Multi-Body Dynamic Modeling of the Expected Performance of Accelerated Pavement Testing Facilities

Accelerated Pavement Testing (APT) facilities are nowadays considered fundamental for the thorough understanding of the performance of pavements. The amount of information that can be derived from APT investigations can serve as the basis for a more performance-related pavement design but also for the development of new pavement types and innovative materials. In the design and use of such facilities, special care should be placed in the modeling of the loading systems which are employed to produce accelerated damage. Such an analysis is important both in the preliminary design phase, in which technological solutions are found in order to simulate the effects of heavy vehicles on the pavement, and in the various phases of investigation, when the recorded damage has to be clearly related with effective loading conditions. In this respect, modeling can be a valuable support to the evaluation of the data which can be acquired by means of a proper instrumentation of the facility. In order to address such issues, the Authors have developed a design procedure which together with typical stationary calculations includes the adoption of Multi-Body (MB) and Finite Elements (FE) models of the testing system. As proven by the first implementation exercises of the design procedure, the use of MB and FE models allows the evaluation of the dynamics of the system in a wide variety of testing conditions. Thus, stresses and strains in the structure of the APT facility can be estimated and the dynamic forces and torques which arise during testing at the tire-pavement interface can be predicted. Given the width of the design problem, this paper gives only a general overview of the structure of the proposed procedure, with its application to a specific case which has been studied in depth. Refinements are still under way and will hopefully yield a set of modeling methods which in the future will be available for the design of new APT facilities and for the assessment of the performance of existing systems. INTRODUCTION The design and construction of long-lasting pavements is one of the goals which highway engineers have continuously tried to reach for centuries. Such an effort has required experimental and theoretical research which in time has increased its level of complexity: while initial studies were essentially based on the observation of pavement sections subjected to traffic and on the index-characterization of the materials used in construction, current investigations are based on a more detailed description of material behavior and on the modeling of pavement performance under controlled or monitored loading conditions. In such a context, Accelerated Pavement Testing (APT) facilities have proven to be extremely powerful research tools, since they can simulate long-term effects of traffic loading in a relatively short time period, with the corresponding evaluation of the progressive changes in pavement response and distress. Quite obviously, the accelerated character of this kind of testing is a key element for the development of projects focused on the design and modeling of perpetual pavements, conceived in such a way to extend service life well beyond the levels associated to standard pavement structures. APT programs are nowadays active worldwide and address almost all relevant aspects of pavement engineering. Valuable sources of information with respect to past achievements and future perspectives are provided by TRB Committee AFD40 (formerly A2B09) and by the European COST-Transport action COST 347. When compared with the original prototypes developed at the beginning of the 20 century [1,2], current APT devices are quite complex, with a wide array of operative options and technological refinements which are implemented in order to maximize the simulation of the effects caused by actual heavy vehicles and/or aircraft landing gears. Moreover, whether of the linear of circular type, all APT systems are designed in such a way to make their use economically feasible, with a convenient limitation of energy consumption and testing time. In many cases research institutions have developed their own testing prototypes, conceived to suit specific needs; however, in other cases they have preferred to adopt systems already used in other countries which to some extent could be considered as standard devices with a rich set of test data available for comparative purposes. In the Politecnico di Torino, the whole issue of vehicle-road interaction has been recently approached by combining the efforts and resources of the Pavement Engineering and Vehicle Dynamics research groups. Topics of interest which have been treated both experimentally and theoretically range from the evaluation of the effects caused by pavement roughness to the dynamic design of geometrical road elements. More recently, the joint research group has also started working on the design of APT facilities which is in fact a theme at the boundary between pavement and vehicle engineering: as illustrated in this paper, this has been done by developing a design procedure which together with typical stationary calculations includes the adoption of Multi-Body (MB) and Finite Elements (FE) models of the testing system. As proven by the first implementation exercises of the design procedure, the use of MB and FE models allows the evaluation of the dynamics of the system in a wide variety of testing conditions. Thus, stresses and strains in the structure of the APT facility can be estimated and the dynamic forces and torques which arise during testing at the tire-pavement interface can be predicted. This second aspect of analysis is especially important when considering side and longitudinal forces, the importance of which is generally overlooked in the design of APT facilities even though it has been clearly recognized that they may greatly affect both the interaction between the components of the test system and the development of structural and functional distresses in the pavement. As shown in the design example illustrated in this paper, such a limitation can be overcome by means of an adequate modeling of the APT system: in fact, its results provide the basis for the definition of the location and type of on-board sensors used to measure shear forces applied to the pavement and of methods to be employed for their active control. The development and use of the proposed design procedure requires a deep knowledge of tire and vehicle dynamics and should be supplemented by direct testing in order to make realistic assumptions of the many structure and materials parameters utilized in modeling. Given the width of the design problem, this paper gives only a general overview of the structure of the proposed procedure, with its application to a specific case which has been studied in depth. Refinements are still under way and will hopefully yield a set of modeling methods which in the future will be available for the design of new APT facilities and for the assessment of the performance of existing systems. DESIGN PROCEDURE Figure 1 gives a schematic illustration of the design procedure which is being developed by the Pavement Engineering and Vehicle Dynamics research groups. The first step in design consists in performing the basic static calculations which are necessary to establish the main dimensions of the structure. The basic parameters of the APT device (circular or linear layout, engine power, number of wheels of the trolleys, static load acting on the wheels, etc.) have to be chosen at this step. As better explained in the following paragraphs, the adoption of an MB model in this first step of design would be too expensive in terms of time, due to the large number of uncertain parameters which should be evaluated and modified. In fact, an MB model considers the inertia of all the main components, which are connected by elements characterized by their own stiffness and damping coefficients. After the definition of a first approximation layout, it is possible to implement the MB model of the APT facility. First of all, in semi-stationary conditions, it is necessary to make a comparison between the results of the static calculations and the output of the model, in order to assess its validity. Then it is possible to carry out an analysis of the behavior of the system in dynamic conditions, for example when the pavement surface is not perfectly flat, to investigate the forces and the torques acting at the tire-pavement interface and between the different components of the testing facility. The MB model can also be useful to optimize the structural design of the APT system and, as mentioned previously, to decide how to locate the sensors on its moving parts in order to measure or estimate the dynamic tire-pavement forces. Finally, for an in-depth design of the structure of the APT facility, it is necessary to set up an FE model of the machine and to make it run in co-simulation with the MB model. This type of modeling is quite complex and should be performed on the final layout of the facility; the corresponding results can be used to better understand the performance of the APT system and to provide a continuous feedback to measurements carried out during testing. This paper presents the results obtained in the design steps of Figure 1 which correspond to the static calculations and to the implementation and use of the MB model. The calculation examples refer to the specific case of a rotational APT system which has been thoroughly examined to test the applicability of the procedure and which could be actually built by employing the indicated technological components. FIGURE 1 Flux diagram of the design procedure. Preliminary Assumptions The first choice for the designer of an APT facility consists in defining the configuration of the system, which can be either of the rotational or linear type. Both configurations have several advantages and disadvantages, so the choice should be made based on a balanced evaluation of a number of factors which may have different weights depending upon the intended use of the facility. The linear configuration has the advantage of occupying a small area; furthermore, it is usually transportable and can be located in different sites depending upon specific needs. However, it has the limitation of permitting only small values of longitudinal speed of the loading trolleys. The inertial force necessary to obtain a speed of 40-50 km/h with an acceptable (not too large) spatial length of the test facility is too high both in terms of power required by the system of propulsion and of strains exerted on the structure. The rotational configuration permits a very slow acceleration of the testing equipment (only during transients, necessary to make the machine start and stop) without significant dynamic forces or torques on the structure and on the system of propulsion. The power system of the testing facility can be designed as a function of the static load acting on the trolleys of the testing equipment. Taking into account the observations illustrated above, the design procedure was applied to the case of a rotational APT facility, with a loading system composed of four trolleys connected by means of rigid horizontal arms to a rotating central shaft (Figure 2). In order to avoid the superposition of dynamic loading effects on the pavement, it was hypothesized that the trolleys should have a single axle configuration (Figure 3) with the possibility of using super single tires. Such a choice also allows a more simple modeling of pavement damage, which according to traditional approaches is always referred to single axles. FIGURE 2 Sketch of the APT facility considered in the study. For a system of the type indicated in Figure 2, the connection between the arms and the trailers should be made by employing ball recirculation bearings, characterized by a low friction. Their function is to prevent the rotation of each trolley around the axis of the wheels and to transmit the horizontal force necessary to make the system rotate along a circular trajectory. In the preliminary phase of design some hypotheses had also to be made on the type of loading trolleys. Therefore, it was assumed that commercial suspensions, such as the one shown in Figure 3, should be utilized: this allows the dynamics of the loads to be very similar to the typical behavior of a heavy truck. The system represented in Figure 3 is a trailing arms suspension, with an integrated steering system based on a hydraulic power circuit. It can be equipped with a system of hydraulic springs, which can be used for the dynamic variation of the load acting on the pavement. FIGURE 3 Sketch of the suspension system of the trolley. With respect to the maximum static load acting on each trolley, in the calculations reference was made to a value of 120 kN, which can be obtained by means of a system of steel blocks piled on the each individual chassis (Figure 4). It is important to highlight the fact that by adopting the abovementioned solution for the trolley-arm connection, the vertical load, even in dynamic conditions, is entirely sustained by the tires and not by the bearings which connect the structure of the APT facility to the trolleys. For the configuration schematically shown in Figure 4, centrifugal forces, which are generated by the motion of the trolleys, are absorbed by the lever arms (through the bearings) and not by the tires of the moving trolley. Only the sideslip angles due to the steering angle of the wheels give origin to a force which is transmitted to the structure of the trolley (suspension and chassis). It has to be underlined that a commercial trailer for a truck can sustain a maximum level of lateral acceleration equal to 0.5g. A typical configuration (for example, with a diameter of 20 m) of a circular APT facility can easily give origin to a level of lateral acceleration greater than 1.5g, which corresponds to the force absorbed by the arms of the machine (and not by the suspensions). As a consequence, in designing the facility it is possible to refer to a level of lateral acceleration of the trolleys which exceeds the maximum value which it could have on the road. However, care should be taken in checking that the imposed steering angle does not give origin to a force which exceeds the structural resistance of the trolley. Connection with the