Use of Ballast Support Condition Back-Calculator for Quantification of Ballast Pressure Distribution Under Concrete Sleepers

In North America, most rail corridors are constructed using ballasted track. Monitoring the ballast support condition and improving upon current sub-structure/ballast maintenance strategies will ensure safe railroad operations. However, it is inherently difficult to evaluate the pressure distribution at the sleeperballast interface. Researchers at University of Illinois at Urbana-Champaign (UIUC) have developed an instrumentation strategy and analysis tool, the support condition back-calculator, to quantify ballast pressure distributions under concrete sleepers without interrupting the traffic. This laboratory-validated non-intrusive method uses concrete sleepers’ bending moment profile and rail seat loads as inputs to back-calculate the reaction distribution through the use of an optimization algorithm. To better understand the in-service ballast support conditions, this technique was deployed in the field on a Class I heavy haul freight railroad in the United States. Concrete surface strain gauges were installed on concrete sleepers to measure their in-field bending moments. Wheel Impact Load Detectors (WILD) were used to measure rail seat input loads. The focus of this paper is to quantify the ballast pressure distributions beneath concrete sleepers on the heavy-haul tangent track. An evaluation of ballast pressure distribution variations between adjacent sleepers and through tonnage accumulation are also included. The information presented in this paper demonstrates the potential of the backcalculator for monitoring the ballast condition and will assist the rail industry in optimizing tamping cycle, enhancing safety, and developing more representative sleeper flexural designs for North America railroad applications. 2 BALLAST SUPPORT CONDITION BACKCALCULATOR BACKGROUND The methodology of the back-calculator is to use the rail seat loads and the bending moments along the concrete sleeper to back-calculate the ballast support condition beneath the sleeper. Based on force equilibrium and the basic principles of statics, for a twodimensional subject, only one combination of reaction forces (one support condition) can account for a certain moment profile under a set of applied loads. Therefore, if the concrete sleeper is simplified as a two-dimensional beam, then its ballast support condition can be back-calculated from the sleeper’s bending moments and the corresponding rail seat loads. To quantify the sleeper bending moments in the field concrete surface strain gauges were used to measure the bending strains of the sleeper, which were converted into bending moments using the appropriate calibration factors (RailTEC 2013). Rail seat loads are indirectly computed from wheel loads provided by a nearby Wheel Impact Load Detector (WILD) site using the recommended equation given in American Railway Engineering and Maintenance-of-Way Association (AREMA) Manual for Railway Engineering (MRE) (2016). 2.1 Two-dimensional sleeper model To further simplify and bound the problem, a two-dimensional sleeper model, shown in Figure 1, was developed. The model represented a 260 cm (102 in.) long concrete sleeper typically used in North American heavy haul freight railroad, and it was divided into six discrete bins of equal size, with the width of each bin being 43 cm (17 in.). Each bin carried a certain percentage of the total ballast reaction force, and the reaction force within each bin was assumed to be uniformly distributed. The reaction force distribution in Figure 1 demonstrates a scenario where the ballast support is uniform along the entire sleeper, but it is not intended to represent an actual result from the back-calculator. Concrete surface strain gauges were generally placed along the top chamfer of the sleeper, and they were taken into account in the twodimensional model (Fig. 1). The rail seat loads were assumed to be uniformly distributed over each of the 15 cm (6 in.) rail seats. The two-dimensional sleeper model includes two boundary conditions for computation. First, based on force equilibrium, the total ballast reaction force should equal the total rail seat loads, thus the sum of all six bins should be 100%. Second, the value of each bin should not be less than 0, as it is unrealistic to have a negative reaction force. 2.2 Optimization process Once the two rail seat load magnitudes are input into the back-calculator, it then executes an optimization process to generate combinations of reaction forces that could satisfy the two boundary conditions. For each reaction force combination, the back-calculator would generate the bending moment profile of the sleeper based on the rail seat loads and compare it to the actual input bending moment profile. The optimization process stops when the difference between the calculated and actual bending moment profiles reached its minimum, and the reaction force combination that generated this calculated bending moment profile became the resultant support condition. The ballast reaction forces could then be converted into ballast pressures by dividing the forces over the bottom width of the sleeper. In the optimization process, Simulated Annealing and Bi-polar Pareto Distribution were used as the optimization algorithm and the random variable generator. The benefits of implementing them together were that they could find better solutions in less time (Englander & Englander 2014), and they were able to avoid getting stuck in local optima (Kirkpatrick et al. 1983). The maximum computational time for a given set of inputs was approximately one minute, which was considered to be short and reasonable for achieving the objectives associated with the back-calculator. 3 FIELD EXPERIMENTATION PLAN To estimate and analyze the field ballast conditions under revenue service loads using the ballast support condition back-calculator, field experimentation was conducted at a tangent location on a Class I heavy haul freight railroad in the United States. The sleepers installed at this location had the same length as that of the two-dimensional sleeper model, and the concrete surface strain gauges were installed at the exact locations as those represented in the model to measure the bending moments experienced by the sleepers. As shown in Figure 2, the test site was divided into two zones, spaced approximately 18 m (60 ft) apart, with each zone consisting of five sleepers. Based on visual inspection, Zone 1 was selected as a poorly supported zone because, upon train passes, this zone was observed to deflect more than Zone 2 (Wolf 2015). Two thermocouples were installed on a sleeper between the two zones, one at the sleeper top chamfer and one near the sleeper bottom covered in Figure 1. Two-dimensional sleeper model (with assumed uniform support condition). ballast. These were deployed to measure the temperature gradient between top and bottom of the sleeper (Wolf et al. 2016). The wheel load data provided by the nearby WILD site were used to approximate the rail seat loads experienced by the sleepers. Since the wheels passing through the test site had a consistent nominal wheel load of 160 kN (36 kips), the rail seat load could be approximated to be 80 kN (18 kips) by using the AREMA recommended equation (AREMA 2016), and this value was used as the input rail seat loads for the support condition back-calculator. 4 PRILIMINARY RESULTS FROM BALLAST SUPPORT CONDITION BACKCALCULATOR 4.1 Ballast pressure limit states Ballast pressure distributions were used to present the resultant support conditions so that the back-calculator results could be correlated with AREMA recommended ballast properties. Three ballast pressure limit states were introduced to further aid the evaluation of the ballast condition. 1. The ballast pressure under an assumed uniform support condition was calculated to be 221 kPa (32 psi). 2. AREMA MRE specified the allowable ballast pressure under concrete sleepers to be 586 kPa (85 psi). 3. The ballast pressure corresponding to the AREMA allowable subgrade bearing stress of 172 kPa (25 psi) could be calculated using the Talbot equation below. 5 4 8 . 16       