CN112115599B - Method for calculating hole spacing of weakened top plate of intensive drilling - Google Patents
Method for calculating hole spacing of weakened top plate of intensive drilling Download PDFInfo
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Abstract
The invention discloses a method for calculating the hole spacing of a densely drilled weakened roof plate, which comprises the following steps of firstly deducing a theoretical calculation formula of the development radius of a plastic zone around a single drilled hole according to the boundary of the plastic zone of a rock mass around the drilled hole; the influence of actual engineering on the development of the plastic zone is considered in a plastic zone development calculation formula, and the mechanical property of rock mass in-situ rock around the drill hole is obtained; meanwhile, grading the surrounding rock crushing degree around the drill hole to determine an amplification factor, and further calculating to obtain the plastic zone development radius of the intensive drill hole; finally, the spacing between the holes of the densely drilled and weakened top plate can be determined. The reasonable space between the dense drilling holes can enable the pressure relief areas of the drilling holes to be mutually overlapped and communicated, so that the artificial rock mass structure weakening zone is formed. The invention can effectively control the hole spacing of the intensive drilling holes while ensuring the effect of weakening the top plate, greatly lightens the workload of construction operation and further improves the safety coefficient and the production efficiency of a mine.
Description
Technical Field
The invention belongs to the technical field of mine roof rock stratum control, and particularly relates to a method for calculating hole spacing of a densely drilled weakened roof.
Background
The weakened top plate reduces the exposed area of the top plate by changing the physical and mechanical properties of the rock mass of the top plate, prevents or weakens the incoming pressure of the large-area top plate, achieves safe and efficient production of a working surface, and is an important means for fully mechanized mining of mines.
The current common methods for weakening the roof mainly include energy-gathering blasting and hydraulic fracturing. But the cumulative blasting is difficult to ensure the cutting rate and the blasting crack direction among the blasting holes, has the problems of low blasting controllability, serious disturbance influence on surrounding rocks of the roadway and the like, and is not suitable for high-gas mines. Although hydraulic fracturing has small disturbance to surrounding rocks of a roadway and strong applicability, the fracture angle, the fracture height and the fracture penetration rate are limited, the field operation is complex, and the learning cost is high. The scholars for solving the problems provide a dense drilling weakening roof topping pressure relief technology which can effectively make up for part of defects of the method and can effectively solve the problem of overlarge rock burst during small coal pillar mining in the process of gob-side entry retaining in coal mine deep mining; and the roof can be cut off and pressure relief in time aiming at the conditions that the hard roof of the goaf cannot be collapsed in time and the elastic potential energy in the roof is accumulated in a large amount. However, the specific parameters of the hole spacing in the dense drilling construction of the method are not scientifically calculated. The distance between the drill holes is used as a key parameter of the technology, and if the distance between the selected holes is too large, the requirement for weakening the top plate cannot be met, and the pressure relief effect cannot be achieved; if the selected hole spacing is too small, although the roof weakening pressure relief effect can be achieved, the labor cost is greatly increased.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems, the invention provides a method for calculating the hole spacing of the densely drilled weakened roof plate, which can calculate the hole-drilling construction spacing according to different surrounding rock conditions and meet the actual engineering requirements.
The technical scheme is as follows: in order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: a dense drilling weakened roof hole pitch calculation method comprises the following steps:
s1, setting the radial stress action of the whole drill hole to be consistent according to the stress condition of the surrounding rock of the drill hole, and establishing a two-dimensional polar coordinate system by taking the center of the drill hole as the center of a circle with reference to FIG. 6;
s2, according to the elasticity mechanics, the formula of the stress component of the rock mass around the drilled hole under the polar coordinate is as follows:
in the formula, rho is a polar coordinate value of any point of a rock body around a drill hole; a is the radius of the drill hole, mm; p is the horizontal ground stress of the position where the drill hole is located, and is MPa; sigma ρ Is the radial stress at any point of the rock mass around the drill hole, MPa; sigma θ The circumferential stress at any point of the rock mass around the drill hole is MPa; tau is ρ The radial shear stress at any point of the rock mass around the drill hole is MPa; tau is θ The circumferential shear stress at any point of the rock mass around the drilled hole is MPa;
s3, according to the balance condition and the Moire intensity condition, based on the parameter sigma of the step S2 ρ 、σ θ And τ ρ And obtaining an extreme stress formula of a plane state of any point in the rock mass around the drilled hole, wherein the extreme stress formula is as follows:
in the formula, σ 1 The maximum principal stress in the plane at any point of the rock mass around the drill hole is MPa; sigma 2 The minimum principal stress in a plane at any point of a rock mass around a drilled hole is MPa; sigma ρ The radial stress at any point of the rock mass around the drill hole is MPa; sigma θ The circumferential stress at any point of the rock mass around the drill hole is MPa; tau. ρ Radial shear stress at any point of a rock mass around a drill hole is MPa;
further, listing the shear stress value tau of the rock mass around the drill hole on the plane n And the rock mass around the borehole being subjected to a normal stress sigma in the plane n The common solution formula is:
in the formula, τ n The shear stress value of the rock mass around the drilled hole on the plane is MPa; sigma n The normal stress of the rock mass around the drill hole on the plane is MPa; sigma 1 The maximum main stress in a plane at any point of a rock mass around a drilled hole is MPa; sigma 2 Is the minimum principal stress in the plane at any point of the rock mass around the drill hole, MPa;
simultaneously according to the Mohr-Coulomb yield condition, i.e. shear stress tau on a certain plane of the rock mass n When the limit value is reached, the rock mass yields; the limit value, the cohesive force C after the damage of the rock mass around the drill hole and the internal friction angle of the rock mass around the drill hole
And the rock mass around the drilled hole is subjected to a positive stress sigma on the plane n In relation, the formula is:
in the formula, τ n For the rock mass surrounding the borehole to be sheared on the planeStress value, MPa; c is the cohesion of the damaged rock mass around the drill hole, and is MPa; sigma n The normal stress on the plane of the rock mass around the drill hole is MPa;
the internal friction angle and degree of the rock mass around the drilled hole;
further, the formula (2), the formula (3) and the formula (4) are combined to obtain the yield condition formula of any point of the rock mass around the drill hole:
in the formula, σ ρ The radial stress at any point of the rock mass around the drill hole is MPa; sigma θ The circumferential stress at any point of the rock mass around the drill hole is MPa; tau is ρ The radial shear stress at any point of the rock mass around the drill hole is MPa; c is the cohesion of the damaged rock mass around the drill hole, and is MPa;
is the internal friction angle of the rock mass around the drilled hole.
S4, according to the stress distribution rule and the elastic theory of the rock mass around the drill hole, obtaining the development radius of the plastic zone of the drill hole when the stress state of the rock mass around the drill hole meets the yield condition, namely, the formula (1) in the step S2 and the formula (5) in the step S3 are combined to obtain the calculation formula of the development radius of the plastic zone of the rock mass around the drill hole:
in the formula: r is a polar coordinate value of any point on the boundary line of the elastoplasticity zone of the rock mass around the drill hole; rho is a polar coordinate value of any point of a rock mass around the drill hole; a is the drilling radius, mm; c is the cohesion of the damaged rock mass around the drill hole, and is MPa;
the internal friction angle and degree of the rock mass around the drilled hole; p is the horizontal ground stress of the position where the drill hole is located, and is MPa;
s5, based on the development radius of the plastic zone of the drill hole in the step S4, the calculation formula for obtaining the spacing between the densely drilled and weakened top plate holes is as follows:
L＝2Ru (7)
in the formula, L is the interval between the densely drilled and weakened top plate holes, and is mm; r is a polar coordinate value of any point on the boundary line of the elastoplasticity zone of the rock mass around the drill hole; u is the amplification coefficient of the boundary radius of the drill hole, and can be 1.2-1.6 according to different geological conditions;
has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
the invention provides a method for calculating the hole spacing of a densely drilled weakened roof plate, which is characterized in that the development condition of a plastic zone of a single hole is calculated based on an elastic-brittle-plastic model and MoCoulomb criteria of a rock, multiple influence factors are comprehensively considered, and a proper hole spacing is calculated, so that the plastic zones of densely drilled rock masses can be mutually superposed and communicated to form an artificial rock mass structure weakened zone, and the problem of overlarge rock burst during mining in the process of coal mine deep mining is scientifically and effectively solved; and can be used for solving the problems of strong mine pressure such as forced caving of top coal and the like.
Drawings
FIG. 1 is a plan view of a drill hole layout for a densely drilled weakened roof topping pressure relief process;
FIG. 2 is a sectional view taken along line I-I of FIG. 1;
FIG. 3 is a schematic view of a borehole imager;
FIG. 4 is a schematic illustration of an in situ rock borehole shear tool;
FIG. 5 is a schematic diagram of a hydraulic fracturing in-situ geostress testing system;
FIG. 6 is a elastoplastic zone development of a single drilled hole of surrounding rock;
FIG. 7 is a schematic view of a densely drilled weakened top plate constituting an artificial weakened zone;
in the figure, 1-upper section roadway; 2-upper section working face; 3-a goaf; 4-lower section working face; 5-roof cutting, pressure relief and dense drilling of the roadway; 6-immediate ejection; and 7, forcibly setting the top and densely drilling.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples. The embodiments described herein are part of the embodiments of the present invention and not all of the embodiments. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention.
The invention relates to a method for calculating the hole spacing of a densely drilled weakened top plate, which is an important parameter calculation method for densely drilled top plate weakening. The technology of weakening the top plate by the dense drilling holes can be applied to hard top plate roof cutting pressure relief, forced top coal caving and the like, an artificial weakening zone is formed by the dense drilling holes, and the top plate can be cut or the top coal begins to collapse along the weakening zone under the influence of the self weight of a rock body or unbalanced high stress of mining. The hole spacing for densely drilled holes is calculated as follows, taking the geological conditions of a mine as an example:
s1, referring to the arrangement mode of the stope face in the figures 1 and 2, in order to enable the immediate roof 6 of the stope face to collapse in time and reduce the maintenance difficulty of a tight roadway, arranging roadway roof cutting and pressure relief intensive drill holes 5 in the roadway of the working face of the upper section along the roof on one side of the coal pillar, wherein the radius of the intensive drill holes is 30mm, and the roadway roof cutting and pressure relief intensive drill holes 5 are perpendicular to the immediate roof 6 of the roadway along the extending direction of the roadway; if the working face is required to be subjected to forced caving, forced caving dense drill holes 7 can be distributed at the position, close to the coal wall, of the stope face.
S2, accurately measuring rock mechanical parameters of the related roof surrounding rock under the influence of mining disturbance, and arranging in-situ test holes within 5-10m of the advanced open-off cut; referring to fig. 4, under the influence of working face extraction after roadway excavation obtained by actual measurement of an underground in-situ test system, the cohesion C of damaged rock mass around the drilled hole of top plate surrounding rock is 1.1MPa, and the internal friction angle of rock mass around the drilled hole
Is 30 degrees; referring to FIG. 5, water pressure is usedCracking the in-situ ground stress test system to obtain that the ground stress of the surrounding rock of the mine roof is 14 MPa; referring to fig. 3, the development degree of the surrounding rock fractures within a certain time after single drilling is analyzed through a drilling peeping instrument, referring to fig. 7, the group effect of the dense drilling is considered, and an amplification factor u is selected and taken as 1.5 according to the development condition of the surrounding rock fractures and the mutual coupling action of the dense drilling.
S3, referring to FIG. 6, setting the radial stress action of the whole drill hole to be consistent according to the stress condition of the surrounding rock of the drill hole, and establishing a two-dimensional polar coordinate system by taking the center of the drill hole as the center of a circle; the formula of the stress component in the rock mass around the drilled hole under the polar coordinate is obtained according to the elasticity mechanics as follows:
in the formula, rho is a polar coordinate value of any point of a rock body around a drill hole; a is the drilling radius, mm; p is the horizontal ground stress of the position where the drill hole is located, and is MPa; sigma ρ The radial stress at any point of the rock mass around the drill hole is MPa; sigma θ The circumferential stress at any point of the rock mass around the drill hole is MPa; tau. ρ The radial shear stress at any point of the rock mass around the drill hole is MPa; tau. θ The circumferential shear stress at any point of the rock mass around the drilled hole is MPa;
s4, according to the balance condition and the Moire intensity condition, based on the parameter sigma of the step S3 ρ 、σ θ And τ ρ And obtaining an extreme stress formula of a plane state of any point in the rock mass around the drilled hole, wherein the extreme stress formula is as follows:
in the formula, σ 1 The maximum main stress in a plane at any point of a rock mass around a drilled hole is MPa; sigma 2 The minimum principal stress in a plane at any point of a rock mass around a drilled hole is MPa; sigma ρ The radial stress at any point of the rock mass around the drill hole is MPa; sigma θ At any point of the rock mass surrounding the boreholeHoop stress, MPa; tau is ρ The radial shear stress at any point of the rock mass around the drill hole is MPa;
further, listing the shear stress value tau of the rock mass around the drill hole on the plane n And the normal stress sigma applied to the rock mass around the borehole in the plane n The common solution formula is:
in the formula, τ n The shear stress value of the rock mass around the drilled hole on the plane is MPa; sigma n The normal stress on the plane of the rock mass around the drill hole is MPa; sigma 1 The maximum main stress in a plane at any point of a rock mass around a drilled hole is MPa; sigma 2 The minimum principal stress in a plane at any point of a rock mass around a drilled hole is MPa;
meanwhile, according to the Mohr-Coulomb yield condition, namely when the shear stress on a certain plane of the rock mass reaches a limit value, the rock mass yields; the extreme value, the cohesive force C after the damage of the rock mass around the drill hole and the internal friction angle of the rock mass around the drill hole
And the rock mass around the drilled hole is subjected to a positive stress sigma on the plane n In this regard, the formula is:
in the formula, τ n The shear stress value of the rock mass around the drilled hole on the plane is MPa; c, the cohesion of the damaged rock mass around the drilled hole is MPa; sigma n The normal stress on the plane of the rock mass around the drill hole is MPa;
the internal friction angle and degree of the rock mass around the drill hole;
further, the formula (2), the formula (3) and the formula (4) are combined to obtain the yield condition formula of any point of the rock mass around the drill hole:
in the formula, σ ρ The radial stress at any point of the rock mass around the drill hole is MPa; sigma θ The circumferential stress at any point of the rock mass around the drill hole is MPa; tau is ρ The radial shear stress at any point of the rock mass around the drill hole is MPa; c, the cohesion of the damaged rock mass around the drilled hole is MPa;
is the internal friction angle of the rock mass around the drilled hole.
S5, according to the stress distribution rule and the elastic theory of the rock mass around the drill hole, obtaining the development radius of the plastic zone of the drill hole when the stress state of the rock mass around the drill hole meets the yield condition, namely, the formula (1) in the step S3 and the formula (5) in the step S4 are combined to obtain the calculation formula of the development radius of the plastic zone of the rock mass around the drill hole:
in the formula: r is a polar coordinate value of any point on the boundary line of the elastoplasticity zone of the rock mass around the drill hole; rho is the polar coordinate value of any point of the rock mass around the drill hole; a is the radius of the drill hole, mm; c, the cohesion of the damaged rock mass around the drilled hole is MPa;
the internal friction angle and degree of the rock mass around the drilled hole; p is the horizontal ground stress of the position where the drill hole is located, and is MPa;
s6, based on the development radius of the drilling plastic zone in the step S5, the calculation formula for obtaining the spacing between the densely drilled and weakened top plate holes is as follows:
L＝2Ru (7)
in the formula, L is the interval between the densely drilled and weakened top plate holes, and is mm; r is a polar coordinate value of any point on the boundary line of the elastoplasticity zone of the rock mass around the drill hole; u is the amplification coefficient of the boundary radius of the drill hole, and the value of the formula u is 1.5;
and calculating to obtain the spacing L of the weakened roof plate of the dense drilling hole as 119mm based on the parameter R in the step S5 and the parameter u in the step S6, wherein 110-130mm is selected as the spacing of the dense drilling hole in consideration of tolerance due to certain errors in engineering construction.
Claims (2)
1. A method for calculating the hole spacing of a densely drilled weakened top plate is characterized by comprising the following steps:
s1: setting the radial stress action of the whole drill hole to be consistent according to the stress condition of the surrounding rock of the drill hole, and establishing a two-dimensional polar coordinate system by taking the center of the drill hole as the center of a circle;
s2: according to the elastic mechanics, obtaining a formula of the stress component of the rock mass around the drilled hole under the polar coordinate;
s3: obtaining an extreme stress formula of a plane state of any point of the rock mass around the drilling hole according to the balance condition and the Moire strength condition, and calculating to obtain a yield condition formula of any point of the rock mass around the drilling hole by combining the original rock stress of the rock mass around the drilling hole when the rock mass around the drilling hole meets the Moire-coulomb yield condition:
s3.1: according to the balance condition and the Moire strength condition, the extreme stress formula of the plane state of any point in the rock mass around the drilled hole is obtained as follows:
in the formula, σ 1 The maximum main stress in a plane at any point of a rock mass around a drilled hole is MPa; sigma 2 The minimum principal stress in a plane at any point of a rock mass around a drilled hole is MPa; sigma ρ The radial stress at any point of the rock mass around the drill hole is MPa; sigma θ The circumferential stress at any point of the rock mass around the drill hole is MPa; tau is ρ Radial shear stress at any point of a rock mass around a drill hole is MPa;
s3.2: according to the Mohr-Coulomb yield condition, namely when the shear stress of the rock mass on a certain plane reaches a limit value, the rock mass yields; obtaining the cohesive force C of the extreme value after the damage of the rock mass around the drill hole and the internal friction angle of the rock mass around the drill hole
And the rock mass around the drilled hole is subjected to a positive stress sigma on the plane n The formula of (1) is:
in the formula, τ n The value of the shear stress borne by the rock mass on the plane is MPa; c is the cohesion of the damaged rock mass around the drill hole, and is MPa; sigma n The normal stress of the rock mass around the drill hole on the plane is MPa;
the internal friction angle and degree of the rock mass around the drill hole;
s3.3: calculating the shear stress value tau of the rock mass on the plane according to the main stress in the plane at any point of the rock mass around the drilled hole n And the normal stress sigma applied to the rock mass around the borehole in the plane n The formula of (1) is:
in the formula, τ n The value of the shear stress borne by the rock mass on the plane is MPa; sigma n The normal stress of the rock mass around the drill hole on the plane is MPa; sigma 1 The maximum principal stress in the plane at any point of the rock mass around the drill hole is MPa; sigma 2 The minimum principal stress in a plane at any point of a rock mass around a drilled hole is MPa;
s3.4: based on the formulas in the steps S3.1, S3.2 and S3.3, the yield condition formula of any point of the rock mass around the drilled hole is obtained in a simultaneous manner and is as follows:
in the formula, σ ρ Is the radial stress at any point of the rock mass around the drill hole, MPa; sigma θ The circumferential stress at any point of the rock mass around the drill hole is MPa; tau is ρ The radial shear stress at any point of the rock mass around the drill hole is MPa; c is the cohesion of the damaged rock mass around the drill hole, and is MPa;
the internal friction angle and degree of the rock mass around the drilled hole;
s4: according to the elastic theory, calculating the stress state of the rock mass around the drill hole when the yield condition is met to obtain a calculation formula of the development radius of the plastic zone; the development radius of the plastic zone is obtained by the formula of the step S2 and the step S3.4, and the calculation formula of the development radius of the plastic zone is obtained by the simultaneous method as follows:
in the formula: r is a polar coordinate value of any point on the boundary line of the elastoplasticity zone of the rock mass around the drill hole; rho is the polar coordinate value of any point of the rock mass around the drill hole; a is the drilling radius, mm; c is the cohesion of the damaged rock mass around the drill hole, and is MPa;
the internal friction angle and degree of the rock mass around the drilled hole; p is the horizontal ground stress of the position where the drill hole is located, and is MPa;
s5: calculating to obtain a numerical value of the hole spacing of the densely drilled weakened top plate based on the development radius of the plastic zone in the step S4; the calculation formula of the spacing between the holes of the densely drilled weakened top plate is as follows:
L＝2Ru
in the formula, L is the interval between the densely drilled and weakened top plate holes, and is mm; r is a polar coordinate value of any point on the boundary line of the elastoplasticity zone of the rock mass around the drill hole; and u is the enlargement factor of the radius of the drill hole boundary.
2. The method for calculating the hole spacing of the densely drilled and weakened top plate according to claim 1, wherein the method comprises the following steps: the formula of the stress component of the rock mass around the borehole in the coordinate system in the step S2 is as follows:
in the formula, rho is a polar coordinate value of any point of a rock body around a drill hole; a is the radius of the drill hole, mm; p is the horizontal ground stress of the position where the drill hole is located, and is MPa; sigma ρ The radial stress at any point of the rock mass around the drill hole is MPa; sigma θ The circumferential stress at any point of the rock mass around the drill hole is MPa; tau is ρ Radial shear stress at any point of a rock mass around a drill hole is MPa; tau is θ The circumferential shear stress at any point of the rock mass around the drill hole is MPa.
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