Quantitative analysis method for stability of surrounding rock based on microseismic cumulative damage under unloading in roadway

Abstract

The present application relates to the field of surrounding rock stability analysis, in order to realize the quantitative evaluation of surrounding rock stability, provide the quantitative analysis method of surrounding rock stability based on roadway unloading microseismic cumulative damage, from the physical mechanism of elastic wave propagation of cavity-containing medium, based on the three-dimensional diffraction path model is constructed based on the geometric diffraction theory, realize the high-precision spatial positioning of microseismic damage source;Through the high ground stress unloading model test of cavity-containing rock sample, the key coefficient of microseismic monitoring information and surrounding rock mechanical parameters is calibrated;Further, the multi-event cumulative damage superposition criterion is proposed, the discrete microseismic monitoring data is converted into the quantitative reduction basis of surrounding rock mechanical parameters, finally, the dynamic quantitative evaluation of surrounding rock stability of deep roadway unloading induced microseismic damage is realized through numerical simulation, a complete closed loop from monitoring signal to quantitative conclusion of surrounding rock stability is formed, the quantitative analysis ability and engineering guidance value of microseismic monitoring technology in deep underground engineering are significantly improved.

Description

Technical Field

[0001] This invention relates to the field of surrounding rock stability analysis, specifically a quantitative analysis method for surrounding rock stability based on cumulative damage from microseismic events during roadway unloading. Background Technology

[0002] After the excavation of deep underground caverns, the original triaxial stress equilibrium of the surrounding rock is disrupted, and the rock mass in a high-stress environment undergoes severe stress redistribution due to the unloading effect of excavation. This mechanical process leads to internal fracturing and damage in the surrounding rock, while the elastic strain energy stored in the rock mass is released to the outside in various forms, including microseismic elastic waves, frictional heat energy, surface energy of new fractures, and plastic deformation work. Among these, the microseismic elastic wave signals radiated by rock fracturing carry rich information such as the source mechanism, fracturing scale, and energy release, which can be used for rock mass physical and mechanical parameter inversion, damage and failure type identification, damage source location, surrounding rock stability evaluation, and geological hazard early warning. Therefore, microseismic monitoring technology has become one of the important means of surrounding rock stability analysis in deep underground engineering.

[0003] However, directly applying microseismic monitoring data induced by roadway unloading to the stability analysis of surrounding rock in deep roadways still faces the following three prominent challenges:

[0004] First, there is the problem of accurately locating microseismic damage sources in cavitary media within roadways. In the unique cavity-containing medium of roadway surrounding rock, elastic waves generated by rock fractures are blocked by the cavity and cannot penetrate in a straight line. Instead, they diffract around the cavity edges before continuing to propagate in a straight line. Traditional time-difference positioning algorithms based on the assumption of straight-line elastic wave propagation suffer from significant fundamental errors under these conditions: the assumption of a straight path leads to a severe mismatch between theoretical and measured wave arrival times, incorrectly interpreting the time delay caused by diffraction as an increase in the source distance, ultimately resulting in large deviations in the positioning results. Existing microseismic monitoring technologies have not yet effectively solved the problem of high-precision location of microseismic damage sources under the influence of diffraction effects in cavitary media within roadways.

[0005] Second, there is a lack of quantitative mapping between microseismic monitoring data and surrounding rock mechanical parameters. During the outward radiation of microseismic elastic waves, primary fractures within the rock mass in a certain area around the seismic source open, expand, and connect, causing permanent deterioration of the rock's mechanical properties (such as cohesion, internal friction angle, and elastic modulus). The actual extent of this damage zone is often larger than the scale of the seismic source fracture surface itself. However, current technology lacks effective means to quantitatively correlate microseismic monitoring information (such as source radius and radiated energy) with the extent of surrounding rock damage and the degree of reduction in rock mechanical parameters. Microseismic data analysis often remains at the level of event location and energy statistics, making it difficult to directly assess the actual damage level and stability state of the surrounding rock near the seismic source from the monitoring data, and thus failing to provide reasonable rock mechanical parameters for subsequent numerical simulation analysis.

[0006] Third, there is a lack of reasonable quantitative description methods for the cumulative damage effect of multiple microseismic events. Deep tunnel excavation and unloading is a continuous disturbance process, during which the surrounding rock often experiences numerous microseismic events. The same spatial location may be subjected to repeated damage from multiple microseismic events. The weakening of rock mass mechanical parameters by each damage event has an irreversible cumulative characteristic. However, existing analytical methods mostly treat single microseismic events in isolation, lacking reasonable quantitative criteria and superposition description methods for the spatially overlapping cumulative effect of multiple events. This makes it difficult to reflect the true process of the gradual evolution of surrounding rock damage until instability.

[0007] The combined constraints of the above three issues have prevented microseismic monitoring from fully playing its quantitative guiding role in the stability analysis of surrounding rock damaged by unloading-induced microseismic damage in deep tunnels. Summary of the Invention

[0008] To achieve quantitative assessment of surrounding rock stability, this invention provides a method for quantitative analysis of surrounding rock stability based on cumulative damage from microseismic events during roadway unloading.

[0009] The technical solution adopted by the present invention to solve the above problems is:

[0010] Quantitative analysis methods for surrounding rock stability based on cumulative microseismic damage during tunnel unloading include:

[0011] Step 1: Locate the source of microseismic events in the surrounding rock of a three-dimensional tunnel based on geometric diffraction theory;

[0012] Step 2: Calibrate the microseismic damage parameters of the surrounding rock of the roadway through unloading model tests using cavitary rock samples, including: the microseismic damage coefficient η and the damage radius coefficient k, where, , This represents the total cumulative radiated energy of microseismic events. To unload and release total energy during the excavation of the tunnel cavity. , The radius of the earthquake source is 1. This represents the actual damage radius;

[0013] Step 3: Based on the measured microseismic waveform data, determine the source radius of each microseismic event using the Brune source model. Based on the damage radius coefficient k, the damage range induced by each microseismic event is equivalent to the area centered on the epicenter and extending outwards. spherical damage area with radius [missing information] ;

[0014] Step 4: Determine the damage coefficient of each microseismic event in the surrounding rock of the roadway based on the actual working conditions and the calibrated microseismic damage parameters of the roadway surrounding rock under unloading. The rock mechanical parameters corresponding to the microseismic event are equivalently reduced based on the damage coefficient.

[0015] Step 5: Based on the location of the seismic source of the microseismic event and its corresponding spherical damage area, and combined with the equivalent reduced rock mechanical parameters, simulation calculations are performed to achieve the surrounding rock stability analysis.

[0016] Furthermore, step 1 specifically includes:

[0017] Step 11: Arrange micro-seismic sensors at equal intervals around the surrounding rock of the excavated tunnel;

[0018] Step 12: Construct a three-dimensional geometric model of the tunnel diffraction propagation path;

[0019] Step 13: Calculate the theoretical arrival time of the microseismic elastic wave signal;

[0020] Step 14: Construct the objective function of the elastic wave arrival time residual for microseismic events;

[0021] Step 15: Solve for the three-dimensional spatial coordinates of the microseismic event source based on the objective function.

[0022] Further, in step 11, 3-5 monitoring sections are selected, with a spacing of 5-10 meters between adjacent sections. Within each monitoring section, microseismic sensors are arranged at equal 45° intervals along the circumferential direction.

[0023] Furthermore, step 12 specifically involves: simplifying the deep underground tunnel cavity into a shape with a radius of... For a cylinder whose axis extends infinitely along the z-axis, elastic waves originate from the source. Starting from the point of incidence, the propagation proceeds tangentially along a straight line to the surface of the cylinder. Then it travels along the cylindrical surface of the tunnel, diffracting and crawling to the exit tangent point. Finally, it leaves the cylindrical surface along a tangential straight line and propagates to the sensor. ;in, The central angle corresponding to the point of incident tangency. Here are the axial coordinates corresponding to the incident tangent point. The central angle corresponding to the point of tangency at the exit point. The axial coordinates corresponding to the exit tangent point;

[0024] The geometric model of the diffraction propagation path in a three-dimensional tunnel is represented as follows: ,

[0025] ,

[0026] , , ,

[0027] .

[0028] Furthermore, the objective function in step 14 is: In the formula, When the elastic wave of the rock mass reaches the j-th microseismic sensor, as observed in actual measurements; The theoretical time for the rock mass elastic wave to reach the j-th microseismic sensor is given, where n is the total number of sensors.

[0029] Furthermore, step 2 specifically includes:

[0030] Step 21: Set up the test system, including preparing rock samples with cavities, and setting up a triaxial loading system and a cavity hydraulic loading / unloading system;

[0031] Step 22: Obtain the total energy released during tunnel cavity excavation and unloading based on the experimental system. Total cumulative radiation energy from microseismic events focal radius ;

[0032] Step 23: Determine the location of each microseismic event, perform CT scans on rock samples before and after the test to identify and determine the actual damage area radius corresponding to each microseismic event. ;

[0033] Step 24: Calculate the microseismic damage coefficient η and the damage radius coefficient k;

[0034] Step 25: Conduct unloading model tests on rock samples with cavities under different working conditions, and calculate the microseismic damage coefficient and damage radius coefficient corresponding to each group of tests; use multiple regression analysis to establish the functional relationship between parameters η and k and working conditions.

[0035] Furthermore, step 23 uses the Brune source model to determine the source radius of the microseismic event. Specifically, it includes:

[0036] Microseismic waveform data were collected to obtain the source displacement spectrum of the S-wave. The displacement spectrum is a curve showing the change of rock particle amplitude displacement with frequency.

[0037] The S-wave corner frequency was obtained by fitting and inverting the source displacement spectrum. The corner frequency is the frequency value corresponding to the intersection of the straight segment and the extension of the attenuation segment in the displacement spectrum curve;

[0038] Calculating the focal radius of microseismic events using the Brune source model : In the formula, For S-wave velocity; These are the source model constants.

[0039] Furthermore, in step 25, different working conditions include combinations of different rock strengths, rock mass integrity coefficients, initial geostress states, and unloading rates.

[0040] Furthermore, step 4 also includes calculating the cumulative damage variable. , , Let be any point in space; and the rock mechanical parameters corresponding to the microseismic event are equivalently reduced based on the cumulative damage variable.

[0041] Furthermore, when performing equivalent reduction, a linear form is used for equivalent reduction.

[0042] The advantages of this invention compared to the prior art are:

[0043] (1) A quantitative analysis method for the stability of surrounding rock under microseismic damage, driven by the fusion of monitoring data and physical simulation, has been developed.

[0044] This invention organically integrates three methods: microseismic monitoring data-driven analysis (microseismic source location and radiation energy calculation), indoor model test calibration (multivariate regression curves of η and k), and numerical simulation stability evaluation (analysis of the distribution characteristics of surrounding rock stress field, displacement field, and plastic zone). This forms a quantitative analysis method for the stability of microseismic damage in deep roadways driven by monitoring data and physical simulation. It overcomes the limitations of single analysis methods and provides a scientific basis for the stability analysis and disaster early warning of microseismic damage in surrounding rock induced by unloading in deep roadways.

[0045] (2) A high-precision localization method for microseismic damage sources in cavity media based on geometric diffraction theory was constructed.

[0046] To address the challenge of inaccurate seismic source localization in roadway surrounding rock due to non-linear diffraction caused by cavities, this invention introduces geometric diffraction theory into the field of microseismic localization in roadway surrounding rock. By simplifying the roadway cavity into a three-dimensional cylinder, a three-dimensional diffraction propagation path geometric model is established, comprising a spatial linear incident segment, a cylindrical spiral crawling segment, and a spatial linear exit segment. This fundamentally overcomes the applicability limitations of traditional time-difference localization algorithms based on the assumption of linear propagation in media containing roadway cavities. Simultaneously, a star-shaped microseismic monitoring sensor network layout around the roadway is designed, and a method is proposed to optimize the three-dimensional spatial coordinates of the microseismic source using a weighted residual objective function based on the arrival time of the microseismic elastic wave. This achieves high-precision three-dimensional spatial localization of microseismic damage sources in deep roadway media containing cavities.

[0047] (3) A model test calibration method for the microseismic damage coefficient η and the damage radius coefficient k was proposed.

[0048] To address the difficulty in quantifying and assessing the extent of microseismic damage to surrounding rock induced by unloading in tunnels and the degree of reduction in rock mass mechanical parameters, this invention proposes a microseismic damage coefficient η, defined as the ratio of cumulative microseismic radiation energy to the total energy released during unloading, and a damage radius coefficient k, defined as the ratio of the actual damage radius to the source radius. A high-stress unloading model test system for cavitary rock samples was designed to simulate the entire process of tunnel excavation and unloading under different lithologies, stress states, and unloading rates. Through orthogonal experimental design and multivariate regression analysis, multivariate regression curves were constructed relating the surrounding rock parameters η and k to rock strength, rock mass integrity, stress state, and unloading rate for different lithologies. This provides crucial data for determining the extent of microseismic damage to surrounding rock in deep tunnels and for quantitatively reducing the rock mass mechanical parameters within the damaged area.

[0049] (4) A cumulative damage variable considering the overlapping area of ​​multiple microseismic events was proposed for surrounding rock damage analysis.

[0050] In view of the actual situation that the surrounding rock of a roadway may suffer repeated damage from multiple microseismic events in the same spatial area, this invention proposes a cumulative damage superposition criterion for overlapping areas of multiple microseismic events, namely, a normalized cumulative damage variable. The incremental damage to the rock mass caused by each microseismic event is reasonably integrated according to the superposition principle, ensuring that the cumulative damage variable never exceeds 1, which conforms to physical constraints. Based on this, the equivalent reduction relationship between the cumulative damage variable and the main mechanical parameters of the surrounding rock (cohesion, internal friction angle, and elastic modulus) is given, providing reasonable parameter inputs for the numerical analysis of surrounding rock stability considering the gradual evolution of damage. Attached Figure Description

[0051] Figure 1 The flowchart shows the method for quantitative analysis of surrounding rock stability based on cumulative damage from microseismic events during tunnel unloading.

[0052] Figure 2 A modular flowchart of a quantitative analysis method for surrounding rock stability based on cumulative damage from microseismic events during tunnel unloading;

[0053] Figure 3 A flowchart of a high-precision method for locating microseismic damage sources in three-dimensional tunnel surrounding rock based on geometric diffraction theory;

[0054] Figure 4 A schematic diagram of the geometric model of the diffraction propagation path in a three-dimensional tunnel.

[0055] Figure 5 A flowchart of a method for reducing the mechanical parameters of surrounding rock and evaluating its stability, taking into account the cumulative damage effect of microseismic events. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0057] like Figure 1 As shown, the quantitative analysis method for surrounding rock stability based on cumulative microseismic damage during tunnel unloading includes:

[0058] Step 1: Locate the source of microseismic events in the surrounding rock of a three-dimensional tunnel based on geometric diffraction theory;

[0059] Step 2: Calibrate the microseismic damage parameters of the surrounding rock of the roadway through unloading model tests using cavitary rock samples, including: the microseismic damage coefficient η and the damage radius coefficient k, where, , This represents the total cumulative radiated energy of microseismic events. To unload and release total energy during the excavation of the tunnel cavity. , The radius of the earthquake source is 1. This represents the actual damage radius;

[0060] Step 3: Based on the measured microseismic waveform data, determine the source radius of each microseismic event using the Brune source model. Based on the damage radius coefficient k, the damage range induced by each microseismic event is equivalent to the area centered on the epicenter and extending outwards. spherical damage area with radius [missing information] ;

[0061] Step 4: Determine the damage coefficient of each microseismic event in the surrounding rock of the roadway based on the actual working conditions and the calibrated microseismic damage parameters of the roadway surrounding rock under unloading. The rock mechanical parameters corresponding to the microseismic event are equivalently reduced based on the damage coefficient.

[0062] Step 5: Based on the location of the seismic source of the microseismic event and its corresponding spherical damage area, and combined with the equivalent reduced rock mechanical parameters, simulation calculations are performed to achieve the surrounding rock stability analysis.

[0063] For ease of explanation, the following description uses a modular flowchart as an example. Figure 2 As shown.

[0064] S1: High-precision positioning of microseismic damage sources in three-dimensional tunnel surrounding rock based on geometric diffraction theory.

[0065] This step aims to address the source location error caused by the non-linear propagation of elastic waves in hollow media within deep roadways. By constructing a propagation path model that considers the diffraction effect of microseismic elastic waves along the roadway, and combining it with a star-shaped sensor network around the roadway and a location algorithm, high-precision location of microseismic damage sources in the surrounding rock of the roadway based on geometric diffraction theory is achieved. Specific steps are as follows: Figure 3 As shown, it includes:

[0066] (1) Deployment of star-shaped microseismic sensor network in ring tunnel

[0067] Microseismic sensors are arranged at equal intervals around the surrounding rock of the excavated roadway. As a preferred implementation, this example uses 3-5 monitoring sections with a spacing of 5-10 meters between adjacent sections. Within each monitoring section, sensors are arranged at equal 45° intervals along the circumference, forming a "star-shaped" signal monitoring and sensing layout network that provides 360° full coverage of the space around the roadway.

[0068] Wireless signal transmission modules are installed at intervals inside the tunnel wall to synchronously transmit real-time microseismic signal data collected by each sensor to the ground analysis module at the tunnel entrance, providing real-time data for subsequent seismic source location and damage analysis.

[0069] (2) Construct a three-dimensional geometric model of the diffraction propagation path in the tunnel.

[0070] In a real deep tunnel microseismic monitoring environment, the seismic source (location of rock damage and fracture) is... With sensors There is a cavity in the tunnel that acts as an obstacle. Microseismic elastic waves cannot directly penetrate the cavity to propagate; instead, they diffract around the edge of the cavity before reaching the sensor. Traditional positioning methods based on the assumption of straight-line propagation will produce significant errors under these conditions.

[0071] To solve the above problems, this step simplifies the deep underground tunnel cavity into a cavity with a radius of... A cylinder whose axis extends infinitely along the z-axis. In three-dimensional space, elastic waves originate from the source. propagation to sensor At that time, due to the obstruction of the tunnel cavity, the actual propagation path consists of the following three segments, such as... Figure 4 As shown,

[0072] ① Spatial incident line segment

[0073] Micro-seismic elastic waves from the source Starting from the point of incidence, the propagation proceeds tangentially along a straight line to the surface of the cylinder. Let the coordinates of the incident tangent point be... ,in The central angle corresponding to the point of incident tangency. This represents the axial coordinate corresponding to the point of incidence. The length of the incident segment of the straight line in space. for:

[0074] .

[0075] ② Cylindrical diffraction segment

[0076] Micro-vibration elastic wave propagation from the incident tangent point Starting from this point, it travels along the cylindrical surface of the tunnel, diffracting and crawling until it reaches the exit tangent point. Let the coordinates of the exit tangent point be... ,in The central angle corresponding to the point of tangency at the exit point. Let be the axial coordinates corresponding to the point of tangency at the exit. According to the generalized Fermat principle, the diffraction of an elastic wave at a medium interface follows the path corresponding to the shortest time. For a cylindrical surface, the connection... , The shortest path between two points is its transmission line, which is: a helix with a constant pitch, and this helical creeping segment... arc length Increment of the central angle between two points and axial displacement increment The decision was made jointly as follows: .

[0077] ③ Spatial exit straight segment

[0078] Micro-vibration elastic wave self-emission tangent point It propagates along a tangential straight line away from the cylindrical surface and reaches the sensor. The length of the straight segment of the exit line in this space. for: .

[0079] ④ Total length of three-dimensional diffraction wave propagation path

[0080] Combining the three propagation paths mentioned above, the total path length of the three-dimensional diffraction propagation of the elastic wave is... The complete expression for its expansion is: .

[0081] Among them, the point of incidence and the point of tangency at the point of exit Position parameters and It is not an independent variable, but is determined by the uniqueness of the shortest propagation path time (i.e., the uniqueness of the generalized Fermat principle), that is, for a given source... and sensors Spatial location, find two points on the cylindrical surface and This makes the total length of the above propagation paths... Reach the global minimum.

[0082] To further explain, the above-mentioned three-dimensional diffraction model has two special forms:

[0083] (i) When the epicenter With sensors When two points are located on the same cross-section of the cylindrical section of the tunnel, and the line connecting the two points is blocked by the tunnel cavity, that is... The aforementioned three-dimensional diffraction spiral crawling wave propagation model degenerates into a two-dimensional planar circular arc segment diffraction wave propagation model perpendicular to the tunnel axis, with a total wave propagation path length of...

[0084] .

[0085] (ii) When the epicenter With sensors When two points are on the same side of the tunnel and the line connecting them is not blocked by the tunnel cavity, the three-dimensional diffraction effect disappears, and the wave propagates along the shortest straight path, i.e., the central angle difference. The aforementioned three-dimensional diffraction wave propagation model degenerates into a conventional one-dimensional straight-line wave propagation model, with the total length of the straight-line segment of the wave propagation path being... .

[0086] The relationship between the two degradation scenarios verifies the theoretical self-consistency of the three-dimensional diffraction model of this invention.

[0087] (3) Calculate the theoretical arrival time of the microseismic elastic wave signal

[0088] In real-time positioning calculations for engineering projects, indoor wave velocity tests are conducted on rock samples from the surrounding rock of the tunnel beforehand to obtain the average propagation velocity of elastic waves (P-waves or S-waves) in the surrounding rock. The three-dimensional spatial region around the tunnel where damage may occur (preferably within a cross-section of xoy equal to 3 times the tunnel diameter, and longitudinally along the tunnel excavation length z) is divided into a mesh and discretized into dense mesh nodes. Each mesh node... As a candidate epicenter location.

[0089] Assume that the theoretical arrival time of the elastic wave from the candidate seismic source point corresponding to the i-th grid node to the j-th sensor in the ring tunnel star-shaped sensor network is, , The wave speed.

[0090] (4) Construct the objective function of elastic wave arrival time residual for microseismic events

[0091] The core task in determining the seismic source is to find a specific three-dimensional spatial grid node, and the theoretical time from this node to each sensor is... Compared with actual observation The goal is to minimize the sum of errors between them. Therefore, we define the objective function. for,

[0092] In the formula, n is the total number of sensors.

[0093] (5) Optimize the solution of the three-dimensional spatial coordinates of the source of the microseismic event.

[0094] Traverse all preset mesh nodes in the three-dimensional space of the surrounding rock that may be damaged around the tunnel, and calculate each candidate point. Corresponding objective function value When the algorithm meets the convergence condition, the global case is taken. The grid node coordinates corresponding to the minimum value (i.e., the optimal position) As the location of the vibration source ,Right now: .

[0095] S2: Model test calibration of microseismic damage parameters (k, η) of unloading surrounding rock in roadways.

[0096] Rock mass fracturing and damage (microseismic events) are always accompanied by energy dissipation, and the main mechanical parameters of the surrounding rock in the affected area (including elastic modulus, cohesion, and internal friction angle) will be weakened to varying degrees. To quantitatively describe the degree of reduction in the mechanical parameters of the surrounding rock caused by microseismic damage and the spatial extent of the damage, this invention proposes two key calibration parameters—the microseismic damage coefficient η and the damage radius coefficient. The value curve was calibrated through a high-pressure unloading model test of a rock sample containing a cavity.

[0097] (1) Definition and physical meaning of microseismic damage coefficient η

[0098] The total energy released during cavity unloading damage evolution during rock mass excavation unloading The energy is released in the form of elastic waves, frictional heat generation, formation of new fracture surfaces, and plastic deformation. This invention defines the microseismic damage coefficient η as: the total radiated energy of a microseismic event. Release of total energy through excavation and unloading of tunnel cavities The ratio is used to quantitatively characterize the proportion of elastic wave energy released during microseismic activity during unloading, and thus to quantitatively reflect the degree of surrounding rock damage. Its expression is: .

[0099] This reflects the proportion of detectable elastic wave energy released in the total energy released during roadway unloading, and its magnitude is positively correlated with the brittleness and damage degree of the rock mass. Generally speaking, the higher the in-situ stress, the greater the rock brittleness and compressive strength, and the better the rock mass integrity. The higher the value, the better. Since elastic wave radiation energy is only one form of the total energy released during unloading,... The value of is much less than 1.

[0100] (2) Microseismic damage radius coefficient Definition and physical meaning

[0101] This invention employs the Brune model method, simplifying the seismic source as a circular fault. After a microseismic event occurs, the elastic waves released by the source cause permanent deterioration damage to the original structural planes within a certain area of ​​the rock mass around the source, including the opening, expansion, and connection of micro-cracks, leading to a weakening of the rock mass's mechanical parameters. Therefore, the actual damage area is much larger than the size of the seismic source.

[0102] Microseismic damage radius coefficient in this invention The definition is: the actual damage area radius corresponding to the i-th microseismic damage event. Its focal radius The ratio. Used to quantitatively describe the proportional relationship between the source scale of a single microseismic event and the actual extent of surrounding rock damage caused by that source. Its expression is: In the formula, The source radius (m) is used in the Brune model to define the source radius as the radius of a circular fault. It is used to describe the equivalent scale of the "source body" where stress rapidly decreases and elastic waves radiate at the site of a microseismic event inside the rock. The actual damage radius (m) is used to describe the area where the mechanical properties of the rock mass centered on the earthquake source are permanently deteriorated during the propagation of the elastic waves released at the earthquake source.

[0103] (3) Test system for high geostress unloading damage model of rock samples with cavities

[0104] The geological conditions and stress environment of deep tunnels differ significantly, and the values ​​of the microseismic damage coefficient η and the damage radius coefficient k are related to the rock strength. Rock mass integrity coefficient Between geostress conditions and unloading rate Closely related For the maximum principal stress, The intermediate principal stress, The minimum principal stress is defined as η. To investigate the relationship between the aforementioned influencing factors and the damage parameters η and k, this invention designs a test system and method for calibrating the η and k value curves using a high-stress unloading damage model of cavitary rock samples. It mainly includes the following components:

[0105] ①Preparation of rock samples containing cavities

[0106] Cubic rock samples were collected from the tunnel construction site and prepared according to rock lithology, hardness, and integrity coefficient. A cylindrical cavity was prefabricated in the center of each rock sample, extending through the thickness direction, to simulate the cavity formed during tunnel excavation. The inner wall of the cavity was precision-machined to ensure surface flatness to meet hydraulic sealing requirements. High-frequency micro-vibration sensors and strain sensors were installed on the cavity wall to collect real-time data on rock mass micro-vibration signals induced during unloading and time-history data of radial displacement of the cavity wall, respectively.

[0107] ② Triaxial Loading System: Hydraulic jacks are symmetrically arranged in the x, y, and z orthogonal directions of the rock sample to form a triaxial loading system simulating initial geostress. This system can synchronously apply loads to the rock sample according to a preset stress path until the target stress state is reached. And satisfy different lateral pressure coefficients The loading requirements are designed to simulate different burial depths and structural stress environments.

[0108] ③ Cavity Hydraulic Loading / Unloading System: Sealed pistons are installed at both ends of the rock sample cavity to form a closed hydraulic chamber. A high-precision servo hydraulic source is used to inject liquid medium into the cavity and pressurize it to the target hydraulic value. This system is used to approximate the stress state of the surrounding rock in the tunnel wall before excavation. The hydraulic system features pressure stabilization and controllable rate unloading functions to simulate the following three typical unloading types:

[0109] (i) Rapid unloading (<0.1 s): Simulating blasting excavation conditions;

[0110] (ii) Medium-speed unloading (1~5 s): Simulating mechanical tunneling excavation conditions;

[0111] (iii) Slow unloading (>10 s): Simulates the stress relaxation and creep unloading conditions of the surrounding rock.

[0112] (4) Unloading and releasing total energy Measurement and calculation

[0113] During the cavity hydraulic unloading process, the radial displacement of the borehole wall is synchronously collected by strain sensors installed on the borehole wall. With hydraulic The time history data. According to the principle of energy conservation, the total work done by the hydraulic system on the borehole wall during the unloading process is the total energy released by the cavity unloading. The calculation formula is as follows: In the formula, R is the cavity radius (m); L is the cavity axial length (m), which is taken as the thickness of the test rock sample; Let be the radial displacement rate of the hole wall, and take . ;

[0114] , These represent the start and end times of unloading, respectively.

[0115] (5) Total cumulative radiation energy of microseismic events Measurement and calculation

[0116] During the cavity hydraulic unloading process, high-frequency microseismic sensors deployed on the borehole wall are used to synchronously acquire microseismic waveform data induced by damage inside the rock sample (i.e., the amplitude-displacement u-time t variation curve of rock particles). Figure). Fourier transform of the acquired microseismic waveforms yields the source displacement spectrum (i.e., the amplitude-displacement u-frequency f variation curve of rock particles). (Figure). Then multiply the source displacement spectrum by... Obtain the source velocity spectrum (i.e., the velocity of rock particles). - Frequency f variation curve picture).

[0117] The total radiated energy of each microseismic event is accumulated in chronological order. The total cumulative radiation energy is obtained by summing the radiation energy of all microseismic events identified during the observation period: In the formula, The density of the rock sample is (kg / m³). Let be the spatial distance (m) from the source of the i-th microseismic event to the sensor. The elastic wave velocity (m / s) can be taken as the propagation velocity of either p-wave or s-wave in the rock sample medium. The coefficient is used to account for the non-uniformity of energy radiation in different directions for different wave types (P-wave or S-wave) (0.52 for P-wave and 0.63 for S-wave). This is the radiant flux, the result of integrating the frequency with respect to the square of the velocity spectrum. It is calculated using the following formula: , The corner frequency (Hz) is the source displacement spectrum. The frequencies corresponding to the inflection points between the flat mid-section and the attenuation section.

[0118] (6) Determination and calculation of damage coefficient η

[0119] The total energy released during unloading was calculated based on the above cavity hydraulic unloading test. Total cumulative radiation energy from microseismic events Then, the microseismic damage coefficient η is calculated using the following formula. ,

[0120] This characterizes the proportion of energy released in the form of detectable elastic waves during rock mass fracturing. Its magnitude is positively correlated with the brittleness and degree of damage of the rock mass. Generally speaking, the higher the in-situ stress, the greater the rock brittleness and compressive strength, and the better the rock mass integrity, the greater the potential for damage. The higher the value, the better. Since the energy released by elastic waves is only one form of the total energy released during cavity unloading,... The value of is much less than 1, and is generally between 0 and 0.3.

[0121] (7) Radius of the earthquake source Measurement and calculation

[0122] Based on the microseismic waveform data collected during the model test, the source displacement spectrum of the S-wave was obtained. (i.e., the amplitude-displacement u-frequency f variation curve of rock particles), the S-wave corner frequency is obtained by fitting and inverting the source displacement spectrum. (Right now: The frequency value corresponding to the intersection of the straight segment and the extension of the attenuation segment in the curve); then, the radius of the circular fault source of the i-th microseismic event is calculated using the Brune model. : In the formula, The S-wave velocity of the rock sample from the S-source region; This is a source model constant, which can be taken as 2.34 for the Brune model.

[0123] (8) Determination and calculation of damage radius coefficient k

[0124] To establish the focal radius Compared with the actual damage radius The quantitative relationship between them. The location of each microseismic event is determined using the method of S1 of this invention: the method for determining the source of microseismic damage in roadway surrounding rock based on geometric diffraction theory. Simultaneously, high-resolution CT scans are performed on rock samples before and after the experiment. As a preferred implementation method, the CT scan identification accuracy is not less than 0.5 mm to clearly distinguish the initiation and propagation morphology of microcracks at the location of each microseismic event, and to identify and delineate the actual damage area radius corresponding to each microseismic event. .

[0125] Through statistical analysis, the average damage radius coefficient of rock samples under specific stress and unloading conditions was calculated for multiple microseismic events: .

[0126] (9) Multifactor regression calibration of microseismic damage parameters η and k

[0127] Through orthogonal experimental design, systematic studies were conducted on different rock strengths ( ), rock mass integrity factor ( ), initial geostress state ( ), unloading rate Unloading model tests of cavity-containing rock samples under combined conditions were conducted, and the microseismic damage coefficient η and damage radius coefficient k corresponding to each group of tests were calculated respectively.

[0128] Using multiple regression analysis, the functional relationships between parameters η and k and the aforementioned main factors were established: , .

[0129] Furthermore, empirical relationship calibration curves of microseismic damage parameters η and k as a function of various factors were plotted, providing key parameter values ​​for the analysis of the extent and degree of damage induced by unloading of surrounding rock in deep roadways.

[0130] S3: Equivalent quantification of the range and degree of microseismic damage to the surrounding rock of the tunnel.

[0131] In deep, high-stress environments, tunnel excavation and unloading cause stress redistribution, leading to internal rock mass damage and fracturing, which in turn induces microseismic events, resulting in a gradual weakening of the rock mass's mechanical parameters. Rock mass stability analysis considering microseismic damage effects requires addressing two core issues: first, determining the spatial location of each microseismic event; and second, determining the extent of each microseismic event's impact on the rock mass damage.

[0132] (1) Spatial center location of each microseismic event The determination

[0133] After the tunnel is excavated, microseismic signal sensors are embedded in the surrounding rock according to the ring-tunnel star-shaped microseismic sensor network layout scheme described in step S1 of this invention to conduct real-time monitoring of microseismic activity during the construction period. Based on the measured microseismic waveform data, the high-precision localization method for microseismic damage sources in the surrounding rock of the tunnel, which considers three-dimensional geometric diffraction, proposed in step S1, is used to determine the spatial coordinates of the source of each microseismic event. .

[0134] (2) Equivalent sphere quantification of damage range of microseismic events

[0135] During microseismic monitoring, it is difficult to directly measure the actual size and morphology of the internal damage and fracture surfaces of rock masses. To address this issue, this invention proposes an equivalent sphere quantification method for the damage range of microseismic events:

[0136] First, based on measured microseismic waveform data, the source radius of each microseismic event is determined using the Brune source model according to the method proposed in step S2. ;

[0137] Secondly, the multifactor regression expression of the damage radius coefficient calibrated through model experiments in step S2 of this invention is invoked. Determine the damage radius coefficient corresponding to each microseismic event. .

[0138] Then, the actual surrounding rock damage radius corresponding to each microseismic event is calculated. : .

[0139] Finally, the damage extent corresponding to the complex rupture surfaces induced by each microseismic event is equivalent to that at the epicenter location. Centered on, with spherical damage area with radius [missing information] The equivalent damage sphere volume corresponding to the i-th microseismic event is: .

[0140] Using the above method, the spatially irregular actual microseismic damage area is transformed into an equivalent set of spheres with a clear center position and radius, providing a basis for damage zone modeling in subsequent numerical simulation of surrounding rock stability.

[0141] S4: Reduction of surrounding rock mechanical parameters and stability evaluation considering microseismic cumulative damage effects

[0142] (1) Determination of the microseismic damage coefficient η

[0143] Based on the actual uniaxial compressive strength of the surrounding rock of the roadway Rock mass integrity coefficient Initial geostress conditions ( and excavation unloading rate The multi-factor regression relationship of the microseismic damage coefficient, calibrated through model tests in step S2 of this invention, is invoked. Determine the damage coefficients of each microseismic event in the surrounding rock of the roadway. .

[0144] (2) Cumulative damage superposition in the overlapping area of ​​multiple microseismic events

[0145] During the excavation and unloading process, the surrounding rock of a tunnel experiences numerous microseismic events, and a single spatial point may suffer repeated damage from multiple microseismic events. To reasonably describe the reduction of rock mass mechanical parameters due to this cumulative damage effect, this invention proposes the following cumulative damage superposition criterion:

[0146] For any point in space Statistically collect all spherical damage regions covering this point. Define the cumulative damage variable at this point. for: The physical meaning of this superposition criterion is that each microseismic event produces an independent "damage increment" on the rock mass, and the damage effects of each event are superimposed according to the principle of irreversible accumulation in damage mechanics. When the point is covered by only a single damage area, ;when When a point is covered by multiple overlapping damage areas, The value gradually approaches 1 with increasing coverage times, and never exceeds 1, which conforms to the basic constraints of damage mechanics.

[0147] (3) Equivalent reduction of rock mass mechanical parameters in the damaged zone

[0148] For any point in the surrounding rock space The normalized cumulative damage variable is used. The rock mechanical parameters of the grid region corresponding to this point are equivalently reduced. As a preferred implementation, the reduction formula adopts the following linear form: ; ; In the formula, , The equivalent cohesion of the rock mass before and after reduction; , The equivalent internal friction angle of the rock mass before and after reduction; , This represents the equivalent elastic modulus of the rock mass before and after reduction.

[0149] (4) Establishment of numerical simulation model for microseismic damage and analysis of surrounding rock stability

[0150] A three-dimensional numerical simulation model of the tunnel was established using finite difference numerical analysis software. The spatial locations of various microseismic events after the actual tunnel excavation were determined according to step S3. and its corresponding spherical damage area Based on the above equivalent reduction formula, the rock mass elements in each spherical damage area around the roadway in the model are assigned reduced rock mechanical parameters. , , .

[0151] Numerical calculations are used to obtain the stress field distribution, displacement field distribution, and plastic zone distribution characteristics of the surrounding rock under the condition of considering the cumulative damage effect of microseismic events. Based on this, the stability state of the surrounding rock under different cumulative damage levels is quantitatively assessed. The flowchart of the method for reducing the mechanical parameters of surrounding rock and evaluating stability considering the cumulative damage effect of microseismic events is shown below. Figure 5 As shown.

[0152] Ultimately, a quantitative analysis method for surrounding rock stability considering the cumulative microseismic damage effect was developed, based on the synergy of microseismic monitoring data-driven analysis, microseismic damage parameter test calibration, and numerical simulation stability evaluation. This method provides an important reference for early warning of surrounding rock disasters in deep tunnels.

[0153] This invention starts from the physical mechanism of elastic wave propagation in cavity media, constructs a three-dimensional diffraction path model based on geometric diffraction theory, and realizes high-precision spatial positioning of microseismic damage sources. Through high-stress unloading model tests of cavity rock samples, it calibrates the key coefficients linking microseismic monitoring information and surrounding rock mechanical parameters. Furthermore, it proposes a multi-event cumulative damage superposition criterion, transforming discrete microseismic monitoring data into a quantitative reduction basis for surrounding rock mechanical parameters. Finally, through numerical simulation, it realizes the dynamic quantitative assessment of surrounding rock stability under unloading-induced microseismic damage in deep tunnels, forming a complete closed loop from monitoring signals to quantitative conclusions on surrounding rock stability. This significantly improves the quantitative analysis capability and engineering guidance value of microseismic monitoring technology in deep underground engineering.

Claims

1. A quantitative analysis method for surrounding rock stability based on cumulative damage from microseismic events during tunnel unloading, characterized in that, include: Step 1: Locate the source of microseismic events in the surrounding rock of a three-dimensional tunnel based on geometric diffraction theory; Step 2: Calibrate the microseismic damage parameters of the surrounding rock of the roadway through unloading model tests using cavitary rock samples, including: the microseismic damage coefficient η and the damage radius coefficient k, where, , This represents the total cumulative radiated energy of microseismic events. To unload and release total energy during the excavation of the tunnel cavity. , The radius of the earthquake source is 1. The actual damage radius; Step 2 specifically includes: Step 21: Set up the test system, including preparing rock samples with cavities, and setting up a triaxial loading system and a cavity hydraulic loading / unloading system; Step 22: Obtain the total energy released during tunnel cavity excavation and unloading based on the experimental system. Total cumulative radiation energy from microseismic events focal radius ; Step 23: Determine the location of each microseismic event, perform CT scans on rock samples before and after the test to identify and determine the actual damage area radius corresponding to each microseismic event. ; Step 24: Calculate the microseismic damage coefficient η and the damage radius coefficient k; Step 25: Conduct unloading model tests on rock samples with cavities under different working conditions, and calculate the microseismic damage coefficient and damage radius coefficient for each group of tests; use multiple regression analysis to establish the functional relationship between parameters η and k and working conditions. Step 3: Based on the measured microseismic waveform data, determine the source radius of each microseismic event using the Brune source model. Based on the damage radius coefficient k, the damage range induced by each microseismic event is equivalent to the area centered on the epicenter and extending outwards. spherical damage area with radius [missing information] ; Step 4: Determine the damage coefficient of each microseismic event in the surrounding rock of the roadway based on the actual working conditions and the calibrated microseismic damage parameters of the roadway surrounding rock under unloading. The rock mechanical parameters corresponding to the microseismic event are equivalently reduced based on the damage coefficient. Step 5: Based on the location of the seismic source of the microseismic event and its corresponding spherical damage area, and combined with the equivalent reduced rock mechanical parameters, simulation calculations are performed to achieve the surrounding rock stability analysis.

2. The quantitative analysis method for surrounding rock stability based on cumulative microseismic damage during roadway unloading as described in claim 1, characterized in that, Step 1 is as follows: Step 11: Arrange micro-seismic sensors at equal intervals around the surrounding rock of the excavated tunnel; Step 12: Construct a three-dimensional geometric model of the tunnel diffraction propagation path; Step 13: Calculate the theoretical arrival time of the microseismic elastic wave signal; Step 14: Construct the objective function of the elastic wave arrival time residual for microseismic events; Step 15: Solve for the three-dimensional spatial coordinates of the microseismic event source based on the objective function.

3. The quantitative analysis method for surrounding rock stability based on cumulative microseismic damage during roadway unloading, as described in claim 2, is characterized in that... Step 11: Select 3-5 monitoring sections with a spacing of 5-10 meters between adjacent sections. Within each monitoring section, microseismic sensors are arranged at equal 45° intervals along the circumferential direction.

4. The quantitative analysis method for surrounding rock stability based on cumulative microseismic damage during tunnel unloading, as described in claim 2, is characterized in that... Step 12 specifically involves: simplifying the deep underground tunnel cavity into a shape with a radius of... For a cylinder whose axis extends infinitely along the z-axis, elastic waves originate from the source. Starting from the point of incidence, the propagation proceeds tangentially along a straight line to the surface of the cylinder. Then it travels along the cylindrical surface of the tunnel, diffracting and crawling to the exit tangent point. Finally, it leaves the cylindrical surface along a tangential straight line and propagates to the sensor. ;in, The central angle corresponding to the point of incident tangency. Here are the axial coordinates corresponding to the incident tangent point. The central angle corresponding to the point of tangency at the exit point. The axial coordinates corresponding to the exit tangent point; The geometric model of the diffraction propagation path in a three-dimensional tunnel is represented as follows: , ， ， ， ， 。 5. The quantitative analysis method for surrounding rock stability based on cumulative microseismic damage during tunnel unloading, as described in claim 2, is characterized in that... The objective function in step 14 is: In the formula, When the elastic wave of the rock mass reaches the j-th microseismic sensor, as observed in actual measurements; The theoretical time for the rock mass elastic wave to reach the j-th microseismic sensor is given, where n is the total number of sensors.

6. The quantitative analysis method for surrounding rock stability based on cumulative microseismic damage during tunnel unloading, as described in claim 1, is characterized in that... Step 23: Determine the focal radius of the microseismic event using the Brune source model. Specifically, it includes: Microseismic waveform data were collected to obtain the source displacement spectrum of the S-wave. The displacement spectrum is a curve showing the change of rock particle amplitude displacement with frequency. The S-wave corner frequency was obtained by fitting and inverting the source displacement spectrum. The corner frequency is the frequency value corresponding to the intersection of the straight segment and the extension of the attenuation segment in the displacement spectrum curve; Calculating the focal radius of microseismic events using the Brune source model : In the formula, For S-wave velocity; These are the source model constants.

7. The quantitative analysis method for surrounding rock stability based on cumulative microseismic damage during roadway unloading as described in claim 1, characterized in that, In step 25, different working conditions include combinations of different rock strengths, rock mass integrity coefficients, initial geostress states, and unloading rates.

8. The quantitative analysis method for surrounding rock stability based on cumulative microseismic damage during roadway unloading as described in claim 1, characterized in that, Step 4 also includes calculating the cumulative damage variable. , , Let be any point in space; The rock mechanical parameters corresponding to the microseismic event were equivalently reduced based on the cumulative damage variable.

9. The quantitative analysis method for surrounding rock stability based on cumulative microseismic damage during roadway unloading, as described in claim 8, is characterized in that... When performing equivalent reduction, a linear form is used.

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