CN117268617B - Stress tensor determination method comprising three-layer medium model - Google Patents

Stress tensor determination method comprising three-layer medium model Download PDF

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CN117268617B
CN117268617B CN202311187700.1A CN202311187700A CN117268617B CN 117268617 B CN117268617 B CN 117268617B CN 202311187700 A CN202311187700 A CN 202311187700A CN 117268617 B CN117268617 B CN 117268617B
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strain
stress
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elastic modulus
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CN117268617A (en
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郑民总
李邵军
杜效鹄
周兴波
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Wuhan Institute of Rock and Soil Mechanics of CAS
China Renewable Energy Engineering Institute
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China Renewable Energy Engineering Institute
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    • G—PHYSICS
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Abstract

The application provides a stress tensor determination method comprising a three-layer dielectric model. Accurate acquisition of stress states is of great importance in engineering practice. The core-in stress relief method calculates the stress tensor by measuring strain with a triaxial strain gauge. However, the analytical solution of the current stress calculation is based on a two-layer model, and the situation of three-layer medium cannot be calculated. The application provides a method for calculating triaxial strain unit stress tensor in a three-layer medium model. On the basis of numerical simulation, four equivalent elastic parameters of the three-layer model are searched by utilizing a genetic algorithm. By utilizing the equivalent elastic parameters and the analytic solutions of the double-layer model, the correction coefficient of the stress observation equation, namely the K value of the three-layer model, can be calculated, so that the accurate and effective stress tensor measurement effect can be realized, and the data use requirement of the actual engineering can be met.

Description

Stress tensor determination method comprising three-layer medium model
Technical Field
The application relates to the field of ground stress monitoring, in particular to a stress tensor determination method comprising a three-layer medium model.
Background
Accurate acquisition of the ground stress state is an important task in engineering practice, and the core-in-sheath stress relief method is the most direct and effective method in the ground stress measurement, which can measure all stress components at one time.
The borehole core stress relief method calculates six stress components by measuring the strain change of the borehole wall before and after core relief. The earlier-occurring borehole wall strain measurement method (CSIR triaxial STRAIN CELL) is used for directly pasting a strain measurement element on the borehole wall, and the measurement method is used for directly pasting a strain gauge on the borehole wall, so that the technical difficulty is high, and the success rate is low. In order to improve the success rate of the test, a strain measurement method (CSIRO HI cell) of the borehole wall of a hollow inclusion appears, wherein after a strain measurement element is firstly stuck on a prefabricated epoxy resin thin cylinder, an epoxy resin adhesive is used for filling the pore between a strain gauge and the borehole wall during the ground stress measurement. The borehole wall strain measurement (CSIR) measurement process involves only one medium of rock, as shown in part (a) of a schematic view of one scenario of prior art strain measurement shown in fig. 1. The single layer dielectric stress solution model is built from Kirsch solutions of stress distribution around circular openings in rock dielectric under far field stress. The strain measurement (CSIRO) of the wall of the hollow inclusion borehole comprises a rock layer and an epoxy resin layer medium in the measurement process, and the hollow inclusion borehole wall is a double-layer medium model, as shown in part (b) of fig. 1. The double layer dielectric stress solution model is given by Duncan Fama (1980) based on the bonded elastic annular layer theory, and corrects errors caused by that strain gauges are not directly adhered to the wall of a borehole.
However, in engineering practice, there often occur cases where the elastic parameters of the hollow inclusion material and the couplant material are inconsistent, especially where strain measurement elements are employed for long-term monitoring of stress changes. When the filler is inconsistent with the material of the hollow inclusion, the stress resolving model comprises rock, couplant and the hollow inclusion three-layer medium, as shown in part (c) of fig. 1. The three-layer medium model has no analytical solution like a single-layer medium and a double-layer medium at present, but only adopts numerical simulation to obtain a relation matrix of stress and strain, and then reversely calculates the stress according to a strain test result. However, the numerical solution is greatly affected by the model, and when the model parameters change, different numerical models need to be built for calculation, which is inconvenient to use in actual engineering. In practice, the reason why the stress-strain observation coefficient matrix is different between the single-layer dielectric model and the double-layer dielectric model is that the K values in the two stress analysis solution models are different, and the single-layer dielectric model is a special case that K is 1 in the double-layer dielectric model.
That is, in the prior art, strain measurement schemes based on a dielectric model have the disadvantage of limited accuracy.
Disclosure of Invention
The application provides a stress tensor determining method comprising a three-layer medium model, which can realize an accurate and effective stress tensor measuring effect by constructing an accurate and effective three-layer medium model for strain monitoring points and meet the data use requirements of actual engineering.
The application provides a stress tensor determination method comprising a three-layer medium model, which comprises the following steps:
After an analysis task of a stress tensor corresponding to the strain monitoring point is determined, the inner diameter R of the inner layer of the drill hole where the strain monitoring point is located, the outer diameter R 1 of the inner layer, the position rho of the strain monitoring point in the drill hole and the outer diameter R 2 of the middle layer are obtained, wherein a three-layer medium model of the drill hole comprises a rock layer, a middle layer and the inner layer from outside to inside;
Obtaining the elastic modulus E of the rock layer, the Poisson ratio mu of the rock layer, the elastic modulus E 2 of the middle layer, the Poisson ratio mu 2 of the middle layer, the elastic modulus E 1 of the inner layer and the Poisson ratio mu 1 of the inner layer;
Based on the inner diameter R of the inner layer, the outer diameter R 1 of the inner layer, the position rho of the strain monitoring point in the drill hole, the outer diameter R 2 of the middle layer, the elastic modulus E of the rock layer, the Poisson ratio mu of the rock layer, the elastic modulus E 2 of the middle layer, the Poisson ratio mu 2 of the middle layer, the elastic modulus E 1 of the inner layer and the Poisson ratio mu 1 of the inner layer, loading a three-dimensional stress tensor sigma m on the three-layer medium model, and simulating to obtain a strain observation matrix epsilon of the strain monitoring point;
Setting equivalent elastic parameters E ', mu', E 1 'and mu 1' of the three-layer medium model as unknown quantities, and establishing estimation functions sigma s＝F(E',μ,E1,μ1 and epsilon of stress tensors sigma s by a strain observation matrix epsilon;
Solving optimal estimated values E' *、μ'*、E1'* and mu 1'* of equivalent elastic parameters of the three-layer medium model for minimizing an objective function, wherein the objective function is expressed as: The objective function is the euclidean distance between σ m and σ s, F of the order is F norm;
On the basis of the optimal estimated values E' *、μ'*、E1'* and mu 1'*, calculating correction coefficients K 1、K2、K3 and K 4 of the strain gauge of the three-layer medium model, which are not directly adhered to the hole wall;
and (3) embedding the correction coefficients K 1、K2、K3 and K 4 into a stress observation equation, and solving the corresponding stress tensor of the strain monitoring point.
From the above, the present application has the following advantages:
In an application scene of strain monitoring, after an analysis task of a strain tensor corresponding to a strain monitoring point is determined, the inner diameter R of an inner layer of a drill hole where the strain monitoring point is located, the outer diameter R 1 of the inner layer, the position rho of the strain monitoring point in the drill hole and the outer diameter R 2 of an intermediate layer are obtained, wherein a three-layer medium model of the drill hole comprises a rock layer, the intermediate layer and the inner layer from outside to inside, the elastic modulus E of the rock layer, the Poisson ratio mu of the rock layer, the elastic modulus E 2 of the intermediate layer, the Poisson ratio mu 2 of the intermediate layer, the elastic modulus E 1 of the inner layer and the Poisson ratio mu 1 of the inner layer are obtained, a three-dimensional stress tensor sigma m is loaded on the three-layer medium model, a strain observation matrix epsilon of the strain monitoring point is obtained through simulation, an estimation function sigma s＝F(E',μ,E1,μ1 and epsilon of the stress tensor is established by the strain observation matrix epsilon, so that the optimal value E' *、μ'*、E1'* and the optimal value of the three-layer medium model equivalent elastic parameter of an objective function sigma s are obtained, and mu representing the objective function is represented as: The method comprises the steps of calculating correction coefficients K 1、K2、K3 and K 4 of a strain sheet of a three-layer medium model, which are not directly adhered to a hole wall, on the basis of optimal estimated values E' *、μ'*、E1'* and mu 1'*, wherein the objective function is Euclidean distance between sigma m and sigma s, the I F is F norm, sheathing the correction coefficients K 1、K2、K3 and K 4 into a stress observation equation, and solving a stress tensor corresponding to a strain monitoring point.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic view of a prior art strain measurement scenario;
FIG. 2 is a flow chart of a method of determining a stress tensor according to the present application;
FIG. 3 is a schematic flow chart of K value calculation of a three-layer dielectric model according to the present application;
fig. 4 is a schematic view of a scenario of the stress relief method numerical simulation model of the present application.
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to fall within the scope of the application.
The terms first, second and the like in the description and in the claims and in the above-described figures, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments described herein may be implemented in other sequences than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or modules is not necessarily limited to those steps or modules that are expressly listed or inherent to such process, method, article, or apparatus. The naming or numbering of the steps in the present application does not mean that the steps in the method flow must be executed according to the time/logic sequence indicated by the naming or numbering, and the execution sequence of the steps in the flow that are named or numbered may be changed according to the technical purpose to be achieved, so long as the same or similar technical effects can be achieved.
The division of the modules in the present application is a logical division, and may be implemented in another manner in practical applications, for example, a plurality of modules may be combined or integrated in another system, or some features may be omitted or not implemented, and further, coupling or direct coupling or communication connection between the modules shown or discussed may be through some interfaces, and indirect coupling or communication connection between the modules may be electrical or other similar manners, which are not limited in the present application. The modules or sub-modules described as separate components may be physically separated or not, or may be distributed in a plurality of circuit modules, and some or all of the modules may be selected according to actual needs to achieve the purpose of the present application.
Before describing the stress tensor determination method comprising the three-layer medium model provided by the application, the background content related to the application is first described.
According to the stress tensor determining method comprising the three-layer medium model, the accurate and effective three-layer medium model is built for the strain monitoring points, so that an accurate and effective stress tensor measuring effect can be achieved, and the data use requirements of actual engineering are met.
The method for determining the stress tensor of the three-layer medium model provided by the application is started to be described below.
First, referring to fig. 2, fig. 2 shows a flow chart of a method for determining a stress tensor including a three-layer dielectric model according to the present application, and the method for determining a stress tensor including a three-layer dielectric model according to the present application may specifically include steps S201 to S207 as follows:
Step S201, after determining an analysis task of a stress tensor corresponding to a strain monitoring point, acquiring an inner diameter R of an inner layer of a drill hole where the strain monitoring point is located, an outer diameter R 1 of the inner layer, a position rho of the strain monitoring point in the drill hole and an outer diameter R 2 of an intermediate layer, wherein a three-layer medium model of the drill hole comprises a rock layer, the intermediate layer and the inner layer from outside to inside;
It can be seen here that the application constructs a three-layer medium model for the strain monitoring point, the three-layer medium model is matched with the drilling hole where the strain monitoring point is located, and the three-layer medium model relates to a rock layer, a middle layer and an inner layer at the drilling hole, wherein the middle layer can also be called as a middle layer medium and a middle ring layer, and the inner layer can be called as an inner layer medium and an inner ring layer.
In actual operation, the analysis task of the stress tensor corresponding to the specific strain monitoring point is usually initiated in a processing task mode, and the analysis task can be initiated manually by a related user (staff) or automatically by a system according to a preset initiation strategy, and is configured adaptively according to actual needs.
Meanwhile, some basic data of the strain monitoring point or the drill hole where the strain monitoring point or the drill hole is located in the subsequent step S202 may be directly carried in the task information when the task is initiated, so that the subsequent need may be directly extracted, or the acquisition address/path of the data may be carried in the task information when the task is initiated, so that the subsequent need may be acquired according to the acquisition address/path indicated by the task information, or may be acquired by only indicating the specific strain monitoring point or the drill hole where the strain monitoring point is located, and may be retrieved locally or on other devices/systems, or may also be obviously flexible through outputting a corresponding input window to enable the user (staff) to manually enter …, or the like, where one or more of the acquisition modes may be configured/selected according to actual needs.
It should be understood that, the inner diameter R of the inner layer of the drill hole where the strain monitoring point is located, the outer diameter R 1 of the inner layer, the position ρ of the strain monitoring point in the drill hole and the outer diameter R 2 of the middle layer obtained in step S201 are three-layer medium models related to the application for preliminary construction.
Step S202, obtaining the elastic modulus E of the rock layer, the Poisson ' S ratio mu of the rock layer, the elastic modulus E 2 of the middle layer, the Poisson ' S ratio mu 2 of the middle layer, the elastic modulus E 1 of the inner layer and the Poisson ' S ratio mu 1 of the inner layer;
After the basic parameters of the three-layer medium model related to the application are obtained in the previous step 201 and the three-layer medium model is initially constructed, the elastic modulus E of the rock layer, the poisson ratio mu of the rock layer, the elastic modulus E 2 of the middle layer, the poisson ratio mu 2 of the middle layer, the elastic modulus E 1 of the inner layer and the poisson ratio mu 1 of the inner layer obtained from the microcosmic layer can be combined to provide data of fine aspects for the three-layer medium model, perfect the fine aspects of the three-layer medium model and provide a good model foundation for subsequent data processing.
Step S203, loading a three-layer medium model with a three-dimensional stress tensor sigma m on the basis of the inner diameter R of the inner layer, the outer diameter R 1 of the inner layer, the position rho of a strain monitoring point in a drill hole, the outer diameter R 2 of the middle layer, the elastic modulus E of the rock layer, the Poisson ratio mu of the rock layer, the elastic modulus E 2 of the middle layer, the Poisson ratio mu 2 of the middle layer, the elastic modulus E 1 of the inner layer and the Poisson ratio mu 1 of the inner layer, and simulating to obtain a strain observation matrix epsilon of the strain monitoring point;
Based on the parameters (formed three-layer medium model) obtained in the step S201 and the step S201, a corresponding three-dimensional stress tensor (recorded as sigma m) can be loaded in the construction environment of the three-layer medium model, so that a strain observation matrix epsilon for obtaining strain monitoring points is solved, and a specific basis is provided for construction of a later estimation function.
Step S204, setting equivalent elastic parameters E ', mu', E 1 ', mu 1' of the three-layer medium model as unknown quantities, and establishing estimation functions sigma s＝F(E',μ,E1,μ1 and epsilon of stress tensors sigma s by a strain observation matrix epsilon;
The estimation functions σ s＝F(E,μ,E1,μ1, ε of the stress tensor σ s are briefly described here (the reasoning process involved here for the core setup of the application):
The basic principle of measuring the ground stress of the raw rock by the sleeve core stress relief method is to install a deformation or strain testing element in a drill hole, use a core drill with larger testing aperture, concentrically sleeve the testing hole, isolate the core with the sensor element from surrounding rock mass, and determine the stress by measuring the change value of the surface strain of the hole aperture or the hole wall before and after the sleeve drill.
The stress relief method of the drilling sleeve core is based on the on-line elastic theory, the rock is regarded as a homogeneous isotropic line elastomer, the strain value of the wall of the drilling hole is measured, and the stress observation equation of the following (1) is established:
Eεk＝Ak1σx+Ak2σy+Ak3σz+Ak4τxy+Ak5τyz+Ak6τxz k＝1～n,
Wherein E is the elastic modulus of the rock, epsilon k is the positive strain of measuring points of different orientations of the drill hole, k is the measuring point number, A k1～Ak6 is a relation matrix of stress and strain, sigma x、σy、σz、τxy、τxz and tau yz are 6 different stress components, and the optimal value of the 6 stress components is solved by adopting a least square method through the following formula (2), namely, the optimal value of the stress components is obtained by solving a normal equation set.
When the hollow inclusion measurement method is adopted, the stress calculation model comprises a rock and epoxy resin double-layer medium, the double-layer medium stress calculation model is given by Duncan Fama (1980) based on the bonded elastic annular layer theory, and the observation coefficient calculation expression of A k1～Ak6 is the following formula (3):
Wherein E and mu are the elastic modulus and Poisson's ratio, θ and μ of the rock, respectively For the angle of the strain monitoring point in the drill hole, K 1、K2、K3 and K 4 represent correction coefficients that the strain gauge is not directly adhered to the hole wall, and the calculation formula is as follows:
wherein the parameter concerned is represented by the following formula (5):
wherein E and mu are the elastic modulus and Poisson's ratio of rock respectively, E 1 and mu 1 are the elastic modulus and Poisson's ratio of the inner annular layer respectively, R 1 and R are the outer diameter and inner diameter of the inner annular layer respectively, and ρ is the mounting position of the strain gauge (strain monitoring point).
Based on these, according to the above test theory, the equation (1) estimates the stress tensor σ s from the strain observation matrix ε, which can be simplified to be represented by the following equation (6):
[σs]＝[A][ε]，
wherein A is a relation matrix of stress and strain, and A= [ A k1,Ak1,...,Ak6 ]. For the two-layer dielectric model, given the borehole size, as can be seen from the above formulas (3) to (6), the relation matrix a of stress and strain is a function of K value, and is represented by the following formula (7):
Aki＝f(K) i＝1～6，
Wherein k= [ K 1,K2,K3,K4 ] which is a function of the elastic modulus E of the rock, poisson's ratio μ, the elastic modulus E 1 of the inner annular layer, and poisson's ratio μ 1, as shown in the following formula (8):
Kj＝g(E,μ,E1,μ1) j＝1～4，
For the single layer media model, in formula (8), e=e 1,μ＝μ1, then there is formula (9) below:
Kj＝g(E,μ,E,μ) j＝1～4，
If the three-layer dielectric stress calculation model is the same as the single-layer and double-layer dielectric models, the K value thereof can be calculated according to the equivalent elastic parameters E ', μ', E 1 ', and μ 1', then the following formula (10) is given:
Kj＝g(E*,μ*,E1 *,μ1 *) j＝1～4，
It can be seen that for a three-layer dielectric model, the equivalent elastic parameters E ', μ', E 1 ', and μ 1' of the three-layer dielectric model need to be known in order to calculate the stress tensor from the analytical solutions of the single-layer and dual-layer dielectric models.
In contrast, the application obtains the strain observation matrix epsilon under the stress tensor sigma s of the three-layer medium model through numerical simulation, takes the equivalent elastic parameters E ', mu', E 1 'and mu 1' of the three-layer medium model as unknowns, establishes the estimation function of the stress tensor sigma s by the strain observation matrix epsilon, and solves the 4 unknown quantities to be solved of the three-layer medium model.
Step S205, solving the optimal estimated values E' *、μ'*、E1'* and μ 1'* of the equivalent elastic parameters of the three-layer dielectric model that minimizes the objective function, where the objective function is expressed as: The objective function is the euclidean distance between σ m and σ s, F of the order is F norm;
After the estimation function sigma s of the stress tensor sigma s is configured in the front, the objective function for which the present application is configured can be continued On the basis of the method, the optimal estimated values E' *、μ'*、E1'* and mu 1'* of the minimum values are obtained through searching and solving, and the determination of the equivalent elastic parameters of the three-layer medium model is completed.
The objective function referred to herein may be specifically constructed by using a Ga genetic algorithm in practical application, and in this case, the objective function may be an fitness function corresponding to the Ga genetic algorithm.
For Ga genetic algorithm (Genetic Algorithm, ga), which is a global optimization method, simulating the rule of 'win-survival' in the natural biological evolution process, introducing replication, hybridization, mutation and the like into the algorithm, adopting simple coding technology to represent various complex structures, the direction of search is guided to learn and determined by simple genetic operation and natural selection of superior and inferior of a group of coded codes, so that a more convenient floor application scheme is provided for the application in detail.
Of course, it is understood that in practical application, other types of searching algorithms may be used to search the optimal values to be determined herein (i.e. the optimal estimated values E' *、μ'*、E1'* and μ 1'* of the equivalent elastic parameters of the three-layer dielectric model that minimize the objective function), and the values may be adjusted according to the actual needs.
Step S206, calculating correction coefficients K 1、K2、K3 and K 4 of the strain gauge of the three-layer medium model, which are not directly adhered to the hole wall, on the basis of the optimal estimated values E' *、μ'*、E1'* and mu 1'*;
Therefore, after the optimal estimated values E' *、μ'*、E1'* and mu 1'* of the equivalent elastic parameters of the three-layer medium model are determined, correction coefficients K 1、K2、K3 and K 4, which are mentioned in the reasoning process and are not directly adhered to the hole wall, of the strain gauge of the three-layer medium model can be calculated based on the optimal estimated values, so that data support is provided for the calculation of the follow-up specific stress tensor.
Specifically, the calculation here for the correction coefficients K 1、K2、K3 and K 4 is:
On the basis of the optimal estimated values E' *、μ'*、E1'* and mu 1'*, correction coefficients K 1、K2、K3 and K 4 (specific formula contents are not repeated here for avoiding repeated contents) of the strain gauge of the three-layer medium model, which is not directly adhered to the hole wall, are calculated through the formula (4) and the formula (5).
And S207, embedding correction coefficients K 1、K2、K3 and K 4 into a stress observation equation, and solving the corresponding stress tensor of the strain monitoring point.
Corresponding to the content of the application observation equation related to the previous reasoning process, the correction coefficients K 1、K2、K3 and K 4 determined in the previous step S207 may be sleeved into the stress observation equation, that is, the equations (1) to (3), to determine the stress tensor corresponding to the strain monitoring point to be determined in the current processing task.
Specifically, for the above processing logic of the stress tensor, a more complete understanding may also be obtained by referring to a schematic flow chart of K-value calculation of the three-layer dielectric model of the present application shown in fig. 3 (taking Ga algorithm for the above optimal estimation search as an example).
To facilitate a more complete understanding of the foregoing, a more visual description may be provided by way of the following set of examples in actual practice.
The stress test numerical model can refer to a scene diagram of the stress relief method numerical simulation model of the application shown in fig. 4, wherein the model is 4m in the x direction, 2m in the y direction and 4m in the z direction of the drilling shaft. The drilling model in the rock has three layers of medium, namely a rock layer, a middle layer and an inner layer. Numerical simulations were performed using FLAC 3D software, applying 6 stress components σ x、σy、σz、τxy、τxz and τ yz at the boundaries. The stress-strain relation of the elastic model meets the linear superposition principle, so that for a three-layer medium model with given 6 elastic parameters, K values inverted based on a Ga algorithm under any stress loading condition sigma m and a corresponding strain matrix epsilon are consistent. The compressive stress sign is negative in each stress component value σx＝－30MPa,σy＝－20MPa,σz＝－10MPa,τxy＝20MPa,τyz＝10MPa,τxz＝－10MPa,FLAC3D. The elastic modulus and poisson ratio of the inner layer medium are set to be E 1＝30GPa,μ1 =0.2, the elastic modulus and poisson ratio of the stone layer are set to be e=25gpa, μ=0.3, and the elastic modulus and poisson ratio of the middle layer medium are set to be E 2＝7GPa,μ2 =0.25, at which time the model comprises three layers of mediums. The stress σ m was applied at the model boundary shown in fig. 4, and the 9 strains at different orientations of the borehole were obtained after solving for the balance, as shown in table 1 below. As shown in the Ga inversion algorithm flow in FIG. 3, an estimation function of stress tensor sigma s is established by a strain observation matrix epsilon, and an adaptation function of a Ga genetic algorithm is established by taking equivalent elastic parameters E ', mu', E 1 'and mu 1' of a three-layer medium model as unknowns.
TABLE 1 drilling 9 azimuth Strain (Unit: mu epsilon)
According to Matlab's genetic algorithm toolbox, the upper and lower limits of E ' and E 1 were set to 100GPa and 0GPa, respectively, and the upper and lower limits of μ ' and μ 1 ' were set to 0 and 0.5, respectively, and inversion gave E ' *＝26.62GPa,μ′*＝0.289,E1'*＝18.54GPa,μ1'* =0.42. Finally, K1 *＝1.1184,K2 *＝0.6818,K3 *＝1.0674,K4 *＝0.9393. is calculated according to the formula (4) and the formula (5), and according to the stress calculation methods of the formulas (1) to (3), K * values (4) are substituted to obtain an estimated value σx *＝－30.0MPa,σy *＝－20.0MPa,σz *＝－10.0MPa,τxy *＝20.0MPa,τyz *＝10.0MPa,τxz *＝－10.0MPa, of the stress component, and an estimated value sigma s of the stress component is basically consistent with a loading value sigma m. It can be seen that for the three-layer medium model, after the K value is obtained through inversion of the Ga genetic algorithm, the stress tensor can be accurately calculated by the stress calculation analysis solution of the double-layer medium model, so that the effectiveness and the accuracy of inversion of the K value in the three-layer medium model based on the Ga genetic algorithm are demonstrated.
It can be seen from the above examples that the objective function involved in the process of searching the optimal estimated values E' *、μ'*、E1'* and mu 1'* of the equivalent elastic parameters of the three-layer medium model which minimizes the objective function can be specifically constructed in the application environment of Matlab, and the Ga genetic algorithm is taken as an example, that is, the objective function can be specifically constructed in the application environment of Matlab by adopting the Ga genetic algorithm, so that a more convenient floor application scheme is provided for the application in detail.
Meanwhile, it can be noted that the application can be particularly used for loading the three-dimensional stress tensor sigma m of the three-layer medium model in the FLAC 3D application environment, so as to simulate and obtain the strain observation matrix epsilon of the strain monitoring points.
Of course, for what application environment is to load the three-layer dielectric model with the three-dimensional stress tensor sigma m, in practical application, the application of the application such as Ga genetic algorithm, FLAC 3D and Matlab can be adaptively configured according to practical needs, and in a further development point, the application of the application follows the idea of using the existing tools to conveniently realize the floor application of the scheme of the application, but not the scheme that the scheme is necessarily realized by using the tools, and for the related tools/application environments, the application can be either ready or self-configured, and the application is not limited in this particular.
From the above scheme, it can be seen that, under the application scenario of strain monitoring, after the analysis task of the strain monitoring point corresponding to the stress tensor is determined, the inner diameter R of the inner layer of the drill hole where the strain monitoring point is located, the outer diameter R 1 of the inner layer, the position ρ of the strain monitoring point in the drill hole and the outer diameter R 2 of the middle layer are obtained, wherein the three-layer medium model of the drill hole comprises a rock layer, the middle layer and the inner layer from outside to inside, the elastic modulus E of the rock layer, the poisson ratio μ of the rock layer, the elastic modulus E 2 of the middle layer, the poisson ratio μ 2 of the middle layer, the elastic modulus E 1 of the inner layer and the poisson ratio μ 1 of the inner layer are obtained, on the basis of these parameters, the three-layer medium model is loaded with a three-dimensional stress tensor σ m, the strain observation matrix epsilon of the strain monitoring point is obtained by simulation, the three-layer medium model equivalent elastic parameters E ', μ ', E 1 ', and μ 1 ' are unknown quantities, an estimated function σ s＝F(E',μ,E1,μ1 of the stress tensor s is established by the strain observation matrix epsilon, and an estimated function is obtained, and an optimal function is represented by three-layer equivalent function, and an optimal value, and an estimated value of the elastic medium E23, and an optimal value is represented by the estimated value as σ 23 '.The method comprises the steps of calculating correction coefficients K 1、K2、K3 and K 4 of a strain sheet of a three-layer medium model, which are not directly adhered to a hole wall, on the basis of optimal estimated values E' *、μ'*、E1'* and mu 1'*, wherein the objective function is Euclidean distance between sigma m and sigma s, the I F is F norm, sheathing the correction coefficients K 1、K2、K3 and K 4 into a stress observation equation, and solving a stress tensor corresponding to a strain monitoring point.
After the analysis of the stress tensor is completed and the specific measurement result of the application tensor is obtained, the method for determining the application tensor can also relate to a subsequent data use link.
Specifically, the measurement of related data in the engineering is mainly served for the actual engineering, and a data basis is provided for the actual engineering, so as to play a role in guiding engineering operation, wherein the analysis of stress tensors can be mainly used for the analysis of stability of engineering rock mass, and correspondingly, the step S207 is a method according to claim 1, and is characterized in that correction coefficients K 1、K2、K3 and K 4 are sleeved into a stress observation equation, and after the stress tensors corresponding to the strain monitoring points are solved, the method for determining the stress tensors of the application can further comprise the following steps:
And (3) based on the corresponding stress tensor of the strain monitoring points, analyzing the stability of the rock mass of the engineering where the strain monitoring points are located.
It will be appreciated that the work of analysis of the stability of the rock mass concerned, developed in the case where the strain monitoring point corresponds to the stress tensor, is within the scope of conventional operations, the disclosure of which is mainly supplementary to the solution according to the application and therefore will not be developed in detail.
And for the concrete content of the rock mass stability analysis work, it can be understood that the existing analysis strategy can be adopted, the analysis strategy can be continuously optimized, and the newly developed analysis strategy can be adopted, so that the rock mass stability analysis work is possible and can be adjusted according to actual needs.
The stress tensor determination method comprising the three-layer dielectric model provided by the application is described in detail, and specific examples are applied to illustrate the principle and the implementation of the application, and the description of the examples is only used for helping to understand the method and the core idea of the application; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in light of the ideas of the present application, the present description should not be construed as limiting the present application.

Claims (7)

1. A method for determining a stress tensor comprising a three-layer dielectric model, the method comprising:
After an analysis task of a stress tensor corresponding to a strain monitoring point is determined, acquiring an inner diameter R of an inner layer of a drill hole where the strain monitoring point is located, an outer diameter R 1 of the inner layer, a position rho of the strain monitoring point in the drill hole and an outer diameter R 2 of an intermediate layer, wherein a three-layer medium model of the drill hole comprises a rock layer, the intermediate layer and the inner layer from outside to inside;
Acquiring the elastic modulus E of the rock layer, the Poisson ratio mu of the rock layer, the elastic modulus E 2 of the middle layer, the Poisson ratio mu 2 of the middle layer, the elastic modulus E 1 of the inner layer and the Poisson ratio mu 1 of the inner layer;
Loading a three-dimensional stress tensor sigma m on the three-layer medium model on the basis of the inner diameter R of the inner layer, the outer diameter R 1 of the inner layer, the position rho of the strain monitoring point in the drill hole, the outer diameter R 2 of the middle layer, the elastic modulus E of the rock layer, the Poisson ratio mu of the rock layer, the elastic modulus E 2 of the middle layer, the Poisson ratio mu 2 of the middle layer, the elastic modulus E 1 of the inner layer and the Poisson ratio mu 1 of the inner layer, and simulating to obtain a strain observation matrix epsilon of the strain monitoring point;
Setting equivalent elastic parameters E ', mu ', E 1 ' and mu 1 ' of a three-layer medium model as unknown quantities, and establishing an estimation function sigma s＝F(E′,μ′,E1′,μ1 ', epsilon of a stress tensor sigma s by using the strain observation matrix epsilon;
solving optimal estimated values E' *、μ′*、E1′* and mu 1′* of equivalent elastic parameters of the three-layer medium model, wherein the optimal estimated values are the minimum objective function, and the objective function is expressed as: s= |σ m-σs||F 2, the objective function is the euclidean distance between σ m and σ s, and|·| F is the F norm;
On the basis of the optimal estimated values E' *、μ′*、E1′* and mu 1′*, calculating correction coefficients K 1、K2、K3 and K 4 of the strain gauge of the three-layer medium model, which are not directly adhered to the hole wall;
And sleeving the correction coefficients K 1、K2、K3 and K 4 into a stress observation equation, and solving the corresponding stress tensor of the strain monitoring point.
2. The method of claim 1, wherein calculating correction coefficients K 1、K2、K3 and K 4 for strain gages of the three-layer dielectric model that are not directly adhered to the hole wall based on the optimal estimated values E' *、μ′*、E1′* and μ 1′* comprises:
Substituting the optimal estimated values E' *、μ′*、E1′* and mu 1′* into parameters E, mu, E 1 and mu 1 in the following formula, and calculating correction coefficients K 1、K2、K3 and K 4 of the strain gauge of the three-layer medium model, which are not directly adhered to the hole wall, through the following formula:
among them, there are:
3. the method of claim 1, wherein the stress observation equation comprises:
Eεk＝Ak1σx+Ak2σy+Ak3σz+Ak4τxy+Ak5τyz+Ak6τxz ＝1～n,
Wherein epsilon k is the positive strain of measuring points of different orientations of the drill, sigma x、σy、σz、τxy、τxz and tau yz are 6 different stress components, k is the measuring point number, A k1～Ak6 is the relation matrix of stress and strain, and the optimal values of sigma x、σy、σz、τxy、τxz and tau yz are solved by adopting a least square method through the following formula:
When the hollow inclusion measurement method is adopted, the observation coefficient calculation expression of A k1～A k6 is as follows:
Wherein θ and Is the angle of the strain monitoring point within the borehole.
4. The method of claim 1, wherein loading the three-layer dielectric model with a three-dimensional stress tensor σ m based on the inner diameter R of the inner layer, the outer diameter R 1 of the inner layer, the location ρ of the strain monitoring point within the borehole, the outer diameter R 2 of the intermediate layer, the elastic modulus E of the rock layer, the poisson's ratio μ of the rock layer, the elastic modulus E 2 of the intermediate layer, the poisson's ratio μ 2 of the intermediate layer, the elastic modulus E 1 of the inner layer, and the poisson's ratio μ 1 of the inner layer simulates a strain observation matrix ε for the strain monitoring point, comprising:
In the FLAC 3D application environment, the three-dimensional stress tensor sigma m is loaded on the three-layer medium model on the basis of the inner diameter R of the inner layer, the outer diameter R 1 of the inner layer, the position rho of the strain monitoring point in the drill hole, the outer diameter R 2 of the middle layer, the elastic modulus E of the rock layer, the Poisson ratio mu of the rock layer, the elastic modulus E 2 of the middle layer, the Poisson ratio mu 2 of the middle layer, the elastic modulus E 1 of the inner layer and the Poisson ratio mu 1 of the inner layer, so that the strain observation matrix epsilon of the strain monitoring point is obtained through simulation.
5. The method according to claim 1, characterized in that the objective function is constructed specifically using a Ga genetic algorithm.
6. The method according to claim 5, wherein the objective function is constructed using Ga genetic algorithm, in particular in Matlab's application environment.
7. The method of claim 1, wherein the fitting the correction coefficients K 1、K2、K3 and K 4 to a stress observation equation, after solving for the strain monitor point corresponding stress tensor, further comprises:
And based on the corresponding stress tensor of the strain monitoring points, unfolding the rock mass stability analysis of the engineering where the strain monitoring points are located.
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