Experimental Alternative to the Determination of the Thermal Dependence of the Complex Modulus of Asphalt Mixes in Dry Tropical Areas

Current pavement design methods do not allow for the reduction of early deformation of the surface layers of bituminous pavements in the city of Ouagadougou. Weather conditions combined with traffic, particularly during heat waves, are factors. The temperature at the surface of the bituminous pavement can reach 62˚C but the complex modulus associated with this temperature is not taken into account in the design, hence the interest in proposing laws of dependence of the complex moduli is taken into account in the maximum temperatures of the pavement surface. The objective of this paper is to propose an experimental method to determine the temperature dependence of the complex moduli of asphalt mixes for temperatures between 40˚C and 70˚C. This experimental method consists of performing axial compression tests on cylindrical asphalt specimens. It was applied to three different formulas of bituminous mixes, intended for the wearing course, obtained from mixes of crushed granites, granular classes 6/10, 4/6 and 0/4, pure bitumens of grade 50/70, 35/50 and modified bitumen of grade 10/65. The comparative study of the experimental results obtained with the results of a semi-empirical methodology revealed a root mean square deviation from the mean of between 6.58% and 14.8% of the norms of the complex moduli (modulus of rigidity) of the asphalt mixes for a fixed frequency of solicitations of 10 Hz. The consistency of these results with data from the literature led to the initial conclusion that asphalt mixes formulated with 35/50 and 10/65 bitumen would have better compressive strength than those formulated with 50/70 bitumen, for exposure temperatures between 40˚C and 70˚C. This experimental approach could be an alternative to the complex modulus test for determining the modulus of rigidity for design purposes under real pavement exposure conditions in the city of Ouagadougou during heat waves.

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.

Study on High-Speed Magnitude Approximation for Complex Vectors

High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The performance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms, the approximation formula under the least mean square error criterion is derived. For the iterative algorithms, a modified CORDIC (coordinate rotation digital computer) algorithm is developed. This modified CORDIC algorithm is proved to be with a maximum relative error about one half that of the original CORDIC algorithm. Finally, the effects of the finite register length on these algorithms are also concerned, which shows that 9 to 12-bit coefficients are sufficient for practical applications.

Frequency domain analysis of pre-stressed elastomeric vibration isolators

Two types of elastomeric vibration isolators used for equipment vibration isolation in aerospace vehicles are considered for the present study. These isolators are constructed using elastomers mounted in steel encasings. These isolators are initially deformed statically and dynamic loads are applied on the deformed configuration. To capture the static deformation, equivalent static load corresponding to its load rating and specified displacements are created. Static deformation is computed using Finite Element methods with four node axi-symmetric element which include the geometric non-linear effect for steel and with standard Yeoh hyper-elastic material model for elastomers(Muhammed and Zu, 2012) [1]. Yeoh material constants are derived from uni-axial tension test data of the elastomer specimen. These isolators are subjected to harmonic and random excitations in the pre-deformed state. For numerical analysis, elastomeric constants at dynamic conditions are obtained as complex function of frequency using Dynamic Mechanical Analyzer(DMA) for a range of frequencies. The standard material model of Yeoh is modified incorporating frequency dependant material characteristics and damping in the range of frequencies of interest. A multiplicative non-separable variables law is derived for Yeoh material model to include the effect of static pre-stress, based on the methodology given in literature(Nashif et al.,1985;Beda et al., 2014) [2,3]. The modifications of Yeoh model suitable for frequency domain analysis is the novelty in the present study. In the analysis, while dynamic loads are applied, the configuration is updated considering initial static loading. The frequency response of the isolators is computed using material properties evaluated at progressive dynamic strains until a match in natural frequency is observed. Appropriate damping corrections are then incorporated to match the test observed transmissibility. Then updated material properties are used to compute the random response which showed good agreement with results of experiments, validating the approach taken for the development of this model.

Microscopic and Dynamic Rheological Characteristics of Crumb Rubber Modified Asphalt

A test for crumb rubber modified asphalt containing 20% crumb rubber particles（30 mesh） was performed using a scanning electron microscope（SEM）.The experimental results indicate that the crumb rubber particles are evenly distributed in the asphalt.Shear rate sweep and shear-temperature sweep tests on the crumb rubber modified asphalt at-20-80 ℃ using a dynamic shear rheology（DSR） instrument,were carried out.The tests show that the complex modulus decreases with increasing temperature;at equivalent temperature,higher load frequencies lead to a larger complex modulus,and this value increasingly decreases as the temperature increases;the phase angle increases with temperature and decreases as the load frequency increases.It can be concluded that the rutting resistance limiting temperature of crumb rubber modified asphalt is 78 ℃,and the anti-fatigue limiting temperature is 16 ℃,which shows that the asphalt has preferable rutting resistance characteristics at high temperature,as well as anti-fatigue characteristics.In addition,the complex modulus master curve at different temperatures was plotted according to the time temperature equivalence principle,which allows the study of the dynamic state behavior of crumb rubber modified asphalt at a wide range of load frequency.

Modelling the Rheological Properties of Epoxy Asphalt Concrete

This paper presents an investigation into modelling the rheological properties of epoxy asphalt concrete( EAC) by using the Huet-Sayegh model. Complex modulus tests were conducted on EAC specimens at various temperature and loading frequency conditions. Dynamic modulus and phase angles obtained from the complex modulus tests were used in the construction of the Huet-Sayegh model. The dynamic modulus master curve was developed by the Huet-Sayegh model as well as the Burgers model for comparison purpose. The results showed that EAC exhibits typical rheological behavior whose dynamic modulus decreases with the increase of temperature while increases with the increase of frequency,and phase angles increase with the decrease of frequencies and the increase of temperatures. The Huet-Sayegh model predicts the dynamic modulus master curve of EAC very well and much better than the Burgers model over a wide range of frequencies.

An Optimum Analysis Method of Sandwich Structures Made from Elastic-viscoelastic Materials

Due to a viscoelastic damping middle layer,sandwich structures have the capacity of energy consumption.In this paper,we describe the frequency-dependent property of viscoelastic materials using complex modulus model,and iterative modal strain energy method and iterative complex eigenvalue method are presented to obtain frequency and loss factor of sandwich structures.The two methods are effective and exact for the large-scale complex composite sandwich structures.Then an optimum analysis method is suggested to apply to sandwich structures.Finally,as an example,an optimum analysis of a clamped-clamped sandwich beams is conducted,theoretical closed-form solution and numerical predictions are studied comparatively,and the results agree well.

Determination of complex Young's modulus of viscoelastic bars using forced longitudinal vibration of slender rods

A method to identify complex Young＇s modulus of viscoelastic materials using forced longitudinal vibration of slender rods is proposed. The method differs from the beam one. Experimental tests were carried out at room temperature with different lengths in 108 mm, 100 mm, 90 ram, 83.5 mm, 80 ram, 74.5 mm, 70 mm for the polycarbonate bars, and the curves of ratios A2/A1 between two ends of a viscoelastic bar versus frequencies are obtained, furthermore, the corresponding 3 dB bandwidth and the storage and loss modulus can be calculated. Sufficient number of obtained complex Young＇s modulus at different frequency allows us to calculate other ones using the least square method. If the step of the tested frequency is 5 Hz, the maximum error of results can be less than 6%. By comparison with the measurement methods which the previous literature mentioned, this new method simplifies the calculation, and the physical meaning appears apparently and clearly.

Linear viscoelastic behavior of asphalt binders and mixtures containing very high percentages of reclaimed asphalt pavement

The primary aim of this study is to correlate the impact of aggregates,if any,on the viscoelastic behavior of rejuvenated asphalt mixtures containing very high amounts of reclaimed asphalt pavement(RAP)(>50%).First,gradation of 100%RAP was rectified,using a modified Bailey method by adding virgin aggregates to achieve two coarse dense-graded and one fine dense-graded blends.Complex modulus test was then performed from−35 to+35℃and 0.01–10 Hz.In addition to performance grade(PG)testing,extracted and recovered binders from different asphalt mixtures underwent shear complex modulus test within−8℃to high temperature PG and frequencies from 0.001 to 30 Hz.Cole−Cole,Black space,complex modulus and phase angle master curves were constructed and ShiftHomothety-Shift in time-Shift(SHStS)transformation was used to compare the linear viscoelastic behavior of asphalt binders and mixtures.The influence of aggregates on the viscoelastic behavior of asphalt mixtures depends on temperature and/or frequency.The role of asphalt binders in the behavior of asphalt mixtures is more pronounced at high temperatures and the effect of the aggregate structure increases as the temperature falls.The maximum difference(60%to 70%)in the viscoelastic behavior of the binder and mixture based on SHStS transformed Cole−Cole curves is within the phase angle of 15°–20°.

Evaluation of the cracking and aging susceptibility of asphalt mixtures using viscoelastic properties and master curve parameters

Aging can significantly affect the performance of asphalt mixtures, causing increase in stiffness, reduction in relaxation capability and increase in cracking susceptibility. It is also well known that fundamental viscoelastic properties are used for design and modelling of asphalt mixtures and pavement structures to addressing rutting, fatigue and thermal cracking concerns. The objective of this paper is to study how the viscoelastic properties of asphalt mixture change over time, and evaluate and identify the cracking and aging susceptibility of asphalt mixtures with different mix variables during material selection and mixture design. Ten mixtures are evaluated using different laboratory conditioning protocols to simulate a range of aging levels in the field. The complex modulus test is then conducted on the lab aged mixtures to measure the viscoelastic properties in order to construct the dynamic modulus and phase angle master curves. The mixture Glover-Rowe(G-Rm) parameter and the shape parameters of the dynamic modulus and phase angle master curves, including inflection point frequency(-β/γ), difference between the glassy modulus and the inflection point modulus(γ), peak value of phase angle(a) and the horizontal position(frequency) of the peak phase angle value(c), are determined and evaluated for the mixtures with different aging conditions and mix variables. The study indicates the ability of the G-Rmparameter and all the master curve shape parameters to capture the effect of different aging conditions on linear viscoelastic mixture properties, as well as the cracking and aging susceptibility of asphalt mixtures.

Conductivity and dielectric studies on LiCeO_2

LiCeO2 was prepared by a solid-state reaction method using microwave heat treatment and identified by X-ray diffractometry.LiCeO2 has monoclinic crystal structure whose conductivity and dielectric properties were studied over a range of frequency(42 Hz to 1 MHz) and temperatures(30-500 °C) using ac technique of complex impedance analyzer HIOKI 3532.Combined impedance and modulus plots were used as tools to analyze the sample behaviour as a function of frequency at different temperatures.The d.c.conductivity...

Dynamic behavior of sandwich beams with different compositions of magnetorheological fluid core

Magnetorheological fluid(MRF)sandwich beams belong to a class of adaptive beams that consists of MRF sandwiched between two or more face layers and have a great prospective for use in semi-active control of beam vibrations due to their superior vibration suppression capabilities.The composition of MRF has a strong influence on the MRF properties and hence affects the vibration characteristics of the beam.In this work,six MRF samples(MRFs)composed of combination of two particle sizes and three weight fractions of carbonyl iron pow-der(CIP)were prepared and their viscoelastic properties were measured.The MRFs were used to fabricate different MRF core sandwich beams.Additionally,a sandwich beam with commer-cially available MRF 132DG fluid as core was fabricated.The modal parameters of the cantilever MRF sandwich beams were determined at different magnetic fields.Further,sinusoidal sweep excitation tests were performed on these beams at different magnetic fields to investigate their vibration suppres-sion behavior.MRF having larger particle size and higher weight fraction of CIP resulted in higher damping ratio and vibration suppression.Finally,optimal particle size and weight fraction of CIP were determined based on the maximization of damping ratio and minimization of weight of MRF.

Application of extreme gradient boosting in predicting the viscoelastic characteristics of graphene oxide modified asphalt at medium and high temperatures

Complex modulus(G^(*))is one of the important criteria for asphalt classification according to AASHTO M320-10,and is often used to predict the linear viscoelastic behavior of asphalt binders.In addition,phase angle(φ)characterizes the deformation resilience of asphalt and is used to assess the ratio between the viscous and elastic components.It is thus important to quickly and accurately estimate these two indicators.The purpose of this investigation is to construct an extreme gradient boosting(XGB)model to predict G^(*)andφof graphene oxide(GO)modified asphaltat medium and high temperatures.Two data sets are gathered from previously published experiments,consisting of 357 samples for G^(*)and 339 samples forφ,and the se are used to develop the XGB model using nine inputs representing theasphalt binder components.The findings show that XGB is an excellent predictor of G^(*)andφof GO-modified asphalt,evaluated by the coefficient of determination R^(2)(R^(2)=0.990 and 0.9903 for G^(*)andφ,respectively)and root mean square error(RMSE=31.499 and 1.08 for G^(*)andφ,respectively).In addition,the model’s performance is compared with experimental results and five other machine learning(ML)models to highlight its accuracy.In the final step,the Shapley additive explanations(SHAP)value analysis is conducted to assess the impact of each input and the correlation between pairs of important features on asphalt’s two physical properties.