scholarly journals An Improved Bingham Model and the Parameter Identification of Coal (Rock) Containing Water Based on the Fractional Calculus Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Feng He ◽  
Song Yang ◽  
Tianjiao Ren ◽  
Hongjie Bian ◽  
Haoran Li
Keyword(s):  
Fractional Calculus ◽  
Least Squares Method ◽  
Creep Model ◽  
Creep Process ◽  
Relaxation Equation ◽  
Bingham Model ◽  
Creep Equation ◽  
Nonlinear Fitting ◽  
Transient Strain ◽  
Coal Rock

The rheological properties of coal (rock) containing water cannot be characterized by the traditional Bingham model. This problem was addressed in this study through theoretical analysis and experimental research. Based on fractional calculus theory, a fractional calculus soft element was introduced into the traditional Bingham model. An improved Bingham model creep equation and a relaxation equation were obtained through theoretical derivations. Triaxial creep experiments of coal (rock) with different moisture contents were conducted. The parameters of the improved Bingham model were obtained by the least-squares method. Conclusions are as follows: (1) in the improved Bingham model, the stage of nonlinear accelerated creep could be characterized by the creep curves of the soft element; (2) with the increasing moisture content of the coal (rock), the transient strain and the slope of the steady creep stage increased and the total creep time showed a decreasing trend; and (3) the parameters of the creep model were obtained by nonlinear fitting of experimental data, and the fitted curve could better describe the whole creep process. The rationality of the improved creep model was verified. It can provide a theoretical basis for the study and engineering analysis of coal (rock).

scholarly journals Study on Creep Characteristics and Constitutive Relation of Fractured Rock Mass

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Maotong Li ◽  
Kesheng Li ◽  
Deng Zhang ◽  
Chuanxiao Liu ◽  
Depeng Ma
Keyword(s):  
Rock Mass ◽  
Creep Curve ◽  
Fractured Rock ◽  
Damage Variable ◽  
Creep Model ◽  
Creep Process ◽  
Fractured Rock Mass ◽  
Creep Equation ◽  
Creep Characteristics ◽  
Fractured Coal

In order to effectively describe the whole creep process of fractured rock mass, triaxial unloading creep tests were carried out on prefractured coal samples using constant axial pressure and graded unloading confining pressure, and the axial and lateral creep laws of fractured coal samples with different dip angles were studied. Combined with the characteristics of creep curve and based on Kachanov’s creep damage theory, the damage variable is introduced into the constitutive relation and creep equation, and the evolution equation of damage variable with time in the whole creep process is derived. At the same time, a new method to calculate the initial damage is proposed. The elastoplastic body with damage variable is connected with the Burgers model in series. Meanwhile, lade criterion and switch element are introduced into the creep model to establish a new fracture damage creep model. The one-dimensional and three-dimensional damage creep equations are derived. The damage creep equation is obtained according to the superposition principle. A simple and feasible method for parameter identification of the model is given based on the characteristics of creep curve. The applicability of the model is verified by comparing the creep test curve of fractured coal sample with the theoretical curve. The results show that the two models are in good agreement. The model can not only accurately reflect the nonlinear characteristics of creep curves in the attenuation and isokinetic stages but also describe the accelerated creep characteristics of fractured rocks.

scholarly journals A Phenomenological Primary–Secondary–Tertiary Creep Model for Polymer-Bonded Composite Materials

Polymers ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 2353
Author(s):  
Xiaochang Duan ◽  
Hongwei Yuan ◽  
Wei Tang ◽  
Jingjing He ◽  
Xuefei Guan
Keyword(s):  
Composite Materials ◽  
Creep Behavior ◽  
Reference Model ◽  
Creep Model ◽  
Creep Process ◽  
Validation Dataset ◽  
Testing Conditions ◽  
Proposed Model ◽  
Testing Data ◽  
Bonded Composite

This study develops a unified phenomenological creep model for polymer-bonded composite materials, allowing for predicting the creep behavior in the three creep stages, namely the primary, the secondary, and the tertiary stages under sustained compressive stresses. Creep testing is performed using material specimens under several conditions with a temperature range of 20 °C–50 °C and a compressive stress range of 15 MPa–25 MPa. The testing data reveal that the strain rate–time response exhibits the transient, steady, and unstable stages under each of the testing conditions. A rational function-based creep rate equation is proposed to describe the full creep behavior under each of the testing conditions. By further correlating the resulting model parameters with temperature and stress and developing a Larson–Miller parameter-based rupture time prediction model, a unified phenomenological model is established. An independent validation dataset and third-party testing data are used to verify the effectiveness and accuracy of the proposed model. The performance of the proposed model is compared with that of an existing reference model. The verification and comparison results show that the model can describe all the three stages of the creep process, and the proposed model outperforms the reference model by yielding 28.5% smaller root mean squared errors on average.

Analysis of Thick-Walled Pipeline Elements Operating in Creep Conditions

2015 ◽  
Vol 712 ◽  
pp. 63-68
Author(s):  
Przemysław Osocha ◽  
Bohdan Węglowski
Keyword(s):  
Finite Element ◽  
Test Data ◽  
Creep Test ◽  
Power Plants ◽  
Steam Pressure ◽  
Creep Model ◽  
Creep Process ◽  
Fe Model ◽  
Element Analysis ◽  
Wide Range

In some coal-fired power plants, pipeline elements have worked for over 200 000 hours and increased number of failures is observed. The paper discuses thermal wear processes that take place in those elements and lead to rupture. Mathematical model based on creep test data, and describing creep processes for analyzed material, has been developed. Model has been verified for pipeline operating temperature, lower than tests temperature, basing on Larson-Miller relation. Prepared model has been used for thermal-strength calculations based on a finite element method. Processes taking place inside of element and leading to its failure has been described. Than, basing on prepared mathematical creep model and FE model introduced to Ansys program further researches are made. Analysis of dimensions and shape of pipe junction and its influence on operational element lifetime is presented. In the end multi variable dependence of temperature, steam pressure and element geometry is shown, allowing optimization of process parameters in function of required operational time or maximization of steam parameters. The article presents wide range of methods. The creep test data were recalculated for operational temperature using Larson-Miller parameter. The creep strain were modelled, used equations and their parameters are presented. Analysis of errors were conducted. Geometry of failing pipe junction was introduced to the Ansys program and the finite element analysis of creep process were conducted.

scholarly journals Research on Rock Creep Characteristics Based on the Fractional Calculus Meshless Method

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Gang Peng ◽  
Zhanqing Chen ◽  
Jiarui Chen
Keyword(s):  
Fractional Calculus ◽  
Meshless Method ◽  
Test System ◽  
Constitutive Relationship ◽  
Creep Process ◽  
Kelvin Model ◽  
Related Data ◽  
Model Based ◽  
Rock Creep ◽  
Generalized Kelvin Model

The application of fractional calculus in the rheological problems has been widely accepted. In this study, the constitutive relationship of the generalized Kelvin model based on fractional calculus was studied, and the meshless method was introduced so as to derive a new meshless algorithm formula based on the fractional calculus of the generalized Kelvin model. By using the MTS815.02 hydraulic servo rock mechanics test system, the creep test of mudstones is carried out, and the related data of the creep process were obtained. Based on the generalized Kelvin model of fractional calculus, the related creep parameters of the argillaceous sandstone under compression were fitted. The results showed that the solution of the generalized Kelvin model based on fractional calculus was greatly consistent with the numerical method solution. Meanwhile, the meshless algorithm based on fractional calculus had a favorable stability and accuracy.

scholarly journals Nonlinear Viscoelastic-Plastic Creep Model of Rock Based on Fractional Calculus

2022 ◽  
Vol 2022 ◽  
pp. 1-7
Author(s):  
Erjian Wei ◽  
Bin Hu ◽  
Jing Li ◽  
Kai Cui ◽  
Zhen Zhang ◽  
...  
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Engineering Application ◽  
Creep Model ◽  
Nonlinear Viscoelastic ◽  
Rock Creep ◽  
Order Change ◽  
Creep Constitutive Model ◽  
Plastic Creep

A rock creep constitutive model is the core content of rock rheological mechanics theory and is of great significance for studying the long-term stability of engineering. Most of the creep models constructed in previous studies have complex types and many parameters. Based on fractional calculus theory, this paper explores the creep curve characteristics of the creep elements with the fractional order change, constructs a nonlinear viscoelastic-plastic creep model of rock based on fractional calculus, and deduces the creep constitutive equation. By using a user-defined function fitting tool of the Origin software and the Levenberg–Marquardt optimization algorithm, the creep test data are fitted and compared. The fitting curve is in good agreement with the experimental data, which shows the rationality and applicability of the proposed nonlinear viscoelastic-plastic creep model. Through sensitivity analysis of the fractional order β2 and viscoelastic coefficient ξ2, the influence of these creep parameters on rock creep is clarified. The research results show that the nonlinear viscoelastic-plastic creep model of rock based on fractional calculus constructed in this paper can well describe the creep characteristics of rock, and this model has certain theoretical significance and engineering application value for long-term engineering stability research.

scholarly journals Nonlinear Viscoelastic–Plastic Creep Model Based on Coal Multistage Creep Tests and Experimental Validation

Energies ◽  
2019 ◽  
Vol 12 (18) ◽  
pp. 3468 ◽  
Author(s):  
Junxiang Zhang ◽  
Bo Li ◽  
Conghui Zhang ◽  
Peng Li
Keyword(s):  
Creep Behavior ◽  
Physical Property ◽  
Creep Model ◽  
Creep Process ◽  
Creep Tests ◽  
Model Based ◽  
Nonlinear Viscoelastic ◽  
Improved Model ◽  
And Control ◽  
Plastic Creep

The development of fractures, which determine the complexity of coal creep characteristics, is the main physical property of coal relative to other rocks. This study conducted a series of multistage creep tests to investigate the creep behavior of coal under different stress levels. A negative elastic modulus and a non-Newtonian component were introduced into the classical Nishihara model based on the theoretical analysis of the experimental results to propose a nonlinear viscoelastic–plastic creep model for describing the non-decay creep behavior of coal. The validity of the model was verified by experimental data. The results show that this improved model can preferably exhibit decelerating, steady state, and accelerating creep behavior during the non-decay creep process. The fitting accuracy of the improved model was significantly higher than that of the classical Nishihara model. Given that acceleration creep is a critical stage in predicting the instability and failure of coal, its successful description using this improved model is crucial for the prevention and control of coal dynamic disasters.

Nonlinear Damage Creep Model of Coal or Rock Containing Gas

2012 ◽  
Vol 204-208 ◽  
pp. 289-296
Author(s):  
Xiao Bin Yang ◽  
Yang Li ◽  
Hai He Guan ◽  
Tian Yang Li ◽  
Jie Shan He
Keyword(s):  
Gas Absorption ◽  
Creep Model ◽  
Creep Experiment ◽  
Creep Equation ◽  
Stick Slip ◽  
Kelvin Model ◽  
Creep Properties ◽  
Material Parameters ◽  
Whole Process ◽  
Creep Curves

In order to study the creep properties of coal or rock containing gas, the creep properties of coal or rock without gas were studied firstly. Through analyzing the previous creep experiment results of coal or rock, one nonlinear damage creep model of coal or rock was founded based on the general Kelvin model. In this model, assumed that the damage is a function of stress level and time, and introduced one nonlinear hardened function into the general Kelvin model, the nonlinear damage fading creep equation and the nonlinear damage creep whole process equation were obtained. Besides this model, considering the composite structure of coal or rock, gas and gas absorption layer, and assuming that this structure has the stick-slip property under the outside load, so a stick-slip module was added in the general Kelvin model and a new nonlinear damage creep model of coal or rock containing gas was founded. Given the value of the material parameters in the two equations, the creep curves varied with the time were drawn under different axial compression. Through the theoretical curves, the nonlinear damage creep model in this paper was proved to be rational.

scholarly journals New Maxwell Creep Model Based on Fractional and Elastic-Plastic Elements

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Hao Tang ◽  
Dongpo Wang ◽  
Zhao Duan
Keyword(s):  
Rock Salt ◽  
Damage Mechanics ◽  
Rheological Behaviour ◽  
Creep Model ◽  
Creep Data ◽  
Creep Equation ◽  
New Model ◽  
Elastic Plastic ◽  
Simulation Performance ◽  
Model Based

Creep models are mainly used to describe the rheological behaviour of geotechnical materials. An important research focus for studying creep in geotechnical materials is the development of a model with few parameters and good simulation performance. Hence, in this study, by replacing the Newtonian dashpot and spring in the classical Maxwell model with fractional and elastic-plastic elements, a new Maxwell creep model based on fractional derivatives and continuum damage mechanics was developed. One- and three-dimensional (1D/3D) creep equations of the new Maxwell creep model were derived. The 1D creep equation of the new model was used to fit existing creep data of rock salt, and the 3D creep equation was used to fit the creep data of remolded loess. The model curves matched the creep data very well, showing considerably higher accuracy than other models. Furthermore, a sensitivity study was carried out, showing the effects of the fractional derivative order β and exponent α on the creep strain of rock salt. This new model is simple with few parameters and can effectively simulate the complete creep behaviour of geotechnical materials.

Study on Nonlinear Viscoelasto-Plastic Creep Model of Deep Soft Rock

2012 ◽  
Vol 430-432 ◽  
pp. 168-172 ◽  
Author(s):  
Yan Chun Wang ◽  
Yong Yan Wang
Keyword(s):  
Least Squares Method ◽  
Soft Rock ◽  
Creep Model ◽  
Nonlinear Creep ◽  
Test Results ◽  
Mechanical Behaviors ◽  
Exponential Equation ◽  
Creep Stage ◽  
Three Stages ◽  
Plastic Creep

Based on the mechanical behaviors of deep soft rock at the accelerating creep stage, a nonlinear rheological cell containing exponential equation replaces classic linear cell, a new nonlinear viscoelasto-plastic creep model of deep soft rock is established on the basis of Nishihara model, and the model can describe the three stages of rock nonlinear creep. Using the least squares method of Matlab to investigate test results, the result shows the new nonlinear creep model accords better with the creep test curves, and verify correctness of the new model.

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