CN116611265A - Method and device for predicting stress and strain of deep anisotropic rock - Google Patents

Abstract

This application provides a method and device for predicting the stress and strain of deep anisotropic rocks, including: the obtained rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, and first micro-element strength random distribution parameters , the random distribution parameter of the second microelement strength, the minimum principal stress or confining pressure of deep rock, the residual stress of deep rock, and the value of the reference item corresponding to the item to be predicted are substituted into the target statistical damage model of anisotropic rock under high confining pressure , to predict the stress or strain in the deep anisotropic rock deformation process, wherein the item to be predicted is one of stress or strain, and the corresponding reference item is the other of stress or strain. In this way, the present invention can more accurately predict the stress and strain of the deep anisotropic rock by introducing the influencing parameters related to the deformation process of the deep anisotropic rock.

Description

A method and device for predicting stress and strain of deep anisotropic rock

Technical Field

The present application relates to the technical field of rock mechanics, and in particular to a method and device for predicting stress and strain of deep anisotropic rocks.

Background Art

With the rapid development of my country's social economy, the construction of hydropower and transportation projects in the high mountain valleys of central and western China has also flourished. The underground projects related to them are mostly characterized by super-long, deep burial, high ground stress, and high external water pressure, which has aroused the attention to scientific issues such as rock mechanics characteristics and stress-strain of deep rock engineering.

Nowadays, Cao Wengui and other scholars have proposed a variety of methods for predicting rock stress and strain based on statistical damage theory. Among them, Cao Wengui took the Mohr-Coulomb strength criterion as the research object, assuming that the curve form of the strength criterion is a parabola, and established a rock micro-element strength measurement expression through mathematical derivation. By considering the damage mechanics theory, that is, considering the strain equivalence theory proposed by scholar J. Lemaitre, the above-established micro-element strength measurement expression was mathematically deduced to obtain a measurement expression that can reflect the close influence of rock stress state on micro-element strength. Then, the micro-element strength random distribution parameters m and F ₀ of homogeneous rock were determined through mathematical derivation, and finally a mathematical model for predicting stress and strain of homogeneous rock statistical damage was obtained.

However, deep rocks include not only homogeneous rocks but also anisotropic rocks, and the above method can only predict the stress and strain of homogeneous rocks.

Summary of the invention

In view of this, the purpose of the present application is to provide a method and device for predicting the stress and strain of deep anisotropic rocks, which can predict the stress and strain of heterogeneous deep rocks, thereby better assisting the implementation of deep rock development projects.

The present application embodiment provides a method for predicting stress and strain of deep anisotropic rock, the prediction method comprising:

Obtain the rock elastic modulus and rock Poisson's ratio of the deep anisotropic rock to be predicted;

Obtaining the deep rock micro-element strength determined based on the measurement formula of the micro-element strength of deep anisotropic rock;

Obtain the first microelement strength random distribution parameter and the second microelement strength random distribution parameter of the statistical damage model of anisotropic rock deformation process under high confining pressure;

Obtaining the minimum principal stress or confining pressure of deep rock, the residual stress of deep rock, and the value of the reference item corresponding to the item to be predicted; wherein the item to be predicted is one of stress or strain, and the corresponding reference item is the other of stress or strain;

The stress or strain in the deformation process of deep anisotropic rock is predicted based on the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, minimum principal stress or confining pressure of deep rock, residual stress of deep rock and the value of reference item corresponding to the item to be predicted.

Optionally, a measurement formula for the micro-element strength of the deep anisotropic rock is constructed in the following manner:

Based on the Hoek-Brown strength criterion and the stress influencing parameters of anisotropic rocks, the maximum principal stress calculation formula of undamaged rocks is constructed.

Obtain the mathematical expression of the initial damage model of the rock and soil material determined based on the Lemaitre strain equivalence theory;

The maximum principal stress calculation formula is integrated with the mathematical expression of the initial damage model to determine the initial measurement formula of the micro-element strength of the deep anisotropic rock;

Obtain the damage variable calculation formula for deep anisotropic rock;

The damage variable calculation formula is substituted into the initial measurement formula to determine the measurement formula of the micro-element strength of the deep anisotropic rock.

Optionally, the maximum principal stress calculation formula of the undamaged rock is:

in, is the maximum principal stress of undamaged rock, is the minimum principal stress or confining pressure of undamaged rock, is the minimum principal stress or confining pressure of rock, is the uniaxial compressive strength of anisotropic rock, is the anisotropy parameter, , is the maximum uniaxial compressive strength value measured by the uniaxial compressive strength test of anisotropic rock, is the minimum uniaxial compressive strength value measured by the uniaxial compressive strength test of anisotropic rock, is the dimensionless empirical constant of rock, is the error coefficient, is the critical confining pressure coefficient, , is the error term caused by the high confining pressure condition on deep rocks.

Optionally, the measurement formula of the micro-element strength of the deep anisotropic rock is:

in, , , F is the micro-element strength of deep rock, is the maximum principal stress of the rock, is the residual stress of rock.

Optionally, the stress or strain in the deformation process of deep anisotropic rock is predicted according to the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, deep rock minimum principal stress or confining pressure, deep rock residual stress and the value of the reference item corresponding to the item to be predicted, including:

Substituting the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, minimum principal stress or confining pressure of deep rock, residual stress of deep rock and the numerical value of the reference item corresponding to the item to be predicted into the target statistical damage model of anisotropic rock under high confining pressure, the stress or strain prediction of deep anisotropic rock in the deformation process is performed;

Wherein, the target statistical damage model is:

Where, E is the elastic modulus of rock, is the rock Poisson's ratio, is the micro-element strength of deep rock, is the random distribution parameter of the first microelement intensity, is the random distribution parameter of the second microelement intensity, The minimum principal stress or confining pressure of deep rock, Residual stress in deep rock, is the maximum principal stress of deep rock, is the strain of deep rock.

Optionally, the calculation formula of the first micro-element intensity random distribution parameter and the calculation formula of the second micro-element intensity random distribution parameter are determined in the following manner:

Obtain the extreme characteristic expression of the anisotropic rock stress-strain curve under high confining pressure, and the corresponding relationship between the stress and strain at the peak;

Substitute the mathematical expression of the target statistical damage model into the extreme value characteristic expression and the corresponding relationship between the stress and strain at the peak value, and determine the calculation formula of the first microelement strength random distribution parameter and the calculation formula of the second microelement strength random distribution parameter.

Optionally, the damage variable calculation formula of the deep anisotropic rock is determined by the following method:

Based on the initial damage model, the residual strength characteristics of deep anisotropic rock are introduced to construct the first damage model of deep anisotropic rock deformation process under triaxial compression conditions;

Substituting the deformation relation of undamaged rock determined according to the generalized Hooke's law into the first damage model to determine a second damage model in the deep anisotropic rock deformation process;

A formula is derived based on conventional triaxial compression conditions and the mathematical expression of the second damage model to determine a damage variable calculation formula for the deep anisotropic rock.

The embodiment of the present application also provides a device for predicting stress and strain of deep anisotropic rock, the prediction device comprising:

The first acquisition module is used to obtain the rock elastic modulus and rock Poisson's ratio of the deep anisotropic rock to be predicted;

A second acquisition module is used to acquire the deep rock micro-element strength determined based on a measurement formula of the micro-element strength of deep anisotropic rock;

The third acquisition module is used to obtain the first microelement strength random distribution parameter and the second microelement strength random distribution parameter of the statistical damage model of the anisotropic rock deformation process under high confining pressure;

The fourth acquisition module is used to obtain the minimum principal stress or confining pressure of deep rock, the residual stress of deep rock and the value of the reference item corresponding to the item to be predicted; wherein the item to be predicted is one of stress or strain, and the corresponding reference item is the other of stress or strain;

The prediction module is used to predict the stress or strain in the deformation process of deep anisotropic rock according to the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, minimum principal stress or confining pressure of deep rock, residual stress of deep rock and the value of reference item corresponding to the item to be predicted.

Optionally, the prediction device further includes a construction module, and the construction module is used to:

Based on the Hoek-Brown strength criterion and the stress influencing parameters of anisotropic rocks, the maximum principal stress calculation formula of undamaged rocks is constructed.

Obtain the mathematical expression of the initial damage model of the rock and soil material determined based on the Lemaitre strain equivalence theory;

The maximum principal stress calculation formula is integrated with the mathematical expression of the initial damage model to determine the initial measurement formula of the micro-element strength of the deep anisotropic rock;

Obtain the damage variable calculation formula for deep anisotropic rock;

The damage variable calculation formula is substituted into the initial measurement formula to determine the measurement formula of the micro-element strength of the deep anisotropic rock.

Optionally, the maximum principal stress calculation formula of the undamaged rock is:

in, is the maximum principal stress of undamaged rock, is the minimum principal stress or confining pressure of undamaged rock, is the minimum principal stress or confining pressure of rock, is the uniaxial compressive strength of anisotropic rock, is the anisotropy parameter, , is the maximum uniaxial compressive strength value measured by the uniaxial compressive strength test of anisotropic rock, is the minimum uniaxial compressive strength value measured by the uniaxial compressive strength test of anisotropic rock, is the dimensionless empirical constant of rock, is the error coefficient, is the critical confining pressure coefficient, , is the error term caused by the high confining pressure condition on deep rocks.

Optionally, the measurement formula of the micro-element strength of the deep anisotropic rock is:

in, , , F is the micro-element strength of deep rock, is the maximum principal stress of the rock, is the residual stress of rock.

Optionally, when the prediction module is used to predict the stress or strain in the deformation process of deep anisotropic rock according to the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, deep rock minimum principal stress or confining pressure, deep rock residual stress and the value of the reference item corresponding to the item to be predicted, the prediction module is used to:

Substituting the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, minimum principal stress or confining pressure of deep rock, residual stress of deep rock and the numerical value of the reference item corresponding to the item to be predicted into the target statistical damage model of anisotropic rock under high confining pressure, the stress or strain in the deformation process of deep anisotropic rock is predicted;

Wherein, the target statistical damage model is:

Where, E is the elastic modulus of rock, is the rock Poisson's ratio, is the micro-element strength of deep rock, is the random distribution parameter of the first microelement intensity, is the random distribution parameter of the second microelement intensity, The minimum principal stress or confining pressure of deep rock, Residual stress in deep rock, is the maximum principal stress of deep rock, is the strain of deep rock.

Optionally, the prediction device further includes a first determination module, and the first determination module is used to determine the calculation formula of the first micro-element intensity random distribution parameter and the calculation formula of the second micro-element intensity random distribution parameter in the following manner:

Obtain the extreme characteristic expression of the anisotropic rock stress-strain curve under high confining pressure, and the corresponding relationship between the stress and strain at the peak;

Substitute the mathematical expression of the target statistical damage model into the extreme value characteristic expression and the corresponding relationship between the stress and strain at the peak value, and determine the calculation formula of the first microelement strength random distribution parameter and the calculation formula of the second microelement strength random distribution parameter.

Optionally, the prediction device further includes a second determination module, wherein the second determination module is configured to:

Based on the initial damage model, the residual strength characteristics of deep anisotropic rock are introduced to construct the first damage model of deep anisotropic rock deformation process under triaxial compression conditions;

Substituting the deformation relation of undamaged rock determined according to the generalized Hooke's law into the first damage model to determine a second damage model in the deep anisotropic rock deformation process;

A formula is derived based on conventional triaxial compression conditions and the mathematical expression of the second damage model to determine a damage variable calculation formula for the deep anisotropic rock.

An embodiment of the present application also provides an electronic device, comprising: a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the electronic device is running, the processor and the memory communicate via the bus, and when the machine-readable instructions are executed by the processor, the steps of the prediction method as described above are performed.

An embodiment of the present application further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the prediction method described above are executed.

Thus, the present invention firstly takes the Hoek-Brown strength criterion as the research object, which has the advantages of being easy to use and suitable for actual engineering, and is accepted and applied by most engineers; secondly, the present invention introduces the error term affected by high confining pressure conditions , establish a measurement formula for deep rock micro-element strength, the expression and parameters have physical meanings, and the parameters in the error term The rock anisotropy parameter k _α is taken into account, so that the established expression can consider the stress and strain prediction of anisotropic rock; secondly, the present invention introduces the concept of critical confining pressure of rock, considers the mechanical behavior of the anisotropic rock transforming from brittle to ductile state under high confining pressure, so that the established rock micro-element strength measurement expression has more physical basis and persuasiveness; finally, the present invention determines the new random distribution parameters m and F ₀ of the micro-element strength of anisotropic rock through the measurement formula of the deep anisotropic rock micro-element strength established above, using a mathematical derivation method, so as to better predict the stress and strain of deep anisotropic rock.

In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, preferred embodiments are specifically cited below and described in detail with reference to the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

FIG1 is a flow chart of a method for predicting stress and strain of deep anisotropic rock provided in an embodiment of the present application;

FIG2 is a schematic diagram of a structure of a device for predicting stress and strain of deep anisotropic rock provided in an embodiment of the present application;

FIG3 is a second schematic diagram of the structure of a device for predicting stress and strain of deep anisotropic rock provided in an embodiment of the present application;

FIG. 4 is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application.

DETAILED DESCRIPTION

To make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. The components of the embodiments of the present application usually described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application claimed for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, each other embodiment obtained by those skilled in the art without making creative work belongs to the scope of protection of the present application.

With the rapid development of my country's social economy, the construction of hydropower and transportation projects in the high mountain valleys of central and western China has also flourished. The underground projects related to them are mostly characterized by super-long, deep burial, high ground stress, and high external water pressure, which has aroused the attention to scientific issues such as rock mechanics characteristics and stress-strain of deep rock engineering.

Nowadays, Cao Wengui and other scholars have proposed a variety of methods for predicting rock stress and strain based on statistical damage theory. Among them, Cao Wengui took the Mohr-Coulomb strength criterion as the research object, assuming that the curve form of the strength criterion is a parabola, and established a rock micro-element strength measurement expression through mathematical derivation. By considering the damage mechanics theory, that is, considering the strain equivalence theory proposed by scholar J. Lemaitre, the above-established micro-element strength measurement expression was mathematically deduced to obtain a measurement expression that can reflect the close influence of rock stress state on micro-element strength. Then, the micro-element strength random distribution parameters m and F ₀ of homogeneous rock were determined through mathematical derivation, and finally a mathematical model for predicting stress and strain of homogeneous rock statistical damage was obtained.

However, deep rocks include not only homogeneous rocks but also anisotropic rocks, and the above method can only predict the stress and strain of homogeneous rocks.

Based on this, the embodiments of the present application provide a method and device for predicting the stress and strain of deep anisotropic rocks, which can predict the stress and strain of heterogeneous deep rocks, thereby better assisting the implementation of deep rock development projects.

Please refer to Figure 1, which is a flow chart of a method for predicting stress and strain of deep anisotropic rock provided in an embodiment of the present application. As shown in Figure 1, the prediction method provided in an embodiment of the present application includes:

S101. Obtain rock elastic modulus and rock Poisson's ratio of deep anisotropic rock to be predicted.

Here, deep rock refers to the rock at a relatively deep depth from the surface. Generally, the rock 3 km from the surface is called deep rock. Rock anisotropy - one of the physical and mechanical properties of rock, refers to the phenomenon that rock has different physical and mechanical properties in different directions.

The values of the rock elastic modulus and the rock Poisson's ratio are related to the type and properties of the rock, and can be specifically determined through a triaxial confining pressure test.

S102. Obtaining the deep rock micro-element strength determined based on a measurement formula of the micro-element strength of deep anisotropic rock.

Here, the measurement formula of the microelement strength of deep anisotropic rock is used to determine the value of the microelement strength of deep rock, and the measurement formula of the microelement strength of deep anisotropic rock is also the measurement formula of the microelement strength of high confining pressure anisotropic rock.

The measurement formula of the micro-element strength of deep anisotropic rock is:

(1)

here, , , F is the micro-element strength of deep rock, is the maximum principal stress of the rock, is the minimum principal stress or confining pressure of deep rock, is the dimensionless empirical constant of rock, is the anisotropy parameter, is the uniaxial compressive strength of anisotropic rock, is the critical confining pressure coefficient, , is the residual stress of rock, E is the elastic modulus of rock, is the Poisson's ratio of rock.

Among them, the uniaxial compressive strength of anisotropic rock It can be determined by the uniaxial compressive strength test of rock, and the anisotropic parameter The residual stress of rock is determined according to the maximum uniaxial compressive strength and the minimum uniaxial compressive strength measured by the anisotropic rock uniaxial compressive strength test. According to the triaxial confining pressure test of rock, the dimensionless empirical constant of rock Can be pre-specified based on experience.

In one embodiment, the measurement formula of the micro-element strength of the deep anisotropic rock is constructed in the following manner:

Step 1: Based on the Hoek-Brown strength criterion and the stress influencing parameters of anisotropic rocks, a calculation formula for the maximum principal stress of undamaged rocks is constructed.

The maximum principal stress calculation formula of the undamaged rock is:

(2)

in, is the maximum principal stress of undamaged rock, is the minimum principal stress or confining pressure of undamaged rock, is the minimum principal stress or confining pressure of rock, is the uniaxial compressive strength of anisotropic rock, is the anisotropy parameter, , is the maximum uniaxial compressive strength value measured by the uniaxial compressive strength test of anisotropic rock, is the minimum uniaxial compressive strength value measured by the uniaxial compressive strength test of anisotropic rock, is the dimensionless empirical constant of rock, is the error coefficient, is the error term caused by the high confining pressure on rock, is the critical confining pressure coefficient, .

Step 2: Obtain the mathematical expression of the initial damage model of the rock and soil material determined based on the Lemaitre strain equivalence theory.

The mathematical expression of the initial damage model is:

(3)

in, is the rock stress, is the stress on undamaged rock, is the damage variable, i = 1, 2, 3.

It should be noted that in order to establish a mathematical model that considers rock statistical damage that is more consistent with the actual situation, that is, to build a more accurate damage model, the following conditions must be met:

(1) It is believed that rock is composed of countless tiny units, and the rock units that bear the load are abstracted into undamaged parts and damaged parts.

(2) Considering only the triaxial compression state of rock, the rock will only be damaged in the radial direction but not in the radial direction. Therefore, for conventional triaxial tests, the following can be obtained:

(4)

Where: , are the principal stress and minimum principal stress or confining pressure of rock respectively; , are the principal stress and minimum principal stress or confining pressure of undamaged rock, respectively, where: The value can be preset by relevant personnel.

(3) The materials of various parts of the rock are mixed together, so the strains must be coordinated during the deformation process. Therefore, during the deformation process of the rock, the strain of the undamaged part and the strain of the damaged part all satisfy the following formula:

(5)

Where: is the strain of the rock, is the strain of the undamaged part, is the strain of the damaged part, i=1, 2 and 3.

Step 3: The maximum principal stress calculation formula is integrated with the mathematical expression of the initial damage model to determine the initial measurement formula of the micro-element strength of the deep anisotropic rock.

Here, the measurement formula determined based on formula (2) is:

(6)

Where F is the micro-element strength of deep rock.

The maximum principal stress calculation formula is integrated with the mathematical expression of the initial damage model, that is, formula (3) is substituted into formula (6), and the determined initial metric formula is:

(7)

Step 4: Obtain the damage variable calculation formula for deep anisotropic rock.

In one embodiment provided in the present application, the damage variable calculation formula of the deep anisotropic rock is determined in the following manner:

Step 4.1: Based on the initial damage model, the residual strength characteristics of deep anisotropic rock are introduced to construct the first damage model of deep anisotropic rock deformation process under triaxial compression conditions.

Here, the first damage model is a model that reflects the brittle ductile mechanical behavior damage of rock under triaxial compression conditions. The mathematical expression of the first damage model is as follows:

(8)

in, is the residual stress of rock, which can be measured by triaxial confining pressure test of rock; D is the damage variable, which reflects the degree of rock damage.

Step 4.2: Substitute the deformation relationship of undamaged rock determined according to the generalized Hooke's law into the first damage model to determine the second damage model in the deep anisotropic rock deformation process.

Here, the deformation relationship of undamaged rock determined by the generalized Hooke's law is substituted into the first damage model to determine the second damage model in the deep anisotropic rock deformation process. It is also necessary to consider the strain consistency in the rock deformation process, that is, it is necessary to combine formula (5).

Here, the deformation relationship of undamaged rock is determined according to the generalized Hooke's law:

(9)

is the elastic modulus of rock, is the rock Poisson's ratio, is the strain of damaged rock, i, j, k = 1, 2, 3.

Thus, by substituting equation (9) into equation (8) and combining it with equation (5), we get equation (10), as shown below:

(10)

The formula (10) is a mathematical expression of the second damage model in the deep anisotropic rock deformation process.

Step 4.3: Derivation of a formula based on conventional triaxial compression conditions and the mathematical expression of the second damage model to determine a damage variable calculation formula for the deep anisotropic rock.

Here, the conventional triaxial compression condition is the condition specified by formula (4). The formula derivation based on the conventional triaxial compression condition and the mathematical expression of the second damage model is actually based on formula (10) and formula (4) to determine the damage variable calculation formula of the deep anisotropic rock:

(11)

Step 5: Substitute the damage variable calculation formula into the initial measurement formula to determine the measurement formula for the micro-element strength of the deep anisotropic rock.

Here, substituting the damage variable calculation formula into the initial measurement formula is to substitute formula (11) into formula (7). In this way, the measurement formula of the micro-element strength of the deep anisotropic rock can be determined, namely, formula (1).

S103, obtaining the first microelement strength random distribution parameter and the second microelement strength random distribution parameter of the statistical damage model of the anisotropic rock deformation process under high confining pressure.

Here, the first microelement strength distribution parameter is determined based on the peak microelement strength, residual stress of rock, strain of rock, elastic modulus of rock, Poisson's ratio of rock, maximum principal stress of rock, minimum principal stress or confining pressure of rock, anisotropic rock uniaxial compressive strength, anisotropy parameter, dimensionless empirical constant of rock, and peak damage variable.

The second micro-element strength random distribution parameter is determined based on the first micro-element strength distribution parameter, the peak micro-element strength and the peak damage variable.

S104. Obtain the minimum principal stress or confining pressure of the deep rock, the residual stress of the deep rock, and the numerical value of the reference item corresponding to the item to be predicted.

Here, the minimum principal stress or confining pressure of the deep rock is preset by relevant personnel. The item to be predicted is one of the stress or strain, and the corresponding reference item is the other of the stress or strain.

For example, when the item to be predicted is stress, the corresponding reference item is strain; when the item to be predicted is strain, the corresponding reference item is stress.

Among them, the numerical value of the reference item can be determined through experiments.

S105. Predict the stress or strain in the deep anisotropic rock deformation process based on the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, minimum principal stress or confining pressure of deep rock, residual stress of deep rock and the value of the reference item corresponding to the item to be predicted.

In one embodiment provided in the present application, according to the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, minor principal stress or confining pressure, deep rock residual stress and the value of the reference item corresponding to the item to be predicted, the stress or strain in the deep anisotropic rock deformation process is predicted, including:

Substituting the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, minimum principal stress or confining pressure, deep rock residual stress and the numerical value of the reference item corresponding to the item to be predicted into the target statistical damage model of anisotropic rock under high confining pressure, the stress or strain in the deformation process of deep anisotropic rock is predicted;

Wherein, the target statistical damage model is:

(12)

Where, E is the elastic modulus of rock, is the rock Poisson's ratio, is the micro-element strength of deep rock, is the random distribution parameter of the first microelement intensity, is the random distribution parameter of the second microelement intensity, The minimum principal stress or confining pressure of deep rock, Residual stress in deep rock, is the maximum principal stress of deep rock, is the strain of deep rock.

Here, the mathematical expression (12) of the target statistical damage model is determined based on equations (1) and (10), and the determination process is as follows.

After determining the measurement formula (1) of the micro-element strength of deep anisotropic rock, assuming that the micro-element strength obeys the Weibull distribution and considering the influence of damage variables on the damage measurement, the damage evolution model of anisotropic rock under high confining pressure can be established as follows:

(13)

From formula (13), it can be seen that in addition to the parameters m and F0 _that can affect the damage evolution law of rock materials, the determination method of strength F is the key to the damage evolution model. Among them, formula (7) can obtain the expression of strength F of anisotropic rock under high confining pressure considering the influence of damage threshold.

Substituting formula (13) into formula (10), the target statistical damage model of anisotropic rock under high confining pressure can be obtained, that is, formula (12) is determined. The target statistical damage model is a three-dimensional mathematical model of statistical damage of anisotropic rock under high confining pressure considering brittle-ductile mechanical behavior.

In this way, after formula (12) is determined, the calculation formula for the first micro-element intensity random distribution parameter and the calculation formula for the second micro-element intensity random distribution parameter can be determined based on the formula.

In one embodiment provided in the present application, the calculation formula for the first micro-element strength random distribution parameter and the calculation formula for the second micro-element strength random distribution parameter are determined in the following manner: an extreme characteristic expression of the anisotropic rock stress-strain curve under high confining pressure and a corresponding relationship between the stress and strain at the peak are obtained; the mathematical expression of the target statistical damage model is substituted into the extreme characteristic expression and the corresponding relationship between the stress and strain at the peak, respectively, to determine the calculation formula for the first micro-element strength random distribution parameter and the calculation formula for the second micro-element strength random distribution parameter.

Here, the process of determining the calculation formula of the first micro-element intensity random distribution parameter and the calculation formula of the second micro-element intensity random distribution parameter is explained by deducing the following formula.

First, assume that the stress at the peak point of the anisotropic rock stress-strain curve under high confining pressure is σ _p and the strain is ε _p . According to the extreme value characteristics of the curve, we can obtain:

(14)

Among them, the stress and strain at the peak value must also satisfy the following formula:

(15)

Then, when the anisotropic rock reaches the peak stress, it is in a damaged state. Substituting equation (12) into equations (14) and (15) respectively, the calculation formula of the first microelement strength random distribution parameter m and the calculation formula of the second microelement strength random distribution parameter m can be obtained by mathematically deriving the two equations simultaneously. The calculation formula is:

(16)

(17)

Where: χ = m _p k _α σ ₃ , F _p and D _p are the values of the anisotropic rock material strength F and damage variable D under high confining pressure conditions of peak stress characteristic value, that is, F _p is the peak micro-element strength, and D _p is the peak damage variable.

Among them, the peak micro-element strength Fp can be determined by equation (1) and equation (15), and _the peak damage variable parameter Dp can be obtained _by the following equation:

(18)

Where: is the cross-sectional area of the damaged rock, is the total cross-sectional area of the rock unit.

In this way, the random distribution parameters m and F ₀ of the new micro-element strength of anisotropic rock are determined.

Thus, the present invention firstly takes the Hoek-Brown strength criterion as the research object, which has the advantages of being easy to use and suitable for actual engineering, and is accepted and applied by most engineers; secondly, the present invention introduces the error term affected by high confining pressure conditions , establish a measurement formula for deep rock micro-element strength, the expression and parameters have physical meanings, and the parameters in the error term The rock anisotropy parameter k _α is taken into account, so that the established expression can consider the stress and strain prediction of anisotropic rock; secondly, the present invention introduces the concept of critical confining pressure of rock, considers the mechanical behavior of the anisotropic rock transforming from brittle to ductile state under high confining pressure, so that the established rock micro-element strength measurement expression has more physical basis and persuasiveness; finally, the present invention determines the new random distribution parameters m and F ₀ of the micro-element strength of anisotropic rock through the measurement formula of the deep anisotropic rock micro-element strength established above, using a mathematical derivation method, so as to better predict the stress and strain of deep anisotropic rock.

Please refer to Figures 2 and 3. Figure 2 is a schematic diagram of the structure of a device for predicting stress and strain of deep anisotropic rock provided in an embodiment of the present application. Figure 2 is a schematic diagram of the structure of a device for predicting stress and strain of deep anisotropic rock provided in an embodiment of the present application. As shown in Figure 2, the prediction device 200 includes:

The first acquisition module 210 is used to acquire the rock elastic modulus and rock Poisson's ratio of the deep anisotropic rock to be predicted;

A second acquisition module 220 is used to acquire the deep rock micro-element strength determined based on a measurement formula of the micro-element strength of deep anisotropic rock;

The third acquisition module 230 is used to obtain the first microelement strength random distribution parameter and the second microelement strength random distribution parameter of the statistical damage model of the anisotropic rock deformation process under high confining pressure;

The fourth acquisition module 240 is used to obtain the minimum principal stress or confining pressure of the deep rock, the residual stress of the deep rock, and the value of the reference item corresponding to the item to be predicted; wherein the item to be predicted is one of stress or strain, and the corresponding reference item is the other of stress or strain;

The prediction module 250 is used to predict the stress or strain in the deep anisotropic rock deformation process based on the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, minimum principal stress or confining pressure of deep rock, residual stress of deep rock and the value of the reference item corresponding to the item to be predicted.

Optionally, as shown in FIG3 , the prediction device 200 further includes a construction module 260, and the construction module 260 is used to:

Based on the Hoek-Brown strength criterion and the stress influencing parameters of anisotropic rocks, the maximum principal stress calculation formula of undamaged rocks is constructed.

Obtain the mathematical expression of the initial damage model of the rock and soil material determined based on the Lemaitre strain equivalence theory;

The maximum principal stress calculation formula is integrated with the mathematical expression of the initial damage model to determine the initial measurement formula of the micro-element strength of the deep anisotropic rock;

Obtain the damage variable calculation formula for deep anisotropic rock;

The damage variable calculation formula is substituted into the initial measurement formula to determine the measurement formula of the micro-element strength of the deep anisotropic rock.

Optionally, the maximum principal stress calculation formula of the undamaged rock is:

in, is the maximum principal stress of undamaged rock, is the minimum principal stress or confining pressure of undamaged rock, is the minimum principal stress or confining pressure of rock, is the uniaxial compressive strength of anisotropic rock, is the anisotropy parameter, , is the maximum uniaxial compressive strength value measured by the uniaxial compressive strength test of anisotropic rock, is the minimum uniaxial compressive strength value measured by the uniaxial compressive strength test of anisotropic rock, is the dimensionless empirical constant of rock, is the error coefficient, is the critical confining pressure coefficient, , is the error term caused by the high confining pressure condition on deep rocks.

Optionally, the measurement formula of the micro-element strength of the deep anisotropic rock is:

in, , , F is the micro-element strength of deep rock, is the maximum principal stress of rock, is the residual stress of rock.

Optionally, when the prediction module 250 is used to predict the stress or strain in the deformation process of deep anisotropic rock according to the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, deep rock minimum principal stress or confining pressure, deep rock residual stress and the value of the reference item corresponding to the item to be predicted, the prediction module 250 is used to:

Substituting the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, minimum principal stress or confining pressure of deep rock, residual stress of deep rock and the numerical value of the reference item corresponding to the item to be predicted into the target statistical damage model of anisotropic rock under high confining pressure, the stress or strain in the deformation process of deep anisotropic rock is predicted;

Wherein, the target statistical damage model is:

Where, E is the elastic modulus of rock, is the rock Poisson's ratio, is the micro-element strength of deep rock, is the random distribution parameter of the first microelement intensity, is the random distribution parameter of the second microelement intensity, The minimum principal stress or confining pressure of deep rock, Residual stress in deep rock, is the maximum principal stress of deep rock, is the strain of deep rock.

Optionally, the prediction device 200 further includes a first determination module 270, and the first determination module 270 is used to determine the calculation formula of the first micro-element intensity random distribution parameter and the calculation formula of the second micro-element intensity random distribution parameter in the following manner:

Obtain the extreme characteristic expression of the anisotropic rock stress-strain curve under high confining pressure, and the corresponding relationship between the stress and strain at the peak;

Substitute the mathematical expression of the target statistical damage model into the extreme value characteristic expression and the corresponding relationship between the stress and strain at the peak value, and determine the calculation formula of the first microelement strength random distribution parameter and the calculation formula of the second microelement strength random distribution parameter.

Optionally, the prediction device 200 further includes a second determination module 280, and the second determination module 280 is used to:

Based on the initial damage model, the residual strength characteristics of deep anisotropic rock are introduced to construct the first damage model of deep anisotropic rock deformation process under triaxial compression conditions;

Substituting the deformation relation of undamaged rock determined according to the generalized Hooke's law into the first damage model to determine a second damage model in the deep anisotropic rock deformation process;

A formula is derived based on conventional triaxial compression conditions and the mathematical expression of the second damage model to determine a damage variable calculation formula for the deep anisotropic rock.

Please refer to Fig. 4, which is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. As shown in Fig. 4, the electronic device 400 includes a processor 410, a memory 420 and a bus 430.

The memory 420 stores machine-readable instructions executable by the processor 410. When the electronic device 400 is running, the processor 410 communicates with the memory 420 through the bus 430. When the machine-readable instructions are executed by the processor 410, the steps of the prediction method in the method embodiment shown in Figure 1 above can be executed. The specific implementation method can be found in the method embodiment, which will not be repeated here.

An embodiment of the present application also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the prediction method in the method embodiment shown in FIG. 1 can be executed. The specific implementation method can be found in the method embodiment, which will not be repeated here.

Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

In the several embodiments provided in the present application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. The device embodiments described above are merely schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some communication interfaces, and the indirect coupling or communication connection of devices or units can be electrical, mechanical or other forms.

The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a non-volatile computer-readable storage medium that can be executed by a processor. Based on this understanding, the technical solution of the present application can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk, and other media that can store program codes.

Finally, it should be noted that the above-described embodiments are only specific implementation methods of the present application, which are used to illustrate the technical solutions of the present application, rather than to limit them. The protection scope of the present application is not limited thereto. Although the present application is described in detail with reference to the above-mentioned embodiments, ordinary technicians in the field should understand that any technician familiar with the technical field can still modify the technical solutions recorded in the above-mentioned embodiments within the technical scope disclosed in the present application, or can easily think of changes, or make equivalent replacements for some of the technical features therein; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims (10)

1. A method for predicting stress and strain of deep anisotropic rock, characterized in that the prediction method comprises: Obtain the rock elastic modulus and rock Poisson's ratio of the deep anisotropic rock to be predicted; Obtaining the deep rock micro-element strength determined based on the measurement formula of the micro-element strength of deep anisotropic rock; Obtain the first microelement strength random distribution parameter and the second microelement strength random distribution parameter of the statistical damage model of anisotropic rock deformation process under high confining pressure; Obtaining the minimum principal stress or confining pressure of deep rock, the residual stress of deep rock, and the value of the reference item corresponding to the item to be predicted; wherein the item to be predicted is one of stress or strain, and the corresponding reference item is the other of stress or strain; The stress or strain in the deformation process of deep anisotropic rock is predicted based on the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, minimum principal stress or confining pressure of deep rock, residual stress of deep rock and the value of reference item corresponding to the item to be predicted. 2. The prediction method according to claim 1 is characterized in that the measurement formula of the micro-element strength of the deep anisotropic rock is constructed in the following manner: Based on the Hoek-Brown strength criterion and the stress influencing parameters of anisotropic rocks, the maximum principal stress calculation formula of undamaged rocks is constructed. Obtain the mathematical expression of the initial damage model of the rock and soil material determined based on the Lemaitre strain equivalence theory; The maximum principal stress calculation formula is integrated with the mathematical expression of the initial damage model to determine the initial measurement formula of the micro-element strength of the deep anisotropic rock; Obtain the damage variable calculation formula for deep anisotropic rock; The damage variable calculation formula is substituted into the initial measurement formula to determine the measurement formula of the micro-element strength of the deep anisotropic rock. 3. The prediction method according to claim 2, characterized in that the maximum principal stress calculation formula of the undamaged rock is: in, is the maximum principal stress of undamaged rock, is the minimum principal stress or confining pressure of undamaged rock, is the minimum principal stress or confining pressure of rock, is the uniaxial compressive strength of anisotropic rock, is the anisotropy parameter, , is the maximum uniaxial compressive strength value measured by the uniaxial compressive strength test of anisotropic rock, is the minimum uniaxial compressive strength value measured by the uniaxial compressive strength test of anisotropic rock, is the dimensionless empirical constant of rock, is the error coefficient, is the critical confining pressure coefficient, , is the error term caused by the high confining pressure condition on deep rocks. 4. The prediction method according to claim 2, characterized in that the measurement formula of the micro-element strength of the deep anisotropic rock is: in, , , F is the micro-element strength of deep rock, is the maximum principal stress of the rock, is the residual stress of rock. 5. The prediction method according to claim 1 is characterized in that the stress or strain in the deformation process of deep anisotropic rock is predicted according to the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, deep rock minimum principal stress or confining pressure, deep rock residual stress and the value of the reference item corresponding to the item to be predicted, comprising: Substituting the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, minimum principal stress or confining pressure of deep rock, residual stress of deep rock and numerical values of reference items corresponding to the items to be predicted into the target statistical damage model of anisotropic rock under high confining pressure, the stress or strain prediction of deep anisotropic rock during deformation is performed; Wherein, the target statistical damage model is: Where, E is the elastic modulus of rock, is the rock Poisson's ratio, is the micro-element strength of deep rock, is the random distribution parameter of the first microelement intensity, is the random distribution parameter of the second microelement intensity, The minimum principal stress or confining pressure of deep rock, Residual stress in deep rock, is the maximum principal stress of deep rock, is the strain of deep rock. 6. The prediction method according to claim 5, characterized in that the calculation formula of the first micro-element intensity random distribution parameter and the calculation formula of the second micro-element intensity random distribution parameter are determined by the following method: Obtain the extreme characteristic expression of the anisotropic rock stress-strain curve under high confining pressure, and the corresponding relationship between the stress and strain at the peak; Substitute the mathematical expression of the target statistical damage model into the extreme value characteristic expression and the corresponding relationship between the stress and strain at the peak value, and determine the calculation formula of the first microelement strength random distribution parameter and the calculation formula of the second microelement strength random distribution parameter. 7. The prediction method according to claim 2, characterized in that the damage variable calculation formula of the deep anisotropic rock is determined by the following method: Based on the initial damage model, the residual strength characteristics of deep anisotropic rock are introduced to construct the first damage model of deep anisotropic rock deformation process under triaxial compression conditions; Substituting the deformation relation of undamaged rock determined according to the generalized Hooke's law into the first damage model to determine a second damage model in the deep anisotropic rock deformation process; A formula is derived based on conventional triaxial compression conditions and the mathematical expression of the second damage model to determine a damage variable calculation formula for the deep anisotropic rock. 8. A prediction device for stress and strain of deep anisotropic rock, characterized in that the prediction device comprises: The first acquisition module is used to obtain the rock elastic modulus and rock Poisson's ratio of the deep anisotropic rock to be predicted; A second acquisition module is used to acquire the deep rock micro-element strength determined based on a measurement formula of the micro-element strength of deep anisotropic rock; The third acquisition module is used to obtain the first microelement strength random distribution parameter and the second microelement strength random distribution parameter of the statistical damage model of the anisotropic rock deformation process under high confining pressure; The fourth acquisition module is used to obtain the minimum principal stress or confining pressure of deep rock, the residual stress of deep rock and the value of the reference item corresponding to the item to be predicted; wherein the item to be predicted is one of stress or strain, and the corresponding reference item is the other of stress or strain; The prediction module is used to predict the stress or strain in the deformation process of deep anisotropic rock according to the rock elastic modulus, rock Poisson's ratio, deep rock micro-element strength, first micro-element strength random distribution parameter, second micro-element strength random distribution parameter, minimum principal stress or confining pressure of deep rock, residual stress of deep rock and the value of reference item corresponding to the item to be predicted. 9. An electronic device, characterized in that it comprises: a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the electronic device is running, the processor and the memory communicate through the bus, and the machine-readable instructions are executed by the processor to execute the steps of the prediction method as described in any one of claims 1 to 7. 10. A computer-readable storage medium, characterized in that a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the steps of the prediction method according to any one of claims 1 to 7 are executed.