Underground deep deformation estimation method based on ground surface settlement remote sensing monitoring

Abstract

The invention relates to an underground deep deformation estimation method based on ground surface settlement remote sensing monitoring, which comprises the following steps of: on the basis of dividing a goaf stratum into a caving zone, a fissure zone, a bending zone and a loose zone, according to a goaf deformation mechanism, transverse deformation diffusion and deformation body expansibility of each layer zone; and an in-layer deformation and interlayer deformation transfer formula of each layer belt is established, and a layer-by-layer superposition method for final permanent deformation of the stratum of the goaf is realized. According to layer-by-layer transmission of goaf settlement deformation from deep deformation to earth surface deformation, relational expressions between earth surface deformation and underground deep deformation in different stages are provided respectively, and finally, according to a final permanent deformation value of a goaf stratum, an underground arbitrary-depth stratum deformation estimation method in different stages based on earth surface deformation remote sensing monitoring is provided. According to the method, the problem that the surrounding rock deformation load cannot be estimated according to actual measurement in tunnel and underground engineering safety evaluation through coal mining deformation in the mining active period is solved.

Description

Technical Field

[0001] The present invention belongs to the field of ground geological disaster prevention and control induced by coal mining, and specifically relates to a method for estimating ground subsidence and overlying rock strata subsidence deformation during an active period of a coal goaf area. Background Art

[0002] Fundamentally solving and managing the problem of coal mine goafs has become an urgent need for urban construction within the goaf area. Coal mine goafs will cause ground geological disasters such as ground subsidence, surface collapse, and ground fissures, which will cause serious damage to surface buildings (structures), railways, roads, rivers, and underground pipelines within the goaf area, which will seriously restrict the development of national land space planning and urban and rural construction. Accurate prediction of ground subsidence and movement and deformation of overlying strata in coal goaf areas is an important basis for evaluating the foundation suitability of urban buildings, underground spaces, and transportation infrastructure within the goaf area and preventing and controlling geological disasters in the goaf area.

[0003] The collapse and settlement deformation of coal goaf areas and the overlying movement deformation are formed by the synergistic deformation superposition under different deformation mechanism conditions of the destruction zone and deformation zone of each rock stratum overlying the goaf. In the traditional coal goaf surface settlement and overlying stratum movement deformation estimation methods, whether empirical function method, time function method, random medium method, or even numerical method, they can only reflect the comprehensive driving mechanism of coal goaf collapse deformation or a certain aspect of the deformation characteristics of destruction deformation, and can only partially reflect the coal goaf collapse deformation mechanism or the comprehensive effect of synergistic deformation superposition under different deformation mechanism conditions.

[0004] InSAR (interferometric radar) technology, which has emerged in recent years, can quickly obtain the scope and deformation field of large-scale subsidence basins, and has been well applied in surface deformation monitoring. The settlement of goaf areas is a continuous change during the active period. Based on the InSAR surface monitoring results, it plays an important role in inverting the settlement and deformation of deep rock strata in the active period of goaf areas. Therefore, a method for estimating deep settlement deformation during the active period of coal goaf based on remote sensing monitoring is proposed.

[0005] Regardless of the empirical function method, the time function method, or the random medium method, traditional methods can only reflect one aspect of the characteristics of the driving mechanism of the collapse and deformation of coal goaf areas. However, the collapse and deformation are caused by the coordinated deformation of strata with different deformation mechanisms, and the collapse and deformation of goaf areas are mainly in the active period. The settlement of goaf areas is a continuous change during the active period, and the settlement and deformation of each rock layer during the active period are also different. Summary of the invention

[0006] Technical problem: The purpose of the present invention is to provide a method for estimating deep underground deformation based on remote sensing monitoring of surface subsidence. According to the movement and deformation mechanism of different areas of the overlying strata in the goaf, the deformation transfer and diffusion mechanism within and between layers and the expansion of the deformation body, a deformation transfer calculation method within and between layers is adopted. The surface movement deformation of the coal goaf is obtained by superimposing layer by layer from bottom to top.

[0007] Technical solution: In order to achieve the above-mentioned purpose, the present invention adopts the following technical solution for estimating deep underground deformation based on remote sensing monitoring of surface subsidence:

[0008] The estimation of deep underground deformation includes the four-zone stratum division of the goaf area, the calculation of the final settlement of the goaf area, the InSAR monitoring of the surface deformation of the goaf area, the stages of goaf deformation, and the settlement deformation of each rock layer when the surface settlement rate is the largest; it is carried out in four periods.

[0009] Initial period of mining: During the period of t0-t1, settlement occurs in the caving zone of the coal mining area and gradually transfers to the surface. The minimum deformation can be monitored by synthetic aperture radar interferometry (InSAR) on the surface.

[0010] Active acceleration period of mining deformation: During the period t1-t2, the bottom settlement drives the settlement of the upper rock layer, the settlement rate of the overlying rock layer gradually accelerates, and the surface settlement rate gradually increases to the maximum surface settlement rate;

[0011] Active decay period of mining deformation: t2-t3 period, during which the compaction of rock formations is dominant, the settlement rate of overlying rock formations gradually slows down, and the settlement rate of the surface gradually decreases;

[0012] Mining deformation decay period: from time point t3 to the end of compaction and consolidation of loose layer soil, the surface deformation rate in this stage is less than the minimum deformation rate that can be monitored on the surface;

[0013] in;

[0014] t0: the time point when the initial deformation of the caving zone in coal mining excavation occurs; t1: the time point when the settlement deformation of the surface appears in the synthetic aperture radar interferometry InSAR monitoring; t2: the time point when the maximum settlement rate of the surface appears in the synthetic aperture radar interferometry InSAR monitoring; t3: the surface deformation rate monitored by synthetic aperture radar interferometry InSAR is less than the specification requirements.

[0015] The initial period of mining: based on the sub-meter deformation monitoring accuracy of InSAR technology, the surface settlement of 1 mm is defined as the final value of the surface deformation in this stage, and the settlement deformation characteristics of the deep rock strata are inverted.

[0016] The inversion of the settlement deformation characteristics of deep rock formations includes:

[0017] Loose zone inversion: Surface settlement w(0,z) = 1mm, substitute the following formula to get the loose zone bottom settlement value w s That is S BZ,max ,

[0018]

[0019] Where: w(x,z) is the deformation settlement curve of the loose belt; x is the horizontal distance from any settlement point in the loose belt to the settlement center; z is the vertical distance from any settlement point in the loose belt to the settlement center. BZ,max is the maximum settlement value at the top of the initial deformation curve; i0 is the width coefficient of the initial deformation curve; B is the horizontal range of the bulk deformation diffusion, and N is the bulk volume change coefficient during the bulk deformation diffusion.

[0020] Inversion of bending zone settlement: The bottom of the loose zone is close to the top of the bending zone. At this time, the settlement value of the top of the bending zone is equal to the settlement value w of the bottom of the loose zone s ; The bending zone is regarded as elastic continuous deformation when settlement occurs, and its calculation model is regarded as a beam model with constraints at both ends. Different composite beams in the bending zone deform simultaneously.

[0021] w 顶梁 =w s

[0022]

[0023] Where: w 顶梁 is the settlement of the composite beam at the top of the bending zone; w s is the bottom settlement value of the loose zone; w t1 w is the final settlement value of the t-th composite beam in the bending zone at this stage; t2 is the settlement of the t-th composite beam in the bending zone at the maximum settlement rate; w 顶梁2 is the settlement of the top composite beam at the maximum settlement rate

[0024] Fracture zone settlement inversion; the bottom of the bending zone is close to the top of the fracture zone w FZ(0，z) =w 1梁 ; The bending deformation of the fracture zone is calculated by taking the bottom settlement of the bending zone as the settlement boundary of the top of the fracture zone; the deformation and settlement of the top of the fracture zone is substituted into the following formula to obtain the deformation and settlement of the bottom of the fracture zone w CZ (0,z)

[0025]

[0026]

[0027]

[0028]

[0029] Where: l CZ is the lateral impact range of the lower part of the fracture zone; l FZ is the lateral impact range of the upper part of the fracture zone; l0 is the lateral size of the coal seam working face; h0 is the coal seam mining height; α m is the internal friction angle of rock layer m; H is the comprehensive fracture angle of the rock layer in the fracture zone; CZ H is the height of the caving zone; FZ is the height of fracture zone development; w FZ (x,z) is the deformation settlement curve of the fracture zone; x is the horizontal distance from any settlement point in the fracture zone to the settlement center, and z is the vertical distance from any settlement point in the fracture zone to the settlement center; s max0 is the maximum settlement value of the settlement trough at the bottom of the fracture zone; i (z) is the width coefficient of the fracture zone settlement trough.

[0030] Inversion of settlement of caving zone: After the collapse of rock formations in the caving zone, a crushing and expansion effect will occur, that is, the total volume of the crushed rock formation is larger than the total volume of the original rock; the volume of the goaf multiplied by the rock mass crushing and expansion coefficient is the volume of the caving zone, and the height of the top of the settlement trough at the top of the caving zone is the settlement of the caving zone.

[0031]

[0032] Where: V0 is the volume of the rock formation settlement trough at the top of the caving zone, N is the coefficient of change of the bulk volume during bulk deformation and diffusion, and w0(x) is the settlement curve at the top of the caving zone.

[0033] The active acceleration period of mining deformation: deep settlement drives the settlement of overlying rock layers. In this stage, the deformation of overlying rock layers undergoes settlement in the same proportion from the initial stage to the final stage. The deformation in the deformation zone is calculated according to the elevation linear interpolation method.

[0034] The amount of settlement W at any height z inside the rock layer z Calculated by linear interpolation, the formula is:

[0035]

[0036] Where: z is the distance from the surface to the lower boundary of the rock layer, ranging from 0≤z≤H, W z is the settlement at that point; W z1 is the initial settlement at that point; W z2 is the amount of sedimentation at the point with the maximum sedimentation rate; W t is the surface subsidence; W b It is the amount of surface settlement at the time of maximum surface settlement rate.

[0037] The active decay period of mining deformation is dominated by the compaction of rock strata. In this stage, the initial caving zone has completely settled, and the rock strata gradually reach a stable state from bottom to top. The time for each rock stratum to reach a stable state is approximately expressed as a function F (x) , the known surface settlement value W during the active decay period of mining 地表 , obtain the time when the sedimentation value occurs through InSAR, and substitute this time into the function F (x) Determine the location partition where the rock layer reaches stability at this moment; the lower part of this partition has completed settlement and reached the final settlement value, while the upper part is in the compaction consolidation stage and is still undergoing settlement deformation and is calculated using the linear interpolation method;

[0038] The time for each rock layer to reach a stable state is approximately expressed as a function F (x)

[0039]

[0040] Where: W cz W is the final settlement value of the caving zone; 地表 is the final surface settlement value, T 终 is the complete settlement time of the overlying rock layer, T vmax The time when the maximum surface subsidence rate occurs.

[0041] The four-zone stratigraphic division of the goaf includes:

[0042] Approximate estimation of the height of the caving zone:

[0043]

[0044] Where: H CZ is the height of the caving zone; h0 is the height of coal seam mining

[0045] Fracture zone development height H FZ Empirical calculation formula;

[0046] When the overburden is medium-hard and the uniaxial compressive strength is 20-40MPa:

[0047]

[0048] When the overburden is weak and the uniaxial compressive strength is 10-20MPa:

[0049]

[0050] Where: H FZ is the height of fracture zone development; h0 is the height of coal seam mining;

[0051] Loose belt height H LZ is the thickness of the soil layer above the bedrock layer, which can be obtained according to the geological survey report;

[0052] Height of bending zone H BZ The calculation can be done by:

[0053] H BZ =H0-H LZ -H FZ -H CZ +h0

[0054] Where: H BZ is the height of the bending zone; H0 is the depth of coal seam; H CZ H is the height of the caving zone; FZ H is the height of fracture zone development; LZ Loose zone height; h0 is the coal seam mining height.

[0055] The calculation of the final settlement of the goaf includes:

[0056] Calculation of settlement of caving zone:

[0057] The settlement value in the middle of the interface between the caving zone and the fracture zone, that is, the difference between the initial expansion coefficient and the residual expansion coefficient of the caving zone, can be obtained:

[0058] h CZ =H CZ (K s -K f )

[0059] Where: h CZ K is the maximum value of the collapse settlement in the middle of the interface between the caving zone and the fracture zone; CZ K is the height of the caving zone; s is the initial expansion coefficient; K f is the residual expansion coefficient;

[0060] Fracture zone settlement calculation:

[0061] The horizontal range of the fracture zone, the height of the interface between the caving zone and the fracture zone is H zi =H cz :

[0062]

[0063]

[0064] Where: l CZ is the lateral impact range of the lower part of the fracture zone; l FZ is the lateral impact range of the upper part of the fracture zone; l0 is the lateral size of the coal seam working face; h0 is the coal seam mining height; α m is the internal friction angle of rock layer m; Comprehensive fracture angle of rock formation in fracture zone; H CZH is the height of the caving zone; FZ The height of the fracture zone development.

[0065] According to the Peck formula, the deformation curve of the fracture zone is described according to the Gaussian curve distribution:

[0066] s max0 =h CZ

[0067]

[0068]

[0069] Where: h CZ is the maximum value of collapse settlement in the middle of the interface between the caving zone and the fracture zone; s max0 is the maximum value of the deformation curve at the interface between the caving zone and the fracture zone; w FZ(X,Z) is the settlement deformation curve of the fracture zone, x is the horizontal distance from any settlement point in the fracture zone to the settlement center, z is the vertical distance from any settlement point in the fracture zone to the settlement center; s max0 is the maximum settlement value of the settlement trough at the bottom of the fracture zone; i(z) is the width coefficient of the deformation curve at the interface between the caving zone and the fracture zone, that is, the horizontal distance from the center point of the deformation curve with the maximum settlement value to its inflection point; α m is the internal friction angle of rock layer m; Comprehensive fracture angle of rock strata in fracture zone.

[0070] Calculation of bending zone settlement:

[0071] Along the longitudinal section, the i-th rock layer overlying the curved zone of the goaf is regarded as a unit width beam model, and the deformation function w of the i-th rock layer is BZ,i (x) is the basic unknown, which corresponds to the deformation and settlement equation w BZ,i (x) is:

[0072]

[0073] Where: w BZ,i (x) is the rock deformation and settlement equation, E BZ,i is the elastic modulus of the i-th rock layer in the bending zone; I BZ,i is the section moment of inertia of the ith rock layer in the bending zone; and are the loads transferred by the overlying strata of the ith stratum in the bending zone in the supporting section and the goaf, respectively; and are the foundation coefficients of the i-th rock layer in the bending zone in the supporting section and the goaf area respectively; To transfer load; is the foundation parameter; Flexural rigidity; is the correlation parameter of beam length;

[0074] At the junction of the coal wall support influence zone and the stress recovery zone, the composite beam Z i The sinking, rotation angle, bending moment and shear force are all equal. According to the above three groups of conditions, the values ​​of each parameter can be obtained as follows:

[0075]

[0076]

[0077] Where: To transfer load; is the foundation parameter; Flexural rigidity; is the correlation parameter of beam length; is the length of the composite beam in the coal wall support influence zone, is the stress recovery distance of coal mine goaf; and are the loads transferred by the overlying strata of the ith stratum in the bending zone in the supporting section and the goaf, respectively; and are the foundation coefficients of the i-th rock layer in the bending zone in the supporting section and the goaf area respectively.

[0078] Loose belt settlement calculation:

[0079] The loose zone conforms to the deformation characteristics of soil bulk medium. Using random medium theory, according to Litvinishen's derivation, it satisfies the second-order parabolic partial differential equation. For layered homogeneous bulk medium, the three characteristic parameters A(z), B(z), and N(z) will be constants that do not change with the z value, and the horizontal deviation of bulk deformation diffusion does not exist, that is, A(z) = 0, B(z) = B, N(z) = N; the deformation diffusion equation in bulk medium is:

[0080]

[0081] Wherein: x is the horizontal distance from the center line of the deformation curve sedimentation tank; z is the vertical distance upward along the center line of the deformation curve sedimentation tank; w(x,z) is the deformation of any point in the dispersed medium; A(z), B(z), and N(z) are the characteristic parameters of the deformation and diffusion of the dispersed medium, respectively. A(z) reflects the horizontal deviation degree of the dispersion deformation diffusion, B(z) reflects the horizontal range of the dispersion deformation diffusion, and N(z) reflects the volume change of the dispersion during the dispersion deformation diffusion.

[0082] Using Fourier transform, the simultaneous equations can be solved as:

[0083]

[0084] Where: s BZ,max is the maximum settlement value at the top of the initial deformation curve; i0 is the width coefficient of the initial deformation curve.

[0085] The InSAR monitoring of surface deformation in goaf areas includes:

[0086] Using SARscape software and the interference superposition methods of PS-InSAR and SBAS-InSAR, the ground subsidence time series of the study area was monitored and corrected, and the ground subsidence time series of the goaf was monitored and corrected, and the time series diagram of the subsidence rate of the goaf in the active period was obtained.

[0087] The mining deformation stages include:

[0088] The duration of active period in goaf and the maximum surface Sinking speed calculate

[0089] Duration of active period of goaf:

[0090] T=2.5H0

[0091] Where: T is the total movement duration, H0 is the average mining depth

[0092] The maximum surface sinking velocity is estimated by the following formula:

[0093]

[0094] Where V max is the maximum surface sinking velocity, K is the sinking coefficient, C is the working face advancement velocity, H0 is the average mining depth, W max is the maximum surface subsidence value;

[0095] The time when the maximum surface subsidence rate occurs is obtained from the time series diagram of the subsidence rate in the goaf area obtained by InSAR monitoring, and the goaf active period is divided into the goaf active acceleration period and the goaf active decay period based on this time.

[0096] When the surface settlement rate is the maximum, the settlement deformation of each rock layer includes:

[0097] When the surface subsidence rate reaches the maximum, the caving zone has completely settled. The subsidence values ​​of the overlying layers are calculated from top to bottom.

[0098] Loose zone settlement inversion:

[0099] The time when the maximum surface settlement rate occurs and the surface settlement value at that time, i.e., the settlement value at the top of the loose zone when the surface has the maximum settlement rate, are determined through the maximum surface settlement rate and the surface settlement rate time series diagram;

[0100] The monitoring results of SBAS-InSAR are used as the settlement boundary of the top of the loose zone and substituted into the following formula to obtain the settlement value of the bottom of the loose zone;

[0101]

[0102] Where: w(x,z) is the deformation settlement curve of the loose belt; x is the horizontal distance from any settlement point in the loose belt to the settlement center; z is the vertical distance from any settlement point in the loose belt to the settlement center. BZ,max is the maximum settlement value at the top of the initial deformation curve; i0 is the width coefficient of the initial deformation curve; B is the horizontal range of the bulk deformation diffusion, and N is the bulk volume change coefficient during the bulk deformation diffusion.

[0103] Curved Zone Inversion

[0104] The bottom settlement of the loose zone obtained by inversion is taken as the settlement boundary of the top of the bending zone. The overlying rock layer of the bending zone is regarded as elastic continuous deformation. The bending zone conforms to the infinitely long transversely isotropic layered elastic deformation characteristics. Its calculation model is regarded as a beam model with two ends constrained under the load transferred from the upper rock layer. Since the parameters of the bending zone beam model are completely invariant with the final deformation, they are substituted into the following calculation formula to obtain the settlement deformation of each beam in the bending zone:

[0105]

[0106] Where: and are the loads transferred by the overlying strata of the ith stratum in the bending zone in the supporting section and the goaf, respectively; is the foundation coefficient of the i-th rock layer within the support range of the bending zone; The foundation coefficient of the i-th rock layer within the goaf of the curved belt is; To transfer loads; is the foundation parameter; Flexural rigidity; is the correlation parameter of beam length;

[0107] Fracture zone inversion:

[0108] The bending deformation of the fracture zone is calculated by taking the bottom settlement of the bending zone as the settlement boundary of the top of the fracture zone, and substituting the deformation and settlement of the top of the fracture zone into the following formula:

[0109]

[0110] Where: w FZ (x,z) is the deformation settlement curve of the fracture zone; x is the horizontal distance from any settlement point in the fracture zone to the settlement center, and z is the vertical distance from any settlement point in the fracture zone to the settlement center; s max0is the maximum settlement value of the settlement trough at the bottom of the fracture zone; i (z) is the width coefficient of the fracture zone settlement trough; l FZ It is the lateral influence range of the upper part of the fracture zone.

[0111] Obtain the deformation and subsidence of the bottom of the fracture zone;

[0112] The caving zone has completely settled when the surface subsidence rate reaches the maximum, and the deformation and subsidence amount is consistent with that when it is completely settled.

[0113] w cz =w vmax .

[0114] Where: W cz is the final settlement value of the caving zone; w vmax It is the deformation and settlement value of the caving zone when the surface subsidence rate reaches the maximum.

[0115] The said specification is the "Specification for the Installation of Coal Pillars and Compressed Coal Mining in Buildings, Water Bodies, Railways and Main Wells and Lanes", referred to as the "Three-Down" specification.

[0116] The requirement is: during the duration of the movement process, the surface subsidence rate is less than 50mm / month (1.7mm / d) (the inclination of the ore layer is less than 45°), or less than 30mm / month (the inclination of the ore layer is greater than 45°).

[0117] Beneficial effects: (1) According to the movement and deformation mechanism of different areas of the overlying strata in the goaf, the deformation transfer and diffusion mechanism within and between different layers and the expansion of the deformation body are used. The surface movement and deformation of the coal goaf are obtained by stacking layer by layer from bottom to top. The SBAS-InSAR technical means are used to detect the settlement time series of the goaf during the active period to obtain the surface settlement during the active period, and the settlement deformation of each rock layer is inverted from top to bottom using the layer-by-layer inversion method (2) The present invention can not only invert the surface movement and settlement deformation of the goaf at any time during the active period, but also invert the deep settlement deformation of the overlying rock layers. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] Figure 1 It is a time series diagram of the subsidence of the overlying strata during the active mining period;

[0119] Figure 2 It is the calculation zoning diagram of the settlement deformation estimation method of the overlying strata in the goaf area;

[0120] Figure 3 It is a graph of the duration of surface movement;

[0121] Figure 4 is a distribution diagram of the coal wall support influence area and the stress recovery area in the embodiment;

[0122] Figure 5is a graph showing the relationship between the final settlement values ​​of different layers and deep layers in the embodiment;

[0123] Figure 6 is the point time series deformation curve;

[0124] Figure 7 is the settlement rate curve of the goaf;

[0125] Figure 8 It is a graph showing the changing relationship of settlement in different layers when the surface settlement rate is the largest. DETAILED DESCRIPTION

[0126] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0127] The invention discloses a method for estimating underground deep deformation based on remote sensing monitoring of surface subsidence, comprising four-zone stratum division of goaf area; calculation of final subsidence of goaf area; InSAR monitoring of surface deformation of goaf area; stage division of goaf deformation; and estimation of underground deep deformation.

[0128] The calculation zoning characteristics of the overlying strata in the coal goaf area are that the overlying strata are vertically divided into: caving zone, fracture zone, bending zone, and loose zone. The lateral range of each vertical layer of the overlying strata: the lateral range of the caving zone is controlled by the span of the goaf working face; the lateral range of the fracture zone is controlled by the comprehensive fracture angle of the fractured rock layer; the lateral range of the bending zone is controlled by the lateral support pressure angle; the lateral range of the loose zone is controlled by the deformation diffusion angle of the bulk medium. The calculation zoning is as follows: Figure 2 shown.

[0129] Assumptions for calculation of overlying strata in coal mining areas: (1) Both coal seams and overlying rock strata are nearly horizontal layered occurrences. When the coal seam dip angle α is less than 15° (the angle between the coal seam and the horizontal plane), the inclination state of the coal seam and rock strata is not considered; (2) The deformation mechanisms of the upper and lower layers on the boundary of the layer zone are different. The movement deformation curve can be a discontinuous distribution, but the maximum movement deformation curve is used; (3) The coal seam mining is in a fully mined state, and the mining process, insufficient mining and time factors are not considered; (4) The fracture zone conforms to the deformation characteristics of the block medium, and its fragmentation and expansion after deformation and destruction are not large, and its volume change is not considered; (5) The curved zone conforms to the infinitely long transversely isotropic layered elastic deformation characteristics, and the difference in foundation reaction force affected by the mining area is considered; (6) The loose zone conforms to the deformation characteristics of the soil medium, and its volume change during the deformation diffusion process is considered;

[0130] The method for estimating deep underground deformation based on remote sensing monitoring of surface subsidence is specifically as follows:

[0131] Division of four zones of stratigraphy in goaf

[0132] Determine the location of the key layer

[0133] According to the key layer theory, assuming that the first rock layer is a hard rock layer, the rock layers above it up to the mth layer deform in coordination with it, and the m+1th layer does not deform in coordination with it, then the m+1th layer is the second hard rock layer. The load transfer of the mth layer and the m+1th layer to the first hard rock layer is compared, such as:

[0134]

[0135] Where: h BZ,i , γ BZ,i , E BZ,i The thickness, bulk density, and elastic modulus of the i-th rock layer in the bending zone are respectively; start from the 1st rock layer in the bending zone and calculate upward layer by layer, and judge the above formula. When the above formula is satisfied, no more calculation is done upward, and the rock layers from the 1st layer to the mth layer are the composite beam calculation units. Start from the m+1th layer and search for the next section again according to the above method.

[0136] Calculate the breaking distance of each hard rock layer. The breaking of hard rock layers is the breaking problem of the elastic foundation plate. However, in order to simplify the calculation, the breaking distance of hard rock layers is calculated using the fixed-end beam model. Then the breaking distance of the kth hard rock layer is l k It can be calculated by the following formula:

[0137]

[0138] In the formula, h k is the thickness of the kth hard rock layer; σ k is the tensile strength of the kth hard rock layer; q k is the load borne by the kth hard rock layer.

[0139] Compare the fracture distances and determine the location of the key layer.

[0140] If the kth hard rock layer is the key layer, its breaking distance should be smaller than the breaking distance of all the hard rock layers above it, that is, it satisfies:

[0141] l k <l k+1 (k=1.2.…,n-1)

[0142] If the kth hard rock layer has a fracture distance l k If the recalculated breaking distance of the kth hard rock layer is smaller than the breaking distance of the k+1th hard rock layer, then take l k = l k+1This means that the breaking of the kth hard rock layer is controlled by the k+1th hard rock layer, that is, before the k+1th hard rock layer breaks, the kth hard rock layer does not break. Once the k+1th hard rock layer breaks, its load acts on the kth hard rock layer, causing the kth hard rock layer to break.

[0143] Starting from the bottom hard rock layer, we can identify the k <l k+1 Is it established, and when l k > k+1 Recalculate the breaking distance of the kth hard rock layer.

[0144] Calculation of the height of the caving zone: The height of the caving zone can be estimated approximately:

[0145]

[0146] Where: Hcz is the height of the caving zone; h0 is the mining height of the coal seam

[0147] Calculation of fracture zone height:

[0148] Fracture zone height H FZ Empirical calculation formula, when it is soft overburden (uniaxial compressive strength 10 ~ 20MPa):

[0149]

[0150] Where: H F z is the height of the caving zone; h0 is the height of coal seam mining

[0151] Calculation of bending zone height: The bending zone height can be calculated based on the spatial relationship of the strata.

[0152] H BZ =H0-H LZ -H FZ -H CZ +h0

[0153] Where: H0 is the depth of coal seam; H LZ is the height of the loose belt; H CZ H is the height of the caving zone; FZ is the height of the fracture zone; h0 is the thickness of the coal seam

[0154] Loose zone height: The thickness of the loose zone is the thickness of the soil layer above the bedrock layer, which can be obtained according to the geological survey report.

[0155] Calculation of final settlement of goaf

[0156] Calculation of settlement deformation of caving zone:

[0157] The initial settlement deformation curve of the caving zone is an elastic simply supported beam disturbance curve. The width of the curve is the span of the goaf, and the maximum deformation in the middle of the curve is h. CZ , the deformation at the end of the curve is zero. The settlement value in the middle of the interface between the caving zone and the crack zone, that is, the difference between the initial expansion coefficient and the residual expansion coefficient of the caving zone, can be obtained:

[0158] h CZ =H CZ (K s -K f )

[0159] Where: Hcz is the height of the caving zone; h0 is the mining height of the coal seam; K s is the rock expansion coefficient; h CZ K is the maximum value of the collapse settlement in the middle of the interface between the caving zone and the fracture zone; s is the initial expansion coefficient; K f is the residual expansion coefficient;

[0160] Calculation of Fracture Zone Settlement and Deformation

[0161] The horizontal range of the fracture zone, the height of the interface between the caving zone and the fracture zone is H zi =H cz :

[0162]

[0163]

[0164]

[0165]

[0166]

[0167] Where: l CZ is the lateral impact range of the lower part of the fracture zone; l FZ is the lateral influence range of the upper part of the fracture zone; l0 is the lateral size of the coal seam working face; α m is the internal friction angle of the m rock layer; q is the load transferred from the upper rock layer to the fracture zone; It is the comprehensive fracture angle of the rock formation in the fracture zone; is the comprehensive internal friction angle of the rock formation in the fracture zone; is the average elastic modulus of the rock formation in the fracture zone; is the average tensile strength of the rock formation in the fracture zone; is the average bulk density of the fracture zone rock layer; α i is the internal friction angle of each rock layer in the fracture zone; i h is the density of each rock layer for the load transferred from the bending zone to the fracture zone; iThe thickness of each rock layer for the load transferred from the bending zone to the fracture zone; E i is the elastic modulus of each rock layer that transfers load from the bending zone to the fracture zone; n is the number of each rock layer that transfers load from the bending zone to the fracture zone; is the number of each rock layer in the fracture zone;

[0168] According to the Peck formula, the deformation curve of the fracture zone is described according to the Gaussian curve distribution:

[0169]

[0170] Where: w FZ (x,z) is the settlement deformation curve of the fracture zone, where x is the horizontal distance from any settlement point in the fracture zone to the settlement center, and z is the vertical distance from any settlement point in the fracture zone to the settlement center; s max0 is the maximum value of the deformation curve at the interface between the caving zone and the fracture zone; i(z) is the width coefficient of the deformation curve at the interface between the caving zone and the fracture zone, i.e., the horizontal distance from the center point of the deformation curve with the maximum settlement value to its inflection point;

[0171] According to the initial settlement and the lateral range of the fracture zone, we can get:

[0172] s max0 =h CZ

[0173]

[0174] The deformation curve of the fracture zone can be expressed as:

[0175]

[0176] Calculation of Settlement Deformation of Bending Strip

[0177] The overlying rock layer of the bending zone can be regarded as elastic continuous deformation, the rock layer is a transversely isotropic material, and a single rock layer can be regarded as a plate-like structure. The bending zone conforms to the infinitely long transversely isotropic layered elastic deformation characteristics, and its deformation curve is calculated using the Winkler elastic foundation beam theory. Its calculation model can be regarded as a beam model with both ends constrained under the load transferred by the upper rock layer. In actual situations, the two ends of the beam are clamped by the underlying and overlying rock layers, and there is a certain degree of movement and rotation at the end of the beam corresponding to the extension line of the goaf range. The range of the settlement deformation curve is calculated according to the elastic foundation beam calculation disturbance deformation range.

[0178] Along the longitudinal section, the i-th rock layer overlying the curved zone of the goaf is regarded as a unit width beam model for the elastic foundation effect of the underlying rock layer and the load transfer effect of the overlying rock layer. BZ,i (x) is the basic unknown, which corresponds to the deformation and settlement equation w BZ,i (x) is:

[0179]

[0180] Where: They are the correlation parameters of transferred load, foundation parameters, flexural stiffness and beam length.

[0181] Calculate the length of each rock layer in the coal wall support influence zone and stress recovery zone as follows: Figure 4 shown.

[0182] At the junction of the coal wall support influence zone and the stress recovery zone, the composite beam Z i The sinking, rotation, bending moment and shear force are all equal, that is:

[0183]

[0184] According to the above three sets of boundary conditions, the values ​​of each parameter can be obtained as follows:

[0185]

[0186]

[0187] The calculation of foundation reaction force is based on Winkler elastic foundation beam theory. The foundation coefficient of the i-th rock layer within the support range of the bending zone is:

[0188]

[0189] The foundation coefficient of the i-th rock layer within the goaf of the curved belt is:

[0190]

[0191] Where: h n is the thickness of the nth layer; E n is the elastic modulus of the nth layer; a and b are the number of rock layers in the caving zone and the fracture zone respectively; k CZ is the equivalent foundation coefficient of the caving zone, which can be expressed as s according to the assumption that the maximum settlement at the interface between the fracture zone and the bending zone is continuous. max0 =h CZ To perform inverse calculation.

[0192] Calculation of loose belt settlement deformation

[0193] The loose zone conforms to the deformation characteristics of soil bulk medium. Using random medium theory, according to Litvinishen's derivation, it satisfies the second-order parabolic partial differential equation:

[0194]

[0195] Where: x is the horizontal distance from the center line of the deformation curve sedimentation tank; z is the vertical distance upward along the center line of the deformation curve sedimentation tank; w(x,z) is the deformation of any point in the granular medium; A(z), B(z), and N(z) are the characteristic parameters of the deformation and diffusion of the granular medium, A(z) reflects the horizontal deviation degree of the granular deformation and diffusion, B(z) reflects the horizontal range of the granular deformation and diffusion, and N(z) reflects the volume change of the granular medium during the granular deformation and diffusion;

[0196] For layered homogeneous bulk media, the three characteristic parameters A(z), B(z), and N(z) will be constants that do not change with the z value, and the horizontal deviation of bulk deformation diffusion does not exist, that is, A(z) = 0, B(z) = B, and N(z) = N. The deformation diffusion equation in bulk media is:

[0197]

[0198] Using Fourier transform, the simultaneous equations can be solved as:

[0199]

[0200] When w(x,z) is in the form of a Gaussian distribution function, the maximum settlement s at the top of the deformation curve at a certain depth z in the bulk medium max (z) and the deformation curve width coefficient i(z) are:

[0201]

[0202]

[0203] Where s BZ,max is the maximum settlement value at the top of the initial deformation curve; i0 is the width coefficient of the initial deformation curve.

[0204] InSAR monitoring of surface deformation in goaf areas

[0205] InSAR Surface Monitoring

[0206] Using SARscape software and the two interference superposition methods of PS and SBAS, the ground subsidence time series of the study area was monitored and corrected, and the ground subsidence time series of the goaf was monitored and corrected. The average deformation rate, subsidence rate curve and subsidence time series diagram of the goaf in the active period were obtained.

[0207] Stages of mining deformation

[0208] Calculation of the duration of active period in goaf and the maximum ground subsidence velocity

[0209] According to the "Three-Down" standard formula, the active deformation period of the Shanxi Carboniferous-Permian coal mining area is

[0210] H0≤300m, T=(2.0~2.3)H0

[0211] 300m <H0<500m,T=(1.3~2.0)H0

[0212] H0≥500m, T=(1.0~1.3)H0

[0213] The maximum surface sinking velocity is estimated by the following formula:

[0214]

[0215] Where V max is the maximum surface sinking velocity, K is the sinking coefficient, C is the working face advancement velocity, and H0 is the average mining depth

[0216] The InSAR surface monitoring indicates the time point t1 when the surface of the goaf monitoring area begins to settle and deform; the InSAR surface deformation rate is less than the minimum deformation rate time point t of the "Three Below" specification (the "Three Below" specification is the "Specifications for the Installation of Coal Pillars and Compressed Coal Mining in Buildings, Water Bodies, Railways and Main Wells and Lanes"). 3， According to the calculated maximum surface deformation rate and the deformation time series diagram obtained by InSAR surface monitoring, the maximum time point t2 of the surface settlement rate is obtained, and the active mining period is divided into the active acceleration period of mining deformation and the decay period of mining deformation.

[0217] Settlement deformation of each rock layer when the surface settlement rate is the largest

[0218] When the surface subsidence rate reaches the maximum, the caving zone has settled completely, and the fracture zone, bending zone and loose zone are in the changing stage. The settlement value is calculated in the order of loose zone, bending zone, fracture zone and caving zone from top to bottom.

[0219] Loose zone settlement inversion:

[0220] The time when the maximum surface settlement rate occurs and the surface settlement value at that time, that is, the settlement value at the top of the loose zone when the surface has the maximum settlement rate, are determined through the maximum surface settlement rate and the surface settlement rate time series diagram.

[0221] Substitute the monitoring results of SBAS-InSAR as the settlement boundary of the top of the loose zone into the following formula:

[0222]

[0223] The bottom settlement value of the loose belt can be obtained

[0224] Inversion of flexural zone subsidence

[0225] The bottom settlement of the loose zone obtained by inversion is used as the settlement boundary of the top of the bending zone. The overlying rock layer of the bending zone can be regarded as elastic continuous deformation. The bending zone conforms to the infinitely long transversely isotropic layered elastic deformation characteristics. Its calculation model can be regarded as a beam model with two ends constrained under the load transferred by the upper rock layer. Since the parameters of the bending zone beam model are completely time-invariant with the final deformation, they can be brought into the following calculation formula to obtain the settlement deformation of each beam in the bending zone.

[0226]

[0227] Fracture zone settlement inversion:

[0228] The bending deformation of the fracture zone is calculated by taking the bottom settlement of the bending zone as the settlement boundary of the top of the fracture zone. Substitute the deformation and settlement of the top of the fracture zone into the following formula:

[0229]

[0230] The deformation and subsidence at the bottom of the fracture zone can be obtained.

[0231] The caving zone has completely settled when the surface subsidence rate reaches the maximum, and the deformation and settlement amount is consistent with that when it is completely settled.

[0232] w cz =w vmax .

[0233] Where: W cz is the final settlement value of the caving zone; w vmax It is the deformation and settlement value of the caving zone when the surface subsidence rate reaches the maximum.

[0234] Inversion of settlement in the initial period of mining

[0235] Based on the sub-meter deformation monitoring accuracy of InSAR technology, the surface settlement of 1 mm is defined as the final value of the surface deformation in this stage, and the settlement and deformation characteristics of the deep rock strata are inverted.

[0236] Loose zone inversion: Surface settlement w(0,z) = 1mm, substituting into the following formula, we can get the settlement w at the bottom of the loose zone s .

[0237]

[0238] Inversion of bending zone settlement; the bottom of the loose zone is close to the top of the bending zone, and the settlement value at the top of the bending zone is equal to the settlement value w at the bottom of the loose zone s The bending zone can be regarded as elastic continuous deformation when settlement occurs, and its calculation model can be regarded as a beam model with constraints at both ends, and different composite beams in the bending zone deform simultaneously.

[0239] w n梁 =w s

[0240]

[0241] Where: w n梁 is a composite beam with curved top, w t1 w is the final settlement value of the t-th composite beam in the bending zone at this stage; t2 is the settlement of the tth composite beam in the bending zone at the maximum settlement rate.

[0242] Fracture zone settlement inversion: The bottom of the bending zone is close to the top of the fracture zone. FZ(0，z) =w 1梁 ; The bending deformation of the fracture zone is calculated by taking the bottom settlement of the bending zone as the settlement boundary of the top of the fracture zone. Substituting the deformation and settlement of the top of the fracture zone into the following formula, the deformation and settlement of the bottom of the fracture zone w can be obtained: CZ 0,z).

[0243]

[0244]

[0245]

[0246]

[0247] Where: s max0 is the maximum settlement value of the settlement trough at the bottom of the fracture zone; i (z) is the width coefficient of the fracture zone settlement trough. CZ is the lateral impact range of the lower part of the fracture zone; l FZ is the lateral influence range of the upper part of the fracture zone; l0 is the lateral size of the coal seam working face; α m is the internal friction angle of rock layer m; It is the comprehensive fracture angle of the rock formation in the fracture zone;

[0248] Inversion of settlement of caving zone: After the collapse of rock formations in the caving zone, a crushing and expansion effect will occur, that is, the total volume of the crushed rock formation is larger than the total volume of the original rock. The volume of the goaf multiplied by the rock mass crushing and expansion coefficient is the volume of the caving zone, and the height of the top of the settlement trough at the top of the caving zone can be obtained, which is the settlement of the caving zone.

[0249]

[0250] Where: V0 is the volume of the rock stratum settlement trough at the top of the caving area, N(z) reflects the change of bulk volume during bulk deformation and diffusion, and w0(x) is the settlement curve at the bottom of the fracture zone.

[0251] Estimation of deep underground deformation

[0252] According to the surface settlement at this moment, it is judged that this is the deformation acceleration period or deformation attenuation period, and the judgment is made according to the formula provided in the "Three Lower" specification. The "Three Lower" specification is the "Specifications for the Retention of Coal Pillars and Compressed Coal Mining in Buildings, Water Bodies, Railways and Main Shafts and Lanes"

[0253] The requirement is: during the duration of the movement process, the surface subsidence rate is less than 50mm / month (1.7mm / d) (the ore layer inclination is less than 45°), or less than 30mm / month (the ore layer inclination is greater than 45°). Subsidence inversion during the active acceleration period of mining;

[0254] During the active acceleration period of mining, the deep settlement drives the settlement of the overlying rock layer, and the deformation in the deformation zone is calculated according to the elevation linear interpolation method. The settlement W(z) at any height z inside the rock layer can be calculated by linear interpolation, and the formula is:

[0255]

[0256] Where: z is the distance from the surface to the lower boundary of the rock layer, ranging from 0≤z≤H, W z is the settlement at that point; W z1 is the initial settlement at that point; W z2 is the amount of sedimentation at the point with the maximum sedimentation rate; W t is the surface subsidence; W b It is the amount of surface settlement at the time of maximum surface settlement rate.

[0257] Inversion of settlement during active decay period of mining:

[0258] Active decay period of mining: dominated by the compaction of rock formations, the initial caving zone has completely settled in this stage, and the rock formations gradually reach a stable state from bottom to top. The time for each rock formation to reach a stable state can be approximately expressed as a function F(x). The surface settlement value W is known during the active decay period of mining. 地表 , obtain the time when the sedimentation value occurs through InSAR, and substitute this time into the function F (x) The location partition where the rock layer reaches stability at this moment can be determined. The lower part of this partition has completed settlement and reached the final settlement value, while the upper part is in the compaction consolidation stage and is still undergoing settlement deformation. The linear interpolation method is used for calculation.

[0259] The time it takes for each rock layer to reach a stable state can be approximately expressed as the function F (x)

[0260]

[0261] Where: W cz W is the final settlement value of the caving zone; 地表 is the final surface settlement value, T 终 is the complete settlement time of the overlying rock layer, T vmaxThe time when the maximum surface subsidence rate occurs.

[0262] Specific case implementation 1:

[0263] Geological strata of a coal mine

[0264] The total thickness of the coal-bearing strata is 163.50m, the average total thickness of the coal seams is 26.34m, and the coal content coefficient is 16.11%. The lithological characteristics of the coal mine strata are shown in Table 2.

[0265] Table 2 Coal Mine Strata Lithology Characteristics

[0266]

[0267]

[0268] Final settlement deformation calculation (1) Four-zone stratum division in the goaf

[0269] Overlying rock formation parameters

[0270] According to the comprehensive columnar diagram of the coal mine, the coal seam thickness h0 = 4.95m and the coal seam inclination is 9°

[0271] The formation parameters of the goaf are shown in Table 3.

[0272] Table 3. Strata parameters of goaf area

[0273]

[0274] Key layer position calculation

[0275] The critical layer theory determines that the curved sinking zone is divided into composite beams.

[0276] ① Determine the location of the hard layer in the overburden

[0277] Calculate from the first rock layer in the bending zone upwards layer by layer. When the formula is satisfied, no more calculation is done upwards. The rock layers from the first layer to the mth layer are the composite beam calculation units. From the m+1th layer, search for the next section again according to the above method. As shown in Table 4.

[0278] Table 4 Calculation of hard layer position

[0279]

[0280] ② Calculate the breaking distance

[0281] The above three hard layers are divided into three layers, and the fracture distance of the hard rock layer is calculated separately.

[0282] The breaking distance of the kth hard rock layer is l k It can be calculated that

[0283]

[0284] ③Determine the location of the key layer

[0285] According to calculations, the third layer of overlying rock in the coal seam is the key layer that controls the fourth and fifth layers of overlying rock above it. The third layer deforms in coordination with the fourth and fifth layers of rock, and they have the same curvature.

[0286] Calculation of height of each layer

[0287] According to the above steps, the height of each layer is calculated as shown in Table 5 below.

[0288] Table 5 Height of each layer

[0289]

[0290] The bending zone ranges from 594.36 m, and the distribution of rock layers is shown in Table 6 below.

[0291] Table 6 Distribution of rock layers in the bending zone

[0292]

[0293] Residual expansion coefficient: K f =1.05

[0294] According to the coal seam position and underground relationship, the coal seam inclination angle is 9°

[0295] The settlement value in the middle of the interface between the caving zone and the fracture zone, that is, the difference between the initial expansion coefficient and the residual expansion coefficient of the caving zone, can be obtained:

[0296] h CZ =H CZ (K s -K f )=3.15m

[0297] ② Calculation of settlement and deformation of active late stage fracture zone

[0298] The specific values ​​according to the fracture zone calculation method are shown in Table 7 below

[0299] Table 7 Calculation values ​​of fracture zone

[0300]

[0301] The settlement deformation curve of the fracture zone can be expressed as:

[0302]

[0303] ③ Calculation of settlement and deformation of the active late bending zone

[0304] Calculate the length of each rock layer in the coal wall support influence zone and stress recovery zone as follows: Figure 4 shown.

[0305] The curved sinking zone is divided into 3 beams; the calculation parameter values ​​are shown in Table 8 and Table 9

[0306] Table 8 Goaf calculation parameter values

[0307]

[0308] Table 9 Coal pillar side calculation parameter values

[0309]

[0310] Once the length of the elastic foundation beam, the overlying load and the foundation coefficient are determined, the values ​​of each parameter can be solved and substituted into the settlement curves of various depths in the curved subsidence zone.

[0311] The calculated foundation coefficients are shown in Table 10.

[0312] Table 10 Parameter calculation results

[0313]

[0314] Substituting the maximum settlement value of the midpoint of each beam into the formula, we can obtain that the maximum settlement value of beam No. 1 is 2.984m; the maximum settlement value of beam No. 2 is 1.976m; and the maximum settlement value of beam No. 3 is 0.927m.

[0315] ④ Calculation of settlement and deformation of loose zone at the end of active period

[0316] The relationship between the model parameters B and N and the soil properties, the deformation diffusion effect of hard soil is obvious, the value of B is larger, the soft soil is easily affected by disturbance and volume compression occurs, and the value of N is larger. For parameter B, hard soil is between 1.3 and 3.2m, soft soil is between 0.4 and 1.5m, the compression modulus is greater than 20MPa and the range is 1.29 to 3.4m, and the compression modulus is less than 10MPa and the range is 0.5 to 1.5m. For parameter N, hard soil is between 0.001 and 0.012m -1 The soft soil is between 0.02 and 0.03m -1 In summary, B is 1.3 and N is 0.02.

[0317] The settlement of the bottom of the loose zone is consistent with that of the top of the bending zone, so the bending deformation curve of the loose zone is:

[0318]

[0319] Substituting the top settlement value into the parameters, we can get: w = 0.777618 ≈ 0.78m

[0320] ⑤ Distribution of sedimentation at the end of active period

[0321] According to the calculation results of the "four zones", the curves of the final settlement values ​​of different layers and deep layers are drawn, such as Figure 5 As shown in the curve, the surface collapse of the loose zone is 0.78 meters, which gradually reaches 0.927 meters with the increase of depth; the maximum settlement value of the curved sinking zone changes with the change of the composite beam parameters, and does not change with the increase of depth within the depth range where the composite beam parameters remain unchanged; the maximum settlement value of the fracture zone increases with the increase of depth; the rock mass of the caving zone is fully broken and fills the goaf, and the final settlement reaches 4.9 meters.

[0322] (3) InSAR monitoring of surface deformation in goaf areas

[0323] In order to solve the problem of ground subsidence caused by the mining of No. 2 and No. 5 coal seams in the coal mine, SARscape software and SBAS method were used to monitor and correct the ground subsidence time series in the goaf area, and the average deformation rate and settlement time series diagram of the study area from October 2020 to 2022 were obtained.

[0324] The analysis was mainly based on the SBAS monitoring results. The results showed that there was obvious subsidence in the goaf. The points in the gray area were selected for time series deformation analysis. The analysis results are as follows: Figure 6 According to the settlement data of the goaf, the settlement rate curve of the area is calculated, such as Figure 7 shown.

[0325] (4) Stages of mining deformation

[0326] Calculation of the duration of active period in goaf and the maximum surface subsidence rate

[0327] The deformation period of the active period in the coal mining area is calculated according to the "Three Down" standard formula as follows, and the entire active period is divided into the deformation acceleration period and the attenuation period according to the time of the maximum surface subsidence rate.

[0328] H0≥500m,T=(1.0~1.30)H0=1.15H0=744d

[0329] The maximum surface sinking velocity is estimated by the following formula:

[0330]

[0331] According to the deformation curve of point time series and the settlement rate curve of goaf area, in October 2021, V max When the surface subsidence reaches 0.47 mm / d, the surface subsidence at this time is taken as the surface subsidence value W when the surface subsidence velocity reaches the maximum during the active period. Vmax =32.5mm

[0332] Inversion of overlying strata subsidence during maximum surface subsidence rate

[0333] When the surface subsidence rate reaches the maximum during the active period, the caving zone has completely collapsed and is stable, and the upper rock layers are in the compaction stage and are still in the deformation period; at this time, the surface sinks 0.325m

[0334] Calculation of loose belt settlement:

[0335] The settlement of the loose zone is calculated by taking the surface settlement as the settlement boundary of the top of the loose zone. Substitute it into the above formula, when Z = 8.75m, W = 0.325m. Substituting it into s BZ,max =0.387m

[0336] Calculation of bending zone settlement:

[0337] The settlement of the bottom of the loose zone is used as the settlement of the top of the beam of the bending zone 3 to calculate the settlement boundary of the bending zone. Since the parameters of the bending zone remain unchanged at this time and have been stated in the above calculation, the settlement values ​​of each beam are calculated as shown in Table 11 below.

[0338] Table 11 Settlement values ​​of each beam in the bending zone

[0339]

[0340] Calculation of fracture zone settlement:

[0341] The settlement of the lower part of the bending zone 1 beam is taken as the settlement boundary of the top of the fracture zone. At this time, the deformation diffusion parameter B of the fracture zone soil and the volume change parameter N of the rock and soil body are consistent with the final settlement.

[0342] B=2.0

[0343] N=-0.0026m -1

[0344] Substitute it into the formula to calculate the settlement of the lower part of the fracture zone:

[0345]

[0346] w FZ (x,z)=1.31m

[0347] Subsidence distribution when the surface subsidence rate is the largest during the active period

[0348] According to the calculation results of the "four zones", the change curves of the settlement values ​​at different layers and deep layers when the surface settlement rate is the largest are drawn, such as Figure 8As shown in the curve, the surface collapse of the loose zone is 0.325 meters, which gradually reaches 0.387 meters with the increase of depth; the maximum settlement value of the curved sinking zone changes with the change of the composite beam parameters, and does not change with the increase of depth within the depth range where the composite beam parameters remain unchanged. The 3rd beam of the curved zone reaches 0.387m, the 2nd beam reaches 0.823m, and the 1st beam reaches 1.24m; the maximum settlement value of the fracture zone increases with the increase of depth and reaches 1.31m; the rock mass in the caving zone is fully crushed and fills the goaf, and the final settlement reaches 4.9 meters.

[0349] (5) Estimation of deep underground deformation

[0350] According to the surface settlement at this moment, it is judged that this is the active acceleration period or the late deformation attenuation period. According to the "Three Lower" standards, the judgment is shown in Table 12.

[0351] Table 12 Characteristic quantities corresponding to each period of surface movement

[0352]

[0353] Inversion of settlement during the active acceleration period of mining:

[0354] During the deformation acceleration period, deep settlement drives the settlement of overlying rock layers, and the deformation within the deformation zone is calculated using the elevation linear interpolation method.

[0355] The amount of settlement W at any height z inside the rock layer z It can be calculated by linear interpolation, the formula is:

[0356]

[0357] Where: z is the distance from the surface to the lower boundary of the rock layer, ranging from 0≤z≤H, W z is the settlement at that point; W z1 is the initial settlement at that point; W z2 is the amount of sedimentation at the point with the maximum sedimentation rate; W t is the surface subsidence; W b It is the amount of surface settlement at the time of maximum surface settlement rate.

[0358] Inversion of settlement during active decay period of mining:

[0359] Active decay period of mining: dominated by the compaction of rock formations, the initial caving zone has completely settled in this stage, and the rock formations gradually reach a stable state from bottom to top. The time for each rock formation to reach a stable state can be approximately expressed as a function F(x). The surface settlement value W is known during the active decay period of mining. 地表 , obtain the time when the sedimentation value occurs through InSAR, and substitute this time into the function F (x)The location partition where the rock layer reaches stability at this moment can be determined. The lower part of this partition has completed settlement and reached the final settlement value, while the upper part is in the compaction consolidation stage and is still undergoing settlement deformation. The linear interpolation method is used for calculation.

[0360] The time it takes for each rock layer to reach a stable state can be approximately expressed as the function F (x)

[0361]

[0362] Where: W cz W is the final settlement value of the caving zone; 地表 is the final surface settlement value, T 终 is the complete settlement time of the overlying rock layer, T vmax The time when the maximum surface subsidence rate occurs.

Claims

1. A method for estimating deep underground deformation based on remote sensing monitoring of surface subsidence, characterized in that: The estimation of deep underground deformation includes the four-zone stratum division of the goaf area, the calculation of the final settlement of the goaf area, the InSAR monitoring of the surface deformation of the goaf area, the stages of goaf deformation, and the settlement deformation of each rock layer when the surface settlement rate is the largest; it is carried out in four periods. Initial period of mining: During the period of t0-t1, settlement occurs in the caving zone of the coal mining area and gradually transfers to the surface. The minimum deformation can be monitored by synthetic aperture radar interferometry (InSAR) on the surface. Active acceleration period of mining deformation: During the period t1-t2, the bottom settlement drives the settlement of the upper rock layer, the settlement rate of the overlying rock layer gradually accelerates, and the surface settlement rate gradually increases to the maximum surface settlement rate; Active decay period of mining deformation: t2-t3 period, during which the compaction of rock formations is dominant, the settlement rate of overlying rock formations gradually slows down, and the settlement rate of the surface gradually decreases; Mining deformation decay period: from time point t3 to the end of compaction and consolidation of loose layer soil, the surface deformation rate in this stage is less than the minimum deformation rate that can be monitored on the surface; in; t0: the time point when the initial deformation of the caving zone in coal mining excavation occurs; t1: the time point when the settlement deformation of the surface appears in the synthetic aperture radar interferometry InSAR monitoring; t2: the time point when the maximum settlement rate of the surface appears in the synthetic aperture radar interferometry InSAR monitoring; t3: the surface deformation rate monitored by synthetic aperture radar interferometry InSAR is less than the specification requirements.

2. The method for estimating deep underground deformation based on remote sensing monitoring of surface subsidence according to claim 1, characterized in that: The initial period of mining: based on the sub-meter deformation monitoring accuracy of InSAR technology, the surface settlement of 1 mm is defined as the final value of the surface deformation in this stage, and the settlement deformation characteristics of the deep rock strata are inverted.

3. The method for estimating deep underground deformation based on remote sensing monitoring of surface subsidence according to claim 2, characterized in that: The inversion of the settlement deformation characteristics of deep rock formations includes: Loose zone inversion: Surface settlement w(0,N) = 1mm, substitute the following formula to get the loose zone bottom settlement value w s That is S BZ,max , Where: w(x,z) is the deformation settlement curve of the loose belt; x is the horizontal distance from any settlement point in the loose belt to the settlement center; z is the vertical distance from any settlement point in the loose belt to the settlement center; s BZ,max is the maximum settlement value at the top of the initial deformation curve; i0 is the width coefficient of the initial deformation curve; B is the horizontal range of the bulk deformation diffusion, and N is the bulk volume change coefficient during the bulk deformation diffusion. Inversion of bending zone settlement: The bottom of the loose zone is close to the top of the bending zone. At this time, the settlement value of the top of the bending zone is equal to the settlement value w of the bottom of the loose zone s ; The bending zone is regarded as elastic continuous deformation when settlement occurs, and its calculation model is regarded as a beam model with constraints at both ends. Different composite beams in the bending zone deform simultaneously. In 顶梁 =in s Where: w 顶梁 is the settlement of the composite beam at the top of the bending zone; w s is the bottom settlement value of the loose zone; w t1 w is the final settlement value of the t-th composite beam in the bending zone at this stage; t2 is the settlement of the t-th composite beam in the bending zone at the maximum settlement rate; w 顶梁2 is the settlement of the top composite beam at the maximum settlement rate Fracture zone settlement inversion; the bottom of the bending zone is close to the top of the fracture zone w FZ(0，z) =w 1梁 ; The bending deformation of the fracture zone is calculated by taking the bottom settlement of the bending zone as the settlement boundary of the top of the fracture zone; the deformation and settlement of the top of the fracture zone is substituted into the following formula to obtain the deformation and settlement of the bottom of the fracture zone w CZ (0,z) Where: l CZ is the lateral impact range of the lower part of the fracture zone; l FZ is the lateral impact range of the upper part of the fracture zone; l0 is the lateral size of the coal seam working face; h0 is the coal seam mining height; α m is the internal friction angle of rock layer m; H is the comprehensive fracture angle of the rock layer in the fracture zone; CZ H is the height of the caving zone; FZ is the height of fracture zone development; w FZ (x,z) is the deformation settlement curve of the fracture zone; x is the horizontal distance from any settlement point in the fracture zone to the settlement center, and z is the vertical distance from any settlement point in the fracture zone to the settlement center; s max0 is the maximum settlement value of the settlement trough at the bottom of the fracture zone; i (z) is the width coefficient of the fracture zone settlement trough. Inversion of settlement of caving zone: After the collapse of rock formations in the caving zone, a crushing and expansion effect will occur, that is, the total volume of the crushed rock formation is larger than the total volume of the original rock; the volume of the goaf multiplied by the rock mass crushing and expansion coefficient is the volume of the caving zone, and the height of the top of the settlement trough at the top of the caving zone is the settlement of the caving zone. Where: V0 is the volume of the rock formation settlement trough at the top of the caving zone, N is the coefficient of change of the bulk volume during bulk deformation and diffusion, and w0(x) is the settlement curve at the top of the caving zone.

4. The method for estimating deep underground deformation based on remote sensing monitoring of surface subsidence according to claim 1, characterized in that: The active acceleration period of mining deformation: deep settlement drives the settlement of overlying rock layers. In this stage, the deformation of overlying rock layers undergoes settlement in the same proportion from the initial stage to the final stage. The deformation in the deformation zone is calculated according to the elevation linear interpolation method. The amount of settlement W at any height z inside the rock layer z Calculated by linear interpolation, the formula is: Where: W z is the settlement at any height z inside the rock layer; z is the distance from the surface to the lower boundary of the rock layer, ranging from 0≤z≤H, W z1 is the initial settlement at that point; W z2 is the amount of sedimentation at the point with the maximum sedimentation rate; W t is the surface subsidence; W b It is the amount of surface settlement at the time of maximum surface settlement rate.

5. The method for estimating deep underground deformation based on remote sensing monitoring of surface subsidence according to claim 1, characterized in that: The active decay period of goaf deformation is dominated by the compaction of rock strata. In this stage, the initial caving zone has completely settled, and the rock strata gradually reach a stable state from bottom to top. The time for each rock stratum to reach a stable state is approximately expressed as a function F(x). The surface settlement value W is known during the active decay period of goaf. 地表 , obtain the time when the sedimentation value occurs through InSAR, and substitute this time into the function F (x) Determine the location partition where the rock layer reaches stability at this moment; the lower part of this partition has completed settlement and reached the final settlement value, while the upper part is in the compaction consolidation stage and is still undergoing settlement deformation and is calculated using the linear interpolation method; The time for each rock layer to reach a stable state is approximately expressed as the function F(x) Where: W cz W is the final settlement value of the caving zone; 地表 is the final surface settlement value, T 终 is the complete settlement time of the overlying rock layer, T vmax The time when the maximum surface subsidence rate occurs.

6. The method for estimating deep underground deformation based on remote sensing monitoring of surface subsidence according to claim 1, characterized in that The four-zone stratigraphic division of the goaf includes: Approximate estimation of the height of the caving zone: Where: H CZ is the height of the caving zone; h0 is the height of coal seam mining Fracture zone development height H FZ Empirical calculation formula; When the overburden is medium-hard and the uniaxial compressive strength is 20·40MPa: When the overburden is weak and the uniaxial compressive strength is 10-20MPa: Where: H FZ is the height of fracture zone development; h0 is the height of coal seam mining; Loose belt height H LZ is the thickness of the soil layer above the bedrock layer, which can be obtained according to the geological survey report; Height of bending zone H BZ The calculation can be done by: H BZ =H0-H LZ -H FZ -H CZ +h0 Where: H BZ is the height of the bending zone; H0 is the depth of coal seam; H CZ H is the height of the caving zone; FZ H is the height of fracture zone development; LZ Loose zone height; h0 is the coal seam mining height.

7. The method for estimating deep underground deformation based on remote sensing monitoring of surface subsidence according to claim 1, characterized in that The calculation of the final settlement of the goaf includes: Calculation of settlement of caving zone: The settlement value in the middle of the interface between the caving zone and the fracture zone, that is, the difference between the initial expansion coefficient and the residual expansion coefficient of the caving zone, can be obtained: h CZ =H CZ (K s -K f ) Where: h CZ H is the maximum value of collapse settlement in the middle of the interface between the caving zone and the fracture zone; CZ K is the height of the caving zone; s is the initial expansion coefficient; K f is the residual expansion coefficient; Calculation of fracture zone settlement: The horizontal range of the fracture zone, the height of the interface between the caving zone and the fracture zone is H zi =H cz : Where: l CZ is the lateral impact range of the lower part of the fracture zone; l FZ is the lateral impact range of the upper part of the fracture zone; l0 is the lateral size of the coal seam working face; h0 is the coal seam mining height; α m is the internal friction angle of rock layer m; Comprehensive fracture angle of rock formation in fracture zone; H CZ H is the height of the caving zone; FZ The height of the fracture zone development. According to the Peck formula, the deformation curve of the fracture zone is described according to the Gaussian curve distribution: s max0 =h CZ Where: h CZ is the maximum value of collapse settlement in the middle of the interface between the caving zone and the fracture zone; s max0 is the maximum value of the deformation curve at the interface between the caving zone and the fracture zone; w FZ(X,Z) is the settlement deformation curve of the fracture zone, where x is the horizontal distance from any settlement point in the fracture zone to the settlement center, and z is the vertical distance from any settlement point in the fracture zone to the settlement center; i(z) is the width coefficient of the deformation curve at the interface between the caving zone and the fracture zone, i.e., the horizontal distance from the center point of the deformation curve with the maximum settlement value to its inflection point; l CZ is the lateral impact range of the lower part of the fracture zone; l FZ is the lateral influence range of the upper part of the fracture zone; α m is the internal friction angle of rock layer m; Comprehensive fracture angle of rock strata in fracture zone. Calculation of bending zone settlement: Along the longitudinal section, the i-th rock layer overlying the curved zone of the goaf is regarded as a unit width beam model, and the deformation function w of the i-th rock layer is BZ,i (x) is the basic unknown, which corresponds to the deformation and settlement equation w BZ,i (x) is: Where: w BZ,i (x) is the rock deformation and settlement equation, E BZ,i is the elastic modulus of the i-th rock layer in the bending zone; I BZ,i is the section moment of inertia of the ith rock layer in the bending zone; and are the loads transferred by the overlying strata of the ith stratum in the bending zone in the supporting section and the goaf, respectively; and are the foundation coefficients of the i-th rock layer in the bending zone in the supporting section and the goaf area respectively; To transfer loads; is the foundation parameter; Flexural rigidity; is the correlation parameter of beam length; At the junction of the coal wall support influence zone and the stress recovery zone, the composite beam Z i The sinking, rotation angle, bending moment and shear force are all equal. According to the above three groups of conditions, the values ​​of each parameter can be obtained as follows: Where: To transfer loads; is the foundation parameter; Flexural rigidity; is the correlation parameter of beam length; is the length of the composite beam in the coal wall support influence zone, is the stress recovery distance of coal mine goaf; and are the loads transferred by the overlying strata of the ith stratum in the bending zone in the supporting section and the goaf, respectively; and are the foundation coefficients of the i-th rock layer in the bending zone in the supporting section and the goaf area respectively. Loose belt settlement calculation: The loose zone conforms to the deformation characteristics of soil bulk medium. Using random medium theory, according to Litvinishen's derivation, it satisfies the second-order parabolic partial differential equation. For layered homogeneous bulk medium, the three characteristic parameters A(z), B(z), and N(z) will be constants that do not change with the z value, and the horizontal deviation of bulk deformation diffusion does not exist, that is, A(z) = 0, B(z) = B, N(z) = N; the deformation diffusion equation in bulk medium is: Wherein: w(x,z) is the deformation of any point in the bulk medium; x is the horizontal distance from the center line of the deformation curve sedimentation tank; z is the vertical distance upward along the center line of the deformation curve sedimentation tank; A(z), B(z), and N(z) are the characteristic parameters of the deformation and diffusion of the bulk medium, respectively. A(z) reflects the horizontal deviation degree of the bulk deformation and diffusion, B(z) reflects the horizontal range of the bulk deformation and diffusion, and N(z) reflects the bulk volume change during the bulk deformation and diffusion. Using Fourier transform, the simultaneous equations can be solved as: Where: s BZ,max is the maximum settlement value at the top of the initial deformation curve; i0 is the width coefficient of the initial deformation curve.

8. The method for estimating deep underground deformation based on remote sensing monitoring of surface subsidence according to claim 1, characterized in that The InSAR monitoring of surface deformation in goaf areas includes: Using SARscape software and the interference superposition methods of PS-InSAR and SBAS-InSAR, the ground subsidence time series of the study area was monitored and corrected, and the ground subsidence time series of the goaf was monitored and corrected, and the time series diagram of the subsidence rate of the goaf in the active period was obtained.

9. The method for estimating deep underground deformation based on remote sensing monitoring of surface subsidence according to claim 1, characterized in that The mining deformation stages include: The duration of active period in goaf and the maximum surface Sinking speed calculate Duration of active period of goaf: Y=2.5H0 Where: T is the total movement duration, H0 is the average mining depth The maximum surface sinking velocity is estimated by the following formula: Where V max is the maximum surface sinking velocity, K is the sinking coefficient, C is the working face advancement velocity, H0 is the average mining depth, W max is the maximum surface subsidence value; The time when the maximum surface subsidence rate occurs is obtained from the time series diagram of the subsidence rate in the goaf area obtained by InSAR monitoring, and the goaf active period is divided into the goaf active acceleration period and the goaf active decay period based on this time.

10. The method for estimating deep underground deformation based on remote sensing monitoring of surface subsidence according to claim 1, characterized in that When the surface settlement rate is the maximum, the settlement deformation of each rock layer includes: When the surface subsidence rate reaches the maximum, the caving zone has completely settled. The subsidence values ​​of the overlying layers are calculated from top to bottom. Loose zone settlement inversion: The time when the maximum surface settlement rate occurs and the surface settlement value at that time, i.e., the settlement value at the top of the loose zone when the surface has the maximum settlement rate, are determined through the maximum surface settlement rate and the surface settlement rate time series diagram; The monitoring results of SBAS-InSAR are used as the settlement boundary of the top of the loose zone and substituted into the following formula to obtain the settlement value of the bottom of the loose zone; Where: w(x,z) is the deformation settlement curve of the loose belt; x is the horizontal distance from any settlement point in the loose belt to the settlement center; z is the vertical distance from any settlement point in the loose belt to the settlement center; s BZ,max is the maximum settlement value at the top of the initial deformation curve; i0 is the width coefficient of the initial deformation curve; B is the horizontal range of the bulk deformation diffusion, and N is the bulk volume change coefficient during the bulk deformation diffusion. Curved Zone Inversion The bottom settlement of the loose zone obtained by inversion is taken as the settlement boundary of the top of the bending zone. The overlying rock layer of the bending zone is regarded as elastic continuous deformation. The bending zone conforms to the infinitely long transversely isotropic layered elastic deformation characteristics. Its calculation model is regarded as a beam model with two ends constrained under the load transferred from the upper rock layer. Since the parameters of the bending zone beam model are completely invariant with the final deformation, they are substituted into the following calculation formula to obtain the settlement deformation of each beam in the bending zone: Where: w BZ,i (x) is the rock deformation and settlement equation, E BZ,i is the elastic modulus of the i-th rock layer in the bending zone; I BZ,i is the section moment of inertia of the ith rock layer in the bending zone; and are the loads transferred by the overlying strata of the ith stratum in the bending zone in the supporting section and the goaf, respectively; and are the foundation coefficients of the i-th rock layer in the bending zone in the supporting section and the goaf area respectively; To transfer loads; is the foundation parameter; Flexural rigidity; is the dependency parameter of the beam length. Fracture zone inversion: The bending deformation of the fracture zone is calculated by taking the bottom settlement of the bending zone as the settlement boundary of the top of the fracture zone, and substituting the deformation and settlement of the top of the fracture zone into the following formula: Where: w FZ (x,z) is the deformation settlement curve of the fracture zone; x is the horizontal distance from any settlement point in the fracture zone to the settlement center, and z is the vertical distance from any settlement point in the fracture zone to the settlement center; s max0 is the maximum settlement value of the settlement trough at the bottom of the fracture zone; i (z) is the width coefficient of the fracture zone settlement trough; l FZ It is the lateral influence range of the upper part of the fracture zone. Obtain the deformation and subsidence of the bottom of the fracture zone; The caving zone has completely settled when the surface subsidence rate reaches the maximum, and the deformation and subsidence amount is consistent with that when it is completely settled. IN cz =in vmax 。 Where: W cz is the final settlement value of the caving zone; w vmax It is the deformation and settlement value of the caving zone when the surface subsidence rate reaches the maximum.

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