CN115169752A - Coal mine roof initial pressure step pitch prediction method based on virtual work theory - Google Patents
Coal mine roof initial pressure step pitch prediction method based on virtual work theory Download PDFInfo
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Abstract
The invention belongs to the field of mine pressure and rock stratum control, and discloses a method for predicting the initial pressure step pitch of a coal mine roof based on a virtual work theory. The method is simple and convenient, can effectively predict the step pitch of the initial pressure of the top plate, guides underground supporting and protecting work, and reduces the damage of personnel and equipment caused by the initial pressure.
Description
Technical Field
The invention belongs to the field of mine pressure and rock stratum control, and particularly relates to a method for predicting a coal mine roof primary pressure step distance based on a virtual work theory.
Background
The basic roof is the roof located directly above or above the coal seam, also known as the old roof. When the working face is pushed forward from the open-off cut, the exposed area of the top plate is enlarged, the direct roof is collapsed to fill the goaf, and the old roof is still supported on the two coal walls completely to form a double-support beam component. When the span of the plate girder is increased to a certain range along with the propulsion of the working face, the old roof collapses under the action of the dead weight of the old roof and the overlying rock stratum. At this time, the working face is no longer under the shield of the old roof, the roof rapidly sinks and is broken, and the first large-area caving of the old roof of the goaf is generally called primary caving. The pressure of the working face is increased due to the primary collapse of the old roof.
The accident of the top plate is one of main accidents under the coal mine, the damage is great, and the primary pressure is stronger and more harmful than the periodic pressure, so that the primary pressure step pitch of the top plate can be effectively predicted, the supporting and pressure reducing work can be reasonably carried out, and the accidents of personnel and equipment are reduced.
Disclosure of Invention
In view of this, the invention aims to provide a method for predicting the initial pressure step of a coal mine roof based on the virtual work theory, which is simple and convenient, can effectively predict the initial pressure step of the roof, guides underground supporting and protecting work, and reduces the damage of personnel and equipment caused by the initial pressure.
In order to achieve the purpose of the invention, the technical scheme is as follows:
a coal mine roof initial pressure step pitch prediction method based on a virtual work theory is characterized by comprising the following steps of:
s1, determining the length of a working face, the width of a transportation gateway and a return air gateway, the average thickness of a top plate and the mechanical characteristics of top plate rocks according to the actual condition of the working face, wherein the top plate reaches a plastic limit state along with the propulsion of the working face in an underground coal mine, and a plastic hinge line in a four-slope top form appears;
s2, calculating the virtual work done by the external force:
virtual work done by external forceWVolume and load of "four-pitched roof" obtained by the cut-and-fill methodqThe product of (a) and (b) yields:
wherein the content of the first and second substances,
equal to the volume of the destructive mechanism in the virtual displacement mode;
substituting the parameters to obtain:
；
in the formula (I), the compound is shown in the specification,
W: the virtual work done for the external force is,
δ: the flexibility of the center of the top plate,
a: the sum of the length of the working face and the width of the two gate grooves,
b: the step pitch is pressed for the first time,
q: covering a load on the top plate;
s3, calculating total internal force virtual dissipation energy:
the total internal force virtual dissipation energy is the work of the limit bending moment at the top of the four-slope top and the plastic hinge line of the plate frame on the relative corner, namely:
in the formula (I), the compound is shown in the specification,
T: the general deficiency of internal force consumes the energy to dissipate,
k: the number of the plastic twisted wires is equal to that of the plastic twisted wires,
l: the length of the plastic strand is greater than the length of the plastic strand,
φ: the relative angle of rotation is such that,
M p : the plastic twisted wire has ultimate bending moment per unit length;
and (3) solving the relative rotation angle of the plastic twisted line by using space geometry:
the relative angle of rotation of the plastic hinge line EF,
，
relative angles of rotation of the plastic hinge lines AE, BE, CF and DF,
，
the relative rotation angles of the plastic twisted lines AB and CD,
，
the relative rotation angles of the plastic strand lines AC, BD,
，
substituting the above parameters to obtain total internal force deficiency energy dissipationTThe calculation formula of (2) is as follows:
s4, obtaining the corresponding relation between the ultimate load and the plate size in the plastic ultimate state, the physical property and the mechanical property according to the fact that the virtual work done by the external force is equal to the total virtual dissipation of the internal force;
order toW=TTo get solved
，
Average thickness ofhThe top plate of (a) is provided,
，
is obtained by substituting the yield limit of the roof strata
；
The upper formula is the load under the plastic limit stateqRepresentative value of twisted wiretThe corresponding relationship of (a) to (b),tbyqTaking the minimum to obtain:
，
taking a positive value:
is substituted to obtain
；
In the formula (I), the compound is shown in the specification,
the limit load is the limit load in the plastic limit state;
s5, calculating the initial pressure step:
the length of the plate is long along with the advance of the working face under the coal minebWhen the critical value is reached, the top plate enters a plastic limit state, and the load on the top plate is taken as the limit load, namelyq=q Pole(s) The load on the top plate, the sum of the length of the working face and the width of the two crossroads, the physical and mechanical properties of the rock stratum of the top plate and the average thickness of the top plate are knownhThe length of the plate can be calculated by the following formulabValue of (2), plate lengthbNamely the initial pressure step distance, the calculation formula is as follows:
wherein the content of the first and second substances,
，hthe average thickness of the top plate is,qan overburden load is applied to the top plate.
The invention has the beneficial effects that: the invention provides a method for predicting the initial pressure step of a coal mine roof based on a virtual work theory, which comprises the steps of firstly determining the length of a working face, the width of a transportation gate way and a return air gate way, the average thickness of the roof and the mechanical characteristics of roof rocks according to the actual condition of the working face, then determining the load of an overlying rock layer supported by the roof of the working face according to a key layer theory, leading the roof to reach a plastic limit state along with the propulsion of the working face, generating a plastic hinge line in a four-slope roof form, and predicting the initial pressure step of the roof according to the corresponding relation between the load when the roof enters the plastic limit state and the size of the roof when the plastic hinge line appears. The method is simple and convenient, and can effectively predict the initial pressure step distance of the top plate, guide underground supporting and protecting work and reduce the damage of personnel and equipment caused by initial pressure.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification. In the drawings:
FIG. 1 is a top view of a top plate in a plastic limit state, wherein the BA direction is a working surface advancing direction;
FIG. 2 is a schematic diagram of the volume of the four-slope top obtained by the 'cut and supplement method';
FIG. 3 is a perspective view of the top plate in a plastic limit state;
FIG. 4 shows the relative rotation angles of plastic twisted lines AE, BE, CF, DFθSolving an auxiliary graph;
FIG. 5 shows the relative rotation angle of the plastic hinge line EFαA schematic view;
FIG. 6 shows the opposite rotation angle of plastic hinge line AB and CDφA schematic diagram;
FIG. 7 shows the relative rotation angle of the plastic twisted lines AC and BDβSchematic representation.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
In order to make the technical solutions better understood by those skilled in the art, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only partial embodiments of the present application, but not all embodiments. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments in the present application without making any creative effort shall fall within the protection scope of the present application.
As shown in fig. 1 to 7, a method for predicting the initial pressure step of a coal mine roof based on the virtual work theory, which assumes that the roof thickness is uniform and does not affect the stress analysis of the roof, comprises the following steps:
s1, determining the length of a working face, the width of a transportation crossheading and a return air crossheading, the average thickness of a top plate and the mechanical characteristics of rocks of the top plate according to the actual condition of the working face, wherein the top plate reaches a plastic limit state along with the advance of the working face in a coal mine well, and a plastic hinge line in a four-slope top form appears;
s2, calculating the virtual work done by the external force:
virtual work done by external forceWVolume and load of "four-pitched roof" determined by the cut-and-fill methodqThe product of (a) and (b) yields:
wherein the content of the first and second substances,
equal to the volume of the destructive mechanism in the virtual displacement mode;
the cutting and supplementing method is embodied as volume reduction of triangular prismRemoving two tetrahedron volumes to obtain the volume of the' four-slope top
Virtual work done by external force
；
In the formula (I), the compound is shown in the specification,
δ: the flexibility of the center of the top plate,
a: the sum of the length of the working surface and the width of the two crossroads (the transportation crossroad and the return air crossroad),
b: the step pitch is pressed for the first time,
q: covering a load on the top plate;
s3, calculating total internal force virtual dissipation energy:
the total virtual dissipation energy of the internal force is the work of the limit bending moment at the tops of the four slope tops and the plastic hinge lines of the plate frames on the relative corner, namely:
in the formula (I), the compound is shown in the specification,
T: the internal force is always deficient and energy is dissipated,
k: the number of the plastic twisted wires is equal to that of the plastic twisted wires,
l: the length of the plastic twisted wire is as long as,
φ: the relative angle of rotation is such that,
M p : plastic twisted wire unit length ultimate bending moment;
the relative rotation angles of the plastic twisted lines are solved by using the space geometry, and the actual relative rotation angles of the plastic twisted lines AE, BE, CF and DF are shown in figure 3θAnd a coordinate system as shown in figure 4 is established,θthe included angle between the face ABE 'and the face BDF' E 'is obtained, the normal vector of the face ABE' and the normal vector of the face BDF 'E' are respectively obtained, and the included angle between the normal vectors and the dihedral angle is obtained through solution
The lengths of the plastic twisted lines AE, BE, CF and DF being equal to
So the virtual work done by the four plastic hinge lines:
plastic hinge line EF relative angleαCalculated from a cross-section perpendicular to the direction of advancement of the working surface, according to the infinitesimal nature of the virtual displacement
Virtual work done by plastic hinge EF
；
Plastic twisted line AB, CD relative cornerφDerived from a section parallel to the direction of advancement of the working surface, and having the same principle
Deficiency and exhaustion of the lung meridian
；
In the same way, the relative rotation angle of the plastic twisted line AC and BD
Deficiency of the Qi
；
S4, obtaining the corresponding relation between the ultimate load and the plate size in the plastic limit state, and the physical and mechanical properties according to the condition that the virtual work done by the external force is equal to the total virtual dissipation of the internal force;
based on the principle of virtual workW=TTo get solved
Because of infinitesimal of virtual displacement, the deflection of the top plate center is infinitely close to zero, so that the deflection of the top plate center is as follows:
has an average thickness ofhThe top plate of (a) is provided,
substituting for the yield limit of the roof strata to obtain:
a、bin the known manner, it is known that,q、tunknown, the above formula is the load under plastic limit stateqRepresentative value of twisted wiretThe corresponding relationship of (2).
tByqTaking the minimum to obtain:
；
taking a positive value:
substituting to obtain:
；
the upper formula is the corresponding relation between the lower limit load of the plastic limit state and the size, physical property and mechanical property of the top plate, the upper load of the top plate is known in the underground coal mine, and the plate length is increased along with the advance of the working surfacebWhen the critical value is reached, the top plate enters a plastic limit state, and the corresponding relation in the formula is met.
S5, calculating the step pitch of the first pressure:
order to
And calculating and sorting to obtain:
the length of the plate is long along with the advance of the working face under the coal minebWhen the critical value is reached, the top plate enters a plastic limit state, and the load on the top plate is taken as the limit load, namelyq=q Pole(s) The load on the top plate, the sum of the length of the working surface and the width of the two crossroads, the physical and mechanical properties of the rock stratum of the top plate and the average thickness of the top plate are knownhThe length of the plate can be calculated by the above formulabValue of (2), plate lengthbNamely the initial pressure step.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement, component separation or combination and the like made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.
Claims (1)
1. A coal mine roof initial pressure step pitch prediction method based on a virtual work theory is characterized by comprising the following steps of:
s1, determining the length of a working face, the width of a transportation gateway and a return air gateway, the average thickness of a top plate and the mechanical characteristics of top plate rocks according to the actual condition of the working face, wherein the top plate reaches a plastic limit state along with the propulsion of the working face in an underground coal mine, and a plastic hinge line in a four-slope top form appears;
s2, calculating the virtual work done by the external force:
virtual work done by external forceWVolume and load of "four-pitched roof" obtained by the cut-and-fill methodqThe product of (a) and (b) yields:
wherein the content of the first and second substances,
equal to the volume of the destructive mechanism in the form of virtual displacement;
substituting each parameter to obtain:
；
in the formula (I), the compound is shown in the specification,
W: the virtual work done by the external force is provided,
δ: the deflection of the center of the top plate,
a: the sum of the length of the working face and the width of the two gate grooves,
b: the step pitch is pressed for the first time,
q: covering a load on the top plate;
s3, calculating total internal force virtual dissipation energy:
the total virtual dissipation energy of the internal force is the work of the extreme bending moment at the top of the four-slope roof and the plastic hinge line of the plate frame on the relative corner, and the total virtual dissipation energy of the internal forceTThe calculation formula of (c) is:
s4, obtaining the corresponding relation between the ultimate load and the plate size in the plastic ultimate state, the physical property and the mechanical property according to the fact that the virtual work done by the external force is equal to the total virtual dissipation of the internal force;
order toW=TTo get solved
，
Average thickness ofhThe top plate of (a) is provided,
，
is obtained by substituting the yield limit of the roof strata
；
The upper formula is the load under the plastic limit stateqRepresentative value of twisted wiretThe corresponding relationship of (a) to (b),tbyqTaking the minimum to obtain:
，
taking a positive value:
is substituted to obtain
；
In the formula (I), the compound is shown in the specification,
the limit load is the limit load in the plastic limit state;
s5, calculating the step pitch of the first pressure:
the length of the plate is long along with the advance of the working face under the coal minebWhen the critical value is reached, the top plate enters a plastic limit state, and the load on the top plate is taken as the limit load, namelyq=q Pole(s) The load on the top plate, the sum of the length of the working surface and the width of the two crossroads, the physical and mechanical properties of the rock stratum of the top plate and the average thickness of the top plate are knownhThe length of the plate can be calculated by the following formulabValue of (2), plate lengthbNamely the initial pressure step distance, the calculation formula is as follows:
wherein the content of the first and second substances,
，hthe average thickness of the top plate is,qan overburden load is applied to the top plate.
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| CN116988831A (en) * | 2023-09-27 | 2023-11-03 | 太原理工大学 | Roof fracture form-based coal mine initial mining period I-shaped filling method |
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