Method for predicting vault collapse in near-horizontal, thin-bedded formations

Abstract

The embodiment of the present application provides a near-horizontal thin-layered stratum underground cavern vault collapse prediction method, a mechanics model is constructed based on an elastic thin plate theory, the length a of a stable layer rock plate and the critical stress sigma of a stable layer rock plate boundary are calculated through collected data crvx , and the stable layer height H is finally determined; a mechanics model is constructed based on a cantilever beam theory, the vertical force borne by each layer of rock plate in a collapse layer from an overlying rock mass and the temporary load when the fracture starts to occur are calculated through the thickness of each layer of rock plate in the collapse layer; the fracture length is calculated based on the vertical force borne by each layer of rock plate in the collapse layer from the overlying rock mass and the critical load when the fracture starts to occur; and the collapse amount is calculated through the fracture length and the stable layer height H. The present application provides a basis for determining the support control parameters of the near-horizontal layered stratum underground cavern, and ensures the stability of the surrounding rock of the underground cavern.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of underground cavern stability prediction, and particularly relates to a near-horizontal thin-bedded stratum underground cavern vault collapse prediction method. BACKGROUND

[0002] Reasonable prediction of the collapse range (collapse amount) of the vault during underground cavern excavation can guide engineers to reasonably design the support structure, including selecting appropriate anchor rod length and model, determining the spacing and arrangement of anchor rods, and the model and installation spacing of steel arches, so as to optimize the design scheme, avoid excessive support or insufficient support, and realize an economic, efficient and safe construction process.

[0003] In the prior art, the methods of theoretical analysis, numerical simulation, model test, case analysis or probability assessment are generally used for collapse prediction. However, whether through theoretical analysis, numerical simulation, model test, case analysis or probability assessment, most of them focus on the collapse arch analysis of underground cavern engineering under the condition of homogeneous rock mass or thick-bedded rock mass, and do not give full attention and consideration to the thin-bedded structure characteristics and rock mass mechanical anisotropy of near-horizontal thin-bedded rock mass.

[0004] Compared with other rock masses, the near-horizontal thin-bedded rock mass is more prone to shear slip along the bedding plane in the collapse mechanism; the collapse range is usually limited to the thickness of the rock stratum and distributed along the bedding plane; the collapse characteristics are characterized by interlayer fragmentation and local breakage; and the thin-bedded rock mass is more prone to cause safety problems in construction due to poor stability. The deficiencies and defects of the prior art make the existing collapse arch prediction method difficult to accurately reflect the actual situation when applied to near-horizontal thin-bedded underground caverns, and the accuracy and reliability of the prediction results are greatly discounted. Therefore, there is an urgent need for a prediction method that can reasonably predict the vault collapse of near-horizontal thin-bedded underground caverns while considering the structure characteristics of layered rock mass. SUMMARY

[0005] The present application provides a near-horizontal thin-bedded stratum underground cavern vault collapse prediction method to solve the technical problem that the prior art is difficult to predict the vault collapse of near-horizontal thin-bedded underground caverns while considering the structure characteristics of layered rock mass.

[0006] To solve the above technical problems, the present application provides a near-horizontal thin-bedded stratum underground cavern vault collapse prediction method, comprising the following steps:

[0007] Step S1: Collecting the tensile strength σ t , the average layer thickness t of the rock plate in the stable layer, the Poisson's ratio μ, the rock bedding plane cohesion q t , the rock elastic modulus E, the cavern excavation radius r, the uniaxial compressive strength σ ci of the rock, the rock bulk density γ, the geological strength index GSI, and the constant m of the intact rocki and rock mass disturbance factor D';

[0008] Step S2: based on the elastic thin plate theory, a mechanical model is constructed, and the length a of the stable layer rock plate and the critical stress σ of the stable layer rock plate boundary are calculated based on the data collected in step S1 crvx , and finally the stable layer height H is determined;

[0009] Step S3: based on the cantilever beam theory, a mechanical model is constructed, and the vertical force borne by each layer of rock plate in the collapse layer and the temporary load when the fracture begins to occur are calculated based on the thickness of each layer of rock plate in the collapse layer;

[0010] Step S4: based on the vertical force borne by each layer of rock plate in the collapse layer and the critical load when the fracture begins to occur, the fracture length is calculated; and the collapse amount is calculated by the fracture length and the stable layer height H.

[0011] Preferably, the expression for calculating the length a of the stable layer rock plate in step S2 is:

[0012]

[0013] Preferably, the expression for calculating the critical stress σ of the stable layer rock plate boundary in step S2 is: crvx

[0014]

[0015] In the formula, σ cmax represents the triaxial compressive strength of the rock.

[0016] Preferably, the stable layer height H in step S2 is solved by the following two formulas:

[0017]

[0018] In the formula, σ ci represents the compressive strength of the rock; m b , s and a0 represent rock material constants; θ represents the angle between the critical stable layer boundary vector and the horizontal direction; σ r and σ θ respectively represent the radial stress and the tangential stress at a distance R from the center of the tunnel.

[0019] Preferably, the expression for calculating the vertical force borne by each layer of rock plate in the collapse layer in step S3 is:

[0020]

[0021] In the formula, q i ​represents the vertical force that the i-th rock slab in the collapse layer bears from the overlying rock mass; γ represents the rock mass gravity; w represents the rock slab width in the collapse layer; t i represents the thickness of the i-th rock slab in the collapse layer.

[0022] Preferably, the method for calculating the temporary load in step S3 comprises:

[0023] Step S31: analyzing the collapse law of the rock slab in the collapse layer by using a cantilever beam to obtain a mechanical model;

[0024] Step S32: based on the mechanical model, obtaining a buckling curve equation of the cantilever beam under uniform load from material mechanics;

[0025] Step S33: based on the buckling curve equation, obtaining a cross-sectional normal stress equation at the crack of the i-th layer in the collapse layer;

[0026] Step S34: after decomposing the cross-sectional normal stress equation, obtaining a critical load at which the fracture begins to occur.

[0027] Preferably, the expression of the buckling curve equation in step S32 is:

[0028]

[0029] In the formula, X represents the coordinate of the cantilever beam axis, i.e. the distance from the fixed end; Y represents the deflection at this point, i.e. the vertical distance from the original beam axis; E represents the rock elastic modulus; I represents the cross-sectional moment of inertia of the rock slab in the collapse layer; and l represents the length of the rock slab in the collapse layer.

[0030] Preferably, the expression of the cross-sectional normal stress σ xi at the crack of the i-th layer in the collapse layer in step S33 is:

[0031]

[0032] In the formula, X i and Y i represent the position coordinates of the crack of the i-th layer in the collapse layer; q i represents the vertical force that the i-th rock slab in the collapse layer bears from the overlying rock mass; l i represents the length of the i-th rock slab in the collapse layer; and t i represents the thickness of the i-th rock slab in the collapse layer.

[0033] Preferably, the expression of the critical load q k in step S34 is:

[0034]

[0035] Wherein, t represents the average layer thickness of the rock slab thickness; k represents the number of layers where the fracture begins to occur; l k represents the length of the kth layer of rock slab within the collapse layer; σ t represents the tensile strength of the rock.

[0036] Preferably, the step S4 comprises:

[0037] Step S41: when the current rock slab bears the vertical force transmitted from the overlying rock mass is less than the critical load, the fracture length is 0; when the current rock slab bears the vertical force transmitted from the overlying rock mass is not less than the critical load, the fracture length of the current rock slab is calculated by the following formula: i :

[0038] △ i =(1-λ i )l i =0.54l i ;

[0039] Wherein, λ i represents the proportion coefficient of the length of the unbroken part in the ith layer within the collapse layer to the length of the layer of rock slab;

[0040] Step S42: the collapse amount Q is calculated by the following formula:

[0041]

[0042] Wherein, γ represents the specific weight of the rock mass; n represents the number of rock slabs within the collapse layer.

[0043] The beneficial effects of the present application at least include: reasonably predicting the collapse of the underground cavern vault of the near-horizontal thin-layered stratum, the structural characteristics of the layered rock mass need to be considered, the present application respectively generalizes the layered rock mass into a rock beam mechanical model or a rock slab mechanical model; due to the relatively thin layer thickness of the thin-layered rock mass and the weak interlayer bonding force, the deformation and failure mode of the thin-layered rock mass under the stress state is significantly different from that of the thick-layered rock mass; for the thin-layered rock mass, the bending and shearing resistance is often weak, under the load of the vault, the thin layer is more likely to move, separate and even slide between layers, thereby increasing the risk of vault collapse, and the multi-factor consideration ensures the accuracy and reliability of the prediction of the present application. The present application provides a basis for determining the support control parameters of the underground cavern of the near-horizontal layered stratum, reduces unnecessary conservative design and excessive support, avoids collapse accidents, reduces the repair and rework costs caused by collapse, and ensures the stability of the surrounding rock of the underground cavern. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 The figure is a method flowchart of the embodiment of the present application;

[0045] Figure 2 The figure is a theoretical generalization model schematic diagram of the near-horizontal thin-layered rock mass of the embodiment of the present application;

[0046] Figure 3 A mechanical model diagram of a four-side simply supported rectangular roof of an embodiment of the present application constructed based on the thin plate theory;

[0047] Figure 4 A schematic diagram of the geometric relationship of a near-horizontal thin-layer rock mass of an embodiment of the present application;

[0048] Figure 5 A mechanical model diagram of an embodiment of the present application for analyzing the rock plate collapse law in the collapse layer through a cantilever beam;

[0049] Figure 6 A collapse diagram of an embodiment of the present application;

[0050] Figure 7 A BBM model diagram constructed by an embodiment of the present application;

[0051] Figure 8 A numerical simulation result diagram of an embodiment of the present application. DETAILED DESCRIPTION

[0052] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0053] To facilitate the description of the embodiments of the present application, the symbols appearing in the embodiments are explained as follows:

[0054] q t : the adhesion force of the upper rock mass layer in the vertical rock plate direction;

[0055] q x : the longitudinal pressure of the rock plate in the X direction;

[0056] q y : the longitudinal pressure of the rock plate in the Y direction;

[0057] q xy : the shear stress in the rock plate;

[0058] α: the longitudinal pressure ratio of the rock plate in the X and Y directions;

[0059] a: the length of the rock plate;

[0060] b: the width of the rock plate;

[0061] t: the thickness of the rock plate (average layer thickness);

[0062] E: Elastic modulus of rock;

[0063] μ: Poisson's ratio of rock;

[0064] D: Flexural stiffness of rock slab;

[0065] w: Deflection equation of rock slab;

[0066] A: Maximum deflection of rock slab;

[0067] M x , M y : Internal force bending moment in X, Y directions of rock slab;

[0068] σ x , σ y : Stress in X, Y directions of rock slab;

[0069] σ crvx : Minimum critical stress on the boundary of rock slab;

[0070] R: Distance from the center of the tunnel;

[0071] r: Excavation radius of cavern;

[0072] θ: Angle between the boundary vector of the critical stable layer and the horizontal direction;

[0073] H: Limiting height of the critical stable layer;

[0074] σ r , σ θ : Radial stress and tangential stress at a distance R from the center of the tunnel;

[0075] GSI: Geological strength index;

[0076] m i : Constant of intact rock;

[0077] m b , s, a0: Rock material constants;

[0078] D': Disturbance factor of rock mass;

[0079] σ ci : Uniaxial compressive strength of rock;

[0080] σ cmax : Triaxial compressive strength of rock;

[0081] σ t : Tensile strength of rock;

[0082] σ vx : Average stress per unit thickness in the x direction of the rock slab;

[0083] σ hy: average stress in unit thickness of rock plate in y direction;

[0084] q: vertical force borne by rock plate in collapse layer from overlying rock mass;

[0085] l: length of rock plate in collapse layer;

[0086] I: moment of inertia of cross section of rock plate in collapse layer;

[0087] σ xi : normal stress of cross section at crack of i-th layer in collapse layer;

[0088] I zi : moment of inertia of cross section of i-th layer of rock plate in collapse layer;

[0089] t i : thickness of i-th layer of rock plate in collapse layer;

[0090] l i : length of i-th layer of rock plate in collapse layer;

[0091] q i : vertical force borne by i-th layer of rock plate in collapse layer from overlying rock mass;

[0092] w: width of rock plate in collapse layer;

[0093] γ: specific weight of rock mass;

[0094] q k : critical load at which fracture begins to occur in collapse layer;

[0095] △ i : fracture length of i-th layer of rock plate in collapse layer;

[0096] Q: collapse amount in collapse layer;

[0097] Equivalent cohesion of rock mass;

[0098] Equivalent friction angle of rock mass and cohesion

[0099] σ 3max : maximum value of minimum principal stress;

[0100] σ cm : compressive strength of rock mass;

[0101] L: depth of underground cavern.

[0102] As Figure 1 shown, the embodiment of the present application provides a method for predicting collapse of crown of underground cavern in near-horizontal thin-bedded stratum.

[0103] Layered rock mass has significant structural effect, and after the excavation of the cavern, the structural effect of the rock mass is activated, and the rock mass changes from a nearly continuous medium to a plate-crack medium, forming a typical rock plate structure, whose mechanical action characteristics follow the deformation and failure rules of a typical "beam" or "plate".

[0104] In the initial stage of the excavation of the cavern, the boundaries of the rock stratum are embedded in the rock stratum, and the movement and rotational deformation are both limited, so the rock stratum can be regarded as a rock plate structure with four edges being fixedly supported. With the continuous structural bending deformation of the rock stratum at the top and bottom of the cavern to the initial free surface, the maximum bending moment and the maximum shear force in the rock plate are distributed at the boundary of the rock plate, so the rock plate always first appears fracture failure at the upper part of the fixedly supported edges of the four edges, and then changes to a simply supported edge constraint, and then the internal fracture or instability of the rock plate. Therefore, the boundary conditions of the rock plate gradually change with the evolution of the surrounding rock over time, and the rock plate changes from a four-edge fixedly supported rock plate to a four-edge simply supported rock plate structure. In this process, a critical stable layer appears, and the rock plate changes from a planar stable equilibrium state to a curved surface stable equilibrium state with slight deflection, and below the layer, the layered rock plate collapses. Therefore, a theoretical generalization model is established as shown in Figure 2

[0105] The rock plate mechanical model based on the thin plate theory is as follows.

[0106] 1) The critical stable layer is a four-edge simply supported rock plate structure;

[0107] 2) Small deformation, elastic body analysis, and thin plate small deflection bending theory calculation are selected;

[0108] 3) When the thin plate changes from a planar stable equilibrium state to a curved surface stable equilibrium state with slight deflection, the cross section remains planar;

[0109] 4) The vertical rock plate direction is subjected to the vertical bonding force q t of the upper rock mass layer;

[0110] 5) The rock plate is subjected to horizontal stress, and the longitudinal pressure of the rock plate in the X direction is q x , and the longitudinal pressure in the Y direction is q y , and it is assumed that q y = αq x . According to the plate length a, the width b, the plate thickness t, the elastic modulus E, the Poisson's ratio μ, the bending stiffness D, the deflection w, the internal force bending moment M x , M y , the roof stress σ x , and σ y , a four-edge simply supported rectangular roof mechanical model is established as shown in Figure 3

[0111] ​​The limit stress equation is constructed as follows.

[0112] The deflection distribution and the slope of deflection of the rock plate at the four peripheral boundaries are both zero, so the corresponding boundary conditions are:

[0113]

[0114] The deflection surface equation of the rock plate under the action of only horizontal stress is:

[0115]

[0116] In the formula, x and y represent the horizontal and vertical coordinate values of different positions of the rock plate.

[0117] For the rock plate in the critical stable layer under the action of horizontal stress, there is a limit state, which makes the rock plate in the limit equilibrium state under the plane state, at this time the shear stress is zero, and formula (2) becomes:

[0118]

[0119] Taking the Fourier series as the deflection surface equation of the critical state plate, it meets the boundary conditions of the four-side simply supported plate:

[0120]

[0121] After arrangement, we have:

[0122]

[0123] In the formula, the coefficient A mn cannot be all zero, so we have:

[0124]

[0125] q x = σ vx t;

[0126] q y = σ hy t;

[0127] q y = αq x ;

[0128] After arrangement, we have:

[0129]

[0130] Obviously, when m = n = 1, there is the minimum critical stress:

[0131]

[0132] At this time, the deflection surface equation is:

[0133]

[0134] where w is the first order deflection function of the rock plate; A is a constant to be determined.

[0135] For a four-side simply supported thin plate subjected to vertical force in the vertical direction of the rock plate, the deflection surface equation (6) of the four-side simply supported rock plate boundary condition should also be satisfied.

[0136] According to the straight normal assumption of the thin plate bending, the total potential energy of the thin plate bending is obtained without considering the strain component:

[0137]

[0138] According to the relationship between the mechanical response and the deflection in the elastic mechanics, there is:

[0139]

[0140] Further, according to the equation (8) and the equation (9), each mechanical response is represented by w, and then substituted into the total potential energy equation (7) of the rock plate, the total potential energy δV of the thin plate bending can be obtained.

[0141] Because the deflection is small and does not cause the tension and compression of the plate neutral plane, only the bending and torsional deformation energy and the potential energy change of the force acting on the neutral plane are considered. The stability criterion of the energy method is that when the thin plate is transformed from the planar stable equilibrium state to the micro-bending curved surface stable equilibrium state, the potential energy change of the load is equal to the change of the strain energy of the thin plate, i.e. δU = δV.

[0142] The potential energy change of the rock plate caused by the horizontal force and the vertical force is:

[0143]

[0144] The bending strain energy of the rock plate is:

[0145]

[0146] When the plate edge is simply supported or fixed, the second term in δU and δV does not cause the change of the strain energy and can be ignored, so there is: xy

[0147]

[0148] Since A is a constant, there is Therefore, the undetermined coefficient A can be obtained, which is substituted into the deflection surface equation (6) to obtain:

[0149]

[0150] where D = Et 3 ​ / [12(1-μ 2 )].

[0151] According to the internal force bending moment formula of elastic mechanics, the bending moment of the equal thickness thin plate is obtained as:

[0152]

[0153] According to the stress derivation formula of elastic mechanics, the top plate stress of the equal thickness thin plate is obtained as:

[0154]

[0155] The critical stable layer limit height solving equation is as follows.

[0156] The above limit stress equation of the critical stable layer in the rock plate is derived based on the elastic thin plate theory and by using the energy method. The limit height equation of the critical stable layer is further derived by introducing the Hoek-Brown strength criterion. According to the above derivation, the stress of the stable layer in the rock plate is:

[0157]

[0158]

[0159] The plastic zone stress expression of the unsupported underground cavern surrounding rock based on the H-B strength criterion under the action of the original rock stress field is introduced as:

[0160]

[0161] Figure 4 It is a geometric relationship diagram, and the following expressions can be obtained from the diagram:

[0162]

[0163] Take a = b, α = 1, r, q t , t, E, μ, σ t , σ cmax It is known that the data is collected, and the meanings of other parameters are as follows:

[0164] r: cavern excavation radius, m;

[0165] q t : layer cohesion, Pa;

[0166] t: average layer thickness, m;

[0167] E: rock elastic modulus, Pa;

[0168] μ: Poisson's ratio;

[0169] σ t: Rock tensile strength, Pa;

[0170] σ cmax : Rock triaxial compressive strength, Pa;

[0171] θ: The angle between the critical stable layer boundary vector and the horizontal direction.

[0172] Under the limit state, there is σ x = σ t , and the simultaneous equations (18) to (22) can be obtained:

[0173]

[0174] The limit height H of the stable layer can be solved by the simultaneous equations (22) to (25).

[0175] The amount of rock slab collapse in the collapse layer is calculated as follows.

[0176] For the rock slab in the collapse layer, a cantilever beam can be used to analyze its collapse law. The rock slab in the collapse layer mainly bears the vertical force q transmitted from the overlying rock mass, which is considered as uniform compression. The mechanical model is shown in Figure 5 .

[0177] From the buckling curve equation of the cantilever beam under uniform load in material mechanics:

[0178]

[0179] In the formula, X represents the coordinate of the cantilever beam axis, i.e. the distance from the fixed end; Y represents the deflection at that point, i.e. the vertical distance from the original beam axis.

[0180] The normal stress of the cross section at the crack of the i-th layer in the collapse layer is:

[0181]

[0182] In the formula, X i and Y i represent the position coordinates of the i-th layer in the collapse layer where the crack occurs.

[0183] If X i = λ i l i , λ i represents the proportion coefficient of the unbroken part of the i-th layer in the collapse layer to the length of the rock slab, then:

[0184]

[0185] When λ i = 0.46, the calculation shows that:

[0186]

[0187] In the formula, k represents the number of layers that start to break, and the limit state is At this time, the critical load that starts to break can be solved:

[0188]

[0189] When q i <q k , no breakage occurs, and the breakage length Δ i = 0.

[0190] When q i ≥ q k , the breakage length Δ i = (1- λ i )l i = 0.54l i .

[0191] After the vault rock slab breaks, collapse will occur, and from formula (28), the length of each broken rock slab in the collapse layer is positively correlated with the thickness of the rock slab, and the geometric relationship shows that the total thickness of the rock slab in the collapse layer is the height of the stable layer, and the collapse range can be reflected by calculating the amount of collapse, so:

[0192]

[0193] l1=l2=L=l k =r;

[0194] l k+1 =0.46r

[0195] l k+2 =0.46 2 r

[0196] M M;

[0197] l i =0.46 i-k r

[0198]

[0199] In the formula, n represents the number of rock slabs in the collapse layer.

[0200] The embodiment of the present application can predict the collapse of the near-horizontal thin-layer rock mass tunnel by collecting physical quantities during construction and through formula (32).

[0201] For the parameter value range and basis in the calculation process, see Tables 1 and 2. The tunnel excavation data of a certain pumping storage project are used for checking calculation, and according to the field construction design data, indoor rock test, and reference to the “Technical Specification for Deep Buried Tunnels of Hydropower Projects” NB / T 11092-2023, it can be obtained that:

[0202] The chamber excavation hole diameter r = 2.6m, the rock layer surface cohesion q t = 0.1MPa, the rock tensile strength σ t = 2.5MPa, the average layer thickness of the rock plate in the stable layer is taken as a thin layer t = 0.1m, and the average layer thickness of the rock plate in the collapse layer is taken as a thin layer t n = 0.05m, the rock elastic modulus E = 20GPa, the Poisson's ratio μ = 0.28, the rock uniaxial compressive strength σ ci = 50MPa, the rock volume density γ = 26KN / m 3 , the geological strength index GSI = 20, the complete rock constant m i = 6, the blasting excavation disturbance D = 1.0.

[0203] Table 1: Field data

[0204]

[0205] Table 2: Laboratory test data

[0206]

[0207] The stable layer height H = 3.21m and the collapse amount Q = 144.04kN (single width) can be calculated by the calculation process of the embodiment of the present application, and the collapse is as shown in Figure 6 .

[0208] The following uses a numerical simulation method to carry out actual verification.

[0209] The BBM model in 3DEC is used for numerical calculation, the rock mass is simulated by the bonded block, and the bonding parameters such as bonding strength and stiffness can represent the connection between the rock mass or joints. Compared with the traditional 3DEC block combination, the bonded block in the BBM model can set different bonding strength parameters in different directions, which can more truly reflect the anisotropic mechanical characteristics of layered rock mass. When the bonding is damaged, the mechanical response and state change of the rock mass from complete to broken can be reflected, the gradual failure process can be simulated, and the gradual mechanical response and structural failure development path from local bonding damage to overall structural instability can be observed. Therefore, it is suitable for simulating the deformation and collapse analysis of the arch top range of the horizontal thin-layered stratum underground chamber under the action of excavation unloading.

[0210] A 2.5D model is established, a 40m x 0.5m x 40m plane model, and the underground chamber hole diameter is 2.6m. In the range of 20m x 20m of the model, the underground chamber arch top is cut into thin-layered blocks by horizontal and vertical joints and set as a BBM model. In order to more finely reflect the thin-layered rock mass, the vertical joint interval is 5 times the horizontal joint interval, which meets the thin plate proportion requirement, as shown inFigure 7

[0211] In the discrete element method 3DEC, the blocks can be rigid blocks, elastic blocks and plastic blocks that can be damaged. In the model composed of rigid blocks, the parameters to be calibrated are less than the other two blocks, the calculation time is shorter than the other two blocks, and the correction program is simpler than the other two blocks, but the rigid block model cannot reflect the volume strain of the rock, and there is a self-locking phenomenon between the rock blocks, which needs to be set. A relatively low internal friction angle of contact is needed to reduce this effect. The model composed of elastic blocks needs to be calibrated Parameters, calculation time and calibration procedures are moderate compared to the other two blocks, and the elastic block model allows block deformation, and the strain of the model is closer to the true state than the rigid block. The plastic block is closer to the internal situation of the real rock particle than the rigid block and the elastic block, but the calculation time is longer, and the correction program is more complicated. In addition, in the BBM model, the macroscopic mechanical behavior of the model is mainly represented by the mechanical behavior of the block contact, and the mechanical behavior of the bonded block itself is not considered, so the model will only occur in the contact between the blocks. Considering the above, the elastic block model is used for analysis, and the constitutive model of the model contact adopts the built-in Coulomb slip model of the block discrete element method (3DEC).

[0212] Because in the numerical model, the elastic-plastic constitutive model based on M-C (Mohr-Coulomb) failure criterion is adopted. However, the analytical solution of the present application adopts Hoek-Brown criterion, so it is necessary to convert Hoek-Brown parameters m i , GSI and σ ci Into the parameters c、 According to the Hoek-Brown failure criterion, the equivalent friction angle and cohesion of the rock mass are calculated as follows:

[0213]

[0214] σ 3max = 0.47·σ cm (γL) 0.94 (34)

[0215]

[0216] wherein, σ 3max refers to the maximum value of the minimum principal stress, σ cm is the compressive strength of the rock mass, and L is the depth of the underground cavern.

[0217] ​For the underground cavern, L = 100 m is taken as the depth, and the horizontal lateral pressure coefficient of the initial stress field is 1.0. Therefore, for the horizontal layer contact cohesion force and the horizontal layer internal friction angle can be determined by equations (33) to (35). For the non-horizontal layer contact cohesion force J C and the non-horizontal layer internal friction angle can be determined by laboratory tests. The relevant parameters of the block and the contact are shown in Table 3:

[0218] Table 1: Calibration of the mesoscopic parameters of the BBM model

[0219]

[0220] The numerical calculation shows that the critical stable layer height H = 3.10 m, and the estimated collapse volume Q ≈ 130 kN (single width). The collapse calculation results are shown in Figure 8 .

[0221] To compare the rationality of the numerical calculation results, the error is calculated according to the following equation:

[0222]

[0223] Compared with the theoretical stable layer height H = 3.21 m and the theoretical collapse volume Q = 144.04 kN calculated by the prediction method of the embodiment of the present application, the error of the stable layer height is 3.4%, and the error of the collapse volume height is 9.75%. The errors are all less than 10%, so it is judged that the numerical calculation results are in good agreement with the analytical results. At the same time, it is observed that the collapse form and the failure mode are consistent with the theoretical model assumption, which verifies the rationality of using 3DEC-BBM to numerically simulate the calculation model.

[0224] The technical features of the above embodiments can be combined in any way. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described, and only the preferred embodiments of the present application are expressed, which are described in more detail and in more detail. However, it cannot be understood as limiting the scope of the present patent. As long as the combination of these technical features does not exist, it should be considered as the scope of the present specification.

[0225] It should be noted that for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are within the scope of the present application. Therefore, the scope of protection of the present patent should be subject to the appended claims.

Claims

1. A method for predicting the collapse of a roof of a subsurface cavern in a near- horizontal, thin-bedded formation, the method comprising: The method comprises the following steps: ​ Step S1: collecting rock tensile strength σ t , average layer thickness t of rock plate in stable layer, Poisson's ratio μ, rock layer surface cohesion q t , rock elastic modulus E, underground cavern excavation radius r, rock uniaxial compressive strength σ ci , rock mass specific gravity γ, geological strength index GSI, intact rock constant m i and rock mass disturbance factor D'; Step S2: based on the elastic thin plate theory, a mechanical model is constructed, and the length a of the stable layer rock plate and the critical stress σ of the stable layer rock plate boundary are calculated based on the data collected in step S1 crvx and finally determine the stable layer height H; Step S3: constructing a mechanical model based on the cantilever beam theory, calculating the vertical force borne by each layer of rock plate in the caving layer from the overlying rock mass and the temporary load at which the fracture begins, through the thickness of each layer of rock plate in the caving layer; Step S4: calculating the fracture length based on the vertical force borne by each layer of rock plate in the caving layer from the overlying rock mass and the critical load at which the fracture begins, and calculating the caving amount through the fracture length and the stable layer height H.

2. A method of predicting the collapse of a vault in a near- horizontal, thin-bedded formation according to claim 1, wherein: The expression for calculating the stable layer rock plate length a in step S2 is:

3. A method of predicting the collapse of a vault in a near- horizontal, thin-bedded formation according to claim 2, wherein: The expression for calculating the critical stress σ of the stable layer rock plate boundary in step S2 is as follows: crvx The expression for calculating the critical stress σ of the stable layer rock plate boundary in step S2 is as follows: In the formula, σ cmax represents the triaxial compressive strength of the rock.

4. A method of predicting the collapse of a vault in a near- horizontal, thin-bedded formation according to claim 3, wherein: The stable layer height H in step S2 is solved by the following two formulas: where σ ci represents the compressive strength of the rock; m b , s, and a0represent constants of the rock material; θ represents the angle between the critical stable boundary of the strata and the horizontal direction; σ r and σ θ respectively represent the radial stress and the tangential stress at a distance R from the center of the underground cavern.

5. A method for predicting the collapse of a vault in a near- horizontal, thin-bedded formation according to claim 1, wherein: The expression for calculating the vertical force borne by each layer of rock plate in the caving layer from the overlying rock mass in step S3 is: In the formula, q i represents the vertical force borne by the i-th rock slab in the collapsed layer from the overlying rock mass; γ represents the rock mass density; w represents the rock slab width in the collapsed layer; t i represents the thickness of the i-th rock slab in the collapsed layer; n represents the number of rock slabs in the collapsed layer.

6. A method of predicting the collapse of a vault in a near- horizontal, thin-bedded formation according to claim 5, wherein: The method for calculating the temporary load in step S3 comprises: Step S31: analyzing the caving law of the rock plate in the caving layer by using the cantilever beam to obtain a mechanical model; Step S32: obtaining the buckling curve equation of the cantilever beam under uniform load based on the mechanical model; Step S33: obtaining the cross-sectional normal stress equation at the i-th layer crack in the caving layer based on the buckling curve equation; Step S34: obtaining the critical load at which the fracture begins after decomposing the cross-sectional normal stress equation.

7. A method of predicting the collapse of a vault in a near- horizontal, thin-bedded formation according to claim 6, wherein: The expression of the buckling curve equation in step S32 is: In the formula, X represents the coordinate of the cantilever beam axis, i.e. the distance from the fixed end; Y represents the deflection at this point, i.e. the vertical distance from the original beam axis; E represents the elastic modulus of the rock; I represents the cross-sectional moment of inertia of the rock plate in the caving layer; l represents the length of the rock plate in the caving layer; and q represents the vertical force borne by the rock plate in the caving layer from the overlying rock mass.

8. A method of predicting the collapse of a vault in a near- horizontal, thin-bedded formation according to claim 7, wherein: The cross-sectional normal stress at the crack of the i-th layer in the collapsed layer in step S33 The expression is: wherein X i and Y i represents the position coordinate of the crack occurrence position of the i-th layer in the collapsed layer; q i represents the vertical force borne by the i-th layer of rock slab in the collapsed layer; l i represents the length of the i-th layer of rock slab in the collapsed layer; t i represents the thickness of the i-th layer of rock slab in the collapsed layer.

9. A method of predicting the collapse of a vault in a near- horizontal, thin-bedded subterranean cavern according to claim 8, wherein: The critical load q in step S34 k The expression is: In the formula, k represents the number of layers in which the fracture occurs; l k represents the length of the kth layer of rock slab in the collapsed layer; σ t represents the tensile strength of the rock.

10. A method for predicting the collapse of a ceiling in a subterranean cavern in a near- horizontal, thinly bedded formation according to claim 1, wherein: Step S4 comprises: Step S41: when the current rock plate bears the vertical force transmitted from the overlying rock mass less than the critical load, the fracture length is 0; when the current rock plate bears the vertical force transmitted from the overlying rock mass not less than the critical load, the fracture length of the current rock plate is calculated by the following formula i : Δ i = (1 - λ i )l i = 0.54l i ; where λ i represents the proportion coefficient of the length of the unbroken part in the i-th layer in the collapsed layer to the rock slab of this layer; Step S42: calculating the caving amount Q through the following formula: In the formula, γ represents the bulk weight of the rock mass; n represents the number of rock plates in the collapsed layer; l i represents the plate length of the i th layer of rock plates in the collapsed layer; t i represents the plate thickness of the i th layer of rock plates in the collapsed layer; w represents the plate width of the rock plates in the collapsed layer; and k represents the number of layers in which the fracture occurs.

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