CN116611265A - Method and device for predicting stress and strain of deep anisotropic rock - Google Patents
Method and device for predicting stress and strain of deep anisotropic rock Download PDFInfo
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Abstract
The application provides a method and a device for predicting stress and strain of deep anisotropic rock, comprising the following steps: substituting the obtained numerical values of the rock elastic modulus, the rock poisson ratio, the deep rock infinitesimal strength, the first infinitesimal strength random distribution parameter, the second infinitesimal strength random distribution parameter, the minimum principal stress or confining pressure of the deep rock, the residual stress of the deep rock and the reference item corresponding to the item to be predicted into a target statistical damage model of the anisotropic rock under high confining pressure, and predicting the stress or strain in the deep anisotropic rock deformation process, wherein the item to be predicted is one of the stress or the strain, and the corresponding reference item is the other of the stress or the strain. In this way, the stress and strain of the deep anisotropic rock can be predicted more accurately by introducing the influencing parameters related to the deformation process of the deep anisotropic rock.
Description
Technical Field
The application relates to the technical field of rock mechanics, in particular to a method and a device for predicting stress and strain of deep anisotropic rock.
Background
Along with the high-speed development of the social economy of China, the construction of projects such as water and electricity, traffic and the like of the mountain gorges Gu Ou in the middle and the west is also vigorously developed. The related underground engineering mostly has the characteristics of overlength, large burial depth, high ground stress, high external water pressure and the like, thereby bringing importance to scientific problems of rock mechanical properties, stress strain and the like of the deep rock engineering.
Today, cao Wengui et al have proposed various methods for predicting rock stress and strain based on statistical damage theory. Wherein Cao Wengui students take Mohr-Coulomb intensity criterion as research object, assume that the curve form of the intensity criterion is parabolic, deduce and establish rock microcell intensity measurement expression by mathematical method, obtain measurement expression capable of reflecting rock stress state and having close influence on microcell intensity by mathematical deduction method by considering damage mechanics theory, namely strain equivalence theory proposed by scholars J.Lemaitre, and determine microcell intensity random distribution parameters m and F of homogeneous rock by mathematical deduction method 0 Finally, a mathematical model of the statistical damage prediction stress and strain of the homogeneous rock is obtained.
However, deep rock includes anisotropic type rock in addition to homogeneous type rock, and the above method can only predict stress and strain of homogeneous type rock.
Disclosure of Invention
In view of the above, an object of the present application is to provide a method and apparatus for predicting stress and strain of deep anisotropic rock, which can predict stress and strain of heterogeneous deep rock, thereby better assisting implementation of deep rock development engineering.
The embodiment of the application provides a method for predicting stress and strain of deep anisotropic rock, which comprises the following steps:
acquiring the rock elastic modulus and the rock poisson ratio of the deep anisotropic rock to be predicted;
acquiring deep rock micro-element strength determined based on a measurement formula of the deep anisotropic rock micro-element strength;
acquiring a first infinitesimal strength random distribution parameter and a second infinitesimal strength random distribution parameter of a statistical damage model in an anisotropic rock deformation process under high confining pressure;
acquiring the minimum main stress or confining pressure of the deep rock, the residual stress of the deep rock and the numerical value of a reference item corresponding to the item to be predicted; wherein the term to be predicted is one of stress or strain, and the corresponding reference term is the other of stress or strain;
And predicting the stress or strain in the deformation process of the deep anisotropic rock according to the rock elastic modulus, the rock poisson ratio, the deep rock microcell strength, the first microcell strength random distribution parameter, the second microcell strength random distribution parameter, the minimum main 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.
Alternatively, the metric formula for the infinitesimal strength of the deep anisotropic rock is constructed by:
constructing a maximum principal stress calculation formula of undamaged rock based on a Hoek-Brown strength criterion and stress influence parameters of anisotropic rock;
acquiring a mathematical expression of an initial damage model of the rock-soil body material determined based on a Lemaitre strain equivalence theory;
fusing the maximum principal stress calculation formula with the mathematical expression of the initial damage model to determine an initial measurement formula of the infinitesimal strength of the deep anisotropic rock;
obtaining a damage variable calculation formula of the deep anisotropic rock;
substituting the damage variable calculation formula into the initial measurement formula to determine the measurement formula of the infinitesimal strength of the deep anisotropic rock.
Optionally, the calculation formula of the maximum principal stress of the undamaged rock is as follows:
wherein ,maximum principal stress of undamaged rock, +.>Minimum principal stress or confining pressure for undamaged rock, < >>For rock minimum principal stress or confining pressure, < ->For anisotropic rock uniaxial compressive strength +.>As a parameter of the anisotropy of the sheet,，for the maximum uniaxial compressive strength value measured by the anisotropic rock uniaxial compressive strength test, +.>For the minimum uniaxial compressive strength value measured by the anisotropic rock uniaxial compressive strength test, < >>Is a dimensionless empirical constant of rock, +.>Is error coefficient +.>Is the critical confining pressure coefficient of the pressure sensor,，is an error term of the influence of high confining pressure conditions on deep rock.
Optionally, the measurement formula of the infinitesimal strength of the deep anisotropic rock is:
wherein ,，，Fis the strength of deep rock element>Is the maximum principal stress of the rock, +.>Is the residual stress of the rock.
Optionally, the predicting the stress or strain in the deep anisotropic rock deformation process according to the rock elastic modulus, the rock poisson ratio, the deep rock microcell strength, the first microcell strength random distribution parameter, the second microcell strength random distribution parameter, the minimum main 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 includes:
Substituting the rock elastic modulus, the rock poisson ratio, the deep rock infinitesimal strength, the first infinitesimal strength random distribution parameter, the second infinitesimal strength random distribution parameter, the minimum principal stress or confining pressure of the deep rock, the residual stress of the deep rock and the numerical value of a reference item corresponding to a to-be-predicted item into a target statistical damage model of the anisotropic rock under high confining pressure, and predicting the stress or strain in the deep anisotropic rock deformation process;
wherein, the target statistical damage model is:
wherein E is the elastic modulus of the rock,is the Poisson's ratio of->Is the strength of deep rock element>For the first infinitesimal intensity random distribution parameter, ">For the second infinitesimal intensity random distribution parameter, ">The minimum principal stress or confining pressure of the deep rock,residual stress of deep rock->Is the maximum principal stress of the deep rock, +.>Is the strain of the deep rock.
Optionally, the calculation formula of the first infinitesimal intensity random distribution parameter and the calculation formula of the second infinitesimal intensity random distribution parameter are determined by the following methods:
obtaining an extreme value characteristic expression of an anisotropic rock stress-strain curve under high confining pressure and a corresponding relation of stress and strain at a peak value;
And substituting the mathematical expression of the target statistical damage model into the extremum characteristic expression and the corresponding relation of stress and strain at the peak value respectively, and determining a calculation formula of the first infinitesimal intensity random distribution parameter and a calculation formula of the second infinitesimal intensity random distribution parameter.
Optionally, the damage variable calculation formula of the deep anisotropic rock is determined by:
introducing deep anisotropic rock residual strength characteristics based on the initial damage model, and constructing a first damage model in the deep anisotropic rock deformation process under the triaxial compression condition;
substituting a deformation relation formula for determining undamaged rock according to a generalized Hooke's law into the first damage model, and determining a second damage model in the deep anisotropic rock deformation process;
and carrying out formula deduction based on the conventional triaxial compression conditions and the mathematical expression of the second damage model, and determining a damage variable calculation formula of the deep anisotropic rock.
The embodiment of the application also provides a device for predicting the stress and the strain of the deep anisotropic rock, which comprises:
the first acquisition module is used for acquiring the rock elastic modulus and the rock poisson ratio of the deep anisotropic rock to be predicted;
The second acquisition module is used for acquiring the deep rock micro-element strength determined based on a measurement formula of the deep anisotropic rock micro-element strength;
the third acquisition module is used for acquiring a first infinitesimal strength random distribution parameter and a second infinitesimal strength random distribution parameter of the statistical damage model in the anisotropic rock deformation process under high confining pressure;
the fourth acquisition module is used for acquiring the minimum main 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; wherein the term to be predicted is one of stress or strain, and the corresponding reference term is the other of stress or strain;
the prediction module is used for predicting the stress or strain in the deformation process of the deep anisotropic rock according to the rock elastic modulus, the rock poisson ratio, the deep rock microcell strength, the first microcell strength random distribution parameter, the second microcell strength random distribution parameter, the minimum main 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.
Optionally, the prediction apparatus further includes a construction module, where the construction module is configured to:
Constructing a maximum principal stress calculation formula of undamaged rock based on a Hoek-Brown strength criterion and stress influence parameters of anisotropic rock;
acquiring a mathematical expression of an initial damage model of the rock-soil body material determined based on a Lemaitre strain equivalence theory;
fusing the maximum principal stress calculation formula with the mathematical expression of the initial damage model to determine an initial measurement formula of the infinitesimal strength of the deep anisotropic rock;
obtaining a damage variable calculation formula of the deep anisotropic rock;
substituting the damage variable calculation formula into the initial measurement formula to determine the measurement formula of the infinitesimal strength of the deep anisotropic rock.
Optionally, the calculation formula of the maximum principal stress of the undamaged rock is as follows:
wherein ,maximum principal stress of undamaged rock, +.>Minimum principal stress or confining pressure for undamaged rock, < >>For rock minimum principal stress or confining pressure, < ->For anisotropic rock uniaxial compressive strength +.>As a parameter of the anisotropy of the sheet,，for the maximum uniaxial compressive strength value measured by the anisotropic rock uniaxial compressive strength test, +.>For the minimum uniaxial compressive strength value measured by the anisotropic rock uniaxial compressive strength test, < > >Is a dimensionless empirical constant of rock, +.>Is error coefficient +.>Is the critical confining pressure coefficient of the pressure sensor,，is an error term of the influence of high confining pressure conditions on deep rock.
Optionally, the measurement formula of the infinitesimal strength of the deep anisotropic rock is:
wherein ,，，Fis the strength of deep rock element>Is the maximum principal stress of the rock, +.>Is the residual stress of the rock.
Optionally, when the prediction module is configured to predict the stress or strain in the deep anisotropic rock deformation process according to the rock elastic modulus, the rock poisson ratio, the deep rock microcell strength, the first microcell strength random distribution parameter, the second microcell strength random distribution parameter, the deep rock minimum principal stress or confining pressure, the deep rock residual stress, and the value of the reference item corresponding to the item to be predicted, the prediction module is configured to:
substituting the rock elastic modulus, the rock poisson ratio, the deep rock infinitesimal strength, the first infinitesimal strength random distribution parameter, the second infinitesimal strength random distribution parameter, the minimum principal stress or confining pressure of the deep rock, the residual stress of the deep rock and the numerical value of a reference item corresponding to a to-be-predicted item into a target statistical damage model of the anisotropic rock under high confining pressure, and predicting the stress or strain in the deep anisotropic rock deformation process;
Wherein, the target statistical damage model is:
wherein E is the elastic modulus of the rock,is the Poisson's ratio of->Is the strength of deep rock element>For the first infinitesimal intensity random distribution parameter, ">For the second infinitesimal intensity random distribution parameter, ">The minimum principal stress or confining pressure of the deep rock,deep rockResidual stress of stone->Is the maximum principal stress of the deep rock, +.>Is the strain of the deep rock.
Optionally, the predicting device further includes a first determining module, where the first determining module is configured to determine a calculation formula of the first infinitesimal intensity random distribution parameter and a calculation formula of the second infinitesimal intensity random distribution parameter by:
obtaining an extreme value characteristic expression of an anisotropic rock stress-strain curve under high confining pressure and a corresponding relation of stress and strain at a peak value;
and substituting the mathematical expression of the target statistical damage model into the extremum characteristic expression and the corresponding relation of stress and strain at the peak value respectively, and determining a calculation formula of the first infinitesimal intensity random distribution parameter and a calculation formula of the second infinitesimal intensity random distribution parameter.
Optionally, the prediction apparatus further includes a second determining module, where the second determining module is configured to:
Introducing deep anisotropic rock residual strength characteristics based on the initial damage model, and constructing a first damage model in the deep anisotropic rock deformation process under the triaxial compression condition;
substituting a deformation relation formula for determining undamaged rock according to a generalized Hooke's law into the first damage model, and determining a second damage model in the deep anisotropic rock deformation process;
and carrying out formula deduction based on the conventional triaxial compression conditions and the mathematical expression of the second damage model, and determining a damage variable calculation formula of the deep anisotropic rock.
The embodiment of the application also provides electronic equipment, which comprises: a processor, a memory and a bus, said memory storing machine readable instructions executable by said processor, said processor and said memory communicating over the bus when the electronic device is running, said machine readable instructions when executed by said processor performing the steps of the predictive method as described above.
The embodiments of the present application also provide a computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of the prediction method as described above.
Therefore, the application firstly takes the Hoek-Brown strength criterion as a research object, has the advantages of simple and convenient use and fitting with the actual engineering, and is accepted and applied by most engineering personnel; second, the present application is implemented by introducing an error term that is affected by high ambient pressure conditionsEstablishing a measurement formula of deep rock infinitesimal strength, wherein the expression and the parameters have physical significance, and the parameters in the error term are +.>Taking into account rock anisotropy parametersk α Enabling the established expression to take into account stress and strain predictions for anisotropic rock; secondly, the application introduces the rock critical confining pressure concept, considers the mechanical behavior of the rock from the brittle to ductile state under the high confining pressure of the anisotropic rock, and enables the established rock micro-element strength measurement expression to have more physical basis and persuasion; finally, the application adopts the mathematical derivation method to determine the random distribution parameter of the micro-element strength of the new anisotropic rock through the established measurement formula of the micro-element strength of the deep anisotropic rockmAndF 0 thereby better predicting the stress and strain of the deep anisotropic rock.
In order to make the above objects, features and advantages of the present application more comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for predicting stress and strain of deep anisotropic rock according to an embodiment of the present application;
FIG. 2 is a schematic structural diagram of a stress and strain predicting device for deep anisotropic rock according to an embodiment of the present application;
FIG. 3 is a schematic diagram of a device for predicting stress and strain of deep anisotropic rock according to an embodiment of the present application;
fig. 4 is a schematic structural diagram of an electronic device according to an embodiment of the present application.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are only some embodiments of the present application, not all embodiments. The components of the embodiments of the present application generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the application, as presented in the figures, is not intended to limit the scope of the application, as claimed, but is merely representative of selected embodiments of the application. Based on the embodiments of the present application, every other embodiment obtained by a person skilled in the art without making any inventive effort falls within the scope of protection of the present application.
Along with the high-speed development of the social economy of China, the construction of projects such as water and electricity, traffic and the like of the mountain gorges Gu Ou in the middle and the west is also vigorously developed. The related underground engineering mostly has the characteristics of overlength, large burial depth, high ground stress, high external water pressure and the like, thereby bringing importance to scientific problems of rock mechanical properties, stress strain and the like of the deep rock engineering.
Today, cao Wengui et al have proposed various methods for predicting rock stress and strain based on statistical damage theory. Wherein Cao Wengui students take Mohr-Coulomb intensity criterion as research object, assume that the curve form of the intensity criterion is parabolic, deduce and establish rock microcell intensity measurement expression by mathematical method, obtain measurement expression capable of reflecting rock stress state and having close influence on microcell intensity by mathematical deduction method by considering damage mechanics theory, namely strain equivalence theory proposed by scholars J.Lemaitre, and determine microcell intensity random distribution parameters m and F of homogeneous rock by mathematical deduction method 0 Finally, a mathematical model of the statistical damage prediction stress and strain of the homogeneous rock is obtained.
However, deep rock includes anisotropic type rock in addition to homogeneous type rock, and the above method can only predict stress and strain of homogeneous type rock.
Based on the above, the embodiment of the application provides a method and a device for predicting the stress and the strain of deep anisotropic rock, which can predict the stress and the strain of heterogeneous deep rock, thereby better assisting the implementation of deep rock development engineering.
Referring to fig. 1, fig. 1 is a flowchart of a method for predicting stress and strain of deep anisotropic rock according to an embodiment of the present application. As shown in fig. 1, the prediction method provided by the embodiment of the present application includes:
s101, acquiring the rock elastic modulus and the rock poisson ratio of the deep anisotropic rock to be predicted.
Here, the deep rock is a rock deeper from the ground surface, and the rock at 3KM from the ground surface is generally referred to as the deep rock. Rock anisotropy-one of the petrophysical and mechanical properties refers to the phenomenon that rock has different physical and mechanical properties in different directions.
The rock elastic modulus and the rock poisson ratio are related to the type and the attribute of the rock, and can be determined specifically through a triaxial confining pressure test.
S102, acquiring deep rock micro-element strength determined based on a measurement formula of the micro-element strength of the deep anisotropic rock.
Here, the measurement formula of the infinitesimal strength of the deep anisotropic rock is used for determining the value of the infinitesimal strength of the deep rock, and the measurement formula of the infinitesimal strength of the deep anisotropic rock is also the measurement formula of the infinitesimal strength of the high confining pressure anisotropic rock.
The measurement formula of the infinitesimal strength of the deep anisotropic rock is as follows:
（1）
here the number of the elements is the number,，，Fis the strength of deep rock element>Is the maximum principal stress of the rock, +.>Is the minimum principal stress or confining pressure of the deep rock, +.>Is a dimensionless empirical constant of rock, +.>Is anisotropic parameter->For anisotropic rock uniaxial compressive strength +.>Is the critical confining pressure coefficient of the pressure sensor,，is the residual stress of the rock, E is the elastic modulus of the rock, < ->Is the poisson's ratio.
Wherein, the anisotropic rock uniaxial compressive strengthThe anisotropic parameter +.>The residual stress of the rock is determined according to the maximum uniaxial compressive strength value and the minimum uniaxial compressive strength value measured by the anisotropic rock uniaxial compressive strength test>According to the triaxial confining pressure test of the rock, the dimensionless empirical constant of the rock is +. >Can be specified empirically in advance.
In one embodiment, the metric formula for the infinitesimal strength of the deep anisotropic rock is constructed by:
and 1, constructing a maximum principal stress calculation formula of the undamaged rock based on Hoek-Brown strength criterion and stress influence parameters of the anisotropic rock.
The calculation formula of the maximum principal stress of the undamaged rock is as follows:
（2）
wherein ,maximum principal stress of undamaged rock, +.>Minimum principal stress or confining pressure for undamaged rock, < >>For rock minimum principal stress or confining pressure, < ->For anisotropic rock uniaxial compressive strength +.>As a parameter of the anisotropy of the sheet,，for the maximum uniaxial compressive strength value measured by the anisotropic rock uniaxial compressive strength test, +.>For the minimum uniaxial compressive strength value measured by the anisotropic rock uniaxial compressive strength test, < >>Is a dimensionless empirical constant of rock, +.>Is error coefficient +.>Is an error term of rock affected by high confining pressure conditions,is critical confining pressure coefficient->。
And 2, acquiring a mathematical expression of an initial damage model of the rock-soil body material determined based on the Lemaitre strain equivalence theory.
The mathematical expression of the initial damage model is as follows:
（3）
wherein ,Is rock stress->Stress on undamaged rock, +.>In order to damage the variable quantity,i=1、2、3。
it should be noted that, in order to build a mathematical model which is more consistent with the actual situation and considers rock statistical damage, that is, to build a more accurate damage model, the following conditions should be satisfied:
(1) Rock is considered to be made up of numerous tiny units, and the load bearing rock units are abstracted into undamaged and damaged portions.
(2) Considering only the triaxial compression state of the rock, the rock is only damaged and not radially generated, so for the conventional triaxial test there can be:
（4）
in the formula ：，the main stress and the minimum main stress or confining pressure of the rock are respectively;，Main stress and minimum main stress or confining pressure, respectively, to which undamaged rock is subjected, wherein +.>The value of (2) may be preset by the relevant personnel.
(3) The materials of all parts of the rock are mixed together, so that the strain is consistent in the deformation process, and the strain of the undamaged part and the strain of the damaged part in the rock deformation process all meet the following formula:
(5)
in the formula ：for the strain of rock->Is the strain of the intact part, +.>I=1, 2, and 3 for strain of the damaged portion.
And step 3, fusing the maximum principal stress calculation formula with the mathematical expression of the initial damage model, and determining an initial measurement formula of the infinitesimal strength of the deep anisotropic rock.
Here, the metric formula determined based on the formula (2) is:
（6）
wherein F is the strength of deep rock infinitesimal.
Fusing the maximum principal stress calculation formula with the mathematical expression of the initial damage model, namely substituting the formula (3) into the formula (6), wherein the determined initial measurement formula is as follows:
（7）
and 4, obtaining a damage variable calculation formula of the deep anisotropic rock.
In one embodiment provided by the application, the damage variable calculation formula of the deep anisotropic rock is determined by the following method:
and 4.1, introducing the residual strength characteristic of the deep anisotropic rock based on the initial damage model, and constructing a first damage model in the deformation process of the deep anisotropic rock under the triaxial compression condition.
Here, the first damage model is a model reflecting the damage of the brittle ductile mechanical behavior of the rock under the triaxial compression condition, and the mathematical expression of the first damage model is as follows:
（8）
wherein ,the residual stress of the rock can be measured by a triaxial confining pressure test of the rock; d is a damage variable and reflects the damage degree of the rock.
And 4.2, substituting a deformation relation formula for determining undamaged rock according to a generalized Hooke's law into the first damage model, and determining a second damage model in the deep anisotropic rock deformation process.
Here, the deformation relation of the undamaged rock determined according to the generalized hook law is substituted into the first damage model, and when the second damage model in the deep anisotropic rock deformation process is determined, the strain consistency in the rock deformation process needs to be considered, namely the combination formula (5) is also needed.
Here, the deformation relation for intact rock is determined according to the generalized hook's law as:
（9）
for the elastic modulus of rock>Is the Poisson's ratio of->In order to damage the strain of the rock,i、j、k=1,2,3。
thus, formula (9) is substituted into formula (8), and formula (5) is combined to obtain formula (10), as follows:
（10）
the equation (10) is a mathematical expression of a second damage model during the deep anisotropic rock deformation.
And 4.3, carrying out formula deduction based on the conventional triaxial compression conditions and the mathematical expression of the second damage model, and determining a damage variable calculation formula of the deep anisotropic rock.
Here, the normal triaxial compression condition is a condition specified by the formula (4), the formula derivation is performed based on the normal triaxial compression condition and the mathematical expression of the second damage model, and the damage variable calculation formula of the deep anisotropic rock is determined actually based on the formula (10) and the formula (4):
（11）
And 5, substituting the damage variable calculation formula into the initial measurement formula to determine the measurement formula of the infinitesimal strength of the deep anisotropic rock.
Here, the damage variable calculation formula is substituted into the initial measurement formula, and the formula (11) is substituted into the formula (7), so that the measurement formula of the infinitesimal strength of the deep anisotropic rock, that is, the formula (1) can be determined.
S103, acquiring a first infinitesimal strength random distribution parameter and a second infinitesimal strength random distribution parameter of a statistical damage model of the anisotropic rock deformation process under high confining pressure.
Here, the first infinitesimal strength distribution parameter is determined based on a peak infinitesimal strength, a residual stress of the rock, a strain of the rock, an elastic modulus of the rock, a poisson ratio of the rock, a maximum principal stress of the rock, a minimum principal stress or confining pressure of the rock, an anisotropic uniaxial compressive strength of the rock, an anisotropic parameter, a dimensionless empirical constant of the rock, and a peak damage variable.
The second infinitesimal intensity random distribution parameter is determined based on the first infinitesimal intensity distribution parameter, the peak infinitesimal intensity, and the peak damage variable.
S104, acquiring 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 for the relevant personnel. The term to be predicted is one of stress or strain, and the corresponding reference term is the other of stress or strain.
For example, when the term to be predicted is stress, the corresponding reference term is strain; when the term to be predicted is strain, the corresponding reference term is a stress term.
Wherein the values of the reference items can be determined experimentally.
S105, predicting the stress or strain in the deformation process of the deep anisotropic rock according to the rock elastic modulus, the rock poisson ratio, the deep rock micro-element strength, the first micro-element strength random distribution parameter, the second micro-element strength random distribution parameter, the minimum main 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.
In one embodiment of the present application, predicting the stress or strain in the deformation process of the deep anisotropic rock according to the rock elastic modulus, the rock poisson ratio, the deep rock microcell strength, the first microcell strength random distribution parameter, the second microcell strength random distribution parameter, the small principal stress or confining pressure, the residual stress of the deep rock and the numerical value of the reference item corresponding to the item to be predicted includes:
Substituting the rock elastic modulus, the rock poisson ratio, the deep rock infinitesimal strength, the first infinitesimal strength random distribution parameter, the second infinitesimal strength random distribution parameter, the minimum principal stress or confining pressure, the residual stress of the deep rock and the numerical value of a reference item corresponding to a to-be-predicted item into a target statistical damage model of the anisotropic rock under high confining pressure, and predicting the stress or strain in the deep anisotropic rock deformation process;
wherein, the target statistical damage model is:
（12）
wherein E is the elastic modulus of the rock,is the Poisson's ratio of->Is the strength of deep rock element>For the first infinitesimal intensity random distribution parameter, ">For the second infinitesimal intensity random distribution parameter, ">The minimum principal stress or confining pressure of the deep rock,residual stress of deep rock->Is the maximum principal stress of the deep rock, +.>Is the strain of the deep rock.
Here, the mathematical expression (12) of the target statistical damage model is determined based on the expression (1) and the expression (10), and the determination process is as follows.
After determining the measurement formula (1) of the infinitesimal strength of the deep anisotropic rock, assuming that the infinitesimal strength is compliant with Weibull distribution and considering the influence of damage variables on damage measurement, the anisotropic rock damage evolution model under high confining pressure can be established as follows:
（13）
From the formula (13), it can be seen that except for the parametersmAndF 0 besides influencing the rock material damage evolution law, the determination method of the strength F is the key of the damage evolution model. Wherein, the formula (7) can obtain an anisotropic rock high ambient pressure strength F expression considering the influence of the damage threshold.
Substituting the formula (13) into the formula (10) to obtain a target statistical damage model of the anisotropic rock under high confining pressure, namely determining the formula (12), wherein the target statistical damage model is a three-dimensional mathematical model of the anisotropic rock under high confining pressure, which considers brittle mechanical behavior statistical damage.
Thus, after equation (12) is determined, a calculation formula for the first infinitesimal intensity random distribution parameter and a calculation formula for the second infinitesimal intensity random distribution parameter can be determined based on the equation.
In one embodiment of the present application, the calculation formula of the first infinitesimal intensity random distribution parameter and the calculation formula of the second infinitesimal intensity random distribution parameter are determined by: obtaining an extreme value characteristic expression of an anisotropic rock stress-strain curve under high confining pressure and a corresponding relation of stress and strain at a peak value; and substituting the mathematical expression of the target statistical damage model into the extremum characteristic expression and the corresponding relation of stress and strain at the peak value respectively, and determining a calculation formula of the first infinitesimal intensity random distribution parameter and a calculation formula of the second infinitesimal intensity random distribution parameter.
Here, the determination process of the calculation formula of the first and second infinitesimal intensity random distribution parameters is explained by the following formula derivation.
First, the stress at the peak point of the stress-strain curve of anisotropic rock under high confining pressure is set asσ p The strain isε p From the extremum characteristics of the curve, it is possible to:
(14)
wherein the stress and strain at the peak also need to satisfy the following formula:
(15)
then, when the anisotropic rock reaches the peak stress, the anisotropic rock is in a damaged state, the formula (12) is respectively substituted into the formulas (14) and (15), and the first infinitesimal strength random distribution parameter can be obtained by mathematically deriving and combining the two equationsmAnd the second infinitesimal intensity random distribution parameterThe calculation formula of (2), namely:
（16）
（17）
in the formula ：χ=m p k α σ 3 ，F p andD p the values of the strength F and the damage variable D of the anisotropic rock material under the condition of high confining pressure of the peak stress characteristic value are respectivelyF p The peak value of the intensity of the infinitesimal,D p peak impairment variable.
Wherein the peak infinitesimal intensityF p The peak damage variable parameter can be determined by the formula (1) and the formula (15)D p The method can be obtained by the following formula:
（18）
in the formula ：to damage the rock cross-section->Is the total cross-sectional area of the rock unit.
Thus, the random distribution parameter of the microcell strength of the new anisotropic rock is determinedmAndF 0 。
therefore, the invention firstly takes the Hoek-Brown strength criterion as a research object, has the advantages of simple and convenient use and fitting with the actual engineering, and is accepted and applied by most engineering personnel; second, the present invention is implemented by introducing an error term that is affected by high ambient pressure conditionsEstablishing a measurement formula of deep rock infinitesimal strength, wherein the expression and the parameters have physical significance, and the parameters in the error term are +.>Taking into account rock anisotropy parametersk α Enabling the established expression to take into account stress and strain predictions for anisotropic rock; secondly, the invention introduces the rock critical confining pressure concept, considers the mechanical behavior of the rock from the brittle to ductile state under the high confining pressure of the anisotropic rock, and enables the established rock micro-element strength measurement expression to have more physical basis and persuasion; finally, the invention adopts the mathematical derivation method to determine the random distribution parameter of the micro-element strength of the new anisotropic rock through the established measurement formula of the micro-element strength of the deep anisotropic rockmAndF 0 thereby better predicting the stress and strain of the deep anisotropic rock.
Referring to fig. 2 and 3, fig. 2 is a schematic structural diagram of a stress and strain predicting device for deep anisotropic rock according to an embodiment of the present application, and fig. 2 is a schematic structural diagram of a second stress and strain predicting device for deep anisotropic rock according to an embodiment of the present application. As shown in fig. 2, the prediction apparatus 200 includes:
a first obtaining module 210, configured to obtain a rock elastic modulus and a rock poisson ratio of the deep anisotropic rock to be predicted;
a second obtaining module 220, configured to obtain deep rock micro-element strength determined based on a measurement formula of the deep anisotropic rock micro-element strength;
the third obtaining module 230 is configured to obtain a first infinitesimal strength random distribution parameter and a second infinitesimal strength random distribution parameter of the statistical damage model in the anisotropic rock deformation process under high confining pressure;
a fourth obtaining module 240, configured to obtain a minimum main stress or confining pressure of the deep rock, a residual stress of the deep rock, and a value of a reference term corresponding to the term to be predicted; wherein the term to be predicted is one of stress or strain, and the corresponding reference term is the other of stress or strain;
the prediction module 250 is configured to predict stress or strain in the deformation process of the deep anisotropic rock according to the rock elastic modulus, the rock poisson ratio, the deep rock microcell strength, the first microcell strength random distribution parameter, the second microcell strength random distribution parameter, 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.
Optionally, as shown in fig. 3, the prediction apparatus 200 further includes a construction module 260, where the construction module 260 is configured to:
constructing a maximum principal stress calculation formula of undamaged rock based on a Hoek-Brown strength criterion and stress influence parameters of anisotropic rock;
acquiring a mathematical expression of an initial damage model of the rock-soil body material determined based on a Lemaitre strain equivalence theory;
fusing the maximum principal stress calculation formula with the mathematical expression of the initial damage model to determine an initial measurement formula of the infinitesimal strength of the deep anisotropic rock;
obtaining a damage variable calculation formula of the deep anisotropic rock;
substituting the damage variable calculation formula into the initial measurement formula to determine the measurement formula of the infinitesimal strength of the deep anisotropic rock.
Optionally, the calculation formula of the maximum principal stress of the undamaged rock is as follows:
wherein ,maximum principal stress of undamaged rock, +.>Minimum principal stress or confining pressure for undamaged rock, < >>For rock minimum principal stress or confining pressure, < ->For anisotropic rock uniaxial compressive strength +.>As a parameter of the anisotropy of the sheet,，for the maximum uniaxial compressive strength value measured by the anisotropic rock uniaxial compressive strength test, +. >For the minimum uniaxial compressive strength value measured by the anisotropic rock uniaxial compressive strength test, < >>Is a dimensionless empirical constant of rock, +.>Is error coefficient +.>Is the critical confining pressure coefficient of the pressure sensor,，is an error term of the influence of high confining pressure conditions on deep rock.
Optionally, the measurement formula of the infinitesimal strength of the deep anisotropic rock is:
wherein ,，，Fis the strength of deep rock element>Is the maximum principal stress of the rock, +.>Is the residual stress of the rock. />
Optionally, when the prediction module 250 is configured to predict the stress or strain in the deep anisotropic rock deformation process according to the rock elastic modulus, the rock poisson ratio, the deep rock microcell strength, the first microcell strength random distribution parameter, the second microcell strength random distribution parameter, the deep rock minimum principal stress or confining pressure, the deep rock residual stress, and the value of the reference term corresponding to the term to be predicted, the prediction module 250 is configured to:
substituting the rock elastic modulus, the rock poisson ratio, the deep rock infinitesimal strength, the first infinitesimal strength random distribution parameter, the second infinitesimal strength random distribution parameter, the minimum principal stress or confining pressure of the deep rock, the residual stress of the deep rock and the numerical value of a reference item corresponding to a to-be-predicted item into a target statistical damage model of the anisotropic rock under high confining pressure, and predicting the stress or strain in the deep anisotropic rock deformation process;
Wherein, the target statistical damage model is:
wherein E is the elastic modulus of the rock,is the Poisson's ratio of->Is the strength of deep rock element>For the first infinitesimal intensity random distribution parameter, ">For the second infinitesimal intensity random distribution parameter, ">The minimum principal stress or confining pressure of the deep rock,residual stress of deep rock->Is the maximum principal stress of the deep rock, +.>Is the strain of the deep rock.
Optionally, the prediction apparatus 200 further includes a first determining module 270, where the first determining module 270 is configured to determine a calculation formula of the first infinitesimal intensity random distribution parameter and a calculation formula of the second infinitesimal intensity random distribution parameter by:
obtaining an extreme value characteristic expression of an anisotropic rock stress-strain curve under high confining pressure and a corresponding relation of stress and strain at a peak value;
and substituting the mathematical expression of the target statistical damage model into the extremum characteristic expression and the corresponding relation of stress and strain at the peak value respectively, and determining a calculation formula of the first infinitesimal intensity random distribution parameter and a calculation formula of the second infinitesimal intensity random distribution parameter.
Optionally, the prediction apparatus 200 further includes a second determining module 280, where the second determining module 280 is configured to:
Introducing deep anisotropic rock residual strength characteristics based on the initial damage model, and constructing a first damage model in the deep anisotropic rock deformation process under the triaxial compression condition;
substituting a deformation relation formula for determining undamaged rock according to a generalized Hooke's law into the first damage model, and determining a second damage model in the deep anisotropic rock deformation process;
and carrying out formula deduction based on the conventional triaxial compression conditions and the mathematical expression of the second damage model, and determining a damage variable calculation formula of the deep anisotropic rock.
Referring to fig. 4, fig. 4 is a schematic structural diagram of an electronic device according to an embodiment of the 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, and when the electronic device 400 is running, the processor 410 communicates with the memory 420 through the bus 430, and when the machine-readable instructions are executed by the processor 410, the steps of the prediction method in the method embodiment shown in fig. 1 can be executed, and the specific implementation can be referred to the method embodiment and will not be described herein.
The embodiment of the present application further provides a computer readable storage medium, where a computer program is stored, where the computer program may execute the steps of the prediction method in the embodiment of the method shown in fig. 1 when the computer program is executed by a processor, and a specific implementation manner may refer to the embodiment of the method and will not be described herein.
It will be clear to those skilled in the art that, for convenience and brevity of description, specific working procedures of the above-described systems, apparatuses and units may refer to corresponding procedures in the foregoing method embodiments, and are not repeated herein.
In the several embodiments provided by the present application, it should be understood that the disclosed systems, devices, and methods may be implemented in other manners. The above-described apparatus embodiments are merely illustrative, for example, the division of the units is merely a logical function division, and there may be other manners of division in actual implementation, and for example, multiple units or components may be combined or integrated into another system, or some features may be omitted, or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed with each other may be through some communication interface, device or unit indirect coupling or communication connection, which may be in electrical, mechanical or other form.
The units described as separate units may or may not be physically separate, and units shown as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of 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 the embodiments of the present application may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a non-volatile computer readable storage medium executable by a processor. Based on this understanding, the technical solution of the present application may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
Finally, it should be noted that: the above examples are only specific embodiments of the present application, and are not intended to limit the scope of the present application, but it should be understood by those skilled in the art that the present application is not limited thereto, and that the present application is described in detail with reference to the foregoing examples: any person skilled in the art may modify or easily conceive of the technical solution described in the foregoing embodiments, or perform equivalent substitution of some of the technical features, while remaining within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present application, and are intended to be included in the scope of the present application. Therefore, the protection scope of the application is subject to the protection scope of the claims.
Claims (10)
1. A method of predicting stress and strain in deep anisotropic rock, the method comprising:
acquiring the rock elastic modulus and the rock poisson ratio of the deep anisotropic rock to be predicted;
acquiring deep rock micro-element strength determined based on a measurement formula of the deep anisotropic rock micro-element strength;
Acquiring a first infinitesimal strength random distribution parameter and a second infinitesimal strength random distribution parameter of a statistical damage model in an anisotropic rock deformation process under high confining pressure;
acquiring the minimum main stress or confining pressure of the deep rock, the residual stress of the deep rock and the numerical value of a reference item corresponding to the item to be predicted; wherein the term to be predicted is one of stress or strain, and the corresponding reference term is the other of stress or strain;
and predicting the stress or strain in the deformation process of the deep anisotropic rock according to the rock elastic modulus, the rock poisson ratio, the deep rock microcell strength, the first microcell strength random distribution parameter, the second microcell strength random distribution parameter, the minimum main 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.
2. The prediction method according to claim 1, wherein the metric formula for the infinitesimal strength of the deep anisotropic rock is constructed by:
constructing a maximum principal stress calculation formula of undamaged rock based on a Hoek-Brown strength criterion and stress influence parameters of anisotropic rock;
acquiring a mathematical expression of an initial damage model of the rock-soil body material determined based on a Lemaitre strain equivalence theory;
Fusing the maximum principal stress calculation formula with the mathematical expression of the initial damage model to determine an initial measurement formula of the infinitesimal strength of the deep anisotropic rock;
obtaining a damage variable calculation formula of the deep anisotropic rock;
substituting the damage variable calculation formula into the initial measurement formula to determine the measurement formula of the infinitesimal strength of the deep anisotropic rock.
3. The prediction method according to claim 2, wherein the maximum principal stress calculation formula of the undamaged rock is:
wherein ,maximum principal stress of undamaged rock, +.>Minimum principal stress or confining pressure for undamaged rock, < >>For rock minimum principal stress or confining pressure, < ->For anisotropic rock uniaxial compressive strength +.>Is anisotropic parameter->，For the maximum uniaxial compressive strength value measured by the anisotropic rock uniaxial compressive strength test, +.>For the minimum uniaxial compressive strength value measured by the anisotropic rock uniaxial compressive strength test, < >>Is a dimensionless empirical constant of rock, +.>Is error coefficient +.>Is critical confining pressure coefficient->，Is an error term of the influence of high confining pressure conditions on deep rock.
4. The prediction method according to claim 2, wherein the metric formula of the microcell strength of the deep anisotropic rock is:
wherein ,，，Fis the strength of deep rock element>Is the maximum principal stress of the rock, +.>Is the residual stress of the rock.
5. The method according to claim 1, wherein predicting the stress or strain in the deep anisotropic rock deformation process according to the rock elastic modulus, the rock poisson ratio, the deep rock microcell strength, the first microcell strength random distribution parameter, the second microcell strength random distribution parameter, the deep rock minimum principal stress or confining pressure, the deep rock residual stress, and the values of the reference items corresponding to the items to be predicted, comprises:
substituting the rock elastic modulus, the rock poisson ratio, the deep rock infinitesimal strength, the first infinitesimal strength random distribution parameter, the second infinitesimal strength random distribution parameter, the minimum principal stress or confining pressure of the deep rock, the residual stress of the deep rock and the numerical value of a reference item corresponding to a to-be-predicted item into a target statistical damage model of the anisotropic rock under high confining pressure, and predicting the stress or strain in the deep anisotropic rock deformation process;
wherein, the target statistical damage model is:
wherein E is the elastic modulus of the rock,is the Poisson's ratio of- >Is the strength of deep rock element>For the first infinitesimal intensity random distribution parameter, ">For the second infinitesimal intensity random distribution parameter, ">Minimum principal stress or confining pressure of deep rock, < ->Residual stress of deep rock->Is the maximum principal stress of the deep rock, +.>Is the strain of the deep rock.
6. The prediction method according to claim 5, wherein the calculation formula of the first infinitesimal intensity random distribution parameter and the calculation formula of the second infinitesimal intensity random distribution parameter are determined by:
obtaining an extreme value characteristic expression of an anisotropic rock stress-strain curve under high confining pressure and a corresponding relation of stress and strain at a peak value;
and substituting the mathematical expression of the target statistical damage model into the extremum characteristic expression and the corresponding relation of stress and strain at the peak value respectively, and determining a calculation formula of the first infinitesimal intensity random distribution parameter and a calculation formula of the second infinitesimal intensity random distribution parameter.
7. The prediction method according to claim 2, wherein the damage variable calculation formula of the deep anisotropic rock is determined by:
Introducing deep anisotropic rock residual strength characteristics based on the initial damage model, and constructing a first damage model in the deep anisotropic rock deformation process under the triaxial compression condition;
substituting a deformation relation formula for determining undamaged rock according to a generalized Hooke's law into the first damage model, and determining a second damage model in the deep anisotropic rock deformation process;
and carrying out formula deduction based on the conventional triaxial compression conditions and the mathematical expression of the second damage model, and determining a damage variable calculation formula of the deep anisotropic rock.
8. A device for predicting stress and strain of deep anisotropic rock, the device comprising:
the first acquisition module is used for acquiring the rock elastic modulus and the rock poisson ratio of the deep anisotropic rock to be predicted;
the second acquisition module is used for acquiring the deep rock micro-element strength determined based on a measurement formula of the deep anisotropic rock micro-element strength;
the third acquisition module is used for acquiring a first infinitesimal strength random distribution parameter and a second infinitesimal strength random distribution parameter of the statistical damage model in the anisotropic rock deformation process under high confining pressure;
The fourth acquisition module is used for acquiring the minimum main 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; wherein the term to be predicted is one of stress or strain, and the corresponding reference term is the other of stress or strain;
the prediction module is used for predicting the stress or strain in the deformation process of the deep anisotropic rock according to the rock elastic modulus, the rock poisson ratio, the deep rock microcell strength, the first microcell strength random distribution parameter, the second microcell strength random distribution parameter, the minimum main 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.
9. An electronic device, comprising: a processor, a memory and a bus, said memory storing machine readable instructions executable by said processor, said processor and said memory communicating via said bus when the electronic device is running, said machine readable instructions when executed by said processor performing the steps of the prediction method according to any of claims 1 to 7.
10. A computer readable storage medium, characterized in that it has stored thereon a computer program which, when executed by a processor, performs the steps of the prediction method according to any of claims 1 to 7.
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| 曹文贵等: "深部岩石统计损伤本构模型研究", 《水文地质工程地质》, vol. 43, no. 4, pages 60 - 65 * |
| 李文成: "基于Hoek-Brown强度准则岩石损伤本构研究", 《中国优秀硕士学位论文全文数据库 基础科学辑》, pages 23 - 53 * |
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