QUALITATIVE EVALUATION OF STOCHASTIC ...

QUALITATIVE EVALUATION OF STOCHASTIC FACTORS AFFECTING THE TRAFFIC SPEED DEFLECTOMETER RESULTS Adam Zofka, Ph.D.*# Professor phone: +48 22 3900407 email: [email protected] Miroslaw Graczyk, Ph.D. # Professor phone: +48 22 8145467 email: [email protected] Jozef Rafa, Ph.D.& Associate Professor phone: +48 226837907 email: [email protected] * corresponding author # Road and Bridge Research Institute (IBDiM) Address: 1 Instytutowa Str., PL 03-302 Warsaw, Poland &

Military University of Technology (WAT) Address: gen. Sylwestra Kaliskiego 2, PL 00-908 Warsaw, Poland

Submission date: August 1, 2014 Word count: 8 figures + 2 tables+ 4944 words = 7444 words

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ABSTRACT This paper presents a qualitative evaluation of selected stochastic factors affecting the measurements and interpretation of the Traffic Speed Deflectometer (TSD) results. Although the idea of measuring pavement deflections at traffic speeds in a continuous manner is not new, only recent years brought worldwide interest to that topic partially due to availability of the commercial TSD device. The TSD is a very effective tool for pavement structural assessment at the network level. However, since the device is still relatively new, special attention should be made to all aspects of data flow starting with the acceptance testing, calibration, verification and measurement procedures as well as data quality assurance and finally data interpretation algorithms. This paper focuses on one of the most important element of data flow which are the actual measurements. In particular, this study demonstrates how selected external factors can affect the TSD measurements through the probabilistic model. Proposed model accounts for two stochastic parameters present during the TSD operations: wind and pavement roughness. The parametric study demonstrated the importance of these two factors and the need to account for the associated dynamic effects on the rear axle of the TSD trailer and especially on its right wheel in front of which the TSD sensors are located. Further, the comparison between the dynamic force distributions determined from the proposed probabilistic model and actual force measurements on the rear axle of the TSD semi-trailer showed a good qualitative agreement which implies that the concept behind the proposed model is correct. Paper concludes that proposed methodology can at least partially explain the dynamic load effects during the TSD measurements, however further research is needed to fine-tune all related parameters.

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INTRODUCTION In many countries pavement structures are increasingly exposed to the higher than designed traffic loadings which causes accelerated damage growth and premature failures amplified further by the severe climate changes. This leads to the growing number of pavements in the deteriorated condition that do not necessary show the damage through the surface distresses. For that reason there is an urgent need to implement quick and reliable method(s) able to acquire information on the pavement bearing capacity especially on the network level. Typically, bearing capacity is assessed using pavement deflections due to either static, dynamic or moving load. Deflections or their derivative parameters can be then implemented into pavement management systems (PMS) in order to directly capture the structural aspect of the pavement condition and more effectively manage maintenance and rehabilitation activities under common budget constraints (1)-(4). Deflections have been traditionally measured using static devices, such as falling weight deflectometer (FWD) or Benkelman beam. The main disadvantage of these method is that they are relatively slow and thus ineffective to implement at the network level. Further, they create unsafe working conditions for their operators as they require lane closure and traffic redirection. On the other hand, recent technological developments have allowed to commercialize new devices that are able to record pavement deflections under the moving load (5)(6). An example of such a device is the Traffic Speed Deflectometer (TSD) that continuously measures pavement response as it is moving at the highway speed (7)(8). Several highway agencies around the world are currently assessing and/or implementing the TSD, and generally the TSD is considered as productive, safe and effective tool for the network level evaluation. However, there is still a significant effort to be made in order to fully understand all phenomena present during the TSD operations and to determine how they affect the actual measurements as well as the postprocessing algorithms. Traffic Speed Deflectometer (TSD) The TSD device is a semi-trailer truck with a standard 2-axle tractor that host the driver and the operator in the passenger seat. The single axle semi-trailer host the data acquisition system (DAQ) together with the measurement system and the fixed (dead) load attached to the bottom of the main body towards the rear axle. The main part of the measurement system is the horizontal beam hold in that position by the array of high-speed actuators and equipped with a number of Doppler sensors (7)-(9). The pavement deflection velocities measured by these sensors are divided by the instantaneous vehicle speed which gives the deflection slopes. Slopes can be used directly in the analysis (10) or the absolute deflections can be obtained by integrating the deflection slopes numerically (11) or by fitting the slopes to the solution of a suitable pavement mechanical model containing typically viscoelastic elements (7)(12). Once the slopes and corresponding deflection basins are determined, the TSD data allows to calculate wellestablished structural parameters (similar to the FWD) such as normalized maximum deflection d0, strain at the bottom of asphalt layer, Structural Number (SN), radius of curvature and effective pavement modulus. Alternatively, indices related to the structural condition such as Structural Adequacy Index (SAI), Structural Condition Index (SCI), Remaining Service Life (RSL) and/or Surface Curvature Index (SCI) (at various distances) can be also determined which alleviates the adaptation process of the TSD into agency’s operations and enhances its PMS algorithms.

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Potential factors affecting the measurements and data interpretation Although the concept behind continuous deflection measurements is simple and studied for 30+ years, the practical realization of this idea leads to complex system. There is a number of factors affecting the measurements and subsequent data interpretation. Further, since aforementioned parameters and indices are not equally affected by all factors, implementing results from the continuous deflection devices such as TSD requires extensive knowledge acquired from in-depth studies and scientific analysis. In attempt to systematize the factors affecting the TSD measurements, the following list was created. It should be noted that most likely this is a non-exhausted list and all factors should be considered as ‘potentially’ affecting the derived parameters and/or indices until studies in controllable field experiment. Also, the list was created based on the available literature (1)(3)(11)(13)(14) and observations made during TSD operations by the Road and Bridge Research Institute (IBDiM) in Poland. For convenience, all factors are subdivided into four groups without any particular order: 1) External environmental factors:  wind during measurements,  temperature history (air and pavement),  temperature during the measurements (air and pavement). 2) Pavement physical condition and geometric factors:  roughness,  tire-pavement contact interaction,  layer structure and materials,  gradient,  superelevation/curvature,  cross-slope. 3) Internal factors (TSD truck itself):  operational factors: i) calibration procedure, ii) efficiency of data acquisition, iii) accuracy of Distance Measurement Instrument (DMI), iv) quality assurance procedures,  physical factors: i) semi-trailer dimensions, ii) speed during measurements, iii) axle distribution, iv) suspension characteristic, v) wheel arrangement, vi) tire pressure and temperature, vii) number of Doppler sensors. 4) Post-processing mechanical model and interpretation of data:  dynamic force effects,  normal and tangential load components,  heat propagation effects,  moving load,  material models for pavement layers,

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 deflection contribution from the TSD tractor. It should be also mentioned that the importance of these factors changes depending on the application, i.e. the influence of some factors can be disregarded at the network level while the same factors may play an important role at the project level. Further, the detailed discussion of each of these factors is beyond the feasible scope of this paper but it is expected that majority of these factors continue to be further explored in the future research studies. In the study presented in this paper, an attempt was made to qualitatively evaluate two factors, namely wind effect and pavement roughness. Both factors were treated as random variables described by appropriate probability distributions. Corresponding probabilistic models were proposed and used in order to demonstrate the contribution of considered factors to the dynamic force on the rear TSD semitrailer axle. STUDY OBJECTIVES Three main objectives considered in this study can be formulated as follows: 1. To propose probabilistic model that accounts for two random factors - wind and pavement roughness, potentially affecting the TSD measurements. 2. To demonstrate the contribution of considered factors to the dynamic force on the rear TSD semi-trailer axle (right and left wheel). 3. To compare modelled variability in the force on the rear TSD semi-trailer axle with the actual field measurements. PROPOSED PROBABILISTIC MODEL This section presents the proposed probabilistic approach in capturing random effects of wind and pavement roughness. The description comprises three parts: first appropriate models for both effects are outlined and then probabilistic approach based on the Monte Carlo simulations is explained in details. Wind effect model Considerations on the aerodynamic phenomena of moving large vehicles has been researched in many studies since at least 1970’s (15)-(21). While several different approaches have been reviewed, this study adopts the methodology proposed in (16) including refinements presented in (17). This method considers a set of three aerodynamic forces and three moments acting on a vehicle. Under the assumption of steady-state conditions and disregarding any turbulent conditions (that could be expressed in terms of admittance function (19)), forces are attached to the center of gravity G and moments are acting around three principal axes of a vehicle (x, y, z) (see Figure 1a). The forces and moments are defined as: Fx drag force [N] Fy lift force [N] Fz side force [N] Mx rolling moment [Nm] My yawing moment [Nm] Mz pitching moment [Nm] The quantitative description of the wind consists of the relative wind velocity vector V and associated relative wind direction α (see Figure 1b). The magnitude of both quantities can be calculated from trigonometry using the TSD speed and the actual wind velocity vector U and angle β as follows:

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FIGURE 1 a) Sign convention and aerodynamic forces and moments acting on the moving TSD, b) XZ plane: definition of the relative wind velocity vector V (U - average wind velocity vector, R – relative air velocity induced by TSD, α – relative wind direction, β – wind direction) (after (17)) In order to calculate the aerodynamic quantities shows in Figure 1a, special coefficients were developed based on the wind tunnel experiments on the truck similar to the TSD (17)(22). The dimensionless coefficients are expressed in terms of the simple trigonometric functions and relative wind direction α: ( ) Eq.3 ( ) Eq.4 Eq.5 Eq.6 Eq.7 Finally the aerodynamic forces and moments can be calculated as follows: Eq.7 Eq.8

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Eq.9 Eq.10 Eq.11 where: ρ - air density [kg/m3] which can be calculated from the ideal gas law based on the temperature T [K] and pressure p [Pa] as follows: Eq.11a 2 A - reference area (A=c·w) [m ] (c and w are defined in Figure 2), h - height of the center of gravity [m] (defined in Figure 2). It should be mentioned that this study assumes that My (yawing moment) does not contribute significantly to the dynamic load distribution on the rear axle of the TSD semi-trailer. Other assumptions regarding the aerodynamics are included in the (17). One of the most important that is worth emphasizing is that aerodynamic coefficients defined by Equations 3-7 do not only depend on the vehicle shape (see for example (20)) but also on the aerodynamic characteristic of the infrastructure (e.g. bridge, flat road, embankments, cross-slope, superelevation) as well as on the methodology used in the experiment to acquire aerodynamic measurements (17)(19)(21)(23). From the simple equilibrium considerations (see Figure 2), one can derive the dynamic contributions from all considered aerodynamic forces and moments separately to the left (FL) and to the right (FR) wheel of the rear axle of the TSD semi-trailer:

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FIGURE 2 Dimensions of the TSD semi-trailer required by proposed model; FL left wheel force, FR right wheel force, G center of gravity, h – height of G (all dimensions in [m]).

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The Fstat is defined as the load measured by the scale on the stationary vehicle. Equations 12 and 13 present a deterministic form of the wind contribution in the proposed approach. Figure 3 shows the example of the wind effect on the FL and FR as a function of relative wind velocity V and associated relative wind direction α. Fixed values for all other parameters are listed in Table 1. It should be noted Figure 3 shows only the example of deterministic analysis (all factors are fixed) which is needed for the proposed probabilistic model (some factors will be assumed random). TABLE 1 Parameter values for Figure 3 Parameter Value [units] a 8 [m] a1 6.5 [m] b 2 [m] c 2.5 [m] w 2.5 [m] h 0.95 [m] Fstat 49,354 [N] R 22.29 [m/s] ρ 1.21 [kg/m3] A (=c·w) 6.25 [m2]

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FIGURE 3 Example of wind contribution (color-coded % of static load) on the left FL and right FR wheel of the TSD semi-trailer as a function of relative wind velocity V and

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associated relative wind direction α (using Equations 12 and 13 and deterministic parameters from Table 1). Figure 3 clearly shows the influence of relative speed and direction of the wind on both wheels. The influence is reversed for both wheels which should expected considering the structure of Equations 12 and 13 and sign convention (Figure 1). Furthermore, one could infer that the influence is relatively small and starts only at significant wind velocities. However, one should keep in mind that Figure 3 presents the effects in terms of relative wind velocity which is a vector sum of the TSD truck velocity (R) as well as the actual wind velocity (U) (Equation 1). Pavement roughness model Dynamic amplification of the static axle load by the pavement roughness has been extensively studied in many research projects all over the world (24)-(33). All studies agree that this is a real issue and most likely it has a dramatic impact on the pavement condition. It has been reported that the dynamic amplification varies depending on the suspension type, vehicle speed, tire pressure, tire tread pattern, axle and wheel configuration as well as pavement stiffness. In some studies (for example in (27)-(29)), the pavement roughness caused up to 50% or more increase in the static axle load. This is a significant effect which potentially translates to the premature pavement failure accelerated roughly five times (from the “fourth power law”). In a number of studies, the dynamic amplification to the static load caused by the pavement roughness was expressed in terms of the Dynamic Load Coefficient (DLC) (24)(29),(31)-(33). The DLC is defined as dimensionless measure of the dynamic variation of the axle load and is calculated as one standard deviation over the mean static load. Various studies reported the DLC values ranging from 0.05 to 0.4 and correlated with various parameters for different suspension types and tire configurations. In the presented study, the search was conducted for the DLC model that would fulfill the following criteria:  model was determined for a truck somewhat similar to the TSD truck,  model can be implemented in the probabilistic approach,  model contains at least two inputs including pavement roughness and truck speed. The appropriate model was identified in the study conducted recently for the FHWA (24). By combining two equations for the Dynamic Impact Factor (DI) at the 95% reliability level, the following DLC model was obtained: Eq.14 where: DLC* - DLC value for the normal distribution of the axle load, κ – coefficient related mostly to the suspension type (assumed κ = 0.0016), R – truck speed [km/h], IRI – International Roughness Index [m/km]. In the proposed probabilistic approach Equation 14 is used to determine normal distribution for the dynamic axle load based on the average static axle load Fstat and random R and IRI values sampled from their corresponding distributions. Just as the verification check, DLC* values are demonstrated for a few different conditions:  IRI=1 m/km and R=80 km/h, DLC*= 0.064 (very smooth pavement)  IRI=2.5 m/km and R=80 km/h, DLC*= 0.16 (fair pavement)  IRI=4 m/km and R=80 km/h, DLC*= 0.25 (rough pavement)

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It can be concluded that above DLC* values are located within a reasonable range and thus Equation 14 can be used as rough estimate of DLC* and dynamic amplification of the axle load. Probabilistic approach - Monte Carlo analysis Proposed probabilistic approach uses outlined deterministic models for the wind and roughness effects together with a mix of deterministic and probabilistic inputs. Generally, quantities that describe physical features of the TSD semi-trailer are taken as deterministic inputs while other quantities are treated as independent probabilistic variables with assumed probability density functions (PDFs). The types of the PDFs assumed in this study are based on the analysis of the actual TSD measurements but parameter values in the PDFs do not necessary match any particular data. In other words, assumed PDFs in the proposed approach match qualitatively some observed data but do not necessary fit it quantitatively. Table 2 presents six independent random variables and parameters in the associated PDFs whiles Figure 4 plots the actual PDFs. TABLE 2 Random variable and associated PDFs Random variable name [units] PDF type PDF parameters N (0, 20) Wind direction (β) [m/s] normal N (4.9, 1.7) Wind speed (U) [deg] normal N (22.3, 0.05) TSD speed (R) [m/s] normal N (14.5, 1.5) normal Air temperature (T) [⁰C] N (1027, 0.5) Atmospheric pressure (p) [hPa] normal IRI [m/km] log normal lnN (-0.26, 0.39)

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FIGURE 4 PDFs for random variables with the parameter values presented in Table 2. Proposed probabilistic approach uses Monte Carlo analysis and comprises the following general steps:

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1) 2) 3) 4)

Assume all deterministic parameters. Assume PDFs for random variables. Calculate all intermediate quantities (derivative parameters) Within each Monte Carlo loop: a. Sample PDFs and using Equations 12 and 13 (for wind effect), and Equation 14 (for roughness) calculate dynamic contribution to the static load. 5) Assemble all dynamic contributions and present variability of axle force under assumed conditions. Figure 5 shows the results from 10,000 Monte Carlo trials for the considered random parameters presented in Table 2 and all aforementioned deterministic parameters. Several observations can be immediately made:  variation in the axle load due to roughness (+/- 20%) is significantly larger compared to the variation due to the wind effect (+/-4%),  all distributions have the average and median value close to the Fstat and distributions do not vary between left and right side; these are the correct trends since: a) mean wind direction is 0⁰ (directly towards the TSD truck) (see Table 2 and Figure 5), and b) selected roughness model does not differentiate between left and right side of the semitrailer and it is always symmetric around Fstat. While Figure 5 show the correct and encouraging trends, the next sections presents a parametric study on the influence of wind direction in particular on the right wheel load since the Doppler sensors are located directly in front of that wheel.

FIGURE 5 Distributions of the wheel dynamic loads due to the wind effect (a and b) and due to the pavement roughness (c and d). PARAMETRIC STUDY Figure 5 presents only one specific mean wind direction β =0⁰, i.e. wind vector is opposite to the travel direction. In order to investigate if there is any critical wind direction, additional 8 cases of

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wind direction were simulated (Figure 6). All parameters stay the same as in the previous simulation except for the wind mean directions that differ by 45⁰ for 8 cases.

FIGURE 6 Considered wind direction distributions (mean direction rotated by 45⁰, same standard deviations equal to 20⁰). Figure 7 presents the results of 8 cases in terms of the combined dynamic load on the right wheel load, i.e. contributions from both wind effect and pavement roughness were treated as independent variables and were sum up in each Monte Carlo loop. Distributions in Figure 7 confirm model sensitivity to the mean wind direction, i.e. one can notice the “loading” effect (distribution peak to the right from the static load) and “unloading” effect (peak to the left i.e. below 100% of static load) as the mean wind direction circles around the moving TSD truck. As could be expected the critical wind direction is somewhere among the “N” directions (β between 0⁰ and 180⁰) however a single direction cannot be identified since the dynamic forces depend not only on the β direction but also on the relative wind direction α and other probabilistic parameters.

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FIGURE 7 Combined dynamic load on the right rear wheel of the TSD semi-trailer for 8 cases of wind direction (100,000 Monte Carlo simulation in each case). COMPARISON WITH FIELD DATA In the final step, comparison was made between the results for the dynamic load from the proposed probabilistic approach and the actual force data collected during the TSD measurements. As mentioned before, the inputs to the proposed approach did not necessary match any specific field measurements so at this stage only qualitative agreement was desirable.

FIGURE 8 Comparison between model simulations (case “S” from parametric study) and actual force measurements on the TSD semi-trailer.

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Comparison with the actual TSD is presented in Figure 8. Taking into account a stochastic nature of the proposed approach as well as considering that these are just preliminary results, an excellent agreement was achieved in terms of the mean value of the dynamic force. The distribution spread coming the simulations is apparently larger than the actual measurements (CoV of 2.9% versus 1.6% for field data) but again further refinement of the prosed approach and incorporating additional effects mentioned earlier should improve precision of the proposed approach without decreasing its accuracy. CONCLUSIONS This paper demonstrated the contributions of selected external factors, namely wind and pavement roughness affecting the TSD measurements. Appropriate physical models were incorporated into probabilistic approach in order to capture stochastic characteristic of both phenomena. In particular, parametric study demonstrated the importance wind direction and the need to account for the associated dynamic effects on the rear axle of the TSD trailer. Comparison with the actual TSD measurements of the dynamic force showed very promising qualitative agreement which provides at least partial verification of the proposed probabilistic approach. It is expected that the research on many aspects related to the TSD will continue. In terms of issues discussed in the paper, potential further research directions could be as follows:  investigate to what degree different parameters such as d0, SCI, strains at the bottom layer, are affected by the variations in the dynamic forces acting on the rear axle of the TSD semitrailer,  compare with the actual TSD measurements at different conditions  considering installing wind velocity and direction sensors on the truck  conduct aerodynamic modelling or wind-tunnel experiments for the TSD truck  conduct analytical and experimental studies on the dynamic effect due to the pavement roughness – fine-tune existing models or develop new approaches based on multi degree-offreedom truck including nonlinear and viscoelastic behavior of the truck elements such as suspension and tires,  investigate if including dynamic forces improves correlation between TSD and FWD results. ACKNOWLEDGEMENTS Authors would like to thank Mr. Jacek Sudyka from the Road and Bridge Research Institute (IBDiM) in Poland for providing all necessary information on the TSD as well as data for comparison. Many thanks go also to Ms. Miglė Paliukaitė from the Road Research Institute (RRI) in Lithuania for helping in preparation of this manuscript. REFERENCES (1) Bryce J., Flintsch G., Katicha S., Diefenderfer B., Developing a Network-Level Structural Capacity Index for Structural Evaluation of Pavements. Final Report VCTIR 13-R9, Virginia Department of Transportation, 2013. (2) Stubstad R., Carvalho R., Briggs R., Selezneva O., Simplified Techniques for Evaluation and Interpretation of Pavement Deflections for Network-Level Analysis: Guide for Assessment of Pavement Structure Performance for PMS, Report FHWA-HRT-12-025, 2012.

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