynamic axle loads of vehicles are directly measured and are used to compare with the loads obtained from their identification via bending moments. The bridge is modeled by a uniform thickness steel plate sitting on roller supports, while the vehicle is modeled by a two-axle moving platform. During the passage of the vehicle, its dynamic axle loads as well as the bending moments of the bridge are simultaneously recorded. Based on these obtained bending moments, axle load identification is performed. Two identification methods, named the conventional regularization and regularization with USC, are employed, and their identified dynamic axle loads are compared with those obtained from the measurements. The experiments are conducted for various weights and speeds of the vehicle. Two roughness conditions of the bridge surface are considered. The obtained experimental results reveal that the regularization with USC can provide good estimates of the front and rear dynamic axle loads of the vehicle. Its identification accuracy is found to be much better than that obtained using the conventional regularization. In the case of the smooth bridge surface, identification errors of less than 10% can be achieved for heavy vehicles regardless of their speeds.

Utilizing Clustering Techniques in Estimating Traffic Data Input for Pavement Design

This paper presents an objective approach for establishing similarities in vehicle classification and axle load distributions between traffic data collection sites. It is based on clustering techniques that identify in succession groups of sites of decreasing similarity on the basis of the attributes specified (e.g., either the percentage of vehicles by class or the percentage of axles by load interval, respectively). This method is implemented in identifying clusters of sites with similar vehicle class distribution and axle load distributions, respectively. Extended coverage weigh-in-motion data (i.e., more than 299 days/year) from the long-term pavement performance database was used for this purpose. These data included 178 sites distributed through seven states. The paper explains the clustering methodology for one of these states and presents the clustering results for all seven states. This methodology allows estimation of traffic input to the new mechanistic-empirical pavement design guide from limited site-specific traffic data.

MAINTENANCE COSTS OF ROAD PAVEMENT AND MOTOR VEHICLES ON THE ROUTE VILNIUS – KAUNAS – KLAIPEDA

The article describes the impact of axle loads of vehicles on the road pavement. Pavement deterioration intensity and the charge imposed on vehicles the axle load of which exceeds the set norm are analyzed on the road under investigation according to the results of weighing axle loads of vehicles as well as appropriate calculation methodologies. The work presents regressive equations according to which maintenance costs of vehicles can be predicted taking the condition of pavement into consideration.

Identification of vehicle axle loads from bridge responses using updated static component technique

The identification of the axle loads of a moving vehicle from bridge response is studied. The objective is to develop the weigh-in-motion (WIM) technique to estimate the vehicle weight from the bridge responses without any disturbance to the vehicle’s traveling speed. The least-squares method using conventional regularization is considered, since it can provide not only the static gross weight but also the dynamic axle loads of the vehicle. However, the accuracy of the identified results from the method greatly depends on an assigned regularization parameter, which is very sensitive to the vehicle–bridge properties such as the speed of the vehicle or the roughness amplitude of the bridge surface. Therefore, it is difficult for it to be precisely assigned in practice. To overcome this problem, regularization using the updated static component (USC) technique is proposed. The technique extracts the static components of the identified axle loads and leaves only the associated dynamic components to be identified. Then the iteration of the identification is imposed to improve the accuracy of the identified results. The numerical examples of identification of the axle loads of a two-axle vehicle moving on a simply-supported bridge under various speeds of the vehicle and surface roughness amplitudes of the bridge are considered. It is found that, employing the proposed USC technique, the required parameter for the regularization becomes much less sensitive. In addition, the identified results obtained from the technique are substantially accurate compared to those from the conventional regularization.

Moving Axle Load From Multi-Span Continuous Bridge: Laboratory Study

Laboratory study on the identification of moving vehicle axle loads on a multi-span continuous bridge from the measured bending moment responses is presented. A bridge-vehicle system model was fabricated in the laboratory. The bridge was modeled as a three span continuous beam and the car was modeled as a vehicle model with two-axle loads. A number of strain gauges were adhered to the bottom surface of the beam to measure the bending moment responses. Using measured bending moment responses as an input, the corresponding inverse problem was solved to identify moving loads. The moving forces were identified when considering bending moment responses from all spans of the beam. In order to avoid the lower identification accuracy around the inner supports of continuous bridge and to improve the computation efficiency, the moving force identification from the target (one selected) span of the continuous bridge was studied. The rebuilt responses were reconstructed from the identified loads as a forward problem. To study the accuracy of the method the relative percentage errors were calculated with respect to the measured and the rebuilt bending moment responses. The rebuilt bending moment responses obtained from the identified forces are in good agreement with the measured bending moment responses. This indirectly shows that the method is capable of identifying moving loads on continuous supported bridges.

Vehicle axle loads identification using finite element method

Existing methods on moving force identification are usually based on modal decomposition and are subject to modal truncation error in the dynamic responses. A new moving load identification method is presented basing on finite element method and condensation technique. The measured displacements are formulated as the shape functions of the finite elements of the structure which is modeled as a straight beam. The measured responses can be limited to a small number of master degrees-of-freedom of the structural system. Numerical simulations and experimental results demonstrate the efficiency and accuracy of the method to identify a system of general moving loads or interaction forces between the vehicle and the bridge deck. The number of master degrees-of-freedom of the system should be selected smaller than or equal to the number of measured points, and the identified results are relatively not sensitive to the sampling frequency, velocity of vehicle, measurement noise level and road surface roughness when a minimum of eight beam-column finite elements are used to model the bridge with measured information from three measuring points.

The influence of the depth of the ground water table on free field road traffic‐induced vibrations

AbstractThis paper describes the influence of seasonal variations of the ground water table on free field traffic‐induced vibrations. The passage of a truck on two types of road unevenness is considered: a joint in a road pavement consisting of concrete plates and a speed bump with a sinusoidal profile. Free field vibrations are computed with a two‐step solution procedure, where the computation of the vehicle axle loads is decoupled from the solution of the road–soil interaction problem. The impedance of the soil is calculated using a boundary element method, based on the Green's functions for a dry layer on top of a saturated half‐space. It is demonstrated that, in the low‐frequency range of interest, wave propagation in the saturated half‐space can be modelled with an equivalent single phase medium as an alternative to Biot's poroelastic theory for saturated porous media. The relation between the free field velocity and the depth of the ground water table is dominated by three phenomena: (1) the compressibility of the soil decreases due to the presence of the pore water, (2) the ground water table introduces a layering of the soil which may cause resonance of the dry layer and (3) refracted P‐waves in the dry layer interfere with surface waves. If the depth of the ground water table is large with respect to the wavelength of the vibrations in the soil, the response tends to the response of a dry half‐space. The average free field velocity is equal to the velocity in the absence of ground water. If the depth of the ground water table is small with respect to the wavelength of the vibrations in the soil, the response tends to the response of a saturated half‐space and resonance of the dry layer does not occur. The average free field velocity is smaller than the velocity in the absence of ground water. The interference of refracted P‐waves and surface waves causes an additional oscillation of the response as a function of the excitation frequency and the distance between the road and the receiver. Copyright © 2004 John Wiley & Sons, Ltd.

Moving force identification based on the frequency–time domain method

This paper addresses the problem on the identification of moving vehicle axle loads based on measured bridge responses using a frequency–time domain method. The focus is on the evaluation of two solutions to the overdetermined set of equations established as part of the identification method. The two solutions are (i) direct calculation of the pseudo-inverse and (ii) calculation of the pseudo-inverse via the singular value decomposition (SVD) technique. For this purpose, a bridge–vehicle system model was fabricated in the laboratory and the bending moment responses of bridge model were measured as a two-axle vehicle model moved across the bridge deck. The moving axle loads are then calculated from the measured responses via the two solutions to the over-determined set of equations. The effects of changes in the bridge–vehicle system, measurement and algorithm parameters on the two solutions are evaluated. Case studies show that the moving force identification is more feasible and its accuracy acceptable with the use of the SVD technique. This technique can effectively enhance the identification method and improve the identification accuracy over that of the direct pseudo-inverse solution.

Analysis of high-speed vehicle-bridge interactions by a simplified 3-D model

In this study, the analysis of high-speed vehicle-bridge interactions by a simplified 3-dimensional finite element model is performed. Since railroads are constructed mostly as double tracks, there exists eccentricity between the vehicle axle and the neutral axis of cross section of a railway bridge. Therefore, for the more efficient and accurate vehicle-bridge interaction analysis, the analysis model should include the eccentricity of axle loads and the effect of torsional forces acting on the bridge. The investigation into the influences of eccentricity of the vehicle axle loads and vehicle speed on vehicle-bridge interactions are carried out for two cases. In the first case, only one train moves on its track and in the other case, two trains move respectively on their tracks in the opposite direction. From the analysis results of an existing bridge, the efficiency and capability of the simplified 3-dimensional model for practical application can be also verified.

Control of Live Load on Bridges

Application of field testing for an efficient evaluation and control of live-load effects on bridges is described. A system is considered that involves monitoring of various parameters, including vehicle weight, dynamic load component, and load effects (moment, shear force, stress, strain) in bridge components, and verification of the minimum load-carrying capacity of the bridge. Therefore, an important part of the study is development of a procedure for measuring live-load spectra on bridges. Truck weight, including gross vehicle weight, axle loads, and spacing, is measured to determine the statistical parameters of the actual live load. Strain and stress are measured in various components of girder bridges to determine component-specific load. Minimum load-carrying capacity is verified by proof load tests. It has been confirmed that live-load effects are strongly site specific and component specific. The measured strains were relatively low and considerably lower than predicted by analysis. Dynamic load factor decreases with increasing static load effect. For fully loaded trucks, it is lower than the code-specified value. Girder distribution factors observed in the tests are also lower than the values specified by the design code. The proof load test results indicated that the structural response is linear with the absolute value of measured strain considerably lower than expected. Field tests confirmed that the tested bridges are adequate to carry normal truck traffic.

EFFECT OF AXLE LOAD, TIRE INFLATION PRESSURE, AND TILLAGE SYSTEM ON SOIL PHYSICAL PROPERTIES AND CROP YIELD OF A JORDANIAN SOIL

The effects of tillage treatment, tire inflation pressure, and vehicle axle load resulting from wheeled traffic onsoil tilled in the fall were evaluated by measuring the changes in soil physical properties (bulk density, air porosity, andinfiltration rate) and by measuring changes in crop yield in comparison with controlled plots. Results included the effectsof these parameters and their interactions at four depths (0 to 40 cm) on soil bulk density and soil air porosity. Also,infiltration rate measurements for all treatments and for control plots are reported. Data obtained from the experimentalplots showed that infiltration rate was strongly affected by tillage treatments from 0 to 20 cm. Dry bulk density and airporosity were affected from 0 to 20 cm by tillage treatments and from 20 to 40 cm by tire inflation pressure and axle load.The crop (barley) response in terms of yield was found to be affected by tillage treatment, tire inflation pressure, and theinteraction between tire inflation pressure and axle load.

Measurement of Truck Load on Bridges in Detroit, Michigan, Area

The objective of the study was to determine the actual truck loads on selected bridges in the Detroit, Michigan, area. Seven representative bridges were selected. The measurements were taken by using a weigh-in-motion system. For each measured truck, the record included vehicle speed, axle spacing, and axle loads. The variation in the accuracy of the gross vehicle weight (GVW) measurement was estimated to be ±5 percent and that of the axle weights was estimated to be ±20 percent for most types of trucks. Selected bridges were instrumented, and measurements were taken for 2 or 3 consecutive days. There was a considerable variation in traffic volumes and the weights of trucks, even within a given geographic area. The estimated average daily truck traffic varied from 500 to 1,500 in one direction. The maximum observed truck weights varied from 360 kN (81 kip) to 1100 kN (250 kip). The maximum observed axle weights varied from 90 kN (20 kip) to 225 kN (50 kip). The percentage of trucks exceeding the legal limits in Michigan varied depending on the road. The heaviest GVWs and axle weights were observed on Interstate highways. The largest percentage of overloaded trucks was observed for 11-axle vehicles. The maximum lane moments and shears from the trucks varied between 0.6 and 2.0 times AASHTO load and resistance factor design values. It was found that there are similarities in GVW and lane moment distributions.

Measurement of Truck Load on Bridges in Detroit, Michigan, Area

The objective of the study was to determine the actual truck loads on selected bridges in the Detroit, Michigan, area. Seven representative bridges were selected. The measurements were taken by using a weighin-motion system. For each measured truck, the record included vehicle speed, axle spacing, and axle loads. The variation in the accuracy of the gross vehicle weight (GVW) measurement was estimated to be ±5 percent and that of the axle weights was estimated to be ±20 percent for most types of trucks. Selected bridges were instrumented, and measurements were taken for 2 or 3 consecutive days. There was a considerable variation in traffic volumes and the weights of trucks, even within a given geographic area. The estimated average daily truck traffic varied from 500 to 1,500 in one direction. The maximum observed truck weights varied from 360 kN (81 kip) to 1100 kN (250 kip). The maximum observed axle weights varied from 90 kN (20 kip) to 225 kN (50 kip). The percentage of trucks exceeding the legal limi...

On-Site Calibration Evaluation Procedures for WIM Systems

The feasibility of two methods for evaluating and calibrating weigh-in-motion (WIM) systems is explored. The first method uses a combination of test trucks and vehicle simulation models. The computer model VESYM was used for the simulations. The models for the test trucks were calibrated using acceleration measurements on board the vehicles. Although, this approach does not allow calculation of the discrete value of the dynamic axle load over WIM sensors, it can be used effectively in establishing the extent of variation at a particular WIM site. This information leads to an effective WIM system calibration method. The second method for calibrating WIM systems compares static and dynamic axle loads of vehicles through automatic vehicle identification (AVI). The AVI facilities developed for the Heavy Vehicle Electronic License Plate project on the I-5 corridor was used for this purpose. The static axle load of AVI-equipped vehicles was obtained from the Oregon Department of Transportation for two sites, Woodburn southbound and Ashland northbound. The WIM load data were obtained from Lockheed IMS for all the AVI-equipped WIM systems on the I-5 corridor. The data were analyzed to match AVI numbers, dates, and times of weighing. Time limits for traveling between sites were established to ensure that trucks could not stop and load or unload cargo between sites. Errors were calculated as the percentage difference between WIM and static loads for individual axles and axle groups. Calibration factors were derived to minimize the residual sum of squares of the errors.

On-Site Calibration Evaluation Procedures for WIM Systems

The feasibility of two methods for evaluating and calibrating weigh-in-motion (WIM) systems is explored. The first method uses a combination of test trucks and vehicle simulation models. The computer model VESYM was used for the simulations. The models for the test trucks were calibrated using acceleration measurements on board the vehicles. Although, this approach does not allow calculation of the discrete value of the dynamic axle load over WIM sensors, it can be used effectively in establishing the extent of variation at a particular WIM site. This information leads to an effective WIM system calibration method. The second method for calibrating WIM systems compares static and dynamic axle loads of vehicles through automatic vehicle identification (AVI). The AVI facilities developed for the Heavy Vehicle Electronic License Plate project on the I-5 corridor was used for this purpose. The static axle load of AVI-equipped vehicles was obtained from the Oregon Department of Transportation for two sites, Wo...

鐵道軌間の寸法と車輪の軌道に對する壓力との關係

When the lateral forces such as wind pressures, centrifugal forces &c act on a railway vehicle, the pressure of wheels on rails will increase on the one side and diminish on the other. When a wheel of a vehicle passes over a weak spot on the rail along the oneside, the pressure of that along the other side will either increase or decrease. Such increments of wheel pressure are worth while careful consideration and the increments are greater in the case of narrow gauge railways than in the case of broad ones. Therefore it follows that the admissible axle loads of vehicles of a narrow gauge railways must be lower than that of broad ones, on condition that the permanent ways are of the same strength and that the vehicles are of the same size. It may also be stated that the use of sharp curves must be restricted more in narrow gauge railways than in broad ones, if the vehicles are of the same size. The argument is sometimes raised against broad gauges that the curve resistance will be greater as compared with that in narrow gauges. But this is of less importance, as the curve resistance is affected more by the lengths of wheel base of vehicles rather than the gauge and is also a small fraction of the train resistance in general.