Rock mass cavern earthquake dynamic stability analysis method considering layer vibration degradation

Abstract

A rock mass cavern seismic dynamic stability analysis method considering layer vibration degradation comprises the following steps: determining transverse isotropic elastic mechanical behaviors, strength criteria and plastic potential functions of a layered rock mass, and constructing an elastic-plastic degradation constitutive model of the layered rock mass; determining a stratified rock mass layer surface strength parameter calculation formula under the earthquake action, determining a stratified rock mass rock mass strength parameter calculation formula, and establishing a stratified rock mass strength parameter evolution rule considering the layer surface vibration degradation effect; defining a layer damage degree index, and constructing a layered rock mass damage degree evaluation index under the earthquake action; and calculating the earthquake stability safety degree coefficient of the rock mass underground cavern, and determining the earthquake stability safety degree interval of the rock mass underground cavern. According to the method, the layer vibration degradation effect is considered, the safety evaluation result is more accurate, the application range is wide, the principle is simple, the physical significance is clear, the earthquake stability of the rock mass underground cavity is effectively analyzed, and the method has good practical engineering application prospects.

Description

Technical Field

[0001] The present invention relates to an improvement of a method for analyzing the seismic stability of an underground rock cavern, belongs to the field of geotechnical earthquake engineering, and particularly relates to a method for analyzing the seismic dynamic stability of a rock cavern taking into account layer vibration degradation. Background Art

[0002] Layered rock masses are a widespread engineering rock mass, commonly found in projects such as hydropower projects, transportation tunnels, and deep mines. These projects often contain multiple chambers, such as underground chamber clusters in hydropower station buildings, double-track tunnels in mountain roads and railways, and tunnel clusters in mines. Due to the mutual influence between adjacent chambers, their mechanical properties and engineering impacts are more complex than those of a single tunnel. Under earthquakes, the complexity of the mechanical properties of layered rock masses is further amplified, and the shear strength of the layers undergoes dynamic degradation during the earthquake, thus affecting the seismic stability of underground rock structures. Existing studies using pseudo-static methods or traditional elastic-plastic mechanics models for seismic stability analysis of layered rock caverns typically fail to consider the deterioration effect of layer vibration under earthquakes. Consequently, they fail to reflect the attenuation characteristics of rock material strength parameters, resulting in inaccurate analysis and calculation results, hindering a thorough understanding of the seismic response of layered rock caverns and leading to unsafe seismic stability assessments of underground rock caverns.

[0003] The Chinese patent application with application number CN202010602536.6 and application date June 29, 2020, reveals a composite criterion calculation method for the dynamic stability of surrounding rock under blast loads, including model establishment and load analysis; determination of dynamic displacement; determination of dynamic function K; energy analysis; and analysis of sudden changes in surrounding rock instability. This scheme can accurately analyze the dynamic stability of surrounding rock, but does not consider the layer vibration degradation effect, resulting in inaccurate seismic stability evaluation results of underground caverns in rock masses.

[0004] The information disclosed in this background technology section is only intended to increase the understanding of the overall background of this patent application, and should not be regarded as an admission or any form of suggestion that the information constitutes the prior art already known to a person skilled in the art. Summary of the Invention

[0005] The purpose of the present invention is to overcome the problem in the prior art that the quasi-static method or traditional elastoplastic mechanics model cannot reflect the attenuation characteristics of the strength parameters of rock materials, and to provide a method for analyzing the seismic stability of underground caverns in rock masses that takes into account the degradation of layer vibration, so that the seismic stability evaluation results of underground caverns in rock masses are safer and more accurate.

[0006] To achieve the above objectives, the technical solution of the present invention is: a method for analyzing the seismic dynamic stability of a rock cavern considering layer vibration degradation, the method comprising the following steps:

[0007] The first step is to clarify the transversely isotropic elastic mechanical behavior of layered rock mass, the strength criterion of layered rock mass, and the plastic potential function of layered rock mass, and to construct the elastic-plastic degradation constitutive model of layered rock mass;

[0008] The second step is to determine the calculation formula of the strength parameters of the layer under earthquake action, determine the calculation formula of the strength parameters of the layered rock mass and rock blocks, and establish the evolution law of the strength parameters of the layered rock mass considering the deterioration effect of the layer vibration;

[0009] Step 3: Based on the rock failure index RFD m , define the level of destruction index RFD j , construct the LRFD, an evaluation index of layered rock mass damage under earthquake action;

[0010] The fourth step is to use programming software to implement the elastic-plastic degradation constitutive model of the layered rock mass constructed in the first step, the evolution law of the layered rock mass strength parameters established in the second step, and the layered rock mass destructiveness evaluation index constructed in the third step respectively;

[0011] The fifth step is to use the elastic-plastic degradation constitutive model of layered rock mass, the evolution law of layered rock mass strength parameters and the layered rock mass destructibility evaluation index implemented by programming in the fourth step to calculate the seismic stability safety factor of the rock mass underground cavern and determine the seismic stability safety range of the rock mass underground cavern.

[0012] In the first step, the transversely isotropic elastic mechanical behavior of the layered rock mass is clarified, specifically:

[0013] The relationship between the stress increment and strain increment of layered rock mass in the global coordinate system can be expressed by the following formula (1):

[0014]

[0015] In the first step, the strength criteria of the layered rock mass are defined, specifically:

[0016] The strength criterion of layered rock mass consists of the rock block strength criterion and the layer strength criterion. The rock block strength criterion is composed of the shear failure yield function and tensile failure yield function The layer strength criterion is composed of shear failure yield function and tensile failure yield function composition.

[0017] In the first step, the plastic potential function of the layered rock mass is determined, specifically:

[0018] The plastic potential function of layered rock mass consists of the block plastic potential function and the layer plastic potential function. The block plastic potential function adopts the function and Indicates that they are used to determine the directions of the shear plastic strain increment and the tensile plastic strain increment of the rock block, respectively. Function Satisfying the non-associative flow law, the function Comply with the law of associated flow;

[0019] The layer plastic potential function uses the function and Indicates the direction of shear plastic strain increment and tensile plastic strain increment, respectively, and the potential function Satisfying the non-associated flow law, the potential function Satisfy the associated flow law.

[0020] In the second step, the calculation formula of the layer strength parameter under earthquake action is determined, specifically:

[0021] The main factors affecting the degradation of strength parameters of layered rock mass layers under earthquake action are vibration wear and relative velocity, which are characterized by the vibration wear coefficient η(t) and the relative influence coefficient γ(t). Assuming that the vibration wear coefficient η(t) and the relative influence coefficient γ(t) are relatively independent, then at any earthquake duration t, the vibration degradation coefficient D(t) of the layered rock mass layer is D(t) = η(t)γ(t). Therefore, the strength parameters of the layered rock mass layer can be calculated by equations (2) and (3):

[0022]

[0023] In formula (2) and formula (3), c j (t), are the cohesion and internal friction angle of the layer at any earthquake duration t, c j0 、 are the initial cohesion and initial internal friction angle of the layer, respectively.

[0024] The calculation formula for the strength parameters of the layered rock mass in the second step is as follows:

[0025] The calculation formulas for the strength parameters of layered rock blocks are expressed by the following two formulas:

[0026]

[0027] Where: c m0 and φ m0 are the benchmark values ​​of rock cohesion and internal friction angle respectively; c mN and φ mNare the current cohesion value and internal friction angle value of the rock block; c mr and φ mr are the residual cohesion and residual internal friction angle of the rock block, respectively; and are the equivalent plastic strain values ​​corresponding to the rock cohesion and internal friction angle when they reach the residual value; κ m is the current value of equivalent plastic strain of rock block;

[0028] In the second step, the calculation formula for the strength parameters of the layered rock mass is determined, specifically:

[0029] The calculation formulas for the strength parameters of layered rock blocks can be expressed by equations (4) and (5):

[0030]

[0031] In formula (4) and formula (5), c m0 and φ m0 are the benchmark values ​​of rock cohesion and internal friction angle respectively; c mN and φ mN are the current cohesion value and internal friction angle value of the rock block; c mr and φ mr are the residual cohesion and residual internal friction angle of the rock block, respectively; and are the equivalent plastic strain values ​​corresponding to the rock cohesion and internal friction angle when they reach the residual value; κ m is the current value of equivalent plastic strain of rock block;

[0032] In the second step, the evolution law of the strength parameters of the layered rock mass considering the vibration degradation effect of the layer is established, specifically:

[0033] Combining the calculation formulas of the strength parameters of the layered rock mass and the rock block strength parameters, the evolution law of the layered rock mass strength parameters considering the layer vibration degradation effect under earthquake action is established, as shown in the following formula (6):

[0034]

[0035] In the third step, the layer damage index RFD is defined j , specifically:

[0036] Definition of level destructive index RFD j , as shown in formula (7):

[0037]

[0038] in,

[0039]

[0040] In formula (7): g i (θ) is the plastic potential function of the layer, and are the equivalent plastic strain on the level and its corresponding limit equivalent plastic strain, F j A represents the yield function of the layer; j 、B j 、C j Both are layer strength criterion coefficients.

[0041] The third step of evaluating the damage degree of layered rock mass under earthquake action, LRFD, is specifically:

[0042] Rock block failure and layer failure are the two main types of failure of layered rock mass. Since rock mass always fails along or through its weakest part, the failure of layered rock mass depends on rock failure or layer failure or both. Therefore, in RFD, m and RFD j The larger value between them is taken as the evaluation index of the damage degree of layered rock mass under earthquake action, as shown in formula (9):

[0043] LRFD=max(RFD m RFD j );

[0044] In formula (9), LRFD is the evaluation index of layered rock mass damage; RFD m RFD is the index of rock failure; j It is an indicator of the level of damage.

[0045] The fifth step is to calculate the safety factor of the seismic stability of the underground cavern in the rock mass, specifically:

[0046] S1. Determine the design peak acceleration a based on the design intensity level of the project site m ;

[0047] S2. Select the earthquake motion time history a(t) that meets the site conditions and perform baseline correction and filtering on the earthquake wave data. Adjust the earthquake wave peak acceleration a0 proportionally so that a0 is equal to the fortification peak acceleration, that is, a0 = a m ;

[0048] S3. Establish a numerical calculation model of the rock mass underground cavern, perform static analysis and calculation, and generate a numerical calculation model containing an initial ground stress field;

[0049] S4. The processed seismic wave a(t) is used as the initial seismic motion time history and input into the numerical calculation model. Then, by gradually amplifying the amplitude of the initial input seismic acceleration time history, the critical seismic motion time history that causes the underground cavern to become unstable is searched and its peak acceleration is determined to be a. l ;

[0050] S5, using a0 and a l Establish the seismic stability criterion of rock mass underground caverns and define the seismic stability safety factor of rock mass underground caverns

[0051] The fifth step determines the safety range of seismic stability of the underground cavern in the rock mass, specifically:

[0052] The LRFD mutation of layered rock mass destruction index is used as the criterion for local instability of cave group structure. When the peak acceleration a0 of the initial input earthquake motion time a(t) is known, the seismic load is applied step by step until the value of the LRFD evaluation index of the internal characteristic point of the cave surrounding rock shows a mutation, and the peak overload acceleration a at this time is obtained. N1 Calculate the safety factor of seismic stability of the underground cavern in the rock mass at this time: DOFS N1 :

[0053]

[0054] Using the sudden displacement of the cavern surrounding rock surface as the overall instability criterion for the cavern group structure as the safety factor of the seismic stability of the rock mass underground cavern will be conservative, so DOFS N1 Set as the lower limit of the safety factor of the seismic stability of the underground cavern in the rock mass, continue to apply the seismic load step by step until the surface displacement of the cavern surrounding rock changes suddenly, and obtain the peak overload acceleration a at this time N2 Calculate the safety factor of seismic stability of the underground cavern in the rock mass at this time: DOFS N2 :

[0055]

[0056] DOFS N2 The overall stability of the cave structure that can be reflected is closer to the limit state, so DOFS N2 Set as the upper limit of the safety factor of the seismic stability of the rock mass underground cavern, and finally determine the safety range of the seismic stability of the rock mass underground cavern [DOFS N1 , DOFS N2 ].

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] 1. The present invention addresses the problem of considering the effects of layer vibration degradation in a rock cavern seismic dynamic stability analysis method. This method considers the effects of layer vibration degradation, establishes a layered rock mass elastic-plastic degradation model, the evolution law of layered rock mass strength parameters, and an evaluation index for layered rock mass destructibility. Furthermore, it proposes a method for calculating the safety factor for seismic stability of underground rock caverns, and determines the safe range for seismic stability of underground rock caverns. This method overcomes the shortcomings of the pseudo-static method or traditional elastic-plastic mechanical model in the calculation process, which fail to consider the dynamic changes in rock material strength parameters and result in unsafe calculation results. Therefore, the present invention considers the effects of layer vibration degradation, making the seismic stability evaluation results safer and more accurate.

[0059] 2. The present invention provides a method for analyzing the seismic dynamic stability of rock caverns that takes into account the degradation of surface vibration. The principle is simple and the physical meaning is clear. It can obtain a high-reliability safety interval for the seismic stability of rock underground caverns, and provide theoretical support for studying the mechanical response law and disaster mechanism of rock underground caverns under earthquake action. It has good practical engineering application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a flow chart of the present invention.

[0061] Figure 2 This is a flow chart of the calculation of the earthquake stability safety interval of the present invention.

[0062] Figure 3 It is a schematic diagram of the calculation model of the circular double-chamber structure of the present invention.

[0063] Figure 4 It is a schematic diagram of the seismic wave time history curve of the present invention.

[0064] Figure 5 This is a graph showing how the LRFD of the internal characteristic points of the surrounding rock vary with the seismic stability safety factor.

[0065] Figure 6 This is a graph showing how the displacement of characteristic points on the surrounding rock surface changes with the seismic stability safety factor. DETAILED DESCRIPTION

[0066] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0067] Example 1:

[0068] A method for analyzing the seismic dynamic stability of a rock cavern considering the deterioration of the layer vibration is provided. The specific process of the method for analyzing the seismic dynamic stability of a rock cavern considering the deterioration of the layer vibration is shown in FIG. Figure 1 , including the following steps:

[0069] The first step is to clarify the transversely isotropic elastic mechanical behavior of layered rock mass, the strength criterion of layered rock mass, and the plastic potential function of layered rock mass, and to construct the elastic-plastic degradation constitutive model of layered rock mass;

[0070] The second step is to determine the calculation formula of the strength parameters of the layer under earthquake action, determine the calculation formula of the strength parameters of the layered rock mass and rock blocks, and establish the evolution law of the strength parameters of the layered rock mass considering the deterioration effect of the layer vibration;

[0071] Step 3: Based on the rock failure index RFD m , define the level of destruction index RFD j , construct the LRFD, an evaluation index of layered rock mass damage under earthquake action;

[0072] The fourth step is to use programming software to implement the elastic-plastic degradation constitutive model of the layered rock mass constructed in the first step, the evolution law of the layered rock mass strength parameters established in the second step, and the layered rock mass destructiveness evaluation index constructed in the third step respectively;

[0073] The fifth step is to use the elastic-plastic degradation constitutive model of layered rock mass, the evolution law of layered rock mass strength parameters and the layered rock mass destructibility evaluation index implemented by programming in the fourth step to calculate the seismic stability safety factor of the rock mass underground cavern and determine the seismic stability safety range of the rock mass underground cavern.

[0074] Example 2:

[0075] Example 2 is basically the same as Example 1, except that:

[0076] The transversely isotropic elastic mechanical behavior of layered rock mass, the strength criterion of layered rock mass, and the plastic potential function of layered rock mass are clarified, and the elastic-plastic degradation constitutive model of layered rock mass is constructed. The specific steps are as follows:

[0077] 2.1. If the layered rock mass is regarded as a transversely isotropic elastic material, the relationship between the stress increment and the strain increment of the layered rock mass in the global coordinate system can be expressed by formula (1):

[0078]

[0079] In formula (1), A is the elastic stiffness matrix in the global coordinate system, which can be obtained by formula (11):

[0080] [A]=[R][C][R] T (11)

[0081] In formula (11), the elastic stiffness matrix C in the local coordinate system can be obtained by inverting the elastic flexibility matrix D in the local coordinate system, as shown in formula (12). R is the coordinate transformation matrix, which is calculated by formula (13):

[0082]

[0083] In formula (12), E1 is the Young's modulus in the transverse isotropic surface, E3 is the Young's modulus perpendicular to the transverse isotropic surface, and v 12 is the Poisson’s ratio in the transversely isotropic plane, v 13 is the Poisson’s ratio in the perpendicular transverse isotropic plane, G 13 is the shear modulus perpendicular to the transverse isotropic plane, G 12 is the shear modulus in the transverse isotropic plane

[0084]

[0085] In formula (13), l1, l2, l3, m1, m2, m3, n1, n2, and n3 are the direction cosine components of the three coordinate axes of the local coordinate system in the global coordinate system, which are calculated by formula (14). The subscript numbers 1, 2, and 3 correspond to the coordinates of the T axis, N axis, and S axis in the local coordinate system, respectively;

[0086]

[0087] In formula (14), dip and dd are the layer dip and layer inclination, respectively.

[0088] 2.2 Determination of Strength Criteria for Layered Rock Mass

[0089] The strength criterion of layered rock mass consists of the rock mass strength criterion and the layer strength criterion. The rock mass strength criterion is composed of the shear failure yield function and tensile failure yield function As shown in Equations (15) and (16), the layer strength criterion is composed of the shear failure yield function and tensile failure yield function Composition, as shown in formula (17) and formula (18):

[0090]

[0091] In formula (15) and formula (16), σ1 and σ3 are the first principal stress and the third principal stress respectively; c m 、φ m are the cohesion and internal friction angle of the rock block, respectively. is the tensile strength of the rock mass, and its maximum value

[0092] f j s =τ j -c j +σ 3′3′ tanφ j(17)

[0093]

[0094] In formula (17) and formula (18): c j 、φ j is the cohesion and internal friction angle of the layer; σ 1′3′ , σ 2′3′ is the shear stress in the direction parallel to the plane; σ 3′3′ is the tensile stress in the direction perpendicular to the plane; is the tensile strength of the layer.

[0095] 2.3. Determine the plastic potential function of rock blocks and layers:

[0096] The plastic potential function of layered rock mass consists of the plastic potential function of rock blocks and the plastic potential function of layers. The plastic potential function of rock blocks adopts the function and Indicates that they are used to determine the directions of the shear plastic strain increment and the tensile plastic strain increment of the rock block, respectively. Function Satisfying the non-associated flow law, expressed by formula (19), the function It complies with the law of associated flow, which is expressed by formula (20):

[0097]

[0098] In formula (19): m is the rock dilatancy angle,

[0099]

[0100] The plastic potential function of the layer is used to adopt the function and Indicates the direction of shear plastic strain increment and tensile plastic strain increment, respectively, and the potential function Satisfying the non-associated flow law, the potential function Satisfying the associated flow law, it is expressed by equations (21) and (22) respectively:

[0101]

[0102] In formula (21) and formula (22): τ j is the shear stress of the layer, σ 3′3′ is the normal stress of the layer, ψ j is the shear dilatancy angle of the layer.

[0103] Example 3:

[0104] Example 3 is basically the same as Example 1, except that:

[0105] Determine the calculation formula for the strength parameters of layered rock mass under earthquake action, determine the calculation formula for the strength parameters of layered rock mass blocks, and establish the evolution law of layered rock mass strength parameters considering the layer vibration degradation effect. The specific steps are as follows;

[0106] 3.1. The main factors affecting the degradation of strength parameters of layered rock mass under earthquake action are vibration wear and relative velocity, which are characterized by the vibration wear coefficient η(t) and the relative influence coefficient γ(t);

[0107] 3.2. Determine the calculation formula for the layer strength parameters of layered rock mass

[0108] Assuming that the vibration wear coefficient η(t) and the relative influence coefficient γ(t) are relatively independent, then at any earthquake duration t, the vibration degradation coefficient of the layered rock mass surface is expressed by formula (23):

[0109] D(t)=η(t)γ(t) (23)

[0110] In formula (23), D(t) is the vibration degradation coefficient of the layered rock mass, η(t) is the vibration wear coefficient, and γ(t) is the relative velocity influence coefficient;

[0111] The vibration wear coefficient η(t) is related to the number of cyclic shearing times K(t) and the cyclic shearing amplitude J(t), which is expressed by formula (24). The relative velocity influence coefficient γ(t) is expressed by formula (25);

[0112] η(t)=R0+(1-R0)e aJ(t) +(1-R0)(1-e aJ(t) )e bJ(t) (twenty four)

[0113] In formula (24): a and b are unknown coefficients; R0 is the convergence value of the wear influence coefficient; e is a natural constant;

[0114] γ(γ)=P0+(1-P0)e -mV(t) (25)

[0115] In formula (25), P0 is the convergence value of the relative velocity influence coefficient; m is the undetermined coefficient; V(t) is the relative motion velocity between blocks; e is a natural constant;

[0116] Combining equations (23), (24), and (25), the vibration degradation coefficient of the layered rock mass is expressed by equation (26):

[0117] D(t)=[P0+(1-P0)e -mV(t) ][R0+(1-R0) eaJ(t)+(1-R0)(1-e aJ(t) )e bJ(t) ] (26)

[0118] In formula (26), P0 is the convergence value of the relative velocity influence coefficient; R0 is the convergence value of the wear influence coefficient; a, b, and m are all unknown coefficients; P0, R0, a, b, and m can all be obtained through cyclic shear tests on layered rock masses;

[0119] Therefore, at any earthquake duration time t, the strength parameters of the layered rock mass are calculated by formula (27):

[0120]

[0121] In formula (27): c j (t), are the cohesion and internal friction angle of the layer at any earthquake duration time t, c j0 、 are the initial cohesion and initial internal friction angle of the layer, respectively.

[0122] 3.3 In the established elastic-plastic degradation constitutive model of layered rock mass, the degree of plastic damage after yielding of layered rock mass is expressed by the equivalent plastic strain To reflect the process of rock mass yielding and fracture, the cohesion (c) and internal friction angle (φ) are regarded as equivalent plastic strain. The function is as follows:

[0123]

[0124] In formula (28): the mechanical parameters c0 and φ0 are the initial values ​​of the layered rock mass before damage yield; and is the degradation value of mechanical parameters under certain equivalent plastic strain;

[0125] and The equivalent plastic strain A function of .

[0126] 3.4. Calculation formula for determining rock block strength parameters of layered rock masses

[0127] Will and Considered as equivalent plastic strain The linear function of , then the strength parameter calculation formula of layered rock mass is expressed by formula (4) and formula (5):

[0128]

[0129] In formula (4) and formula (5), c m0and φ m0 are the benchmark values ​​of rock cohesion and internal friction angle respectively; c mN and φ mN are the current cohesion value and internal friction angle value of the rock block; c mr and φ mr are the residual cohesion and residual internal friction angle of the rock block, respectively; and are the equivalent plastic strain values ​​corresponding to the rock cohesion and internal friction angle when they reach the residual value; κ m is the current value of the equivalent plastic strain of the rock block.

[0130] 3.5 Establishing the evolution law of strength parameters of layered rock mass considering the deterioration effect of interfacial vibration

[0131] Combining the above equations (27), (4) and (5), the evolution law of the strength parameters of layered rock mass considering the layer vibration degradation effect under earthquake action is established, as shown in equation (6):

[0132]

[0133] In formula (6): c m0 and φ m0 are the benchmark values ​​of rock cohesion and internal friction angle respectively; c mN and φ mN are the current cohesion value and internal friction angle value of the rock block; c mr and φ mr are the residual cohesion and residual internal friction angle of the rock block, respectively; and are the equivalent plastic strain values ​​corresponding to the rock cohesion and internal friction angle when they reach the residual value; κ m is the current value of the equivalent plastic strain of the rock block, D(t) is the vibration degradation coefficient of the rock layer at the time of earthquake duration t, c j (t), are the cohesion and internal friction angle of the layer at any earthquake duration time t; c j0 、 are the initial cohesion and initial internal friction angle of the rock layer, respectively.

[0134] Example 4:

[0135] Example 4 is basically the same as Example 1, except that:

[0136] Based on the rock failure index RFD m , define the level of destruction index RFD j , construct the LRFD evaluation index for layered rock mass damage under earthquake action, the specific steps are as follows:

[0137] 4.1. The rock failure index RFDm is proposed based on the continuum mechanics theory and the stress and strain analysis of the true triaxial test of rock. This index can quantitatively characterize the fracture location and damage degree of the rock. The calculation expression of RFDm is shown in formula (29). The value range is 0-2. When RFDm is less than 1, it represents the degree of damage development before the peak; when RFDm is equal to 1, it represents the degree of damage development at the peak state of the rock; when RFDm is greater than 1, it represents the degree of damage development after the peak state of the rock; when RFDm is equal to 2, it is at the residual stress level.

[0138] The rock mass failure LRFD mutation criterion is specifically:

[0139]

[0140] in,

[0141]

[0142] (29) Where: F represents the yield function of the rock mass. Before the peak failure (F < 0), g j (θ) is the plastic potential function, θ is the Lode angle; p and q are the mean stress and equivalent shear stress, respectively; σ1, σ2, σ3 are the maximum principal stress, intermediate principal stress, and minimum principal stress, respectively; A, B, and C are the rock strength criterion coefficients; for the post-peak failure stage (F ≥ 0), and They are the current equivalent plastic strain of rock material and its corresponding limit equivalent plastic strain, RFD at the peak failure stage m The indicators actually reflect the development of damage induced by changes in the volume and shape of rock materials.

[0143] 4.2. Based on the surrounding rock damage index RFD m Definition of rock layer failure index RFD for layered rock mass yield failure j , as shown in formula (7):

[0144]

[0145] In formula (7): g i (θ) is the plastic potential function of the layer, and are the equivalent plastic strain on the level and its corresponding limit equivalent plastic strain, F j A represents the yield function of the layer; j 、B j 、C j Both are layer strength criterion coefficients.

[0146] 4.3. Rock failure and layer failure are the two main types of failure in layered rock mass. Since rock mass always fails along or through its weakest part, the failure of layered rock mass depends on rock failure or layer failure or both. Therefore, in RFD, m and RFD j The larger value between them is taken as the evaluation index of the damage degree of layered rock mass under earthquake action, as shown in formula (8):

[0147] LRFD=max(RFD m , RFD j ) (8)

[0148] In formula (8), LRFD is the evaluation index of the damage degree of layered rock mass, and its value range is 0-2. When LRFD is less than 1, it indicates the development degree of damage before the peak of layered rock mass. When LRFD is equal to 1, it indicates the development degree of damage at the peak of layered rock mass. When LRFD is greater than 1, it indicates the development degree of damage after the peak of layered rock mass. When RFD is greater than 1, it indicates the development degree of damage after the peak of layered rock mass. m When RFD is equal to 2, the layered rock mass is in a residual stress state; m RFD is the index of rock failure; j It is an indicator of the level of damage.

[0149] Example 5:

[0150] Example 5 is basically the same as Example 1, except that:

[0151] Programming software is used to implement the elastic-plastic degradation constitutive model of layered rock mass, the evolution law of layered rock mass strength parameters, and the layered rock mass failure evaluation index. The specific steps are as follows:

[0152] 5.1. Based on the Microsoft Visual Studio 2010 software platform, the elastic-plastic degradation constitutive model of layered rock mass and the calculation formula of rock block strength parameters in the evolution law of layered rock mass strength parameters are compiled using C++ language, and a dynamic link library file .dll is generated. This file is then placed in the numerical calculation software FLAC 3D The default installation directory is C:\ProgramFiles\Itasca\Flac3d600\exe64\plugins\cmodel, software FLAC 3D The .dll file can be automatically called at startup:

[0153] 5.2. Based on FLAC 3D The software platform uses Fish language to compile and realize the layered rock mass destruction evaluation index and the layer strength parameter calculation formula in the layered rock mass strength parameter evolution law, and generates 3D.f3dat files that run directly on the software platform;

[0154] Example 6:

[0155] Example 6 is basically the same as Example 1, except that:

[0156] Based on the above-mentioned elastic-plastic degradation constitutive model of layered rock mass, the evolution law of layered rock mass strength parameters and the layered rock mass failure evaluation index, FLAC 3D Numerical calculation software is used to carry out seismic stability analysis of rock mass underground caverns, calculate the seismic stability safety factor of rock mass underground caverns, and determine the seismic stability safety range of rock mass underground caverns. The specific steps are as follows:

[0157] S1. Determine the design peak acceleration a based on the design intensity level of the project site m ;

[0158] S2. Select the earthquake motion time history a(t) that meets the site conditions and perform baseline correction and filtering on the earthquake wave data. Adjust the earthquake wave peak acceleration a0 proportionally so that a0 is equal to the fortification peak acceleration, that is, a0 = a m ;

[0159] S3. Establish a numerical calculation model of the rock mass underground cavern, perform static analysis and calculation, and generate a numerical calculation model containing an initial ground stress field;

[0160] S4. The processed seismic wave a(t) is used as the initial seismic motion time history and input into the numerical calculation model. Then, by gradually amplifying the amplitude of the initial input seismic acceleration time history, the critical seismic motion time history that causes the underground cavern to become unstable is searched and its peak acceleration is determined to be a. l ;

[0161] S5, using a0 and a l Establish the seismic stability criterion of rock mass underground caverns and define the seismic stability safety factor of rock mass underground caverns

[0162] The LRFD mutation of layered rock mass destruction index is used as the criterion for local instability of cave group structure. When the peak acceleration a0 of the initial input earthquake motion time a(t) is known, the seismic load is applied step by step until the value of the LRFD evaluation index of the internal characteristic point of the cave surrounding rock shows a mutation, and the peak overload acceleration a at this time is obtained. N1 Calculate the safety factor of seismic stability of the underground cavern in the rock mass at this time: DOFS N1 :

[0163]

[0164] Using the sudden displacement of the cavern surrounding rock surface as the overall instability criterion for the cavern group structure as the safety factor of the seismic stability of the rock mass underground cavern will be conservative, so DOFS N1 Set as the lower limit of the safety factor of the seismic stability of the underground cavern in the rock mass, continue to apply the seismic load step by step until the surface displacement of the cavern surrounding rock changes suddenly, and obtain the peak overload acceleration a at this time N2 Calculate the safety factor of seismic stability of the underground cavern in the rock mass at this time: DOFS N2 :

[0165]

[0166] DOFS N2 The overall stability of the cave structure that can be reflected is closer to the limit state, so DOFS N2 Set as the upper limit of the safety factor of the seismic stability of the rock mass underground cavern, and finally determine the safety range of the seismic stability of the rock mass underground cavern [DOFS N1 , DOFS N2 ],like Figure 2 shown.

[0167] Example 7:

[0168] Example 7 is basically the same as Example 1, except that:

[0169] The numerical calculation and analysis of the dynamic overload of the double-cavity model are as follows:

[0170] like Figure 3 As shown in the figure, a circular double-cavity numerical calculation model is established in FLAC3D software with dimensions of 100m*2m*100m (length*width*height), a circular cavern radius of 5m, a center distance of 20m between the two caverns, a tetrahedral unit, a total number of nodes of 148242, and a total number of units of 690935. The circular double-cavity calculation model is designed for earthquake intensity VI, with a design peak acceleration of 0.1g.

[0171] like Figure 4 As shown in the figure, the 2022 A earthquake wave is selected as the seismic motion input time history, A1 is the position of the characteristic point inside the surrounding rock, and A2 is the position of the characteristic point on the surface of the surrounding rock. Based on the elastic-plastic degradation constitutive model of layered rock mass established in the above steps, the evolution law of the strength parameters of layered rock mass considering the layer vibration degradation effect, and the layered rock mass destructibility evaluation index, the FLAC3D numerical calculation software is used to carry out the seismic stability analysis of the rock cavern, calculate the seismic stability safety factor of the rock cavern, and determine the seismic stability safety range of the rock cavern;

[0172] The calculation results are as follows Figure 5 and Figure 6 As shown, Figure 5is the relationship between the LRFD of the internal characteristic points of the surrounding rock and the seismic stability coefficient, Figure 6 The displacement of the characteristic points on the surrounding rock surface changes with the earthquake stability safety factor, which is given by Figure 5 It can be seen that when the seismic stability coefficient DOFS = 2.2, the LRFD value of the characteristic point A1 inside the surrounding rock suddenly changes, which indicates that the internal rupture of the middle partition wall where the characteristic point A1 is located suddenly intensifies, and a through area with LRFD>1 appears at the middle partition wall. The local area of ​​the circular double cavern is unstable, but the bearing capacity of the circular double cavern is not lost at this time, and the overall structure is not unstable. Therefore, the lower limit of the seismic stability safety factor of the circular double cavern is DOFS. N1 =2.2; Figure 6 It can be seen that when the seismic stability coefficient DOFS = 3.3, the displacement of the characteristic point A2 on the surrounding rock surface fluctuates significantly. At this moment, the circular double-cavity structure loses its overall stability and loses its bearing capacity. Then the upper limit of the seismic stability safety coefficient of the circular double-cavity structure is taken as DOFS N2 =3.3, therefore, the seismic stability safety interval of the circular double cavern is [2.2, 3.3].

[0173] The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiment. Any equivalent modifications or changes made by ordinary technicians in this field based on the contents disclosed in the present invention should be included in the protection scope recorded in the claims.

Claims

1. A method for analyzing the seismic dynamic stability of rock caverns considering layer vibration degradation, characterized in that: The method for analyzing the seismic dynamic stability of a rock cavern considering layer vibration degradation comprises the following steps: The first step is to clarify the transversely isotropic elastic mechanical behavior of layered rock mass, the strength criterion of layered rock mass, and the plastic potential function of layered rock mass, and to construct the elastic-plastic degradation constitutive model of layered rock mass; The second step is to determine the calculation formula of the strength parameters of the layer under earthquake action, determine the calculation formula of the strength parameters of the layered rock mass and rock blocks, and establish the evolution law of the strength parameters of the layered rock mass considering the deterioration effect of the layer vibration; Step 3: Based on the rock failure index RFD m , define the level of destruction index RFD j , construct the LRFD, an evaluation index of layered rock mass damage under earthquake action; The fourth step is to use programming software to implement the elastic-plastic degradation constitutive model of the layered rock mass constructed in the first step, the evolution law of the layered rock mass strength parameters established in the second step, and the layered rock mass destructiveness evaluation index constructed in the third step respectively; The fifth step is to use the elastic-plastic degradation constitutive model of layered rock mass, the evolution law of layered rock mass strength parameters and the layered rock mass destructibility evaluation index implemented by programming in the fourth step to calculate the seismic stability safety factor of the rock mass underground cavern and determine the seismic stability safety range of the rock mass underground cavern.

2. The method for analyzing the seismic dynamic stability of rock caverns considering layer vibration degradation according to claim 1 is characterized by: In the first step, the transversely isotropic elastic mechanical behavior of the layered rock mass is clarified, specifically: The relationship between the stress increment and strain increment of layered rock mass in the global coordinate system can be expressed by the following formula (1):

3. The method for analyzing the seismic dynamic stability of rock caverns considering layer vibration degradation according to claim 2 is characterized by: The first step is to define the strength criteria of the layered rock mass, specifically: The strength criterion of layered rock mass consists of the rock block strength criterion and the layer strength criterion. The rock block strength criterion is composed of the shear failure yield function and tensile failure yield function The layer strength criterion is composed of shear failure yield function and tensile failure yield function composition.

4. The method for analyzing the seismic dynamic stability of rock caverns considering layer vibration degradation according to claim 3 is characterized by: In the first step, the plastic potential function of the layered rock mass is defined as follows: The plastic potential function of layered rock mass consists of the block plastic potential function and the layer plastic potential function. The block plastic potential function adopts the function and Indicates that they are used to determine the directions of the shear plastic strain increment and the tensile plastic strain increment of the rock block, respectively. Function Satisfying the non-associative flow law, the function Comply with the law of associated flow; The layer plastic potential function uses the function and Indicates the direction of shear plastic strain increment and tensile plastic strain increment, respectively, and the potential function Satisfying the non-associated flow law, the potential function Satisfy the associated flow law.

5. The method for analyzing the seismic dynamic stability of rock caverns considering layer vibration degradation according to claim 1 is characterized in that: In the second step, the calculation formula of the layer strength parameter under earthquake action is determined as follows: The main factors affecting the degradation of strength parameters of layered rock mass layers under earthquake action are vibration wear and relative velocity, which are characterized by the vibration wear coefficient η(t) and the relative influence coefficient γ(t). Assuming that the vibration wear coefficient η(t) and the relative influence coefficient γ(t) are relatively independent, then at any earthquake duration t, the vibration degradation coefficient D(t) of the layered rock mass layer is D(t) = η(t)γ(t). Therefore, the strength parameters of the layered rock mass layer can be calculated by equations (2) and (3): In formula (2) and formula (3), c j (t), are the cohesion and internal friction angle of the layer at any earthquake duration t, c j0 、 are the initial cohesion and initial internal friction angle of the layer, respectively.

6. The method for analyzing the seismic dynamic stability of rock caverns considering layer vibration degradation according to claim 5 is characterized by: In the second step, the calculation formula for the strength parameters of the layered rock mass is determined as follows: The calculation formulas for the strength parameters of layered rock blocks can be expressed by equations (4) and (5): In formula (4) and formula (5), c m0 and φ m0 are the benchmark values ​​of rock cohesion and internal friction angle respectively; c mN and φ mN are the current cohesion value and internal friction angle value of the rock block; c mr and φ mr are the residual cohesion and residual internal friction angle of the rock block, respectively; and are the equivalent plastic strain values ​​corresponding to the rock cohesion and internal friction angle when they reach the residual value; κ m is the current value of equivalent plastic strain of rock block; In the second step, the evolution law of the strength parameters of the layered rock mass considering the vibration degradation effect of the layer is established, specifically: Combining the calculation formulas of the strength parameters of the layered rock mass and the rock block strength parameters, the evolution law of the layered rock mass strength parameters considering the layer vibration degradation effect under earthquake action is established, as shown in the following formula (6):

7. The method for analyzing the seismic dynamic stability of rock caverns considering layer vibration degradation according to claim 6 is characterized in that: In the third step, the layer damage index RFD is defined j , specifically: Definition of level destructive index RFD j , as shown below: in, In formula (7): g i (θ) is the plastic potential function of the layer, and are the equivalent plastic strain on the level and its corresponding limit equivalent plastic strain, F j A represents the yield function of the layer; j 、B j 、C j Both are layer strength criterion coefficients.

8. The method for analyzing the seismic dynamic stability of rock caverns considering layer vibration degradation according to claim 7 is characterized in that: The third step is to construct the LRFD, an evaluation index of the layered rock mass damage degree under earthquake action, which is specifically: Rock block failure and layer failure are the two main types of failure of layered rock mass. Since rock mass always fails along or through its weakest part, the failure of layered rock mass depends on rock failure or layer failure or both. Therefore, in RFD, m and RFD j The larger value between them is taken as the evaluation index of the damage degree of layered rock mass under earthquake action, as shown in formula (9): LRFD=max(RFD m ,RFD j ) (9); In formula (9), LRFD is the evaluation index of layered rock mass damage; RFD m RFD is the index of rock failure; j It is an indicator of the level of damage.

9. The method for analyzing the seismic dynamic stability of rock caverns considering layer vibration degradation according to claim 1 is characterized by: The fifth step is to calculate the safety factor of the seismic stability of the underground cavern in the rock mass, specifically: S1. Determine the design peak acceleration a based on the design intensity level of the project site m ; S2. Select the earthquake motion time history a(t) that meets the site conditions and perform baseline correction and filtering on the earthquake wave data. Adjust the earthquake wave peak acceleration a0 proportionally so that a0 is equal to the fortification peak acceleration, that is, a0 = a m ; S3. Establish a numerical calculation model of the rock mass underground cavern, perform static analysis and calculation, and generate a numerical calculation model containing an initial ground stress field; S4. The processed seismic wave a(t) is used as the initial seismic motion time history and input into the numerical calculation model. Then, by gradually amplifying the amplitude of the initial input seismic acceleration time history, the critical seismic motion time history that causes the underground cavern to become unstable is searched and its peak acceleration is determined to be a. l ; S5, using a0 and a l Establish the seismic stability criterion of rock mass underground caverns and define the seismic stability safety factor of rock mass underground caverns 10. The method for analyzing the seismic dynamic stability of rock caverns considering layer vibration degradation according to claim 9, characterized in that: The fifth step determines the safety range of seismic stability of the underground cavern in the rock mass, specifically: The LRFD mutation of layered rock mass destruction index is used as the criterion for local instability of cave group structure. When the peak acceleration a0 of the initial input earthquake motion time a(t) is known, the seismic load is applied step by step until the value of the LRFD evaluation index of the internal characteristic point of the cave surrounding rock shows a mutation, and the peak overload acceleration a at this time is obtained. N1 Calculate the safety factor of seismic stability of the underground cavern in the rock mass at this time: DOFS N1 : Using the sudden displacement of the cavern surrounding rock surface as the overall instability criterion for the cavern group structure as the safety factor of the seismic stability of the rock mass underground cavern will be conservative, so DOFS N1 Set as the lower limit of the safety factor of the seismic stability of the underground cavern in the rock mass, continue to apply the seismic load step by step until the surface displacement of the cavern surrounding rock changes suddenly, and obtain the peak overload acceleration a at this time N2 Calculate the safety factor of seismic stability of the underground cavern in the rock mass at this time: DOFS N2 : DOFS N2 The overall stability of the cave structure that can be reflected is closer to the limit state, so DOFS N2 Set as the upper limit of the safety factor of the seismic stability of the rock mass underground cavern, and finally determine the safety range of the seismic stability of the rock mass underground cavern [DOFS N1 , DOFS N2 ].

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