CN115270062A - Stress relief method for calculating crustal stress by taking irregular drilling hole shape into consideration - Google Patents

Stress relief method for calculating crustal stress by taking irregular drilling hole shape into consideration Download PDF

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CN115270062A
CN115270062A CN202211186394.5A CN202211186394A CN115270062A CN 115270062 A CN115270062 A CN 115270062A CN 202211186394 A CN202211186394 A CN 202211186394A CN 115270062 A CN115270062 A CN 115270062A
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秦雨樵
汤华
吴振君
葛修润
张勇慧
袁从华
邓琴
尹小涛
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Wuhan Institute of Rock and Soil Mechanics of CAS
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Abstract

The invention discloses a method for calculating the crustal stress by a stress relief method considering the shape of an irregular drilling hole, which comprises the steps of calculating a mapping function expression of any irregular drilling hole shape, substituting the mapping function expression into a complex function expression to respectively deduce the relation between the far-field crustal stress and the drilling hole wall stress under a planar strain condition and a reverse planar shear strain condition, and obtaining an analytical expression between the three-dimensional crustal stress and the hole wall stress under the three-dimensional condition; carrying out a rock mechanical parameter test by sidewall coring, and obtaining an analytical expression between the hole wall strain and the far-field ground stress at one point of the irregular drilling hole in any direction by combining the analytical expression between the three-dimensional ground stress and the hole wall stress under a three-dimensional condition; obtaining the magnitude of the far-field ground stress component through a least square method and an analytical expression between the hole wall strain and the far-field ground stress in any direction at one point of the irregular drilling hole; the problem that the existing stress relief method is poor in accuracy when the ground stress is measured can be solved.

Description

Method for calculating crustal stress by stress relief method considering irregular drilling hole shape
Technical Field
The invention belongs to the technical field of geotechnical measurement, and particularly relates to a method for calculating the ground stress by a stress relieving method considering the shape of an irregular drill hole.
Background
The ground stress refers to the stress caused by gravity, structural stress or human activities and existing in rock mass, and is a basic parameter for researching all deep rock mass mechanics problems. The high ground stress area has great influence on the construction of underground plants and tunnels, the problem of large deformation such as lateral bulging and bottom bulging is caused in soft rock strata, and engineering hazards such as rock burst and large-scale collapse are caused in hard rock strata, so that the construction safety of engineering is directly threatened, the construction progress is delayed, and great loss is caused. For deep oil and gas exploration and exploitation engineering, the ground stress is a key parameter for determining reservoir transformation design and well wall stability of a deep oil and gas exploitation well; especially, when the direction of the horizontal well is consistent with the minimum horizontal main stress, cracks formed by multi-stage fracturing are perpendicular to the direction of the horizontal section, the exposed flood discharge area is increased, and therefore the gas production efficiency is improved. At present, the well logging method commonly used in deep drilling can accurately reflect the direction information of the ground stress, but the magnitude of the ground stress can only be obtained by an in-situ test method.
At present, the stress relieving method is an in-situ test method for obtaining the ground stress recommended by the international committee for testing rock mechanics, and the method assumes that a drill hole is cylindrical and obtains the ground stress by measuring the strain of the hole wall and the inverse calculation of the deformation parameter of the rock mass. However, with the rapid development of the caliper measurement and imaging devices such as mechanical calipers, ultrasonic logging instruments, and resistance logging instruments, researchers have acquired more and more real shape data of deep boreholes and pointed out that deep boreholes exhibit very significant irregular characteristics. Under the influence of various factors such as formation properties, high ground stress action and the like, the shape of the hole wall presents obvious eccentricity and ovalization, and simultaneously, under the action of a drilling process and drilling fluid scouring, the surface of the hole wall is rough and uneven and is filled with sharp corners and pits. The irregular shapes directly influence the distribution rules of stress, displacement and strain at the hole wall of the drill hole, and if the measured strain quantity is still brought into the traditional stress calculation method, a large system error can be generated, so that the accuracy of the ground stress test is reduced.
Therefore, a ground stress calculation method which can take the influence of irregular drilling hole shapes on the stress, displacement and strain distribution at the hole wall of the drilling hole into consideration and enable the calculation of the stress relief method to be more accurate is urgently needed.
Disclosure of Invention
Aiming at the defects or the improvement requirements of the prior art, the invention provides a method for calculating the crustal stress by a stress solution method considering the shape of an irregular drilling hole, which comprises the steps of calculating a mapping function expression of any irregular drilling hole shape, substituting the mapping function expression into a complex function expression, and respectively deducing the relation between the far-field crustal stress and the drilling hole wall stress under the planar strain condition and the reverse planar shear strain condition to obtain an analytic expression between the three-dimensional crustal stress and the hole wall stress under the three-dimensional condition; carrying out a rock mechanical parameter test by sidewall coring, and obtaining an analytical expression between the hole wall strain and the far-field ground stress at one point of the irregular drilling hole in any direction by combining the analytical expression between the three-dimensional ground stress and the hole wall stress under a three-dimensional condition; obtaining the magnitude of the far-field ground stress component through a least square method and an analytical expression between the hole wall strain and the far-field ground stress in any direction at one point of the irregular drilling hole; according to the method, the influence of the irregular drilling hole form is considered in the method for calculating the crustal stress by the stress relief method for the first time, so that the accuracy of calculating the crustal stress by the stress relief method is improved; the analytical expression of the stress calculation by the stress relief method is deduced by introducing a complex function method, so that the method is easy to realize by programming, and the efficiency and the accuracy of the stress calculation by the stress relief method are improved; the method can solve the problems that when the existing stress relief method is used for calculating the crustal stress, irregular drilling holes directly influence the stress and strain distribution rule at the hole walls of the drilling holes, so that the crustal stress calculation can generate large system errors, and the measurement accuracy is poor.
In order to achieve the above object, the present invention provides a method for calculating a stress by a stress relief method considering an irregular borehole shape, comprising the steps of:
s1, acquiring the real form of a drill hole;
s2, calculating a mapping function expression of any irregular drilling hole shape according to the real drilling hole shape;
s3, substituting the mapping function expression of any irregular drilling hole shape into the complex function expression of the plane strain problem to deduce and obtain a relational expression between the far-field ground stress and the drilling hole wall stress under the plane strain condition of any irregular drilling hole shape;
s4, substituting the mapping function expression of any irregular drilling hole shape into the complex function expression of the inverse plane shear strain problem to deduce and obtain a relational expression between the far field ground stress and the drilling hole wall stress under the inverse plane shear strain condition of any irregular drilling hole shape;
s5, combining the step S3 and the step S4 to obtain an analytical expression between the three-dimensional ground stress and the hole wall stress under the three-dimensional condition;
s6: taking out the core of the deep test section by using side wall coring equipment; carrying out a rock mass mechanics parameter test to determine rock mass deformation parameters; deducing to obtain an analytic expression between the hole wall strain and the far-field ground stress in any direction at one point of the irregular drilling hole by combining an elastic mechanical stress-strain constitutive equation, rock mechanical parameters and the analytic expression between the three-dimensional ground stress and the hole wall stress under three-dimensional conditions;
s7: adopting local wall surface stress relief method equipment to perform an earth stress test in the deep drilling hole to obtain strain changes in at least 6 directions at the hole wall;
s8: and obtaining the magnitude of the far-field ground stress component through a least square method and an analytical expression between the strain of the hole wall and the far-field ground stress at one point of the irregular drilling hole in any direction.
Further, the expression of the mapping function of the arbitrary irregular borehole shape in step S2 takes the form of a lorentzian series, which is represented by equation (1):
Figure 834427DEST_PATH_IMAGE001
（1）
wherein,
Figure 474224DEST_PATH_IMAGE002
the coordinate complex expression form in the actual coordinate space;
Figure 286323DEST_PATH_IMAGE003
a mapping function for any irregular borehole shape;
Figure 787711DEST_PATH_IMAGE004
the expression form of coordinate complex numbers in the mapping space is any irregular drilling hole shape; r, C1, C2 … …
Figure 267234DEST_PATH_IMAGE005
K +1 real constants;
Figure 500769DEST_PATH_IMAGE006
expressing the number of the Lorong stages
Figure 675530DEST_PATH_IMAGE006
An item;
Figure 855975DEST_PATH_IMAGE007
indicating any irregular borehole shape
Figure 986742DEST_PATH_IMAGE007
Counting;
the boundary point search method is adopted to calculate R, C and C2 … …
Figure 719075DEST_PATH_IMAGE008
The values of the k +1 real constants and the expression of the mapping function meeting the precision test requirement are obtained.
Further, the specific calculation of the mapping function expression meeting the precision test requirement comprises the following steps:
s21, dividing the unit circle into a plurality of equal parts
Figure 505765DEST_PATH_IMAGE009
Calculating any point on the unit circle and a mapping point on a corresponding real drilling hole to obtain an initial mapping function expression;
s22, calculating mapping points under initial mapping through an initial mapping function expression;
s23, judging whether the precision of the initial mapping function meets the test requirement or not; if the precision meets the test requirement, the obtained initial mapping function is the mapping function expression which is required to be accurate enough; if the precision does not meet the test requirement, the next step is carried out;
s24, calculating the ratio of the distance between any two adjacent points to the perimeter of the mapping hole, determining the corresponding position of each mapping point on the real drilled hole, establishing a second mapping expression with the point on the unit circle, and carrying out the next step;
and S25, repeating the steps S22 to S24 until the required mapping function precision meets the test requirement to obtain the mapping function which finally meets the requirement.
Further, the precision calculation of the mapping function is represented by equation (2):
Figure 286640DEST_PATH_IMAGE010
（2）
wherein,
Figure 854936DEST_PATH_IMAGE011
the coordinate value of the boundary of the drill hole in the mapping coordinate space is obtained;
Figure 367957DEST_PATH_IMAGE012
the arithmetic mean value of the distances between the mapping points on all the mapping chambers and the corresponding mapping points on the real drill holes is obtained;
Figure 32157DEST_PATH_IMAGE013
the actual borehole boundary overall length.
Further, the obtaining of the relation between the far-field ground stress and the borehole wall stress under the reverse plane shear strain condition of any irregular borehole shape in step S4 includes:
s41, constructing a stress function expression of the borehole wall under the condition of reverse plane shear strain;
s42, constructing a stress function expression of the stress boundary condition under the reverse plane shear strain condition;
and S43, obtaining a relational expression between the far-field ground stress and the borehole wall stress under the reverse plane shear strain condition according to the steps S41 and S42.
Further, the expression of the stress function of the borehole wall under the reverse plane shear strain condition is represented by equations (13) and (14):
Figure 351143DEST_PATH_IMAGE014
（13）
Figure 659764DEST_PATH_IMAGE015
（14）
in the formula,
Figure 219053DEST_PATH_IMAGE002
the coordinate complex expression form in the actual coordinate space is adopted;
Figure 245915DEST_PATH_IMAGE006
expressing the number of the Lorong stages
Figure 103012DEST_PATH_IMAGE006
An item;
Figure 390774DEST_PATH_IMAGE007
indicating any irregular borehole shape
Figure 511177DEST_PATH_IMAGE007
Point;
Figure 133657DEST_PATH_IMAGE016
at the k point and
Figure 794445DEST_PATH_IMAGE017
a coefficient of correlation;
Figure 77659DEST_PATH_IMAGE018
the shear stress of the hole wall on a far field xz plane;
Figure 228018DEST_PATH_IMAGE019
the shear stress of the hole wall on a far-field yz plane;
Figure 963893DEST_PATH_IMAGE020
is a narrative unit;
Figure 428372DEST_PATH_IMAGE021
are coefficient terms that are expanded in a lorentzian series.
Further, the stress function expression of the stress boundary condition under the reverse plane shear strain condition is represented by equation (15):
Figure 441458DEST_PATH_IMAGE022
（15）
in the formula,
Figure 638085DEST_PATH_IMAGE017
is a stress function of a stress boundary condition under a reverse plane shear strain condition;
Figure 985889DEST_PATH_IMAGE023
is the bulk modulus;
Figure 988480DEST_PATH_IMAGE024
is a differential sign;
Figure 980707DEST_PATH_IMAGE025
is a unit arc length on any irregular borehole shape;
Figure 987715DEST_PATH_IMAGE020
is a narrative unit;
Figure 698182DEST_PATH_IMAGE026
the stress function of the hole wall of the drill hole under the condition of reverse plane shear strain is obtained;
Figure 238885DEST_PATH_IMAGE027
is a function of
Figure 475831DEST_PATH_IMAGE028
The conjugate value of (c).
Further, the relational expression between the far-field ground stress and the borehole wall stress under the reverse plane shear strain condition is represented by the formula (16):
Figure 14260DEST_PATH_IMAGE029
（16）
in the formula,
Figure 87389DEST_PATH_IMAGE030
the shear stress of the hole wall of the drilled hole on an xz plane;
Figure 431783DEST_PATH_IMAGE031
the shear stress of the hole wall of the drilled hole on the yz plane;
Figure 398602DEST_PATH_IMAGE032
is a function of
Figure 498145DEST_PATH_IMAGE033
The first derivative in the actual coordinate space.
Further, the derivation of the relationship between far-field ground stress and borehole wall stress under the planar strain condition in step S3 includes the following steps:
s31: constructing a complex function expression of the practical coordinate space drilling stress boundary condition under the plane strain condition;
s32: constructing a boundary value expression of a first stress function and a second stress function of a mapping coordinate space under a plane strain condition;
s33: constructing a relational expression which is expressed by the residual terms of the first stress function in the mapping coordinate space and the residual terms of the second stress function in the mapping coordinate space through the coordinate values at the drill hole boundary in the mapping coordinate space under the plane strain condition;
s34: solving the relational expression obtained in the step S33 by comparing the coefficients of the same-order terms to obtain a linear algebraic equation set on a complex field, thereby further determining the expressions of the first stress function and the second stress function in the mapping coordinate space;
s35: and constructing expressions of the normal stress of the hole wall in the x direction, the normal stress in the y direction and the shear stress on the xy plane under the planar strain condition through mapping a first stress function and a second stress function of a coordinate space, and further obtaining a relational expression between the far-field ground stress and the hole wall stress of the drill hole under the planar strain condition.
Further, the relation between the far-field ground stress and the borehole wall stress under the in-plane strain condition is represented by equations (9) and (11):
Figure 917625DEST_PATH_IMAGE034
(9)
Figure 65710DEST_PATH_IMAGE035
（11）
wherein,
Figure 260936DEST_PATH_IMAGE036
is the normal stress in the x direction under the plane strain condition;
Figure 406747DEST_PATH_IMAGE037
is the normal stress in the y direction under planar strain;
Figure 438157DEST_PATH_IMAGE038
is the shear stress on the xy plane under the plane strain condition;
Figure 124353DEST_PATH_IMAGE039
a first stress function that is a mapped coordinate space;
Figure 800185DEST_PATH_IMAGE040
is composed of
Figure 257842DEST_PATH_IMAGE041
A first order integral derivative value in the mapped coordinate space;
Figure 448652DEST_PATH_IMAGE042
a second stress function that is a mapped coordinate space;
Figure 141802DEST_PATH_IMAGE043
is the real part of the complex number;
Figure 531195DEST_PATH_IMAGE044
a first stress function that is an actual coordinate space;
Figure 81125DEST_PATH_IMAGE045
is composed of
Figure 962493DEST_PATH_IMAGE044
The first derivative of (a);
Figure 850813DEST_PATH_IMAGE046
is composed of
Figure 235658DEST_PATH_IMAGE044
The second derivative of (d);
Figure 18806DEST_PATH_IMAGE047
a second stress function that is a real coordinate space;
Figure 184208DEST_PATH_IMAGE048
is composed of
Figure 219161DEST_PATH_IMAGE047
The first derivative of (a);
Figure 599457DEST_PATH_IMAGE049
is composed of
Figure 428873DEST_PATH_IMAGE050
An expression in a mapped coordinate space;
Figure 81571DEST_PATH_IMAGE051
is composed of
Figure 44848DEST_PATH_IMAGE052
A first order integral derivative value in the mapped coordinate space;
Figure 138706DEST_PATH_IMAGE053
is composed of
Figure 201340DEST_PATH_IMAGE054
An expression in a mapped coordinate space;
Figure 652919DEST_PATH_IMAGE055
is a mapping function;
Figure 29674DEST_PATH_IMAGE056
is composed of
Figure 633830DEST_PATH_IMAGE055
A first order integral derivative value in the mapped coordinate space;
Figure 867365DEST_PATH_IMAGE002
the coordinate complex expression form in the actual coordinate space;
Figure 432339DEST_PATH_IMAGE057
is composed of
Figure 222572DEST_PATH_IMAGE002
The conjugate value of (a);
Figure 556601DEST_PATH_IMAGE058
is composed of
Figure 961038DEST_PATH_IMAGE059
Conjugate values at the borehole boundary in the mapped coordinate space.
In general, compared with the prior art, the above technical solutions conceived by the present invention can achieve the following beneficial effects:
the invention relates to a method for calculating the crustal stress by a stress relief method considering the shape of an irregular drill hole, which comprises the steps of calculating a mapping function expression considering any irregular drill hole shape after acquiring the real shape of the drill hole, substituting the mapping function expression into a complex function expression of a plane strain problem to deduce and obtain a relational expression between the far-field crustal stress and the wall stress of the drill hole under the plane strain condition; substituting the mapping function expression into a complex function expression of the inverse plane shear strain problem to deduce and obtain a relational expression between far-field ground stress and borehole wall stress under the inverse plane shear strain condition; obtaining an analytical expression between the three-dimensional ground stress and the hole wall stress under the three-dimensional condition by combining a relational expression between the far-field ground stress and the hole wall stress under the planar strain condition and a relational expression between the far-field ground stress and the hole wall stress under the reverse planar shear strain condition; determining rock mass deformation parameters through a rock mass mechanics parameter test carried out by side wall coring; deducing to obtain an analytical expression between the hole wall strain and the far field ground stress in any direction at one point of the irregular drilling hole by combining an elastic mechanical stress-strain constitutive equation, rock mechanical parameters and the analytical expression between the three-dimensional ground stress and the hole wall stress under the three-dimensional condition; adopting a local wall surface stress relief method to perform an earth stress test in the deep drilling hole to obtain strain changes in at least 6 directions at the hole wall; obtaining the magnitude of the far-field ground stress component through a least square method and an analytical expression between the hole wall strain and the far-field ground stress at any direction of one point of the irregular drilling hole; the influence of irregular drilling hole shapes is considered in the method for calculating the crustal stress by the stress relief method for the first time, and the accuracy of calculating the crustal stress by the stress relief method is improved; the analytical expression of the stress calculation by the stress relief method is deduced by introducing a complex function method, so that the method is easy to realize by programming, and the efficiency and the accuracy of the stress calculation by the stress relief method are improved; the method can solve the problems that when the existing stress relief method is used for calculating the crustal stress, irregular drilling holes directly influence the stress and strain distribution rule at the hole walls of the drilling holes, so that the crustal stress calculation can generate large system errors, and the measurement accuracy is poor.
Drawings
FIG. 1 is a schematic flow chart of a method for calculating a stress by stress relief method in consideration of an irregular borehole shape according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a mapping function expression for calculating any irregular borehole shape according to the stress-relief-method crustal stress calculation method considering the irregular borehole shape in the embodiment of the present invention;
FIG. 3 is a schematic flow chart of the derivation of the relationship between the far-field ground stress and the borehole wall stress under the plane strain condition in the method for calculating the ground stress by the method of stress relief considering the irregular borehole shape according to the embodiment of the present invention;
fig. 4 is a schematic flow chart of derivation of a relational expression between far-field ground stress and borehole wall stress under a reverse plane shear strain condition in a stress-relieving-method ground stress calculation method considering an irregular borehole shape according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1 to 4, the present invention provides a method for calculating a stress relief method considering an irregular borehole shape, comprising the steps of:
s1, obtaining the real shape of a drilled hole through a caliper, an ultrasonic imaging technology or a micro-resistance scanning technology;
s2, calculating a mapping function expression of any irregular drilling hole shape according to the real shape of the drilling hole; the mapping function for any irregular borehole shape in the infinite domain takes the form of a lorentzian series, represented by equation (1):
Figure 137941DEST_PATH_IMAGE001
（1）
wherein,
Figure 590919DEST_PATH_IMAGE002
the coordinate complex expression form in the actual coordinate space;
Figure 418935DEST_PATH_IMAGE003
a mapping function for any irregular borehole shape;
Figure 197536DEST_PATH_IMAGE004
the expression form of coordinate complex numbers of any irregular drilling hole shape in a mapping space is adopted; r, C1, C2 … …
Figure 533839DEST_PATH_IMAGE005
K +1 real constants;
Figure 180721DEST_PATH_IMAGE006
expressing the number of the Lorong stages
Figure 223763DEST_PATH_IMAGE006
An item;
Figure 970003DEST_PATH_IMAGE007
indicating any irregular borehole shape
Figure 606651DEST_PATH_IMAGE007
Counting;
the method for searching boundary points is adopted to calculate R, C1 and C2 … …
Figure 667011DEST_PATH_IMAGE008
The k +1 real constants are used for obtaining a mapping function expression meeting the precision test requirement; the specific calculation of the mapping function expression meeting the precision test requirement comprises the following steps:
s21, dividing the unit circle into a plurality of equal parts
Figure 954773DEST_PATH_IMAGE009
Calculating the relation between any point on the unit circle and the mapping point on the corresponding real drilling hole to obtain an initial mapping function expression; specifically, the unit circle is divided into an average according to the degree of irregularity of the drilled hole and the accuracy of the mapping function
Figure 871914DEST_PATH_IMAGE009
Segment, point on unit circle
Figure 386072DEST_PATH_IMAGE060
The coordinates are
Figure 358444DEST_PATH_IMAGE061
The 1 st point coordinate is (1,0), and the mapping point on the real borehole is
Figure 376079DEST_PATH_IMAGE062
The coordinates are
Figure 729700DEST_PATH_IMAGE063
Finding the initial mapping function expression under the relation
Figure 324629DEST_PATH_IMAGE064
；
S22, expressing by an initial mapping function
Figure 992371DEST_PATH_IMAGE064
Calculating mapping points under initial mapping;
s23, judging whether the precision of the initial mapping function meets the test requirement or not; if the precision meets the test requirement, the obtained initial mapping function is the mapping function expression which is required to be accurate enough; if the precision does not meet the test requirement, the next step is carried out;
wherein the precision calculation of the mapping function is represented by equation (2):
Figure 661250DEST_PATH_IMAGE065
（2）
wherein,
Figure 264401DEST_PATH_IMAGE011
mapping the coordinate value of the boundary of the drill hole in the coordinate space;
Figure 221992DEST_PATH_IMAGE066
the arithmetic mean value of the distances between the mapping points on all the mapping chambers and the corresponding mapping points on the real drill holes is obtained;
Figure 224583DEST_PATH_IMAGE013
the actual borehole boundary total length;
s24, calculating the ratio of the distance between any two adjacent points to the perimeter of the mapping hole shape, determining the corresponding position of each mapping point on the real drilling hole, and establishing a second mapping expression with a point zeta i (1, alpha i) on a unit circle
Figure 341444DEST_PATH_IMAGE067
Carrying out the next step;
s25, repeating the steps S22 to S24 until the required precision meets the test requirement to obtain the mapping function which finally meets the precision requirement
Figure 974551DEST_PATH_IMAGE068
；
And S3, substituting the mapping function expression of any irregular drilling hole shape into the complex function expression of the plane strain problem to deduce and obtain a relational expression between the far-field ground stress and the drilling hole wall stress under the plane strain condition of any irregular drilling hole shape, wherein the specific calculation process is as follows:
s31: constructing a complex function expression of the practical coordinate space drilling stress boundary condition under the plane strain condition; the complex function expression of the boundary condition of the actual coordinate space borehole stress under the planar strain condition is represented by formula (3):
Figure 799199DEST_PATH_IMAGE069
(3)
in the formula,
Figure 605481DEST_PATH_IMAGE070
、
Figure 717794DEST_PATH_IMAGE071
external forces in the x and y directions respectively;
Figure 380856DEST_PATH_IMAGE025
is a unit arc length on any irregular borehole shape;
Figure 375357DEST_PATH_IMAGE020
is a narrative unit;
Figure 923013DEST_PATH_IMAGE002
the coordinate complex expression form in the actual coordinate space is adopted;
Figure 499619DEST_PATH_IMAGE072
a first stress function that is a mapped coordinate space;
Figure 474528DEST_PATH_IMAGE042
a second stress function that is a mapped coordinate space;
Figure 284221DEST_PATH_IMAGE044
a first stress function that is an actual coordinate space;
Figure 432306DEST_PATH_IMAGE045
is composed of
Figure 988052DEST_PATH_IMAGE044
The first derivative of (a);
Figure 773343DEST_PATH_IMAGE073
is composed of
Figure 476857DEST_PATH_IMAGE045
The conjugate value of (a);
Figure 100736DEST_PATH_IMAGE047
a second stress function that is an actual coordinate space;
Figure 166781DEST_PATH_IMAGE074
is composed of
Figure 483493DEST_PATH_IMAGE047
Conjugate values at the borehole boundary in the actual coordinate space;
Figure 674303DEST_PATH_IMAGE075
is composed of
Figure 977240DEST_PATH_IMAGE072
Conjugate values at the borehole boundary in actual coordinate space;
Figure 773157DEST_PATH_IMAGE076
is composed of
Figure 323087DEST_PATH_IMAGE042
Conjugate values at the borehole boundary in the actual coordinate space;
Figure 329089DEST_PATH_IMAGE077
is composed of
Figure 294771DEST_PATH_IMAGE059
Conjugate values at the borehole boundary in the actual coordinate space;
s32: constructing a boundary value expression of a first stress function and a second stress function of a mapping coordinate space under a plane strain condition; mapping a first stress function of a coordinate space under a planar strain condition
Figure 741933DEST_PATH_IMAGE078
And a second stress function
Figure 39928DEST_PATH_IMAGE042
The boundary value expression of (a) is represented by formula (4) and formula (5), respectively:
Figure 408593DEST_PATH_IMAGE079
(4)
Figure 302599DEST_PATH_IMAGE080
(5)
in the formula,
Figure 807530DEST_PATH_IMAGE011
the coordinate value of the boundary of the drill hole in the mapping coordinate space is obtained;
Figure 43471DEST_PATH_IMAGE081
is composed of
Figure 899431DEST_PATH_IMAGE082
A boundary value of (d);
Figure 331549DEST_PATH_IMAGE083
is composed of
Figure 956566DEST_PATH_IMAGE084
A boundary value of (a);
Figure 19200DEST_PATH_IMAGE085
is the poisson ratio;
Figure 470779DEST_PATH_IMAGE086
and
Figure 847533DEST_PATH_IMAGE087
respectively the surface force of the hole edge;
Figure 123794DEST_PATH_IMAGE088
、
Figure 685225DEST_PATH_IMAGE089
、
Figure 984619DEST_PATH_IMAGE090
are parametric values related to the far-field ground stress;
Figure 774852DEST_PATH_IMAGE091
is composed of
Figure 171198DEST_PATH_IMAGE092
The remainder of (1);
Figure 778897DEST_PATH_IMAGE093
is composed of
Figure 690221DEST_PATH_IMAGE094
The remainder of (1);
Figure 408779DEST_PATH_IMAGE095
as a mapping function
Figure 659631DEST_PATH_IMAGE059
A borehole boundary value in the mapped coordinate space;
s33: constructing a relational expression which is expressed by the residual terms of the first stress function in the mapping coordinate space and the residual terms of the second stress function in the mapping coordinate space through the coordinate values at the drill hole boundary in the mapping coordinate space under the plane strain condition; namely, constructing a first stress function in the mapping coordinate space under the condition of plane strain
Figure 806274DEST_PATH_IMAGE096
Remainder of (2)
Figure 80260DEST_PATH_IMAGE097
And mapping a second stress function in the coordinate space
Figure 727142DEST_PATH_IMAGE098
The remainder of
Figure 832501DEST_PATH_IMAGE099
By mapping the coordinate values at the borehole boundaries in coordinate space
Figure 516424DEST_PATH_IMAGE011
The relational expression of the expression; the following expressions (6) to (8) indicate:
Figure 153072DEST_PATH_IMAGE100
（6）
Figure 275749DEST_PATH_IMAGE101
(7)
Figure 173298DEST_PATH_IMAGE102
(8)
wherein,
Figure 418335DEST_PATH_IMAGE103
is a stress boundary condition expression under the plane strain condition;
Figure 932493DEST_PATH_IMAGE104
finger pair
Figure 593281DEST_PATH_IMAGE103
Calculating conjugation;
Figure 719238DEST_PATH_IMAGE011
mapping the coordinate value of the boundary of the drill hole in the coordinate space;
Figure 276121DEST_PATH_IMAGE105
as a mapping function
Figure 808734DEST_PATH_IMAGE106
A first derivative at a borehole boundary in a mapped coordinate space;
Figure 335530DEST_PATH_IMAGE107
as a function of the mapping
Figure 207671DEST_PATH_IMAGE095
First derivative at borehole boundary in mapped coordinate space
Figure 810822DEST_PATH_IMAGE105
The conjugate value of (d);
Figure 565151DEST_PATH_IMAGE091
for mapping a first stress function in a coordinate space
Figure 36584DEST_PATH_IMAGE092
The remainder of (2);
Figure 887865DEST_PATH_IMAGE108
for mapping a first stress function in a coordinate space
Figure 520972DEST_PATH_IMAGE109
A first derivative at a borehole boundary in a mapped coordinate space;
Figure 28176DEST_PATH_IMAGE110
for mapping a first stress function in a coordinate space
Figure 411622DEST_PATH_IMAGE109
First derivative at borehole boundary in mapped coordinate space
Figure 992776DEST_PATH_IMAGE108
The conjugate value of (d);
Figure 186997DEST_PATH_IMAGE111
for mapping a second stress function in the coordinate space
Figure 915919DEST_PATH_IMAGE112
The remainder of (1);
Figure 729154DEST_PATH_IMAGE113
as a function of a second stress in the mapped coordinate space
Figure 305760DEST_PATH_IMAGE114
Conjugate values at the borehole boundary in the mapped coordinate space;
Figure 280669DEST_PATH_IMAGE115
is composed of
Figure 762466DEST_PATH_IMAGE116
The conjugate value of (a);
Figure 238447DEST_PATH_IMAGE058
as a function of the mapping
Figure 794193DEST_PATH_IMAGE059
Conjugate values at the borehole boundary in the mapped coordinate space;
Figure 736741DEST_PATH_IMAGE117
is an expression related to the boundary condition;
s34: solving the formula (6) and the formula (7) by comparing coefficients of the same-order terms, a linear algebraic equation set on a complex field can be obtained, and a first stress function in a mapping coordinate space is further determined
Figure 17419DEST_PATH_IMAGE109
And a second stress function
Figure 906877DEST_PATH_IMAGE042
The expression of (1);
s35: constructing expressions of the normal stress of the hole wall in the x direction, the normal stress in the y direction and the shear stress on the xy plane under the planar strain condition through a first stress function and a second stress function of a mapping coordinate space, and further obtaining a relational expression between the far-field ground stress and the hole wall stress of the drill hole under the planar strain condition; normal stress of hole wall in x direction under plane strain condition
Figure 707343DEST_PATH_IMAGE036
Positive stress in y-direction
Figure 86372DEST_PATH_IMAGE037
And shear stress in the xy plane
Figure 480444DEST_PATH_IMAGE118
By mapping a first stress function of the coordinate space
Figure 783381DEST_PATH_IMAGE072
And a second stress function
Figure 579298DEST_PATH_IMAGE042
The relational expressions shown are as shown in formulas (9) to (12):
Figure 129228DEST_PATH_IMAGE034
(9)
Figure 869651DEST_PATH_IMAGE119
（10）
Figure 100912DEST_PATH_IMAGE035
（11）
Figure 548074DEST_PATH_IMAGE120
（12）
wherein,
Figure 851929DEST_PATH_IMAGE036
is a positive stress in the x direction;
Figure 955014DEST_PATH_IMAGE037
is a positive stress in the y direction;
Figure 114600DEST_PATH_IMAGE118
is the shear stress in the xy plane;
Figure 416268DEST_PATH_IMAGE072
a first stress function that is a mapped coordinate space;
Figure 245684DEST_PATH_IMAGE121
as a first stress function of the mapped coordinate space
Figure 711431DEST_PATH_IMAGE072
A first order integral derivative value in the mapped coordinate space;
Figure 346812DEST_PATH_IMAGE042
a second stress function that is a mapped coordinate space;
Figure 706249DEST_PATH_IMAGE122
is the real part of the complex number;
Figure 96779DEST_PATH_IMAGE044
a first stress function that is an actual coordinate space;
Figure 174457DEST_PATH_IMAGE045
a first stress function of the actual coordinate space
Figure 347949DEST_PATH_IMAGE044
The first derivative of (a);
Figure 201373DEST_PATH_IMAGE046
a first stress function of the actual coordinate space
Figure 372592DEST_PATH_IMAGE044
The second derivative of (a);
Figure 734303DEST_PATH_IMAGE047
a second stress function that is a real coordinate space;
Figure 39382DEST_PATH_IMAGE048
a second stress function as an actual coordinate space
Figure 373412DEST_PATH_IMAGE047
The first derivative of (a);
Figure 856477DEST_PATH_IMAGE049
a first stress function of the actual coordinate space
Figure 439905DEST_PATH_IMAGE044
First derivative of (2)
Figure 424041DEST_PATH_IMAGE050
In the space of mapping coordinatesAn expression in (1);
Figure 737211DEST_PATH_IMAGE051
is composed of
Figure 515811DEST_PATH_IMAGE052
A first order integral derivative value in the mapped coordinate space;
Figure 586535DEST_PATH_IMAGE053
a second stress function for the actual coordinate space
Figure 482685DEST_PATH_IMAGE123
First derivative of
Figure 525727DEST_PATH_IMAGE054
An expression in a mapped coordinate space;
Figure 599862DEST_PATH_IMAGE055
is a mapping function;
Figure 423462DEST_PATH_IMAGE056
as a mapping function
Figure 483822DEST_PATH_IMAGE055
A first order integral derivative value in the mapped coordinate space;
Figure 522316DEST_PATH_IMAGE002
the coordinate complex expression form in the actual coordinate space is adopted;
Figure 642719DEST_PATH_IMAGE057
is composed of
Figure 688035DEST_PATH_IMAGE002
The conjugate value of (a);
Figure 676720DEST_PATH_IMAGE058
as a function of the mapping
Figure 694354DEST_PATH_IMAGE059
Conjugate values at the borehole boundary in the mapped coordinate space;
and S4, substituting the mapping function expression of any irregular drilling hole shape into the complex function expression of the reverse plane shear strain problem to deduce and obtain a relational expression between the far field ground stress and the drilling hole wall stress under the reverse plane shear strain condition of any irregular drilling hole shape, wherein the specific calculation process is as follows:
s41, constructing a stress function of the hole wall of the drill hole under the condition of reverse plane shear strain
Figure 687456DEST_PATH_IMAGE033
The expression of (1); represented by formula (13) and formula (14):
Figure 157752DEST_PATH_IMAGE014
（13）
Figure 700860DEST_PATH_IMAGE015
（14）
in the formula,
Figure 635318DEST_PATH_IMAGE002
the coordinate complex expression form in the actual coordinate space;
Figure 97523DEST_PATH_IMAGE006
expressing the number of the Lorong stages
Figure 179748DEST_PATH_IMAGE006
An item;
Figure 651181DEST_PATH_IMAGE007
indicating any irregular borehole shape
Figure 440145DEST_PATH_IMAGE007
Point;
Figure 464732DEST_PATH_IMAGE016
at the k point and
Figure 909619DEST_PATH_IMAGE017
a coefficient of correlation;
Figure 43797DEST_PATH_IMAGE018
the shear stress of the hole wall on a far field xz plane;
Figure 687268DEST_PATH_IMAGE019
the shear stress of the hole wall on a far-field yz plane;
Figure 491276DEST_PATH_IMAGE020
is a narrative unit;
Figure 298827DEST_PATH_IMAGE021
coefficient terms expanded in a Loran series;
Figure 112062DEST_PATH_IMAGE017
is a stress function of a stress boundary condition under a reverse plane shear strain condition;
s42, constructing a stress function of the stress boundary condition of the borehole wall under the condition of reverse plane shear strain
Figure 610039DEST_PATH_IMAGE017
The expression of (2); represented by formula (15):
Figure 975161DEST_PATH_IMAGE022
（15）
in the formula,
Figure 129062DEST_PATH_IMAGE023
is the bulk modulus;
Figure 277147DEST_PATH_IMAGE124
is a differential sign;
Figure 472374DEST_PATH_IMAGE025
is a unit arc length on any irregular drilling hole shape;
Figure 618184DEST_PATH_IMAGE020
is a narrative unit;
Figure 649594DEST_PATH_IMAGE033
the stress function of the hole wall of the drill hole under the condition of reverse plane shear strain is obtained;
Figure 601370DEST_PATH_IMAGE027
is a function of
Figure 277202DEST_PATH_IMAGE033
The conjugate value of (a);
s43, obtaining a relational expression between the far-field ground stress and the borehole wall stress under the reverse plane shear strain condition according to the steps S41 and S42; represented by formula (16):
Figure 469280DEST_PATH_IMAGE029
（16）
in the formula,
Figure 863352DEST_PATH_IMAGE030
the shear stress of the hole wall of the drilled hole on the xz plane;
Figure 353239DEST_PATH_IMAGE031
the shear stress of the hole wall of the drilled hole on the yz plane;
Figure 8211DEST_PATH_IMAGE032
is a function of
Figure 495824DEST_PATH_IMAGE033
A first derivative in actual coordinate space;
s5, combining the step S3 and the step S4 to obtain an analytical expression between the three-dimensional ground stress and the hole wall stress under the three-dimensional condition;
s6, taking out the core of the deep test section by using side wall coring equipment; carrying out a rock mass mechanics parameter test to determine rock mass deformation parameters; deducing to obtain an analytical expression between the hole wall strain and the far field ground stress in any direction at one point of the irregular drilling hole by combining an elastic mechanical stress-strain constitutive equation, rock mechanical parameters and the analytical expression between the three-dimensional ground stress and the hole wall stress under the three-dimensional condition;
s7, adopting local wall surface stress relief method equipment to test the stress of the spread ground in the deep drilling hole, and measuring to obtain the strain changes in at least 6 directions at the hole wall;
and S8, obtaining the magnitude of the far-field ground stress component through a least square method and an analytical expression between the hole wall strain and the far-field ground stress at one point of the irregular drilling hole in any direction.
The method comprises the steps of obtaining the real form of a drill hole through a caliper, an ultrasonic imaging technology or a micro-resistance scanning technology, calculating a mapping function expression of any irregular drill hole shape according to the real form of the drill hole, substituting the mapping function expression into a complex function expression to respectively deduce the relation between far-field ground stress and drill hole wall stress under a plane strain condition and a reverse plane shear strain condition, and obtaining an analytic expression between the three-dimensional ground stress and the hole wall stress under the three-dimensional condition; carrying out a rock mechanical parameter test by sidewall coring, and obtaining an analytical expression between the hole wall strain and the far-field ground stress at one point of the irregular drilling hole in any direction by combining the analytical expression between the three-dimensional ground stress and the hole wall stress under a three-dimensional condition; obtaining the magnitude of the far-field ground stress component through a least square method and an analytical expression between the hole wall strain and the far-field ground stress in any direction at one point of the irregular drilling hole; the influence of irregular drilling hole shapes is considered in the method for calculating the crustal stress by the stress relief method for the first time, and the accuracy of calculating the crustal stress by the stress relief method is improved; the analytical expression of the crustal stress calculated by the stress relief method is deduced by introducing a complex variable function method, so that the calculation can be easily realized by programming, and the accuracy and efficiency of the stress relief method calculation method are improved; the method can solve the problems that when the existing stress relief method is used for measuring the crustal stress, the irregular drill holes directly influence the stress and strain distribution rule at the hole walls of the drill holes, so that the crustal stress calculation can generate large system errors, and the measurement accuracy is poor.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A method for calculating the geostress by stress relief considering the shape of an irregular borehole, comprising the steps of:
s1, acquiring the real form of a drill hole;
s2, calculating a mapping function expression of any irregular drilling hole shape according to the real drilling hole shape;
s3, substituting the mapping function expression of any irregular drilling hole shape into the complex function expression of the plane strain problem to deduce and obtain a relational expression between the far-field ground stress and the drilling hole wall stress under the plane strain condition of any irregular drilling hole shape;
s4, substituting the mapping function expression of any irregular drilling hole shape into the complex function expression of the inverse plane shear strain problem to deduce and obtain a relational expression between the far field ground stress and the drilling hole wall stress under the inverse plane shear strain condition of any irregular drilling hole shape;
s5, combining the step S3 and the step S4 to obtain an analytical expression between the three-dimensional ground stress and the hole wall stress under the three-dimensional condition;
s6: taking out the core of the deep test section by using side wall coring equipment; carrying out a rock mass mechanics parameter test to determine rock mass deformation parameters; deducing to obtain an analytical expression between the hole wall strain and the far field ground stress in any direction at one point of the irregular drilling hole by combining an elastic mechanical stress-strain constitutive equation, rock mechanical parameters and the analytical expression between the three-dimensional ground stress and the hole wall stress under the three-dimensional condition;
s7: adopting local wall surface stress relief method equipment to perform an earth stress test in the deep drilling hole to obtain strain changes in at least 6 directions at the hole wall;
s8: and obtaining the magnitude of the far-field ground stress component through a least square method and an analytical expression between the strain of the hole wall and the far-field ground stress at one point of the irregular drilling hole in any direction.
2. The method of calculating stress by stress relief division considering irregular borehole shapes according to claim 1, wherein the expression of the mapping function of any irregular borehole shape in step S2 is in the form of a lorentz series, represented by formula (1):
Figure 203510DEST_PATH_IMAGE001
（1）
wherein,
Figure 469406DEST_PATH_IMAGE002
the coordinate complex expression form in the actual coordinate space;
Figure 812663DEST_PATH_IMAGE003
a mapping function for any irregular borehole shape;
Figure 94478DEST_PATH_IMAGE004
the expression form of coordinate complex numbers in the mapping space is any irregular drilling hole shape; r, C1, C2 … …
Figure 574001DEST_PATH_IMAGE005
K +1 real constants;
Figure 276377DEST_PATH_IMAGE006
expressing the number of the Lorong stages
Figure 965985DEST_PATH_IMAGE006
An item;
Figure 146430DEST_PATH_IMAGE007
indicating any irregular borehole shape
Figure 621405DEST_PATH_IMAGE007
Point;
calculation of R, C by boundary point search method1、C2……
Figure 229104DEST_PATH_IMAGE008
The values of the k +1 real constants and the expression of the mapping function meeting the precision test requirement are obtained.
3. The method for calculating the stress by the method of relieving stress according to the method of claim 2, wherein the specific calculation of the expression of the mapping function satisfying the accuracy test requirement comprises the steps of:
s21, dividing the unit circle into a plurality of equal parts
Figure 546953DEST_PATH_IMAGE009
Calculating any point on the unit circle and a mapping point on a corresponding real drilling hole to obtain an initial mapping function expression;
s22, calculating mapping points under initial mapping through the initial mapping function expression;
s23, judging whether the precision of the initial mapping function meets the test requirement or not; if the precision meets the test requirement, the obtained initial mapping function is the mapping function expression which is required to be accurate enough; if the precision does not meet the test requirement, the next step is carried out;
s24, calculating the ratio of the distance between any two adjacent points to the perimeter of the mapping hole, determining the corresponding position of each mapping point on the real drilled hole, establishing a second mapping expression with the point on the unit circle, and carrying out the next step;
and S25, repeating the steps S22 to S24 until the required mapping function precision meets the test requirement to obtain the mapping function which finally meets the requirement.
4. The method of calculating stress-relieving crustal stress according to claim 3, wherein the calculation of the accuracy of the mapping function is represented by equation (2):
Figure 390144DEST_PATH_IMAGE010
（2）
wherein,
Figure 109838DEST_PATH_IMAGE011
mapping the coordinate value of the boundary of the drill hole in the coordinate space;
Figure 268199DEST_PATH_IMAGE012
the arithmetic mean value of the distances between the mapping points on all the mapping chambers and the corresponding mapping points on the real drilled holes is obtained;
Figure 73344DEST_PATH_IMAGE013
is the actual borehole boundary overall length.
5. The method of calculating the stress by stress relief method taking into account the irregular borehole shape according to any of claims 1 to 4, wherein the obtaining of the relation between the far-field earth stress and the borehole wall stress under the reverse plane shear strain condition of any irregular borehole shape in step S4 comprises:
s41, constructing a stress function expression of the borehole wall under the condition of reverse plane shear strain;
s42, constructing a stress function expression of the stress boundary condition under the condition of the reverse plane shear strain;
and S43, obtaining a relational expression between the far-field ground stress and the borehole wall stress under the reverse plane shear strain condition according to the steps S41 and S42.
6. The method of calculating stress by stress relief method taking into account an irregular borehole shape according to claim 5, wherein the expression of the stress function of the borehole wall under the anti-plane shear strain condition is represented by equations (13) and (14):
Figure 595592DEST_PATH_IMAGE014
（13）
Figure 294427DEST_PATH_IMAGE015
（14）
in the formula,
Figure 243928DEST_PATH_IMAGE002
the coordinate complex expression form in the actual coordinate space;
Figure 270790DEST_PATH_IMAGE006
expressing the number of the Lorong stages
Figure 472095DEST_PATH_IMAGE006
An item;
Figure 900803DEST_PATH_IMAGE007
on any irregular borehole shape
Figure 145839DEST_PATH_IMAGE007
Point;
Figure 925577DEST_PATH_IMAGE016
at the k point and
Figure 789627DEST_PATH_IMAGE017
a coefficient of correlation;
Figure 181163DEST_PATH_IMAGE018
the shear stress of the hole wall on a far field xz plane;
Figure 3626DEST_PATH_IMAGE019
the shear stress of the hole wall on a far-field yz plane;
Figure 5080DEST_PATH_IMAGE020
is a narrative unit;
Figure 797455DEST_PATH_IMAGE021
for systems developed in accordance with the Loran seriesSeveral items.
7. The method of calculating stress by stress relief method taking into account irregular borehole shape according to claim 6, wherein the stress function expression of the stress boundary condition under the reverse plane shear strain condition is represented by equation (15):
Figure 935176DEST_PATH_IMAGE022
（15）
in the formula,
Figure 538326DEST_PATH_IMAGE017
is a stress function of a stress boundary condition under a reverse plane shear strain condition;
Figure 27077DEST_PATH_IMAGE023
is the bulk modulus;
Figure 232930DEST_PATH_IMAGE024
is a differential sign;
Figure 615370DEST_PATH_IMAGE025
is a unit arc length on any irregular borehole shape;
Figure 779635DEST_PATH_IMAGE020
is a narrative unit;
Figure 224523DEST_PATH_IMAGE026
is a stress function of the hole wall of the drill hole under the condition of reverse plane shear strain;
Figure 873548DEST_PATH_IMAGE027
is a function of
Figure 985860DEST_PATH_IMAGE028
The conjugate value of (c).
8. The method of calculating the stress-relieving crustal stress in consideration of the irregular borehole shape according to claim 7, wherein the relational expression between the far-field crustal stress and the borehole wall stress under the reverse plane shear strain condition is represented by equation (16):
Figure 55447DEST_PATH_IMAGE029
（16）
in the formula,
Figure 643423DEST_PATH_IMAGE030
the shear stress of the hole wall of the drilled hole on the xz plane;
Figure 191079DEST_PATH_IMAGE031
the shear stress of the hole wall of the drilled hole on the yz plane;
Figure 423478DEST_PATH_IMAGE032
is a function of
Figure 273753DEST_PATH_IMAGE033
The first derivative in the actual coordinate space.
9. The method for calculating the division crustal stress by stress relief considering the irregular borehole shape according to claim 8, wherein the derivation of the relationship between the far-field crustal stress and the borehole wall stress under the plane strain condition in step S3 comprises the steps of:
s31: constructing a complex function expression of the practical coordinate space drilling stress boundary condition under the plane strain condition;
s32: constructing a boundary value expression of a first stress function and a second stress function of a mapping coordinate space under a plane strain condition;
s33: constructing a relational expression which is expressed by the residual terms of the first stress function in the mapping coordinate space and the residual terms of the second stress function in the mapping coordinate space through the coordinate values at the drill hole boundary in the mapping coordinate space under the plane strain condition;
s34: solving the relational expression obtained in the step S33 by comparing the coefficients of the same-order terms to obtain a linear algebraic equation set in a complex field, thereby further determining expressions of a first stress function and a second stress function in a mapping coordinate space;
s35: and constructing expressions of the normal stress of the hole wall in the x direction, the normal stress in the y direction and the shear stress on the xy plane under the planar strain condition through mapping a first stress function and a second stress function of a coordinate space, and further obtaining a relational expression between the far-field ground stress and the hole wall stress of the drill hole under the planar strain condition.
10. The method for calculating the stress by the method of relieving stress according to claim 9, wherein the relationship between the far-field ground stress and the borehole wall stress under the in-plane strain condition is represented by the following equations (3) to (5):
Figure 224392DEST_PATH_IMAGE034
(9)
Figure 700372DEST_PATH_IMAGE035
（11）
wherein,
Figure 787277DEST_PATH_IMAGE036
is the normal stress in the x direction under the plane strain condition;
Figure 198667DEST_PATH_IMAGE037
is the positive stress in the y direction under the planar strain condition;
Figure 744923DEST_PATH_IMAGE038
the shear stress on the xy plane under the plane strain condition;
Figure 634382DEST_PATH_IMAGE039
a first stress function that is a mapped coordinate space;
Figure 841372DEST_PATH_IMAGE040
is composed of
Figure 282718DEST_PATH_IMAGE041
A first order integral derivative value in the mapped coordinate space;
Figure 942370DEST_PATH_IMAGE042
a second stress function that is a mapped coordinate space;
Figure 510885DEST_PATH_IMAGE043
is the real part of the complex number;
Figure 572382DEST_PATH_IMAGE044
a first stress function that is an actual coordinate space;
Figure 325575DEST_PATH_IMAGE045
is composed of
Figure 597156DEST_PATH_IMAGE044
The first derivative of (a);
Figure 93996DEST_PATH_IMAGE046
is composed of
Figure 744420DEST_PATH_IMAGE044
The second derivative of (a);
Figure 302135DEST_PATH_IMAGE047
a second stress function that is an actual coordinate space;
Figure 670800DEST_PATH_IMAGE048
is composed of
Figure 971331DEST_PATH_IMAGE047
The first derivative of (a);
Figure 600896DEST_PATH_IMAGE049
is composed of
Figure 961470DEST_PATH_IMAGE050
An expression in a mapping coordinate space;
Figure 83010DEST_PATH_IMAGE051
is composed of
Figure 531440DEST_PATH_IMAGE052
A first order integral derivative value in the mapped coordinate space;
Figure 749931DEST_PATH_IMAGE053
is composed of
Figure 281407DEST_PATH_IMAGE054
An expression in a mapping coordinate space;
Figure 732986DEST_PATH_IMAGE055
is a mapping function;
Figure 640899DEST_PATH_IMAGE056
is composed of
Figure 120422DEST_PATH_IMAGE055
A first order integral derivative value in the mapped coordinate space;
Figure 947432DEST_PATH_IMAGE002
the coordinate complex expression form in the actual coordinate space;
Figure 512406DEST_PATH_IMAGE057
is composed of
Figure 692851DEST_PATH_IMAGE002
The conjugate value of (a);
Figure 167826DEST_PATH_IMAGE058
is composed of
Figure 775525DEST_PATH_IMAGE059
Conjugate values at the borehole boundary in the mapped coordinate space.
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CN114720305A (en) * 2022-02-28 2022-07-08 中国科学院武汉岩土力学研究所 Rock shear strength and uniaxial compressive strength in-situ test system and test method

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