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

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).

A new fractal viscoelastic element: Promise and applications to Maxwell-rheological model

This paper proposes a fractal viscoelastic element via He?s fractal derivative, its properties are analyzed in details by the two-scale transform for the first time. The element is used to establish a fractal Maxwell-rheological model(FMRM), which unifies the fractal creep equation and relaxation equation, and includes the classic elastic model and the classical Maxwell-rheological model as two special cases. This paper sheds a bright light on viscoelasticity, and the model can find wide applications in rock mechanics, plastic mechanics, and non-continuum mechanics.

Study on Prediction Method for Postconstruction Settlement of Loess Fill Foundation in Northern Shaanxi, China

In order to solve the problem of shortage of construction land in the loess hilly and gully area of northern Shaanxi, the local people usually adopted the method of excavating and filling. The postconstruction settlement was an important index to evaluate the stability of the loess fill foundation. Through laboratory test analysis, the stress-strain and the strain-time relationship of compacted loess were obtained. It showed that the stress-strain curves varied as power functions, and the relationship between strain and time was hyperbolic. Based on the layerwise summation method, a creep equation to predict the postconstruction settlement of loess fill foundation was established. The field monitoring data show that the fitting effect is better. Using this equation, the postconstruction settlement of loess fill foundation with different compaction coefficients and thickness was predicted. Finally, the stability evaluation criteria of loess fill foundation with various thickness and compaction coefficient were proposed. This method provided a new idea to solve the problem of postconstruction settlement of loess fill foundation.

Study on Creep Characteristics and Constitutive Relation of Fractured Rock Mass

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.

New Developments in Understanding Harper–Dorn, Five-Power Law Creep and Power-Law Breakdown

This paper discusses recent developments in creep, over a wide range of temperature, that may change our understanding of creep. The five-power law creep exponent (3.5–7) has never been explained in fundamental terms. The best the scientific community has done is to develop a natural three power-law creep equation that falls short of rationalizing the higher stress exponents that are typically five. This inability has persisted for many decades. Computational work examining the stress-dependence of the climb rate of edge dislocations may rationalize the phenomenological creep equations. Harper–Dorn creep, “discovered” over 60 years ago, has been immersed in controversy. Some investigators have insisted that a stress exponent of one is reasonable. Others believe that the observation of a stress exponent of one is a consequence of dislocation network frustration. Others believe the stress exponent is artificial due to the inclusion of restoration mechanisms, such as dynamic recrystallization or grain growth that is not of any consequence in the five power-law regime. Also, the experiments in the Harper–Dorn regime, which accumulate strain very slowly (sometimes over a year), may not have attained a true steady state. New theories suggest that the absence or presence of Harper–Dorn may be a consequence of the initial dislocation density. Novel experimental work suggests that power-law breakdown may be a consequence of a supersaturation of vacancies which increase self-diffusion.

New Developments in Understanding Harper-Dorn, Five- power Law Creep and Power-law Breakdown

This paper discusses recent developments in creep, over a wide range of temperature, that mqy change our understanding of creep. The five-power law creep exponent (3.5 to 7) has never been explained in fundamental terms. The best the scientific community has done is to develop a natural three power-law creep equation that falls short of rationalizing the higher stress exponents that are typically five. This inability has persisted for many decades. Computational work examining the stress-dependence of the climb rate of edge dislocations we may rationalize the phenomenological creep equations. Harper-Dorn creep, “discovered” over 60 years ago has been immersed in controversy. Some investigators have insisted that a stress exponent of one is reasonable. Others believe that the observation of a stress exponent of one is a consequence of dislocation network frustration. Others believe the stress exponent is artificial due to the inclusion of restoration mechanisms such as dynamic recrystallization or grain growth that is not of any consequence in the five power-law regime. Also, the experiments in the Harper-Dorn regime, which accumulate strain very slowly (sometimes over a year) may not have attained a true steady state. New theories suggest that absence or presence of Harper-Dorn may be a consequence of the initial dislocation density. Novel experimental work suggests that power-law breakdown may be a consequence of a supersaturation of vacancies which increase self-diffusion.

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

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 the Creep Behaviors of Interactive Marine-Terrestrial Deposit Soils

The interactive marine-terrestrial (IMT) deposit soils were formed in the complex depositional environment; their mechanical properties are different from the other deposits. The creep behaviors of Dalian clayey soils were studied according to one-dimensional creep tests and drained triaxial creep tests. Based on the creep test results, the empirical model was established to describe the one-dimensional creep behavior and triaxial creep behavior, respectively. The results showed that Dalian deposits have typical nonlinear creep behavior. With the increasing of consolidation pressure, the strain is increased, the stability time is extended, and the demarcation point between primary and secondary consolidation is more obvious. The deposits belong to medium to high secondary compressibility soil, and the secondary consolidation coefficient is decreased with the increasing of consolidation time and increased with consolidation pressure increasing. The ratio between secondary consolidation coefficient and compression index at different depths changes from 0.033 to 0.058, which conform to Mesri conclusion. Under low deviator stress, the creep processes showed the characteristic of attenuation creep and shear contraction. However, it showed the characteristic of acceleration creep, shear contraction, and shear dilatancy under damage deviator stress. The axial strain rate decreased with the increasing of creep time and increased with the deviator stress increasing, while the deviator stress has little effect on the m values. The tests results agree well with the calculation results, which showed that the creep equation is suitable for describing the creep behaviors of Dalian interactive marine-terrestrial deposits.