CN111914456B - Method for predicting development of air leakage crack of regenerated roof by finite difference method and similar experiment - Google Patents

Method for predicting development of air leakage crack of regenerated roof by finite difference method and similar experiment Download PDF

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CN111914456B
CN111914456B CN202010777410.2A CN202010777410A CN111914456B CN 111914456 B CN111914456 B CN 111914456B CN 202010777410 A CN202010777410 A CN 202010777410A CN 111914456 B CN111914456 B CN 111914456B
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roof
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CN111914456A (en
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鲁义
陈健
晏志宏
王平
李贺
谷旺鑫
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Hunan University of Science and Technology
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Abstract

The invention discloses a method for predicting the development of an air leakage crack of a regenerated top plate by a finite difference method and similar experiments, which comprises the steps of changing the width of solid coal, simulating the crack development condition of the regenerated top plate in the tunneling process of a roadway driving face according to finite difference software, determining the change rule of the width of the solid coal and the crack development depth and obtaining the functional relation between the width of the solid coal and the position deviation of a key block of the regenerated top plate; manufacturing a key block similar model according to the simulation result, and respectively performing a mechanical similar experiment under the action of static load and dynamic load, thereby determining a creep characteristic curve of the key block; then, representing the dynamic change process of the actual key block by changing the rotation angle of the key block similar model, and determining the influence of the rotation angle on the creep performance of the key block of the regenerated top plate; and finally, solving a function of the porosity of the key block of the regenerated roof along with time by combining the functions according to the characteristics of the power function, and finally predicting the development condition of the air leakage crack of the regenerated roof according to a plurality of function fitting.

Description

Method for predicting development of air leakage crack of regenerated roof by finite difference method and similar experiment
Technical Field
The invention relates to a method for predicting the development of an air leakage crack of a regenerated roof plate, in particular to a method for predicting the development of the air leakage crack of the regenerated roof plate by a finite difference method and a similar experiment.
Background
The regenerated top plate is a lower-layer mining top plate formed by compacting an upper-layer collapsed rock stratum under the action of stratum pressure and performing natural cementation or artificial treatment. The top plate formed by the method can reduce the mining cost and shorten the construction period, but compared with other types of top plates, the top plate has some obvious differences, on one hand, the regenerated top plate is loose and broken, has lower strength and is easy to form air leakage cracks, on the other hand, the coal covering the regenerated top plate is rich in content, and the coal covering the regenerated top plate can be oxidized and spontaneously combusted through the formed air leakage crack channels, even gas explosion is caused. Therefore, research on the development process and the development degree of the crack of the regenerated roof plate leaking air is a problem which needs to be solved at present.
At present, the similar physical models for the research on the fracture development of the regenerated roof are few, but the research on the fracture development of the rock stratum is very deep at home and abroad, and the two types are mainly: firstly, simulation tests are carried out by using software, for example, the invention patent with the application number of 201811055893.4 discloses a quantitative description method of a coal seam fracture field, the fracture area between fracture blocks is quantitatively calculated by a masonry beam theory, and a porosity space distribution function is fitted according to an established roof fracture field coordinate system, so that the relation between the permeability and the porosity of a porous medium is solved; for another example, the invention patent with application number 201811324625.8 calculates the damage tensor defined by each group of constructed rock-like fracture samples, deduces an effective stress formula of a rock-like fracture pattern and a geometric damage constitutive model of the rock-like fracture samples, and completes the research on the mechanical properties of the rock-like fracture samples through numerical simulation software; the other is to carry out similar mechanics experiments, for example, the invention patent with the application number of 201810367298.8 provides an experimental device for researching the forming process of the key block of the top plate and the crack propagation rule of the key block rock under the disturbance action and gradually destabilizing under the initial stress condition, and the action mechanism of the destabilization caused by the critical condition of the destabilization sliding of the key block and the disturbance action is determined based on the device; for example, the invention patent with application number 201910305195.3 discloses a method for establishing an overburden platform based on geometric similarity, recording the development conditions of rock stratum fractures at different stages of an excavation process by using a camera, and determining the fractal dimension and fracture development characteristic curve of the excavation process through image processing software.
From the above, it can be seen that the research result of fracture development of the existing roof rock stratum is significant, but the research content mainly focuses on the critical conditions causing roof instability, the existing state of fractures and the evolution process. Due to the particularity of the components of the regenerated roof plate and the dynamic process of crack development, the requirement of the development process of the air leakage crack of the regenerated roof plate is difficult to quantitatively predict only according to the synchronous observation of the crack state and the critical condition causing instability. Therefore, how to accurately predict the development condition of the air leakage crack of the regenerated roof is the research direction of the industry.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method for predicting the development of the air leakage crack of the regenerated roof by a finite difference method and a similar experiment.
In order to achieve the purpose, the invention adopts the technical scheme that: a method for predicting the growth of a regenerated roof air leakage crack by a finite difference method and a similar experiment comprises the following specific steps:
A. firstly, measuring and calculating a plurality of physical parameters of a regeneration roof and a roadway which need to be predicted, wherein the physical parameters are as follows: the average thickness, the volume modulus, the shear modulus, the internal friction angle, the cohesion, the tensile strength, the size of a roadway driving face and the size of a supporting coal pillar of the regenerated roof cementing regeneration zone;
B. establishing a roadway driving surface model by using finite difference software FLAC 3D simulation software in combination with the physical parameters, wherein a supporting structure on one side of a roadway in the roadway driving surface model is a supporting coal pillar, and a supporting structure on the other side of the roadway in the roadway driving surface model is solid coal; then, carrying out meshing on the roadway driving surface model;
C. calculating the position of a key layer of a regenerated roof, the position of a key block, the development conditions of transverse cracks and longitudinal cracks of the regenerated roof of the current roadway driving face model by adopting FLAC 3D simulation software according to a known key layer and key block theory; then adjusting the width of the solid coal in the roadway driving face model, and calculating the position of a key layer of the regenerated roof, the position of a key block and the crack development process of the regenerated roof under the current width again; adjusting for many times to obtain the development conditions of key layer positions, key block positions, transverse cracks and longitudinal cracks of the regenerated roof, which respectively correspond to the different entity coal widths;
the key layer and key block theory is as follows:
q1|m+1＜q1|m
in the formula, q1|m+1Is the load of the m +1 layer; q. q.s1|mIs the load of m layers;
if the above formula is true, the m +1 layer is a key layer;
D. according to the development conditions of the transverse cracks and the longitudinal cracks of the regenerated roof respectively corresponding to different entity coal widths in the step C, determining the functional relationship between the development depth of the transverse cracks and the development depth of the longitudinal cracks of the regenerated roof respectively corresponding to the entity coal widths, and determining the relationship can determine the change rule of the fractures of the regenerated roof in the mining process, wherein the specific steps are as follows:
Figure BDA0002618957580000031
Figure BDA0002618957580000032
in the formula, LxThe development depth of the transverse crack of the regenerated roof is determined; b is the solid coal width; l iszThe development depth of the longitudinal crack of the regenerated roof is obtained; f is a functional relation corresponding to the development depth of the transverse crack of the regenerated roof and the width of the solid coal;
Figure BDA0002618957580000033
the initial transverse crack depth of the regenerated roof; g is a functional relation corresponding to the development depth of the longitudinal cracks of the regenerated roof and the width of the solid coal;
Figure BDA0002618957580000034
the initial longitudinal fracture depth of the regenerated roof;
E. and C, performing stress analysis on the key block of the regenerated top plate through the software simulation result in the step C to determine the static load q borne by the key block, wherein the calculation formula of the static load q is as follows:
Figure BDA0002618957580000035
in the formula, F is the load and dead weight of the rock mass; theta is a key block rotation angle; h is the critical block thickness; l is the key block length;
and C, according to the simulation result of the step C, obtaining the influence of different entity coal widths on the position offset, the shape and the size of the key block of the regeneration top plate, and further obtaining an offset function of the entity coal width corresponding to the central point of the key block of the regeneration top plate:
Figure BDA0002618957580000036
in the formula (I), the compound is shown in the specification,
Figure BDA0002618957580000037
a critical block position offset for the regeneration ceiling; (A, B and C) are coordinates of the central point of the key block when the width of the solid coal is equal to that of the supporting coal pillar; (X, Y, Z) is a key block center point offset function; the influence effect of the change of the entity coal width on the disturbance of the regenerated top plate can be determined by establishing the function; on the other hand, the effect of the change can be enhanced by using the vector to represent the displacement of the key block.
F. According to the mechanical similarity principle, sampling on site from the regenerated roof to be predicted, making a plurality of key block similar models with the same structure according to the functional relation obtained in the step E (the key block similar models have the same structure with the key blocks of the regenerated roof), selecting one of the key block similar models, and measuring the initial porosity n according to the Archimedes principle0：
Figure BDA0002618957580000041
In the formula, m' is the weight of the key block similar model after being soaked in distilled water for 24 hours; m is the mass of the key block similar model in drying; m iswFor models similar to the key blockMass of the same volume of distilled water;
G. selecting a key block similar model from the step F to enable the key block similar model to be in a horizontal state, and then carrying out a static load mechanics similar experiment when the static load is q by adopting a pressure bearing plate method to obtain the creep deformation epsilon of the key block similar modelsThe relationship with time t, namely:
Figure BDA0002618957580000042
in the formula, h is a creep deformation function relation of the key block similar model under the action of static load;
Figure BDA0002618957580000043
the key block is similar to the instantaneous elastic deformation of the model at the moment of applying the static load;
H. selecting a key block similar model from the step F to enable the key block similar model to be in a horizontal state, then performing dynamic load mechanics similar experiment in a constant amplitude load control mode by adopting a fatigue testing machine, wherein the loading waveform is a sine wave, the cyclic load upper limit stress is selected to be q, and obtaining the creep deformation epsilon of the key block similar modeldThe relationship with time t, namely:
εd＝r(t)
in the formula, r is the creep deformation functional relation of the key block similar model under the action of dynamic load;
I. and F, selecting a plurality of key block similar models again, dividing every two of the plurality of key block similar models into a group, enabling the included angles between the two key block similar models in each group and the horizontal plane to be the same, and simultaneously enabling the included angles between each group and the horizontal plane to be different, then repeating the static load mechanics similar experiment of the step G and the dynamic load mechanics similar experiment of the step H for one of the groups in sequence, and obtaining the function change relation between the creep deformation epsilon and different included angles theta after each group is completed, namely:
ε＝w(θ)
in the formula, w is a functional relation between creep deformation epsilon and an included angle theta of the similar model of the key block relative to a horizontal plane; a dynamic change process of the key blocks of the actual roadway regeneration roof is represented by the key block similar model rotation angle, so that the creep process of the key blocks of the regeneration roof can be better reflected by respectively carrying out a mechanical similarity experiment under the action of static load and dynamic load.
J. Since any function can be expressed in the form of a power series when the function satisfies the guidance requirement, the porosity n and the strain rate of creep deformation
Figure BDA0002618957580000051
Can be expressed as:
Figure BDA0002618957580000052
in the formula, a0，a1，a2，amAre all constants;
K. and D, fitting and solving the functional relation among the step D, the step G, the step H and the step J to obtain a function of the time change of the development process of the air leakage crack of the regenerated roof, and finally predicting the development condition of the air leakage crack of the regenerated roof according to the obtained function.
Compared with the prior art, the method comprises the steps of firstly measuring and calculating a plurality of physical parameters of the regenerated roof and the roadway to be predicted, establishing a roadway driving face model by using finite difference software FLAC 3D simulation software and combining the physical parameters, and respectively simulating the development conditions of longitudinal and transverse cracks of the regenerated roof in the tunneling process of the roadway driving face by changing the width of solid coal of the roadway driving face model, so as to determine the function change rule of the width of the solid coal, the development depth of the transverse cracks and the development depth of the longitudinal cracks and obtain the function relation between the width of the solid coal and the position offset of key blocks of the regenerated roof; then, a plurality of key block similar models are manufactured according to the obtained functional relation, and the key block similar models are subjected to mechanical similar experiments under the action of static load and dynamic load respectively, so that creep characteristic curves of the key block similar models are determined; on the basis, the actual rotation angle of the key block of the regeneration top plate is simulated by changing the included angle between the key block similar model and the horizontal plane, so that the dynamic change process of the key block of the actual regeneration top plate is represented, and further the function change relation between different included angles (rotation angles) and creep deformation is obtained; finally, according to the characteristics of the power function, combining the obtained multiple function relations, solving a time-varying function of the porosity of the key block of the regeneration top plate; and finally, accurately predicting the development condition of the air leakage crack of the regenerated roof according to the function.
Drawings
FIG. 1 is an overall flow diagram of the present invention;
FIG. 2 is a trace plot of the deviation of the solid coal width from the key block center point position in the present invention;
FIG. 3 is a diagram of creep characteristic changes of a key block similarity model for static load and dynamic load respectively;
FIG. 4 is a diagram of creep deformation of a key block similarity model as a function of rotation angle;
FIG. 5 is a graph of the development of the regenerated roof leak-off crack of the present invention over time.
Detailed Description
The present invention will be further explained below.
As shown in fig. 1, the method comprises the following specific steps:
A. firstly, measuring and calculating a plurality of physical parameters of a regeneration roof and a roadway which need to be predicted, wherein the physical parameters are as follows: the average thickness, the volume modulus, the shear modulus, the internal friction angle, the cohesion, the tensile strength, the size of a roadway driving face and the size of a supporting coal pillar of the regenerated roof cementing regeneration zone are shown in the table 1;
TABLE 1
Figure BDA0002618957580000061
B. Establishing a roadway driving surface model by using finite difference software FLAC 3D simulation software in combination with the physical parameters, wherein a supporting structure on one side of a roadway in the roadway driving surface model is a supporting coal pillar, and a supporting structure on the other side of the roadway in the roadway driving surface model is solid coal; then, carrying out meshing on the roadway driving surface model;
C. calculating the position of a key layer of a regenerated roof, the position of a key block, the development conditions of transverse cracks and longitudinal cracks of the regenerated roof of the current roadway driving face model by adopting FLAC 3D simulation software according to a known key layer and key block theory; then adjusting the width of the solid coal in the roadway driving face model, and calculating the position of a key layer of the regenerated roof, the position of a key block and the crack development process of the regenerated roof under the current width again; adjusting for many times to obtain the development conditions of key layer positions, key block positions, transverse cracks and longitudinal cracks of the regenerated roof, which respectively correspond to the different entity coal widths; (as shown in FIG. 2)
The key layer and key block theory is as follows:
q1|m+1＜q1|m
in the formula, q1|m+1Is the load of the m +1 layer; q. q.s1|mIs the load of m layers;
if the above formula is true, the m +1 layer is a key layer;
D. according to the development conditions of the transverse cracks and the longitudinal cracks of the regeneration roof respectively corresponding to different solid coal widths in the step C, determining the functional relationship between the development depth of the transverse cracks and the development depth of the longitudinal cracks of the regeneration roof respectively corresponding to the solid coal widths, which specifically comprises the following steps:
Figure BDA0002618957580000071
Figure BDA0002618957580000072
in the formula, LxThe development depth of the transverse crack of the regenerated roof is determined; b is the solid coal width; l iszThe development depth of the longitudinal crack of the regenerated roof is obtained; f is a functional relation corresponding to the development depth of the transverse crack of the regenerated roof and the width of the solid coal;
Figure BDA0002618957580000073
the initial transverse crack depth of the regenerated roof; g is a functional relation corresponding to the development depth of the longitudinal cracks of the regenerated roof and the width of the solid coal;
Figure BDA0002618957580000074
the initial longitudinal fracture depth of the regenerated roof;
E. and C, performing stress analysis on the key block of the regenerated top plate through the software simulation result in the step C to determine the static load q borne by the key block, wherein the calculation formula of the static load q is as follows:
Figure BDA0002618957580000075
in the formula, F is the load and dead weight of the rock mass; theta is a key block rotation angle; h is the critical block thickness; l is the key block length;
and C, according to the simulation result of the step C, obtaining the influence of different entity coal widths on the position offset, the shape and the size of the key block of the regeneration top plate, and further obtaining an offset function of the entity coal width corresponding to the central point of the key block of the regeneration top plate:
Figure BDA0002618957580000076
in the formula (I), the compound is shown in the specification,
Figure BDA0002618957580000077
a critical block position offset for the regeneration ceiling; (A, B and C) are coordinates of the central point of the key block when the width of the solid coal is equal to that of the supporting coal pillar; (X, Y, Z) is a key block center point offset function;
F. according to the mechanical similarity principle, sampling on site from the regenerated roof to be predicted, making a plurality of key block similarity models with the same structure according to the functional relation obtained in the step E, selecting one of the key block similarity models, and measuring the initial porosity n according to the Archimedes principle0：
Figure BDA0002618957580000078
In the formula, m' is the weight of the key block similar model after being soaked in distilled water for 24 hours; m is the mass of the key block similar model in drying; m iswMass of distilled water at the same volume as the key block similarity model;
G. selecting a key block similar model from the step F to enable the key block similar model to be in a horizontal state, and then carrying out a static load mechanics similar experiment when the static load is q by adopting a pressure bearing plate method to obtain the creep deformation epsilon of the key block similar modelsThe relationship with time t, namely: (as shown by the solid line in FIG. 3)
Figure BDA0002618957580000081
In the formula, h is a creep deformation function relation of the key block similar model under the action of static load;
Figure BDA0002618957580000082
the key block is similar to the instantaneous elastic deformation of the model at the moment of applying the static load;
H. selecting a key block similar model from the step F to enable the key block similar model to be in a horizontal state, then performing dynamic load mechanics similar experiment in a constant amplitude load control mode by adopting a fatigue testing machine, wherein the loading waveform is a sine wave, the cyclic load upper limit stress is selected to be q, and obtaining the creep deformation epsilon of the key block similar modeldThe relationship with time t, namely: (as shown by the dotted line in FIG. 3)
εd＝r(t)
In the formula, r is the creep deformation functional relation of the key block similar model under the action of dynamic load;
I. and F, selecting a plurality of key block similar models again, dividing every two of the plurality of key block similar models into a group, enabling the included angles between the two key block similar models in each group and the horizontal plane to be the same, and simultaneously enabling the included angles between each group and the horizontal plane to be different, then repeating the static load mechanics similar experiment of the step G and the dynamic load mechanics similar experiment of the step H for one of the groups in sequence, and obtaining the function change relation between the creep deformation epsilon and different included angles theta after each group is completed, namely: (as shown in FIG. 4)
ε＝w(θ)
In the formula, w is a functional relation between creep deformation epsilon and an included angle theta of the similar model of the key block relative to a horizontal plane;
J. since any function can be expressed in the form of a power series when the function satisfies the guidance requirement, the porosity n and the strain rate of creep deformation
Figure BDA0002618957580000083
Can be expressed as:
Figure BDA0002618957580000084
in the formula, a0，a1，a2，amAre all constants;
K. and D, fitting and solving the functional relation among the step D, the step G, the step H and the step J to obtain a function (a function curve is shown in figure 5) of the time variation of the development process of the air leakage crack of the regenerated roof, and finally predicting the development condition of the air leakage crack of the regenerated roof according to the obtained function.
According to the field test experience, the porosity n of a critical block sample of the regenerated top plate is about 0.1, and according to the characteristics of a power function and infinitesimal high order, a high order power term with m being more than or equal to 3 can be ignored, so that:
the functional relationship between the porosity n and the time t under the action of static load is as follows:
Figure BDA0002618957580000091
secondly, the function relation of the porosity n and the time t under the action of dynamic load is as follows:
Figure BDA0002618957580000092
in the formula (I), the compound is shown in the specification,
Figure BDA0002618957580000093
is a constant.

Claims (1)

1. A method for predicting the growth of a regenerated roof air leakage crack by a finite difference method and a similar experiment is characterized by comprising the following specific steps:
A. firstly, measuring and calculating a plurality of physical parameters of a regeneration roof and a roadway which need to be predicted, wherein the physical parameters are as follows: the average thickness, the volume modulus, the shear modulus, the internal friction angle, the cohesion, the tensile strength, the size of a roadway driving face and the size of a supporting coal pillar of the regenerated roof cementing regeneration zone;
B. establishing a roadway driving face model by using FLAC 3D simulation software in combination with the physical parameters, wherein a supporting structure on one side of a roadway in the roadway driving face model is a supporting coal pillar, and a supporting structure on the other side of the roadway in the roadway driving face model is solid coal; then, carrying out meshing on the roadway driving surface model;
C. calculating the position of a key layer of a regenerated roof, the position of a key block, the development conditions of transverse cracks and longitudinal cracks of the regenerated roof of the current roadway driving face model by adopting FLAC 3D simulation software according to a known key layer and key block theory; then adjusting the width of the solid coal in the roadway driving face model, and calculating the position of a key layer of the regenerated roof, the position of a key block and the crack development process of the regenerated roof under the current width again; adjusting for many times to obtain the development conditions of key layer positions, key block positions, transverse cracks and longitudinal cracks of the regenerated roof, which respectively correspond to the different entity coal widths;
D. according to the development conditions of the transverse cracks and the longitudinal cracks of the regeneration roof respectively corresponding to different solid coal widths in the step C, determining the functional relationship between the development depth of the transverse cracks and the development depth of the longitudinal cracks of the regeneration roof respectively corresponding to the solid coal widths, which specifically comprises the following steps:
Figure FDA0002618957570000011
Figure FDA0002618957570000012
in the formula, LxThe development depth of the transverse crack of the regenerated roof is determined; b is the solid coal width; l iszThe development depth of the longitudinal crack of the regenerated roof is obtained; f is a functional relation corresponding to the development depth of the transverse crack of the regenerated roof and the width of the solid coal;
Figure FDA0002618957570000013
the initial transverse crack depth of the regenerated roof; g is a functional relation corresponding to the development depth of the longitudinal cracks of the regenerated roof and the width of the solid coal;
Figure FDA0002618957570000014
the initial longitudinal fracture depth of the regenerated roof;
E. and C, performing stress analysis on the key block of the regeneration roof through the software simulation result in the step C to determine the static load q borne by the key block, and simultaneously obtaining the influences of different entity coal widths on the position deviation, the shape and the size of the key block of the regeneration roof according to the simulation result in the step C so as to obtain a deviation function of the entity coal width corresponding to the central point of the key block of the regeneration roof:
Figure FDA0002618957570000021
in the formula (I), the compound is shown in the specification,
Figure FDA0002618957570000022
a critical block position offset for the regeneration ceiling; (A, B and C) are coordinates of the central point of the key block when the width of the solid coal is equal to that of the supporting coal pillar; (X, Y, Z) is a key block center point offset function;
F. according to the principle of mechanical similarity, the regeneration top predicted from the requirementSampling the plate on site, making a plurality of key block similar models with the same structure according to the functional relation obtained in the step E, selecting one of the key block similar models, and measuring the initial porosity n of the selected key block similar model according to the Archimedes principle0：
Figure FDA0002618957570000023
In the formula, m' is the weight of the key block similar model after being soaked in distilled water for 24 hours; m is the mass of the key block similar model in drying; m iswMass of distilled water at the same volume as the key block similarity model;
G. selecting a key block similar model from the step F to enable the key block similar model to be in a horizontal state, and then carrying out a static load mechanics similar experiment when the static load is q by adopting a pressure bearing plate method to obtain the creep deformation epsilon of the key block similar modelsThe relationship with time t, namely:
Figure FDA0002618957570000024
in the formula, h is a creep deformation function relation of the key block similar model under the action of static load;
Figure FDA0002618957570000025
the key block is similar to the instantaneous elastic deformation of the model at the moment of applying the static load;
H. selecting a key block similar model from the step F to enable the key block similar model to be in a horizontal state, then performing dynamic load mechanics similar experiment in a constant amplitude load control mode by adopting a fatigue testing machine, wherein the loading waveform is a sine wave, the cyclic load upper limit stress is selected to be q, and obtaining the creep deformation epsilon of the key block similar modeldThe relationship with time t, namely:
εd＝r(t)
in the formula, r is the creep deformation functional relation of the key block similar model under the action of dynamic load;
I. and F, selecting a plurality of key block similar models again, dividing every two of the plurality of key block similar models into a group, enabling the included angles between the two key block similar models in each group and the horizontal plane to be the same, and simultaneously enabling the included angles between each group and the horizontal plane to be different, then repeating the static load mechanics similar experiment of the step G and the dynamic load mechanics similar experiment of the step H for one of the groups in sequence, and obtaining the function change relation between the creep deformation epsilon and different included angles theta after each group is completed, namely:
ε＝w(θ)
in the formula, w is a functional relation between creep deformation epsilon and an included angle theta of the similar model of the key block relative to a horizontal plane;
J. since any function can be expressed in the form of a power series when the function satisfies the guidance requirement, the porosity n and the strain rate of creep deformation
Figure FDA0002618957570000031
Can be expressed as:
Figure FDA0002618957570000032
in the formula, a0，a1，a2，amAre all constants;
K. and D, fitting and solving the functional relation among the step D, the step G, the step H and the step J to obtain a function of the time change of the development process of the air leakage crack of the regenerated roof, and finally predicting the development condition of the air leakage crack of the regenerated roof according to the obtained function.
CN202010777410.2A 2020-08-05 2020-08-05 Method for predicting development of air leakage crack of regenerated roof by finite difference method and similar experiment Active CN111914456B (en)

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