The Fractional Derivative Constitutive Model And Micro-Mechanisms Of Salt Rock During Creep

Salt rock is always in a low permeability due to the migration of grain boundary in the creep process.This feature makes salt rock being regarded as the ideal rock material to restore the undergrounding energy resources and preserve the nuclear waste for ages.In engineering applications,water solution mining for deep salt mine to form underground space is the preferred way of energy reserves in the world,whose construction is convenient and quick.The service cycle of the underground storage,which is used for oil and CO2 reserve is usually a long period,especially for high level waste disposal.Because nuclear elements have a long half-life,long-term mechanical behavior must be thought in the design of the storage cavern.Therefore,focusing on the underground energy reserves of deep salt rock and carrying out the research of long-term mechanical properties is important to complete our energy underground reserve program in our country.The typical creep curve of salt rock is divided into three stages:initial stage,steady state stage and acceleration stage.The creep of salt rock has very low strain rate in the steady state stage,but it will produce large deformation in a short time when it enters the acceleration stage.Most of the problems of effective volume loss during the operation of salt rock reservoir are caused by accelerated creep.The reduction of effective volume caused by this deformation is usually irreversible.There are many factors affecting the mechanical properties of saline rock.For natural salt rock,the temperature of the salt layer,the kind and content of impurities in saline rock and the stress state around the salt layer all have great influence on the creep process.Therefore,it is important to fully understand the deformation mechanism of salt rock in the process of creep and to predict the deformation amount at each stage of creep.These studies are useful to the construction of underground storage by salt rock.In view of the above research background and existing problems at the present stage,this paper conducted the research from the following aspects:(1)The creep of salt rock under uniaxial and triaxial compressionIn order to describe the deformation characteristics of the creep stage of salt rock scientifically and quantitatively,it is necessary to establish the theoretical constitutive equation.There are many methods to establish constitutive equations,but all of them need experimental data as support.In particular,empirical formulas require a lot of indoor experiments.In this paper,the creep experiment of uniaxial compression of salt rock is carried out,and the creep curve is drawn.For the creep under complex stress conditions,a triaxial compression creep test was carried out.There are a lot of defects in natural salt rock,During the creep process,the evolution of these defects will cause damage accumulation.In order to describe the damage in salt rock,the ultrasonic longitudinal wave velocity measurement experiment and acoustic emission experiment are used as auxiliary in loading process.The results show that the creep of salt rock has three obvious stages when the load is greater than the yield stress.The measured ultrasonic longitudinal wave velocity and acoustic emission event show that the ultrasonic longitudinal wave velocity in the salt rock is decreasing while releasing a large number of acoustic emission signals with the development of micro defects,which fully reflects the creep damage evolution process of salt rock.Further study finds that under low temperature and low stress conditions,salt rock will remain in the initial creep stage for a long time before entering the steady-state stage.Due to the lack of confining pressure,the salt rock eventually generates expansion failure.Triaxial compression creep experiment shows that the change of deviatoric stress is the main reason for the change of strain rate under the same temperature.When the deviatoric stress and confining pressure are within a certain range,the creep strain rate of salt rock is basically the same,indicating that the deformation mechanism of the creep of salt rock is unchanged within this range,and does not change with the variation of deviatoric stress and confining pressure.(2)The micro-structures of salt rock during creep processNatural salt rock is mainly composed of NaCl,which is a polycrystalline material,and there are a lot of defects and impurities(fluid inclusions,other insoluble particles,etc.).The distribution of these defects,the types of impurities,the purity of salt rock and the temperature of environment have great influence on the creep process of salt rock.Therefore,when studying the creep of salt rock,it should not be confined to the indoor uniaxial and triaxial loading experiments,but more importantly,it should start from the mechanism to study the nature of the creep process.In this paper,a micro observation experiment is carried out for the creep of salt rock,and the creep microstructure of salt rock under various factors and different deformation mechanisms are analyzed.The experimental results show that at the end of the initial stage,the creep of salt rock is mainly dislocation slip,which will produce a large number of net slip lines.In the steady creep stage of salt rock,the cross slip of screw dislocation is the dominant deformation mechanism in the region of high stress and high strain rate,while in the region of low stress and low strain rate,the deformation is mainly determined by the climbing of edge dislocation.At the accelerated creep stage of salt rock,when the temperature is high,it will form cellular structure and develop into a large number of small angular subgrains due to the dislocation climbing.Finally,at the end of the acceleration stage,the creep process of the subgrains will change into the subgrains which produce the foam structure with large angle.At this stage,the high-density dislocation accumulation will occur at some grain boundaries and local stress concentration will be generated,when the local stress is too large,a flat trans-crystalline crack will appear.Grain boundary migration is also an important deformation mechanism in the creep process of salt rock.Grain boundary migration in dry salt rock is controlled by dislocation cross-slip and climb of dislocation.The grain boundary migration in wet salt rocks is usually caused by the chemical potential difference between grain boundary water.The migration of grain boundary will cause the "new grain" growing up and swallowing the subgrain in other grains,which will make the plastic deformation easier.The grain boundary migration in dry and wet salt rock is affected by temperature.For wet salt rock,the higher the temperature,the more obvious the grain boundary migration effect under the action of grain boundary water,and the stronger the recovery effect.For dry salt rock,raising the temperature will increase the activity of the atoms inside the grain and the grain boundary migration rate.In the creep process of salt rock,increasing temperature reflected from the macroscopic aspect is that the rheological stress decreases,which is required to achieve the same strain rate;the deformation rate increases under the same rheological stress.(3)The fractional derivative constitutive creep model of salt rockFractional order calculus has its own unique advantages in solving general engineering problems:it contains integer order theory,which means it can change into integer order operation in general sense.A large number of experiments indicate that the stress state at a certain point is not only related to the transient stress state,but also closely related to the loading history in the process of salt rock rheology.To some extent,the introduction(or application)of fractional-order calculus can better explain this process of historical accumulation and has fewer parameters than traditional constitutive models.Therefore,fractional-order calculus plays a great role in promoting viscoelastic theory and creep constitutive model.Natural salt rock may cause damage accumulation during creep.Therefore,the creep constitutive model needs to consider the damage evolution in salt rock,select the appropriate damage variable and introduce the creep constitutive equation of salt rock.In this paper,ultrasonic wave velocity is used to describe damage,and a fractional creep damage constitutive model based on ultrasonic wave velocity is established.As the changes of wave velocity in salt rock measured by ultrasonic experiments can only reflect the changes of damage in the fixed line between two points of the test specimen,the experimental results will be affected by many accidental factors(such as the distribution of defects).Therefore,more information and characteristic quantity with higher dimension should be used to describe the damage.In this paper,according to the effective bearing area theory,a two-dimensional parameter of damage description on the bearing surface is established by using acoustic emission statistics,and then a fractional creep constitutive model of salt rock based on acoustic emission is established.This model has a major defect in describing the creep process with relatively long initial creep time and fluctuating strain rate,which is caused by the incomplete creep information used in the derivation of damage variables.In order to solve the deficiency of the constitutive model above,the energy change in the creep process is added to describe the parameters of damage on the basis of acoustic emission event counting in this paper.By substituting the new damage variables with energy into the constitutive equation,the fractional creep constitutive model of salt rock based on acoustic emission energy can be obtained.Using acoustic emission experimental data of uniaxial creep of salt rock to verify the model,this constitutive model can make up for the deficiency of fractional creep constitutive model of salt rock considering acoustic emission only.(4)The fractal features of salt rock during creepFractal geometry is a branch of mathematics.Its it can clearly describe the irregular phenomena in nature.The concept of fractal dimension provides great help for the quantitative description of irregular physical phenomena.It is found that acoustic emission events in creep process of salt rock have statistical self-similarity in spatial distribution.When the small cube is within the reach of one scale,the fractal dimension of the spatial distribution for acoustic emission events in some moment can be got by solving the slope of the line in double logarithmic axes.The relationship between damage variable and fractal dimension is established,and the obtained fractal dimension can be used to describe the creep damage state of salt rock more precisely and quantitatively.In addition,predicting the creep deformation of salt rock in a certain period in engineering application can be simply and reasonably converted into statistics of acoustic emission signals in a certain period.