CN114894616A - Rock creep model viscous and elastic parameter obtaining method based on deformation modulus - Google Patents

Abstract

The invention discloses a deformation modulus-based method for acquiring viscous and elastic parameters of a rock creep model, which comprises the following steps of: carrying out triaxial compression tests under different confining pressures to obtain the strength and deformation modulus of the rock under different confining pressures; carrying out creep tests on rocks under different confining pressures by adopting a graded loading mode; and obtaining the deformation modulus and the long-term strength under the confining pressure value according to the given confining pressure value and the established confining pressure-deformation modulus relation and confining pressure-long-term strength relation, and obtaining the viscosity and elasticity parameters and the creep-time curve of the model by combining the established relationship between the viscosity and elasticity parameters and the deformation modulus of the burgers creep model. According to the creep model parameter-deformation modulus relation method, only a few rock creep test data under confining pressure are needed to establish the creep model parameter-deformation modulus relation, and the creep model parameters under confining pressure and long-term strength and the test curve reflecting the whole process of accelerated creep of the material can be obtained only through the deformation modulus of the rock under certain confining pressure in the later period, so that the method is provided for the creep rupture behavior research of the material.

Description

A method for obtaining viscoelastic and elastic parameters of rock creep model based on deformation modulus

technical field

The invention relates to a method for obtaining rock creep model parameters by directly calculating the conventional rock deformation modulus, and belongs to the technical field of rock engineering.

Background technique

As the basis of rock engineering design and long-term stability evaluation, rock creep model has always been the focus of researchers in the field of rock engineering. Up to now, people have done a lot of development for rock creep models of different types, different occurrence states and different stress paths. The existing creep constitutive models can basically meet the needs of engineering, but how to determine the viscosity of the creep model? , the elasticity parameter is still the key. In the past, to obtain the parameters of the creep model of the rock, the relationship between creep and time is usually obtained through laboratory tests, and then the parameters of the creep model are obtained by fitting the test data through the constitutive relationship. Although this method is highly accurate, it is time-consuming and labor-intensive.

SUMMARY OF THE INVENTION

Aiming at the deficiencies of the existing creep model parameter acquisition methods, the present invention provides a deformation modulus-based method for acquiring viscoelastic and elastic parameters of rock creep model.

The technical solution adopted by the present invention is:

A method for obtaining viscoelastic and elastic parameters of rock creep model based on deformation modulus, comprising the following steps:

(1) Carry out triaxial compression tests under different confining pressures to obtain the strength and deformation modulus of rocks under different confining pressures;

(2) Take the confining pressure as the abscissa and the deformation modulus as the ordinate, draw the deformation modulus values of the rock under different confining pressures in the coordinate system, and fit the relationship between the two through a function;

(3) The creep test is carried out on rocks under different confining pressures by adopting the hierarchical loading method;

(4) According to the creep deformation data of rock under different confining pressures under different confining pressures, the relationship between rock creep and time is obtained;

(5) According to the creep curve under different axial loading levels, draw the isochronous stress-strain curve of the rock, and determine the long-term strength of the rock according to the isochronous stress-strain curve of the rock;

(6) Taking the confining pressure of the rock as the abscissa and the long-term strength as the ordinate, draw the confining pressure-long-term strength curve, and obtain the relationship between the confining pressure and the long-term strength through function fitting;

(7) According to the relationship between rock creep and time obtained in step (4), the accelerated creep curve is further obtained; the accelerated creep curve is fitted by the damage burgers creep model, and the viscoelastic parameters of the damaged burgers creep model are obtained.

(8) Obtain the deformation modulus under a given confining pressure through step (2), and then combine the viscoelastic parameters of the damaged burgers creep model obtained in step (7) to draw the creep model parameter-deformation modulus curve, and the deformation The modulus is the abscissa and the creep model parameter is the ordinate, and the relationship between the two is fitted by a function;

(9) According to a given confining pressure value, the confining pressure-deformation modulus relationship established in step (2), and the confining pressure-long-term strength relationship established in step (6), the deformation modulus under the confining pressure value is obtained and long-term strength, and then according to the relationship between the viscous and elastic parameters and the deformation modulus of the Burgers creep model established in step (7), the viscosity and elastic parameters and the creep-time curve of the Burgers creep model under the confining pressure are finally obtained.

Preferably, in step (3): the step-by-step loading starts from 60% of the compressive strength under the corresponding confining pressure, and then pressurizes step by step, each time by 5% to 10%, until accelerated creep failure occurs.

Preferably, the expression of the damaged burgers creep model in step (7) is as follows:

where ε is the strain, σ is the stress, m is the parameter reflecting the degree of rock creep damage, t is the time, and _εc is the viscous strain.

The beneficial technical effects of the present invention are:

The method for obtaining the viscous and elastic parameters of the creep model proposed by the invention only needs a few rock creep test data under confining pressure to establish the relationship between confining pressure-deformation modulus, confining pressure-long-term strength and creep model parameter-deformation modulus. In the later stage, only the deformation modulus of the rock under a certain confining pressure can be used to obtain the creep model parameters under the confining pressure and long-term strength and the test curve reflecting the whole process of accelerated creep of the material, which provides a method for the study of material creep failure behavior. The method of the invention can provide accurate and convenient constitutive equation for rock engineering design and evaluation.

Description of drawings

Fig. 1 is the implementation flow chart of the present invention, and the creep model parameter and the creep curve acquisition process based on deformation modulus are provided in the figure;

Figure 2 shows the stress-strain curves of medium-grained sandstone under confining pressures of 1.5MPa, 3.0MPa, 4.5MPa and 6.0MPa;

Fig. 3 is the deformation modulus-confining pressure coordinate point and fitting curve of medium-grained sandstone;

Figure 4 shows the creep curves of 6 stress levels of medium-grained sandstone under a confining pressure of 1.5MPa;

Figure 5 shows the creep curves of 8 stress levels of medium-grained sandstone under confining pressure of 3.0MPa;

Figure 6 shows the creep curves of 7 stress levels of medium-grained sandstone under confining pressure of 4.5MPa;

Figure 7 shows the creep curves of 9 stress levels of medium-grained sandstone under confining pressure of 6.0 MPa;

Fig. 8 is the long-term strength-confining pressure coordinate point and fitting curve of medium-grained sandstone;

与

的两条线近乎重合；Figure 9 shows the parameters of the medium-grained sandstone creep model-deformation modulus coordinates and fitting curves.

and

The two lines are almost coincident;

FIG. 10 is a graph comparing the parameters of the creep model obtained by the deformation modulus according to the method of the present invention and the experimental data.

Detailed ways

As shown in Figure 1, a method for obtaining viscoelastic and elastic parameters of rock creep model based on deformation modulus includes the following steps:

(1) Carry out conventional triaxial compression tests under different confining pressures to obtain the compressive strength and deformation modulus of rocks under different confining pressures.

(2) Take the confining pressure as the abscissa and the deformation modulus as the ordinate, draw the deformation modulus values of the rock under different confining pressures in the coordinate system, and fit the relationship between the two through a suitable function, that is, get Confining pressure-deformation modulus relationship.

(3) The creep test is carried out on rocks under different confining pressures by adopting the hierarchical loading method, that is, the triaxial hierarchical loading creep test under different confining pressures is carried out. The graded loading starts from about 60% of the compressive strength under the corresponding confining pressure, and then is pressurized step by step, with a pressurization range of 5% to 10% each time, until accelerated creep failure occurs.

(4) According to the graded loading creep deformation data of rock under different confining pressures, draw the rock creep-time curve to obtain the relationship between rock creep and time.

(5) According to the creep curve under different axial loading levels, draw the isochronous stress-strain curve of the rock, and determine the long-term strength of the rock according to the isochronous stress-strain curve of the rock.

(6) On the basis of step (5), take the confining pressure of the rock as the abscissa and the long-term strength as the ordinate, draw the confining pressure-long-term strength curve, and obtain the relationship between the confining pressure and the long-term strength through function fitting.

(7) According to the relationship between rock creep and time obtained in step (4), an accelerated creep curve is further obtained. The accelerated creep curve is fitted by the damage burgers creep model, and the viscoelastic parameters of the damaged burgers creep model are obtained.

The expression of the damage burgers creep model is as follows:

where ε is the strain, σ is the stress, m is the parameter reflecting the degree of rock creep damage, t is the time, and _εc is the viscous strain.

(8) Obtain the deformation modulus under a given confining pressure through step (2), and then combine the viscoelastic parameters of the damaged burgers creep model obtained in step (7) to draw the creep model parameter-deformation modulus curve. The deformation modulus is the abscissa and the creep model parameter is the ordinate. The relationship between the two can be fitted by a suitable function, so that the creep model parameters under a given confining pressure can be further obtained.

(9) According to a given confining pressure value, the confining pressure-deformation modulus relationship established in step (2), and the confining pressure-long-term strength relationship established in step (6), the deformation modulus under the confining pressure value is obtained and long-term strength, and then according to the relationship between the viscous and elastic parameters and the deformation modulus of the Burgers creep model established in step (7), the viscosity and elastic parameters and the creep-time curve of the Burgers creep model under the confining pressure are finally obtained.

The method for obtaining the viscous and elastic parameters of the creep model proposed by the invention only needs a few rock creep test data under confining pressure to establish the relationship between confining pressure-deformation modulus, confining pressure-long-term strength and creep model parameter-deformation modulus. In the later stage, only the deformation modulus of the rock under a certain confining pressure can be used to obtain the creep model parameters under the confining pressure and long-term strength and the test curve reflecting the whole process of accelerated creep of the material, which provides a method for the study of material creep failure behavior.

The present invention is further described below by specific application example:

The present invention is a method for obtaining viscoelastic and elastic parameters of rock creep model based on deformation modulus, and its implementation process is shown in Figure 1. The use of accelerated creep curve acquisition includes the following steps:

(1) Carry out conventional triaxial compression test of medium-grained sandstone under different confining pressures (1.5MPa, 3.0MPa, 4.5MPa and 6.0MPa), and obtain the stress-strain curve of medium-grained sandstone (as shown in Figure 2) and four kinds of confining pressures Strength and deformation modulus of lower-medium-grained sandstone.

(2) Taking the confining pressure of the medium-grained sandstone as the abscissa and the deformation modulus as the ordinate, draw the coordinate points of the deformation modulus and the confining pressure of the medium-grained sandstone, and obtain the relationship between the two by fitting, as shown in Figure 3 .

(3) The graded loading method was used to carry out the creep test on the medium-grained sandstone under four confining pressures. The loading started from about 60% of the compressive strength under the corresponding confining pressure, and the first-level loading was performed, and then the stress was 2.0MPa. Gradient loading is carried out in stages, each stage is loaded for 6 hours, until accelerated creep failure occurs.

(4) According to the graded loading creep test data of medium-grained sandstone under four confining pressures, the graded loading creep-time curves of medium-grained sandstone under four confining pressures are drawn, as shown in Figures 4-7.

(5) According to the creep curves under different axial loading levels, the isochronous stress-strain curves of medium-grained sandstone are drawn, and the long-term strengths of medium-grained sandstones under four confining pressures are obtained according to the isochronous stress-strain method for obtaining long-term strength. They are 19.5MPa, 26.5MPa, 29.0MPa and 34MPa respectively.

(6) Taking the confining pressure as the abscissa and the long-term strength as the ordinate, draw the coordinate points of the confining pressure and the long-term strength of the medium-grained sandstone, and get the relationship between the two by fitting, as shown in Figure 8.

(7) Use the damage burgers creep model (the following formula) to fit the accelerated creep curve to obtain the viscoelastic parameters of the damaged burgers creep model

where ε is the strain, σ is the stress, m is the parameter reflecting the degree of rock creep damage, t is the time, and _εc is the viscous strain.

为纵坐标，绘制蠕变模型参数-变形模量数据坐标点，通过合适的函数拟合两者之间的关系，如图9所示。(8) Taking the deformation modulus of medium-grained sandstone as the abscissa, the creep model parameters

As the ordinate, draw the creep model parameter-deformation modulus data coordinate points, and fit the relationship between the two through a suitable function, as shown in Figure 9.

分别为14.26GPa、13.38GPa*h、129.83GPa、172.47GPa*h。(9) Given a certain confining pressure value of 4MPa, according to the fitting relationship between confining pressure-deformation modulus and confining pressure-long-term strength, it is obtained that the deformation modulus of medium-grained sandstone is 5.89GPa and the long-term strength is 28.02MPa when the confining pressure is 4MPa. , and then according to the obtained relationship between the viscoelastic parameters of the Burgers model and the deformation modulus, the viscous and elastic parameters of the Burgers model under the confining pressure are obtained

They are 14.26GPa, 13.38GPa*h, 129.83GPa, and 172.47GPa*h, respectively.

可得加载应力为28.02MPa时的蠕变-时间曲线，如图10所示，通过与实验数据对比，可知通过变形模量获得的蠕变模型参数可较好的描述岩石的加速蠕变行为。(10) Model parameters when accelerated creep occurs under the confining pressure 4MPa obtained above

The creep-time curve when the loading stress is 28.02MPa can be obtained, as shown in Figure 10. By comparing with the experimental data, it can be seen that the creep model parameters obtained by the deformation modulus can better describe the accelerated creep behavior of rock.

The parts not mentioned in the above manner can be realized by adopting or learning from the existing technology.

The above are only the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the principles of the present invention, several improvements and modifications can be made. It should be regarded as the protection scope of the present invention.

Claims (3)

1. a method for obtaining rock creep model viscosity and elasticity parameters based on deformation modulus, is characterized in that comprising the following steps: (1) Carry out triaxial compression tests under different confining pressures to obtain the strength and deformation modulus of rocks under different confining pressures; (2) Take the confining pressure as the abscissa and the deformation modulus as the ordinate, draw the deformation modulus values of the rock under different confining pressures in the coordinate system, and fit the relationship between the two through a function; (3) The creep test is carried out on rocks under different confining pressures by adopting the hierarchical loading method; (4) According to the creep deformation data of rock under different confining pressures under different confining pressures, the relationship between rock creep and time is obtained; (5) According to the creep curve under different axial loading levels, draw the isochronous stress-strain curve of the rock, and determine the long-term strength of the rock according to the isochronous stress-strain curve of the rock; (6) Taking the confining pressure of the rock as the abscissa and the long-term strength as the ordinate, draw the confining pressure-long-term strength curve, and obtain the relationship between the confining pressure and the long-term strength through function fitting; (7) According to the relationship between rock creep and time obtained in step (4), the accelerated creep curve is further obtained; the accelerated creep curve is fitted by the damage burgers creep model, and the viscoelastic parameters of the damaged burgers creep model are obtained.

(8) Obtain the deformation modulus under a given confining pressure through step (2), and then combine the viscoelastic parameters of the damaged burgers creep model obtained in step (7) to draw the creep model parameter-deformation modulus curve, and the deformation The modulus is the abscissa and the creep model parameter is the ordinate, and the relationship between the two is fitted by a function; (9) According to a given confining pressure value, the confining pressure-deformation modulus relationship established in step (2), and the confining pressure-long-term strength relationship established in step (6), the deformation modulus under the confining pressure value is obtained and long-term strength, and then according to the relationship between the viscous and elastic parameters and the deformation modulus of the Burgers creep model established in step (7), the viscosity and elastic parameters and the creep-time curve of the Burgers creep model under the confining pressure are finally obtained. 2. A method for obtaining viscoelastic and elastic parameters of a rock creep model based on deformation modulus according to claim 1, wherein in step (3): grading loading from 60% of the compressive strength under corresponding confining pressure Begin, and then pressurize step by step, with a pressurization range of 5% to 10% each time, until accelerated creep failure occurs. 3. a kind of rock creep model viscous and elastic parameter acquisition method based on deformation modulus according to claim 1, is characterized in that, in step (7), the expression of damage burgers creep model is as follows:

where ε is the strain, σ is the stress, m is the parameter reflecting the degree of rock creep damage, t is the time, and _εc is the viscous strain.

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