CN112487538A - Method for analyzing stability of inner soil discharge field under coal pillar retaining effect - Google Patents

Method for analyzing stability of inner soil discharge field under coal pillar retaining effect Download PDF

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CN112487538A
CN112487538A CN202011425368.4A CN202011425368A CN112487538A CN 112487538 A CN112487538 A CN 112487538A CN 202011425368 A CN202011425368 A CN 202011425368A CN 112487538 A CN112487538 A CN 112487538A
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pillar
bar
coal pillar
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CN112487538B (en
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李广贺
王东
姜聚宇
杨国华
徐勇超
白继元
贺希格图
赵立春
孙有刚
于明宇
王景政
王洪博
何忠厅
艾合麦提江安外尔
马郅翔
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Liaoning Technical University
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Abstract

The invention discloses a method for analyzing the stability of an inner soil discharge field under the action of coal pillar retaining, which comprises the steps of firstly determining the physical and mechanical indexes of a rock mass, measuring the specific size and position information of a retaining coal pillar, enabling the three-dimensional retaining effect of the coal pillar to be equivalent to cohesive force and an inner friction coefficient, dividing a landslide into vertical strips, introducing the equivalent cohesive force and the equivalent inner friction coefficient into a classical residual thrust method, and realizing the stability analysis of the inner soil discharge field under the action of the coal pillar retaining by taking the residual thrust of the lowest strip as 0 as a target in an iterative mode. The method is simple in calculation and convenient to operate, and can provide scientific theoretical basis for design, treatment and safe implementation of similar opencast coal mine slope engineering.

Description

Method for analyzing stability of inner soil discharge field under coal pillar retaining effect
Technical Field
The invention relates to the technical field of surface mining, in particular to a method for analyzing the stability of an inner soil discharge field under the action of a coal pillar retaining.
Background
The stability of the inner soil discharge field is the premise of safe and efficient mining of open pit coal mines, but the inner soil discharge fields of some large-scale open pit coal mines in China, such as Shenhua Baorishele open pit coal mines, three-greens open pit coal mines, Anjia greens open pit coal mines and red sand spring open pit coal mines, are deformed or destabilized to a certain degree, and a plurality of students adopt reserved coal pillars to support and block the inner soil discharge fields so as to improve the stability of the inner soil discharge fields. For the inner soil discharge field stability research, different theories and methods are applied by experts and scholars of geotechnical engineering to research the inner soil discharge field stability, the most common methods at present are a limit balance method, a limit analysis method and a numerical simulation method, the methods are mature, the calculation result is reliable, but the detailed analysis is only carried out on the inner soil discharge field stability of a homogeneous or homogeneous-like rule, the research on the inner soil discharge field stability of an irregular shape under the action of a coal pillar retaining is less, and the mature methods are lacked. Therefore, an analysis method for the stability of the inner soil discharge field under the action of the coal pillar retaining is urgently needed to be found, and the defects in the aspect of an irregular form stability analysis method under the action of the retaining are overcome.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for analyzing the stability of an inner soil discharge field under the action of a coal pillar retaining.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a method for analyzing the stability of an inner soil discharge field under the action of coal pillar retaining comprises the following steps:
step 1: determining the lithology and the occurrence of the stratum in the slope body according to the column shape of the drilled hole or the contour line information of the stratum; determining physical and mechanical indexes of rock and soil mass based on laboratory tests and previous research results;
step 2: defining the shape parameters of the strike length d, the height h, the top width b, the inner bottom angle omega, the outer bottom angle beta of the supporting and retaining coal pillar, the inclination angle alpha of the base of the inner soil discharge field and the slope angle beta of the edge of the inner soil discharge fieldpLongitudinal intercept h of inner soil discharge field side slope linep；
And step 3: converting three-dimensional retaining effect into equivalent cohesive force cdAnd equivalent internal friction coefficient
Figure BDA0002824562870000012
Wherein
Figure BDA0002824562870000013
For equivalent internal friction angle, the procedure is as follows:
step 3.1: equivalent cohesive force cdThe solution process of (2) is as follows:
Figure BDA0002824562870000011
wherein:
Figure BDA0002824562870000021
cmis cohesion of coal, cjCohesion of the basement rock formation;
step 3.2: equivalent internal friction coefficient
Figure BDA0002824562870000026
The solution process of (2) is as follows:
Figure BDA0002824562870000022
wherein the content of the first and second substances,
Figure BDA0002824562870000023
γmthe volume weight of the coal is the weight of the coal,
Figure BDA0002824562870000024
is the internal angle of friction of the basement rock formation,
Figure BDA0002824562870000025
the internal friction angle of coal, k is the lateral pressure coefficient, γpThe unit weight of the waste materials is reduced.
And 4, step 4: under the condition that the landslide mode is arc-substrate combined sliding, dividing a sliding body into n vertical strips, wherein the sliding body on the upper part of an arc sliding surface is divided into k strips, and the sliding body on the upper part of a substrate is divided into n-k strips;
in the n-k strips, the number of the strips containing the coal pillars is u, the number of the strips without the coal pillars is n-k-u, and the number of the strips without the coal pillars from the inner angular points of the coal pillars to the intersection point of the arc sliding surface and the base sliding surface is q;
when the n vertical strips are divided, the strips are encrypted near the supporting and blocking coal pillar, and the strips are divided separately at the inflection point of the step of the side slope and the intersection of the sliding surface and the rock stratum.
And 5: calculating the residual thrust D of any one of k strips divided by a sliding body on the upper part of the arc sliding surface by adopting a residual thrust methodiThe process is as follows:
step 5.1: taking the ith bar on the upper part of the arc sliding surface as a research object, wherein i is 0,1 … k, and assuming that the bottom surface inclination angle of the ith bar is deltaiThe inclination angle of the bottom surface of the i-1 th bar is deltai-1The residual thrust of the ith bar is DiThe residual thrust of the i-1 th bar is Di-1；
Step 5.2: establishing a balance equation for the direction parallel to the bottom surface of the ith bar:
Di＝Wisinδi+Di-1cos(δi-1-δi)-Si
wherein, WiWeight of the ith bar; diThe residual thrust of the ith bar; siIs the tangential force of the bottom surface of the ith bar;
step 5.3: establishing a balance equation for the direction vertical to the bottom surface of the ith bar block:
Ni＝Wicosδi+Di-1sin(δi-1-δi)
wherein N isiThe normal force of the bottom surface of the ith bar;
step 5.4: tangential force of bottom surface of ith bar according to Moore-Coulomb intensity criterion:
Figure BDA0002824562870000031
wherein liThe length of the bottom surface of the ith strip; c. CiThe cohesive force of the bottom surface of the ith bar;
Figure BDA0002824562870000032
the internal friction angle of the bottom surface of the ith strip block; f is a reduction coefficient;
step 5.5: based on the formulas obtained in step 5.2 to step 5.4, it is deduced that:
Figure BDA0002824562870000033
the boundary conditions are as follows: d0When D is 0, considering that the side of the bar cannot provide the pulling forceiIf < 0(i is 0,1 … k), D isi＝0。
Step 6: calculating the residual thrust D of any one of q coal pillar-free strips divided by a sliding body on the upper part of a substrate from the inner corner point of the coal pillar to the intersection point of the arc sliding surface and the sliding surface of the substrate by adopting a residual thrust methodpThe process is as follows:
step 6.1: the p-th coal pillar-free bar on the upper part of the substrate sliding surface is taken as a research object, p is 1,2 … q, and the inclination angle of the substrate of the inner soil discharge field is alpha, so that the method comprises the following steps:
δ1＝δ2......＝δq＝α
step 6.2: according to the mole-coulomb intensity criterion, the bottom surface of the No-coal briquette has:
Figure BDA0002824562870000034
wherein lpIs the length of the bottom surface of the pth coal pillar-free bar block, NpIs the normal force of the bottom surface of the pth coal pillar-free bar block, SpThe tangential force of the bottom surface of the pth coal pillar-free bar block;
step 6.3: the residual thrust of the p-th non-coal-bar block on the upper part of the substrate sliding surface is as follows:
Figure BDA0002824562870000041
wherein, WpThe weight of the p-th rodless piece.
And 7: the equivalent cohesive force and the equivalent internal friction coefficient are brought into a residual thrust method, and the residual thrust D of any one of the u bars containing the coal pillars and divided by the sliding body on the upper part of the substrate is calculatedrThe process is as follows:
step 7.1: taking the r-th coal pillar-containing bar block on the upper part of the substrate sliding surface as a research object, and establishing an equilibrium equation in a direction parallel to the bottom surface of the r-th coal pillar-containing bar block:
Dr＝Wrsinα+Dr-1-Sr
wherein, WrThe weight of the coal-containing strip is calculated by the following formula: wr＝Armγm+(Ar-Arm)γpWhen the slope line equation of the inner soil discharge field is a fixed value, WrDetermined only by the morphological parameters of the coal pillar and its volume weight, SrIs the bottom tangential force of the r-th coal pillar containing bar block, ArmIs the area of the r-th coal pillar containing bar block, ArThe area of the r-th coal pillar-containing bar block;
step 7.3: establishing a balance equation for the direction vertical to the bottom surface of the r-th coal-pillar-containing bar block:
N＝Wcosα
rr
wherein N isrThe normal force of the bottom surface of the r-th coal-containing bar block;
step 7.4: according to the molar-coulomb intensity criterion, the bottom surface of the r coal-containing bar block is as follows:
Figure BDA0002824562870000042
wherein lrThe length of the bottom surface of the r-th coal pillar containing bar block;
step 7.5: the residual thrust of the r-th briquette containing the coal pillar is as follows:
Figure BDA0002824562870000043
and 8: calculating the residual thrust D of any one of n-k-q-u coal pillar-free bars divided by a sliding body on the upper part of a substrate by adopting a residual thrust methodD；
Calculating the residual thrust D of any one of n-k-q-u coal pillar-free bars divided by a sliding body on the upper part of a substrate by adopting a residual thrust methodDThe solving method is the same as the step 6:
Figure BDA0002824562870000044
wherein lDIs the length of the bottom surface of the No-pillar bar block D, WDThe weight of the No. D coal bar block.
And step 9: according to the steps 5 to 8, obtaining the residual thrust D of the lowest strip block by an iterative methodnThe process is as follows:
iterative solution of the residual thrust D of the last stripnComprises the following steps:
Figure BDA0002824562870000051
step 10: adjusting the reduction coefficient F to make the bottom strip DnIf the value is 0, the stability of the inner soil discharge field under the position of the sliding surface can be obtained;
step 11: by adjusting the position of the sliding surface, FminThe stability coefficient of the inner soil discharge field corresponding to the most dangerous slip surface is the stability coefficient Fs of the inner soil discharge field.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: the invention provides a method for analyzing the stability of an inner soil discharge field under the action of a coal pillar retaining, which introduces a three-dimensional retaining effect of a coal pillar into a classical residual thrust method on the basis of equivalent cohesive force and internal friction coefficient, takes the residual thrust of the lowest strip as 0 as a target, and realizes the stability analysis of the inner soil discharge field under the action of the coal pillar retaining in an iterative mode. The method is simple in calculation and convenient to operate, can provide scientific theoretical basis for design, treatment and safety implementation of similar opencast coal mine slope engineering, has a great promoting effect on development of geotechnical and other subjects, and is of great scientific significance.
Drawings
FIG. 1 is a flow chart of a method for analyzing the stability of an internal dump under the action of a pillar retaining in an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating vertical stripe partitioning according to an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of a supporting pillar according to an embodiment of the present invention;
fig. 4 is a diagram illustrating a calculation result of a stability coefficient according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
In this embodiment, taking a certain opencut coal mine area as an example, the strata of the mine area from old to new are respectively: the coal-series stratum mainly takes coal and mudstone as main lithology, and the clay layer and the mudstone layer have softer strength. The discharged materials mainly come from fourth-series clay and third-series conglomerate in a stope, clay, mudstone in a coal-series stratum and the like, and have the characteristics of loose structure and low strength. According to the previous rock test results and the slope stability research results, the determined physical and mechanical parameters of the rock-soil body are shown in table 1, and the lateral pressure coefficient of the coal pillar is 0.33.
TABLE 1 physical and mechanical indexes of rock and soil mass
Figure BDA0002824562870000061
As shown in fig. 1, the method for analyzing the stability of the internal dump under the action of the pillar retaining in this embodiment includes the following steps:
step 1: determining the lithology and the occurrence of the stratum in the slope body according to the column shape or stratum contour line information of the drilled hole, and determining the physical and mechanical indexes of the rock and soil body;
step 2: defining the shape parameters of the strike length d, the height h, the top width b, the inner bottom angle omega, the outer bottom angle beta of the supporting and retaining coal pillar, the inclination angle alpha of the base of the inner soil discharge field and the slope angle beta of the edge of the inner soil discharge fieldpLongitudinal intercept h of inner soil discharge field side slope linep；
In the embodiment, the top width of the coal pillar of the mine is set to be +824, the top width b of the coal pillar is 20, the running length d of the coal pillar is 108m, the inclination angle alpha of the base is 2 degrees, and the side slope angle beta of the inner soil discharge fieldp12 degrees, an outer bottom angle beta of 34 degrees, an inner bottom angle omega of 29 degrees, a top width b of 20m, a coal pillar height of 36.88m, and a longitudinal section of an inner soil discharge field side slope lineDistance hpThe inner soil discharge site is 21.98m, and the shape of the coal pillar is shown in fig. 3.
And step 3: converting three-dimensional retaining effect into equivalent cohesive force cdAnd equivalent internal friction coefficient
Figure BDA0002824562870000063
Wherein
Figure BDA0002824562870000064
For equivalent internal friction angle, the procedure is as follows:
step 3.1: equivalent cohesive force cdThe solution process of (2) is as follows:
Figure BDA0002824562870000062
wherein:
Figure BDA0002824562870000071
cmis cohesion of coal, cjCohesion of the basement rock formation;
step 3.2: equivalent internal friction coefficient
Figure BDA0002824562870000072
The solution process of (2) is as follows:
Figure BDA0002824562870000073
wherein the content of the first and second substances,
Figure BDA0002824562870000074
γmthe volume weight of the coal is the weight of the coal,
Figure BDA0002824562870000075
is the internal angle of friction of the basement rock formation,
Figure BDA0002824562870000076
the internal friction angle of coal, k is the lateral pressure coefficient, γpThe unit weight of the waste materials is reduced.
In this embodiment, c is obtained by calculationd＝35.87kPa，
Figure BDA0002824562870000077
And 4, step 4: under the condition that the landslide mode is arc-substrate combined sliding, dividing a sliding body into n vertical strips, wherein the sliding body on the upper part of an arc sliding surface is divided into k strips, and the sliding body on the upper part of a substrate is divided into n-k strips;
in the n-k strips, the number of the strips containing the coal pillars is u, the number of the strips without the coal pillars is n-k-u, and the number of the strips without the coal pillars from the inner angular points of the coal pillars to the intersection point of the arc sliding surface and the base sliding surface is q;
when the n vertical strips are divided, the strips are encrypted near the retaining coal pillar, and the strips are divided separately at the inflection point of the step of the side slope and the intersection of the sliding surface and the rock stratum, wherein a schematic diagram of the division situation of the vertical strips in the embodiment is shown in fig. 2.
And 5: calculating the residual thrust D of any one of k strips divided by a sliding body on the upper part of the arc sliding surface by adopting a residual thrust methodiThe process is as follows:
step 5.1: taking the ith bar on the upper part of the arc sliding surface as a research object, wherein i is 0,1 … k, and assuming that the bottom surface inclination angle of the ith bar is deltaiThe inclination angle of the bottom surface of the i-1 th bar is deltai-1The residual thrust of the ith bar is DiThe residual thrust of the i-1 th bar is Di-1；
Step 5.2: establishing a balance equation for the direction parallel to the bottom surface of the ith bar:
Di＝Wisinδi+Di-1cos(δi-1-δi)-Si
wherein, WiWeight of the ith bar; diThe residual thrust of the ith bar; siIs the tangential force of the bottom surface of the ith bar;
step 5.3: establishing a balance equation for the direction vertical to the bottom surface of the ith bar block:
Ni＝Wicosδi+Di-1sin(δi-1-δi)
wherein N isiThe normal force of the bottom surface of the ith bar;
step 5.4: tangential force of bottom surface of ith bar according to Moore-Coulomb intensity criterion:
Figure BDA0002824562870000081
wherein liThe length of the bottom surface of the ith strip; c. CiThe cohesive force of the bottom surface of the ith bar;
Figure BDA0002824562870000082
the internal friction angle of the bottom surface of the ith strip block; f is a reduction coefficient;
step 5.5: based on the formulas obtained in step 5.2 to step 5.4, it is deduced that:
Figure BDA0002824562870000083
the boundary conditions are as follows: d0When D is 0, considering that the side of the bar cannot provide the pulling forceiIf < 0(i is 0,1 … k), D isi＝0。
Step 6: calculating the residual thrust D of any one of q coal pillar-free strips divided by a sliding body on the upper part of a substrate from the inner corner point of the coal pillar to the intersection point of the arc sliding surface and the sliding surface of the substrate by adopting a residual thrust methodpThe process is as follows:
step 6.1: the p-th coal pillar-free bar on the upper part of the substrate sliding surface is taken as a research object, p is 1,2 … q, and the inclination angle of the substrate of the inner soil discharge field is alpha, so that the method comprises the following steps:
δ1＝δ2......＝δq＝α
step 6.2: according to the mole-coulomb intensity criterion, the bottom surface of the No-coal briquette has:
Figure BDA0002824562870000084
wherein lpIs the length of the bottom surface of the pth coal pillar-free bar block, NpIs the normal force of the bottom surface of the pth coal pillar-free bar block, SpThe tangential force of the bottom surface of the pth coal pillar-free bar block;
step 6.3: the residual thrust of the p-th non-coal-bar block on the upper part of the substrate sliding surface is as follows:
Figure BDA0002824562870000091
wherein, WpThe weight of the p-th rodless piece.
And 7: the equivalent cohesive force and the equivalent internal friction coefficient are brought into a residual thrust method, and the residual thrust D of any one of the u bars containing the coal pillars and divided by the sliding body on the upper part of the substrate is calculatedrThe process is as follows:
step 7.1: taking the r-th coal pillar-containing bar block on the upper part of the substrate sliding surface as a research object, and establishing an equilibrium equation in a direction parallel to the bottom surface of the r-th coal pillar-containing bar block:
Dr＝Wrsinα+Dr-1-Sr
wherein, WrThe weight of the coal-containing strip is calculated by the following formula: wr＝Armγm+(Ar-Arm)γpWhen the slope line equation of the inner soil discharge field is a fixed value, WrDetermined only by the morphological parameters of the coal pillar and its volume weight, SrIs the bottom tangential force of the r-th coal pillar containing bar block, ArmIs the area of the r-th coal pillar containing bar block, ArThe area of the r-th coal pillar-containing bar block;
step 7.3: establishing a balance equation for the direction vertical to the bottom surface of the r-th coal-pillar-containing bar block:
N＝Wcosα
rr
wherein N isrThe normal force of the bottom surface of the r-th coal-containing bar block;
step 7.4: according to the molar-coulomb intensity criterion, the bottom surface of the r coal-containing bar block is as follows:
Figure BDA0002824562870000092
wherein lrThe length of the bottom surface of the r-th coal pillar containing bar block;
step 7.5: the residual thrust of the r-th briquette containing the coal pillar is as follows:
Figure BDA0002824562870000093
and 8: calculating the residual thrust D of any one of n-k-q-u coal pillar-free bars divided by a sliding body on the upper part of a substrate by adopting a residual thrust methodD；
Calculating the residual thrust D of any one of n-k-q-u coal pillar-free bars divided by a sliding body on the upper part of a substrate by adopting a residual thrust methodDThe solving method is the same as the step 6:
Figure BDA0002824562870000094
and step 9: according to the steps 5 to 8, obtaining the residual thrust D of the lowest strip block by an iterative methodnThe process is as follows:
iterative solution of the residual thrust D of the last stripnComprises the following steps:
Figure BDA0002824562870000101
step 10: adjusting the reduction coefficient F to make the bottom strip DnIf 0, the stability of the inner soil discharge field at the slide surface position can be obtained.
In this embodiment, F is obtained by calculationminThe stability coefficient corresponding to the most dangerous slip surface is the stability coefficient Fs of the inner soil discharge field, and the calculation result of this embodiment is shown in fig. 4.
In the sliding surface position 1, F is 1.567
At slide position 2, F is 1.209
At slide position 3, F is 1.841
Fmin1.209, so the inner soil discharge field stability factor Fs is 1.209.

Claims (8)

1. A method for analyzing the stability of an inner soil discharge field under the action of coal pillar retaining is characterized by comprising the following steps:
step 1: determining the lithology and the occurrence of the stratum in the slope body according to the column shape or stratum contour line information of the drilled hole, and determining the physical and mechanical indexes of the rock and soil body;
step 2: defining the shape parameters of the strike length d, the height h, the top width b, the inner bottom angle omega, the outer bottom angle beta of the supporting and retaining coal pillar, the inclination angle alpha of the base of the inner soil discharge field and the slope angle beta of the edge of the inner soil discharge fieldpLongitudinal intercept h of inner soil discharge field side slope linep；
And step 3: converting three-dimensional retaining effect into equivalent cohesive force cdAnd equivalent internal friction coefficient
Figure FDA0002824562860000011
Wherein
Figure FDA0002824562860000012
Is the equivalent internal friction angle;
and 4, step 4: under the condition that the landslide mode is arc-substrate combined sliding, dividing a sliding body into n vertical strips, wherein the sliding body on the upper part of an arc sliding surface is divided into k strips, and the sliding body on the upper part of a substrate is divided into n-k strips;
in the n-k strips, the number of the strips containing the coal pillars is u, the number of the strips without the coal pillars is n-k-u, and the number of the strips without the coal pillars from the inner angular points of the coal pillars to the intersection point of the arc sliding surface and the base sliding surface is q;
and 5: calculating the residual thrust D of any one of k strips divided by a sliding body on the upper part of the arc sliding surface by adopting a residual thrust methodi；
Step 6: calculating q coal pillars without coal pillars from the inner corner point of the coal pillar to the intersection point of the arc sliding surface and the substrate sliding surface divided by the sliding body on the upper part of the substrate by adopting a residual thrust methodResidual thrust D of any one of the barsp；
And 7: the equivalent cohesive force and the equivalent internal friction coefficient are brought into a residual thrust method, and the residual thrust D of any one of the u bars containing the coal pillars and divided by the sliding body on the upper part of the substrate is calculatedr；
And 8: calculating the residual thrust D of any one of n-k-q-u coal pillar-free bars divided by a sliding body on the upper part of a substrate by adopting a residual thrust methodD；
And step 9: according to the steps 5 to 8, obtaining the residual thrust D of the lowest strip block by an iterative methodn；
Step 10: adjusting the reduction coefficient F to make the bottom strip DnIf the value is 0, the stability of the inner soil discharge field under the position of the sliding surface can be obtained;
step 11: by adjusting the position of the sliding surface, FminThe stability coefficient of the inner soil discharge field corresponding to the most dangerous slip surface is the stability coefficient Fs of the inner soil discharge field.
2. The method for analyzing the stability of the internal dump under the action of the pillar retaining according to claim 1, wherein the process of the step 3 is as follows:
step 3.1: equivalent cohesive force cdThe solution process of (2) is as follows:
Figure FDA0002824562860000021
wherein:
Figure FDA0002824562860000022
cmis cohesion of coal, cjCohesion of the basement rock formation;
step 3.2: equivalent internal friction coefficient
Figure FDA0002824562860000025
The solution process of (2) is as follows:
Figure FDA0002824562860000023
wherein the content of the first and second substances,
Figure FDA0002824562860000024
γmthe volume weight of the coal is the weight of the coal,
Figure FDA0002824562860000026
is the internal angle of friction of the basement rock formation,
Figure FDA0002824562860000027
the internal friction angle of coal, k is the lateral pressure coefficient, γpThe unit weight of the waste materials is reduced.
3. The method for analyzing the stability of the internal dump under the action of the coal pillar retaining according to claim 1, wherein when n vertical bars are divided in the step 4, the bars are encrypted near the retaining coal pillar, and the bars are divided separately at the inflection point of the step of the side slope and the intersection of the sliding surface and the rock stratum.
4. The method for analyzing the stability of the internal dump under the action of the pillar retaining according to claim 1, wherein the process of the step 5 is as follows:
step 5.1: taking the ith bar on the upper part of the arc sliding surface as a research object, wherein i is 0,1 … k, and assuming that the bottom surface inclination angle of the ith bar is deltaiThe inclination angle of the bottom surface of the i-1 th bar is deltai-1The residual thrust of the ith bar is DiThe residual thrust of the i-1 th bar is Di-1；
Step 5.2: establishing a balance equation for the direction parallel to the bottom surface of the ith bar:
Di＝Wisinδi+Di-1cos(δi-1-δi)-Si
wherein, WiWeight of the ith bar; diThe residual thrust of the ith bar; siIs the bottom surface of the ith barThe tangential force of (a);
step 5.3: establishing a balance equation for the direction vertical to the bottom surface of the ith bar block:
Ni＝Wicosδi+Di-1sin(δi-1-δi)
wherein N isiThe normal force of the bottom surface of the ith bar;
step 5.4: tangential force of bottom surface of ith bar according to Moore-Coulomb intensity criterion:
Figure FDA0002824562860000031
wherein liThe length of the bottom surface of the ith strip; c. CiThe cohesive force of the bottom surface of the ith bar;
Figure FDA0002824562860000035
the internal friction angle of the bottom surface of the ith strip block; f is a reduction coefficient;
step 5.5: based on the formulas obtained in step 5.2 to step 5.4, it is deduced that:
Figure FDA0002824562860000032
the boundary conditions are as follows: d0When D is 0, considering that the side of the bar cannot provide the pulling forceiIf < 0(i is 0,1 … k), D isi＝0。
5. The method for analyzing the stability of the internal dump under the action of the pillar retaining according to claim 1, wherein the process of the step 6 is as follows:
step 6.1: the p-th coal pillar-free bar on the upper part of the substrate sliding surface is taken as a research object, p is 1,2 … q, and the inclination angle of the substrate of the inner soil discharge field is alpha, so that the method comprises the following steps:
δ1＝δ2......＝δq＝α
step 6.2: according to the mole-coulomb intensity criterion, the bottom surface of the No-coal briquette has:
Figure FDA0002824562860000033
wherein lpIs the length of the bottom surface of the pth coal pillar-free bar block, NpIs the normal force of the bottom surface of the pth coal pillar-free bar block, SpThe tangential force of the bottom surface of the pth coal pillar-free bar block;
step 6.3: the residual thrust of the p-th non-coal-bar block on the upper part of the substrate sliding surface is as follows:
Figure FDA0002824562860000034
wherein, WpThe weight of the p-th rodless piece.
6. The method for analyzing the stability of the internal dump under the action of the pillar retaining according to claim 1, wherein the process of the step 7 is as follows:
step 7.1: taking the r-th coal pillar-containing bar block on the upper part of the substrate sliding surface as a research object, and establishing an equilibrium equation in a direction parallel to the bottom surface of the r-th coal pillar-containing bar block:
Dr＝Wrsinα+Dr-1-Sr
wherein, WrThe weight of the coal-containing strip is calculated by the following formula: wr＝Armγm+(Ar-Arm)γpWhen the slope line equation of the inner soil discharge field is a fixed value, WrDetermined only by the morphological parameters of the coal pillar and its volume weight, SrIs the bottom tangential force of the r-th coal pillar containing bar block, ArmIs the area of the r-th coal pillar containing bar block, ArThe area of the r-th coal pillar-containing bar block;
step 7.3: establishing a balance equation for the direction vertical to the bottom surface of the r-th coal-pillar-containing bar block:
Nr＝Wrcosα
wherein，NrThe normal force of the bottom surface of the r-th coal-containing bar block;
step 7.4: according to the molar-coulomb intensity criterion, the bottom surface of the r coal-containing bar block is as follows:
Figure FDA0002824562860000041
wherein lrThe length of the bottom surface of the r-th coal pillar containing bar block;
step 7.5: the residual thrust of the r-th briquette containing the coal pillar is as follows:
Figure FDA0002824562860000042
7. the method for analyzing the stability of the internal dump under the action of the pillar retaining according to claim 1, wherein the process of the step 8 is as follows:
calculating the residual thrust D of any one of n-k-q-u coal pillar-free bars divided by a sliding body on the upper part of a substrate by adopting a residual thrust methodDThe solving method is the same as the step 6:
Figure FDA0002824562860000043
wherein lDIs the length of the bottom surface of the No-pillar bar block D, WDThe weight of the No. D coal bar block.
8. The method for analyzing the stability of the internal dump under the action of the pillar retaining according to claim 1, wherein the process of the step 9 is as follows:
iterative solution of the residual thrust D of the last stripnComprises the following steps:
Figure FDA0002824562860000051
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