Burgers Model Research Articles

Preparation and Temperature Susceptibility Evaluation of Crumb Rubber Modified Asphalt Applied in Alpine Regions

In alpine regions, the durability of asphalt pavement is worse due to the harsh climate. However, crumb rubber modified asphalt has the potential to improve the durability of pavement. Based on matrix asphalt, crumb rubber, Trans-Polyoctenamer Rubber Reactive Modifier (TOR), and an orthogonal test, the preparation scheme of crumb rubber modified asphalt suitable for alpine regions was obtained. The crumb rubber was selected 30 mesh, and the content of crumb rubber was 24% of the quality of matrix asphalt. Shearing time was 60 min, and preparation temperature was 205 °C. Shearing rate was 5000 r/min, and optimum TOR content was set as 4.5% of the quality of crumb rubber. The temperature susceptibility of matrix asphalt (JZ), crumb rubber modified asphalt (AR), crumb rubber modified asphalt mixed with TOR (TAR) was investigated. The high temperature performance indexes, including phase angle, the complex modulus index, and rutting factor, and the low temperature performance indexes including creep rate and stiffness modulus, the ratio of creep rate and stiffness modulus, Burgers model parameters, dissipated energy ratio, and the derivative of creep compliance were analyzed in depth with multiple parameters. Meanwhile, the mechanisms of prepared AR and TAR were explored. The results indicate that the PG grading is PG64-22 of JZ, PG70-34 of AR, and PG82-28 of TAR. The deformation resistance of TAR at high temperature is superior to AR. The addition of crumb rubber not only improves the temperature susceptibility, but also enhances its viscoelasticity at low temperatures. After the crumb rubber swell in the asphalt system, the network structures are crosslinked and the physical and chemical effects are produced, such as cracking and repolymerization in the asphalt system. TOR can further enhance the swelling and network crosslinking effects of rubber-asphalt. The TAR has the strongest weather resistance. The study provides guidance for AR and TAR to be used in alpine regions.

Study of a Modified Time Hardening Model for the Creep Consolidation Effect of Asphalt Mixtures.

In the past, most researchers have explained the three-stage creep behavior of asphalt mixture in detail. Still, there is no reasonable model to describe the creep of the consolidation effect. To accurately describe the consolidation effect of an asphalt mixture during the viscoelastic deformation process, a modified time hardening model was established by using the Malthus model and the Logistic function to change its creep strain and creep compliance. According to the characteristics of asphalt mixture creep, a single penetration creep test was conducted for high-elasticity modified asphalt mixtures at different temperatures (20 °C, 40 °C, 60 °C) and various loading levels (0.55 MPa, 0.70 MPa, 0.85 MPa, 1.00 MPa). The test results showed that the effect of stress on deformation within the normal range of variation was more significant than that of temperature. In addition, the test results were simulated by the modified time hardening model using surface fitting and compared with a time hardening model and a modified Burgers model. A fitting analysis showed that the modified time hardening model more accurately represents the asphalt mixture’s consolidation effect and creep behavior. Therefore, the modified time hardening model can better show the consolidation effect in the creep process.

Texture and viscoelastic characteristics of silver carp (Hypophthalmichthys molitrix) surimi affected by combination of washing regimes and hydrogen peroxide.

This study aimed to apply H2 O2 at different concentrations in combination with mince:water (M:W) ratios and different washing cycles (WCs) to produce surimi gel from silver carp without compromising its quality characteristics. Color, texture, microstructure, and rheological properties of surimi gels were investigated. Water holding capacity, texture profile, and gel strength showed a greater dependency on number of WCs than the M:W ratios and percentage of H2 O2 (p < .05), that is, higher WCs, firmer surimi gel. Accordingly, T2 (one WC, 2% H2 O2 , 1:3), T10 (two WC, 1% H2 O2 , 1:2), and T16 (three WC, 1% H2 O2 , 1:2) treatments resulted the most cohesive and resilient surimi compared with the rest (p < .05), confirmed by scanning electron microscopy images. However, all treated fish mince samples with H2 O2 , resulted in a surimi gel with lower texture quality compared with the control surimi prepared by conventional washing process without H2 O2 (p < .05). A temperature sweep test was conducted based on the linear viscoelastic region stress and frequency values and the aforementioned surimi gels exhibited an obvious valley shape pattern at temperature range of 48-62°C. In the creep-recovery test, the Burgers model satisfactorily described the internal structure of the surimi gel samples as the lowest deformation belonged to the control samples followed by T2. However, after 300 s strain, neither of surimi gels were fully recovered their original shape. Altogether, further studies are needed to clarify the effects of H2 O2 in reduction of WCs, without significantly affecting the textural and rheological properties of resultant surimi gel.

The rheological behavior and high-low temperature performance of warm SBS/rubber asphalt

Rubber asphalt pavement has the performance advantages of noise reduction, anti-rutting, and anti-cracking. In this paper, the deformation recovery ability, stress sensitivity, dynamic mechanical performance, and chemical components of a warm mix styrene-butadiene-styrene (SBS)/rubber asphalt before and after aging were analyzed. The results showed that the high-low temperature performance of the asphalt was improved, and the ratio of the viscoelastic component was changed by adding the LKW-II warm mix additive to the asphalt. The high-temperature performance of the warm mix SBS/rubber asphalt was improved after short-term aging. At a proportion of the warm mix additive of 0.1%, the high-temperature rheological performance was substantially improved, the anti-rutting ability was enhanced, and the stress sensitivity was the lowest. At high temperatures, the improvements were relatively small at warm mix additive proportions of 0.3% and 0.5%. The low-temperature performance was significantly improved at a proportion of 0.3%. The Burgers model was used to evaluate the low-temperature mechanical behavior and confirmed the low-temperature performance results. The Fourier transform infrared spectroscopy results showed that no new substances were produced after adding the LKW-II warm mix additive to the SBS/rubber asphalt, and the viscosity was reduced by changing the intermolecular force.

Application of the Grey Model in One-Dimensional Long-Term Creep Analysis of Coral Mud From the South China Sea

Coral mud is widely distributed in the South China Sea. Studying deformation laws of coral mud is important to the infrastructure development in the South China Sea. In this article, a one-dimensional oedometer test of coral mud under near-natural conditions is performed. The exponential fitting model, Burgers model and ODGM model are used to analyse the time-strain relationship of coral mud under different vertical pressures. The self-fitting accuracy and prediction accuracy of the three models under different vertical pressures are compared. Then, the number of data points used in the model was reduced, and the associated change in accuracy and model stability of the three models were analysed. The study found that the ODGM model has high self-fitting, high prediction accuracy, and a high model stability when the number of data points is reduced, which describe the long-term nonlinear deformation of coral mud more accurately.

Exact analytical solutions for bending creep behavior of viscoelastic laminated arches with interlayers

In this work, an exact analytical solution is proposed in order to investigate the bending creep behavior of viscoelastic laminated arches with interlayers under a distributed load. In the analytical model, both the lamina layers and bonding interlayers are considered as viscoelastic materials, which are described by Burgers model for transient and steady-state creep stages. The stress and displacement fields in each viscoelastic lamina layer are obtained on the basis of the exact elasticity theory as well as Boltzman superposition principle. The general solution of stresses and displacements with unknown coefficients is derived by utilizing the Fourier series expansion approach. The interlayer slip effect in the laminated arches is considered in the continuity conditions. By employing analytical Laplace transformation, the coefficients are further determined according to the continuity and load conditions. The present solution is compared to the finite element solution and they show a good agreement. The influences of various parameters are investigated in detail on the bending creep behavior of the arch.

The Viscoelastic Solution to Geertsma’s Subsidence Problem

Abstract This paper presents the viscoelastic analytical solution for stress and displacement due to prescribed time-varying changes in the pore fluid pressure of a disk-shaped inclusion embedded within a semi-infinite, viscoelastic medium. The correspondence principle of viscoelasticity, along with Hankel–Fourier and Laplace transforms, is used to derive the solution. The instantaneous viscoelastic solution, corresponding to the response immediately after the inclusion pore pressure change, recovers the elastic solution to the same problem (Geertsma 1973). Results are presented for fractional Maxwell and Burgers models of viscoelasticity after being applied to a set of experimental data from creep tests on shale. Solution results are demonstrated and discussed for the cases of constant inclusion depletion, as well as delayed injection of fluid into a previously depleted inclusion.

Research on the constitutive model of low-damage corn threshing based on DEM

The constitutive model of corn has an intense influence on the mechanical structure design and machine performance. In this paper, a creep property formula of corn-based on the Burgers model was proposed, which described the change process of the stress–strain trait of corn grain with time. Then, the mathematical model of the “corn-mechanical” interaction system was then established based on the Hertz-Mindlin no-slip model. The kinematic and dynamic formulas of corn ear under the action of threshers were deduced, and the “corn-corn” contact characteristics based on Hertz-Mindlin with bonding model were analyzed. Moreover, a new discrete element model construction method of the corn ear was proposed through particle filling and splicing methods. The simulation experiment was carried out in EDEM to verify the constitutive model and discrete element model of corn ear. The results showed that the particle filling model could better explain the mechanism of corn ear threshing and obtain the force of each corn grain during threshing. The average velocity of corn ear was 55.2 m/s, the maximum value was 216.7 m/s, and the minimum value was 16.2 m/s, while the average normal force was 201.7 N, the maximum force was 342.0 N, and the minimum force was 104.2 N respectively, it verified the feasibility and accuracy of models. Finally, the field experiment was carried out to verify the simulation results, and the corn grain broken rate was 2.16%. These results fill the blank of fundamental theoretical research on the design of corn ear threshing devices and provide a reference for the optimal design of other crop production equipment.

Influence of rockfill particle breakage on long-term settlement of embankment dams

The current research was implemented to monitor and rehabilitate the structural health of Masjed-E-Soleyman dam (MESD). With a height of 177 m, the MESD is one of the highest rockfill dams in Iran, and suffers from extensive and unpredictable settlements and related cracks. To investigate the non-homogeneous (conglomerate) rockfill's brittle behaviour in before–after and during triaxial tests, a series of laboratory tests under conventional stress paths were carried out using a large-scale triaxial apparatus. A numerical time-dependent model was used to find a relationship between particle breakage and the time-dependent settlement of the embankment dam. The core aim of this work was to investigate particle breakage of the conglomerate material in the MESD and to identify the non-homogeneous relative particle breakage index (RPBI) by establishing a relationship between the RPBI for this material and plastic work. The research was divided into three significant steps. The breakage index (before–after tests) was calculated in the first step. The relationship between the breakage index and plastic work (during tests) was then introduced. Finally, the future crest settlement of the MESD was predicted using a numerical viscoelastic Burgers model that was calibrated using accurate monitoring data of the dam.

Rheological behavior of ice‐cream mixes: Impact of temperature and protein concentration

AbstractThis work documented the influence of the protein source (milk protein concentrate 80 [MPC80] and whey protein concentrate 80 [WPC80]), protein content (4–12%), and temperature (5–35°C) on the rheological behavior (flow curve, frequency sweep, and creep–recovery) of ice‐cream mixes (ICMs). The viscosity of the ICMs increased with increasing the protein content and decreased with increasing the temperature. For each protein source, the viscosity was satisfactorily modeled ( &gt; .98, &gt; .98, and E &lt; 10%) using a modified Herschel–Buckley model, where the consistency index was parameterized to account for the protein and temperature effect. The analysis of the frequency sweeps suggested a dominant viscous gel behavior with increasing the protein content, being more pronounced for MPC80. Creep curves were satisfactorily described by the Burger model, while the recovery phase was represented by an empirical model ( &gt; .99). The percentage of recovery (%R) of the ICMs significantly decreased with the protein content.Practical applicationsThe viscosity of ice‐cream mix is a key parameter during the manufacture of ice‐cream. An increment in the protein content imparts viscosity of the mixes and presents many processing challenges. This work presents a mathematical model to predict the viscosity in terms of shear rate, protein content, and temperature.

Interface creep behavior of tensioned GFRP tendons embedded in cemented soils

This paper presents an experimental investigation and modeling of interface creep behavior of glass fiber-reinforced polymer (GRFP) tendons embedded in cemented soils. Rapid and creep pullout tests were carried out on GRFP tendons embedded in cemented soils using a specially developed pullout setup. Interface creep displacement responses for specimens with two different water–cement ratios were derived under various interface shear stress conditions. A modified Burgers model was developed to characterize the interface creep behavior by incorporating a time-dependent viscosity coefficient. This viscosity coefficient was calibrated using creep rate variation obtained experimentally. Regression fittings on a part of interface creep measurements were conducted to determine the value of the parameters of the interface creep model. Additional interface creep measurements were used to validate the applicability of the presented creep testing protocol and the effectiveness of the rheological modeling was validated.

Truncation and convergence dynamics: KdV Burgers model in the sense of Caputo derivative

This study examines the time fractional KdV Burgers equation with the initial conditions by using the extended result on Caputo formula, finite difference method (FDM). For this reason, various fractional differential operators are defined and analyzed. In order to check the stability of the numerical scheme, the Fourier-von Neumann technique is used. By presenting an example of KdV Burgers equation above mentioned issues are discussed and numerical solutions of the error estimates have been found for the FDM. For the errors in $L_2$ and $L_\infty$ the method accuracy has been controlled. Moreover, the obtained results have been compared with the exact solution for different cases of non-integer order and the behavior of the potentials u is presented as a graph. The numerical results have been shown in tables.

Experimental Study on Creep Characteristics of Saturated Q2 Loess

Catastrophic failures often occur to engineered infrastructure in areas underlain by saturated loess due to its high moisture content (degree of saturation &amp;gt;85%), low shear strength, and large deformation. Time effect (rheological property) and water are the most important factors affecting the mechanical properties of saturated loess. The rheological mechanism and characteristics of saturated loess are vital to understanding the interaction between infrastructure and foundation and the trigger of failures. Based on step-load testing, this study obtains the displacement-time relationship of saturated Q2 loess to analyze its creep behavior. Experimental results show that the creep strength of saturated Q2 loess is 75–80% of its unconfined compression strength, and the creep behavior can be simulated by the Burgers model. Additionally, the rheological parameters under different load conditions are obtained using the improved Marquardt iterative method. All these parameters can be used for numerical analysis of the rheological behavior of saturated Q2 loess.

Viscoelastic dynamic response of asphalt pavement with imperfect interface bonding base on transfer matrix

AbstractThe interface bonding condition between asphalt pavement layers is always imperfect because of the differing material properties of different layers and the limitation of construction techniques. Therefore, designing asphalt pavement by considering the interface to be completely continuous is not precise. The viscoelastic character of the asphalt layer contributes significantly to the performance of asphalt pavement. To explore the influence of the imperfect interface on the viscoelastic dynamic response of asphalt pavement, the Hankel–Laplace transformation was applied to convert the partial differential equations to ordinary differential equations and a transfer matrix was introduced to describe the behavior of the imperfect interface. Based on the boundary condition and integral inverse transformation technique, an analytical solution for the displacement, stress, and strain of the pavement can be obtained. By considering the variation in the interface condition and the viscoelastic characteristics of the asphalt layer, the dynamic response of the pavement was calculated based on a practical example. The results show that the interface condition between the asphalt layer and the base course has a marked influence on the viscoelastic dynamic response of the pavement and that enhancing the strength of this interface can reduce the deflection of the pavement. The series elastic component in the modified Burgers model is another significant factor that affects the calculation results of the pavement dynamic response.

Nanoindentation creep and stress relaxation tests of polycarbonate: Analysis of viscoelastic properties by different rheological models

Abstract Feedback-controlled nanoindentation with a Berkovich diamond tip has been used to perform creep and stress relaxation tests on polycarbonate at room temperature for a wide range of loads (10 – 30000 μN) and indentation depths (30 – 3000 nm). The creep compliance J(t) and relaxation modulus G(t) have been calculated from experimental data as a function of time in the range t = 0.1 – 100 (1000) s. The data are analysed by different rheological models which are compared: (1) the Burgers model, (2) the generalised Maxwell/generalised Kelvin model, and two empirical approaches: (3) a logarithmic model, and (4) a power law model. The Burgers model gives a poor description of the material behaviour since it assumes a steady-state flow of material which is not observed in the experimental time range. The generalised models yield a set of discrete relaxation- and retardation time constants. It is shown that these time constants do not correlate with specific molecular moving processes in the polymer, but are only one of several possible parameterisations of the creep and relaxation curves. Numerical differentiation of G(t) and J(t) shows that polycarbonate has continuous relaxation- and retardation time spectra, respectively, and the dynamic viscosity η(t) of the material increases linearly with time. The behaviour of polycarbonate is best represented by the empirical power law model, which allows optimum fit of creep/relaxation curves, relaxation and retardation time spectra and time-dependent viscosity.

Study on the performance and sustainability of modified waste crumb rubber and steel slag powder/SBS composite modified asphalt mastic

This study proposes the incorporation of waste steel slag and waste rubber into asphalt to prepare asphalt mastic with increased mechanical properties and can thus concurrently limit environmental pollution from these wastes. The surface of crumb rubber (CR) was activated by NaClO and was then treated with KH550 silane coupling modifier. Dynamic shear rheometer (DSR), multi-stress creep recovery (MSCR) and zero shear viscosity (ZSV) tests were applied explore the high temperature performance of asphalt mastic. The performance of asphalt mastic was analyzed by Burgers model, and the enhancement mechanism was analyzed by Fourier transform infra-red (FTIR) spectroscopy, scanning electron microscopy (SEM), energy dispersive X-ray (EDX), fluorescent microscopy (FM), and X-ray diffraction (XRD). Experimental results showed that coupling modified CR improved the complex modulus (G*) and rutting factor (G*/sinδ) and reduced the temperature sensitivity of asphalt mastic. The coupling modified CR increased the elasticity coefficient E1, viscosity coefficient η1, relaxation time η1/E1 and delay time η2/E2 of asphalt mastic by 2.8 times, 3.6 times, 1.3 times and 0.9 times, respectively, while steel slag powder (SSP) further enhanced the mechanical properties of the asphalt mastic. FM test showed that coupling modifier CR promoted the swelling of CR and SBS polymer, and hence resulted in a well-developed cross-linked network structure in the asphalt. The positive effect of SSP on the high temperature properties of asphalt mastic suggests that the use of SSP and CR in pavement engineering provides a sustainable solution for the disposal of industrial wastes and the preparation of new asphalt mastic with higher mechanical and thermal properties for practical applications.

Influence of corn resistant starches type III on the rheology, structure, and viable counts of set yogurt

The study intended to explore the influence of corn resistant starches type III (RS3s) prepared by autoclave, debranching, and microwave heat on the rheology, structure, and viable counts of set yogurt. The rheological analysis suggested that RS3s enhanced the elastic and viscous modulus of yogurt, and that microwave-heated RS was the most effective for improving viscoelasticity. Fitting the creep data using the Burger model showed that yogurt with microwave-heated RS increased the structural strength of yogurt, which displayed the highest instantaneous and viscoelastic deformations. The confocal laser scanning microscopy and scanning electron microscopy micrographs demonstrated that autoclaved and debranched RS3s formed large fragments and disrupted the continuity of the milk protein structure; however, microwave-heated RS evenly filled the gel network and formed an interpenetrating network with proteins. The bacterial count and acidity of yogurt indicated that microwave-heated and debranched RS3s promoted the growth of lactic acid bacteria and accelerated the fermentation process of yogurt. The results of this study demonstrated that microwave-heated RS is a favorable supplement to the microstructure and rheological properties of yogurt compared with autoclaved and debranched RS3s.

Studies on the validity of strain sensors for pavement monitoring: A case study for a fiber Bragg grating sensor and resistive sensor

To address the problems associated with the validity of pavement sensor measurement, a method of combining indoor experiments with finite element (FE) simulations for strain measurement in asphalt pavement is developed in this paper to analyze the validity of strain sensors for practical measurements. First, correlation analysis and one-way analysis of variance (ANOVA) between the simulated strain and the measured strain of the resistive (R) sensor and the fiber Bragg grating (FBG) sensor are developed, and the results show that the strain simulation of asphalt mixtures with sensors by means of FE simulation is feasible for short-term loading tests; therefore, the simulated strain without sensors is considered the true strain. The FBG sensor is more appropriate than the R sensor for use in the measurement of horizontal strain based on the stability of the regression model. Furthermore, creep experiments and FE simulations with a modified Burgers model are developed, and the results demonstrate that the FE simulation is also effective for long-term dynamic loading tests. Finally, the effect of the ratio of the modulus of the FBG sensor to that of the asphalt mixture on the stability of the regression model is analyzed, and the results suggest that the stability worsens as the modulus ratio increases at the same temperature, which could guide the selection of encapsulating materials. Moreover, the research method could also provide resources for studying the validity of sensors under more complex loading modes.

The Creep Test Study and Macro‐Detail Analysis of Argillaceous Red Sandstone in Different Water‐Containing States

In order to study the creep characteristics and failure mechanism of argillous red sandstone in a water‐bearing state, uniaxial creep tests of argillous red sandstone under dry and saturated states are carried out under fractional loading. Burgers model is used to fit the test results and identify the parameters, and scanning electron microscopy is carried out on the cross section of the damaged sample. The mechanism of creep difference of argillaceous red sandstone with different water content is studied from the microscopic point of view. The results show that the uniaxial compressive strength of the saturated clay red sandstone is 46% of that of the dry clay red sandstone. The deformation level of the saturated clay red sandstone is lower than that of the dry clay red sandstone. The limit deformation of the creep failure of the water‐bearing clay red sandstone is much smaller than that of the dry clay red sandstone. The long‐term strength of the muddy red sandstone is 46.4 MPa in the dry state and only 14.1 MPa in the saturated state, as calculated at the steady‐state creep rate. It is found that the Burgers model can describe the attenuation and stable creep of muddy red sandstone well. Through macro‐ and microanalysis, it is found that the compression failure form of argillaceous red sandstone belongs to x‐shaped conjugate inclined plane shear failure. After saturation, the internal pores of argillaceous red sandstone become larger, and the cementation ability decreases, resulting in the decrease of rock sample strength.

Nonlinear Creep Model and Parameter Determination of Asphalt

Asphalt is a kind of typical viscoelastic material. Adding different materials in asphalt composite materials is an important way in road engineering materials. The creep experiments under different stress of asphalt, we used the multivariate model to fit the experimental data to get Burgers model and the creep law of asphalt correlation is best. The Burgers model be expanded by Taylor series, the polynomial creep model of creep compliance and relaxation characterized the coefficient of asphalt specimen can be obtained. Compared to other models, the creep law of asphalts well characterized by polynomial model, multivariate model has a wider range of adaptability compared to polynomial model, and polynomial model of mathematical calculation more simple than multivariate model.