Underground engineering long-term stability prediction method based on creep instability discrimination theory

Abstract

The invention discloses an underground engineering long-term stability prediction method based on a creep instability discrimination theory, particularly relates to the technical field of underground engineering safety evaluation, and is used for solving the problems of inaccurate creep instability discrimination and uncertainty and risk of long-term stability prediction in existing soft rock and high-stress underground engineering. Accurate numerical simulation and data fusion of stress distribution, displacement data and creep deformation of an underground engineering rock mass under the action of continuous load are realized by establishing a creep instability judgment criterion containing time-dependent damage parameters and combining a non-local creep model, a finite difference method, a particle swarm optimization algorithm and a least square method; and finally, a prediction model for reflecting the characteristics of the creep deformation of the rock mass along with the time change is constructed, so that accurate and reliable technical support is provided for long-term safety assessment of a project.

Description

Technical Field

[0001] The present invention relates to the technical field of underground engineering safety assessment, and more specifically, the present invention relates to a method for predicting the long-term stability of underground engineering based on the creep instability discrimination theory. Background Art

[0002] In soft rock and high-stress underground engineering, due to the characteristics of the rock mass itself and the complex in-situ stress environment, during long-term service, the engineering structure is prone to be affected by creep, resulting in continuous deformation and even instability. Currently, the mainstream prediction methods mostly use empirical formulas or traditional creep models to evaluate the long-term behavior of the project through the induction of historical data and simplified physical assumptions.

[0003] The methods of the prior art often fail to accurately reflect the complex and non-linear creep process in actual engineering, leading to great uncertainties and risks in the safety assessment of the long-term stability of underground engineering. Summary of the Invention

[0004] In order to overcome the above-mentioned defects of the prior art, an embodiment of the present invention provides a method for predicting the long-term stability of underground engineering based on the creep instability discrimination theory to solve the problems raised in the above background art.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A method for predicting the long-term stability of underground engineering based on the creep instability discrimination theory, comprising the following steps:

[0007] Establish a creep instability discrimination criterion containing time-dependent damage parameters, and define the creep evolution boundary of the rock mass under different stress levels based on the creep instability discrimination criterion;

[0008] Perform numerical simulation on the rock mass parameters of geological exploration based on the non-local creep model and the finite difference method. The non-local creep model includes viscoelastic parameters, damage threshold parameters, and stress relaxation coefficients, and iteratively outputs the stress distribution and displacement data under continuous load;

[0009] Dynamically calibrate the viscoelastic parameters and damage threshold parameters of the non-local creep model through the particle swarm optimization algorithm to match the measured displacement monitoring data;

[0010] Fuse the displacement monitoring data and the numerical simulation results, and use the least squares method to correct the stress relaxation coefficient of the non-local creep model;

[0011] Based on the calibrated viscoelastic parameters and damage threshold parameters, combined with the corrected stress relaxation coefficient, establish a prediction model reflecting the characteristics of the creep deformation of the rock mass in the underground engineering under continuous load over time.

[0012] In a preferred embodiment, a creep instability discrimination criterion containing time-dependent damage parameters is established, and the creep evolution boundaries of rock masses under different stress levels are defined based on the creep instability discrimination criterion, including:

[0013] Obtain the creep deformation data generated by the rock mass of the underground project under continuous loading, and conduct statistical analysis and time history analysis on the creep deformation data to determine the time-dependent variation law of damage evolution during the long-term loading process of the rock mass;

[0014] Determine the time-dependent damage parameters based on the time-dependent variation law, including the duration of continuous loading, the damage evolution rate, and the damage accumulation variable;

[0015] Construct a mathematical model containing time-dependent damage parameters to quantitatively describe the creep evolution characteristics of the rock mass of the underground project under different stress levels;

[0016] Define the creep evolution boundaries of the rock mass under different stress levels based on the mathematical model, and form a creep instability discrimination criterion.

[0017] In a preferred embodiment, the mathematical model containing time-dependent damage parameters is expressed as: Among them, D(T) represents the damage degree of the rock mass under the continuous loading time T, D0 represents the initial damage degree, P1 represents the damage scale factor, T represents the continuous loading time, P2 represents the damage evolution exponent, P3 represents the stress sensitivity coefficient, and S represents the stress level of the rock mass.

[0018] In a preferred embodiment, numerical simulation is carried out on the rock mass parameters of geological exploration based on the non-local creep model and the finite difference method. The non-local creep model includes viscoelastic parameters, damage threshold parameters, and stress relaxation coefficients, and iteratively outputs the stress distribution and displacement data under continuous loading, including:

[0019] Collect the rock mass parameters of the underground project rock mass under different loading conditions;

[0020] Construct the mathematical framework required for the non-local creep model based on the rock mass parameters, and define the relationship between the displacement change and stress distribution during the damage evolution and creep process of the rock mass;

[0021] Apply the finite difference method to discretize the established non-local creep model, and convert the involved continuous variables into discrete variables;

[0022] Use numerical simulation to iteratively solve the stress field and displacement field of the underground project rock mass under different loading conditions, obtain the stress distribution of the underground project rock mass under continuous loading, and output the corresponding displacement data.

[0023] In a preferred embodiment, the non-local creep model is expressed as: where Ξ(ζ, η) represents the local creep strain at the spatial coordinate ζ under the action of a sustained load for a time η, L0 is the initial creep rate constant, Ω represents all possible spatial regions in the rock mass that may be affected by non-local interactions, K(ζ, ξ) is the influence function describing the non-local coupling effect between any two points ζ and ξ in space, Γ(ξ, η) represents the local creep strain rate at the spatial coordinate ξ under the action of a sustained load for a time η, ζ represents a certain position of the rock mass of the underground project in the spatial coordinate system, and ξ represents the position of any influencing point in the spatial coordinates.

[0024] In a preferred embodiment, the finite difference method is applied to discretize the established non-local creep model, specifically as follows:

[0025] The three-dimensional spatial region of the actual engineering rock mass is divided into a number of discrete grid cells according to a preset discretization scale, and the continuous time domain of the sustained load action is divided into multiple equally spaced time steps;

[0026] The non-local creep model is discretized to obtain the following finite difference expression: where represents the local creep strain of the i-th grid cell at the n-th time step, Δη represents the discretized time step, K ij represents the discretized influence function between grid cell i and grid cell j, represents the local creep strain rate of the j-th grid cell at the n-th time step, i represents the number of the spatial grid cell of the rock mass of the underground project in the discretization process of the finite difference method, j represents the number of another grid cell in the discretized grid, N is the total number of grid cells, n is the time step number, and Δζ is the spatial step.

[0027] In a preferred embodiment, the viscoelastic parameters and damage threshold parameters of the non-local creep model are dynamically calibrated by the particle swarm optimization algorithm to match the measured displacement monitoring data, including:

[0028] According to the stress distribution, displacement data, and creep deformation data obtained from numerical simulation under sustained load, the initial values of the parameters in the non-local creep model are determined;

[0029] The particle swarm optimization algorithm is used to perform global search and iterative calculation on each parameter until the output result of the non-local creep model reaches a predetermined consistency with the measured data;

[0030] The optimization process is terminated by setting the number of iterations and the convergence criterion to ensure that the viscoelastic parameters and damage threshold parameters match the measured data.

[0031] In a preferred embodiment, by integrating displacement monitoring data with numerical simulation results, the stress relaxation coefficient of the non-local creep model is corrected using the least squares method, including:

[0032] Comparing and analyzing the displacement monitoring data with the numerical simulation displacement data obtained by using the finite difference method and the non-local creep model to determine the deviation between the displacement monitoring data and the numerical simulation results;

[0033] Quantitatively calculating the deviation between the displacement monitoring data and the numerical simulation results using the least squares method to obtain a preliminary correction coefficient;

[0034] Iteratively adjusting the stress relaxation coefficient according to the preliminary correction coefficient until the mean square error between the displacement monitoring data and the numerical simulation results meets the predetermined convergence condition;

[0035] Updating the non-local creep model with the corrected stress relaxation coefficient.

[0036] In a preferred embodiment, based on the calibrated viscoelastic parameters, damage threshold parameters, and the corrected stress relaxation coefficient, a prediction model reflecting the time-varying characteristics of the creep deformation of the rock mass in underground engineering under sustained loading is established, including:

[0037] Taking the calibrated viscoelastic parameters, damage threshold parameters, and the corrected stress relaxation coefficient as input parameters, integrating the stress distribution, displacement data, and creep deformation data obtained by using the non-local creep model and the finite difference method with the displacement monitoring data obtained on-site;

[0038] Processing the fused data using data fitting and trend analysis methods to construct a prediction model reflecting the time-varying characteristics of the creep deformation of the rock mass in underground engineering under sustained loading and generating a corresponding time-varying prediction curve of the creep deformation;

[0039] Comparing the numerical simulation results with the monitoring data according to the output results of the prediction model and the preset creep instability discrimination criterion to determine the spatial distribution of the potential instability region in the underground engineering and draw the corresponding spatial distribution map.

[0040] In a preferred embodiment, the prediction model reflecting the time-varying characteristics of the creep deformation of the rock mass in underground engineering under sustained loading is: where, Δ C (t) represents the creep deformation at the prediction time t, t represents the duration of the sustained loading, A1 represents the baseline creep deformation, A2 represents the proportional coefficient for characterizing the cumulative creep effect caused by the increase with time, A3 represents the power exponent of the creep evolution, A4 represents the amplitude coefficient of the exponential decay term, and A5 represents the rate coefficient of the exponential decay.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] 1. The method of the present invention makes full use of the time-dependent damage parameter, non-local creep model and finite difference method. By numerically simulating the stress distribution, displacement data and creep deformation data of the rock mass in the underground engineering under continuous load, and then combining with the particle swarm optimization algorithm to dynamically calibrate the viscoelastic parameters and damage threshold parameters, high-precision matching between various parameters and the actual monitoring data is achieved. By fusing the displacement monitoring data and the numerical simulation results, and using the least square method to correct the stress relaxation coefficient, the present invention establishes a prediction model reflecting the variation characteristics of the creep deformation of the rock mass with time, so that the potential instability area of the underground engineering can be accurately defined, and the possibility of engineering safety risks caused by creep instability is effectively reduced.

[0043] 2. Each step of the method is closely connected, and data fusion, parameter calibration and model construction form a closed-loop feedback, which helps to realize the automation and intelligence of the long-term stability prediction of underground engineering. This method not only improves the coincidence degree between the numerical simulation results and the on-site actual monitoring data, but also realizes real-time update through dynamic adjustment, ensuring the accurate description of the complex and non-linear creep process, providing a reliable quantitative basis for the safety assessment of underground engineering, and having significant popularization and application value and practical engineering significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a flowchart of a method for predicting the long-term stability of an underground engineering based on the creep instability discrimination theory of the present invention;

[0045] Figure 2 is a flowchart of a dynamic calibration type long-term stability prediction method based on creep instability discrimination of the present invention;

[0046] Figure 3 is a comparative curve graph of the creep strain-time relationship of double monitoring points of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0048] Embodiment: Figure 1 A method for predicting the long-term stability of an underground engineering based on the creep instability discrimination theory of the present invention is given, which includes the following steps:

[0049] Establish a creep instability discrimination criterion containing time-dependent damage parameters, and define the creep evolution boundary of rock masses under different stress levels based on the creep instability discrimination criterion.

[0050] Numerically simulate the rock mass parameters of geological exploration based on the non-local creep model and the finite difference method. The non-local creep model includes viscoelastic parameters, damage threshold parameters, and stress relaxation coefficients, and iteratively outputs the stress distribution and displacement data under sustained loading.

[0051] Dynamically calibrate the viscoelastic parameters and damage threshold parameters of the non-local creep model through the particle swarm optimization algorithm to match the measured displacement monitoring data.

[0052] Fuse the displacement monitoring data and the numerical simulation results, and use the least squares method to correct the stress relaxation coefficient of the non-local creep model.

[0053] Based on the calibrated viscoelastic parameters, damage threshold parameters, and the corrected stress relaxation coefficient, establish a prediction model reflecting the time-varying characteristics of the creep deformation of rock masses in underground engineering under sustained loading.

[0054] Figure 2 The flow chart of the dynamic calibration long-term stability prediction method based on creep instability discrimination of the present invention is given, which reveals the implementation logic of a long-term stability prediction method for underground engineering based on creep instability discrimination theory: the "data perception" module (marked sensors, geological exploration data, monitoring data) on the left end corresponds to the multi-source information acquisition link in the method, reflecting the data basis for the implementation of the theory; the central "data processing" module (including stress distribution and displacement data output) is mapped to the calculation steps of the non-local creep model, showing the conversion process of geological parameters into mechanical indexes; the "dynamic calibration" module on the right focuses on the particle swarm optimization algorithm (including the circular arrow of initialization → evaluation of particles → update of particles), intuitively presenting "parameter dynamic calibration" - through the closed-loop iteration (circular arrow) formed by the N / Y conditional branch, comparing the measured displacement data with the model prediction value in real time, and driving the continuous optimization of the viscoelastic parameters and damage threshold parameters (corresponding to the bidirectional arrow of the time-varying prediction model in the lower right corner); the red and blue data streams in the figure run through the entire chain of "sensor monitoring → stress analysis → algorithm calibration → model output", especially through the particle swarm loop structure and the stop condition judgment, vividly expressing the dynamic feedback characteristics different from the static model: that is, the parameter boundary established based on the creep instability discrimination criterion continuously approaches the creep law of the real rock mass during the algorithm iteration.

[0055] Establish a creep instability discrimination criterion containing time-dependent damage parameters, and define the creep evolution boundary of rock masses under different stress levels based on the creep instability discrimination criterion, including:

[0056] Obtain the creep deformation data of the rock mass in underground engineering under the action of sustained load, and conduct statistical analysis and time-history analysis on the creep deformation data to determine the time-dependent variation law of damage evolution of the rock mass during the long-term loading process.

[0057] First, at the site of a certain underground project, collect the creep deformation data generated by the rock mass in the underground project under the action of sustained load at different control points (the selection of the number and location of the control points is determined by the specific project, and only an example is given here) through on-site instrument equipment.

[0058] Figure 3 The comparison curve of creep strain-time relationship of the double monitoring points of the present invention is given, which shows the time-varying evolution law of creep strain of the double monitoring points of the surrounding rock of the underground project. The strain of control point 1 (solid line) increases from 0.20 to 0.45 within 12 hours, and shows a significant acceleration characteristic in the later stage (the growth rate increases by about 70% from 6 to 12 hours), while the strain of control point 2 (dashed line) only slowly increases from 0.20 to 0.31. The strain separation phenomenon of the two monitoring points (the difference reaches 0.14 at 12 hours) intuitively verifies the creep instability criterion: the sudden change in the strain growth rate and the exceeding of the magnitude (>0.40) of control point 1 trigger the instability warning, which forms a mapping with the rock mass fracture propagation stage at the engineering site, realizing the advantage of accurately capturing the precursor of instability through multi-node dynamic monitoring.

[0059] The collected data includes the deformation data of each monitoring point changing with time and the corresponding time series data under the condition of fixed sustained load.

[0060] To fully reflect the actual situation of damage evolution of the rock mass during the long-term loading process, conduct statistical analysis and time-history analysis on the collected creep deformation data. Statistical analysis uses conventional statistical methods, such as descriptive statistics and regression analysis, to calculate statistics such as the mean, standard deviation, and variance of the data of each monitoring point; time-history analysis processes the time continuity of the deformation data to clarify the law of gradual accumulation of deformation of the rock mass with time under the action of sustained load, so as to determine the time-dependent variation trend of rock mass damage evolution.

[0061] Determine the time-dependent damage parameters based on the time-dependent variation law, including the duration of sustained load action, the damage evolution rate, and the damage accumulation variable.

[0062] Among them, the duration of sustained load action refers to the actual time interval from the start of load application to the current moment; the damage evolution rate is used to describe the increase amplitude of the rock mass damage degree per unit time; the damage accumulation variable reflects the degree of cumulative damage of the rock mass under the action of long-term load.

[0063] Construct a mathematical model containing time-dependent damage parameters to quantitatively describe the creep evolution characteristics of the rock mass in underground engineering under different stress levels.

[0064] To quantify the above parameters, the following mathematical expression is used to describe the damage evolution process: Among them, D(T) represents the damage degree of the rock mass under the action of the sustained load for time T; D0 represents the initial damage degree, and its value is determined according to the initial state of the rock mass; P1 represents the damage scale factor, and its unit is the same as that of the damage accumulation variable; T represents the action time of the sustained load and is a positive real number; P2 represents the damage evolution exponent, and its value reflects the non - linear degree of damage evolution; P3 represents the stress sensitivity coefficient, and its value reflects the influence of the stress level on the damage evolution rate; S represents the stress level of the rock mass, which usually depends on the stress data obtained from on - site surveys.

[0065] In the above - mentioned mathematical model, each parameter is determined by fitting the on - site collected data and statistical analysis results, so as to ensure that the mathematical model can quantitatively describe the creep evolution characteristics of the rock mass in underground engineering under different stress levels over time.

[0066] It should be noted that the combined form of the exponential function and power function adopted in the model is an empirical expression summarized based on experimental data and historical observations, and this expression can more accurately reflect the non - linear characteristics in the process of rock mass damage evolution under long - term loading conditions.

[0067] Based on the mathematical model, the creep evolution boundary of the rock mass under different stress levels is defined, and a creep instability discrimination criterion is formed.

[0068] Specifically, by taking the derivative and critical - point analysis of the changing trend of D(T) with T and S in the mathematical model, the critical sustained - load action time T c corresponding to when the damage accumulation variable D(T) reaches a specific critical value D c is determined under different stress levels S, thereby defining the creep evolution boundary of the rock mass.

[0069] Here, D c is an empirical threshold determined through a large number of on - site and laboratory tests, and its value is related to the material properties of the rock mass and construction requirements. By solving the inequality D(T)≥D c in the mathematical model, the T c under different stress levels S can be obtained. This solution process can adopt numerical methods (such as Newton iteration method, bisection method, etc.) to ensure that the calculation results are highly consistent with the on - site actual situation.

[0070] Based on the T c obtained from the above - mentioned mathematical modelThe relationship with the corresponding stress level S defines the creep evolution boundary of the rock mass under different stress levels, and thus forms a creep instability criterion with time-dependent damage parameters. This criterion not only reflects the dynamic process of the gradual accumulation of damage in the rock mass under sustained loading over time, but also can clearly indicate at what stress level the creep deformation of the rock mass tends to instability, providing a quantitative basis for the long-term stability prediction of subsequent underground engineering.

[0071] Based on the non-local creep model and the finite difference method, numerical simulation is carried out on the rock mass parameters of geological exploration. The non-local creep model includes viscoelastic parameters, damage threshold parameters and stress relaxation coefficients, and iteratively outputs the stress distribution and displacement data under sustained loading, including:

[0072] Collect the rock mass parameters of the underground engineering rock mass under different loading conditions.

[0073] Through on-site geological exploration and experimental testing, various physical and mechanical parameters of the underground engineering rock mass are obtained. These rock mass parameters include, but are not limited to, the elastic modulus of the rock mass, the Poisson's ratio of the rock mass, the compressive strength, the rock mass density, the initial stress state, and the geometric dimensions and boundary conditions of each constituent layer. After data preprocessing, the foregoing parameters are used to describe the mechanical state of the actual rock mass in subsequent numerical simulations and to ensure the statistical stability and representativeness of each parameter.

[0074] Based on the rock mass parameters, construct the mathematical framework required for the non-local creep model, and define the relationship between the evolution of rock mass damage, the displacement change and the stress distribution during the creep process.

[0075] Based on the rock mass parameters, establish a non-local creep model for describing the deformation evolution process of the underground engineering rock mass under sustained loading. The non-local creep model is expressed by an integral-differential equation in the following form: where, Ξ(ζ, η) represents the local creep strain at the spatial coordinate ζ and under the sustained loading time η; L0 is the initial creep rate constant, and its value is determined according to the initial loading conditions; Ω represents all possible spatial regions in the rock mass that may be affected by non-local interactions; K(ζ, ξ) is the influence function describing the non-local coupling effect between any two points ζ and ξ in space, and the influence function adopts, for example, the form of a Gaussian function, and its parameters are obtained by fitting the on-site data; Γ(ξ, η) represents the local creep strain rate at the spatial coordinate ξ and under the sustained loading time η; ζ represents a certain position of the underground engineering rock mass in the spatial coordinate system, used to describe the distribution of creep strain; ξ represents the position of any influencing point in the spatial coordinate, used to calculate the non-local influence of this point on the creep of the rock mass at the ζ position.

[0076] The integral-differential equation adopted in the above non-local creep model can comprehensively describe the creep behavior caused by non-local interaction within the rock mass under sustained loading. All variables and parameters in its mathematical expression are clarified through field data and experimental results, thus ensuring the full publicity and consistency of the model parameters.

[0077] The established non-local creep model is discretized by using the finite difference method, and the continuous variables involved are transformed into discrete variables.

[0078] To numerically solve the above non-local creep model, the finite difference method is used to discretize the continuous spatial domain and time domain.

[0079] The three-dimensional space region of the actual engineering rock mass is divided into several discrete grid cells according to a pre-set discrete scale, and the continuous time domain of the sustained loading is divided into multiple equally spaced time steps. Let the spatial number of the discretized grid cell be i (where n = 1, 2,... N, and N is the total number of grid cells), and the time step number be n (where n = 0, 1, 2,...). The creep strain within each grid cell is denoted as The time step is denoted as Δη, and the spatial step is denoted as Δζ. On this basis, the above integral-differential equation is discretized to obtain the following finite difference expression: Among them, represents the local creep strain of the i-th grid cell at the n-th time step; Δη represents the discretized time step; K ij represents the discretized influence function between grid cell i and grid cell j, and its value is determined based on the continuous function K(ζ, ξ) and the corresponding grid center coordinates; represents the local creep strain rate of the j-th grid cell at the n-th time step, and its value is determined by field test data or previous simulation results; i represents the number of the spatial grid cell of the underground engineering rock mass during the discretization process by the finite difference method, and each grid cell corresponds to a calculation node; j represents the number of another grid cell in the discretized grid, which is used to calculate the non-local coupling effect between grid cell i and other grid cells j.

[0080] Numerical simulation is used to iteratively solve the stress field and displacement field of the underground engineering rock mass under different loading conditions, obtain the stress distribution of the underground engineering rock mass under sustained loading, and output the corresponding displacement data.

[0081] Using the above finite difference formula, the creep strain of each grid cell at each time step is calculated using an iterative algorithm until a preset convergence criterion is reached. The convergence criterion is that the change in creep strain of all grid cells in two consecutive time steps is lower than the set error threshold. Through this iterative solution process, the stress distribution and displacement evolution data of the entire underground engineering rock mass under sustained loading can be gradually obtained.

[0082] To enable the non-local creep model to reflect the true mechanical behavior of the underground engineering rock mass, the creep strain data and stress distribution data obtained during the iterative calculation process are coupled through the constitutive relationship of the rock mass. Specifically, according to the linear or non-linear constitutive relationship of the rock mass, the stress tensor data of each grid cell is calculated through the strain-stress conversion formula (such as using the generalized Hooke's law), and the displacement field data is further obtained through integral calculation. The constitutive relationship and the strain-stress conversion formula are both determined based on in-situ test data to ensure that the stress distribution and displacement data can accurately reflect the actual situation.

[0083] During the numerical simulation process, the algebraic equations composed of the discrete equations obtained by discretizing the finite difference method are solved through step-by-step iteration, which not only realizes the numerical solution of the integral-differential equation in the non-local creep model but also ensures the consistency of the corresponding relationship between the creep strain, stress, and displacement data at each discrete node.

[0084] In addition, to ensure the rationality of grid division during the finite difference discretization process, the size and shape of the discrete grid cells are optimized. This takes into account both the actual geometric shape and boundary conditions of the underground engineering rock mass and ensures the accuracy and efficiency of numerical calculations. During the grid division process, a set of optimal discrete parameters is determined by comparing the numerical simulation results at multiple discrete scales and used as fixed parameters for subsequent numerical simulations.

[0085] The viscoelastic parameters and damage threshold parameters of the non-local creep model are dynamically calibrated through the particle swarm optimization algorithm to match the measured displacement monitoring data, including:

[0086] Based on the stress distribution, displacement data, and creep deformation data obtained from the numerical simulation under sustained loading, the initial values of the parameters in the non-local creep model are determined.

[0087] First, based on the stress distribution, displacement data, and creep deformation data obtained from the above-mentioned finite difference method numerical simulation under sustained loading, the parameters used to describe the viscoelastic behavior of the rock mass and the parameters used to determine the rock mass damage threshold in the non-local creep model are preliminarily estimated.

[0088] Specifically, through statistical analysis of the actual deformation data obtained at multiple monitoring points at different times, indicators such as the average value, fluctuation range, and trend change of the data at each monitoring point are selected as the basis for the initial estimation of each parameter. For example, the characteristic parameters of the instantaneous and delayed responses of the rock mass after being stressed and the parameters characterizing the critical changes in cumulative damage are both obtained by summarizing a large amount of on-site data, so as to ensure that the initial estimated values of the parameters have sufficient on-site basis and representativeness.

[0089] The particle swarm optimization algorithm is used to globally search and iteratively calculate each parameter until the output result of the non-local creep model reaches a predetermined consistency with the measured data.

[0090] Specifically, a number of candidate solutions are randomly generated in the parameter space. Each candidate solution is represented in the form of a multi-dimensional parameter combination, and these parameter combinations respectively correspond to the parameters describing the viscoelastic behavior of the rock mass and the rock mass damage threshold parameters. Then, for each candidate solution, it is input into the non-local creep model for simulation calculation to obtain the corresponding stress distribution, displacement data, and creep deformation data, and compared with the on-site measured data.

[0091] Among them, the comparison method can adopt the way of error statistics. For example, the deviation values between the simulation data and the measured data at each monitoring point are compared to determine the overall matching quality of the candidate solutions.

[0092] In each round of iteration, the particle swarm optimization algorithm adjusts the parameter values of each candidate solution according to the best performance of each candidate solution in the historical iteration process and the optimal performance among all current candidate solutions. Specifically, when updating the candidate solutions, the algorithm takes into account both the lower error obtained by the candidate solution itself in the past iterations and the best parameter combination in the entire candidate population. By introducing a certain degree of randomness, it prompts each candidate solution to continuously approach the global optimal solution in the parameter space.

[0093] It should be noted that both the randomness and the weight adjustment here are regulated by pre-set control factors, which have been determined through a large number of simulation experiments in the initial stage, so as to ensure that the parameter update process has high stability and convergence speed.

[0094] The optimization process is terminated by setting the number of iterations and the convergence criterion to ensure the matching of the viscoelastic parameters and the damage threshold parameters with the measured data.

[0095] After completing each candidate solution update, the new parameter combination is input into the non-local creep model for simulation again, and the corresponding stress distribution, displacement data and creep deformation data are obtained again, and the overall error between them and the measured data is calculated. The whole process is repeated continuously. When the error change amplitude of all candidate solutions in several consecutive iterations is lower than the preset convergence threshold, or when the number of iterations reaches the preset upper limit, it is considered that the parameter optimization process has reached the convergence state. At this time, the candidate solution with the smallest error is selected as the final optimization result, and the parameters describing the viscoelastic behavior of the rock mass and the rock mass damage threshold parameters contained in the candidate solution are used as the final calibrated parameters.

[0096] The displacement monitoring data and numerical simulation results are integrated, and the stress relaxation coefficient of the non-local creep model is corrected using the least squares method, including:

[0097] The displacement monitoring data are compared with the numerical simulation displacement data obtained using the finite difference method and the non-local creep model to determine the deviation between the displacement monitoring data and the numerical simulation results.

[0098] The monitoring system deployed on site collects displacement monitoring data at key locations in the underground project. The displacement monitoring data reflects the displacement changes of the rock mass over time under continuous load. At the same time, based on the numerical simulation results obtained by combining the non-local creep model with the finite difference method, the displacement data at each discrete calculation node in the corresponding period are also obtained.

[0099] In order to achieve effective fusion between the two, the monitoring data and numerical simulation data are first preprocessed to ensure that they have the same sampling interval and coordinate correspondence in time and space. At the same time, outliers and noise data are eliminated to make the data highly comparable and accurate.

[0100] The preprocessed displacement monitoring data and numerical simulation displacement data are compared and analyzed point by point. Specifically, at each corresponding monitoring point or discrete grid unit, the error between the two is calculated, that is, the difference between the monitoring data and the numerical simulation data is used as the deviation value of the point. Here, each deviation value reflects the difference between the numerical simulation and the actual observation results at the same time and spatial position, and these deviation values are the basis for subsequent correction work.

[0101] To facilitate subsequent calculations, the deviation values of all monitoring points are statistically collated and an overall error evaluation function is constructed. The error evaluation function adopts the principle of least squares method, that is, the squares of the deviation values of each measuring point are summed to quantify the overall error size.

[0102] The least square method is used to quantitatively calculate the deviation between the displacement monitoring data and the numerical simulation results to obtain the preliminary correction coefficient.

[0103] The least squares method is used to quantitatively calculate the above overall error. Specifically, by constructing an objective function, which is expressed as the sum of the squares of the errors at all monitoring points, the smaller its value indicates the higher the degree of agreement between the numerical simulation results and the actual monitoring data.

[0104] To ensure that the objective function can truly reflect the deviation between the two sets of data, a strict data normalization method is adopted to standardize the data at each measuring point according to the corresponding physical dimensions, thereby eliminating the dimensional differences caused by different measuring points, different times, or different spatial scales.

[0105] After determining the objective function, the least squares method is used to solve the optimal solution of the objective function to obtain a preliminary correction coefficient, which is used to adjust the initial value of the stress relaxation coefficient in the non-local creep model.

[0106] Here, the stress relaxation coefficient is a key parameter describing the slow relaxation behavior of rock masses under stress, and its initial value is preset in the previous numerical simulation process. The preliminary correction coefficient calculated by the least squares method in this step is the correction factor that makes the numerical simulation output more consistent with the actual monitoring results.

[0107] According to the preliminary correction coefficient, the stress relaxation coefficient is iteratively adjusted until the mean square error between the displacement monitoring data and the numerical simulation results meets the predetermined convergence condition.

[0108] After applying the preliminary correction coefficient to the initial stress relaxation coefficient, the non-local creep model is run again, and the updated displacement simulation data is obtained using the finite difference method; then the updated displacement data is compared point by point with the monitoring data, and the value of the objective function is recalculated; if the calculated mean square error does not reach the preset convergence condition, the stress relaxation coefficient is continuously adjusted until the change in the objective function value is lower than the set threshold in several consecutive iteration processes or the mean square error reaches the expected convergence standard.

[0109] During the entire iterative process, the adjustment of all parameters maintains a consistent correspondence with the aforementioned displacement monitoring data and numerical simulation data, thereby ensuring that each iteration can be effectively corrected based on the results of the previous iteration.

[0110] To ensure the effectiveness of the iterative process, clear termination conditions and convergence criteria are set for the iterative process, that is, when the mean square error at all measuring points drops below the predetermined convergence threshold, or when the number of iterations reaches the preset upper limit, it is considered that the optimization process has reached a stable state.

[0111] The non-local creep model is updated with the corrected stress relaxation coefficient to ensure that the numerical simulation results are consistent with the displacement monitoring data.

[0112] At this time, the stress relaxation coefficient adopted is the final parameter value after being corrected by the least squares method. This parameter value will be updated into the non-local creep model and used as the basic data for the long-term stability prediction of subsequent underground engineering.

[0113] Based on the calibrated viscoelastic parameters, damage threshold parameters, and the corrected stress relaxation coefficient, a prediction model reflecting the creep deformation characteristics of the rock mass in underground engineering under continuous loading over time is established, including:

[0114] Taking the calibrated viscoelastic parameters, damage threshold parameters, and the corrected stress relaxation coefficient as input parameters, and combining the stress distribution, displacement data, and creep deformation data obtained by using the non-local creep model and the finite difference method, data fusion is carried out with the displacement monitoring data obtained on-site.

[0115] To achieve the matching between data, it is required to preprocess each data source, including time synchronization, spatial correction, and noise filtering, to ensure that the numerical simulation data and the monitoring data are consistent in terms of time, space, and dimension. After each data is normalized, a data matrix is formed according to the monitoring point position and time, thus providing unified, continuous, and consistent input data for the subsequent establishment of the prediction model.

[0116] The fused data is processed by using data fitting and trend analysis methods to construct a prediction model reflecting the creep deformation characteristics of the rock mass in underground engineering under continuous loading over time, and a corresponding time-varying prediction curve of the creep deformation is generated.

[0117] After the data fusion is completed, data fitting and trend analysis methods are used to construct a prediction model reflecting the creep deformation characteristics of the rock mass in underground engineering under continuous loading over time. In the specific implementation process, the following mathematical expression is proposed as the prediction model: Among them, Δ C (t) represents the creep deformation at the prediction time t; t represents the continuous loading time, and its unit is seconds (s) or hours (h), which is determined according to the actual engineering requirements; A1 represents the baseline creep deformation, and its value reflects the initial deformation existing in the rock mass at the initial stage of loading; A2 represents the proportional coefficient used to describe the cumulative creep effect caused by the increase over time, and its value is obtained by data fitting; A3 represents the power exponent of creep evolution, and its value reflects the non-linear degree of the creep deformation changing with time; A4 represents the amplitude coefficient of the exponential decay term, and its value is used to describe the part where the creep deformation of the rock mass tends to be stable after a certain time; A5 represents the rate coefficient of exponential decay, and its value reflects the decay rate of the creep deformation of the rock mass caused by the stress relaxation effect.

[0118] By performing non-linear regression fitting on the fused data matrix, the optimal values of the above parameters A1, A2, A3, A4, and A5 can be determined, minimizing the fitting error between the creep deformation amount output by the mathematical model and the actual monitoring data, thereby generating a time-varying prediction curve reflecting the change of creep deformation amount of the rock mass in the underground project over time under the action of continuous load. This prediction curve can accurately reflect the dynamic evolution process of creep deformation at each continuous time point.

[0119] According to the output results of the prediction model and the preset creep instability discrimination criterion, compare the numerical simulation results with the monitoring data to determine the spatial distribution of the potential instability area of the underground project, and draw the corresponding spatial distribution map.

[0120] After obtaining the time-varying prediction curve, further determine the spatial distribution of the potential instability area of the underground project based on the preset creep instability discrimination criterion.

[0121] In specific implementation, a key parameter, namely the critical creep deformation threshold, is included in the preset creep instability discrimination criterion to determine whether the rock mass is in an unstable state. Let this critical creep deformation threshold be denoted as B1, and its value is determined by on-site experimental data and engineering experience. Subsequently, for the creep deformation amount output by the prediction model at the corresponding positions of each monitoring point, judge whether it satisfies the following conditions:

[0122] If Δ C (t) ≥ B1, it is considered that there is a potential instability risk in the underground project area corresponding to this monitoring point;

[0123] On the contrary, if Δ C (t) < B1, it is considered that this area is in a safe state.

[0124] To accurately draw the spatial distribution, an interpolation method based on geographic information system is used to interpolate the judgment results at each discrete monitoring point in the actual space of the underground project, thereby generating a spatial distribution map of the potential instability area. This spatial distribution map clearly marks the areas where the creep deformation amount of the rock mass exceeds the critical threshold at different positions, providing an intuitive quantitative basis for engineering risk management and subsequent safety assessment.

[0125] The above formulas are all dimensionless and take their numerical calculations. The formula is obtained by collecting a large amount of data for software simulation to get a formula closest to the real situation. The preset parameters and threshold selection in the formula are set by technicians in this field according to the actual situation.

[0126] The above embodiments can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, the processes or functions described in the embodiments of the present application are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wired (such as infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or a data center that contains one or more collections of available media. The available medium can be a magnetic medium (such as a floppy disk, a hard disk, a magnetic tape), an optical medium (such as a DVD), or a semiconductor medium. The semiconductor medium can be a solid-state drive.

[0127] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the systems, devices, and modules described above can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0128] In the several embodiments provided in the present application, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the modules is only a logical function division, and there can be other division methods in actual implementation. For example, multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the couplings, direct couplings, or communication connections shown or discussed with each other can be through some interfaces, and the indirect couplings or communication connections of the devices or modules can be in electrical, mechanical, or other forms.

[0129] The modules described as separate components may or may not be physically separated, and the components shown as modules may or may not be physical modules. They can be located in one place or distributed to multiple network modules. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0130] In addition, in each embodiment of the present application, each functional module can be integrated into a processing module, can exist physically alone for each module, or two or more modules can be integrated into one module.

[0131] If the above-mentioned function is implemented in the form of a software functional module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes such as USB flash drives, mobile hard disks, read-only memories (ROM), random access memories (RAM), magnetic disks, or optical discs.

[0132] As described above, the above are only specific embodiments of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present application can easily think of changes or substitutions, which should all be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

[0133] Finally: The above are only the preferred embodiments of the present invention and are not used to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A long-term stability prediction method for underground engineering based on the creep instability discrimination theory, characterized in that, The steps include: Establish a creep instability criterion containing time-dependent damage parameters, and define the creep evolution boundaries of rock masses under different stress levels based on the creep instability criterion; Conduct numerical simulation on the rock mass parameters of geological exploration based on the non-local creep model and the finite difference method. The non-local creep model includes viscoelastic parameters, damage threshold parameters, and stress relaxation coefficients, and iteratively output the stress distribution and displacement data under sustained load; Dynamically calibrate the viscoelastic parameters and damage threshold parameters of the non-local creep model through the particle swarm optimization algorithm to match the measured displacement monitoring data; Fuse the displacement monitoring data and the numerical simulation results, and use the least squares method to correct the stress relaxation coefficient of the non-local creep model; Based on the calibrated viscoelastic parameters and damage threshold parameters, combined with the corrected stress relaxation coefficient, establish a prediction model reflecting the time-varying characteristics of the creep deformation of the rock mass in underground engineering under sustained load.

2. A long-term stability prediction method for underground engineering based on the creep instability discrimination theory according to claim 1, characterized in that Establish a creep instability criterion containing time-dependent damage parameters, and define the creep evolution boundaries of rock masses under different stress levels based on the creep instability criterion, including: Obtain the creep deformation data generated by the rock mass in underground engineering under sustained load, and conduct statistical analysis and time history analysis on the creep deformation data to determine the time-dependent variation law of damage evolution during the long-term loading process of the rock mass; Determine the time-dependent damage parameters based on the time-dependent variation law, including the duration of sustained load, the damage evolution rate, and the damage accumulation variable; Construct a mathematical model containing time-dependent damage parameters to quantitatively describe the creep evolution characteristics of the rock mass in underground engineering under different stress levels; Define the creep evolution boundaries of rock masses under different stress levels based on the mathematical model, and form a creep instability criterion.

3. A long-term stability prediction method for underground engineering based on the creep instability discrimination theory according to claim 2, characterized in that, The mathematical model containing time-dependent damage parameters is expressed as: Among them, D(T) represents the degree of damage of the rock mass under the action of the sustained load for time T, D0 represents the initial degree of damage, P1 represents the damage scale factor, T represents the time of the sustained load action, P2 represents the damage evolution index, P3 represents the stress sensitivity coefficient, and S represents the stress level of the rock mass.

4. A long-term stability prediction method for underground engineering based on the creep instability discrimination theory according to claim 1, characterized in that, Conduct numerical simulation on the rock mass parameters of geological exploration based on the non-local creep model and the finite difference method. The non-local creep model includes viscoelastic parameters, damage threshold parameters, and stress relaxation coefficients, and iteratively output the stress distribution and displacement data under sustained load, including: Collect the rock mass parameters of the underground engineering rock mass under different load conditions; Construct the mathematical framework required for the non-local creep model based on the rock mass parameters, and define the relationship between the displacement change and stress distribution during the rock mass damage evolution and creep process; Apply the finite difference method to discretize the established non-local creep model, and convert the involved continuous variables into discrete variables; Use numerical simulation to iteratively solve the stress field and displacement field of the underground engineering rock mass under different load conditions, obtain the stress distribution of the underground engineering rock mass under sustained load, and output the corresponding displacement data.

5. A long-term stability prediction method for underground engineering based on creep instability discrimination theory according to claim 4, characterized in that, The non-local creep model is expressed as: where Ξ(ζ, η) represents the local creep strain at the spatial coordinate ζ under the action of a sustained load for a time η, L0 is the initial creep rate constant, Ω represents all possible spatial regions in the rock mass that are affected by non-local interactions, K(ζ, ξ) is the influence function describing the non-local coupling effect between any two points ζ and ξ in space, Γ(ξ, η) represents the local creep strain rate at the spatial coordinate ξ under the action of a sustained load for a time η, ζ represents a certain position of the rock mass of the underground engineering in the spatial coordinate system, and ξ represents the position of any influencing point in the spatial coordinates.

6. A long-term stability prediction method for underground engineering based on creep instability discrimination theory according to claim 4, characterized in that, Apply the finite difference method to discretize the established non-local creep model, specifically: Divide the three-dimensional space area of the actual engineering rock mass into several discrete grid units according to the preset discrete scale, and divide the continuous time domain of sustained load into multiple equally spaced time steps; The non-local creep model is discretized to obtain the following finite-difference expression: where represents the local creep strain of the i-th grid cell at the n-th time step, Δη represents the discretized time step, and K ij represents the discretized influence function between grid cell i and grid cell j, represents the local creep strain rate of the j-th grid cell at the n-th time step, i represents the number of the spatial grid cell of the underground engineering rock mass during the discretization process of the finite-difference method, j represents the number of another grid cell in the discretized grid, N is the total number of grid cells, n is the time step number, and Δζ is the spatial step size.

7. A long-term stability prediction method for underground engineering based on the creep instability discrimination theory according to claim 1, characterized in that Dynamically calibrate the viscoelastic parameters and damage threshold parameters of the non-local creep model through the particle swarm optimization algorithm to match the measured displacement monitoring data, including: Determine the initial values of the parameters in the non-local creep model according to the stress distribution, displacement data, and creep deformation data under sustained load obtained from numerical simulation; Use the particle swarm optimization algorithm to perform global search and iterative calculation on each parameter until the output result of the non-local creep model reaches a predetermined consistency with the measured data; Terminate the optimization process by setting the number of iterations and convergence criteria to ensure that the viscoelastic parameters and damage threshold parameters match the measured data.

8. A long-term stability prediction method for underground engineering based on the creep instability discrimination theory according to claim 1, characterized in that Fuse the displacement monitoring data and the numerical simulation results, and use the least squares method to correct the stress relaxation coefficient of the non-local creep model, including: Compare and analyze the displacement monitoring data with the numerical simulation displacement data obtained by using the finite difference method and the non-local creep model to determine the deviation between the displacement monitoring data and the numerical simulation results; Use the least squares method to quantitatively calculate the deviation between the displacement monitoring data and the numerical simulation results to obtain a preliminary correction coefficient; Iteratively adjust the stress relaxation coefficient according to the preliminary correction coefficient until the mean square error between the displacement monitoring data and the numerical simulation results meets the predetermined convergence condition; Update the non-local creep model with the corrected stress relaxation coefficient.

9. A long-term stability prediction method for underground engineering based on the creep instability discrimination theory according to claim 1, characterized in that Based on the calibrated viscoelastic parameters and damage threshold parameters combined with the corrected stress relaxation coefficient, establish a prediction model reflecting the time-varying characteristics of the creep deformation of the rock mass in the underground project under sustained load, including: Take the calibrated viscoelastic parameters, damage threshold parameters, and corrected stress relaxation coefficient as input parameters, combine the stress distribution, displacement data, and creep deformation data obtained by using the non-local creep model and the finite difference method, and perform data fusion with the displacement monitoring data obtained on-site; Use data fitting and trend analysis methods to process the fused data, construct a prediction model reflecting the time-varying characteristics of the creep deformation of the rock mass in the underground project under sustained load, and generate a corresponding time-varying prediction curve of the creep deformation; According to the output result of the prediction model and the preset creep instability discrimination criterion, compare the numerical simulation result with the monitoring data to determine the spatial distribution of the potential instability area in the underground project, and draw the corresponding spatial distribution map.

10. A long-term stability prediction method for underground engineering based on the creep instability discrimination theory according to claim 9, characterized in that, The prediction model reflecting the characteristics of the creep deformation of rock masses in underground engineering under sustained loading over time is as follows: where, Δ C (t) represents the creep deformation at the predicted time t, t represents the duration of the sustained loading, A1 represents the baseline creep deformation, A2 represents the proportionality coefficient for characterizing the cumulative creep effect caused by the increase over time, A3 represents the power exponent of creep evolution, A4 represents the amplitude coefficient of the exponential decay term, and A5 represents the rate coefficient of exponential decay.

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