RU2029085C1 - Method for determination of directions of action of principal normal stresses under conditions of volumetric state of stress of rock mass - Google Patents

Abstract

FIELD: mining. SUBSTANCE: three clusters of three parallel holes are drilled in rock mass in vertexes of equilateral triangle whose one side is taken as the initial zero direction. Installed in holes are radiators and receivers of elastic vibrations. Measured is time of propagation of elastic waves in space between holes in each hole cluster in measurement points located at same intervals from drilling machine station. Subject to measurement are directions of action of maximum normal stresses in three orthogonal planes and determinations of direction of action of principal normal stresses under conditions of volumetric state of stress of rock mass. EFFECT: higher efficiency. 4 dwg, 4 tbl

Description

 The invention relates to ultrasonic methods for determining the stress-strain state of a rock mass and can be used to determine the directions of action of the main stresses in the rock mass in areas represented by rocks of a relatively uniform structure.

 There is a method of determining the directions of action of the main stresses in a rock mass, including the placement of the source and receivers of elastic vibrations in the development of the rock mass, the excitation of elastic vibrations by an explosion or mechanical shock, measurement of shear wave propagation velocities and their comparison. The source and receivers of elastic vibrations are placed in the plane of the axes of action of the studied principal stresses and the velocities of the propagation of waves polarized perpendicular to the plane of the axes of action of the principal stresses are measured. The measurement results are plotted with the velocity-azimuth axes of the wave propagation and, according to the characteristic features of the indicatrix, highlight the direction of action of the main stresses in the array [1].

The disadvantage of this method is the low accuracy associated with the identification of shear waves, analysis of wave patterns and determining the position of the azimuth of the axes of the maximum and minimum speeds in the rock mass. The low accuracy of the determination is also due to the fact that the measurements are carried out with respect to one plane, the seismic wave receivers are located at an unequal distance from the source. The azimuth of the source-receiver line is chosen A ₁ = 45 ^about , A ₂ = 90 ^about , A ₃ = 180 ^about . The low accuracy of the determination is due to the fact that in a rock mass at operating stresses of 10-30 MPa, the change in the shear wave velocity with increasing stress is much less than for a longitudinal wave.

 A known method adopted for the prototype is to determine the directions of action of the main normal stresses in the massif, consisting in the fact that three parallel boreholes are drilled from three orthogonal planes in a rock massif according to the rectangular velocity rosette pattern, ultrasonic wave sensors are placed in them, and propagation velocities are determined longitudinal waves between each pair of sensors and the maximum and minimum velocity values determine the orientation of the velocity anisotropy ellipse. The direction of the long axis of the ellipse coincides with the direction of the maximum normal stress. The construction of indicatrix parameters of elastic wave propagation velocities in three orthogonal planes allows one to determine the directions of action of the main stresses in the array [2].

 However, this method has low accuracy in determining the directions of action of the main stresses in the array, associated with errors in determining the indicatrix parameters in the corresponding coordinate planes, especially in rocks in which the velocities change with an increase in stresses by only 10-15%. Errors in determining the directions of action of the main stresses in this way can reach 20 or more degrees.

 The purpose of the invention is the creation of a method that improves the accuracy of determining the directions of action of the main normal stresses in the rock mass.

 This goal is achieved by the fact that in the method, including drilling in an array in three orthogonal planes of three clusters of three parallel wells, placing in the wells sources and receivers of elastic vibrations and measuring devices, exciting elastic waves and determining the propagation velocity of longitudinal waves between the wells, the wells are drilled along the vertices of an equilateral triangle, one of the sides in which they take for the initial zero direction. The propagation time of longitudinal waves in the interwell space in each well cluster is measured at measurement points located at an equal distance from the standing point of the drilling rig. The directions of action of the maximum normal stresses in three orthogonal planes are calculated. The directions of action of the main normal stresses in the conditions of the bulk stress state of the array are determined.

A comparative analysis of the proposed method with the prototype shows that the inventive method differs from the known ones in that the wells are drilled along the vertices of an equilateral triangle, one of the sides of which is taken as the initial zero direction. Thus is ensured comprehensive measurements are equal between the wells and the equal angles between the directions of measurement equal to ^60, i.e., an equilateral measurement scheme is provided.

 At each measurement point at the installation sites of the measuring devices, the transit time of the elastic waves in the interwell space is measured. The directions of action of normal stresses in an array of relatively homogeneous rocks are determined by the change in the transit time of elastic waves in the interwell space. The main reason for the change in the transit time of elastic waves in the interwell space is the deformation resulting from the closure of pores and the compaction of microcracks, which leads to an increase in rock density. The degree of closure of pores and microcracks depends on their orientation with respect to current normal stresses in the massif. The greatest closing effect is observed for pores and cracks oriented in the direction of the maximum normal stress in the mass. In the same direction, there is a maximum increase in rock density and, accordingly, the largest decrease in the propagation time of a longitudinal wave. The smallest closure is observed for pores and cracks oriented in the direction of the minimum normal stress in the array and, accordingly, the longest propagation time of the longitudinal wave is observed in this direction.

Thus, a change in the propagation time of elastic waves in any direction depends on a change in deformation (stresses) in that direction, i.e. Δt _φ = Δε _φ ˙K.

+

cos2φ
В уравнение входят три неизвестные величины: ε_max, ε_min и φ. Для их определения необходимы три уравнения, которые можно получить, выполнив три измерения времени прохождения упругих волн между скважинами, пробуренными по вершинам равностороннего треугольника и определив при этом три значения t₁ ⁰, t₂ ⁶⁰, t₃ ¹²⁰.When measuring devices are located in three wells drilled in a plane relative to each other at an angle of 60 ^about deformation in any direction, they can be determined as follows:
ε _φ =

+

cos2φ
The equation contains three unknown quantities: ε _max , ε _min and φ. To determine them, three equations are needed, which can be obtained by performing three measurements of the transit time of elastic waves between wells drilled along the vertices of an equilateral triangle and determining three values of t ₁ ⁰ , t ₂ ⁶⁰ , t ₃ ¹²⁰ .

Измерения времени распространения упругих волн между скважинами, пробуренными по вершинам равностороннего треугольника, можно применять во всех случаях, когда направление действия нормальных напряжений неизвестно даже приближенно.From the analytical solution of the equation, representing the three measured values of t ₁ ⁰ , t ₂ ⁶⁰ and t ₃ ¹²⁰ , we can obtain an expression for determining the angle φ between the direction of maximum deformation (stresses) and the initial zero direction:
tg2φ =

Measurements of the propagation time of elastic waves between wells drilled along the vertices of an equilateral triangle can be used in all cases when the direction of action of normal stresses is unknown even approximately.

 There is no known method for determining the directions of action of normal stresses in a rock mass, based on measuring the propagation time of elastic waves between wells drilled along the vertices of an equilateral triangle.

The method is as follows (Fig. 1 and 2). In a rock mass from a mine in three orthogonal planes, three clusters of parallel wells are drilled along the vertices of an equilateral triangle. One of the sides of an equilateral triangle, for example, the direction between the wells. 1-2, taken as the initial zero direction, which at the same time is taken as the x or y axis. Sensors of elastic vibrations are installed in all well clusters at each measurement point. In well 1 place the emitter And ₁ and the receiver P ₁ elastic waves, in the well. - receiver P ₂ and emitter I ₂ , in wells. 3 - receiver P ₃ and emitter And ₃ elastic vibrations. Emitters and receivers are located in the wells coaxially to each other.

 The sensors are installed in all well clusters at the same distance from the production center, so that the measurement points are on the faces of the represented cube. The center of the represented cube is the standing point of the drilling rig. The beginning of determining the distance to the measurement points located on the faces of the represented cube accept the standing point of the drilling rig. The distance between the wells L (measurement base) is taken equal to L ≥10˙ D, where D is the diameter of the wells.

Before carrying out ultrasonic measurements, three devices Y ₁ , Y ₂ , Y ₃ with sensors are installed into the wells with the help of delivery rods (Fig. 3) and moved along them to the required point in the array. The distance to the measuring point is determined from the standing point of the drilling rig. The sensors are pressed against the walls of the wells by supplying compressed air P using a hand pump. Measurements of the propagation time of a longitudinal wave in the interwell space are carried out at each measurement point. To do this, connect the electric cables of the sensors And ₁ and P ₂ to the device and measure the propagation time of the longitudinal wave t _1-2 ^o between wells. 1-2. Then, the electric cables of the sensors And ₂ and P _{3 are} connected to the device and t _2-3 ^{60 is} determined between the wells. 2-3, then to the device connect the electric cables of the sensors And ₃ and P ₁ and fix t _1-3 ¹²⁰ between wells. 1-3. Similar measurements are carried out in all well clusters.

П₁, П

И₂, П

И₃, т.е. обеспечивается дополнительное прозвучивание межскважинного пространства в направлении 0^о, 60^о, 120^о относительно первоначального направления.The location of the sensors in the wells is aligned with each other (the maximum axes of the radiation patterns of the sensors are strictly directed from the emitter to the receiver) and the use of an equilateral measurement scheme can improve the accuracy of ultrasonic measurements. In addition, improving measurement accuracy is achieved by switching sensors AND

P ₁ , P

And ₂ , P

And ₃ , i.e. provides additional sounding of the interwell space in the direction of 0 ^about , 60 ^about , 120 ^about relative to the original direction.

 To excite and register signals, we used an ultrasonic device UK-10 PMS and sensors with piezoelectric elements operating at resonant frequencies of 25-60 kHz. The error in measuring the propagation time of elastic waves with the UK-10 PMS device was 0.5%.

arctg

где t_I,II,III ⁰, t_I,II,III ⁶⁰, t_I,II,III ¹²⁰ - времена прохождения продольных волн в межскважинном пространстве, измеренные в трех кустах скважин соответственно в направлении 0^о, 60^о, 120^о от первоначального нулевого направления.Using the measured propagation times of the longitudinal waves between the wells of each cluster t _1-2 ⁰ , t _2-3 ⁶⁰ , t _1-3 ¹²⁰ , the directions of action of the maximum normal stresses in the array in three orthogonal planes are determined by the following formula:
φ _1,2,3 =

arctg

where t _{I, II, III ^0,} t _{I, II, III ^60,} t _{I, II, III} ¹²⁰ - propagation times of longitudinal waves in the inter-well space, measured in three bushes wells, respectively, in the direction of ⁰ °, ^{60 °, 120} from initial zero direction.

γ = arccos

β= α±90^о, где t_I,II,III ⁰ - времена прохождения продольных волн в межскважинном пространстве, измеренные в каждом кусте скважин в нулевом направлении, мкс; φ_1,2,3 - направления действия максимальных нормальных напряжений в трех ортогональных плоскостях, градус.Using the directions of action of normal stresses in three orthogonal planes, calculate the directions of action of the main normal stresses for the conditions of the volumetric stress state of the array according to the following formulas:
α = arccos

γ = arccos

β = α ± 90 ^о , where t _{I, II, III} ⁰ are the propagation times of longitudinal waves in the interwell space, measured in each well cluster in the zero direction, μs; φ _1,2,3 - the direction of action of the maximum normal stresses in three orthogonal planes, degrees.

The proposed method was used at mine 2 bis of the Nikitovsky Mercury Plant, where a dead end horizontal mine with a cross-sectional area of S = 15 m ² was built in an untouched massif, in which an observation station was equipped. No mining operations were carried out in the observation area. At the observation station, three bushes of three parallel wells were drilled in three orthogonal planes in the roof and the wall of the mine working, composed of sandstones of a relatively homogeneous structure, to a depth of up to 10 m in three orthogonal planes. Drilling was carried out by the NKR drilling rig using winning bits. The wells of 76 mm diameter were drilled at the vertices of an equilateral triangle, wherein the angles between the holes in one plane made up ^60, and the distance between the wells (measurements database) -. 1 m measurement points in all the bushes wells were located at an equal distance from the point of standing the drilling machine.

Sensors of elastic vibrations were installed in three wells of each cluster at each measurement point, while the emitters and receivers were placed coaxially with each other in the wells. Then, measurements were made of the propagation time of longitudinal waves between the wells, i.e. t _{I, II, III} ⁰ , t _{I, II, III} ⁶⁰ , t _{I, II, III} ¹²⁰ .

arctg

где t_I,II,III ^0,60,120 - времена прохождения продольных волн в межскважинном пространстве, измеренные в каждом кусте скважин в направлении 0^о, 60^о, 120^о относительно первоначального нулевого направления, мкс.The directions of action of the maximum normal stresses in an untouched array in three orthogonal planes were calculated by the following formula:
φ _1,2,3 =

arctg

where t _{I, II, III} ^0,60,120 - propagation times of longitudinal waves in the inter-well space, measured in the wells each bush in the direction ^of 0, ^{60, 120} relative to the initial zero direction microseconds.

arctg

; φ_II= 90^° -

arctg

φ_III= 90^°+

arctg

; φ_IV= 180^° -

arctg

Направления действия главных нормальных напряжений для условий объемного напряженного состояния массива определяли по следующим формулам:
α = arccos

γ = arccos

β= α + 90^o, где t_I,II,III ⁰ - времена прохождения продольных волн в межскважинном пространстве, измеренные в каждом кусте скважин в нулевом направлении, мкс; φ_1,2,3 - направления действия максимальных нормальных напряжений в трех ортогональных плоскостях, градус.When determining the angles, we used the following sign ratios by the corresponding quarters for the angle φ:
φ _I =

arctg

; φ _II = 90 ^° -

arctg

φ _III = 90 ^° +

arctg

; φ _IV = 180 ^° -

arctg

The directions of action of the main normal stresses for the conditions of the bulk stress state of the array were determined by the following formulas:
α = arccos

γ = arccos

β = α + 90 ^o , where t _{I, II, III} ⁰ are the propagation times of longitudinal waves in the interwell space, measured in each well cluster in the zero direction, μs; φ _1,2,3 - the direction of action of the maximum normal stresses in three orthogonal planes, degrees.

 The device UK-10 PMS was used as a generator and a recording device. For measurements, sensors with piezoelectric elements operating at a resonant frequency of 25 kHz were used. The error in measuring the propagation time of longitudinal waves between wells did not exceed 1-2 μs.

 As the basic object for determining the direction of normal stresses in the massif, the end-unloading method developed by VNIMI was used (Methodological instructions for using the unloading method to measure stresses in a rock mass. L .: VNIMI, 1972, 36 pp.).

 The face unloading method was used in the borehole. 1 drilled in the roof in the direction of the z axis and in the well. 2, drilled in the wall of the mine in the direction of the y axis (Figs. 1 and 2).

arctg

где ε⁰, ε⁴⁵, ε⁹⁰ - относительные деформации, измеренные на торце керна скважин по направлениям 0^о, 45^о, 90^о от условного нулевого направления; φ_b - вычисленный угол между направлением ε^o и максимальной деформацией торца керна скважин.When measuring the strain on the core end face to the method used trehdatchikovaya discharge outlet with the orientation of the strain gauges at 0 ^o, 45 ^o, 90 ^o. According to this arrangement of strain gauges, the directions of action of maximum strains were calculated by the following formula:
φ _in =

arctg

where ε ^0, ε ^45, ε ⁹⁰ - relative deformation measured on the wells of the core end in the directions ^of 0, 45 ^o, 90 ^o by conditional zero direction; φ _b is the calculated angle between the direction of ε ^o and the maximum deformation of the end face of the core of the wells.

arctg

II - φ_1,2= 90^o - φ_b;
III - φ_1,2 = 90^o + φ_b;
IV - φ_1,2= 180^o - φ_b.The directions of action of the maximum deformations (stresses) in the array in the xy and xz planes were determined using the following quarter sign ratios for a tensothermal outlet (Fig. 4):
I - φ _1,2 = φ _in =

arctg

II - φ _1,2 = 90 ^o - φ _b ;
III - φ _1,2 = 90 ^o + φ _b ;
IV - φ _1,2 = 180 ^o - φ _b .

 The results of determining the directions of action of the maximum normal stresses in the array using the basic and proposed methods are given in table. 1-3.

Judging by the data of the tables, the use of the proposed method allowed to increase the accuracy of determining the directions of action of the maximum normal stresses in the array compared to the base. The error in determining the directions of action of the maximum normal stresses in the array by the basic method with a reliability of P = 0.95 was δφ _1.2 = ± 9 ^о , by the proposed method - δφ ₁ = ± 2 ^о and δφ ₂ φ ₃ = ± 4 ^о .

 The results of determining the directions of action of the main normal stresses in the array obtained using the proposed method are shown in table. 4.

The table shows that the use of the proposed method has improved the accuracy of determining the directions of action of the main normal stresses in the array. The error in determining the directions of action of the main normal stresses in the array of the proposed method with a reliability of P = 0.95 did not exceed 3 ^about .

 The obtained directions of action of the main stresses in the massif were used in choosing the layout of the workings when working out new horizons.

Claims (1)

METHOD FOR DETERMINING DIRECTIONS OF ACTION OF MAIN NORMAL VOLTAGES IN CONDITIONS OF VOLUME VOLTAGE STATE OF MOUNTAIN ARRAY, including drilling in an array in three orthogonal planes of three clusters of three parallel wells, placement of elastic waves and measuring devices in the boreholes, determining the speed of the waves and the elastic waves waves between wells, characterized in that the well bushes are drilled along the vertices of an equilateral triangle, one of the sides in which take the initial zero direction, set the sensors of elastic vibrations in the wells and measure the propagation time of longitudinal waves in the interwell space in each well cluster at measurement points located at an equal distance from the drilling machine's standing point, calculate the directions of maximum normal stresses in three orthogonal planes along the formula

where t $\genfrac{}{}{0ex}{}{\text{0}}{\text{I}}$ _{, II, III} , t $\genfrac{}{}{0ex}{}{\text{60}}{\text{I}}$ _{II, III} , t $\genfrac{}{}{0ex}{}{\text{120}}{\text{I, I}}$ _{I, III} - the propagation times of longitudinal waves in the interwell space, measured in three well bore in the direction of 0 ^o , 60 ^o and 120 ^o, respectively, from the initial zero direction, and the direction of action of the main normal stresses of the array is determined by the following formulas:

;
β = (α ± 90) ^° ;

where α, β are the directions of action of the main normal horizontal stresses in the array;
g is the direction of action of the main normal vertical voltage of the array.

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