Creep experiment and rheological model of deep saturated rock

By the methods of uniaxial single-stage loading and graded incremental cyclic loading, the creep experiments were performed on the deep saturated rock from Dongguashan Mine, and the creep curves of saturated rock under different loading stresses were obtained. By comparing with the creep rule of dry rock in the same location, the creep rule of deep saturated rock was analyzed. Based on the united rheological mechanical model, the rheological model of deep saturated rock was recognized, and the parameters of the model were determined. The results show that the creep curves are very smooth under low stress, but the phenomena of wave and catastrophe turn up under high stress, and the bearing capacity of rock is weakening over time. The rheological properties of saturated and dry rocks are very different under tlie condition of deep high stress, especially when unloading, degradation and damage of rock quality is more serious, and the effect of water cannot be neglected. The H--HIN--NJS model （Schofield-Scott-Blair model） was selected to represent the rheology rule of deep saturated rock, and the fitting curves of model agree well with the experiment data, so the selected model is reasonable.

Integrated identification method of rheological model of sandstone in Sanmenxia bauxite

Based on the uniaxial compression creep experiments conducted on bauxite sandstone obtained from Sanmenxia,typical creep experiment curves were obtained.From the characteristics of strain component of creep curves,the creep strain is composed of instantaneous elastic strain,ε（me）,instantaneous plastic strain,ε（mp）,viscoelastic strain,ε（ce）,and viscoplastic strain,ε（cp）.Based on the characteristics of instantaneous plastic strain,a new element of instantaneous plastic rheology was introduced,instantaneous plastic modulus was defined,and the modified Burgers model was established.Then identification of direct screening method in this model was completed.According to the mechanical properties of rheological elements,one- and three-dimensional creep equations in different stress levels were obtained.One-dimensional model parameters were identified by the method of least squares,and in the process of computation,Gauss-Newton iteration method was applied.Finally,by fitting the experimental curves,the correctness of direct method model was verified,then the examination of posterior exclusive method of the model was accomplished.The results showed that in the improved Burgers models,the rheological characteristics of sandstone are embodied properly,microscopic analysis of creep curves is also achieved,and the correctness of comprehensive identification method of rheological model is verified.

MORPHOLOGICAL MODEL FOR RHEOLOGICAL PROPERTIES OF PLANT CELL SUSPENSION CULTURE SYSTEM

This paper puts forward a physical and mathematical model for the rheological properties of a plant cell suspension culture system.The model can explain why the system is pseudoplastic satisfactorily,thus the rheological properties of the system as the effect of the flow behavior index on plant cell concentration are interpreted correctly and the mechanism of the rheological properties of the system is further understood.Therefore the model can be applied in the technological design and optimum conditions of the system and the reformation,evaluation and scale up of reactors.

A new shear rheological model for a soft interlayer with varying water content

The rheological behavior of a soft interlayer is critical to understanding slope stability, which is closely related to the water content of the soft interlayer. This study used the soft interlayer of the Permian Maokou Formation in Southwest China as an example to perform ring shear creep tests with different water content amounts. The effect of water content on the creep properties of the soft interlayer was analyzed, and a new shear rheological model was established. This research produced several findings. First, the ring shear creep deformation of the soft interlayer samples varied with the water content and the maximum instantaneous shear strain increment occurred near the saturated water content. As the water content increased, the cumulative creep increment of the samples increased. Second, the water content significantly affected the long-term strength of the soft interlayer, which decreased with the increase of water content, exhibiting a negative linear correlation. Third, a constitutive equation for the new rheological model was derived, and through fitting of the ring shear creep test data, the validity and applicability of the constitutive equation were proven. This study has developed an important foundation for studying the long-term deformation characteristics of a soft interlayer with varying water content.

Modeling the viscoelasto-plastic behavior of waxy crude

Waxy crude oil exhibits complex rheological behavior below the pour point temperature, such as viscoelasticity, yield stress, and thixotropy, owing to the formation of a three-dimensional spongelike interlock network structure. This viscoelasto-thixotropic behavior is an important rheologieal behavior of waxy crude oils, determining the flow recovery and safe restart of crude oil pipelines. Up to now, the thixotropic models for waxy crude have been all viscoplastic models, without considering the viscoelastic part before the yield point. In this work, based on analyzing the variation of the elastic stress and viscous stress in the Mujumbar model, a new viscoelasto-plastic model is proposed, whose shear stress is separated into an elastic component and a viscous component. The elastic stress is the product of the shear modulus and elastic strain; the shear modulus is proportional to the structural parameter. For the elastic strain, we followed the line of Zhu and his coauthors and assumed that it may be expressed by an algebraic equation. The model is validated by stepwise shear rate tests and hysteresis loop tests on Daqing and Zhongyuan waxy crude. The results show that the model＇s fitting and predictive capability is satisfactory.

A nonlinear rheological damage model of hard rock

By adopting cyclic increment loading and unloading method, time-independent and time-dependent strains can be separated. It is more reasonable to describe the reversible and the irreversible deformations of sample separately during creep process. A nonlinear elastic-visco-plastic rheological model is presented to characterize the time-based deformational behavior of hard rock. Specifically, a spring element is used to describe reversible instantaneous elastic deformation. A reversible nonlinear visco-elastic （RNVE） model is developed to characterize recoverable visco-elastic response. A combined model, which contains a fractional derivative dashpot in series with another Hook’s body, and a St. Venant body in parallel with them, is proposed to describe irreversible visco-plastic deformation. Furthermore, a three-stage damage equation based on strain energy is developed in the visco-plastic portion and then nonlinear elastic-visco-plastic rheological damage model is established to explain the trimodal creep response of hard rock. Finally, the proposed model is validated by a laboratory triaxial rheological experiment. Comparing with theoretical and experimental results, this rheological damage model characterizes well the reversible and irreversible deformations of the sample, especially the tertiary creep behavior.

Simulation of rheological behavior of asphalt mixture with lattice model

A three-dimensional(3D) lattice model for predicting the rheological behavior of asphalt mixtures was presented.In this model asphalt mixtures were described as a two-phase composite material consisting of asphalt sand and coarse aggregates distributed randomly.Asphalt sand was regarded as a viscoelastic material and aggregates as an elastic material.The rheological response of asphalt mixture subjected to different constant stresses was simulated.The calibrated overall creep strain shows a good approximation to experimental results.

A RHEOLOGICAL MODEL FOR POLYMER MELTS WITH INTERNAL STRUCTURE IN FLOW FIELDS

Conceptually, an imagined conformation ellipsoid is supposed to represent the shape of a polymer chain for polymer melts in flow fields and to be equivalent to the volume element in a mathematical sense in continuum mechanics. A power law dependence of shear modulus of polymer melts on detC, referred to as envelope volume, is proposed. Based on those assumptions and the non-linear relation of shear modulus, a phenomenological viscoelastic model is derived. The model is tested in simple shear flow, simple elongational flow, oscillatory shear flow, and relaxation process after flow suddenly stopped. The results show that the model works well to predict the change of internal structure and viscoelastic performance of polymer melts in flow fields.

A Nonlinear Rheological Model of Soft Clay and Its Application in Settlement of Sunk Ship

A one-dimensional consolidation-creep model test on the creep deformation of soft muddy clay in the littoral area of Tianjin is performed. A nonlinear rheologic model is established and the model coefficients are determined, in consideration of the characteristics of soft muddy clay. Furthermore, a settlement equation is deduced from the theologic model and verified by the field settlement measurements of Beitang Reservoir dam in Tianjin littoral area. Finally, the settlement e- quation is applied in calculating the settlement of ＂FAIRWAY-＂ suction dredger, which sunk in the external channel of Tianjin Port, induced by the soft clay consolidation of seabed. These results provide useful information for the decision of salvage plan.

Review of Non-Newtonian Mathematical Models for Rheological Characteristics of Viscoelastic Composites

This study presents an overview of viscoelastic characteristics of biocomposites derived of natural-fibre-reinforced thermoplastic polymers and predictive models have been presented in order to understand their rheological behavior. Various constitutive equations are reviewed for a better understanding of their applicability to polymer melt in determining the viscosity. The models to be investigated are the Giesekus-Leonov model, the Upper Convected Maxwell (UCM) model, the White-Metzner model, K-BKZ model, the Oldroyd-B model, and the Phan-Thien-Tanner models. The aforementioned models are the most powerful for predicting the rheological behavior of hybrid and green viscoelastic materials in the presence of high shear rate and in all dimensions. The Phan-Thien Tanner model, the Oldroyd-B model, and the Giesekus model can be used in various modes to fit the relaxation modulus accurately and to predict the shear thinning as well as shear thickening characteristics. The Phan-Thien Tanner, K-BKZ, Upper convected Maxwell, Oldroyd-B, and Giesekus models predicted the steady shear viscosity and the transient first normal stress coefficient better than the White-Metzner model for green-fibre-reinforced thermoplastic composites.

Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅰ:A New Multiple Reptation Model to Predict the Nonlinear Visco-elasticity with Nagai Chain Constraints in Entangled Polymer Melts

An approach of stochastically statistical mechanics and a unified molecular theory of nonlinear viscoelasticity with constraints of Nagai chain entanglement for polymer melts have been proposed. A multimode model structure for a single polymer chain with n tail segments and N reversible entanglement sites on the test polymer chain is developed. Based on the above model structure and the mechanism of molecular flow by the dynamical reorganization of entanglement sites, the probability distribution function of the end-to-end vectr for a single polymer chain at entangled state and the viscoelastic free energy of deformation for polymer melts are calculated by using the method of the stochastically statistical mechanics. The four types of stress-strain relation and the memory function are derived from this thery. The above theoretical relations are verified by the experimentaf data for various polymer melts. These relations are found to be in good agreement with the experimental results

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.

Identification of structure and parameters of rheological constitutive model for rocks using differential evolution algorithm

To determine structure and parameters of a rheological constitutive model for rocks,a new method based on differential evolution(DE) algorithm combined with FLAC3D(a numerical code for geotechnical engineering) was proposed for identification of the global optimum coupled of model structure and its parameters.At first,stochastic coupled mode was initialized,the difference in displacement between the numerical value and in-situ measurements was regarded as fitness value to evaluate quality of the coupled mode.Then the coupled-mode was updated continually using DE rule until the optimal parameters were found.Thus,coupled-mode was identified adaptively during back analysis process.The results of applications to Jinping tunnels in China show that the method is feasible and efficient for identifying the coupled-mode of constitutive structure and its parameters.The method overcomes the limitation of the traditional method and improves significantly precision and speed of displacement back analysis process.

ON THE RHEOLOGICAL MODEL OF STEELS AT ELEVATED TEMPERATURES

Mechanical properties of steels ZG15CrMoV and 35 in the temperature range of 500 to 1400℃ have been experimently researched by means of Gleeble-1500.The experi- mental results is used as input-output responses,a rhelological model with five elements of the mechanical behaviour of steels ZG15CrMoV and 35 at elevated temperatures, i.e[M]=[H_1]-[H_2/[N_2]-[S/N_3],is determined by a system identification method,and the parameters of the model in the temperature range are also identified.

A new general rheological model for rheological lubrication

Limitation and deficiency of main thcoogical models at present are descrital and analyzed, and seteralgeneral rheological models are discussed and compared with each other, and basic demands for a general model aresummarized. The constitutive eqUation is proposetl for a new general theobocal model. The general medel feaaressimple structure and wide coverage, and can take the Place of many edsting thcofogical ed. The whel has suc-cessfully been used for Elastohydrodynamic lubrication calculation.

PREDICTION OF THE RHEOLOGICAL PROPERTIES OF STAR—TYPE BRANCHED POLYMER SOLUTIONS BY MEANS OF THE FIXED SPECTRUM MODEL

The Rouse-Zimm model with slippage was improved and the basic parameters of modelwere modified to explain the rheological properties of star-type branched polymersolutions. The theoretical results show good agreement with experimental data.

Rheological catastrophic model for soft clays

A brief review of the former studies on the mechanisms of soil rheology and microstructure is presented. Then a microstructure model and a set of rheological constitutive relations for sott clays, which describe how the rheological consolidation settlement develops, are established in the framework of the catastrophe theory. The validity of this model is verified by a series of rheological consolidation experiments with different loading rates. The experimental data show that creep deformation can be clearly observed in these tests, and the consolidation settlement is loading rate dependent. The characteristics of the deformation can be explained and reproduced successfully using the model. It can be concluded that only the biggest set of voids would collapse for one load increment. Parameters in the model, k and η, are gained by curve fitting. With only two free parameters, good fits of the data are achieved.

Modeling the Rheological Characteristics of Flexible High-Yield Pulp-Fibre-Reinforced Bio-Based Nylon 11 Bio-Composite

The aim of this work was to develop a mathematical model to investigate the rheological characteristics of viscoelastic pulp-fibre composite materials. The rheological properties of High-Yield Pulp (HYP) reinforced bio-based Nylon 11 (Polyamide 11) (PA11) composite (HYP/PA11) were investigated using a capillary rheometer. Novel predicted multiphase rheological-model-based polymer, fibre, and interphasial phases were developed. Rheological characteristics of the compo-site components influence the development of resultant microstructures;this in turn affects mechanical characteristics of a multiphase composite. The main rheological characteristics of polymer materials are viscosity and shear rate. Experimental and theoretical test results of HYP/PA11 show a steep decrease in apparent viscosity with increasing shear rate, and this melt-flow characteristic corresponds to shear-thinning behavior in HYP/PA11. The non-linear mathematical model to predict the rheological behavior of HYP/PA11 was validated experimentally at 200°C and 5000 S-1?shear rate. Finally, predicted and experimental viscosity results were compared and found to be in a strong agreement.

Study on Theoretical Modeling of Semi-Active Electro-Rheological Fluid Damper

This paper emphases on analyzing and investigating the mechanical behavior of electro-rheological fluid (ERF) semi-active damper. Theoretical model was developed to describe the relationship between electric field and the resistance force of ERF flowing through two parallel plane electrodes. In the model, the pressure drop along electrodes was supposed to consist of two parts: one related with viscosity and the other related with dynamic yield shear stress. The concept of yield stress influence factor was developed in deriving the theoretical formula for calculating the pressure drop in the damper. The influences of some other factors, such as, non-ideal Newtonian fluid and temperature have also been taken into account. Numerical and experimental work have been performed to prove the validity of the proposed model. The comparison of both results shows that the developed model is quite effective and practicable .

Viscoelasto-plastic properties of deep hard rocks under water environment

Using a circular incremental step load and unload method, a set of rheological experiments were performed to study the viscoelasto-plastic properties of amphibolite in Jinchuan No.2 diggings under different environments. Based on the scientific analysis on rheological experimental data, the viscoelasto-plastic properties of amphibolite under different environments were studied. The results show that the instantaneous elastic modulus and viscoplastic properties of amphibolite are affected little, the viscoelastic properties of amphibolite are significantly affected. Based on the experimental results and characteristics of recovered rock specimen, a generalized Kelvin model was chosen to simulate rheological properties of amphibolites and key parameters were obtained. It is found that the creep deformation modulus E1 is significantly influenced by the water, while the instant elastic modulus E2 is not significantly affected. The discreteness of the viscosity coefficient η is large, the influence of water on η is not clear and needs to be further studied.