1er Congrès International sur les Ingénieries Civile, Mécanique et Electrique pour l’Energie CMEEE 2015- ISSN : 2458-6226 Calibration study of HDM-4 Model of structural cracking models for flexible pavements in Moroccan Context. BANNOUR Abdelilah *(1), EL OMARI Mohamed(1), LAKHAL El Khadir(1), AFECHKAR Mohammed(2), LAMRINI Bouchra (3) et JOUBERT Pierre(4) (1): Automation Laboratory of Environment and Transfer Processes, Faculty of Science Semlalia, Cadi Ayyad University, Marrakech, Morocco. (2): Director of the National Centre for Studies and Road Research - NCSRR, Rabat, Morocco. (3): Senior Research Engineer (R & D) charge of Research & Development Modeling, Diagnostics and Process Control, France. (4): HDM-4 Consultant, Trainer HDM at Ponts Formation Council of the National School of Bridges and Roads, France. * abdelilah.bannour@ced.uca.ac.ma ( Recevied June 11, 2015 ; accepted August 23, 2015 ) Abstract The present work aims the study of timing of structural crack Sub-model that has a fairly significant influence on the process of deterioration of road pavements, to do this it is based on the exploitation of the road database resulting visual survey conducted by the NCSRR (National Centre of Studies and Road Research). A follow-up spread over 6 years of 99 test sections located on national territory by considering 10 family’s structures modifying the floor body constituting materials and their thicknesses. Calibration method of road behavior of submodels recommended by the designers of the HDM-4 model is the method "windows". To establish adjustment factors noted Kcia for initiation of cracks and Kcpa for crack propagation. This method is based on a data processing using simple linear regression with equal line. Using the equations of structural cracking HDM-4 model a simulation on Excel, we arrive in this study to results allowing good timing by using the following coefficients: Kcia = 1.27 and Kcpa = 0.79. Key Words: HDM-4; Flexible pavements deterioration; Structural cracking; test section 1‐ Introduction The World Bank has developed computational systems to support professionals involved in pavement management. These models, developed in the 70's, have been important tools for economic development of highways and their technical evaluation1. Moreover, these systems incorporate performance models, which must be calibrated according to specific conditions of the country, or region where they are to be used [1]. Resource allocation decisions concerning the design, preservation and improvement of transportation infrastructure facilities are evaluated and selected based on their long-term economic consequences evaluation involves processing data related to current condition1 and using them to forecast the effect of these decisions on future condition [2]. Planning of road maintenance and development activities, setting priorities for construction, reconstruction and repair of automobile roads, preparing economic evaluation and project justification are inevitably connected with the need to forecast road pavement condition. For this purpose the pavement deterioration models are used, which are often integrated into more complex computing system [3]. Our study is part of the problem of optimizing maintenance roads that generate enormous investment costs. In parallel, the budgets allocated to these operations are very limited. 2- Need and objectives of the study All projections and evaluations depend upon predictions of the rate at which roads in the network will deteriorate and of the effectiveness of different maintenance options, dependent on the current state and projected trends of traffic, economic growth and available resources. At the heart is a model of road deterioration, which may be as simple as a fixed estimate of life (for example, "paved roads need rehabilitation 1er Congrès International sur les Ingénieries Civile, Mécanique et Electrique pour l’Energie CMEEE 2015- ISSN : 2458-6226 every twenty years") or may be more complex, for example, taking into account the traffic projections, existing road structure, and specific standards of service and design [4]. Maintenance and preservation of road assets is a priority road policy of the Government in view of its replacement value estimated at over 50 billion dirhams. Thus, the Government intends to raise the service level of the road network through effective maintenance. In 2014, these operations have focused on building 1000km, widening 630km and the repair or reconstruction of 40 bridges. This road asset preservation effort will continue in 2015 through maintenance of a 2,230 linear km, including 1,130 km covering 600km in Km 500 in strengthening and enlargement [5]. The aim of this study was to propose performance-based model calibration recommendations and to establish the most suitable and appropriate calibration factors for different HDM-4 pavement deterioration models for flexible pavements in different terrains of Morocco. This will also increase predictability of the models and the possibility of conducting an efficient pavements management process. 3- Highway development and management model (HDM-4) Among the most answered models for optimization of road maintenance is HDM4. It is a powerful system: When considering the applications of HDM-4, it is necessary to look at the highway management process in terms of the following functions [6]: (Planning; Programming; Preparation and Operations). Figure 1: HDM-4, System Architecture [6]. It is important that prior of using HDM-4 for the first time in any country, the system should be configured and calibrated for local use. In the HDM-4, thus no attempt for calibration without calibration, however, HDM-4 relationships predict “average expected” values for various variables that can naturally involve large margins of error depending on the situation. Thus the study will produce only an indicative evaluation of the suitability of HDM-4 as a design tool [7]. The HDM-4 relationships for predicting the time to initiation and progression of all structural cracking are as follows: a-Initiation of all structural cracking [8]: Its given by the following formulas (1) In our study, we are taking the following parameters: a0= 13, 20; a1= 0; a2= -20,7. Where: ICA is time to initiation of all structural cracks, in years; Kcia is the cracking initiation factor; SNP is the average annual adjusted structural number of the pavement ; YE4 is the annual number of equivalent standard axles, in millions per lane ; CRT is the crack retardation time due to maintenance, in years and CDS is the construction defects indicator for bituminous surfacing. b- Progression of all structural cracking [8]: The progression of all structural cracking parameter is given by: (2) 1er Congrès International sur les Ingénieries Civile, Mécanique et Electrique pour l’Energie CMEEE 2015- ISSN : 2458-6226 Progression of all cracking commences when δtA> 0 or ACAa > 0. In our study we are considered the following parameters: a0= 1,76 ; a1= 0,32 Where dACA is the incremental change in area of all structural cracking during analysis year, in per cent of total carriageway area; Kcpa is the cracking progression factor ; CRP is the retardation of cracking progression due to prenventive treatment, given by CRP = 1-0,12CRT, SCA = min (ACAa, (100-ACAa)) and ACAa is the area of all structural cracking at the start of the analysis year, in per cent. 4- Calibration methodology To calibrate a pavement performance model, it is necessary to possess a sufficient group of distress data. HDM consists of a series of sub-models that address different aspects of the analysis. Each of these submodels requires certain input data and each produces its own output. In order to apply the model correctly, one needs to ensure that HDM is given the appropriate input data and has been suitably calibrated, [9]. The process of calibration then consists of determining the adjustment factors (ki), which will achieve the best agreement between the model’s predictions and the field data. In order to implement the HDM-4 model, many kinds of procedures to calibrate road networks, vehicle fleets, economic indices, environmental factors, deterioration models, and unit cost are required for matching local conditions. Among others, a calibration procedure for deterioration models is one of the most important requirements for successful implementation, [10]. The "windows" methodology has been used here as it offers the possibility of both relying upon a broader inference space and of integrating data gathered in previous studies with new data. Moreover, this methodology permits section distress measurements to be made in a brief period of time, and consequently a greater number of sections and categories can be evaluated. This is a major advantage of the "windows" method, because the "test sections" calibration methodology makes it necessary to continue measuring data for each selected section for an extended period of time in order to obtain reliable predictive data, [11]. In our study we simulate the degradation process by integrating Excel equations recommended by the designers of HDM-4, as indicated in Volume 6 of the HDM-4 documentation, in fact, some sections of the simulation test by turning the software gave closer result sets of those data by Excel. While, on one hand we have this procedure saves a lot time instead of running the software requiring enough data that are sometimes unnecessary to calibrate and adapt the model for a well-defined context like ours. Secondly mathematical validation of the procedure will be more relevant and credible. 4.1 Experimental study The planning of maintenance and the importance of investment resulting require mastery of evolution degradation Moroccan roads laws. In this context, the Road Directorate under the tutelage of the Minister for Infrastructure, Transport and Logistics, has established a list of 99 tests sections to follow the real evolution of deterioration depending on their ages. These sections were selected; such test section has 1000m (1Km) of the length, to cover all the diversity of the national network (subgrade, traffic, climate and nature of the surfacing layer). The approach is to follow these sections in time, requires ten, fifteen years to see in this context the Roads has granted to the National Research Centre for Studies Road NRCSR ensure that mission monitoring during the period from 1996 to 2001 (6 years), including the collection of data relating to different modes of degradation test sections was made using High performance equipment. Since 1996 a visual inspection of pavement distress has been carried out each year, the aim objective of a visual inspection is to observe pavement cracks, raveling, potholes, and bleeding of binder. The distresses identified were registered in special Road Data Base. But in the present study we will focus only on the degradation on the structural cracking, including its influence on the pavement behavior is noticeable against other types of deterioration. In the same framework, Pavement deflection on each test section was measured using the Benkelman Beam, and the pavement roughness measured by equipment that records the longitudinal profile by an approximation to a longitudinal profile from a moving vehicle. 4.2-Characteristics of sections used in the development of the cracking model In our study, the characteristics of sections used in the development of the cracking model are presented in the next table. 1er Congrès International sur les Ingénieries Civile, Mécanique et Electrique pour l’Energie CMEEE 2015- ISSN : 2458-6226 Table 1: Characteristics of sections used in the development of the cracking model. Pavement type GNT + RS BL + PC + RS + GNT + RS BL + PC + RS + GBB + EB PC + RS + GNT + RS BL + RS + GNT + RS GNT + RS + EB BL + PC + RS + EB BL + PC + RS GNT + GBB + EB BL + PC + RS + GNT + EB Number of sections 17 7 10 3 4 1 4 6 9 5 Range of Surfacing age (years) 0-7 1-6 1-5 5-9 5-7 5 2-22 1-7 1-6 1-14 Range of Total surfacing thickness (mm) 20 20 40-240 20 20 50 40-70 20 50-240 50-130 Cumulative Trafic loading (MESA) 0,004-0,83 0,03-0,81 0,33-1,22 0,1-0,9 0,04-1,30 0.4-0,5 0,4-1 0,02-0,56 0,03-1,8 0,57-1,31 Traffic Volume (AADT) 69-4191 411-8246 1540-17856 330-4191 697-16179 4502-10162 3616-8453 478-2350 662-16494 3420-17576 BL: Blocking; PC: Broken Stone; GNT: No Treated Gravel; GBB: Asphalt Overlay Gravel; RS: Surfacing; EB: Bituminous mixture. 4.3- Variables and experiment factorial design From the analysis of the performance model equations, it is evident that the pavement’s evolution over time fundamentally depends on four global variables traffic, pavement age (calculated from the date of construction or most recent maintenance), dominant climatic conditions and structural capacity. These variables help to define the initiation as well as the progression of the distress. In order to achieve a certain degree of reliability in selecting a group of roads with sufficiently similar characteristics. Thus, the 99 selected tests sections were divided into family structures whose corresponding information is given in the above table 1. The first step consists of defining homogeneous sections according to their most representative variables (structure, traffic, geometry and climate). The performance data obtained from field observations may then be compared with the data obtained through modelling. For another group of sections or for windows with different characteristics, the data should present different trends, which in turn will modify the ki values obtained when performing the calibration. The details of calibration methodology evaluated in this study are shown in Figure 2. Figure 2: Calibration methodology adopted in this study, [12]. « Window » technique has been used for calibration of pavement distress models in the present study because it offers the possibility of relying on a broader inference space and the possibility of integrating data gathered in previous studies with the new data for further refinement of pavement distress models. The another 1er Congrès International sur les Ingénieries Civile, Mécanique et Electrique pour l’Energie CMEEE 2015- ISSN : 2458-6226 reason for suggesting the “window’ technique in this study is the absence of long-term historical pavement performance data for Test Sections in Morocco. 4.4- Methodology for selection of test sections Once the factorials of the experiment have been defined, following two simultaneous compatible criteria as has made the selection of representative sections in each cell: 1- Possession of a sufficient number of sections for each cell category in order to be able to make use of a minimum quantity of distress data and with the aim of attaining adequate calibration of the performance prediction models; 2- Ranges sufficiently small in magnitude whenever possible to ensure the greatest similitude and homogeneity among the characteristics of the different pavement types and thus ensure greater reliability with respect to the calibration. 5- Calibration of pavement performance models The procedure proposed for the statistical calibration of pavement performance models in this study is mainly based on determining the factors that will allow for a more precise or better adjustment of the simulated distress curves with the real performance data. The procedure proposed for calibrating surface distress initiation factors is based on obtaining the coefficient between the observed years of occurrence of the distress to the year of occurrence as predicted by the uncalibrated models. In case of progression factors, the calibration has been done by minimising the squares of the differences between the estimated and observed data or sum of squared differences (SSD). Minimising the SSD will assist in reducing the estimated average error, which in turn will make it possible to locate the calibration factor that ensures the best adjustment of the distress curve and therefore the calibration of the analysed performance model. The following statistical indicators are used for comparison of models: , (3) , (4) (5) AAE : the average absolute error ; RMSE : the root mean square error ; R2 : the goodness-of-fit measure (coefficient of determination) ; n : the number of observations ; Oi : the actual value of distress observation i ; Oavg : the average value of distress observations ; Pi : the predicted value of distress observation. 6- Results and discussion of calibration procedure 6.1- Law of evolution of structural cracking The determination of this degradation evolution laws will be a tool that will contribute to the evaluation of intervention strategies on the road network eventually leading to the best technical and economic choice of maintenance scenario and maintenance of the road network. Figure 3: Law of evolution of structural cracking, Morocco context. Structural cracking is modeled in two discrete phases. In the first, initiation, period the distress has not yet become manifest and the area is zero. After initiation the area gradually progresses; in the case of cracking this follows a sigmoidal curve as shown in Figure 3. Our Moroccan context, taking into account the 10 families 1er Congrès International sur les Ingénieries Civile, Mécanique et Electrique pour l’Energie CMEEE 2015- ISSN : 2458-6226 structure and their characteristics, we guess that the initiation phase begins only from a age of 6 in a surface course, and then the phase Trigger increase is up to age 12 almost double the end of the first phase. Therefore, the moderate traffic (heavy weight) remains the main element involved in the delay of the initiation phase. According to summarized data from different surveys conducted for all test sections, we can learn an approach to a law of evolution of structural cracks diagnosed. The evolution of structural cracks is impressive. Was retained a large sample size of the order of n = 73 by making an approximation of this evolution with a polynomial equation of degree 3, with an explanation of structural cracks rate of 86.7%, which high lighted the robustness of the model. This rate of change is explained characterized by the weakest RMSE, which is worth 32,90. 6.2 Suggested calibration factors Different trial calibration factors have been attempted for the test sections and the calibration factor corresponding to the minimum (RMSE)2 value has been suggested amongst them. The value of suggested calibration factors for initiation and progression structural cracking models are Kcpa = 0,79 and Kcia = 1,27, resulting from the process detailed below: Figure 4: Linear regression line with the equality between the observed crack and that predicted by the HDM-4 Model, eliminating outliers. It is found that the observed values are adequate with that predicted by the HDM-4 by a rate of variation explained in the order of 85.6% characterized by the weakest RMSE based statistical processing of process data is 1.79. All while keeping a more representative size of the sections selected sample. Table 2: Descriptive statistics of correlation between Predicted an Observed cracks. Statistics Nb. of observations Minimum Maximum Q1 Median Q3 Average Variance (n-1) Standard deviation (n-1) Predicted cracks 159 0,000 49,681 0,000 0,000 2,853 1,732 24,706 4,971 Observed Cracks 159 0,000 42,000 0,000 0,000 0,021 0,911 19,110 4,371 1er Congrès International sur les Ingénieries Civile, Mécanique et Electrique pour l’Energie CMEEE 2015- ISSN : 2458-6226 (a) (b) Figure 5: Significant effect of the calibration on the amplitude variation of structural cracking (a) With calibration where Kcpa=0,79 and Kcia=1,27. (b) Without calibration where Kcpa=1 and Kcia=1. Based on a representative sample of large size of the order of n=158, reflecting the entire national road network, which make the credible and convincing work covered. Well according to coefficients selected calibration Kcpa and Kcia, can we conclude that structural cracking appears more slowly than predicted HDM-4, meaning that HDM-4 overestimates the occurrence of structural cracks in Moroccan context, and with a moderate rateas well progression of these cracks over time, evolving more slowly than predicted by the HDM-4, then the onset and progression follow a logical evolution taking into account local specificity (traffic, climate structure pavements, etc. ...). Otherwise the calibration factor Kcia for the initiation of all structural cracking. By increasing the value of Kcia to 1.27, the time to the initiation of all structural cracking is four thirds, implying that the pavement will last longer before cracks appear than that predicted by default by HDM-4. And decreasing the calibration factor Kcpa for the progression of all structural cracking, to 0.79, implies that the pavement will deteriorate, in terms of the rate of crack progression, three quarter less rapidly as that predicted by default by HDM-4. This means that the explanatory variables would be adequately incorporated into the HDM-4 equations that predict superficial distress, corroborating the model's soundness. Within this framework, there is the reduction of amplitudes guessed between observed and predicted as shown in Figure 4, hence the need for calibration. 7- Conclusion Since 1996 the National Centre of Studies and Road Research has monitored a factorial of pavement sections to select, improve and calibrate performance prediction models. Data collected from the performance sections indicate that local calibration of models is essential. So, the following conclusions have been made based on this study:  The methodology "windows" allows a more global vision of the distress of the pavement, as it is not restricted to the study of any pavement in particular. Moreover, it makes it possible to evaluate a large number of sections in a short period of time ;  The validity of the proposed model was tested to test their effectiveness by comparing distress predictions made by deterioration models calibrated with those actually observed on the pavement sections ;  The HDM-4 pavement deterioration models need to be calibrated for the road network in local conditions of Moroccan context, as large variations are found between the suggested calibration factors for initiation and progression of pavement deterioration model in this study and the corresponding default HDM-4 calibration factors as unity. The calibrated HDM-4 pavement deterioration models in this study can’t be used for the prediction of distressed and developing optimal maintenance management strategies for road network of Morocco. Because the full study calibration of HDM-4 requires almost do the same of structural cracking calibration procedure for 1er Congrès International sur les Ingénieries Civile, Mécanique et Electrique pour l’Energie CMEEE 2015- ISSN : 2458-6226 other Pavement degradation mode such as raveling, potholes, rutting and the resultant is roughness. Well extended following this work, will be a future article scientific as like as perspective. References [1] Heman de Solminihac, Priscila Hidalgob, Mauricio Salgadoc and Anfbal Altamirad, Calibration of structural cracking models for asphalt pavements: HDM-4 case, Indian Journal of engineering and Materials sciences, Vol. 10, June 2003, pp. 193-201 [2] Chih-Yuan Chu, Pablo L. Durango-Cohen, Estimation of dynamic performance models for transportation infrastructure using panel data, Transportation Research Part B 42, 2008, pp 57–81 . [3] Aivaras Braga, Donatas Cygas, Adaptation of pavement deterioration models to Lithuanian automobile roads, Journal of civil engineering and management, Vol VIII. N° 3, 2002, pp 214-22 [4] Paterson W.D.O, Road Deterioration and Maintenance Effects: Models for Planning and Management, the Johns Hopkins University Press, Baltimore and London, 1990, 2 P. [5] Projet de loi de finance Marocaine pour l’année budgétaire, 2015, Ministère de l’économie et des finances. [6] Henry G. R. Kerali. J.B. Odoki and Eric E. Stannard. Série développement et gestion des routes Vol. 1Traduction en langue française effectuée par JOUBERT Pierre : Vue d’ensemble de HDM-4 Version2.0, World Road Association (PIARC), 2000, Paris, France. 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