Dynamic Modulus Predictive Models Research Articles

Dynamic modulus characteristics and prediction model of semi-flexible materials filled with high-performance cement paste

The dynamic modulus of asphalt mixture is an important factor in the design of asphalt pavement, and many scholars have proposed different models for estimating the dynamic modulus of asphalt mixture, but there are almost no studies on the prediction of the dynamic modulus of semi-flexible materials. In order to analyze and estimate the dynamic modulus of semi-flexible materials, we set up a high-performance cementitious paste (HPCP) semi-flexible material and a reference group Stone Mastic Asphalt (SMA-16) under multiple conditions, first measured its dynamic modulus in the laboratory, and analyzed the dynamic modulus characteristics of the material, and then used the equation the estimation equation proposed by Witczak et al. (Witczak1-37A) as a benchmark to introduce a new parameter, grouting mass ratio (Pb) to develop a Witczak-G prediction model to compare and validate the predicted dynamic modulus with the measured values. The results show that compared with SMA-16, HPCP semi-flexible material exhibits higher dynamic modulus and lower phase angle, and its temperature sensitivity and deformation resistance are significantly better than those of SMA-16. Under the influence of porosity and Pb factor, the dynamic modulus is positively correlated with both factors, and the phase angle increases first and then decreases, showing strong elastic properties. In this paper, we propose a dynamic modulus prediction model based on viscosity and Pb, Witczak-G, which predicts the highest coefficient of determination (R2) of the predicted dynamic modulus as high as 0.99 after initial fitting and validation, which indicates that the Witczak-G model is suitable for predicting the dynamic modulus of semi-flexible materials injected with HPCP.

Development of Dynamic Modulus Prediction Model Using Artificial Neural Networks for Colombian Mixtures

Development of Dynamic Modulus Prediction Model Using Artificial Neural Networks for Colombian Mixtures

Study on Dynamic Modulus and Damping Characteristics of Modified Expanded Polystyrene Lightweight Soil under Cyclic Load.

In recent years, expanded polystyrene (EPS) lightweight soil has been widely used as subgrade in soft soil areas because of its light weight and environmental protection. This study aimed to investigate the dynamic characteristics of sodium silicate modified lime and fly ash treated EPS lightweight soil (SLS) under cyclic loading. The effects of EPS particles on the dynamic elastic modulus (Ed) and damping ratio (λ) of SLS were determined through dynamic triaxial tests at various confining pressures (σ3), amplitudes, and cycle times. Mathematical models of the Ed of the SLS, cycle times, and σ3 were established. The results revealed that the EPS particle content played a decisive role in the Ed and λ of the SLS. The Ed of the SLS decreased with an increase in the EPS particle content (EC). The Ed decreased by 60% in the 1-1.5% range of the EC. The existing forms of lime fly ash soil and EPS particles in the SLS changed from parallel to series. With an increase in σ3 and amplitude, the Ed of the SLS gradually decreased, the λ generally decreased, and the λ variation range was within 0.5%. With an increase in the number of cycles, the Ed of the SLS decreased. The Ed value and the number of cycles satisfied the power function relationship. Additionally, it can be found from the test results that 0.5% to 1% was the best EPS content for SLS in this work. In addition, the dynamic elastic modulus prediction model established in this study can better describe the varying trend of the dynamic elastic modulus of SLS under different σ3 values and load cycles, thereby providing a theoretical reference for the application of SLS in practical road engineering.

Implementation of ensemble Artificial Neural Network and MEMS wireless sensors for In-Situ asphalt mixture dynamic modulus prediction

Dynamic modulus is an essential mechanical property for pavement structural condition assessment yet obtaining the in-situ dynamic modulus of asphalt mixture efficiently and accurately has never been easy. With the development of sensing technology, a type of Micro-Electromechanical Sensor (MEMS), SmartRock, has been applied in pavement monitoring because of its convenience and high efficiency; but interpreting the collected data as useful engineering information becomes a new challenge. This paper aims to present a data processing algorithm for sensing data in pavement engineering and develop a dynamic modulus predictive model based on the ensemble artificial neural network (ANN) model using SmartRock sensing data. Five asphalt mixtures were tested by the uniaxial dynamic modulus test, and one of the 5 mixes was also used in the third-scale model mobile load simulator (MMLS3) test. SmartRock sensors were installed in the specimens to collect the mechanical response during the tests. The empirical mode decomposition (EMD) method was used for data preprocessing. Dynamic modulus test data, in combination with a small portion of early-stage MMLS3 sensing data, were used as the training dataset, while the remaining MMLS3 data were used as the testing dataset. The results show that the ensemble ANN model is feasible and robust in predicting the dynamic modulus of the asphalt mixture in the MMLS3 test. The parametric analysis shows that the ensemble ANN model has reliable stability. Future studies are recommended to expand the database with more material variety and loading conditions for model verification.

Zeta Potential of Aggregate and Dynamic Modulus of HMA Estimation Using Aggregate Silica Content

The mineralogical composition of an aggregate influences its adhesion with bitumen and therefore its dynamic modulus. However, few studies have been conducted on this aspect. One of the most used properties to describe the impact of aggregate on the adhesiveness phenomena is the zeta potential. In this study, the first mineralogical and chemical properties were considered through the percentage of silica in the rock source of aggregates and the electric aggregate particles charge zeta. Dynamic modulus values used for regression process are determined from complex modulus test on nine asphalt concretes mix designed with aggregate types (basalt of Diack, quartzite of Bakel and Limestone of Bandia). The results showed that aggregate with high percentage of silica have higher zeta potential than aggregate with low percentage of silica. The development of a zeta potential predictive model showed a strong sensitivity to silica. The results of the complex modulus tests showed that Hot Mixture Asphalt (HMA) mixed with aggregate containing high silica contents gave better results than those mixed with aggregates containing low percentage of silica. The dynamic modulus predictive models of HMA developed shows that it is the properties of bitumen that influence more. However, the effect of silica although low, is very marked at low temperatures and high frequencies.

Evaluation and calibration of dynamic modulus prediction models of asphalt mixtures for hot climates: Qatar as a case study

The dynamic modulus (|E*|) of asphalt mixtures is one of the most important inputs in Mechanistic-Empirical (ME) pavement analysis and design. Several models have been developed to predict the dynamic modulus based on mixture volumetrics and material properties. This study aimed to calibrate and validate two commonly used models (i.e., Hirsch model and Alkhateeb model) for predicting the dynamic modulus of asphalt mixtures in Qatar. Based on the study outcomes, the Hirsch model was found to have a high prediction performance of asphalt mixture moduli before calibration with a coefficient of determination (R2) of 87.2 % between predicted and measured values. This R2 value improved slightly after calibration to 89.2 %, Alkhateeb model, on the other hand, had a coefficient of determination of 70.8 % before calibration, which also improved to 89.2 % after calibration. The moduli predicted by the Hirsch model before and after calibration were employed in this study to perform a mechanistic-empirical analysis of the performance of various typical pavement sections in Qatar. According to the findings, the percentage change in the predicted fatigue damage due to the use of the calibrated Hirsch model reached more than 50 % with an average value of 17.33 %, while the percent change in rutting reached 14 % with an average value of 3.65 %. These results highlight the importance of using locally calibrated models for the dynamic modulus in order to improve performance predictions.

Study of in situ dynamic modulus prediction of asphalt mixture utilizing Ground penetrating radar technology

• The small-scale specimen’s applicability in dynamic modulus test was investigated. • Empirical and ANN dynamic modulus prediction models were proposed using GPR data. • The proposed models provided acceptable results at the confidence level of 95%. It is widely known that the asphalt mixture dynamic modulus is the key mechanical property that affects the quality and service life of asphalt pavement greatly. Ground penetrating radar (GPR) technology is a prospective method commonly used in determining the material information of asphalt pavement. Its utilization is supported by studying the relationship between the characterizations of GPR waveform and the parameters representing the condition of asphalt pavement. However, it is rarely applied in dynamic modulus prediction of asphalt mixture. To fill this gap, this study focuses on developing the corresponding dynamic modulus predictive method on the basis of GPR data. First, the applicability of the ϕ 38 mm × h 110 mm small-scale specimen covering wide range of air void content in the uniaxial compression test was analyzed. Then, the empirical and artificial neural network (ANN) dynamic modulus prediction models were developed by taking into account the dielectric constant of asphalt mixture. Last, the two proposed models were validated based on four asphalt mixture lanes in the field. It was found that the test errors of small-scale specimens were smaller than 15 %, and the statistical difference of dynamic moduli and phase angles measured from the full-size and small-scale specimens is insignificant at the 95 % confidence level meaning the size influence can be ignored. According to the verification experiment, the proposed empirical model and ANN model could yield acceptable results with the average prediction error of 19.3 % and 24.8 %, respectively. It is recommended that the two proposed predictive models coupled with GPR data could be used as an alternative to the currently available methods in estimating the dynamic modulus of asphalt mixture in situ.

An evolutionary computing approach for reducing bias in the dynamic modulus predictive models of hot mix asphalt

Various published literature has indicated significant bias issues with dynamic modulus (E∗) predictive models for the hot mix asphalt. This study proposes Gene Expression Programming (GEP) based approach to reduce such bias. Bias analysis was carried out using database developed during national cooperative highway research program. GEP based predictive models for bias correction factors were developed and subsequently used in conjunction with E∗ predictive models to update E∗ values. Application of correction factors and subsequent statistical analysis showed improvement in the accuracy of predicted E∗ values. The extent of improvement (using sum of squared error) was dependent on model under consideration and ranged between 19 and 36%.

Dynamic modulus prediction model and analysis of factors influencing asphalt mixtures using gray relational analysis methods

In the design of asphalt pavement, the dynamic modulus of the asphalt mixture is an indispensable parameter used for checking the fatigue cracking and permanent deformation of the mixture. However, there are many parameters affecting the dynamic modulus. Designers often do not know how to choose among them, and obtaining the parameters required in the traditional prediction model usually require sophisticated instruments, which is not conducive to their development and use by road designers. In this study, the method of gray correlation analysis was used to screen out the important and easy-to-obtain material parameters of an asphalt mixture, and then the multiple linear regression equation was used to establish a prediction model suitable for obtaining the dynamic modulus of asphalt mixtures in Jilin province. Tested against the estimated data, the fitting result is good. This research demonstrates that gray relational theory and multiple linear regression analysis can be applied in the establishment of a dynamic modulus model.

A Novel Neural Computing Model Applied to Estimate the Dynamic Modulus (DM) of Asphalt Mixtures by the Improved Beetle Antennae Search

To accurately estimate the dynamic properties of the asphalt mixtures to be used in the Mechanistic-Empirical Pavement Design Guide (MEPDG), a novel neural computing model using the improved beetle antennae search was developed. Asphalt mixtures were designed conventionally by eight types of aggregate gradations and two types of asphalt binders. The dynamic modulus (DM) tests were conducted under 3 temperatures and 3 loading frequencies to construct 144 datasets for the machine learning process. A novel neural network model was developed by using an improved beetle antennae search (BAS) algorithm to adjust the hyperparameters more efficiently. The predictive results of the proposed model were determined by R and RMSE and the importance score of the input parameters was assessed as well. The prediction performance showed that the improved BAS algorithm can effectively adjust the hyperparameters of the neural network calculation model, and built the asphalt mixture DM prediction model has higher reliability and effectiveness than the random hyperparameter selection. The mixture model can accurately evaluate and predict the DM of the asphalt mixture to be used in MEPDG. The dynamic shear modulus of the asphalt binder is the most important parameter that affects the DM of the asphalt mixtures because of its high correlation with the adhesive effect in the composition. The phase angle of the binder showed the highest influence on the DM of the asphalt mixtures in the remaining variables. The importance of these influences can provide a reference for the future design of asphalt mixtures.

Dynamic Modulus Prediction of a High-Modulus Asphalt Mixture

Dynamic modulus is a key evaluation index of the high-modulus asphalt mixture, but it is relatively difficult to test and collect its data. The purpose is to achieve the accurate prediction of the dynamic modulus of the high-modulus asphalt mixture and further optimize the design process of the high-modulus asphalt mixture. Five high-temperature performance indexes of high-modulus asphalt and its mixture were selected. The correlation between the above five indexes and the dynamic modulus of the high-modulus asphalt mixture was analyzed. On this basis, the dynamic modulus prediction models of the high-modulus asphalt mixture based on small sample data were established by multiple regression, general regression neural network (GRNN), and support vector machine (SVM) neural network. According to parameter adjustment and cross-validation, the output stability and accuracy of different prediction models were compared and evaluated. The most effective prediction model was recommended. The results show that the SVM model has more significant prediction accuracy and output stability than the multiple regression model and the GRNN model. Its prediction error was 0.98–9.71%. Compared with the other two models, the prediction error of the SVM model declined by 0.50–11.96% and 3.76–13.44%. The SVM neural network was recommended as the dynamic modulus prediction model of the high-modulus asphalt mixture.

Dynamic Modulus Predictive Models for In-Service Asphalt Layers in Hot Climate Areas

Dynamic modulus of asphalt mixtures is one of the most important input parameters in design and rehabilitation of asphalt pavements. Dynamic modulus predictive models are alternative methods for laboratory determination of this parameter. These models were developed based on laboratory data. Due to sophisticated and laborious laboratory testing methods, there is a need to develop new models to determine dynamic moduli of in-service asphalt layers. In this study, nine different asphalt pavement sites were selected in two southern provinces of Iran. Falling weight deflectometer (FWD) testing was performed at each site and core samples were taken from the asphalt layers for volumetric analysis. Using the results, dynamic moduli of asphalt layers were determined using six predictive models, including Witczak, modified Witczak, Hirsch, Al-Khateeb, global, and simplified global models. Predicted dynamic moduli were compared with those determined from back-calculation analysis of FWD data. Existing predictive models were calibrated and new models were developed for the prediction of in situ dynamic modulus of asphalt layers in hot climate areas. Performance evaluation and validation of the new models showed high prediction accuracy and low prediction bias with very good correlations between the predicted and back-calculated values (R2=0.96).

Performance Evaluation of Dynamic Modulus Predictive Models for Asphalt Mixtures

Dynamic modulus characterizes the viscoelastic behavior of asphalt materials and is the most important input parameter for design and rehabilitation of flexible pavements using Mechanistic–Empirical Pavement Design Guide (MEPDG). Laboratory determination of dynamic modulus is very expensive and time consuming. To overcome this challenge, several predictive models were developed to determine dynamic modulus of asphalt mixtures instead of laboratory testing. Present study utilizes a large database of 1320 dynamic modulus test results developed at the University of Maryland to evaluate the performance and accuracy of different dynamic modulus predictive models. For this purpose, six conventional dynamic modulus predictive models including Witczak, Modified Witczak, Hirsch, Al-Khateeb, Global and Simplified Global models were considered and dynamic moduli of asphalt mixtures were determined. These moduli were then compared with those determined from laboratory test results. Performance evaluation of the models showed high prediction accuracy and low prediction bias with good correlation between predicted moduli and measured values for Witczak and Global models.

A new dynamic modulus predictive model for asphalt mixtures based on the law of mixtures

The dynamic modulus (|Em*|) of asphalt mixtures is one of most fundamental mechanical parameters used in flexible pavement design, which has been extensively estimated through various predictive models. However, most of existing dynamic modulus predictive models does not fit well for the purpose of the Level 3 (the lowest input level) flexible pavement design in the current AASHTOWare Pavement ME Design due to the following major deficiencies: (1) lacking physical significance; (2) providing poor prediction accuracy; and (3) requiring laboratory testing to obtain key model parameters. To address these deficiencies, this paper is aimed to develop a new model on the basis of the law of mixtures. First, a large database is collected and revised for the new model development. Two exiting law of mixture models are then evaluated in terms of the mode prediction accuracy, and neither of them provided satisfactory prediction results. A new model is subsequently developed, which involves using a parallel form to represent the contribution of each of three phases (asphalt, aggregate and air void) to the |Em*| as well as utilizing a standard sigmoid function to characterize the mechanical response of asphalt mixture. Statistical analysis shows that the new model has comparable prediction performance with traditional Witczak models, but with significantly lower number of input variables and relatively higher model quality. Supplemental data collected from laboratory tests and independent literature sources finally validate that the new model has the capability to provide an accurate prediction of |Em*| with an R2 value up to 0.90. In these regards, the new model is believed to be a good candidate for the |Em*| prediction of asphalt mixtures for a reliable Level-3 flexible pavement design.

Establishing a dynamic elastic modulus prediction model of larch based on nondestructive testing data

To accurately evaluate the dynamic elastic modulus (Ed) of wood in ancient timberwork buildings, the new materials of larch were used as the research object, and the stress wave nondestructive testing method was used to determine it. Based on nondestructive testing data, this paper proposed a method for predicting the Ed of larch using the principle of information diffusion. It selected the distance (D) from the bark to the pith in the cross-section of the wood and the height (H) from the base to the top in the radial section of the wood. The fuzzy diffusion relationships between the two evaluation indexes and the Ed were established using the information diffusion principle and the first- and second-order fuzzy approximate inferences in the fuzzy information optimization process. The calculation results showed that the dynamic elastic modulus model constructed by the information diffusion method can better predict the Ed of larch. The coefficient of determination between the measured value and the predicted value of the Ed was 0.861, they were in good agreement. The weights of the two influencing factors were 0.7 and 0.3, respectively, the average relative error of the fitted sample data was the minimum, which was 8.55%. This prediction model provided a strong basis for field inspection.

Improved models for the prediction of asphalt binder dynamic shear modulus and phase angle

In this paper, new set of models for predicting the dynamic shear modulus and phase angle of asphalt binders from conventional viscosity are developed and presented. Based on theoretical considerations, suitable forms of general logistic functions are introduced to develop new models for binder dynamic shear modulus and phase angle over a wide range of temperature and loading conditions. A nonlinear optimization technique based on the Nelder-Mead optimization method is used to obtain the coefficients for the new binder dynamic shear modulus and phase angle models. The experimental binder testing database consisting of dynamic shear modulus, phase angle, frequency, viscosity measurements of thirty-two (32) unmodified and nine (9) modified binders from different sources is used in the study. A total of 7, 120 binder data points are used for the model development, evaluation and validation. The new models deliver very accurate prediction of the binder dynamic shear modulus and phase angle from the conventional steady-state viscosity indicated by very high goodness of fit using 7,120 binder data points. A new parameter termed the “reduced viscosity” is identified which produces a smooth continuous function of the binder phase angle for both modified and unmodified binders using a single viscosity shift factor. The reduced viscosity is considered as the independent variable in the new dynamic shear modulus and phase angle predictive models.

Evaluation of Dynamic Modulus of HMA Sigmoidal Prediction Models and Optimization by Approach of U.S. Mesh Sieve by AFNOR and LC Mesh Sieve

Pavement design tools are not universal. Indeed, in the sizing of pavements in the USA, the prediction models used in the calculation of the dynamic modulus of HMA are not adapted to the characterization of the mineral skeleton of the HMA mix designed with the French method. This article aims to assess the predictive models of the dynamic modulus used in the mechanistic-empirical design for their use in the design of bituminous pavements, and to develop new predictive models taking into account the sieve series LC and AFNOR standards. A total of six types of mixtures were subjected to the determination of complex modulus testing by direct tensile-compression on cylindrical specimens (26-700 LC) over a temperature range (5) and frequency (5) data. Dynamic modulus prediction models |E*| are studied Witczak model 1999 and model Witczak 2006. These models do not take into account the AFNOR or LC mesh sieve, an approach was made in relation to the US mesh sieve to replace ρ200 (0.075 mm), ρ4 (4.76 mm), ρ38 (9.5 mm) and ρ34 (19 mm) respectively by the AFNOR mesh P0.08 (0.08 mm), R5 (5 mm), R10 (10 mm) and R14 (14 mm). The result is the production of two models whose are evaluated by correlation with the values |E*| of modulus measured in the laboratory is satisfactory (R2 = 0.83 respectively R2 = 0.71 and p-value = 0.00). The optimization of these approximate models gave new models with the same frame as the original models and a better correlation with the data observed in the laboratory (respectively R2 = 0. 95 and R2 = 0.91 p-value = 0.00).

Development of a Dynamic Modulus Prediction Model for Hot Mixture Asphalt and Study of the Impact of Aggregate Type and Its Electrochemical Properties

The most famous model known in prediction of dynamic modulus for asphalt concretes is the Witczak and Hirsh models. These models didn’t use the mineralogical and chemical properties of aggregates. Witczak models used the passing or refusal percentage to sieve diameters and Hirsh model used the volumetric analysis. All models developed until now considered that the aggregates were geotechnical conforming to standards. In this study the first mineralogical and chemical properties were considered through the percentage of silica in the rock source of aggregates and the electric aggregate particles charge zeta. Dynamic modulus values used for regression process are determined from complex modulus test on nine asphalt concretes mix designed with aggregate types (basalt of Diack, quartzite of Bakel and Limestone of Bandia). Between Twelve initial inputs, the statistical regression by exclusion process keeps only seven parameters as input for the model. The mineralogical model showed good accuracy with R2 equal to 0.09. The student test on the model parameters showed that all the parameters included in the model were meaningful with good p inferior to 0.05. The Fisher test on the model showed the same result. The analysis of the sensitivity of the mineralogical model to zeta potential showed that the dynamic modulus increases with the positive zeta-potentials and decreases with the negative zeta-potentials. The analysis of the sensitivity of the mineralogical model to the silica showed that the dynamic modulus decreases with the increase of the silica.

Effect of Blending Degree between Virgin and Aged Binder on Pavement Performance of Recycled Asphalt Mixture with High RAP Content

In this study, the influence of the blending degree between virgin and aged binder on the pavement performance of hot-mix recycled asphalt mixture (HMRAM) with high RAP content is analyzed. The aggregate gradation of AC-16 was selected. The RAP contents were 30, 40, and 50%. HMRAMs with different degrees of blending (DOBs) were prepared by changing the mixing temperature (150, 165, and 180°C) without the occurrence of excessive aging for asphalt binders. An improved Hirsch dynamic modulus prediction model was then used to quantitatively characterize the DOB of HMRAM. Finally, the high-temperature, low-temperature, moisture stability, and fatigue resistance performance of HMRAM were tested and the effect of the DOB between the virgin and aged asphalt binder on the pavement performance was analyzed. The results showed that the DOB between the virgin and aged asphalt binder cannot reach 100% at the three mixing temperatures for HMRAM with 30, 40, and 50% RAP contents, which is inconsistent with the assumption of complete blending in China’s specification. The dynamic stability of the mixture gradually decreases with the increased DOB for HMRAM with a high RAP content, while the moisture stability, low-temperature, and fatigue resistance performance are continuously improved. This means that with the increase in DOB in the stage of open to traffic, meeting high-temperature performance criteria at the design stage may become unsatisfactory for HMRAM. The moisture stability, low-temperature performance, and fatigue resistance performances of HMRAM measured at the design stage were reasonable and conservative. The change in DOB significantly affects the content and properties of total free binder in HMRAM, affecting pavement performance. The content and physical properties of the RAP aggregate also have a significant impact on pavement performance.

Laboratory testing and analysis of dynamic and static resilient modulus of subgrade soil under various influencing factors

In this study, dynamic and static resilient modulus of subgrade soil were conducted for six types of subgrade soil using the stress level and loading range on top of subgrade under moving vehicle loading. The influences of loading frequency, stress level, compaction degree, and moisture content on dynamic and static modulus were investigated. The prediction models of nonlinear parameters of dynamic resilient modulus and the relationship of dynamic and static resilient modulus were developed. Results showed that dynamic resilient modulus of different soils were significantly affected by loading frequency at the loading frequency range of 0.5–3 Hz. Dynamic and static resilient modulus were both positively related with confining pressure and compaction degree, but negatively related to the moisture content of subgrade soil. The nonlinear parameters of dynamic resilient modulus prediction models had the similar form for different types of subgrade soil, while the coefficients of nonlinear parameters varied with the type of subgrade soil. The parameters of the relationships between dynamic and static resilient modulus for different types of soil were also similar in the equation format with different parameter values. The research findings provide valuable information for using realistic subgrade soil modulus in pavement design and analysis.