A novel nonlinear creep model based on damage characteristics of mudstone strength parameters

Mudstone interlayer is a weak layer in rock engineering. When it is subjected to continuous stress higher than its damage threshold, due to the dislocation of particles in mudstone crystals and the expansion of cracks, mudstone strength is gradually damaged and deteriorated and the strain gradually increases, thus accelerating the phenomenon of creep damage. In order to describe the characteristics of the whole process of mudstone aging deformation, based on the damage evolution of strength parameters (cohesion and internal friction coefficient) with stress and time in mudstone creep tests, a novel damage nonlinear viscoelastoplastic body (D-NVPB) is proposed through improving traditional plastic element. D-NVPB describes the nonlinear characteristics of the accelerated creep stage of mudstone. With the element combination method, D-NVPB is connected with the Burgers model in series to form a new nonlinear damage creep model (D-NVEP model). The analysis results of creep characteristics theoretically verified the rationality of the model in describing the instantaneous elasticity, viscoelasticity, and nonlinear viscoplastic characteristics of the complete creep curve of mudstone. With the data obtained in the uniaxial compression creep test of mudstone under the action of a stress level of 14 MPa, based on the Levenberg-Marquardt nonlinear least squares method, the fitting calculation was performed through piecewise fitting and overall fitting. The correlation coefficient was 0.9909, which verified the applicability of the model. The obtained model parameters by the identification were used to predict the mudstone creep curve under the stress levels of 13 MPa and 15 MPa. The good prediction results further verified the feasibility of the model. Compared with the traditional creep model, the D-NVEP model can better describe the nonlinear characteristics of the accelerated creep stage and quantitatively display the strength damage evolution process of rock in the creep failure process.

The analysis of rheological damage of anchorage body based on visco-elasto-plastic model

In order to study the rheological damage of anchorage body, rheological damage model of anchorage body is established in this paper, and it is based on visco-elasto plastic model that is often used to simulate rock rheological characteristics. The expressions of creep constitutive equation and elastic modulus of anchorage body are obtained through the analysis of rheological damage model of anchorage body, and by the fitting calculation results, finding that the theoretical creep curve is matched with the experimental creep curve under certain conditions. The research conclusions have critical significance to the bolting support and design.

CREEP OF A THICKWALLED QUASILINEAR VISCOELASTIC TUBE UNDER A CONSTANT EXTERNAL AND INTERNAL PRESSURE

We consider the creep problem for a quasilinear viscoelastic model of a thickwalled tube, loaded with constant internal and external pressure; the material is supposed to be incompressible. An exact solution to this problem was received by one of the authors in previous papers, assuming the state of a tube to be plain deformation; hereby we study properties of this solution for arbitrary material functions of quasilinear viscoelasticity constitutive relation. A criterion of stress stationarity is derived; the stress field of a thickwalled tube under a constant pressure evolves in time in the case of unbounded creep function and arbitrary nonlinearity function, except some particular types. The monotonicity of stress field components is studied: the radial stress monotonicity depends only on internal and external pressure values (for internal pressure, greater than an external one, it is negative and increases in radii). For other stress components, there are derived sufficient conditions of monotonicity. For an exponential nonlinearity function and unbounded creep function, a creep curve is determined to be concave up at the initial moment, and concave down during prolonged observation; the creep curve of a bipower nonlinearity function model may change its convexity. The stressstrain state of a model with a bounded creep function is proved to be bounded.

DETERMINATION OF RHEOLOGICAL PARAMETERS OF POLYMERIC MATERIALS USING NONLINEAR OPTIMIZATION METHODS

The article is devoted to the problem of processing the experimental creep curves of polymers. The task is to determine their rheological characteristics from tests for any of the simplest types of deformation. The basis for the approximation of the experimental curves is the nonlinear Maxwell-Gurevich equation. The task of finding the rheological parameters of the material is posed as a nonlinear optimization problem. The objective function is the sum of the squared deviations of the experimental values on the creep curve from the theoretical ones. Variable input parameters of the objective function are the initial relaxation viscosity and velocity modulus m*. A theoretical creep curve is constructed numerically using the fourth-order Runge-Kutta method. The nonlinear optimization problem is solved in the Matlab environment using the internal point method. The values m* and are found for which the objective function takes the minimum value. To test the technique, the inverse problem was solved. For given values of the rheological parameters of the material, a theoretical curve of creep under bending was constructed, and the values m* and were found from it. The technique was also tested on experimental stress relaxation curves of secondary polyvinyl chloride and creep curves of polyurethane foam with a pure shear. A higher quality approximation of experimental curves is shown in comparison with existing methods. The developed technique allows us to determine the rheological characteristics of materials from tests for bending, central tension (compression), torsion, shear, and it is enough to test only one type of deformation, and not a series, as was suggested earlier by some researchers

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 Numerical Analysis Method for Creep Lifetime of Gas Turbine Materials by Using the Discrete Cosine Transform

Recently the Discrete Cosine Transform[1], [2], [3] which is a modified Fourier Transform has begun to be used to express coefficients of creep equations using the power law or the exponential law such as Bailey-Norton law[4], [5] and θ Projection[6], [7], [8], [9], [10]. In addition, the Discrete Cosine Transform has begun to be used to express a creep equation itself. We have already found that the Discrete Cosine Transform can express the temperature and stress dependence property of the coefficients of the creep equations at the same time by the two-dimensional Discrete Cosine Transform using 8 × 8 discrete signals[11]. Furthermore, we have already found that the Discrete Cosine Transform can fit measured creep strain values very well from the primary creep region to the tertiary creep region using 8 discrete signals and it can estimate creep strain values between the measured points by interpolation very well[12]. However it has not been known if the Discrete Cosine Transform can predict the long term creep curve by using the short term creep data yet. Therefore, as a next stage, we tried to estimate the long term creep curve from the short term creep data of gas turbine materials by extrapolation using the Discrete Cosine Transform. As a result, we were able to obtain a useful numerical analysis method by utilizing the Discrete Cosine Transform Coefficients and others as a new extrapolation method. It is found that this new numerical method would be able to predict the configuration of 150,000-hour creep curve by using 500-hour to 13,000-hour short term creep data.

Study on the Allowable Exposure Time of Temporary Goaf in the Open Stope and Backfill Mining Method with Large Structure Parameters

Based on the uniaxial rheological experiment data of iron ore rock mass and filling body in large-scale stope obtained by using the rock servo controlling creep equipment, the characteristics of the creep curve were analyzed. The creep models of iron ore and filling body which can show the attenuation creep of rock were constructed. And a nonlinear creep model was obtained. According to the rheological data of the iron ore and the filling body, the parameters of the new nonlinear creep model were identified to obtain the material parameters of the creep model. Then, the creep model parameters were fitted and reduced to calculate the reasonable exposure time of temporary goaf in the large-scale stope. The results show that the reasonable exposure time of stope is 520 ～ 650 days, and the reasonable exposure time of filling body is 410 ～ 520 days. The model can well describe the initial attenuation creep stage and steady creep stage in the creep curve, which proves the correctness and rationality of the model. The study provides a reference for mining design and safety production of similar mines with large-scale stope structure.