Modified Burgers Model Research Articles

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.

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.

Creep Behavior of Intact Loess Followed Unloading Paths

Several high-fill projects are carried out on the Loess Plateau, China, accompanying the progressive failure of slopes due to excavation. The compelling need requires a deep understanding of variation in the creeping behaviors of intact loess exposed to unloading. A series of creep tests of intact loess were performed under two separated unloading paths: decrease in confining pressure at constant deviator stress and decrease in confining pressure at axial stress. The results demonstrated that axial deformation followed the first unloading path always appears as compression while the three forms of axial deformation followed the second path, depending on the applied axial stress level. At a low unloading stress level, the elongation of axial deformation was observed. At a relatively unloading stress level, the axial deformation of the soil experienced the first elongation and then compression. At a high unloading stress level, the axial deformation appeared as compression, and finally, failure occurred with the increase of the unloading stress level. The failure approach index was introduced to use as the criterion for the loess to transform from stable to accelerated creeping. Finally, a modified Burgers model was proposed to characterize the creeping behavior of intact loess followed unloading paths. There was a good comparison between the calculated and measured data of the soil that establishes the rationality and validity of the proposed model.

Comparative Analysis of Viscoelastic Properties of Open Graded Friction Course under Dynamic and Static Loads.

The viscoelastic properties of open graded friction course (OGFC) are closely related to anti-permanent deformation ability, noise reduction ability and durability. To study the viscoelastic parameters of OGFC under dynamic and static loads and to establish the functional relationship between them, uniaxial compression creep tests and dynamic modulus tests were performed to obtain the creep compliance and the dynamic modulus of OGFC. In addition, the Burgers model, modified Burgers model, second-order extensive Maxwell model, Scott-Blair model and modified Sigmoid model were employed to quantitatively analyze the dynamic and static viscoelastic properties of OGFC. Subsequently, the relaxation modulus of OGFC was deduced by the viscoelastic theory. Then, the dynamic modulus of OGFC was calculated according to the deduced relaxation modulus. Based on the calculated values and the measured values of dynamic modulus, the functional relationship of viscoelastic parameters of OGFC under dynamic and static loads was established. The results show that the increase in test temperature has adverse effects on the viscoelastic indexes of OGFC, such as creep compliance, relaxation modulus, and dynamic modulus; the dynamic modulus derived from static creep compliance has a good linear correlation with that obtained by dynamic modulus tests, but the correlation of the phase angle is poor.

Effect of freeze–thaw cycles on the deformation behavior of gravelly soil in the 300 m-high earth core rockfill dam

Many high earth rockfill dams are currently being constructed in the alpine region of Southwest China. Since the effective working time is reduced by the cold climate, it is necessary to solve the problem of intermittent filling of the core wall at low temperature. However, freeze–thaw (FT) cycles in the filling process will change the deformation behavior of gravelly soil. For 300 m-high earth core rockfill dams, the deformation of gravelly soil is a crucial factor in predicting the long-term deformation and settlement after dam construction. To investigate the influence of FT cycles on the deformation characteristics, the deformation of the gravelly soil under different amounts of FT cycles was tested using an MTS-810 test system. The deformation characteristics were discussed, and a modified Burgers model was used to describe the deformation characteristics. The results show that the freeze–thaw action makes the coarse particles break, resulting in an increase in the fine content. The FT cycles can make the creep characteristics of gravelly soil more obvious. The creep strain has a large contribution to the total strain with the increasing in the FT cycles. It is thus suggested that the coverage of thermal insulation material would effectively prevent freezing of the gravelly soil and control the deformation.

Determination and verification of the calculated model parameters of salt rocks taking into account softening and plastic flow

The article suggests using a combination of the modified Burgers model and the Mohr – Coulomb model with the degradation of the adhesion coefficient and the increase in the friction coefficient to determine the parameters of salt rocks. A comparative analysis of long-term laboratory tests and field observations in underground mine workings with the results obtained using a calculated model with certain parameters is carried out. The parameters of the Mohr – Coulomb model with the degradation of the adhesion coefficient and the increase in the friction coefficient were obtained from the statistically processed data of laboratory tests, and the parameters of the modified Burgers model were determined. Using numerical methods, virtual (computer) axisymmetric triaxial tests, both instantaneous and long-term, were performed on the basis of the proposed model with selected parameters. A model problem is solved for comparing the behavior of the model with the data of observation stations in underground mine workings obtained from borehole rod extensometers and contour deformation marks. The analytically obtained coefficients of the nonlinear viscous element of the modified Burgers model for all the analyzed salt rocks did not need to be corrected based on the monitoring results. At the same time, optimization was required for the viscoelastic element coefficients for all the considered rocks. The analysis of the model studies showed a satisfactory convergence with the data on the observation stations. The comparative analysis carried out on the models based on laboratory tests and observations in the workings indicates the correct determination of the parameters for salt rocks and the verification of the model in general.

Experimental Characterization of Viscoelastic Behaviors of Nano-TiO2/CaCO3 Modified Asphalt and Asphalt Mixture.

The purpose of this paper is to promote the application of nano-TiO2/CaCO3 in bituminous materials and present an experimental characterization of viscoelastic behaviors of bitumen and bituminous mixture modified by nano-TiO2/CaCO3. In this work, a series of viscoelastic behavior characterization tests were conducted, including dynamic shear rheometer (DSR) test for bitumen, uniaxial static compression creep test and dynamic modulus test for bituminous mixture. Moreover, various viscoelastic models with clear physical meanings were used to evaluate the influence of nano-TiO2/CaCO3 on the macroscopic performance of bitumen and bituminous mixture. The results show that bitumen and its mixtures are time-temperature dependent. The Christensen-Anderson-Marasteanu (CAM) model of frequency sweep based on DSR test indicated that adding nano-TiO2/CaCO3 can effectively capture the sensitivity of temperature. In addition, the incorporation of nano-TiO2/CaCO3 in bituminous mixture can significantly enhance the high-temperature anti-rutting, and slightly improve the low-temperature anti-cracking as well. At the same time, the modified Burgers model can accurately describe the viscoelastic behavior of bituminous mixtures in the first two creep stages, reflecting the consolidation effect of bituminous mixture. Also, the generalized Sigmoidal model can accurately grasp the characteristics of the relationship between dynamic modulus and reduced frequency and achieve good prediction effects in a wider frequency range.

Study on Mechanical and Viscoelastic Properties of Asphalt Mixture Modified by Diatomite and Crumb Rubber Particles

To optimize the properties of asphalt mixtures and make full use of waste rubber tires, diatomite and crumb rubber particles were applied to reinforce the asphalt mixtures in this study. The rutting tests, the three-point bending tests, the freeze-thaw splitting tests, and the uniaxial compression creep tests were performed to analyze the effects of asphalt types and aggregate gradation on the pavement properties of diatomite and crumb rubber particles reinforced asphalt mixtures (DRPAM). Subsequently, the creep and relaxation characteristics of DRPAM were analyzed by the Burgers model, the modified Burgers model, the second-order extensive Maxwell model, and the Scott–Blair model. The results show that rubber particles and diatomite can reinforce the high temperature, low temperature, and viscoelastic properties of asphalt mixtures, although the improvement effect is weaker than styrene-butadiene-styrene (SBS). Consequently, it is concluded that rubber particle and diatomite compound modified asphalt mixture with suspension dense gradation and SBS binder will have better performance.

Experimental Investigation and Constitutive Modeling of the Uncured Rubber Compound Based on the DMA Strain Scanning Method.

Existing research tends to focus on the performance of cured rubber. This is due to a lack of suitable testing methods for the mechanical properties of uncured rubber, in particular, tensile properties. Without crosslinking by sulfur, the tensile strength of uncured rubber compounds is too low to be accurately tested by general tensile testing machines. Firstly, a new tensile stress testing method for uncured rubber was established by using dynamic thermomechanical analysis (DMA) tensile strain scanning. The strain amplitude was increased under a set frequency and constant temperature. The corresponding dynamic force needed to maintain the amplitude was then measured to obtain the dynamic force-amplitude curve observed at this temperature and frequency. Secondly, the Burgers model is usually difficult to calculate and analyze in differential form, so it was reduced to its arithmetic form under creep conditions and material relaxation. Tensile deformation at a constant strain rate was proposed, so the Burgers model could be modified to a more concise form without any strain terms, making mathematical processing and simulating much more convenient. Thirdly, the rate of the modified Burgers model under constant strain was in good agreement with the test data, demonstrating that the elastic stiffness was 1–2 orders of magnitude less than the tensile viscosity. In the end, it was concluded that large data dispersion caused by the universal tensile test can be overcome by choosing this model, and it may become an effective way to study the tensile modeling of uncured rubber compound.

A modified creep model of polylactic acid (PLA‐max) materials with different printing angles processed by fused filament fabrication

AbstractThe creep behavior caused by the viscous mechanical effect of biodegradable polylactic acid (PLA‐max) material is of great significance to its application. To better understand the creep properties of PLA‐max materials processed by fused filament fabrication, the effects of printing parameters including printing angle and layer thickness on them are studied theoretically and experimentally. The experimental results show that within the range of loading stress and loading time, the creep deformation of the PLA‐max material decreases with the increase of the printing angle or the decrease of the layer thickness. The experimental results are processed and analyzed, and a modified Burger model is proposed to quantitatively analyze the creep deformation of PLA‐max. In this modified Burger model, the four parameters are functions of printing angle and stress level. The modified model can accurately calculate the creep deformation of the specimen at other printing angles, which provides an important reference for the design of functional structures with specific mechanical properties.

Interpreting the creep behavior of asphalt mortar at high temperature through experimental and numerical methods

Rutting or permanent deformation is a major distress for asphalt pavement structures that are subjected to heavy traffic loadings. In this study an experimental study was conducted to evaluate the creep characteristics of asphalt mortar at elevated temperatures. The compressive strength of three types of asphalt mortar gradations used in airfield pavement were tested by the uniaxial compression test at 40 °C, 50 °C and 60 °C. In addition, triaxial creep test was used to test the creep of the three mortars at stress levels of 100 kPa, 300 kPa and 500 kPa. After that, the Burgers model and the modified Burgers model were chosen to simulate the creep curves. Viscoelastic fitting analysis results shown that the correlation R2-value of the two models were found to be greater than 0.95 at each stress level, the Burgers model has an R2 more than 0.98. it indicated that the Burgers model can better describe the creep characteristics of the asphalt mortar under repeated loadings.

Investigating fatigue life prediction of rubber asphalt mixture based on damage evolution using residual strain analysis approach

This study aims to develop the fatigue life (Nf) prediction method of rubber asphalt mixture based on residual strain (RS) analysis by using three-point bending fatigue test. The RS mechanical model established based on the modified Burgers model was used to characterize the evolution laws of RS, the residual viscoelastic strain (RVES) and the residual viscous-flow strain (RVFS), and the mechanical parameter of residual strain ratio (RSR) was defined based on the evolution laws. The correlation analysis was performed to explore the relationship between the Nf and the RSR, and the damage indication was advanced. The damage variable was defined based on the RSR evolution and the established fatigue damage model based on the ExpAssoc damage evolution model was used to perform the damage evolution analysis. The correlation analysis between the RSR and the damage evolution speed (Ds) was conducted to establish the fatigue and remaining fatigue equations. The results showed that RS mainly consisted of RVES and RVFS, and the RVFS was primarily responsible for the material damage. The RS mechanical model can characterize the non-linear evolution laws of RS, RVES and RVFS with sufficient accuracy, and the RVES can be regarded as a constant under given conditions. The RSR characterizing Ds can determine damage evolution and Nf prediction, and define the damage variable by isolating the damage factor from the viscoelastic factor. The established damage model can be capable of capturing the damage evolution of the rubber asphalt mixture. The increased Ds led to the exhibited decrease in the Nf. The established fatigue equation and remaining fatigue equation succeeded in accurately predicting the Nf and remaining fatigue life (Nfr) corresponding to the early damage evolution stage of rubber asphalt mixture, respectively.

Improved nonlinear Burgers shear creep model based on the time-dependent shear strength for rock

Shear strength is an important mechanical index of rock. The adjustment and reorganization of rock structure can be reflected by the variation of shear strength. During rock rheology, the shear strength decreases with time due to rock damage. Therefore, from the point of difference of shear strength, the mechanical properties of rock can be effectively studied. In this paper, for the state of direct shear test, the Kachanov creep damage law was adopted to describe the time characteristics of the rock shear strength during the accelerated creep stage. A nonlinear viscoplastic element on the basis of time-dependent shear strength was established by connecting the plastic element representing shear strength with the viscous element in parallel. After introducing the nonlinear viscoplastic element into the classic Burgers model, the rationality of the model was verified by the shear creep test results of rock discontinuity. Results showed that the modified Burgers model can reflect the mechanical properties of rock in three creep stages. In addition, the model parameter δ can also reflect the evolution of internal cracks in rock during creep.

Moisture content effect on the creep behavior of loess for the catastrophic Baqiao landslide

Understanding the creeping behavior of loess is of great importance as large-scale loess landslides are closely related with creep behavior. At present, it is still challenging to predict and estimate the long-term stability of such landslides. This is in a large degree due to the poor understanding of moisture control on creep behavior of loess. The purpose of this study is to decipher the loess creep behavior under various moisture contents (MCs) using loess specimens obtained from Baqiao landslide, Xi’an of China, using multi-loading triaxial creep tests under different MCs of 9%, 12%, 15%, 18% and 21%. Based on the laboratory test results, a series of relationships between the creep rate at the steady-state creep stage and the initial strain and initial shear modulus are revealed. Meanwhile, a method for obtaining the long-term strength of loess specimens, namely, the Steady-state Creep Rate Slope Method (SCRSM), is proposed. SCRSM resolves the issue in several conventional methods such as the Isochronous Stress-Strain Curve Method, the Tangent Method of Steady Creep Rate when MCs are of concern. Such an improvement is primarily due to a better way of finding the inflection point of the steady-state rate. It is found that SCRSM is robust and accurate to determine the long-term strength of loess specimens. Furthermore, we propose a modified Burgers model with a newly introduced nonlinear parameter n to overcome deficiencies of conventional creep models. This modified Burgers model is flexible to fit the creep test curves of loess, and can describe the curves at the accelerated creep stage more accurately. Lastly, the main factors triggering the Baqiao landslide is analyzed considering stratum lithology, rainfall and excavation. In general, this study provides a basis for understanding the evolutional process of loess landslides as well as guidelines for prevention, controlling and prediction of loess landslides.

Optimizing creep lifetime of friction stir welded PMMA pipes subjected to combined loadings using rheological model

Abstract The most important feature of the polymeric pipes is that they creep even at room temperature. Therefore, investigating the creep behavior of the polymers and their welded joints is a major concern in the mechanical engineering. The aim of this research is to estimate the creep lifetime of the friction stir welded Polymethyl Methacrylate (PMMA) pipes which operate under combined loading. To develop the creep constitutive equations for both weld zone and parent material, creep test samples have been cut from the weld zone and parent material of a PMMA sheet with friction stir butt welded joint. Constant load tests have been carried out at different initial stress and temperature levels. Based on the results of the tests, parameters of the modified Burgers model form of the constitutive equation have been derived. To validate the model, it is introduced to finite element software “ABAQUS” and the simulated creep behavior is compared with the experimental data. Furthermore, the developed constitutive model and the reference stress method (RSM) are used to produce a set of graphs which provide optimum creep lifetime and design conditions for the friction stir welded PMMA pipes that are subjected to combined internal pressure and rotation. The results show that despite using optimum conditions, creep life of the welded pipes is significantly lower than the non-welded pipe.

Thermal creep behavior of shear tabs in fire using modified burgers model

A mechanical model is developed to predict the time-independent (fast) and time-dependent (due to thermal creep) force-rotation characteristics of shear tab connections subjected to fire. The time-independent behavior of the connection is modeled using a group of springs that can predict the rotational stiffness and the strength of the connection when subjected to fire temperatures. A modified Burgers model is incorporated in the mechanical model to include the thermal creep effect. The modified Burgers model is composed of linear springs and viscous dashpots that can predict the time-dependent behavior of the shear tab connection before and after beam-column contact, and bolt bearing. The proposed model shows excellent agreement when compared with experimental results and finite element (FE) simulations. Furthermore, isochronous curves are developed to study explicitly the effect of different parameters, on the strength and rotational capacity of shear tab connections. The proposed model can be considered an important step toward the inclusion of thermal creep in fire design of shear tab connections.

Optimum creep lifetime of Polymethyl Methacrylate (PMMA) tube using rheological creep constitutive models based on experimental data

In this paper, the creep behavior of Polymethyl Methacrylate (PMMA) is investigated both experimentally and numerically at different temperatures (30, 40 and 50 °C) and stress levels. The experimental results show that PMMA has a nonlinear viscoelastic behavior. Hence, to model the creep behavior of PMMA, three types of constitutive models have been proposed: a) the generalized time hardening model, b) Burgers model, c) modified Burgers model. It was found that the generalized time hardening model, which has extensive applications in commercial softwares, predicts the creep behavior of PMMA at higher stress levels but it deviates from the experimental results at lower stress levels. Although, Burgers model predicts the creep behavior of PMMA, to improve the accuracy of the model a modified version of Burgers model has been proposed, which demonstrates very good consistency with the experimental data over the whole range of applied stresses and temperatures. Finally, the results are used to estimate the optimum creep lifetime of a rotating pressurized tube. A set of diagrams, which can be used in industry, have been produced based on each model.

Parameter Sensitivity and Inversion Analysis for a Concrete Face Rockfill Dam Based on CS‐BPNN

The deformation behavior of rockfill is significant to the normal operation of concrete face rockfill dam. Considering both the nonlinear mechanical behavior and long‐term rheological deformation, the E‐ν model and modified Burgers model are coupled to describe the deformation behavior of the rockfill materials. The coupled E‐ν and Burgers model contains numerous parameters with complex relationship, and an efficient and accurate inversion analysis is in demand. The sensitivity of the parameters in the coupled E‐ν and modified Burgers is analyzed using the modified Morris method initially. Then, a new approach of parameter back analysis is proposed by combining back‐propagation neutral network (BPNN) and Cuckoo Search (CS) algorithm. The numerical example shows that parameters K, Rf, and φ0 as well as G are more sensitive to the deformation of the rockfill body. The inversion analysis for these four parameters and η2, E2, and A as well as B in modified Burgers model is performed by the CS‐BPNN algorithm. The numerical results demonstrate that the parameters obtained with the proposed method are reasonable and its feasibility is validated.

Mechanical behavior of sandstone under uniaxial constant cyclical compressive and tensile loading

In order to investigate mechanical behavior of red sandstone under cyclical compressive and tensile loads, a series of short-term uniaxial constant cyclical compressive and tensile loading tests and uniaxial constant cyclical compressive and tensile loading creep tests were conducted. First, based on the results of short-term uniaxial constant cyclical compressive and tensile loading experimental, the permanent residual strain, strains at peak stress were analyzed. Results show that the specimen shows permanent residual strain after suffering short-term cyclic loads; the residual strains and strains at peak stress show the “decay increase” and “steady-state increase” stages with the cyclic number N; the relationship between the strain at peak stress (tensile or compressive stress) and cyclic number can be well described by a modified Burger model. And then, in accordance with the creep experimental results, the creep behavior of the red sandstone was analyzed. Results show that there is obvious instantaneous strain, decay creep, and steady creep under each stress level of tensile or compressive stress stages; the specimen appears accelerated creep stage under the 5th tensile stress of 1.19 MPa. It was also found that power function can better express the relationship between steady strains and cycle number under tensile or compressive stress levels. In the end, a viscoelastic-plastic creep model was proposed; comparison of the test results with the proposed viscoelastic-plastic creep model predictions indicates that the proposed model is capable of describing the creep behavior of red sandstone subjected to cyclic tensile and compressive stress loading.

Study on Creep Characteristics and Constitutive Model for Thalam Rock Mass with Fracture in Tunnel

In the each loading stage, strain and creep strain occurs instantaneously on the axial and lateral of fractured. Instantaneous strain leads to the 80% overall specimen deformation. The axial strain is about 2–3 times larger than the lateral strain. Instantaneous strain completed time and deformations under each loading stage decrease when the loading time increases. With the increasing of loading, axial strain and lateral strain of fractured phyllite present the approximate linear curve growth change. With increasing of axial stress, the relationship between the lateral strain and axial strain transform from the linear increased trend to the index increased trend. With the increasing of moisture content, the axial deformation and lateral deformation of fractured phyllite increase. The curves of axial strain and lateral strain under soaked for 10 and 15 days condition are similar. The modified Burgers model can describe each creep stage of fractured phyllite which have high fitting precision, less fluctuation and high reliability. Therefore, modified Burgers model can provide an effective way to analyze the creep characteristics of fractured phyllite.