Drill hole plane stress measurement method based on hole circumference relative displacement change

Abstract

The invention discloses a drill hole plane stress measurement method based on hole circumference relative displacement change. The method comprises the following steps: step 1, drilling a to-be-measured drill hole at a preset position to a preset measurement depth; 2, a mounting hole is concentrically drilled in the bottom of the drill hole, and a plurality of deformation meters used for measuring the relative displacement of the hole periphery are mounted on the hole periphery of the mounting hole; and step 3, the sleeve core is adopted to remove the to-be-measured drill hole, the relative displacement change of the periphery of the deformation meter mounting hole is obtained through the deformation meter in the removing process, and the plane stress state of the rock around the to-be-measured drill hole is obtained through relative displacement calculation. The method is simple in measurement and high in anti-interference capability, and the stress state of the drill hole can be calculated only by testing the relative displacement of three points around the hole.

Description

Technical Field

[0001] This invention belongs to the technical field of geotechnical engineering and geomechanical measurement, specifically relating to a borehole plane stress measurement method based on the relative displacement change around the borehole. Background Technology

[0002] In geotechnical engineering, mining, and geological hazard assessment, accurate measurement of the stress state within rock masses is crucial. Traditional stress measurement methods, such as hydraulic fracturing and stress relief methods, often suffer from problems such as complex equipment, cumbersome operation, high requirements for the measurement environment, complex calculation models, or susceptibility to the influence of local rock mass properties on the measurement results. For example, borehole-based stress relief methods, while straightforward in principle, typically require installing complex probes containing multiple strain sensors in the borehole and inverting stress by measuring the absolute strain values ​​in multiple directions of the borehole wall. This method demands extremely high precision and stability in sensor installation, and the calculation process relies on complex elasticity formulas, making it prone to errors due to local rock mass inhomogeneity or sensor zero-point drift.

[0003] Therefore, there is an urgent need in this field for a plane stress measurement method that is simple to use, easy to operate, has strong anti-interference ability, and is easy to calculate. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for measuring borehole plane stress based on the relative displacement changes around the borehole. This method is simple to measure, has strong anti-interference capabilities, and only requires testing the relative displacement of three points around the borehole to calculate the stress state of the borehole.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A method for measuring borehole plane stress based on the relative displacement change around the borehole includes the following steps:

[0007] Step 1: Drill the borehole to be measured at the predetermined location to the predetermined measurement depth;

[0008] Step 2: Drill a mounting hole concentrically at the bottom of the borehole, and install multiple deformation gauges around the mounting hole to measure the relative displacement around the hole.

[0009] Step 3: Use a core sleeve to remove the borehole to be measured, and during the removal process, use a deformation gauge to obtain the relative displacement change around the installation hole, and use the relative displacement to calculate the plane stress state of the rock around the borehole to be measured.

[0010] 2. The drilling plane stress measurement method based on the relative displacement change around the hole according to claim 1, characterized in that, in step 2, at least 3 deformation gauges are installed around the hole.

[0011] 3. The borehole plane stress measurement method based on the relative displacement change around the borehole according to claim 1, characterized in that the method for calculating the plane stress of the rock surrounding the borehole to be measured by measuring the relative displacement using a borehole deformability gauge in step 3 includes:

[0012] First, establish a radial plane coordinate system for the borehole to be measured, and determine the angle between each contact point and the X-axis based on the established coordinate system;

[0013] According to the principles of elasticity, after the borehole excavation is completed, the plane stress on the borehole wall is:

[0014]

[0015]

[0016]

[0017] In the formula, , This represents the first and second principal stresses to be determined. The angle between the first principal stress and the X-axis is given. Radial distance, Set the parameter for the angle between a point on the circumference of the hole and the X-axis. , This represents the radial stress in the borehole. This represents the tangential stress in the borehole. The shear stress in the borehole is represented by r, and the borehole radius is represented by r.

[0018] The displacement of the borehole wall is:

[0019]

[0020]

[0021] In the formula, Indicates the radial displacement of the borehole. This represents the tangential displacement of the borehole, and E represents the elastic modulus of the rock mass.

[0022] Considering plane strain problems

[0023]

[0024]

[0025] In the formula, v represents the Poisson's ratio of the rock mass;

[0026] Record any two points on the wall of the hole and Then the initial chord length between points P and Q is

[0027]

[0028] After the stress is relieved, the displacement of the hole wall is as follows:

[0029]

[0030]

[0031] In the formula, x(θ) represents the displacement of the hole wall in the X-axis direction, and y(θ) represents the displacement of the hole wall in the Y-axis direction; (Correct)

[0032] Since the hole wall displacement is much smaller than the borehole radius, a first-order approximation is used.

[0033]

[0034]

[0035] For points P and Q, then we have

[0036]

[0037]

[0038]

[0039]

[0040] In the formula, x i The displacement of point P along the X-axis is represented by y. i x represents the displacement of point P along the Y-axis. j The displacement of point Q along the X-axis is represented by y. j This represents the displacement of point Q along the Y-axis.

[0041] Substitute the values ​​into the equations to obtain the relative displacement of the coordinates.

[0042]

[0043]

[0044] In the formula, This represents the relative displacement of points P and Q along the X-axis. This represents the relative displacement of points P and Q along the Y-axis.

[0045] The change in chord length between points P and Q before and after stress relief is:

[0046]

[0047] Initial chord length vector

[0048]

[0049] In the above formula, for ease of derivation and to simplify the formula, let's denote... , ;

[0050] Displacement difference vector

[0051]

[0052] In the formula, This represents the displacement increment of point P in the X-axis direction. This represents the displacement increment of point P in the Y-axis direction. This represents the displacement increment of point Q along the X-axis. This represents the displacement increment of point Q along the Y-axis.

[0053] String length variation:

[0054]

[0055] By simplifying using trigonometric identities, the expression for the chord length variable can be obtained as follows:

[0056]

[0057] Treating each deformation gauge as a point on the circumference of the hole, and substituting the displacement change measured by each deformation gauge into the above formula, the result can be calculated. , as well as .

[0058] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention can directly solve the plane stress state of the borehole by measuring the relative displacement change of the borehole deformation gauge before and after the borehole stress is relieved. Its measurement method is simple, the equipment requirements are low, no complex sensors are required, and it can be measured by deformation gauge alone. It has high measurement accuracy and strong anti-interference ability, and overcomes the error problems caused by local rock mass inhomogeneity or sensor zero-point drift in the prior art. Attached Figure Description

[0059] Figure 1 The drilling plane coordinate system established for embodiments of the present invention;

[0060] Figure 2 The distribution of the perforation deformation gauges in an embodiment of the present invention is shown. Detailed Implementation

[0061] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0062] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0063] The present invention will be further described below with reference to specific embodiments, but these are not intended to limit the scope of the invention.

[0064] This invention discloses a method for measuring borehole plane stress based on the relative displacement change around the borehole, comprising the following steps:

[0065] Step 1: Drill the hole to be measured to the predetermined measurement depth at the pre-set location;

[0066] Step 2: Drill a mounting hole concentrically at the bottom of the borehole to be measured, and install multiple deformation gauges around the mounting hole to measure the relative displacement around the hole. In this embodiment, the deformation gauges are installed to the predetermined hole depth position by means of a directional mounting rod, and the number of deformation gauges is 3.

[0067] Step 3: After the deformation gauge is installed, the borehole to be measured is removed using a core sleeve. During the removal process, the relative displacement change between three points around the borehole is measured using the deformation gauge, and the plane stress state of the rock around the borehole is obtained by calculating the relative displacement.

[0068] In step 3, the plane stress state of the rock surrounding the borehole to be measured is calculated using relative displacement as follows:

[0069] First, establish a radial screen coordinate system for the drill hole. The farthest point of the rectangular coordinate system is at the center of the hole, with positive E as the X-axis and positive N as the Y-axis, as follows: Figure 1 As shown. Assume the angle between the major principal stress in the far field and the X-axis (positive E direction) is... (Counterclockwise is positive), then , and There are 3 unknowns to be solved.

[0070] The origin of the polar coordinate system is at the center of the hole. Radial distance, Set the parameters for the angle between a point on the perimeter of the hole and the x-axis (measured from due east, counterclockwise is positive). (The relative difference between the direction of the principal stress and the position angle).

[0071] Formulas for stress and displacement in boreholes are established based on the principles of elasticity:

[0072] After the borehole excavation is completed, the stress on the borehole wall is (plane stress).

[0073] (1a)

[0074] (1b)

[0075] (1c)

[0076] In the formula, This represents the radial stress in the borehole. This represents the tangential stress in the borehole. The shear stress in the borehole is represented by r, and the borehole radius is represented by r.

[0077] The displacement of the borehole wall is:

[0078] (2a)

[0079] (2b)

[0080] In the formula, Indicates the radial displacement of the borehole. This represents the tangential displacement of the borehole, and E represents the elastic modulus of the rock mass.

[0081] Considering plane strain problems

[0082] (2c)

[0083] (2d)

[0084] In the formula, v represents the Poisson's ratio of the rock mass;

[0085] Record any two points on the wall of the hole and Then the initial chord length between points P and Q is

[0086] (3)

[0087] After the stress is relieved, the displacement of the hole wall is as follows:

[0088] (4a)

[0089] (4b)

[0090] In the formula, x(θ) represents the displacement of the hole wall in the X-axis direction, and y(θ) represents the displacement of the hole wall in the Y-axis direction;

[0091] Since the hole wall displacement is much smaller than the borehole radius, a first-order approximation can be used.

[0092] (5a)

[0093] (5b)

[0094] For points P and Q, then we have

[0095] (6a)

[0096] (6b)

[0097] (7a)

[0098] (7b)

[0099] In the formula, x i The displacement of point P along the X-axis is represented by y. i x represents the displacement of point P along the Y-axis. j The displacement of point Q along the X-axis is represented by y. j This represents the displacement of point Q along the Y-axis.

[0100] Substituting equation (2) into the equation, we can obtain the relative displacement of the coordinates.

[0101] (8a)

[0102] (8b)

[0103] In the formula, This represents the relative displacement of points P and Q along the X-axis. This represents the relative displacement of points P and Q along the Y-axis.

[0104] For ease of derivation, let's record...

[0105] (9a)

[0106] (9b)

[0107] Substituting equation (2) into equation (9), let... Then there is

[0108] (10a)

[0109] (10b)

[0110] The change in chord length between points P and Q before and after stress relief is:

[0111] (11)

[0112] Initial chord length vector

[0113] (12)

[0114] Displacement difference vector

[0115] (13)

[0116] In the formula, This represents the displacement increment of point P in the X-axis direction. This represents the displacement increment of point P in the Y-axis direction. This represents the displacement increment of point Q along the X-axis. This represents the displacement increment of point Q along the Y-axis.

[0117] String length variation (first-order approximation)

[0118] (14)

[0119] (15)

[0120] For ease of derivation and to simplify the formula, let's call it... , Then there is

[0121] (16a)

[0122] (16b)

[0123] By simplifying using trigonometric identities, the expression for the chord length variable can be obtained as follows:

[0124] (17)

[0125] like Figure 2 As shown, deformers are distributed on the borehole wall. , , There are a total of 3 points, θ1, θ2, and θ3 are all known. From equation (17), the changes in chord length between AB, BC, and CA can be obtained as follows:

[0126] (18a)

[0127] (18b)

[0128] (18c)

[0129] The changes in chord lengths between AB, BC, and CA can all be obtained by measuring the deformation gauge before and after stress relief.

[0130] Further, record (19)

[0131] (20)

[0132] Then there is

[0133] (21a)

[0134] (21b)

[0135] (21c)

[0136] Subtracting equation (21b) from equation (21a) yields...

[0137] (twenty two)

[0138] Further

[0139] (twenty three)

[0140] Subtracting equation (21b) from equation (21c), we obtain...

[0141] (twenty four)

[0142] Further

[0143] (25)

[0144] Combining equations (23) and (25), we have

[0145] (26)

[0146] Further

[0147] (27)

[0148] (28)

[0149] (29)

[0150] Therefore, we obtain

[0151] (30)

[0152] According to equation (21a), we have

[0153] (31)

[0154] at last, Substitute into equation (23) or (25) to calculate. Then calculate according to equation (31). Solve , for

[0155] (32)

[0156]

[0157] The above are merely preferred embodiments of the present invention and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should recognize that any equivalent substitutions and obvious changes made based on the content of this specification should be included within the protection scope of the present invention.

Claims

1. A method for measuring borehole plane stress based on relative displacement changes around the borehole, characterized in that, Includes the following steps: Step 1: Drill the borehole to be measured at the predetermined location to the predetermined measurement depth; Step 2: Drill a mounting hole concentrically at the bottom of the borehole, and install multiple deformation gauges around the mounting hole to measure the relative displacement around the hole. Step 3: Use a core sleeve to remove the borehole to be measured, and during the removal process, use a deformation gauge to obtain the relative displacement change around the installation hole, and use the relative displacement to calculate the plane stress state of the rock around the borehole to be measured.

2. The borehole plane stress measurement method based on relative displacement variation around the borehole according to claim 1, characterized in that, In step 2, at least three deformation gauges are installed around the mounting holes.

3. The borehole plane stress measurement method based on the relative displacement change around the borehole according to claim 1, characterized in that, The method for calculating the plane stress of the rock surrounding the borehole in step 3 using the relative displacement measured by the borehole perimeter deformability gauge includes: First, establish a radial plane coordinate system for the borehole to be measured, and determine the angle between each contact point and the X-axis based on the established coordinate system; According to the principles of elasticity, after the borehole excavation is completed, the plane stress on the borehole wall is: ； ； ； In the formula, , This represents the first and second principal stresses to be determined. The angle between the first principal stress and the X-axis is given. Radial distance, Set the parameter for the angle between a point on the circumference of the hole and the X-axis. , This represents the radial stress in the borehole. This represents the tangential stress in the borehole. The shear stress in the borehole is represented by r, and the borehole radius is represented by r. The displacement of the borehole wall is: ； ； In the formula, Indicates the radial displacement of the borehole. This represents the tangential displacement of the borehole, and E represents the elastic modulus of the rock mass. Considering plane strain problems ； ； In the formula, v represents the Poisson's ratio of the rock mass; Record any two points on the wall of the hole and Then the initial chord length between points P and Q is ； After the stress is relieved, the displacement of the hole wall is as follows: ； ； In the formula, x(θ) represents the displacement of the hole wall in the X-axis direction, and y(θ) represents the displacement of the hole wall in the Y-axis direction; (Correct) Since the hole wall displacement is much smaller than the borehole radius, a first-order approximation is used. ； ； For points P and Q, then we have ； ； ； ； In the formula, x i The displacement of point P along the X-axis is represented by y. i x represents the displacement of point P along the Y-axis. j The displacement of point Q along the X-axis is represented by y. j This represents the displacement of point Q along the Y-axis. Substitute the values ​​into the equations to obtain the relative displacement of the coordinates. ； ； In the formula, This represents the relative displacement of points P and Q along the X-axis. This represents the relative displacement of points P and Q along the Y-axis. The change in chord length between points P and Q before and after stress relief is: ； Initial chord length vector ； In the above formula, for ease of derivation and to simplify the formula, let's denote... , ; Displacement difference vector ； In the formula, This represents the displacement increment of point P in the X-axis direction. This represents the displacement increment of point P in the Y-axis direction. This represents the displacement increment of point Q along the X-axis. This represents the displacement increment of point Q along the Y-axis. String length variation: ； By simplifying using trigonometric identities, the expression for the chord length variable can be obtained as follows: ； Treating each deformation gauge as a point on the circumference of the hole, and substituting the displacement change measured by each deformation gauge into the above formula, the result can be calculated. , as well as .

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