Method for predicting vault caving of underground cavern in nearly horizontal thin strata

Abstract

The embodiment of the invention provides a nearly horizontal thin stratigraphic stratum underground cavern vault caving prediction method, which comprises the following steps: constructing a mechanical model based on an elastic thin plate theory, calculating the length a of a stable layer rock plate and the boundary critical stress sigma crvx of the stable layer rock plate through acquired data, and finally determining the height H of the stable layer; constructing a mechanical model based on a cantilever beam theory, and calculating a vertical acting force transmitted by an overlying rock mass and a temporary load when each layer of rock plate in the slump layer begins to break according to the thickness of each layer of rock plate in the slump layer; the fracture length is calculated based on the vertical acting force transmitted by the overlying rock mass and borne by each layer of rock plate in the collapse layer and the critical load when fracture begins to happen; and calculating the slump according to the fracture length and the height H of the stable layer. And a basis is provided for determining underground cavern support control parameters of the nearly horizontal stratified stratum, and the stability of surrounding rock of the underground cavern is ensured.

Description

Technical Field

[0001] The invention relates to the technical field of underground cavern stability prediction, and in particular to a method for predicting the collapse of underground cavern vaults in a nearly horizontal thin-layered stratum. Background Art

[0002] Reasonable prediction of the collapse range (collapse amount) of the arch during underground cavern excavation can guide engineers to rationally design the support structure, including selecting the appropriate anchor length and model, determining the spacing and arrangement of anchors, and the model and installation spacing of the steel arch frame, thereby optimizing the design scheme, avoiding over-support or under-support, and achieving an economical, efficient and safe construction process.

[0003] In the existing technology, collapse prediction is generally carried out by theoretical analysis, numerical simulation, model test, case analysis or probability evaluation. However, whether it is theoretical analysis, numerical simulation, model test, case analysis or probability evaluation, most of them focus on the collapse arch analysis of underground cavern engineering under homogeneous rock mass or thick rock mass conditions, and fail to pay sufficient attention and consideration to the thin-layer structural characteristics and rock mechanical anisotropy of nearly horizontal thin rock mass.

[0004] Compared with other rock masses, nearly horizontal thin-layer rock masses are more prone to shear slip along bedding planes in terms of collapse mechanism; the collapse range is usually limited by the thickness of the rock layer and distributed along the layer; the collapse characteristics are manifested as interlayer fragmentation and local fracture; due to the poor stability of thin-layer rock masses, it is more likely to cause safety problems during construction. Due to the shortcomings and defects of the existing technology, the existing collapse arch prediction method is often difficult to accurately reflect the actual situation when applied to nearly horizontal thin-layered underground caverns, and the accuracy and reliability of the prediction results are greatly reduced. Therefore, there is an urgent need for a prediction method that can reasonably predict the collapse of the arch roof of nearly horizontal thin-layered underground caverns while taking into account the structural characteristics of the layered rock mass. Summary of the invention

[0005] The present invention proposes a method for predicting the collapse of underground cavern vaults in nearly horizontal thin-layered strata, so as to solve the technical problem that it is difficult to predict the collapse of underground cavern vaults in nearly horizontal thin-layered strata while considering the structural characteristics of layered rock mass in the prior art.

[0006] In order to solve the above technical problems, the present invention provides a method for predicting the collapse of underground cavern vaults in a nearly horizontal thin layer, comprising the following steps:

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

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

[0009] Step S3: construct a mechanical model based on cantilever beam theory, and calculate the vertical force transmitted by the overlying rock mass and the temporary load when the fracture begins to occur on each layer of rock slab in the collapsed layer according to the thickness of each layer of rock slab in the collapsed layer;

[0010] Step S4: Calculate the fracture length based on the vertical force transmitted from the overlying rock mass to each rock slab in the collapsed layer and the critical load when fracture begins; calculate the collapse amount through the fracture length and the height H of the stable layer.

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

[0012]

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

[0014]

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

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

[0017]

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

[0019] Preferably, in step S3, the expression for calculating the vertical force transmitted from the overlying rock mass to each rock slab in the collapsed layer is:

[0020]

[0021] In the formula, q irepresents the vertical force transmitted by the overlying rock mass to the i-th rock slab in the collapsed layer; γ represents the weight of the rock mass; w represents the width of the rock slab in the collapsed layer; t i Indicates the thickness of the i-th rock slab in the collapse layer.

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

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

[0024] Step S32: Based on the mechanical model, the winding curve equation of the cantilever beam under uniformly distributed load in material mechanics is obtained;

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

[0026] Step S34: After decomposing the cross-section normal stress equation, a critical load at which fracture begins to occur is obtained.

[0027] Preferably, the winding curve equation in step S32 is expressed as:

[0028]

[0029] Where X represents the coordinate of the cantilever beam axis, that is, the distance from the fixed end; Y represents the deflection at that point, that is, the vertical distance from the original beam axis; E represents the elastic modulus of rock; I represents the moment of inertia of the rock slab section in the collapsed layer; l represents the length of the rock slab in the collapsed layer.

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

[0031]

[0032] Where, X i and Y i represents the position coordinates of the cracks in the i-th layer of the collapsed layer; q i It indicates that the i-th rock slab in the collapse layer bears the vertical force transmitted from the overlying rock mass; l i represents the length of the i-th rock slab in the collapsed layer; t i Indicates the thickness of the i-th rock slab in the collapse layer.

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

[0034]

[0035] In the formula, t represents the average thickness of the rock plate; k represents the number of layers where the fracture begins; l k represents the length of the k-th rock slab in the collapsed layer; σ t Indicates the tensile strength of rock.

[0036] Preferably, step S4 comprises:

[0037] Step S41: When the vertical force transmitted from the overlying rock mass to the current rock slab is less than the critical load, the fracture length is 0; when the vertical force transmitted from the overlying rock mass to the current rock slab 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 ) i =0.54l i ;

[0039] In the formula, λ i It represents the ratio coefficient of the length of the unbroken part in the i-th layer of the collapsed layer to this layer of rock slab;

[0040] Step S42: Calculate the slump amount Q by the following formula:

[0041]

[0042] Where γ represents the weight of rock mass; n represents the number of rock plates in the collapse layer.

[0043] The beneficial effects of the present invention include at least: to reasonably predict the collapse of the vault of an underground cavern in a nearly horizontal thin-layered stratum, it is necessary to consider the structural characteristics of the layered rock mass. The present invention generalizes the layered rock mass into a rock beam mechanical model or a rock plate mechanical model respectively; since the thickness of the thin-layered rock mass is relatively thin and the interlayer bonding force is weak, its deformation and failure mode under stress state are significantly different from those of the thick-layered rock mass; for thin-layered rock mass, its bending and shearing resistance is often weak, and under the load of the vault, the thin layer is more likely to have interlayer dislocation, separation or even sliding, thereby increasing the risk of vault collapse. Consideration of multiple factors is to ensure the accuracy and reliability of the prediction of the present invention. It provides a basis for determining the support control parameters of underground caverns in nearly horizontal layered strata, reduces unnecessary conservative design and excessive support, avoids collapse accidents, reduces the cost of repair and rework caused by collapse, and ensures the stability of the surrounding rock of the underground cavern. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A schematic diagram of a method flow chart of an embodiment of the present invention;

[0045] Figure 2 A schematic diagram of a theoretical generalized model of a nearly horizontal thin-layer rock mass according to an embodiment of the present invention;

[0046] Figure 3 It is a schematic diagram of a mechanical model of a rectangular top plate with four simply supported sides constructed based on thin plate theory according to an embodiment of the present invention;

[0047] Figure 4 A schematic diagram of the geometric relationship of a nearly horizontal thin rock mass according to an embodiment of the present invention;

[0048] Figure 5 A schematic diagram of a mechanical model for analyzing the collapse law of a rock slab in a collapsed layer by a cantilever beam according to an embodiment of the present invention;

[0049] Figure 6 A schematic diagram of a collapse of an embodiment of the present invention;

[0050] Figure 7 A schematic diagram of a BBM model constructed according to an embodiment of the present invention;

[0051] Figure 8 Schematic diagram of numerical simulation calculation results of an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the protection scope of the present invention.

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

[0054] q t : The vertical direction of the rock slab is subject to the bonding force of the upper rock layer;

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

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

[0057] q xy : Shear stress in the rock slab;

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

[0059] a: length of rock board;

[0060] b: width of rock slab;

[0061] t: rock slab thickness (average layer thickness);

[0062] E: elastic modulus of rock;

[0063] μ: Poisson's ratio of rock;

[0064] D: flexural rigidity of rock slab;

[0065] w: deflection equation of rock slab;

[0066] A: Maximum deflection of rock slab;

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

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

[0069] σ crvx : minimum critical stress on the rock plate boundary;

[0070] R: distance from the tunnel center;

[0071] r: radius of cave excavation;

[0072] θ: angle between the critical stability layer boundary radius and the horizontal direction;

[0073] H: critical stability layer limit height;

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

[0075] GSI: Geological Strength Index;

[0076] m i : intact rock constant;

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

[0078] D′: rock mass disturbance factor;

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

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

[0081] σ t : rock tensile strength;

[0082] σ vx : The average stress per unit thickness in the x direction of the rock plate;

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

[0084] q: The rock slab in the collapse layer bears the vertical force transmitted from the overlying rock mass;

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

[0086] I: moment of inertia of the rock slab section in the collapsed layer;

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

[0088] I zi : moment of inertia of the cross section of the i-th rock slab in the collapsed layer;

[0089] t i : the thickness of the i-th rock slab in the collapsed layer;

[0090] l i : the length of the i-th rock slab in the collapsed layer;

[0091] q i : The i-th rock slab in the collapse layer bears the vertical force transmitted from the overlying rock mass;

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

[0093] γ: rock mass;

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

[0095] △ i : The fracture length of the i-th rock slab in the collapsed layer;

[0096] Q: the amount of collapse in the 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 : rock mass compressive strength;

[0101] L: Depth of underground cavern.

[0102] like Figure 1 As shown, an embodiment of the present invention provides a method for predicting the collapse of underground cavern vaults in nearly horizontal thin-layered strata.

[0103] The layered rock mass has a significant structural effect, and after the excavation of the cavern, the structural effect of the rock mass is activated, transforming from a nearly continuous medium to a plate-cracked medium, forming a typical rock plate structure. Its mechanical action characteristics follow the typical deformation and failure laws of a "beam" or "plate".

[0104] In the early stage of cavern excavation, the boundaries of the rock strata are embedded in the rock strata, and the movement and rotation deformation are restricted. Therefore, it can be regarded as a rock slab structure with four sides constrained by fixed supports. As the rock strata at the top and bottom of the cavern continue to produce structural bending deformation toward the initial free surface, the maximum bending moment and maximum shear force in the rock slab are distributed at the boundary of the rock slab. Therefore, the rock slab always first breaks and fails at the upper part of the fixed edges on all sides, and then turns into simply supported edge constraints, and then the rock slab breaks or becomes unstable inside. Therefore, the boundary conditions of the rock slab gradually change with the passage of time and the evolution of the surrounding rock, from the initial four-sided fixed-supported rock slab to the four-sided simply supported rock slab structure. In this process, a critical stability layer will appear, and the rock slab will transform from a plane stable equilibrium state to a slightly deflected curved surface stable equilibrium state. Under this layer, layered rock slab collapse will occur. Therefore, if the following is established, Figure 2 Theoretical generalization model shown.

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

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

[0107] 2) According to small deformation, elastic body analysis, select the thin plate small deflection bending theory for calculation;

[0108] 3) When the thin plate transforms from a plane stable equilibrium state to a slightly deflected curved surface stable equilibrium state, the cross section remains flat;

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

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

[0111] The ultimate stress equation is constructed as follows.

[0112] The deflection distribution and deflection slope of the rock plate on all four boundaries are 0, so the corresponding boundary conditions are:

[0113]

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

[0115]

[0116] Where x and y represent the horizontal and vertical coordinate values ​​of different positions of the rock slab, respectively.

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

[0118]

[0119] Take the Fourier series as the surface equation of the critical state plate, which meets the boundary conditions of the four-sided simply supported plate:

[0120]

[0121] Arranged:

[0122]

[0123] The coefficient A mn cannot all be zero, so we have:

[0124]

[0125] q x =σ vx t;

[0126] q y =σ hy t;

[0127] q y =αq x ;

[0128] Arranged:

[0129]

[0130] Obviously, when m=n=1, there is a 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 slab; A is an undetermined constant.

[0135] When a thin plate with four sides simply supported is only subjected to vertical forces in the direction perpendicular to the rock plate, the flexure surface equation (6) of the above-mentioned boundary conditions of the rock plate with four sides simply supported should also be satisfied.

[0136] According to the straight normal line assumption of thin plate bending, ignoring the strain component, the total potential energy of thin plate bending is obtained as:

[0137]

[0138] According to the relationship between each mechanical response quantity and deflection in elastic mechanics, we have:

[0139]

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

[0141] Because the deflection is very small and does not cause the stretching and compression of the neutral plane of the plate, 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: when the thin plate changes from a plane stable equilibrium state to a slightly curved surface stable equilibrium state, the change in the potential energy of the load is equal to the change in the strain energy in the thin plate, that is, δU = δV.

[0142] The potential energy change of the rock plate caused by the horizontal force and 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, q in δU xy The second term in and δV does not cause a change in strain energy and can be ignored, so:

[0147]

[0148] Since A is a constant, we have Therefore, the unknown coefficient A can be obtained and substituted into the flexure surface equation (6) to obtain:

[0149]

[0150] Where D = Et 3 / [12(1-μ 2 )].

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

[0152]

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

[0154]

[0155] The equation for solving the critical stability layer limit height is as follows.

[0156] Based on the elastic thin plate theory and the energy method, the ultimate stress equation of the rock plate in the critical stable layer is derived in detail. The ultimate height equation of the critical stable layer is further derived by introducing the Hoek-Brown strength criterion. From the above derivation, it can be seen that the stress of the rock plate in the stable layer is:

[0157]

[0158]

[0159] Here, the stress expression of the plastic zone of the surrounding rock of the circular underground cavern under the action of the original rock stress field based on the HB strength criterion is introduced as follows:

[0160]

[0161] Figure 4 It is a schematic diagram of geometric relationship, from which we can get the following expression:

[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: radius of cave excavation, 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 : triaxial compressive strength of rock, Pa;

[0171] θ: Angle between the critical stability layer boundary radius and the horizontal direction.

[0172] In the limit state, there is σ x =σ t , and by connecting equation (18) to equation (22) in parallel, we can obtain:

[0173]

[0174] By combining equations (22) to (25), the maximum height H of the stable layer can be solved.

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

[0176] For the rock slab in the collapsed layer, the cantilever beam can be used to analyze its collapse law. The rock slab in the collapsed layer mainly bears the vertical force q transmitted by the overlying rock mass, which is regarded as uniformly compressed here. Its mechanical model is as follows: Figure 5 shown.

[0177] According to the winding curve equation of a cantilever beam under uniformly distributed load in material mechanics:

[0178]

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

[0180] The cross-sectional normal stress at the crack of the i-th layer in the collapsed layer:

[0181]

[0182] Where, X i and Y i Indicates the location coordinates of the cracks in the i-th layer within the collapsed layer.

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

[0184]

[0185] After calculation, when λ i =0.46:

[0186]

[0187] In the formula, k represents the number of layers where fracture begins. In the limit state, At this point, the critical load at which fracture begins can be solved:

[0188]

[0189] When i k When no fracture occurs, the fracture length is △ i =0.

[0190] When i ≥q k When the fracture length △ i =(1-λ i ) i =0.54l i .

[0191] After the arch rock slab breaks, collapse will occur. From formula (28), it can be seen that the length of each broken rock slab in the collapse layer is positively correlated with the thickness of the rock slab. The geometric relationship shows that the sum of the thickness of the rock slab in the collapse layer is the height of the stable layer. 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] MM;

[0197] l i =0.46 i-k r

[0198]

[0199] Where n represents the number of rock slabs in the collapsed layer.

[0200] The embodiment of the present invention collects physical quantities during construction and uses formula (32) to predict the collapse of a nearly horizontal thin rock tunnel.

[0201] For the parameter value range and value basis in the calculation process, see Tables 1 and 2. Taking the excavation data of a pumped storage project tunnel for verification, the following can be obtained through on-site construction design data, indoor rock tests, and reference to the Technical Specifications for Deep Buried Tunnels in Hydropower Projects NB / T 11092-2023:​

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

[0203] Table 1: Field data

[0204]

[0205] Table 2: Indoor test data

[0206]

[0207] According to the calculation process of the embodiment of the present invention, the stable layer height H = 3.21m, the slump amount Q = 144.04kN (single width) slump Figure 6 shown.

[0208] The following numerical simulation method is used for actual verification.

[0209] The BBM model in 3DEC is used for numerical calculation. The rock mass is simulated by bonding blocks. The bonding parameters, such as bonding strength and stiffness, can represent the connection between the rock or joints. Compared with the traditional 3DEC which simply uses block combinations, the bonding blocks in the BBM model can set different bonding strengths and other parameters in different directions, which can more truly reflect the anisotropic mechanical characteristics of the layered rock mass. When the bonding is damaged, it can also reflect the mechanical response and state changes of the rock mass from integrity to rupture, and can simulate the progressive damage process. The progressive mechanical response and structural damage development path from local bonding failure to overall structural instability can be observed. Therefore, it is suitable for simulating the deformation and collapse analysis of underground caverns in horizontal thin-layered strata within the vault range under the action of excavation unloading.

[0210] A 2.5D model was established, a plane model of 40m×0.5m×40m, and the underground cavern diameter was 2.6m. Within the 20m×20m range of the model, the underground cavern vault was cut into thin-layered blocks using 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 ratio requirements, such as Figure 7 shown.

[0211] In the discrete element method 3DEC, blocks can be rigid blocks, elastic blocks, and plastic blocks that can be damaged. In the model composed of rigid blocks, the parameters that need to be calibrated are less than those of the other two blocks, the calculation time is shorter than that of the other two blocks, and the correction procedure is simpler than that of the other two blocks. However, the rigid block model cannot reflect the volume strain of the rock, and there is a self-locking phenomenon between the rock blocks. A relatively low contact internal friction angle needs to be set to reduce this effect. The parameters, calculation time, and calibration procedure required for the model composed of elastic blocks are moderate compared to the other two blocks, and the elastic model block allows the block to deform. The strain of the model is closer to the real state than the rigid block. Plastic blocks are closer to the internal conditions of real rock particles than rigid blocks and elastic blocks, but the calculation time is longer and the correction procedure is more complicated. In addition, in the BBM model, the macroscopic mechanical behavior of the model is mainly characterized by the mechanical behavior of block contact, and the mechanical behavior of the bonding block itself is not considered for the time being, so the fracture behavior of the model will only occur in the contact between blocks. Based on the above considerations, the elastic block model is used for analysis, and the constitutive model of the model contact adopts the Coulomb slip model built into the block discrete element method (3DEC).

[0212] Since the numerical model adopts the elastic-plastic constitutive model based on the MC (Mohr-Coulomb) failure criterion, the analytical solution calculated in the present invention adopts the Hoek-Brown criterion, so it is necessary to set the Hoek-Brown parameter m i , GSI and σ ci Convert to Mohr-Coulomb parameter c, According to the Hoek-Brown failure criterion, the equivalent friction angle of the rock mass is calculated and cohesion As shown below:

[0213]

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

[0215]

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

[0217] For the underground cavern, the burial depth is L = 100m, and the horizontal lateral pressure coefficient of the initial ground stress field is considered to be 1.0. Therefore, for the horizontal surface contact cohesion and the horizontal plane internal friction angle It can be determined by equations (33) to (35). For non-horizontal surface contact cohesion J C Internal friction angle of non-horizontal plane It can be determined through indoor tests. The relevant parameters of the block and contact are shown in Table 3:

[0218] Table 1: Calibration of microscopic parameters of BBM model

[0219]

[0220] Through numerical calculation, the critical stable layer height H = 3.10m, the estimated collapse amount Q ≈ 130kN (single width) collapse calculation results are as follows Figure 8 shown.

[0221] In order to compare the rationality of the numerical calculation results, the error is first calculated according to the following formula:

[0222]

[0223] The numerical calculation results are compared with the theoretical stable layer height H=3.21m and the theoretical slump Q=144.04kN calculated by the prediction method of the embodiment of the present invention. The error of the calculated stable layer height is 3.4%, and the error of the slump height is 9.75%, and the errors are no more than 10%. 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 slump morphology and failure mode are consistent with the assumptions of the theoretical model, which verifies the rationality of the calculation model using 3DEC-BBM numerical simulation.

[0224] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. Only the preferred embodiments of the present invention are expressed. The description is more specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. As long as there is no contradiction in the combination of these technical features, they should be considered as the scope recorded in this specification.

[0225] It should be noted that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A method for predicting the collapse of underground cavern vaults in a nearly horizontal thin layer, characterized by: The following steps are involved: Step S1: Collect rock tensile strength σ t , average thickness of rock slabs in the stable layer t, Poisson's ratio μ, rock layer cohesion q t , rock elastic modulus E, underground cave excavation radius r, rock uniaxial compressive strength σ ci , rock bulk density γ, geological strength index GSI, intact rock constant m i and rock mass disturbance factor D′; Step S2: Construct a mechanical model based on the elastic thin plate theory, and calculate the length a of the stable layer rock plate and the critical stress σ of the stable layer rock plate boundary through the data collected in step S1 crvx , and finally determine the stable layer height H; Step S3: construct a mechanical model based on cantilever beam theory, and calculate the vertical force transmitted by the overlying rock mass and the temporary load when the fracture begins to occur on each layer of rock slab in the collapsed layer according to the thickness of each layer of rock slab in the collapsed layer; Step S4: Calculate the fracture length based on the vertical force transmitted from the overlying rock mass to each rock slab in the collapsed layer and the critical load when fracture begins; calculate the collapse amount through the fracture length and the height H of the stable layer.

2. The method for predicting the collapse of underground cavern vaults in a nearly horizontal thin layer of strata according to claim 1, characterized in that: The expression for calculating the length a of the stable layer rock plate in step S2 is:

3. The method for predicting the collapse of underground cavern vaults in a nearly horizontal thin layer of strata according to claim 2, characterized in that: Step S2 calculates the critical stress σ of the stable layer rock plate boundary crvx The expression is: In the formula, σ cmax It represents the triaxial compressive strength of rock.

4. The method for predicting the collapse of underground cavern vaults in a nearly horizontal thin layer of strata according to claim 3, characterized in that: In step S2, the stable layer height H is obtained by combining the following two formulas: In the formula, σ ci Indicates the compressive strength of rock; m b , s and a0 represent rock material constants; θ represents the angle between the critical stability layer boundary radius and the horizontal direction; σ r and σ θ They represent the radial stress and tangential stress at a distance R from the center of the underground cavern, respectively.

5. The method for predicting the collapse of underground cavern vaults in a nearly horizontal thin layer of strata according to claim 1, characterized in that: In step S3, the expression for calculating the vertical force transmitted from the overlying rock mass to each rock slab in the collapsed layer is: In the formula, q i represents the vertical force transmitted by the overlying rock mass to the i-th rock slab in the collapsed layer; γ represents the weight of the rock mass; w represents the width of the rock slab in the collapsed layer; t i Indicates the thickness of the i-th rock slab in the collapse layer.

6. The method for predicting the collapse of underground cavern vaults in a nearly horizontal thin layer of strata according to claim 5, characterized in that: The method for calculating the temporary load in step S3 includes: Step S31: using a cantilever beam to analyze the collapse law of the rock slab in the collapsed layer to obtain a mechanical model; Step S32: Based on the mechanical model, the winding curve equation of the cantilever beam under uniformly distributed load in material mechanics is obtained; Step S33: based on the winding curve equation, obtaining a cross-sectional normal stress equation at the i-th crack in the collapsed layer; Step S34: After decomposing the cross-section normal stress equation, a critical load at which fracture begins to occur is obtained.

7. The method for predicting the collapse of underground cavern vaults in a nearly horizontal thin layer of strata according to claim 6, characterized in that: The expression of the winding curve equation in step S32 is: Where X represents the coordinate of the cantilever beam axis, that is, the distance from the fixed end; Y represents the deflection at that point, that is, the vertical distance from the original beam axis; E represents the elastic modulus of rock; I represents the moment of inertia of the rock slab section in the collapsed layer; l represents the length of the rock slab in the collapsed layer.

8. The method for predicting the collapse of underground cavern vaults in a nearly horizontal thin layer of strata according to claim 7, characterized in that: The cross-sectional normal stress at the crack of the i-th layer in the collapsed layer in step S33 The expression is: In the formula, X i and Y i represents the position coordinates of the cracks in the i-th layer of the collapsed layer; q i It indicates that the i-th rock slab in the collapse layer bears the vertical force transmitted from the overlying rock mass; l i represents the length of the i-th rock slab in the collapsed layer; t i Indicates the thickness of the i-th rock slab in the collapse layer.

9. The method for predicting the collapse of underground cavern vaults in a nearly horizontal thin layer of strata according to claim 8, characterized in that: The critical load q in step S34 k The expression is: In the formula, t represents the average thickness of the rock plate; k represents the number of layers where the fracture begins; l k represents the length of the k-th rock slab in the collapsed layer; σ t Indicates the tensile strength of rock.

10. The method for predicting the collapse of underground cavern vaults in a nearly horizontal thin layer according to claim 1, characterized in that: Step S4 includes: Step S41: When the vertical force transmitted from the overlying rock mass to the current rock slab is less than the critical load, the fracture length is 0; when the vertical force transmitted from the overlying rock mass to the current rock slab is not less than the critical load, the fracture length Δ of the current rock slab is calculated by the following formula: i : D i =(1-λ i )l i =0.54l i ; In the formula, λ i It represents the ratio coefficient of the length of the unbroken part in the i-th layer of the collapsed layer to this layer of rock slab; Step S42: Calculate the slump amount Q by the following formula: Where γ represents the weight of rock mass; n represents the number of rock plates in the collapse layer.

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