CN113505484A - Method for determining maximum damage depth of bottom plate rock stratum of deep stope - Google Patents
Method for determining maximum damage depth of bottom plate rock stratum of deep stope Download PDFInfo
- Publication number
- CN113505484A CN113505484A CN202110790593.6A CN202110790593A CN113505484A CN 113505484 A CN113505484 A CN 113505484A CN 202110790593 A CN202110790593 A CN 202110790593A CN 113505484 A CN113505484 A CN 113505484A
- Authority
- CN
- China
- Prior art keywords
- stress
- elastic
- area
- coal
- semi
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/10—Numerical modelling
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
Abstract
The invention discloses a method for determining the maximum failure depth of a bottom plate rock stratum of a deep stope, which comprises the steps of constructing a bottom plate rock mass stress analysis mechanical model based on a support pressure distribution state model, and establishing an transcendental equation of the compressive strength of a rock mass at any point in a semi-plane body by combining the model; calculating the width of a limit balance area according to the occurrence condition parameters of the coal bed and the mining technical condition parameters, constructing an elastic area stress state model based on a support pressure distribution state model, calculating the width of an elastic booster area, resolving an transcendental equation through the width of the limit balance area and the width of the elastic booster area to obtain a bottom plate failure curve, and calculating to obtain the maximum failure depth of a bottom plate rock stratum; the method is based on the elastoplasticity mechanics theory, obtains the balance condition of the elastic booster zone and the width of the elastic booster zone according to the principle of equal interface stress, provides more accurate boundary conditions for the calculation of the failure depth of the bottom plate of the coal mining working face, and improves the accuracy of the measurement of the failure depth of the bottom plate.
Description
Technical Field
The invention relates to the field of coal mining research, in particular to a method for determining the maximum damage depth of a bottom plate rock stratum of a deep stope.
Background
With the increasing development depth of various mines, the geological environment is more complex, the ground stress is increased, the water inflow is increased, the heat is high, and the like, so that serious engineering disasters and serious accidents are increased, such as ore pressure impact, aggravation of ore pressure display, large deformation of surrounding rocks of a roadway, coal (rock) and gas outburst, gas explosion and the like, and the safety exploitation of deep resources is seriously threatened.
Coal mining is always considered to be an industry with high risk, and the main reason is that the accidents of cluster death and group damage such as gas explosion, water flooding of a mine and the like easily occur in the coal mining process. The gas directly enters the mining space along with the coal bed or the coal-series stratum, the gas is transported to the mining space from the outside of the mining coal bed in few cases, and mine water threatens the mining space and has to meet two conditions, namely a water filling water source and a water filling channel, so that the water filling water source and the water filling channel are researched. The north China coal-stone two-stacked coal field is composed of an upper coal group (Shanxi group) and a lower coal group (Taiyuan group), wherein the bottom of the lower coal group is soluble Ordovician limestone with large thickness and is a typical confined water stratum, a karst fracture confined aquifer has high water head and large water pressure, and the lower coal group is directly threatened to mining near the karst fracture confined aquifer and is the most dangerous bottom plate water inrush source for the lower coal group. Therefore, the problem of safe mining of the next group of coal threatened by the high confined water of the bottom plate lime is urgently solved. The mining and digging operation in the underground coal mining process destroys the balance state of the stress of the original rock of the stratum, causes the redistribution and stress concentration of the stress field of the stratum space around the mining and digging working face, causes the movement and collapse of the top plate rock stratum of the working face, changes the stress field of the bottom plate due to the stress concentration of the top plate, redistributes the stress borne by the bottom plate, causes the damage of the bottom plate, and the stress distribution of the bottom plate depends on the transmission track of the concentrated stress in front of the working face to the rock stratum at the lower part of the bottom plate of the coal bed.
Apart from the movement and collapse of the top plate rock stratum, the heave and uplift (floor heave for short) of the bottom plate rock stratum are also one of the most main ore pressure display forms of underground mines, particularly deeply buried underground mines. On one hand, the floor heave causes the effective space of the roadway to be reduced, the movement of a working face support is influenced, and meanwhile, along with the increase of the damage depth of the floor rock stratum, pressure-bearing underground water of the floor rock stratum is caused to flow into a mining working space, so that the water inflow of a mine is increased, the pressure-bearing water of the floor is caused to protrude, and other major safety problems are caused, and therefore, people pay more attention to the research on the problem that the damage of the floor rock stratum is caused due to the stress concentration formed by mining disturbance.
Although the filling mining method can effectively limit the movement and damage amplitude of the overlying rock stratum of the working face and reduce the propagation of the mining additional stress field in the floor rock stratum, the roof management of the whole caving method is still widely applied to mining practice due to the influences of factors such as filling space limitation, material sources and cost control. Therefore, the stress distribution, the damage depth and the damage track of the bottom plate of the working face of the total caving method under the deep high ground stress environment are researched, and the water filling channel formed by the damage of the bottom plate is further mastered.
The mining and excavating operation in the underground mining process of the coal mine destroys the balance state of the stress of the stratum original rock, causes the redistribution and stress concentration of the internal stress of the coal and rock mass around the stope face, and further causes the movement collapse of the top plate rock layer above the working face and the mining-induced fractures of different types in the peripheral coal mass and the bottom plate rock layer. Obviously, the failure depth of the floor strata is not only related to the structure, physical and mechanical properties, etc. of the floor strata itself, but also directly related to the structure and strength of the roof strata, the strength of the coal body, etc. (these factors mainly affect the bearing pressure in the coal body around the working face, and therefore affect the transmission of mining bearing pressure in the floor strata and the failure depth of the floor). Meanwhile, the shape and size of the working face, the widths of the upper and lower gate grooves of the working face and the like also directly influence the supporting condition of a basic top rock layer above the working face and the constraint mechanism of a lower old bottom rock layer, and all the factors are finally directly reflected on the damage depth of a bottom rock layer caused by the mining of the working face, so that the thickness of an effective water-resisting layer of a coal seam bottom plate is influenced, and the safety of the mining work of the upper part of a confined aquifer is influenced.
On the basis of previous researches, at present, scholars still mainly study the water inrush problem of a bottom plate by considering the strength and lithology of a water-resisting layer, and many scientists in China carry out systematic researches on the aspects of prediction and forecast, water inrush mechanism, prevention and treatment technology and the like of the water inrush problem, and representative achievements mainly comprise a water inrush coefficient theory, a rock-water stress relation method, a lower three-belt theory and the like. By carrying out deep on-site observation on the interior of the coal seam floor and combining research methods and means such as model experiments, numerical simulation and the like, China achieves great performance in aspects such as floor water inrush mechanism, prediction and forecast, mine water disaster prevention and control and the like. The damage of the floor rock stratum is researched to a certain degree in the field of gas research, particularly, when a coal and gas outburst mine adopts a free-space mining method, the damage of the floor rock stratum between an upper free-space layer and a lower free-space layer is researched more mature, but the space position relation between a gas occurrence area and a mining area is already mastered through investigation, and the distance between the upper free-space layer and the lower free-space layer is also formed naturally, so that the field of gas research is equivalent to how two known areas are linked, the research of the floor damage depth is how the floor rock stratum is damaged due to the influence of mining disturbance in the normal mining process, and the research objects between the two are different greatly.
Although China has achieved certain research results in the aspect of coal mine floor water inrush research, people only conduct single research on the floor in a long time. In fact, the depth of the damage of the bottom rock stratum is not only related to the structure, physical and mechanical properties and the like of the bottom rock stratum, but also directly related to the structure, strength and the like of the top rock stratum and the coal body. Meanwhile, the width of a plastic zone and an elastic pressurizing zone in front of the coal wall directly influences the action width of the concentrated stress of the working face and the constraint mechanism of the lower old bottom rock stratum, and all the factors are finally directly reflected on the damage depth of the bottom rock stratum caused by the mining of the working face, so that the safety of the recovery work of the upper part of the confined aquifer is influenced. Therefore, the basic top rock stratum, the coal body and the bottom rock stratum are taken into a whole to be comprehensively considered, the relation between the width of the elastic-plastic area of the coal body and the maximum damage depth of the bottom plate is researched, the damage track of the bottom plate is determined, and a foundation is laid for the safe production of a coal mine.
Through the analysis, although certain results are achieved in the aspects of coal seam floor damage and water inrush research at home and abroad, the following problems exist:
(1) the predecessors partitioned the redistributed stress in front of the working face and given a calculation formula of the width of the plastic region and a qualitative development trend of the elastic supercharging region, but did not give a quantitative solution method for the width of the elastic supercharging region and the balance condition of the elastic supercharging region had no clear expression.
(2) At present, the maximum failure depth of the coal seam floor depends on empirical calculation, theoretical analysis, engineering analogy and the like, and whether the analysis on the failure depth of the coal seam floor in a high stress environment has reference value or not needs to be further researched.
(3) Theoretical analysis is carried out on the damage depth of the bottom plate through the crack model, but the use condition of the crack model is that the ratio of mining width to mining height is large enough to be regarded as a crack, and the accuracy of the damage depth of the bottom plate calculated by the crack model is not enough because the coal seam thickness is large, the lithology of a top plate is not good, and the ratio of the mining width to the mining height is not large enough to be regarded as a crack.
(4) The method is characterized in that a foundation base theory is adopted to calculate the damage depth of a bottom plate rock stratum, firstly, the bottom plate is assumed as the foundation, the foundation is not restrained except the upper load of the foundation, the bottom plate is always in a mine pressure action environment in mining activities, the bottom plate is greatly different from the foundation, and predecessors also develop a double-slip-line theory to calculate the damage depth of the bottom plate and analyze the damage track of the bottom plate on the basis of a slip line theory, so that the accuracy is further improved, but the theory base is still a foundation principle, and the application range is still limited.
(5) The theoretical formula is still not perfect. Although engineering experience is not needed when the maximum failure depth of the bottom plate rock stratum is calculated by using knowledge of fracture mechanics, the influence of the combined action of the plastic zone width and the elastic pressurization zone width formed by the stress concentration of the coal body in front of the stope on the deformation failure characteristics of the bottom plate is not reflected.
(6) In the field measurement, the measurement depth is firstly preliminarily determined through theoretical calculation or field experience before the instrument is buried, but if the actual damage depth is greatly different from the expected damage depth, the measurement result has large error.
Disclosure of Invention
In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for determining the maximum depth of failure of a floor strata of a deep stope.
In order to achieve the aim of the invention, the technical scheme adopted by the invention is as follows:
a maximum failure depth determination method for a deep stope floor strata includes the following steps S1-S5:
s1, constructing a stress analysis mechanical model of the bottom plate rock mass based on the support pressure distribution state model;
s2, establishing an transcendental equation of the compressive strength of the rock mass at any point in the semi-plane body according to the stress analysis mechanical model of the floor rock mass in the step S1;
s3, calculating the width of the limit balance area according to the coal seam occurrence condition parameters and the mining technical condition parameters;
s4, constructing an elastic region stress state model based on the support pressure distribution state model, and calculating the width of the elastic pressurizing region;
and S5, solving the transcendental equation in the step S2 according to the width of the limit balance area in the step S3 and the width of the elastic supercharging area in the step S4 to obtain a bottom plate damage curve, and calculating the maximum damage depth of the bottom plate rock stratum.
The invention has the following beneficial effects:
1. constructing a stress analysis mechanics model of the bottom plate rock mass by supporting a pressure distribution state model, and establishing an transcendental equation of the compressive strength of the rock mass at any point in the semi-plane body by combining the model; establishing an elastic zone stress state model based on a support pressure distribution state model, determining an elastic booster zone width calculation formula, determining a quantitative solution mode of the elastic booster zone width, improving the accuracy of bottom plate damage depth measurement, obtaining the limit balance zone width and the elastic booster zone width through coal bed occurrence condition parameters and mining technical condition parameters, further solving an transcendental equation, perfecting a theoretical formula of the transcendental equation, obtaining a bottom plate damage curve, and further calculating to obtain the maximum damage depth of a bottom plate rock stratum; according to the method, based on an elastoplasticity mechanics theory, according to the principle of equal interface stress, the balance condition of the elastic booster zone and the width of the elastic booster zone are obtained, so that more accurate boundary conditions are provided for calculation of the failure depth of the bottom plate of the coal mining working face, the accuracy of measurement of the failure depth of the bottom plate is improved, the combination of engineering actual measurement data is facilitated, and errors existing in measurement results are reduced;
2. determining a balance condition expression of the elastic supercharging region by constructing a stress state model, further determining a width value of the elastic supercharging region, and perfecting an transcendental equation;
3. the method is determined by a quantitative solving method for the width of the elastic supercharging area, and the accuracy of measuring the damage depth of the bottom plate is improved;
4. by acquiring the field measured data and combining the improved transcendental equation, more accurate boundary conditions are provided for the calculation of the damage depth of the bottom plate of the coal mining working face, the combination of the engineering measured data is facilitated, and the error of the measuring result is reduced.
Drawings
FIG. 1 is a schematic flow chart of a method for determining a maximum depth of failure of a deep stope floor formation according to the present invention;
FIG. 2 is a model diagram of the distribution state of the supporting pressure in the present invention;
FIG. 3 is a schematic diagram of the front stress concentration and mechanics abstraction of the working face in the present invention;
FIG. 4 is a simplified model of the supporting pressure of the first pressure and the periodic pressure on the top of the stope according to the present invention;
FIG. 5 is a mechanical model for analyzing the stress of the bottom plate rock mass in the invention;
FIG. 6 is a flow chart illustrating the substeps of step S2 according to the present invention;
FIG. 7 is a flow chart illustrating the substeps of step S4 according to the present invention;
FIG. 8 is a model of the stress state of the elastically supercharged region in the present invention;
FIG. 9 is a flow chart illustrating the substeps of step S42 according to the present invention;
FIG. 10 is a model of the stress state at the interface between the stress zone of the parent rock and the elastic booster zone according to the present invention;
FIG. 11 is a model of the stress state at the interface of the elastic zone and the limiting equilibrium zone in accordance with the present invention;
FIG. 12 is a flowchart illustrating the substeps of step S43 according to the present invention;
FIG. 13 is a boundary condition coordinate system diagram in the present invention.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
As shown in fig. 1, an embodiment of the present invention provides a method for determining a maximum depth of damage of a deep stope floor rock stratum, including the following steps S1 to S5:
s1, constructing a stress analysis mechanical model of the bottom plate rock mass based on the support pressure distribution state model;
in practice, because the original rock stress balance state is changed after the coal seam is mined, the stress of the working face is redistributed, and a supporting pressure distribution state as shown in fig. 2 is formed, in the mining engineering, the thickness of the basic roof rock layer is generally far smaller than the length of the working face or the basic primary caving step or the periodic caving step, so that the basic roof can be regarded as a thin plate, and the analysis of the stress problem of the basic roof is analyzed by adopting the bending problem of the elastic mechanical thin plate.
The redistribution of the face front stress caused by coal seam mining, resulting in stress concentrations, affects the depth of failure of the face floor strata, as shown in figure 3, the stress concentration and mechanics abstract diagram in front of the working surface is constructed by a supporting pressure distribution state model during the process of basic roof pressure, it can be known that the action form of the non-uniform load in front of the coal wall on the bottom rock stratum is similar to the situation that the semi-plane body is acted by the normal distributed force vertical to the boundary in the elasto-plastic mechanics theory, therefore, the analysis and research on the damage depth of the bottom plate can be carried out by adopting a semi-plane infinite body model, as shown in figure 4, in order to simplify the distribution situation of the supporting pressure of the primary pressure and the periodic pressure of the basic top of the stope, a mechanical model for analyzing the stress of the rock mass of the bottom plate can be constructed, the mechanical model for analyzing the stress of the bottom plate rock mass is shown in figure 5, and the clockwise included angle theta between any point M on the semi-plane body and the vertical direction of the load action position is taken as positive.
S2, establishing an transcendental equation of the compressive strength of the rock mass at any point in the semi-plane body according to the stress analysis mechanical model of the floor rock mass in the step S1;
as shown in fig. 6, in the present embodiment, step S2 includes the following sub-steps:
s21, constructing a semi-plane infinite body model according to the stress analysis mechanical model of the floor rock body in the step S1, and calculating the stress component at any point in the semi-plane body by utilizing an elastic mechanics theory;
in this embodiment, step S21 specifically includes:
constructing a semi-plane infinite body model according to the stress analysis mechanical model of the floor rock body in the step S1, and calculating each point in the semi-plane body by combining the elastic mechanics theory and the parameters in the semi-plane infinite body model
Wherein σxA stress component in the x direction for the load acting at any point M (x, y) within the semi-planar body; sigmayA stress component in the y direction for the load acting at any point M (x, y) within the semi-planar body; tau isxyA shear stress component in the xy plane for a load acting at any point M (x, y) within the semi-plane; x is the number ofaIs the ultimate equilibrium zone width; x is the number ofbIs the width of the elastically boosted region; gamma is the volume weight of any point M (x, y) on an overlying rock stratum; h is the thickness of an overlying rock formation at any point M (x, y); k is the front stress concentration coefficient of the coal wall; n is a radical of0The supporting capacity of the coal side is obtained;
in practice, the amount of the liquid to be used,
firstly, according to the stress analysis mechanical model of the floor rock body in the step S1, combining the non-uniform distribution load effect of the semi-plane body on the boundary, calculating each stress component of the concentrated force at any point in the plane, and expressing as:
wherein, theta1Is the included angle between any point M (x, y) in the semi-plane body and the interface of the elastic booster zone and the original rock stress zone; theta2Is the included angle between any point M (x, y) in the semi-plane body and the interface of the elastic supercharging region and the ultimate balance region; sigmaxStress components in the x direction acting on any point M (x, y) in the semi-plane body through load are concentrated; sigmayA stress component in the y direction acting on any point M (x, y) in the semi-plane body through the load in order to concentrate the force; tau isxyA shear stress component acting on an xy plane at any point M (x, y) in the semi-plane body through a load is concentrated; sigma (xi) is that the semi-plane body is subjected to the action of non-uniformly distributed load on the boundary;
then, as can be seen from the theory of elastic mechanics, when the boundary of the semi-planar body is subjected to a force P perpendicular to the boundary, the stress component at any point M in the plane can be expressed as:
wherein σxIs the stress component of the load acting on any point M (x, y) in the plane in the x direction; sigmayIs the stress component of the load acting on any point M (x, y) in the plane in the y direction; tau isxyIs the shear stress component of the load acting on any point M (x, y) in the plane on the xy plane; r is the distance from any point M (x, y) in the plane to the load; theta is an included angle between any point M (x, y) in the plane and the vertical direction of the load acting position.
As can be seen from fig. 5, the distance differential ξ from the maximum concentrated stress to a point in the elastically boosted region can be expressed as:
and then can obtain
The product of the non-uniform load sigma ([ xi ]) on the boundary of the semi-plane body and the distance differential from the maximum concentrated stress to a certain point of the elastic supercharging area can be regarded as the concentrated force, and is expressed as: dP ═ σ (ξ) d ξ, the stress component caused by this concentration force at any one point M (x, y) is expressed as:
by substituting dP into this component expression, one obtains stress components that further concentrate the force at any point M (x, y) in the plane:
in practice, as shown in FIG. 5, the distance from the maximum concentrated stress to a point in the elastically boosted region can be expressed as: x + ytan θ, then this distance is taken into further concentration of the stress components induced at any point M (x, y) for optimization, which can be expressed as:
wherein A isL、ARThe coefficients of the left and right linear equations, theta, in FIG. 5, respectively3Is the included angle between any point M (x, y) in the semi-plane body and the coal wall surface;
and carrying out integral calculation on each stress component caused by the optimized concentrated force at any point M (x, y), and obtaining each stress component of the concentrated force at any point in the semi-plane body after integral, wherein the stress components are expressed as follows:
wherein σxA stress component in the x direction for the load acting at any point M (x, y) within the semi-planar body; sigmayA stress component in the y direction for the load acting at any point M (x, y) within the semi-planar body; tau isxyA shear stress component acting on the xy plane at any point M (x, y) in the semi-plane for the load; a. theL、ARRespectively taking coefficients of a left side linear equation and a right side linear equation in the base plate rock mass stress analysis mechanical model; theta1The included angle between any point M (x, y) in the semi-plane body and the interface of the elastic booster zone and the original rock stress zone; theta2Is the included angle between any point M (x, y) in the semi-plane body and the interface of the elastic supercharging region and the ultimate balance region; theta3Is the included angle between any point M (x, y) in the semi-plane body and the coal wall surface;
in practice, as shown in fig. 5, the non-uniform distribution of the load on the semi-planar body at its boundary can be expressed as:
the integrated stress components at any point in the semi-plane body can be simplified by utilizing the non-uniform distribution load effect of the semi-plane body on the boundary, and the simplified stress components are obtained and expressed as:
wherein σxTo simplify the stress component of the load acting on any point M (x, y) in the semi-plane body in the x direction; sigmayTo simplify the stress component of the rear load acting at any point M (x, y) in the y direction in the semi-plane body; tau isxyIn order to simplify the shear stress component of the load acting on any point M (x, y) in the semi-plane body on the xy plane; x is the number ofaIs the limit of the width of the equilibrium zone, xbThe width of the elastic booster zone is shown, and gamma is the volume weight of an arbitrary point M (x, y) on an overlying rock stratum; h is the thickness of an overlying rock formation at any point M (x, y); k is the front stress concentration coefficient of the coal wall; n is a radical of0The supporting capability of the coal side is realized.
S22, calculating the main stress according to the stress component simplified in the step S21 by using the elastic mechanics theory;
in this embodiment, the principal stress is calculated from the simplified stress components obtained in step S21 by using the theory of elasticity, and is expressed as:
wherein σ1The maximum principal stress generated at any point M (x, y) in the semi-plane body is the non-uniform load; sigma3Is the minimum principal stress generated by the non-uniform load at any point M (x, y) in the semi-plane body.
In practice, the principal stress formula for elastomechanics solution is expressed as:
the principal stress can be calculated according to the solving formula and the stress components obtained in step S21.
And S23, constructing an transcendental equation of the compressive strength of the rock mass at any point in the semi-plane body according to the main stress obtained in the step S22 by adopting an MC damage criterion.
In this embodiment, the compressive strength of the rock mass at any point in the hemispherical surface is calculated according to the principal stress obtained in step S22 by using the MC failure criterion, and is expressed as:
wherein k is a constant coefficient, RcThe compressive strength of any point of rock mass in the hemispherical surface body;
in practice, the Mohr-Coulomb failure criterion is combined, namely: sigma1-kσ3＝RcAnd calculating the compressive strength of the rock mass at any point in the hemispherical surface according to the main stress obtained in the step S22.
S3, calculating the width of the limit balance area according to the coal seam occurrence condition parameters and the mining technical condition parameters;
in this embodiment, step S3 specifically includes:
and calculating the width of the limit balance area according to the coal bed occurrence condition parameters and the mining technical condition parameters, wherein the width is expressed as:
wherein m is the coal seam mining height, f is the interlayer friction coefficient, gammaiThe volume weight of each overburden, M is the total number of overburden, HiIs the thickness of the overlying strata.
S4, constructing an elastic region stress state model based on the support pressure distribution state model, and calculating the width of the elastic pressurizing region;
as shown in fig. 7, in this embodiment, step S4 specifically includes the following sub-steps:
s41, constructing an elastic pressure increasing area stress state model according to the supporting pressure partition model, and establishing a stress balance equation expressed as:
m(σx+dσx)-mσx-2fσydx＝0
wherein m is the thickness of the coal bed; f is the friction coefficient between the layers; sigmaxThe stress component acted on the coal body in the x direction at any point in the semi-plane body; sigmayThe stress component borne by the coal body in the y direction at any point in the semi-plane body is shown;
in practice, the zones are divided according to the support pressureThe common part of the elastic region and the supercharging region in the model establishes an elastic supercharging region stress state model, as shown in figure 8, the origin of coordinates of the model is a position where the stress is recovered from a stress peak value to an original rock stress, and the length from the origin to the stress peak value is xbAnd taking a differential unit from the position x of the origin to establish a stress balance equation.
S42, respectively constructing stress state models of interfaces of the original rock stress area, the ultimate balance area and the elastic booster area, and establishing an elastic booster area balance equation;
as shown in fig. 9, in this embodiment, step S42 specifically includes the following sub-steps:
s421, according to the generalized Hooke' S law, calculating the stress components borne by the coal body in all directions under the original rock stress state, and expressing as follows:
where μ is a constant and σzThe stress component of the coal body in the z direction at any point in the semi-plane body is obtained;
in practice, the coal body in the original state can be considered as an isotropic elastic body, and because the coal body is constrained by the displacement of the adjacent coal body in the horizontal direction and cannot be deformed, the generalized Hooke's law can be adopted to calculate the strain components of the coal body in the original rock stress state in all directions, and the strain components are expressed as:
wherein E is the elastic modulus of the coal body; epsilonx、εy、εzRespectively are the strain components of the coal body in all directions;
due to the strain component epsilonx，εzAll equal in magnitude to zero, the stress component in the x-direction being equal to the strain component in the y-direction, i.e. σx＝σzAnd the stress components of the coal body in all directions in the original rock stress state can be further calculated.
S422, constructing a stress state model of an interface of the original rock stress region and the elastic booster region, and calculating the stress state of the interface of the original rock stress region and the elastic booster region, wherein the stress state is expressed as:
σyC＝σyB＝γH
wherein σxCThe stress component acted on the coal body in the x direction under the pressure stabilizing area; sigmaxBThe stress component acting on the coal body under the supercharging area in the x direction; sigmayCThe stress component acted on the coal body in the y direction under the pressure stabilizing area; sigmayBThe stress component acted on the coal body in the y direction under the pressurization;
in practice, by constructing a stress state model on the interface between the original rock stress region and the elastic supercharging region, as shown in fig. 10, it can be known that the stress component acting on the coal body in the x direction under the steady pressure region is equal to the stress component acting on the coal body in the x direction under the supercharging region, that is: sigmaxC＝σxBAnd calculating the stress state on the interface of the original rock stress area and the elastic supercharging area.
S423, constructing a stress state model of the interface of the elastic supercharging region and the ultimate balance region, and calculating the stress state of the interface of the elastic supercharging region and the ultimate balance region when the initial pressure or the periodic pressure occurs at the top of the foundation, wherein the stress state is expressed as:
σye＝σyp＝σ1
wherein σxeStress acted on the coal body in the x direction under the elastic supercharging area; sigmaxpThe stress acted on the coal body in the x direction under the limit balance area; sigmayeThe stress component acted on the coal body in the y direction under the elastic supercharging area; sigmaypThe stress component acted on the coal body in the y direction under the limit balance area; sigma1The maximum principal stress generated at the point M for the non-uniform load;
in practice, as can be seen from fig. 2, the stress component applied to the coal body under the limit equilibrium region in the y direction can be represented as:
wherein k is a constant coefficient.
In practice, a model of the stress state at the interface of the elastic zone and the ultimate equilibrium zone is constructed, as shown in fig. 11, and it can be seen that: stress sigma acted by coal body in x direction under elastic supercharging zonexeStress sigma acting on coal body in the x direction under the ultimate balance zonexpEqual, i.e.: sigmaxe＝σxpThe stress state at the interface of the elastic zone and the ultimate equilibrium zone can then be calculated as:
σyC＝σyB＝γH
when the primary pressure or periodic pressure occurs at the basic top, the stress state at the interface of the elastic booster zone and the ultimate balance zone can be obtained when the primary pressure or periodic pressure occurs at the basic top.
S424, constructing an elastic supercharging region balance equation according to the stress state on the interface of the original rock stress region and the elastic supercharging region in the step S422 and the stress state on the interface of the elastic supercharging region and the limit balance region in the step S423, wherein the equation is expressed as:
in practice, it can be seen that in the original rock stress region and the ultimate equilibrium region, the load acts on the stress component σ of any point M in the plane in the x directionx；σyIs the stress component sigma of the load in the y direction at any point M in the planeyLinear relation, and in the elastic pressure increasing region sandwiched between the pressure stabilizing region and the ultimate balance region shown in fig. 2, the dimensions of the stress components in two directions are the same, in the present invention, it is assumed that the relation between the two stress components is as follows; sigmay＝ασx+ β, wherein for the unknowns α, β, two pairs of known stress components in the elastically boosted region sandwiched between the pressure-stabilizing region and the extreme equilibrium region according to fig. 2, namely: (sigma)xC，σyC)、(σxp，σyp) The unknown numbers α and β can be calculated by using the stress state at the interface between the original rock stress region and the elastic booster region in step S422 and the stress state at the interface between the elastic booster region and the ultimate balance region in step S423, and the equilibrium equation of the elastic booster region is further obtained by using the unknown numbers α and β, wherein the calculation formula of the unknown numbers α and β is expressed as:
s43, constructing a boundary condition coordinate system based on the critical pressure partition model, and calculating the width value of the elastic supercharging region according to the stress balance equation in the step S41 and the elastic supercharging region balance equation in the step S42;
as shown in fig. 12, in this embodiment, step S43 specifically includes the following sub-steps:
s431, performing integral calculation on the equilibrium equation of the elastically supercharged region in step S424 and the equilibrium equation of the stress in step S41, and expressing as:
wherein C is a constant;
in practice, the derivation equation may be obtained from the equilibrium equation of the elasticated pressure region in step S41:
and calculating the stress relation of the coal body in the specific direction by using the stress balance equation in the step S41.
S432, constructing a boundary condition coordinate system on the basis of the critical pressure partition model, and solving a width value of the elastic supercharging area, wherein the width value is expressed as:
in practice, the boundary condition coordinate system is constructed from the critical pressure partition model, as shown in fig. 13, from (0, γ H) and (x)b，σ1) Two coordinates are obtained according to the relation of the stress of the coal body in the specific direction in step S431:
C＝lnγH
and solving the above formula to obtain a calculation formula of the width value of the elastic supercharging area, and calculating the width value of the elastic supercharging area according to the actual given project, so as to calculate a bottom plate rock stratum failure curve equation according to the transcendental equation of the compressive strength of the rock mass at any point in the semi-plane body constructed in the step S23.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The principle and the implementation mode of the invention are explained by applying specific embodiments in the invention, and the description of the embodiments is only used for helping to understand the method and the core idea of the invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (9)
1. A method for determining the maximum damage depth of a floor rock stratum of a deep stope is characterized by comprising the following steps:
s1, constructing a stress analysis mechanical model of the bottom plate rock mass based on the support pressure distribution state model;
s2, establishing an transcendental equation of the compressive strength of the rock mass at any point in the semi-plane body according to the stress analysis mechanical model of the floor rock mass in the step S1;
s3, calculating the width of the limit balance area according to the coal seam occurrence condition parameters and the mining technical condition parameters;
s4, constructing an elastic region stress state model based on the support pressure distribution state model, and calculating the width of the elastic pressurizing region;
and S5, solving the transcendental equation in the step S2 according to the width of the limit balance area in the step S3 and the width of the elastic supercharging area in the step S4 to obtain a bottom plate damage curve, and calculating the maximum damage depth of the bottom plate rock stratum.
2. The method for determining the maximum depth of failure of a deep stope floor formation according to claim 1, wherein the step S2 specifically comprises the following sub-steps:
s21, constructing a semi-plane infinite body model according to the stress analysis mechanical model of the floor rock body in the step S1, and calculating each stress component at any point in the semi-plane body by utilizing an elastic mechanics theory;
s22, calculating the main stress according to each stress component in the step S21 by using the theory of elastic mechanics;
and S23, establishing an transcendental equation of the compressive strength of the rock mass at any point in the semi-plane body according to the main stress in the step S22 by adopting an MC damage criterion.
3. The method for determining the maximum depth of failure of a deep stope floor formation according to claim 2, wherein the step S21 specifically comprises:
constructing a semi-plane infinite body model according to the stress analysis mechanical model of the floor rock body in the step S1, and calculating each stress component at any point in the semi-plane body by combining the elastic mechanics theory and parameters in the semi-plane infinite body model, wherein the stress components are expressed as follows:
wherein σxA stress component in the x-direction for the load acting at any point (x, y) within the semi-planar body; sigmayA stress component in the y-direction for the load acting at any point (x, y) within the semi-planar body; tau isxyA shear stress component in the xy plane for a load acting at any point (x, y) in the semi-plane; x is the number ofaIs the limit of the width of the equilibrium zone, xbThe width of the elastic supercharging area is shown as gamma, and the volume weight of any point (x, y) on an overlying rock stratum is shown as gamma; h is the thickness of each overlying rock layer; k is the front stress concentration coefficient of the coal wall; n is a radical of0The supporting capability of the coal side is realized.
4. The method for determining the maximum depth of failure of a deep stope floor formation according to claim 3, wherein the step S22 specifically comprises:
calculating the principal stress from the stress components obtained in step S21 using the theory of elasticity mechanics, as:
wherein σ1The maximum main stress generated by non-uniform load at any point in the semi-plane body; sigma3The minimum principal stress generated by the non-uniform load at any point in the semi-plane body.
5. The method for determining the maximum depth of failure of a deep stope floor formation according to claim 4, wherein the step S23 specifically comprises:
and calculating the compressive strength of the rock mass at any point in the hemispherical surface according to the main stress obtained in the step S22 by using the MC failure criterion, wherein the compressive strength is expressed as:
wherein k is a constant coefficient, RcThe compressive strength of the rock mass at any point in the hemispherical body.
6. The method for determining the maximum depth of failure of a deep stope floor formation according to claim 5, wherein the step S3 specifically comprises:
and calculating the width of the limit balance area according to the coal bed occurrence condition parameters and the mining technical condition parameters, wherein the width is expressed as:
wherein m is the coal seam mining height, f is the interlayer friction coefficient, gammaiThe volume weight of each overburden, M is the total number of overburden, HiIs the thickness of the overlying strata.
7. The method for determining the maximum depth of failure of a deep stope floor formation according to claim 6, wherein the step S4 comprises the following sub-steps:
s41, constructing an elastic pressure increasing area stress state model according to the supporting pressure partition model, and establishing a stress balance equation expressed as:
m(σx+dσx)-mσx-2fσydx＝0
wherein m is the thickness of the coal bed; f is the friction coefficient between the layers; sigmaxThe stress component acted on the coal body in the x direction at any point (x, y) in the semi-plane body is shown; sigmayThe stress component of the coal body in the y direction at any point (x, y) in the semi-plane body is；
S42, respectively constructing stress state models of interfaces of the original rock stress area, the ultimate balance area and the elastic booster area, and establishing an elastic booster area balance equation;
and S43, constructing a boundary condition coordinate system based on the critical pressure partition model, and calculating the width value of the elastic supercharging area according to the stress balance equation in the step S41 and the elastic supercharging area balance equation in the step S42.
8. The method for determining the maximum depth of failure of a deep stope floor formation according to claim 7, wherein the step S42 specifically comprises the following sub-steps:
s421, calculating the stress borne by the coal body in each direction under the original rock stress state according to the generalized Hooke' S law, and expressing as follows:
where μ is a constant and σzThe stress component of the coal body in the z direction at any point in the semi-plane body is obtained;
s422, constructing a stress state model of an interface of the original rock stress region and the elastic booster region, and calculating the stress state of the interface of the original rock stress region and the elastic booster region, wherein the stress state is expressed as:
σyC＝σyB＝γH
wherein σxCStress acted on the coal body in the x direction under the pressure stabilizing area; sigmaxBStress acting on the coal body under the supercharging area in the x direction; sigmayCStress acted on the coal body in the y direction under the pressure stabilizing area; sigmayBStress acted on the coal body in the y direction under the pressurization;
s423, constructing a stress state model of the interface of the elastic supercharging region and the ultimate balance region, and calculating the stress state of the interface of the elastic supercharging region and the ultimate balance region when the initial pressure or the periodic pressure occurs at the top of the foundation, wherein the stress state is expressed as:
σye＝σyp＝σ1
wherein σxeStress acted on the coal body in the x direction under the elastic supercharging area; sigmaxpThe stress acted on the coal body in the x direction under the limit balance area; sigmayeStress acted on the coal body in the y direction under the elastic supercharging area; sigmaypThe stress acted on the coal body in the y direction under the limit balance area;
s424, constructing an elastic supercharging region balance equation according to the stress state on the interface of the original rock stress region and the elastic supercharging region in the step S422 and the stress state on the interface of the elastic supercharging region and the limit balance region in the step S423, wherein the equation is expressed as:
9. the method for determining the maximum depth of failure of a deep stope floor formation according to claim 8, wherein the step S43 specifically comprises the following sub-steps:
s431, performing integral calculation on the equilibrium equation of the elastically supercharged region in step S424 and the equilibrium equation of the stress in step S41, and expressing as:
wherein C is a constant;
s432, constructing a boundary condition coordinate system on the basis of the critical pressure partition model, and solving a width value of the elastic supercharging area, wherein the width value is expressed as:
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110790593.6A CN113505484B (en) | 2021-07-13 | 2021-07-13 | Method for determining maximum damage depth of deep stope floor rock stratum |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110790593.6A CN113505484B (en) | 2021-07-13 | 2021-07-13 | Method for determining maximum damage depth of deep stope floor rock stratum |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113505484A true CN113505484A (en) | 2021-10-15 |
| CN113505484B CN113505484B (en) | 2023-06-27 |
Family
ID=78012577
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110790593.6A Active CN113505484B (en) | 2021-07-13 | 2021-07-13 | Method for determining maximum damage depth of deep stope floor rock stratum |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113505484B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116822330A (en) * | 2023-05-19 | 2023-09-29 | 四川大学 | Proppant elastoplastic embedding process analysis method, device, equipment and storage medium |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2011155862A1 (en) * | 2010-06-08 | 2011-12-15 | Щлюмберже Холдингс Лимитед | Method for determining the stress-strain state of a stratified medium |
| US20160334544A1 (en) * | 2014-01-14 | 2016-11-17 | Repsol, S.A. | Method to generate the in-situ state of stress in a domain ω in a geological structure |
| CN106919770A (en) * | 2017-03-21 | 2017-07-04 | 安徽理工大学 | A kind of damage variable based on numerical simulation determines method |
| CN111967080A (en) * | 2020-08-20 | 2020-11-20 | 中国地质大学（北京） | Tunnel mechanics model construction method based on uniform strength theory |
| CN112343605A (en) * | 2020-11-05 | 2021-02-09 | 西南科技大学 | Rock burst prevention tunnel excavation supporting method based on reduced-scale modified pressure arch |
-
2021
- 2021-07-13 CN CN202110790593.6A patent/CN113505484B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2011155862A1 (en) * | 2010-06-08 | 2011-12-15 | Щлюмберже Холдингс Лимитед | Method for determining the stress-strain state of a stratified medium |
| US20160334544A1 (en) * | 2014-01-14 | 2016-11-17 | Repsol, S.A. | Method to generate the in-situ state of stress in a domain ω in a geological structure |
| CN106919770A (en) * | 2017-03-21 | 2017-07-04 | 安徽理工大学 | A kind of damage variable based on numerical simulation determines method |
| CN111967080A (en) * | 2020-08-20 | 2020-11-20 | 中国地质大学（北京） | Tunnel mechanics model construction method based on uniform strength theory |
| CN112343605A (en) * | 2020-11-05 | 2021-02-09 | 西南科技大学 | Rock burst prevention tunnel excavation supporting method based on reduced-scale modified pressure arch |
Non-Patent Citations (4)
| Title |
|---|
| DING WANG .ETC: "Numerical Analysis on the Slope Stability of the Multi-step Waste Rocks Dump with Retaining Wall", 《ADVANCED MATERIALS RESEARCH》, pages 1 - 7 * |
| 于远祥;柯达;王京滨;王赋宇;陈宝平;: "基于弹性理论的煤帮极限平衡区宽度确定方法探讨", 煤炭学报, vol. 44, no. 11, pages 3340 - 3348 * |
| 佘诗刚等: "中国岩石工程若干进展与挑战", 《岩石力学与工程学报》, vol. 33, no. 3, pages 433 - 457 * |
| 张志呈;: "定向卸压隔振爆破隔振材料的作用机理与试验", 爆破器材, no. 05, pages 1 - 4 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116822330A (en) * | 2023-05-19 | 2023-09-29 | 四川大学 | Proppant elastoplastic embedding process analysis method, device, equipment and storage medium |
| CN116822330B (en) * | 2023-05-19 | 2024-02-20 | 四川大学 | Proppant elastoplastic embedding process analysis method, device, equipment and storage medium |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113505484B (en) | 2023-06-27 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Peng | Topical areas of research needs in ground control–a state of the art review on coal mine ground control | |
| Shabanimashcool et al. | A numerical study of stress changes in barrier pillars and a border area in a longwall coal mine | |
| Ju et al. | Numerical analysis of the dynamic evolution of mining-induced stresses and fractures in multilayered rock strata using continuum-based discrete element methods | |
| Ma et al. | Effect of mining on shear sidewall groundwater inrush hazard caused by seepage instability of the penetrated karst collapse pillar | |
| Wang et al. | Coal mining above a confined aquifer | |
| Suchowerska et al. | Horizontal stress under supercritical longwall panels | |
| Liang et al. | Theoretical models for simulating the failure range and stability of inclined floor strata induced by mining and hydraulic pressure | |
| Pan et al. | Effect of premining on hard roof distress behavior: a case study | |
| Wang et al. | Method to predict the height of the water conducting fractured zone based on bearing structures in the overlying strata | |
| Sinha et al. | Modeling behaviors of a coal pillar rib using the progressive S-shaped yield criterion | |
| Song et al. | Theoretical and numerical investigations on mining-induced fault activation and groundwater outburst of coal seam floor | |
| Li et al. | Study on the influence of the fault dip angle on the stress evolution and slip risk of normal faults in mining | |
| He et al. | A geomechanical method for predicting the height of a water-flowing fractured zone in a layered overburden of longwall coal mining | |
| Chen et al. | Numerical investigation of 3D distribution of mining-induced fractures in response to longwall mining | |
| Li et al. | Effects of an underlying drainage gallery on coal bed methane capture effectiveness and the mechanical behavior of a gate road | |
| Yin et al. | In situ dynamic monitoring of stress revolution with time and space under coal seam floor during longwall mining | |
| Luo et al. | Enhanced subsurface subsidence | |
| Zhou et al. | Determination of the stability of residual pillars in a room-and-pillar mining goaf under eccentric load | |
| Pan et al. | A new model for the identification of subcritical surface subsidence in deep pillarless mining | |
| Ma et al. | An early warning method for water inrush in Dongjiahe coal mine based on microseismic moment tensor | |
| Tan et al. | Researches on floor stratum fracturing induced by antiprocedure mining underneath close-distance goaf | |
| Li et al. | Study on “triangle” water-inrush mode of strong water-guide collapse column | |
| CN113505484A (en) | Method for determining maximum damage depth of bottom plate rock stratum of deep stope | |
| Hongwei et al. | Numerical investigation on the assessment and mitigation of coal bump in an island longwall panel | |
| Sakhno et al. | Numerical modeling of controlling a floor heave of coal mine roadways with a method of reinforcing in wet soft rock |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |