CN107633146B - Method for high-precision conversion of crustal stress calculation results among different scale models - Google Patents
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Abstract
The invention discloses a method for high-precision conversion of a geostress calculation result between models with different scales. The method does not need to regress and calculate the initial stress of the new grid point due to the change of the calculation model grid, and lays a foundation for the follow-up calculation research. The method has the advantages that the calculation efficiency is improved according to the description of the scheme, and compared with the traditional method of fitting the initial stress function in the engineering area by adopting a mathematical statistics method, the calculation precision and reliability are improved.
Description
Technical Field
The invention relates to the field of underground engineering, in particular to a method for converting the calculation result of the crustal stress between models with different scales with high precision.
Background
The initial ground stress field of the rock mass reflects the natural stress state existing in the stratum and is the main load of the deformation of the surrounding rock of the underground cavern group. For the deformation mechanism analysis, the construction method research and the support scheme optimization of the surrounding rock of the underground cavern group, the initial ground stress field of the rock mass is a necessary condition for numerical simulation and stability analysis of underground engineering, and whether the applied initial ground stress field really determines the rationality of the research result to a great extent.
The ground stress is measured actually on site, which is the most direct and effective way to obtain the initial stress field of the underground factory building area, but because the rock mass has complex causes and a lot of influence factors and is limited by objective conditions such as site and test expenses, the obtained ground stress measurement result can only reflect the local stress field of a limited engineering area, and the measured ground stress value has a certain degree of discreteness due to the influence of measurement errors. Therefore, how to invert the initial ground stress field of the underground factory building area by using a small amount of measured data has important practical significance on the design and construction of underground engineering.
At present, the methods for performing inversion and regression analysis on the initial ground stress state of the whole engineering area according to the measured data (stress, displacement) can be roughly divided into two categories: one is a displacement inverse analysis method based on field measured displacement data, and the other is a stress regression method based on measured ground stress data. The invention combines the actually measured ground stress data to select a second method to carry out regression analysis on the initial ground stress field.
In order to obtain a reasonable geostress inversion result, it is usually necessary to perform geostress field inversion in a large range, and the initial stress of discrete points related to mesh generation obtained by the regression analysis is inconvenient to use because the initial stress of a new mesh point needs to be regressed and calculated every time the calculation mesh changes. In order to apply the inversion result of the initial ground stress field to all construction method researches and support design calculation, a mathematical statistics method is mostly adopted at the present stage, the influence of the buried depth and mountain terrain topography on the initial ground stress field is considered, the initial stress of each discrete point obtained by regression analysis is fitted in a three-dimensional space, and then an initial stress function in a project area is obtained. By adopting the method, when the computational grid is changed, the initial stress of the new grid point can be obtained only by substituting the burial depth of the new grid point into the corresponding stress function, and the computational efficiency is improved to a certain extent. However, the method also has a certain defect that the fitting of the initial ground stress function only selects the regression stress values of a small number of units on partial cross sections of the underground plant area for fitting, the obtained initial ground stress function and the regression fitting stress have large errors with the actually measured ground stress, and the reliability of the initial stress field of the underground plant area obtained by regression fitting calculation is to be improved.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for converting the calculation result of the crustal stress between models with different scales with high precision.
In order to achieve the purpose, the invention deduces a stress conversion calculation formula among different models according to a finite element basic theory, can realize the high-precision conversion from the stress calculation result of a large-range ground stress inversion model to a fine calculation model on the basis of an inversion calculation result data file, and when a calculation model grid changes, the initial stress of a new grid point does not need to be regressed and calculated again, thereby laying a foundation for subsequent calculation research and improving the calculation efficiency; compared with the traditional method of fitting the initial stress function in the engineering area by adopting a mathematical statistics method, the method improves the calculation precision and reliability.
Specifically, the invention relates to a method for converting the calculation result of the crustal stress between models with different scales at high precision, which is characterized by comprising the following steps of:
step 1: comprehensively considering the influence of factors such as power station engineering topographic and geological conditions, underground cavern arrangement types, section sizes, distribution conditions of ground stress actual measurement points and the like on the inversion of the ground stress field, and establishing a large-range ground stress inversion model for initial ground stress field inversion;
wherein, unfavorable geological structures such as fault, soft rock are considered to the ground stress inversion model on a large scale, utilize nature demarcation such as valley, gully, simulation range includes: the system comprises a plurality of power station buildings, such as an upper warehouse, a diversion tunnel, an upstream surge chamber, a high-pressure branch pipe, an underground plant, a tail water tunnel, a tail water surge chamber and the like.
Step 2: and (3) according to the initial ground stress point and the measured value thereof actually measured in the factory area, inverting the initial ground stress field by adopting a finite element method and combining a multivariate linear regression method, a neural network method or a direct inverse analysis method.
The step 2 specifically comprises the following steps:
step 2-1: and dividing the actually measured initial ground stress points into 2 groups, namely an inversion point and a verification point, wherein the inversion point is used for inverting the initial ground stress field, and the verification point is used for verifying the rationality of the ground stress field obtained by inversion.
Step 2-2: according to the measured initial ground stress point and the measured value thereof in the factory area, respectively inverting the initial ground stress field by adopting a finite element method and combining a multivariate linear regression method, a neural network method or a genetic algorithm, wherein the basic ideas of the three inversion analysis methods are respectively as follows:
the multivariate linear regression method takes factors which can possibly form an initial ground stress field as undetermined factors, calculates the stress value of a known point position for each undetermined factor by adopting a finite element method, further establishes a multivariate regression equation between the stress value calculated by each undetermined factor and the ground stress value of a known actual measuring point, and obtains the optimal solution of each variable coefficient in the regression equation by using a statistical analysis method according to the principle of minimum sum of squares of residual errors so that the calculated stress field and the actually measured stress field achieve optimal fitting to obtain the initial ground stress field of the engineering area;
the neural network method utilizes the neural network to establish a nonlinear mapping relation between undetermined model boundary conditions (displacement boundaries, stress boundaries and the like) and stress values of positions of actual geostress points in the model, and after the mapping relation is established, the usable model boundary conditions can be obtained through the neural network according to the actual geostress, and then finite element calculation is carried out by utilizing the obtained boundary conditions, so that an initial geostress field of a project area can be obtained;
the direct inverse analysis method takes the minimum approach distance between a calculated value and an actually measured value as a target function, establishes a direct inversion mathematical model of the ground stress field, and adopts an advanced genetic algorithm to carry out rapid optimization so as to obtain the optimal solution of the target function, namely the ground stress field;
step 2-3: and verifying the rationality of the initial ground stress field obtained by inversion based on the actually measured ground stress data, and comprehensively analyzing and fully demonstrating the rationality and reliability of the result of the inverted ground stress field.
And step 3: the method is characterized in that an underground main workshop, a main transformer room, a bus duct and the like are used as main research objects, meanwhile, simplification processing is carried out on part of factory traffic holes, part of diversion holes and part of tail water holes, and a workshop construction method and a support measure fine calculation model are established.
Wherein, the simulation range of the fine calculation model comprises: the distance of 3 times of the height of the main workshop is taken from the upper part of the main workshop, the lower part of the main transformer chamber, the two sides of the axis direction of the main workshop and the bottom plate of the main workshop.
And 4, step 4: and circularly calculating all nodes of the fine model, determining the unit number corresponding to each point in the large-range ground stress inversion model, and calculating corresponding local coordinate values.
The step 4 specifically comprises the following steps:
step 4-1: and selecting coordinate values of the large-range ground stress inversion model nodes under the physical coordinate system (x, y), and mapping the coordinate values to the reference coordinate system (xi, eta), as shown in the figure 1 and the figure 2.
The mapping method between the physical coordinate system (x, y) and the reference coordinate system (xi, eta) is as follows:
for the coordinate mapping of a quadrilateral unit with 4 nodes as shown in fig. 1, since one point in the reference coordinate system (xi, η) corresponds to a corresponding point in the physical coordinate system (x, y), the coordinate mapping relationship x ═ x (xi, η) y ═ y (xi, η) corresponds to the 4 corner points of the unit shape, and the corresponding condition is that the corresponding point corresponds to the 4 corner points of the unit shape
xi＝x(ξi,ηi)yi＝y(ξi,ηi)i＝1,2,3,4 (1)
This indicates that there are 4 node conditions in each of the x-direction and the y-direction, and if the coordinate mapping relationship is expressed by a polynomial, then polynomials each including 4 undetermined coefficients, that is, in each of the x-direction and the y-direction can be written, respectively
x(ξ,η)＝a0+a1ξ+a2η+a3ξηy(ξ,η)＝b0+a1ξ+b2η+b3ξη (2)
In the formula, the coefficient a is determined0,...,a3And b0,...,b3Can be uniquely determined by the node mapping condition (1).
The obtained undetermined coefficient is substituted back to the formula (2), and the formula is rewritten into
In the formula (I), the compound is shown in the specification,
if each node coordinate value in the physical coordinate system (x, y) is arranged and written as a matrix, there is
Further, the formula (3) can be written as
Thus, mapping between the two coordinate systems can be realized.
Step 4-2: the cells of the fine model are mapped to the large model cell reference coordinate system as shown in fig. 2.
Step 4-3: and circulating all the units so as to determine the unit number of each unit node of the refined model corresponding to the large-range ground stress inversion model, and calculating corresponding local coordinate values.
And 5: and calculating the stress value of a specific point in the unit under a specific local coordinate according to the basic theory of finite elements according to the ground stress calculation result of the large-range ground stress inversion model, namely the unit stress matrix and the node displacement.
The step 5 specifically comprises the following steps:
step 5-1: solving according to a finite element method to obtain a stress conversion matrix of any point in the large-range ground stress inversion unit:
σ＝DBae＝Sae
S＝[S1 S1 ... Sn]
Si＝DBi(i＝1,2,...m)
wherein B ═ B1 B2 ... Bm]，
D represents an elastic matrix, B represents a strain conversion matrix, S represents a stress conversion matrix, and m represents the number of unit nodes.
Step 5-2: and (4) solving the obtained local coordinate values according to the step (4), and combining the S matrix of any local coordinate point obtained by calculation in the step (5-1) to obtain the stress of any point in the unit in the fine model.
The method has the advantages that the method is reasonable in design according to the description of the scheme, stress conversion calculation formulas among different models are deduced according to a finite element basic theory, and high-precision conversion from the stress calculation results of the large-range ground stress inversion model to a fine calculation model can be achieved on the basis of the inversion calculation result data file. The method does not need to regress and calculate the initial stress of a new grid point due to the change of the calculation model grid, lays a foundation for the subsequent calculation research, and improves the calculation efficiency; compared with the traditional method of fitting the initial stress function in the engineering area by adopting a mathematical statistics method, the method improves the calculation precision and reliability.
Drawings
FIG. 1 is a schematic diagram of a large model and a fine model unit under physical coordinates according to the present invention;
FIG. 2 is a schematic diagram of the large model and the fine model units in the reference coordinate system according to the present invention;
FIG. 3 is a schematic diagram of a large-scale geostress inversion model of the present invention;
FIG. 4 is a schematic diagram of a refined calculation model of the present invention.
Detailed Description
In order to clearly illustrate the technical features of the present solution, the present solution is explained below by way of specific embodiments.
The implementation provides a method for converting the calculation result of the crustal stress between models with different scales at high precision, which comprises the following steps:
step 1: comprehensively considering the influence of factors such as power station engineering topographic and geological conditions, underground cavern arrangement types, section sizes, distribution conditions of ground stress actual measurement points and the like on the inversion of the ground stress field, and establishing a large-range ground stress inversion model for initial ground stress field inversion;
wherein, unfavorable geological structures such as fault, soft rock are considered to the ground stress inversion model on a large scale, utilize nature demarcation such as valley, gully, simulation range includes: the system comprises a plurality of power station buildings, such as an upper warehouse, a diversion tunnel, an upstream surge chamber, a high-pressure branch pipe, an underground plant, a tail water tunnel, a tail water surge chamber and the like.
Step 2: and (3) according to the initial ground stress point and the measured value thereof actually measured in the factory area, inverting the initial ground stress field by adopting a finite element method and combining a multivariate linear regression method, a neural network method or a direct inverse analysis method.
The step 2 specifically comprises the following steps:
step 2-1: and dividing the actually measured initial ground stress points into 2 groups, namely an inversion point and a verification point, wherein the inversion point is used for inverting the initial ground stress field, and the verification point is used for verifying the rationality of the ground stress field obtained by inversion.
Step 2-2: according to the measured initial ground stress point and the measured value thereof in the factory area, respectively inverting the initial ground stress field by adopting a finite element method and combining a multivariate linear regression method, a neural network method or a genetic algorithm, wherein the basic ideas of the three inversion analysis methods are respectively as follows:
the multivariate linear regression method takes factors which can possibly form an initial ground stress field as undetermined factors, calculates the stress value of a known point position for each undetermined factor by adopting a finite element method, further establishes a multivariate regression equation between the stress value calculated by each undetermined factor and the ground stress value of a known actual measuring point, and obtains the optimal solution of each variable coefficient in the regression equation by using a statistical analysis method according to the principle of minimum sum of squares of residual errors so that the calculated stress field and the actually measured stress field achieve optimal fitting to obtain the initial ground stress field of the engineering area;
the neural network method utilizes the neural network to establish a nonlinear mapping relation between undetermined model boundary conditions (displacement boundaries, stress boundaries and the like) and stress values of positions of actual geostress points in the model, and after the mapping relation is established, the usable model boundary conditions can be obtained through the neural network according to the actual geostress, and then finite element calculation is carried out by utilizing the obtained boundary conditions, so that an initial geostress field of a project area can be obtained;
the direct inverse analysis method takes the minimum approach distance between a calculated value and an actually measured value as a target function, establishes a direct inversion mathematical model of the ground stress field, and adopts an advanced genetic algorithm to carry out rapid optimization so as to obtain the optimal solution of the target function, namely the ground stress field;
step 2-3: and verifying the rationality of the initial ground stress field obtained by inversion based on the actually measured ground stress data, and comprehensively analyzing and fully demonstrating the rationality and reliability of the result of the inverted ground stress field.
And step 3: the method is characterized in that an underground main workshop, a main transformer room, a bus duct and the like are used as main research objects, meanwhile, simplification processing is carried out on part of factory traffic holes, part of diversion holes and part of tail water holes, and a workshop construction method and a support measure fine calculation model are established.
Wherein, the simulation range of the fine calculation model comprises: the distance of 3 times of the height of the main workshop is taken from the upper part of the main workshop, the lower part of the main transformer chamber, the two sides of the axis direction of the main workshop and the bottom plate of the main workshop.
And 4, step 4: and circularly calculating all nodes of the fine model, determining the unit number corresponding to each point in the large-range ground stress inversion model, and calculating corresponding local coordinate values.
The step 4 specifically comprises the following steps:
step 4-1: and selecting coordinate values of the large-range ground stress inversion model nodes under the physical coordinate system (x, y), and mapping the coordinate values to the reference coordinate system (xi, eta), as shown in the figure 1 and the figure 2.
The mapping method between the physical coordinate system (x, y) and the reference coordinate system (xi, eta) is as follows:
for the coordinate mapping of a quadrilateral unit with 4 nodes as shown in fig. 1, since one point in the reference coordinate system (xi, η) corresponds to a corresponding point in the physical coordinate system (x, y), the coordinate mapping relationship x ═ x (xi, η) y ═ y (xi, η) corresponds to the 4 corner points of the unit shape, and the corresponding condition is that the corresponding point corresponds to the 4 corner points of the unit shape
xi＝x(ξi,ηi)yi＝y(ξi,ηi)i＝1,2,3,4 (1)
This indicates that there are 4 node conditions in each of the x-direction and the y-direction, and if the coordinate mapping relationship is expressed by a polynomial, then polynomials each including 4 undetermined coefficients, that is, in each of the x-direction and the y-direction can be written, respectively
x(ξ,η)＝a0+a1ξ+a2η+a3ξηy(ξ,η)＝b0+a1ξ+b2η+b3ξη (2)
In the formula, the coefficient a is determined0,...,a3And b0,...,b3Can be uniquely determined by the node mapping condition (1).
The obtained undetermined coefficient is substituted back to the formula (2), and the formula is rewritten into
In the formula (I), the compound is shown in the specification,
if each node coordinate value in the physical coordinate system (x, y) is arranged and written as a matrix, there is
Further, the formula (3) can be written as
Thus, mapping between the two coordinate systems can be realized.
Step 4-2: the cells of the fine model are mapped to the large model cell reference coordinate system as shown in fig. 2.
Step 4-3: and circulating all the units so as to determine the unit number of each unit node of the refined model corresponding to the large-range ground stress inversion model, and calculating corresponding local coordinate values.
And 5: and calculating the stress value of a specific point in the unit under a specific local coordinate according to the basic theory of finite elements according to the ground stress calculation result of the large-range ground stress inversion model, namely the unit stress matrix and the node displacement.
The step 5 specifically comprises the following steps:
step 5-1: solving according to a finite element method to obtain a stress conversion matrix of any point in the large-range ground stress inversion unit:
σ＝DBae＝Sae
S＝[S1 S1 … Sn]
Si＝DBi(i＝1,2,…m)
wherein B ═ B1 B2 … Bm]，
D represents an elastic matrix, B represents a strain conversion matrix, S represents a stress conversion matrix, and m represents the number of unit nodes.
Step 5-2: and (4) solving the obtained local coordinate values according to the step (4), and combining the S matrix of any local coordinate point obtained by calculation in the step (5-1) to obtain the stress of any point in the unit in the fine model.
The invention is illustrated below by way of an engineering example:
the water-pumping and energy-storing power station comprises buildings such as an upper reservoir, a water delivery system, an underground plant system, a lower reservoir, a ground switch station and the like, wherein the water delivery and power generation system is generally arranged in the NW direction and is positioned in the northeast side mountain body of the Liujia downline. The water delivery system is from the mountain top elevation 1012.00m of the water inlet/outlet section of the upper reservoir to the ditch bottom elevation 488.00m of the stream ditch of the lower reservoir, and the relative height difference of the terrain reaches 524 m. The line layout is basically vertical to the direction of a hillside and is distributed along the mountain, the upper reservoir water inlet/water outlet is directly distributed to the east-west direction of Liu Jia downland northeast mountain ridges from the southwest direction, then the upper reservoir water inlet/water outlet is turned to the southeast direction and enters two estuary plants, the whole is arranged in the southwest direction, a one-hole two-machine arrangement mode is adopted, and 2 main water conveying holes, 4 water conveying branch holes and 4 tail water tunnels are arranged. The power generation system is arranged in a mountain body at the position of about 280m upstream of the right dam head of the two estuary dam lines of the lower reservoir, and the underground plant cavern group mainly comprises a main plant, a main transformer cavern, a bus duct, a high-voltage cable cavern, a factory-entering traffic cavern and the like. And in the engineering, a hydrofracturing method is adopted to carry out the ground stress test in the complete rock bodies of the high-pressure branch pipe parts of the exploration branch tunnel, the plant area and the main transformer tunnel respectively. The number of the ground stress measuring holes is 3, namely zk47, zk79 and zk88, wherein zk47 is located near the upstream wall of the main transformer hole and close to No. 1 and No. 2 bus holes, and 2 measuring points are provided; zk79 is located near the branch pipe of the No. 1 and No. 2 water inlet branch holes, and has 2 measuring points; zk88 is located near the downstream wall of the main workshop, near the 3 and 4 units, and has 6 measuring points.
Step 1: comprehensively considering influences of factors such as power station engineering terrain geological conditions, underground cavern arrangement patterns, section sizes and distribution conditions of ground stress actual measurement points on inversion of a ground stress field, and establishing a large-range ground stress inversion model for initial ground stress field inversion by utilizing natural boundaries such as valleys and gullies and considering unfavorable geological structures such as faults and soft rocks;
the simulation range of the large-range ground stress inversion model comprises partial upper storehouses, diversion tunnels, upstream surge chambers, high-pressure branch pipes, underground plants, tail water tunnels, tail water surge chambers and other station buildings. Use underground factory building as central zone to main factory building axis direction is the X axle, and directional vice factory building direction is positive, and perpendicular to main factory building axis direction is the Y axle, and directional main room direction that becomes is positive, and vertical upwards is the Z axle. The calculation range of the determination is that 1726m is taken in the X-axis direction, 1695m is taken in the Y-axis direction, the elevation 0m is taken in the Z-axis direction to the earth surface, and the distance from the bottom of the model to the bottom of the factory building is about 445 m. 574757 four-node tetrahedral units and 101132 nodes are subdivided in the three-dimensional finite element computational mesh, and the computational mesh is shown in FIG. 3.
Step 2: according to the initial ground stress point and the measured value thereof actually measured in the factory area, a finite element method is adopted, and a multivariate linear regression method, a neural network method or a direct inverse analysis method are combined to invert an initial ground stress field;
according to the actual measurement ground stress data of the underground factory building area, the self weight and the geological structure function are main influence factors formed by the rock mass ground stress field, the finite element method is adopted, the multivariate linear regression method is combined to conduct multivariate regression inversion on the three-dimensional initial ground stress of the factory building area, the measured point ground stress actual measurement value and the regression calculated value are compared with a table 1, and through the comparative analysis of the actual measurement value and the calculated value, the result shows that the reasonable stress field distribution can be obtained through the initial ground stress regression analysis conducted through the three-dimensional stress field numerical simulation and the fitting of the existing actual measurement ground stress data. The regression analysis value is matched with the actually measured ground stress in terms of magnitude, the minimum error is 0.04 percent, the maximum error is 17.01 percent and the errors of the other measuring points are about 5 percent by comparing with the actually measured ground stress point value, and the initial ground stress field obtained by the multivariate regression calculation is reasonable and reliable.
TABLE 1 comparison table of actually measured main stress value and regression calculation value
Note: the stress is positive in tension and negative in pressure.
And step 3: the method comprises the following steps of taking an underground main plant, a main transformer room, a bus duct and the like as main research objects, simplifying part of plant traffic holes, part of diversion holes and part of tail water holes, and establishing a plant construction method and a support measure fine calculation model;
the simulation range of the fine calculation model comprises the upper part of the main workshop, the lower part of the main transformer chamber, two sides of the axis direction of the main workshop and the lower part of a bottom plate of the main workshop, the distance of the height of the workshop is 3 times, and the upper part of the workshop is taken to the earth surface. The three-dimensional finite element computational mesh is subdivided into 594312 four-node tetrahedral units, 102542 nodes, as shown in FIG. 4.
And 4, step 4: and circularly calculating all the nodes of the fine model, determining the unit number of each point in the large model, and calculating corresponding local coordinate values.
And 5: calculating stress values of specific points in the units under specific local coordinates according to a finite element basic theory according to the ground stress calculation result of the large-range ground stress inversion model, namely a unit stress matrix and node displacement;
and deducing a stress conversion formula according to a finite element basic theory and compiling a related program, wherein during stress conversion calculation, the stress of any point in the unit can be solved by calculating an S matrix of any local coordinate point.
And finally, extracting the main stress value corresponding to the measuring point from the calculation result in the step 5, comparing the main stress value with the measured value, judging the feasibility of the scheme, and obtaining the calculated main stress value shown in the table 2.
TABLE 2 comparison table of actual measurement main stress value and inversion value after stress conversion
As can be seen from the analysis of Table 2, compared with the actually measured ground stress point value, the minimum error is 0.22%, the maximum error is 16.45%, and the errors of the other measuring points are about 6%, it can be found that the calculated value of the stress of the measuring points obtained by the analysis method is well matched with the actually measured value, which indicates that the inversion method has certain feasibility under the actual working condition.
The technical features of the present invention, which are not described in the present application, can be implemented by or using the prior art, and are not described herein again, of course, the above description is not limited to the above examples, and the present invention is not limited to the above examples, and variations, modifications, additions or substitutions that can be made by a person skilled in the art within the spirit of the present invention also belong to the protection scope of the present invention.
Claims (3)
1. A method for converting the calculation result of the crustal stress between models with different scales at high precision is characterized by comprising the following steps:
step 1: comprehensively considering the influence of factors of power station engineering topographic and geological conditions, underground cavern arrangement patterns and section sizes and distribution conditions of ground stress actual measurement points on the inversion of the ground stress field, and establishing a large-range ground stress inversion model for initial ground stress field inversion;
step 2: according to the measured initial ground stress point and the measured value thereof in the factory area, a finite element method is adopted, and a multivariate linear regression method, a neural network method or a direct inverse analysis method is combined to invert an initial ground stress field, which specifically comprises the following steps:
step 2-1: dividing the actually measured initial ground stress points into 2 groups, namely an inversion point and a verification point, wherein the inversion point is used for inverting the initial ground stress field, and the verification point is used for verifying the rationality of the ground stress field obtained by inversion;
step 2-2: according to the measured initial ground stress point and the measured value thereof in the factory area, respectively inverting the initial ground stress field by adopting a finite element method and combining a multivariate linear regression method, a neural network method or a genetic algorithm, wherein the basic ideas of the three inversion analysis methods are respectively as follows:
the multivariate linear regression method takes factors which can possibly form an initial ground stress field as undetermined factors, calculates the stress value of a known point position for each undetermined factor by adopting a finite element method, further establishes a multivariate regression equation between the stress value calculated by each undetermined factor and the ground stress value of a known actual measuring point, and obtains the optimal solution of each variable coefficient in the regression equation by using a statistical analysis method according to the principle of minimum sum of squares of residual errors so that the calculated stress field and the actually measured stress field achieve optimal fitting to obtain the initial ground stress field of the engineering area;
the neural network method utilizes the neural network to establish a nonlinear mapping relation between a model boundary condition to be determined and a stress value of a position of an actual ground stress point in the model, and after the establishment of the mapping relation is completed, the usable model boundary condition can be obtained through the neural network according to the actual ground stress, and then finite element calculation is carried out by utilizing the obtained boundary condition, so that an initial ground stress field of an engineering area can be obtained;
the direct inverse analysis method takes the minimum approach distance between a calculated value and an actually measured value as a target function, establishes a direct inversion mathematical model of the ground stress field, and adopts an advanced genetic algorithm to carry out rapid optimization so as to obtain the optimal solution of the target function, namely the ground stress field;
step 2-3: verifying the rationality of the initial ground stress field obtained by inversion based on the actually measured ground stress data, and comprehensively analyzing and fully demonstrating the rationality and reliability of the results of the inversion ground stress field;
and step 3: the method comprises the following steps of taking an underground main plant, a main transformer room and a bus duct as main research objects, simplifying part of plant traffic holes, part of diversion holes and part of tail water holes, and establishing a plant construction method and a support measure fine calculation model;
wherein, the simulation range of the fine calculation model comprises: taking the distance of 3 times of the height of the main workshop from the upstream of the main workshop, the downstream of the main transformer room, the two sides of the main workshop in the axis direction and below a bottom plate of the main workshop, and taking the upper part of the main workshop to the ground surface;
and 4, step 4: performing cyclic calculation on all nodes of the fine model, determining a unit number corresponding to each point in the large-range ground stress inversion model, and calculating a corresponding local coordinate value;
the step 4 specifically comprises the following steps:
step 4-1: selecting coordinate values of large-range ground stress inversion model nodes under a physical coordinate system (x, y), and mapping the coordinate values to a reference coordinate system (xi, eta);
the mapping method between the physical coordinate system (x, y) and the reference coordinate system (xi, eta) is as follows:
the coordinate mapping relation x ═ x (xi, eta) y ═ y (xi, eta), for the coordinate mapping of the node quadrilateral unit, since one point in the reference coordinate system (xi, eta) corresponds to a corresponding point in the physical coordinate system (x, y), the 4 corner points of the unit shape correspond to the corresponding conditions
xi＝x(ξi,ηi) yi＝y(ξi,ηi) i＝1,2,3,4 (1)
This indicates that there are 4 node conditions in each of the x-direction and the y-direction, and if the coordinate mapping relationship is expressed by a polynomial, then polynomials each including 4 undetermined coefficients, that is, in each of the x-direction and the y-direction can be written, respectively
x(ξ,η)＝a0+a1ξ+a2η+a3ξηy(ξ,η)＝b0+a1ξ+b2η+b3ξη (2)
In the formula, the coefficient a is determined0,...,a3And b0,...,b3Can be uniquely determined by the node mapping condition (1);
the obtained undetermined coefficient is substituted back to the formula (2), and the formula is rewritten into
In the formula (I), the compound is shown in the specification,
if each node coordinate value in the physical coordinate system (x, y) is arranged and written as a matrix, there is
Further, the formula (3) can be written as
Therefore, mapping between the two coordinate systems can be realized;
step 4-2: mapping each unit of the fine model to a large model unit reference coordinate system;
step 4-3: circulating all units so as to determine the unit number of each unit node of the refined model corresponding to the large-range ground stress inversion model, and calculating corresponding local coordinate values;
and 5: and calculating the stress value of a specific point in the unit under a specific local coordinate according to the basic theory of finite elements according to the ground stress calculation result of the large-range ground stress inversion model, namely the unit stress matrix and the node displacement.
The step 5 specifically comprises the following steps:
step 5-1: solving according to a finite element method to obtain a stress conversion matrix of any point in the large-range ground stress inversion unit:
σ＝DBae＝Sae
S＝[S1 S1…Sn]
Si＝DBi(i＝1,2,…m)
wherein B ═ B1 B2…Bm]，
D represents an elastic matrix, B represents a strain conversion matrix, S represents a stress conversion matrix, and m represents the number of unit nodes.
Step 5-2: and (4) solving the obtained local coordinate values according to the step (4), and combining the S matrix of any local coordinate point obtained by calculation in the step (5-1) to obtain the stress of any point in the unit in the fine model.
2. The method for high-precision conversion of geostress calculation results among models with different scales according to claim 1, wherein the large-scale geostress inversion model in the step 1 specifically comprises: the fault and soft rock unfavorable geological structure is considered, the valley and the gully are naturally demarcated, and the simulation range comprises partial warehouse entry, diversion tunnels, upstream surge chambers, high-pressure branch pipes, underground plants, tailwater tunnels and tailwater surge chambers of power station buildings.
3. The method for high-precision conversion of the calculation results of the crustal stress between models with different dimensions according to claim 1 or 2, wherein the fine calculation model of the plant construction method and the support measures in the step 3 is specifically as follows: the distance of 3 times of the height of the main workshop is taken from the upper part of the main workshop, the lower part of the main transformer chamber, the two sides of the axis direction of the main workshop and the bottom plate of the main workshop.
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