Academic literature on the topic 'Witczak model'

The overall objective of this study was to assess the use of Level 1 analysis for mechanistic-empirical (ME) rehabilitation designs of deteriorated polymer-modified asphalt concrete (AC) pavements in Nevada using the AASHTOWare® Pavement ME software. This research also explored the possible implementation of a hybrid approach for AC damage characterization to overcome the challenges associated with the use of the Witczak model for estimating the undamaged dynamic modulus master curve of the existing AC layer. Two rehabilitation field projects were used as part of this study. The experimental plan involved falling weight deflectometer (FWD) testing in the right wheelpath before rehabilitation, analysis of core samples, estimation of an equivalent undamaged dynamic modulus, and estimation of equivalent damaged dynamic modulus from FWD backcalculation. The proposed hybrid approach consisted of conducting laboratory dynamic modulus testing on the collected core samples and estimating an equivalent undamaged dynamic modulus at the same FWD testing temperature and loading frequency. The pre-overlay damage, characterized based on the approach in Pavement ME Design software (i.e., using a Witczak prediction model and backcalculated modulus), showed overly high values that did not match with the collected pre-overlay distress data on either of the rehabilitation projects. Based on the findings from this study, the hybrid approach was recommended for implementation by Nevada Department of Transportation (NDOT) when designing AC overlay over polymer-modified asphalt pavements in Nevada. Recommendations for user inputs were also provided for future consideration in Pavement ME Design software.

The mechanical properties of pavement materials are crucial to the design and performance of flexible pavements. One of the most commonly used measures of these properties is the resilient modulus (Er). Many different models were developed to predict the resilient modulus of coarse soils, which are based on the states of stresses and the physical and mechanical properties of the soil. The unconsolidated unsaturated drained cyclic triaxial tests were performed for three variously graded and three well-graded sand specimens to determine the resilient modulus, and to perform predictive modeling using the K-θ, Rahim and George, Uzan, and Universal Witczak models. Obtained Er values directly depended on the confining pressure and deviatoric stress values used during the test. The Octahedral Shear Stress (OSS) model, proposed by the authors of the paper, predicts the resilient modulus with a coefficient of determination (R2) ranging from 0.85 to 0.99. The advantage of the model is the use of small-scale data tables, meaning fixed K1 and K2 regression coefficients, and it can be assigned to a specific specimen type without the need to determine them using the specific deviatoric and confining stresses.

The main purpose of this paper is to model the master curve of dynamic modulus |E*| for Hot Mix Asphalt mix designed with aggregate from Senegal named basalt of Diack and quartzite of Bakel. The prediction model used is the Witczak model, used in the Mechanistic-Empirical Pavement Design Guide. A study has been conducted in the Laboratory of Pavements and Bituminous Materials. Six different HMA (BBSG 0/14 mm) were subjected to complex modulus test by tension-compression according to the European or Canadian procedure using the same range of temperatures and frequencies. For each mixture studied the uniqueness of modulus curves in the Cole-Cole or in Black diagrams have shown that the asphalt mixes are thermorheologically simple materials and the Canadian test process is suitable for determining the HMA complex modulus mix designed with the aggregates from Senegal. This implies their tender with the principle of time-temperature equivalence. The test results were used to model the master curves of HMA studied. A correlation with the results of dynamic modulus measured have shown an accuracy of R2 = 0,99 and p = 0,00 in STATISTICA software, which allows to conclude that the sigmoidal model has good modeling of the dynamic modulus.

To characterize the dynamic modulus (E*) of the asphalt mixtures more accurately, a comparative study was shown in this paper, combining six ML models (BP, SVM, DT, RF, KNN, and LR) with the novelly developed MBAS (modified BAS, beetle antennae search) algorithm to check the potential to replace the empirical model. The hyperparameter tuning process of the six ML models by the proposed MBAS algorithm showed satisfactory results. The calculation and evaluation process demonstrated fast convergence and significantly lower values of RMSE for the five ML models (BP, SVM, DT, RF, and KNN) to determine the E* of the asphalt mixtures. Comparing the performances of the six ML models in the prediction of the E* by the statistical coefficients and Monte Carlo simulation, the RF model showed the highest accuracy, efficiency, and robustness.

Rutting potential of stone mastic asphalt with varying aggregate gradations was assessed in the past mainly by uniaxial compression testing which is not the only test to predict its true performance in the field. Dynamic testing and accelerated wheel tracking test are considered the most suitable laboratory test procedures. Four stone mastic asphalt mixtures were prepared in this study using PG 58-22 binder, Viatop plus CT-40 fiber and four aggregate gradations with nominal maximum sizes of 9.5 mm, 12 mm, 19 mm and 25.4 mm. To access the effects of aggregate gradations, single type of bitumen, filler and fiber was used. Mixtures were tested and evaluated under both type of testing procedures at different temperature levels. A regression model was developed using wheel tracker test data to ascertain significant parameters that are directly influencing the rut depth. The statistics of the model shows an excellent degree of determinacy of 0.92 and a relative accuracy of 0.29. Sigmoidal functions using Witczak equations were determined from dynamic modulus master curves for characterization of mixes and compared with previous studies. Correlation between the wheel tracking factor and a dynamic modulus factor was also established at three frequency levels. The study reveals that a reasonable relationship exists between the wheel tracking factor and dynamic modulus factor for stone mastic asphalt mixtures

This paper presents a simple method to determine dynamic modulus master curve of asphalt layers by con­ducting Falling Weight Deflectometer (FWD) for use in mechanistic-empirical rehabilitation. Ten new and rehabilitated in-service asphalt pavements with different physical characteristics were selected in Khuzestan and Kerman provinces in south of Iran. FWD testing was conducted on these pavements and core samples were taken. Witczak prediction model was used to predict dynamic modulus master curves from mix volumetric properties as well as the bitumen viscosity characteristics. Adjustments were made using FWD results and the in-situ dynamic modulus master curves were ob­tained. In order to evaluate the efficiency of the proposed method, the results were compared with those obtained by us­ing the developed procedure of the state-of-the-practice, Mechanistic-Empirical Pavement Design Guide (MEPDG). Re­sults showed the proposed method has several advantages over MEPDG including: (1) simplicity in directly constructing in-situ dynamic modulus master curve; (2) developing in-situ master curve in the same trend with the main predicted one; (3) covering the large differences between in-situ and predicted master curve in high frequencies; and (4) the value obtained for the in-situ dynamic modulus is the same as the value measured by the FWD for a corresponding frequency.

Resilient modulus (Mr) is a critical input for pavement design as it is the main property used to evaluate the contribution of subgrade to the overall pavement structure. Considering this, practitioners need simple and accurate ways to determine the Mr of in-situ subgrade without the need for expensive and time-consuming testing. The objective of this study is to develop a generalized regression prediction model for in-situ Mr of subgrades, compare it with established prediction models, and assess the model’s predictions on pavement performance using the Mechanistic-Empirical Pavement Design Guide (Pavement ME). The prediction model was built using field data from 30 pavement sections studied in the Long Term Pavement Performance (LTPP) Seasonal Monitoring Program where backcalculated modulus from falling weight deflectometer testing, in-situ moisture contents, and subgrade material properties were considered in the model. Based on the results, it was found that liquid limit, plasticity index, WPI (the product of percent passing #200 and plasticity index), percent coarse sand, percent fine sand, percent silt, percent clay, moisture content, and their respective interactions were significant predictors of in-situ Mr values. The findings showed that the generalized regression approach was able to predict Mr more accurately than predictions from the Witczak model. To assess the application of the predictive model on pavement performance, three LTPP sections located in New York, South Dakota, and Texas were analyzed to predict the rutting performance based on Mr values obtained from the developed generalized prediction model and those obtained from the current Pavement ME model and then compared with rut depths measured in the field. The findings showed that, for coarse-grained subgrades that have a low degree of plasticity, the generalized regression model predicted rutting performance similar to the embedded Pavement ME model. For fine-grained subgrades, the developed model tends to predict lower rut depths which were closer to the field measured rut depths. Overall, the generalized regression approach was successfully applied to create a simple, practical, cost-effective and accurate Mr prediction model that can be used to estimate the stiffness of subgrades when designing and evaluating pavements.

This study evaluated the viscoelastic properties of a performance grade (PG) binder blended with different percentages of binders recovered from reclaimed asphalt pavement (RAP) for conditions (materials, climate, and specifications) prevailing in Oklahoma. The viscoelastic properties of the blended binders were then used to estimate dynamic modulus ( E ∗ ) values of the new mixes with RAP by using the Witczak model through time-temperature superposition (TTS) principles. The recovered binder from RAP was found to be significantly stiffer than the virgin binder (PG 64-22). The addition of RAP increased the complex modulus ( G ∗ ) of the base binder, so did the E ∗ of the corresponding mix. The creep stiffness resistance of the asphalt binder at low service temperatures decreased with the addition of RAP. With up to 10% RAP binder, no notable changes were observed in the viscosity and PG grade of the virgin binder. With 25% and 40% RAP binder, the PGs of the blended binders were found to be PG 70-16 and PG 76-16, respectively. It was observed that the E ∗ master curves predicted from PGs of the blended binders were in close agreement with those estimated from the laboratory-measured E ∗ data. The dynamic shear rheometer (DSR) data of rotational thin film oven (RTFO)-aged blended binders predicted significantly lower E ∗ values compared to the measured ones. The E ∗ values predicted from rotational viscosity (RV) test data were found to be higher than the measured E ∗ values. The findings of this study are expected to provide transportation professionals with a better understanding of new mixes with high RAPs.

Pavement modulus is believed as one of the important features to characterize the pavement condition, specifically the pavement stiffness. The value of pavement modulus may be calculated using the existing Witczak mathematical dynamic pavement modulus prediction formulae. However, the equation developed by Witczak is heavily impacted by temperature while underestimating the impact of other mixing factors thus, only offering an adequate approximation for the circumstances for which they were designed. In this study, the Spectral Analysis of Surface Wave (SASW) test data was used to develop an Artificial Neural Network (ANN) that accurately backcalculates pavement profiles in real-time. The pavement modulus calculated from the equation was validated by using ANN developed in Matlab software to avoid any mistakes during calculation based on the equation. Three parameters, shear wave velocity, depth and thickness from SASW test data were used as inputs and elastic modulus calculated using Witczak pavement modulus equation was used as an output to train the models developed in ANN. Five segments of pavement are presented in this paper where almost compromise that the greater the depth, the lesser the shear wave velocity as well as pavement modulus. Nine neural network models were developed in this study. The network architecture of 4-80-4 is the most optimized network with the highest correlation coefficient of 0.9992, 0.9994, 1.0, 0.9996 for validation, testing, training and all respectively. The created ANN models’ final outputs were reasonable and relatively similar to the real output.

This research characterizes the performance of various plant-produced asphalt concrete mixtures by dynamic modulus|E∗|test using asphalt mixture performance tester (AMPT). Marshall designed specimens of seven different mixtures were prepared using the Superpave gyratory compactor and subjected to sinusoidal compressive loading at various temperatures (4.4 to 54.4°C) and loading frequencies (0.1 to 25 Hz). A catalog of default dynamic modulus values for typical asphalt concrete mixtures of Pakistan was established by developing stress-dependent master curves separately, for wearing and base course mixtures. The sensitivity of temperature and loading frequency on determination of dynamic modulus value was observed by typical isothermal and isochronal curves, respectively. Also, the effects of various variables on dynamic modulus were investigated using statistical technique of two-level factorial design of experiment. Furthermore, two dynamic modulus prediction models, namely, Witczak and Hirsch, were evaluated for their regional applicability. Results indicated that both the Witczak and Hirsch models mostly underpredict the value of dynamic modulus for the selected conditions/mixtures. The findings of this study are envisaged to facilitate the implementation of relatively new performance based mechanistic-empirical structural design and analysis approach.

Nell’ultimo ventennio si è assistito a un rapido incremento dell’utilizzo di materiale fresato nelle pavimentazioni stradali dovuto in parte al risparmio economico derivante dall’utilizzo di questo materiale e in parte ai vantaggi ambientali. Tuttavia, esistono ancora due importanti problematiche alle quali non è stata data una risposta efficace: la prima riguarda la caratterizzazione del bitume invecchiato contenuto nel fresato; la seconda riguarda la possibilità di prevedere le prestazioni delle miscele confezionate utilizzando elevate quantità di fresato. Con riferimento alla prima problematica, i metodi attualmente disponibili sono basati sull’estrazione e sul recupero del bitume contenuto nel fresato per mezzo di solventi. Tali metodi presentano però vari problemi connessi al fatto che l’estrazione e il recupero del bitume può alterarne le proprietà reologiche. Per questo motivo, nel presente lavoro, si è sviluppata una nuova procedura che permette di eseguire un retrocalcolo delle proprietà reologiche del bitume invecchiato e dei blends, composti da bitume invecchiato e bitume vergine, partendo da test su malte composte miscelando la parte fine degli aggregati del fresato e il bitume vergine; utilizzando il modello di Nielsen, appositamente adattato al caso di materiali bituminosi, e il modello di Voigt si riesce a determinare le suddette proprietà reologiche utilizzando i risultati dei test eseguiti sulle malte. Ciò ha un duplice beneficio: da una parte è possibile caratterizzare il bitume invecchiato contenuto nel fresato nelle stesse condizioni di lavoro in cui si trova all’interno della pavimentazione, evitando che subisca ulteriori trattamenti, dall’altra si possono eseguire le prove di caratterizzazione su una delle fasi che maggiormente governano le proprietà delle miscele in conglomerato bituminoso e che quindi regolano le performance delle pavimentazioni. Con riferimento alla seconda problematica, è stata sviluppata una procedura di modellazione multiscala, basata sia su modelli reologici (2 Spring, 2 Parabolic Elements, 1 Dashpot, 2S2P1D model) sia su modelli empirici (Hirsh e Witczak models), che permette di prevedere il comportamento reologico delle miscele in conglomerato bituminoso, contenenti materiale fresato, partendo direttamente dai risultati di prove eseguite sulle malte e tenendo conto della composizione granulometrica degli aggregati e di quella volumetrica delle miscele. La metodologia messa a punto consente di ottenere previsioni affidabili per entrambe le problematiche affrontate, come dimostrato dai risultati delle prove di validazione eseguite nell’ambito della tesi, e di fornire una soluzione innovativa ad alcune questioni che risultano attualmente di particolare rilievo ai fini della estesa utilizzazione del fresato per il confezionamento dei conglomerati bituminosi. In last decades the use of Reclaimed Asphalt Pavement (RAP) materials in asphalt mixtures has seen a significant expansion for economical and environmental reasons. Nevertheless, there are still two important issues which have not been effectively solved: the first regards the characterization of the aged binder contained in RAP; the second concerns the ability to predict the performance of asphalt mixture composed with high RAP content. Regarding the first problem, the current methods are based on extraction and recovery of the RAP binder using solvents; however, these methods are not fully accurate since they can alter the rheological properties of the binder. For this reason, in the present work, a new procedure to back-calculate the rheological properties of the aged binder contained in RAP materials and of the blends composed with fresh and RAP binder, was developed. This is based on DSR tests performed on mortars, composed by mixing the fine fraction of the RAP aggregate with virgin binder. Using the Nielsen model, specifically adapted to asphalt mortars’ case and the Voigt model, the rheological properties of RAP binder can be back-calculated from mortars tests. The present procedure has two advantages: the aged binder contained in RAP is tested as it is after the milling process, avoiding any further treatments, while the testing campaign is centered on the mortar phase, which is one of the most important phases governing the properties of the mixtures and, therefore, the performance of asphalt pavements. Regarding the second problem, a multi-scale approach based on rheological model (2 Spring, 2 Parabolic Elements, 1 Dashpot, 2S2P1D model) and on empirical models (Hirsh e Witczak models) was developed to predict the rheological properties of asphalt mixture containing RAP materials, starting from tests on asphalt mortars and taking into account the grading of the aggregates and the volumetric composition of the mixtures. This methodology allows to make reliable previsions for both the problems addressed, as demonstrated by the results of the validation tests carried out in this doctoral thesis. In addition, the present research provides innovative solutions to address some of the issues which are currently of particular importance for the purposes of extending the use of RAP material in the production of asphalt mixture.

The KENTRACK program is a finite element based railway trackbed structural design program that can be utilized to analyze trackbeds having various combinations of all-granular and asphalt-bound layered support. It is applicable for calculating compressive stresses at the top of subgrade, indicative of potential long-term trackbed settlement failure. Furthermore, for trackbeds containing an asphalt layer, it is applicable for calculating tensile strains at the bottom of the asphalt layer, indicative of potential fatigue cracking. The program was recently expanded to include both English and international units. A procedure has been incorporated to provide a path to save results in a text formation in post-Windows XP operating systems. More importantly, properties of performance graded (PG) asphalt binders and the Witczak E* predictive model have been incorporated in the 4.0 Version of the program. Component layers of typical trackbed support systems are analyzed while evaluating the significance of layer thicknesses and material properties on design and predicted performance. The effect of various material parameters and loading magnitudes on trackbed design and evaluation, as determined and predicted by the computer program, are presented. Variances in subgrade modulus and axle loads and the incorporation of a layer of asphalt within the track structure have significant effects on subgrade vertical compressive stresses and predicted trackbed service lives. The parameter assessments are presented and evaluated using sensitivity analysis.