Surrounding rock stability analysis method and system based on crustal stress field uncertainty quantitative characterization

Abstract

The invention discloses a surrounding rock stability analysis method and system based on crustal stress field uncertainty quantitative characterization. The method comprises the steps that firstly, deep crustal stress measured data are obtained through a hydraulic fracturing method; then constructing a closing pressure probability distribution model, performing 10,000 times of iterative calculation on the closing pressure by adopting a Monte Carlo random sampling technology to obtain a mean value and a variance of three-dimensional stress, and calculating the obtained three-dimensional stress values according to respective directions and inclination angles to obtain a mean value and a variance of six stress components; on the basis, the generated random crustal stress field is used as an initial condition to be input into a surrounding rock mechanical model, and a stability index is counted. Compared with a traditional deterministic method, the method has the advantages that the spatial variability and measurement errors of the crustal stress are fully considered, the variation trend of the stability along with the crustal stress can be given, a scientific basis is provided for deep cavern support design, risk prevention and control and optimization decision making, and the method is suitable for deep underground engineering such as hydropower, traffic and mines.

Description

Technical Field

[0001] This invention relates to the field of rock mass stability evaluation technology for underground engineering, and in particular to a method and approach for analyzing the stability of surrounding rock based on the quantitative characterization of uncertainty in the geostress field. Background Technology

[0002] With the rapid advancement of major water conservancy and hydropower projects and underground tunnels in western my country, underground powerhouses, deep-buried long tunnels, and other structures are generally located in high-intensity seismic zones characterized by high ground stress, strong geological structures, and complex lithology. The ground stress field, as the fundamental load determining the deformation and failure mode of the surrounding rock, directly impacts the safety and economy of support design. However, deep ground stress can only be obtained through point-based tests such as hydraulic fracturing and stress relief. Due to the coupling of multiple uncertainties, including borehole location, rock mass heterogeneity, measurement noise, and simplification of inversion models, a single "deterministic" result often deviates significantly from the actual stress state, leading to over- or under-support, and consequently causing lining cracking, rock bursts, and large deformations.

[0003] Current technologies primarily employ multi-source data weighted averaging or least squares regression to obtain a "unique" initial stress field, which is then substituted into an elastoplastic model to calculate the safety factor. While these methods are simple, they confound different error sources, failing to reveal the weighted contribution of each factor to the surrounding rock response or provide a probabilistic measure of stability. In recent years, although some have treated rock mass parameters as random fields, most still consider in-situ stress as a deterministic value, neglecting the dominant role of stress input errors in subsequent reliability assessments. Some studies use Bayesian updates to invert in-situ stress, but this requires pre-setting prior distributions and involves enormous computational costs, limiting its engineering application. Furthermore, the safety factor method in current standards judges stability based on a "fixed value," failing to answer core questions of concern to operators, such as "what is the probability of failure?" and "is the risk acceptable?", thus failing to meet the risk management needs of deep-buried engineering projects throughout their entire life cycle.

[0004] Therefore, it is urgent to establish a set of methods for quantifying geostress uncertainty and evaluating surrounding rock stability that are oriented towards engineering scale and take into account both computational efficiency and probabilistic accuracy, so as to provide a scientific basis for dynamic design, support optimization and risk decision-making of deep underground engineering. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a method for analyzing the stability of surrounding rock based on the quantitative characterization of the uncertainty of the geostress field. This method can utilize a technical approach that combines in-situ hydraulic fracturing tests, Monte Carlo random sampling, multiple linear regression inversion, and finite element method to integrate "measurement error, model assumptions, and parameter selection" into the evaluation of surrounding rock stability. This forms a set of repeatable, quantitative, and updatable stability criteria, which is beneficial for designers and operation and maintenance units to optimize support and make safety decisions under the premise of considering the uncertainty of the initial geostress field, and effectively suppress the risk of instability induced by underground engineering excavation.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a method for analyzing the stability of surrounding rock based on the quantitative characterization of uncertainty in the geostress field, comprising the following steps:

[0007] Step 1: Conduct a hydraulic fracturing test on site and collect the fracturing pressure of each test section. Tension and closing pressure Obtain stress measurement parameters at various locations in the borehole;

[0008] Step 2: Based on the stress calculation formula, and assuming that the deviations introduced by the calculated parameter values ​​are all normally distributed, the Monte Carlo method is used to calculate the closure pressure. 10,000 random sampling analyses were performed; through simulation calculations, each stress component, including the maximum horizontal principal stress, was systematically evaluated. Minimum horizontal principal stress Vertical stress X-axis normal stress Y-axis normal stress Z-axis normal stress and XY plane shear stress The mean and variance of the sample are used to quantify its uncertainty.

[0009] Step 3: By establishing a finite element model, the geostress components under various working conditions are calculated, and the obtained data are used as the dependent variable. The initial geostress field is then established using multiple linear regression inversion, and 6... Analysis revealed that each stress component originated from -3 Up to 3 Initial stress field models for 7 working conditions; and through R 2 To evaluate the fitting effect, if the fitting effect is not good, adjust the relevant parameters and return to step 3 to invert again until the fitting requirements are met.

[0010] Step 4: Substitute the obtained 7 initial stress components into the calculation formula, and analyze the data of each monitoring point after excavation and application of equivalent support to obtain the maximum and minimum principal stresses of each measuring point, so as to evaluate the stability of the structure and reveal the influence of the initial stress field.

[0011] In a preferred embodiment, step 2 includes the following steps:

[0012] Step 21: The dispersion of the closure pressure measured in the tight rock section by measuring the borehole closure pressure is used as the uncertainty index. It is used as the standard deviation of the closure pressure, and it is regarded as a normal distribution. The stress components of the geostress field are obtained through the stress calculation formula.

[0013] The stress calculation formula is shown below:

[0014] Based on the principles of elasticity, it is derived that there is a radius in the middle. The stress at an infinitesimally small region arbitrarily selected in the plane of the circular hole is expressed by the following formula:

[0015] (1)

[0016] In equation (1), for Radial stress at a point For tangential stress, For shear stress, for The distance from the point to the center of the hole. Let A represent the wellbore radius, and B represent the maximum principal stress. For the round hole to The angle between the point direction and the positive X-axis direction; substituting the relevant parameters into equation (1) yields the stress distribution at any coordinate point in the entire two-dimensional plane. In particular, when calculating the distance from the point to the center of the circular hole... Take as the wellbore radius Right now At this point, the general solution degenerates into the boundary stress state at the hole wall:

[0017] (2)

[0018] As can be seen from equation (2), the tangential stress of the hole wall exhibits a standard cosine-shaped fluctuation with the polar angle θ: peak values ​​appear at θ=0° and 180°, while low values ​​appear at θ=90° and 270°, with the magnitude of these values ​​corresponding precisely to the peaks and troughs of the cosine curve; therefore, the tangential stress concentration is given by these two extreme points:

[0019] (3)

[0020] like ,but Therefore, when the fluid injected into the borehole continuously applies stress to the borehole wall rock, causing the internal pressure to rise to a level sufficient to offset and exceed the in-situ tensile strength of the borehole wall rock in the direction of minimum tangential stress, tensile fracture will first occur at the weakest point. Once fracture initiates, the crack will continue to propagate forward along the plane perpendicular to the minimum principal stress, forming a tensile fracture that penetrates the borehole wall. At this point, the magnitude of the fracture pressure is equal to the sum of the stress concentration value at the borehole wall and the in-situ tensile strength of the rock, while also deducting the influence of the rock pore pressure. The theoretical expression for the fracture pressure is derived as follows:

[0021] (4)

[0022] Once the borehole wall cracks, continuing to pump liquid increases the liquid pressure, and the crack tip will continue to extend deeper under pressure until a new equilibrium is reached; conversely, if the pump is stopped immediately and the circuit is kept closed, the crack extension will stop and the process will quickly enter the closure phase.

[0023] In geostress measurement, the maximum and minimum principal stresses are written as follows: and Through the parameter transformations described above, combined with the formula above, we can derive:

[0024] (5)

[0025] (6)

[0026] Vertical stress The weight of the overlying rock at the measured section location is estimated as follows:

[0027] Burial depth is The vertical stress borne by the measuring point Take the total weight of the overlying rock column, and calculate it according to the following formula, without the need for additional tests;

[0028] (7)

[0029] In equation (7), For rock density, It is the acceleration due to gravity. The depth of the rock measuring point.

[0030] In a preferred embodiment, step 3 includes the following steps:

[0031] In the finite element method (FEM) calculation, six working conditions are set up to calculate the dependent variable, including self-weight, x-axis compressional tectonic motion, y-axis compressional tectonic motion, xy-plane shear tectonic motion, xz-plane shear tectonic motion, and yz-plane shear tectonic motion, respectively, to obtain the initial geostress dependent variable. Then, the self-weight stress field is superimposed with the various tectonic stress fields and combined with multiple linear regression inversion to obtain the final geostress result. The initial stress field is described by the following mathematical expression:

[0032] (8)

[0033] In equation (8), For regression coefficients, It is a random variable.

[0034] In a preferred embodiment, the displacement of each monitoring point in step 4 exhibits a nonlinear decreasing trend as the initial stress field increases.

[0035] The present invention also provides a surrounding rock stability analysis system based on the quantitative characterization of the uncertainty of the geostress field, including a processor, a memory and a bus, wherein the memory stores machine-readable instructions executed by the processor;

[0036] When the system is running, the processor and the memory communicate via a bus, and the machine-readable instructions are executed by the processor as described in the surrounding rock stability analysis method based on the quantitative characterization of the uncertainty of the geostress field.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1. By performing 10,000 Monte Carlo samplings, the measurement error of the closed pressure is directly converted into the statistical moment of the stress field. The Monte Carlo random sampling technique for closed pressure based on multi-source error coupling can effectively avoid the incomplete stability evaluation caused by the error, and further improve the prediction accuracy and coverage.

[0039] 2.6σ analysis generates 7 sets of initial stress fields from -3σ to +3σ, which can cover more than 95% of the measured fluctuation range and provide probabilistic boundaries for subsequent stability calculations;

[0040] 3. Numerical tests simulating excavation and support can ensure that the parameter inversion results conform to the actual engineering conditions to the greatest extent, meet the requirements of stability evaluation, and solve the problems of high measurement difficulty in actual engineering and large amount of calculation in traditional finite element methods.

[0041] 4. The proposed nonlinear stress-displacement reduction law has been verified in the test tunnel section of this project. It can be used for rapid stability evaluation of similar projects such as deep buried tunnels, pumped storage, and deep mining, so as to formulate corresponding construction measures to achieve the goal of safe construction of underground powerhouses. Attached Figure Description

[0042] Figure 1 This is a flowchart of a preferred embodiment of the present invention.

[0043] Figure 2 This is a comparison diagram of the initial stress field inversion of a preferred embodiment of the present invention. Detailed Implementation

[0044] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0045] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0046] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0047] Reference Figure 1-2 A method for analyzing the stability of surrounding rock based on the quantitative characterization of the uncertainty of the geostress field includes the following steps:

[0048] Step 1: Conduct a hydraulic fracturing test on site and collect the fracturing pressure of each test section. Tension and closing pressure Obtain stress measurement parameters at various locations in the borehole;

[0049] It should be noted that the hydraulic fracturing experiment described in this example is an effective method for measuring deep geostress. By artificially inducing fracture propagation, it can accurately obtain the three-dimensional stress parameters of underground rock strata. The advantages of this technology are that it can obtain multiple indicators of the current stress of the strata without knowing the mechanical parameters of the rock, and it is simple to operate, can be continuously or repeatedly tested at any depth, and has a fast measurement speed and reliable results.

[0050] Step 2: Based on the stress calculation formula, and assuming that the deviations introduced by the calculated parameter values ​​are all normally distributed, the Monte Carlo method is used to calculate the closure pressure. 10,000 random sampling analyses were conducted; through simulation calculations, the maximum horizontal principal stress of each stress component was systematically evaluated. Minimum horizontal principal stress Vertical stress X-axis normal stress Y-axis normal stress Z-axis normal stress and XY plane shear stress The mean and variance of the sample are used to quantify its uncertainty.

[0051] The dispersion of the closure pressure measured in the tight rock section by measuring the borehole closure pressure is used as an uncertainty index. It is used as the standard deviation of the closure pressure, which is regarded as a normal distribution. The stress components of the geostress field are obtained through the stress calculation formula.

[0052] The stress calculation formula is shown below:

[0053] Based on the principles of elasticity, it is derived that there is a radius in the middle. The stress at an infinitesimally small region arbitrarily selected in the plane of the circular hole is expressed by the following formula:

[0054] (1)

[0055] In equation (1), for Radial stress at a point For tangential stress, For shear stress, for The distance from the point to the center of the hole. Let A represent the wellbore radius, and B represent the maximum principal stress. For the round hole to The angle between the point direction and the positive X-axis direction; substituting the relevant parameters into equation (1) yields the stress distribution at any coordinate point in the entire two-dimensional plane. In particular, when calculating the distance from the point to the center of the circular hole... Take as the wellbore radius Right now At this point, the general solution degenerates into the boundary stress state at the hole wall:

[0056] (2)

[0057] As can be seen from equation (2), the tangential stress of the hole wall exhibits a standard cosine-shaped fluctuation with the polar angle θ: peak values ​​appear at θ=0° and 180°, while low values ​​appear at θ=90° and 270°, with the magnitude of these values ​​corresponding precisely to the peaks and troughs of the cosine curve; therefore, the tangential stress concentration is given by these two extreme points:

[0058] (3)

[0059] like ,but Therefore, when the fluid injected into the borehole continuously applies stress to the borehole wall rock, causing the internal pressure to rise sufficiently to offset and exceed the in-situ tensile strength of the borehole wall rock in the direction of minimum tangential stress, tensile fracture will first occur at the weakest point. Once fracture initiates, the crack will continue to propagate forward along the plane perpendicular to the minimum principal stress, forming a tensile fracture that penetrates the borehole wall. At this point, the magnitude of the fracture pressure is equal to the sum of the stress concentration value at the borehole wall and the in-situ tensile strength of the rock, while also deducting the influence of the rock pore pressure; the theoretical expression for the fracture pressure is derived as follows:

[0060] (4)

[0061] Once the borehole wall cracks, continuing to pump liquid increases the liquid pressure, and the crack tip will continue to extend deeper under pressure until a new equilibrium is reached; conversely, if the pump is stopped immediately and the circuit is kept closed, the crack extension will stop and the process will quickly enter the closure phase.

[0062] In geostress measurement, the maximum and minimum principal stresses are written as follows: and Through the parameter transformations described above, combined with the formula above, we can derive:

[0063] (5)

[0064] (6)

[0065] Vertical stress The weight of the overlying rock at the measured section location can be estimated as follows:

[0066] Burial depth is The vertical stress borne by the measuring point The total weight of the overlying rock column is approximated by the following formula, which can be used for calculation without additional testing.

[0067] (7)

[0068] In equation (7), For rock density, It is the acceleration due to gravity. The depth of the rock measuring point.

[0069] Step 3: By establishing a finite element model, the geostress components under various working conditions are calculated, and the obtained data are used as the dependent variable. The initial geostress field is then established using multiple linear regression inversion, and 6... Analysis revealed that each stress component originated from -3 Up to 3 Initial stress field models for seven different working conditions were developed and implemented using R... 2 To evaluate the fitting effect, if the fitting effect is not good, adjust the relevant parameters and return to step 3 to invert again until the fitting requirements are met.

[0070] In the finite element method, six working conditions are set to calculate the dependent variable, including self-weight, x-axis compression tectonic motion, y-axis compression tectonic motion, xy-plane shear tectonic motion, xz-plane shear tectonic motion, and yz-plane shear tectonic motion, respectively, to obtain the initial geostress dependent variable. Then, the self-weight stress field is superimposed with the various tectonic stress fields and combined with multiple linear regression inversion to obtain the final geostress result.

[0071] The initial stress field is described by the following mathematical expression:

[0072] (8)

[0073] In equation (8), For regression coefficients, It is a random variable.

[0074] Step 4: Substitute the obtained 7 initial stress components into the calculation formula, and analyze the data of each monitoring point after excavation and application of equivalent support to obtain the maximum and minimum principal stresses of each measuring point, so as to evaluate the stability of the structure and reveal the influence of the initial stress field.

[0075] The evolution of the surrounding rock mechanical response under error domain conditions was quantitatively analyzed by using stress data calculated from the model and evaluating model indicators from a unique analytical perspective. The study shows that the uncertainty of the initial stress field has a significant impact on the stress distribution at key nodes, with greater sensitivity in areas of higher compressive stress. The displacement at each monitoring point exhibits a nonlinear decreasing trend as the initial stress field increases.

Claims

1. A method for analyzing the stability of surrounding rock based on the quantitative characterization of uncertainty in the geostress field, characterized in that, Includes the following steps: Step 1: Conduct a hydraulic fracturing test on site and collect the fracturing pressure of each test section. Tension and closing pressure Obtain stress measurement parameters at various locations in the borehole; Step 2: Based on the stress calculation formula, and assuming that the deviations introduced by the calculated parameter values ​​are all normally distributed, the Monte Carlo method is used to calculate the closure pressure. 10,000 random sampling analyses were performed; through simulation calculations, each stress component, including the maximum horizontal principal stress, was systematically evaluated. Minimum horizontal principal stress Vertical stress X-axis normal stress Y-axis normal stress Z-axis normal stress and XY plane shear stress The mean and variance of the sample are used to quantify its uncertainty. Step 3: By establishing a finite element model, the geostress components under various working conditions are calculated, and the obtained data are used as the dependent variable. The initial geostress field is then established using multiple linear regression inversion, and 6... Analysis revealed that each stress component originated from -3 Up to 3 Initial stress field models for 7 working conditions; and through R 2 To evaluate the fitting effect, if the fitting effect is not good, adjust the relevant parameters and return to step 3 to invert again until the fitting requirements are met. Step 4: Substitute the obtained 7 initial stress components into the calculation formula, and analyze the data of each monitoring point after excavation and application of equivalent support to obtain the maximum and minimum principal stresses of each measuring point, so as to evaluate the stability of the structure and reveal the influence of the initial stress field.

2. The method for analyzing the stability of surrounding rock based on the quantitative characterization of the uncertainty of the geostress field according to claim 1, characterized in that, Step 2 includes the following steps: Step 21: The dispersion of the closure pressure measured in the tight rock section by measuring the borehole closure pressure is used as the uncertainty index. It is used as the standard deviation of the closure pressure, and it is regarded as a normal distribution. The stress components of the geostress field are obtained through the stress calculation formula. The stress calculation formula is shown below: Based on the principles of elasticity, it is derived that there is a radius in the middle. The stress at an infinitesimally small region arbitrarily selected in the plane of the circular hole is expressed by the following formula: （1） In equation (1), for Radial stress at a point For tangential stress, For shear stress, for The distance from the point to the center of the hole. Let A represent the wellbore radius, and B represent the maximum principal stress. For the round hole to The angle between the point direction and the positive X-axis direction; substituting the relevant parameters into equation (1) yields the stress distribution at any coordinate point in the entire two-dimensional plane. In particular, when calculating the distance from the point to the center of the circular hole... Take as the wellbore radius Right now At this point, the general solution degenerates into the boundary stress state at the hole wall: （2） As can be seen from equation (2), the tangential stress of the hole wall exhibits a standard cosine-shaped fluctuation with the polar angle θ: peak values ​​appear at θ=0° and 180°, while low values ​​appear at θ=90° and 270°, with the magnitude of these values ​​corresponding precisely to the peaks and troughs of the cosine curve; therefore, the tangential stress concentration is given by these two extreme points: （3） like ,but ; Therefore, when the fluid injected into the borehole continuously applies stress to the borehole wall rock, causing the internal pressure to rise sufficiently to offset and exceed the in-situ tensile strength of the borehole wall rock in the direction of minimum tangential stress, tensile fracture will first occur at the weakest point. Once fracture initiates, the crack will continue to propagate forward along the plane perpendicular to the minimum principal stress, forming a tensile fracture that penetrates the borehole wall. At this point, the magnitude of the fracture pressure is equal to the sum of the stress concentration value at the borehole wall and the in-situ tensile strength of the rock, while also deducting the influence of the rock pore pressure. The theoretical expression for the fracture pressure is derived as follows: （4） Once the borehole wall cracks, continuing to pump liquid increases the liquid pressure, and the crack tip will continue to extend deeper under pressure until a new equilibrium is reached; conversely, if the pump is stopped immediately and the circuit is kept closed, the crack extension will stop and the process will quickly enter the closure phase. In geostress measurement, the maximum and minimum principal stresses are written as follows: and Through the parameter transformations described above, combined with the formula above, we can derive: （5） （6） Vertical stress The weight of the overlying rock at the measured section location is estimated as follows: Burial depth is The vertical stress borne by the measuring point Take the total weight of the overlying rock column, and calculate it according to the following formula, without the need for additional tests; （7） In equation (7), For rock density, It is the acceleration due to gravity. The depth of the rock measuring point.

3. The method for analyzing the stability of surrounding rock based on the quantitative characterization of the uncertainty of the geostress field according to claim 1, characterized in that, Step 3 includes the following steps: In the finite element method (FEM) calculation, six working conditions are set up to calculate the dependent variable, including self-weight, x-axis compressional tectonic motion, y-axis compressional tectonic motion, xy-plane shear tectonic motion, xz-plane shear tectonic motion, and yz-plane shear tectonic motion, respectively, to obtain the initial geostress dependent variable. Then, the self-weight stress field is superimposed with the various tectonic stress fields and combined with multiple linear regression inversion to obtain the final geostress result. The initial stress field is described by the following mathematical expression: （8） In equation (8), For regression coefficients, It is a random variable.

4. The method for analyzing the stability of surrounding rock based on the quantitative characterization of the uncertainty of the geostress field according to claim 1, characterized in that, In step 4, the displacement of each monitoring point shows a nonlinear decreasing trend as the initial stress field increases.

5. A rock stability analysis system based on quantitative characterization of in-situ stress field uncertainty, comprising a processor, a memory, and a bus, wherein the memory stores machine-readable instructions executed by the processor; characterized in that, When the system is running, the processor and the memory communicate via a bus, and the machine-readable instructions are executed by the processor as described in any one of claims 1 to 4.

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