Tailing dam time-varying reliability analysis method considering freeze-thaw deterioration and earthquake randomness

Abstract

The invention provides a tailing dam time-varying reliability analysis method considering freeze-thaw degradation and earthquake randomness. The method comprises the following steps: acquiring shear strength parameters and permeability coefficient statistical characteristics of a tailing material in a freeze-thaw environment; constructing a physical random seismic motion model, and obtaining a plurality of random seismic motion parameters; according to shear strength parameters, permeability coefficient statistical characteristics and the random seismic oscillation parameters, generating random samples and corresponding assigned probabilities based on a probability space subdivision method of grouping-score deviation; establishing a tailing dam finite element model, and calculating a slope safety coefficient corresponding to each group of samples based on unsaturated seepage analysis and slope stability analysis; based on a probability density evolution theory, establishing and solving a generalized probability density evolution equation, and obtaining a probability density function of a slope safety coefficient and a time-varying evolution process of the probability density function; and solving the failure probability and reliability index of the tailing dam at different moments. The accuracy of reliability evaluation of the tailing dam is effectively improved.

Description

Technical Field

[0001] This application relates to the field of tailings dam stability analysis technology, specifically to a time-varying reliability analysis method for tailings dams that considers freeze-thaw degradation and seismic randomness. Background Technology

[0002] Tailings dams, as critical storage facilities used to store mineral processing waste (tailings) during mining operations, are directly related to mine safety and the safety of the surrounding ecological environment. A dam failure would have catastrophic consequences: First, hundreds of thousands or even millions of cubic meters of tailings slurry could overflow in a short period, destroying downstream residential areas, industrial facilities, and infrastructure; second, tailings containing heavy metals and mineral processing reagents would pollute the soil and water bodies of the basin, causing long-term ecological damage; furthermore, such accidents could trigger severe secondary disasters, including floods caused by river blockages and public health crises resulting from the spread of toxic substances.

[0003] Traditional deterministic analysis methods (such as the limit equilibrium method) have limitations in tailings dam stability assessment. These methods are typically based on fixed parameters and deterministic models, failing to effectively quantify the inherent spatial variability and time dependence of tailings parameters (such as shear strength, permeability coefficient, and compression modulus). Furthermore, they struggle to accurately characterize the multi-field coupling effects of tailings dams in complex environments (such as the interaction between seepage and stress fields), as well as the stochastic dynamic impacts of earthquakes and freeze-thaw cycles. This deterministic framework often masks the true uncertainties of the system, leading to significant deviations between risk assessment results and actual engineering behavior, potentially causing serious safety misjudgments under extreme conditions. For such low-probability, high-consequence events and problems significantly affected by uncertainties, employing reliability analysis theory is one of the most effective approaches. However, while existing reliability calculation methods (Monte Carlo simulation) can effectively quantify the uncertainties in the stability analysis of tailings dams, their application has significant limitations: the method is computationally expensive and requires massive iterations when dealing with multi-field coupling effects; the reliability of its results is highly dependent on the accuracy of the parameter probability distribution, while sufficient data is often lacking in actual engineering; traditional random sampling is inefficient for high-dimensional parameter spaces or low-probability events; and the method can only provide probabilistic results and cannot reveal the failure mechanism.

[0004] Probability density evolution theory (PDEM), as an advanced reliability analysis method, accurately describes the entire process of the dynamic evolution of the probability density function of a tailings dam system under the coupled effects of multiple fields such as seepage and earthquakes. This is achieved through probability space partitioning of random variables, assigning probabilities to a defined point set, and establishing a generalized probability density evolution equation (GDEE) for the response of interest. This method overcomes the limitations of traditional analysis methods and has two significant advantages: first, computational efficiency, which significantly reduces sample requirements compared to Monte Carlo simulations; and second, comprehensive analysis, capable of simultaneously considering complex factors such as parameter randomness, model uncertainty, and time-varying loads, making it suitable for handling dynamic time-varying reliability problems of the entire system. This makes PDEM particularly suitable for assessing the dynamic time-varying reliability of complex engineering structures like tailings dams, which exhibit significant nonlinear characteristics and require long-term service. It not only meets the stringent requirements of risk assessment but also provides a reliable theoretical analysis tool for intelligent mine construction, and has now become one of the most promising frontier directions in geotechnical engineering reliability research.

[0005] Tailings dams, as key facilities in mining engineering, are subject to various uncertainties in their long-term stability, among which material degradation caused by freeze-thaw cycles and the randomness of seismic loads are particularly prominent. Existing reliability analyses of tailings dams based on probability density evolution theory mostly focus on the spatial variability of tailings parameters, neglecting the coupling effect of freeze-thaw environment and seismic randomness, making it difficult to accurately assess the time-varying reliability of tailings dams. Summary of the Invention

[0006] This invention provides a time-varying reliability analysis method for tailings dams that considers freeze-thaw degradation and seismic randomness. It not only considers the spatial variation of tailings parameters, but also freeze-thaw degradation and seismic randomness. It aims to break through the limitations of traditional deterministic analysis methods and realize the accurate assessment of the dynamic reliability of tailings dams under the dual uncertainty coupling effect of freeze-thaw and seismic events. It can provide theoretical support for the safety prevention and control of tailings dams in high-altitude seismic zones.

[0007] Firstly, this application provides a time-varying reliability analysis method for tailings dams that considers freeze-thaw degradation and seismic randomness, the method comprising: Statistical characteristics of shear strength parameters and permeability coefficient of tailings materials under freeze-thaw conditions were obtained; Construct a physical random ground motion model and obtain multiple random ground motion parameters; The shear strength parameter, the statistical characteristics of the permeability coefficient, and the random ground motion parameter are used as random variables. Random samples and their corresponding assigned probabilities are generated using a probability space partitioning method based on grouping-fractional deviation. A finite element model of the tailings dam was established, and the slope safety factor for each sample group was calculated based on unsaturated seepage analysis and slope stability analysis. Based on the probability density evolution theory, the generalized probability density evolution equation is established and solved to obtain the probability density function of the slope safety factor and its time-varying evolution process. Solve for the failure probability and reliability index of tailings dam at different times to achieve overall time-varying reliability assessment of tailings dam.

[0008] Secondly, this application also provides a time-varying reliability analysis device for tailings dams that considers freeze-thaw degradation and seismic randomness, the device comprising: The first acquisition unit is used to acquire the shear strength parameters and permeability coefficient statistical characteristics of tailings materials under freeze-thaw conditions; The second acquisition unit is used to construct a physical random ground motion model and acquire multiple random ground motion parameters; The sample generation unit is used to take the shear strength parameter, the statistical characteristics of the permeability coefficient and the random ground motion parameter as random variables, and generate random samples and corresponding assigned probabilities using a probability space partitioning method based on grouping-fractional deviation. The first model constructs a solution unit to establish a finite element model of the tailings dam, and calculates the slope safety factor corresponding to each sample based on unsaturated seepage analysis and slope stability analysis. The second model constructs a solution unit, which is used to establish and solve the generalized probability density evolution equation based on the probability density evolution theory, and obtain the probability density function of the slope safety factor and its time-varying evolution process. The result output unit is used to solve the failure probability and reliability index of the tailings dam at different times, so as to realize the overall time-varying reliability assessment of the tailings dam.

[0009] Thirdly, this application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements any of the methods described above.

[0010] This application can achieve at least the following beneficial effects: The time-varying reliability analysis method for tailings dams that takes into account freeze-thaw degradation and seismic randomness provided in this application has significant advantages and effectively improves the accuracy and efficiency of tailings dam reliability assessment.

[0011] First, it achieves innovative breakthroughs in modeling. It couples the uncertainty of tailings parameters under freeze-thaw conditions, the random parameters of the physical model of random ground motion in engineering, and the unsaturated seepage of rainfall infiltration into the model. This changes the limitations of traditional methods that only consider static parameters or single disaster factors, and can more comprehensively and realistically reflect the actual situation of tailings dams in complex environments.

[0012] Secondly, it performs excellently in sample generation. It uses a probability space partitioning method based on GF bias to generate random samples, which not only solves the problem of low computational efficiency of traditional Monte Carlo methods in high-dimensional spaces, but also controls the sample coverage of low-probability regions more accurately than traditional Latin hypercube sampling methods, and optimizes the assignment probability of sample points, making the samples more representative and accurate.

[0013] Furthermore, earthquake motion simulation is more scientific. Using a physical model of engineering random earthquake motion instead of traditional earthquake time history superposition preserves the non-stationary frequency domain characteristics of earthquake motion, and can better simulate the impact of earthquakes on tailings dams.

[0014] Finally, it is highly efficient and convenient in probability density calculation. Based on the theory of probability density evolution, the time-varying probability density function of the slope safety factor can be directly obtained by solving the generalized probability density evolution equation, without relying on large-scale sampling of Monte Carlo simulation, which greatly improves the computational efficiency.

[0015] In summary, this method has been optimized and innovated in several key aspects, and can effectively realize the overall time-varying reliability assessment of tailings dams, providing strong support for the safety management of tailings dams. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart illustrating a time-varying reliability analysis method for tailings dams considering freeze-thaw degradation and seismic randomness according to an embodiment of this application is shown. Figure 2 A schematic diagram of a time-varying reliability analysis device for tailings dams considering freeze-thaw degradation and seismic randomness according to an embodiment of this application is shown. Detailed Implementation

[0018] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] Tailings dams, as critical facilities in mining engineering, are subject to various uncertainties in their long-term stability, with material degradation caused by freeze-thaw cycles and the randomness of seismic loads being particularly prominent. Traditional reliability analyses often focus on the spatial variability of tailings parameters, neglecting the coupling effect of freeze-thaw environment and seismic randomness, making it difficult to accurately assess the time-varying reliability of tailings dams. To address this limitation, this invention proposes a time-varying reliability analysis method for tailings dams that considers not only the spatial variability of tailings parameters but also freeze-thaw degradation and seismic randomness.

[0020] Figure 1 This paper illustrates a flowchart of a time-varying reliability analysis method for tailings dams that considers freeze-thaw degradation and seismic randomness according to an embodiment of this application. Figure 1 As can be seen, this embodiment includes: steps S110 to S160: Step S110: Obtain the shear strength parameters and permeability coefficient statistical characteristics of tailings materials under freeze-thaw conditions.

[0021] The parameters of tailings materials under freeze-thaw conditions include, but are not limited to, shear strength parameters and statistical characteristics of permeability coefficient. Both can be obtained experimentally. Among them, shear strength parameters include, but are not limited to, cohesion and internal friction angle.

[0022] Specifically, in some embodiments of this application, obtaining the shear strength parameters and permeability coefficient statistical characteristics of tailings materials under freeze-thaw conditions includes: obtaining the shear strength parameters and permeability coefficient statistical characteristics of tailings materials under multiple freeze-thaw cycles through indoor freeze-thaw cycle tests, triaxial shear tests, and permeability coefficient tests. The shear strength includes cohesion c and internal friction angle φ; the permeability coefficient statistical characteristics include mean, standard deviation, value range, and probability distribution model.

[0023] Through indoor freeze-thaw cycle tests, triaxial shear tests, and permeability coefficient tests, the statistical characteristics of tailings shear strength parameters and permeability coefficient under multiple (e.g., 10) freeze-thaw cycles were obtained. The main characteristics include the mean, standard deviation, range of values, and probability distribution model of the shear strength parameters and permeability coefficient.

[0024] Subsequently, the tailings shear strength parameters (cohesion, internal friction angle) and permeability coefficient were treated as random variables.

[0025] Step S120: Construct a physical random ground motion model and obtain multiple random ground motion parameters.

[0026] The specific details of the physical model for random ground motion in engineering are explained below: In some embodiments of this application, the physical random ground motion model is expressed as equation (1): Equation (1); In equation (1), For seismic acceleration, and epicenter distance The time history amplitude and phase spectra of ground motion acceleration at the location; and These are the random parameter vectors of the amplitude spectrum and the deterministic parameter vectors of the phase spectrum, respectively.

[0027] In the above physical random ground motion model, the Brune dislocation source model is used to reflect the source mechanism, taking into account the damping attenuation effect and dispersion effect of the propagation path, and the local site soil layer is equivalent to a single degree of freedom system. Therefore, the amplitude spectrum and phase spectrum of the model for constructing the physical random ground motion model are respectively Equation (2) and Equation (3): Equation (2); Equation (3); In equations (2) and (3), The parameter representing the dielectric attenuation effect is empirically taken to be 10. -5 s / km, amplitude spectrum random parameter vector , It reflects the intensity of the earthquake source. The Brune focal coefficient, and These are the equivalent damping ratio and equivalent dominant circular frequency of the local site, respectively. , , , For random parameters, epicentral distance It is a random variable.

[0028] Step S130: Based on the shear strength parameter, the statistical characteristics of the permeability coefficient, and the random ground motion parameter, generate random samples and corresponding assigned probabilities using a probability space partitioning method based on group-fraction (GF) bias.

[0029] The physical model input parameters of tailings shear strength, permeability coefficient, and random ground motion under freeze-thaw conditions are treated as random variables. A sampling method based on GF bias is used to generate N random samples (10T). 2 (magnitude).

[0030] In the actual environment of tailings dams, freeze-thaw cycles significantly impact the performance of tailings materials. Shear strength parameters and permeability coefficient statistical characteristics are crucial indicators describing the mechanical and hydraulic properties of tailings materials under freeze-thaw conditions. Shear strength parameters reflect the tailings material's ability to resist shear failure, and their magnitude directly relates to the stability of the tailings dam slope. Permeability coefficient statistical characteristics reflect the tailings material's ability to allow water to pass through, which is essential for studying seepage within the tailings dam. Random ground motion parameters, taking into account the randomness of earthquakes, exert varying degrees of dynamic effects on the tailings dam, making them a significant external factor influencing its safety.

[0031] The group-fraction (GF) bias probability space partitioning method is an advanced mathematical approach. Its core idea is to rationally divide a multidimensional probability space comprised of shear strength parameters, permeability coefficient statistical characteristics, and random ground motion parameters. In this multidimensional space, each parameter represents a dimension, and different combinations of these parameter values ​​constitute the entire probability space. Using the group-fraction (GF) bias method, this complex multidimensional space can be divided into multiple smaller regions.

[0032] After dividing the probability space, random samples can be generated within each defined small region. These random samples are specific combinations of shear strength parameters, permeability coefficient statistical characteristics, and random ground motion parameters, representing various situations that tailings dams may encounter during actual operation. Simultaneously, each generated random sample is assigned a corresponding probability based on the characteristics of its region. This assigned probability reflects the likelihood of the situation represented by the sample occurring in reality.

[0033] Generating random samples and corresponding assigned probabilities in this way allows for a more comprehensive and accurate consideration of various uncertainties in tailings dams under freeze-thaw cycles and random seismic activity. These random samples and assigned probabilities will serve as the foundational data for subsequent analyses, used to establish finite element models of tailings dams, calculate slope safety factors, and ultimately achieve an overall time-varying reliability assessment of the tailings dam, providing a scientific basis for the safety management and decision-making of tailings dams. See Table 1 for details.

[0034] Table 1. Parameter values ​​for simulated seismic motion samples

[0035] Step S140: Establish a finite element model of the tailings dam, and calculate the slope safety factor for each sample group based on unsaturated seepage analysis and slope stability analysis.

[0036] The tailings shear strength parameters, permeability coefficient, and random ground motion parameters generated by the above random sampling are assigned to the finite element model. Unsaturated seepage analysis of the tailings dam under rainfall conditions is performed using the Geostudio SEEP / W module. Based on this, slope stability is calculated using the SLOPE / W module, and the safety factor of the slope is determined under all N sets of input random variables under the same working condition. .

[0037] In some embodiments of this application, the step of establishing a finite element model of the tailings dam and calculating the slope safety factor corresponding to each group of samples based on unsaturated seepage analysis and slope stability analysis includes: using the Geostudio SEEP / W module, based on the water-air two-phase flow control equation and the van enuchten-Mualem constitutive relation model, to perform unsaturated seepage analysis under rainfall infiltration conditions; inputting the random samples and their corresponding assigned probabilities to simulate the seepage field changes of the tailings dam under different freeze-thaw deterioration and seismic actions; and based on the obtained seepage field change information, performing slope stability analysis based on the rigid body limit equilibrium method to calculate the tailings dam slope safety factor corresponding to each group of random samples.

[0038] Preferably, the seepage analysis is based on the principle of water-air two-phase flow. The unsaturated seepage analysis under rainfall infiltration conditions, performed using the Geostudio SEEP / W module based on the water-air two-phase flow governing equations and constitutive models, includes: The governing equations for the water-air two-phase flow are constructed, wherein the governing equation for the water phase is expressed as equation (4): Equation (4); The relative control equation for the gas phase is expressed as equation (5): Equation (5); In equations (4) and (5), Saturation; , Pore ​​water pressure, Pore ​​gas pressure, ; The intrinsic permeability coefficient, ; The relative permeability coefficient of the aqueous phase. The relative permeability coefficient of the gas phase; It is the acceleration due to gravity. The density of the aqueous phase, The density is in the gas phase, kg / m³ 3 ; The viscosity coefficient of the liquid phase. This is the gas phase viscosity coefficient; For liquid phase intrinsic terms, For gas-phase endogenous terms, kg s).

[0039] The governing equations for water-gas two-phase flow contain five unknown parameters: , , , , Therefore, three constitutive relation models need to be introduced in the solution process, including: soil-water characteristic curve, water phase relative permeability coefficient curve and gas phase relative permeability curve; among them, the soil-water characteristic curve adopts the van Genuchten model, which is expressed as equation (6): Equation (6); In equation (6), The matrix suction is calculated to be ( ), This is the intake air value. Residual saturation, These are parameters related to the model's materials.

[0040] The relative permeability coefficient curve relationship of the aqueous phase is adopted using the van Genuchten-Mualem model and is expressed as Equation (7): Equation (7); In equation (7), is the relative permeability coefficient of the aqueous phase.

[0041] The relative permeability curve relationship of the gas phase is adopted using the Brooks-Corey model and is expressed as Equation (8): Equation (8); In equation (8), The matrix suction is calculated to be ( ), This is the intake air value. Residual saturation, These are parameters related to the model's materials.

[0042] When performing slope stability analysis, the rigid body limit equilibrium method is used to calculate the safety factor of the tailings dam slope corresponding to each random sample. Specifically, in some embodiments, the rigid body limit equilibrium model shown in equations (9) and (10) is used for slope stability analysis: Equation (9); Equation (10); In equations (9) and (10), For the slope safety factor, For the first The remaining sliding force of the soil strip, i.e. the pushing force on the next strip; For the first The effective cohesion of the bottom sliding surface of the soil strip, For the first The effective internal friction angle of the bottom sliding surface of the soil strip, For the first Length of the soil strip slip surface For the first The weight of the soil strip, For the first The internal friction angle of the bottom sliding surface of the soil strip. and For the first The pore air pressure and pore water pressure of the soil strip This represents the rate at which shear strength increases with matrix suction. No. Transmission coefficient of earth strip thrust.

[0043] Step S150: Based on the probability density evolution theory, establish and solve the generalized probability density evolution equation to obtain the probability density function of the slope safety factor and its time-varying evolution process.

[0044] Based on probability density evolution theory (PDEM), the finite difference method based on TVD scheme is used to solve for random variables (cohesion c, internal friction angle). Permeability coefficient (Physical model of random ground motion) and slope safety factor The generalized probability density evolution equation between them is obtained. The probability density function and its time-varying evolution.

[0045] In some embodiments of this application, based on the probability density evolution theory, a generalized probability density evolution equation for the slope safety factor as a function of time or working conditions is established, expressed as equation (11): Equation (11); In equation (11), the slope safety factor Its evolution is influenced by random variables, denoted as ; vector Their joint probability density is .

[0046] Specifically, the input random variables include: cohesion. internal friction angle Permeability coefficient Freeze-thaw cycle location , denoted as a vector Their joint probability density is .

[0047] The state variables include: slope safety factor Its evolution (which varies with time or operating conditions) is influenced by random variables, denoted as... .

[0048] According to PDEM, the joint probability density Satisfying the generalized probability density evolution equation (GDEE), we obtain the generalized probability density evolution equation for the slope safety factor as a function of time or working conditions, as expressed in equation (11).

[0049] Then, the generalized probability density evolution equation is numerically solved using the finite difference method based on the TVD scheme to obtain the probability density function of the slope safety factor and its time-varying evolution process.

[0050] Step S160: Solve for the failure probability and reliability index of the tailings dam at different times to achieve an overall time-varying reliability assessment of the tailings dam.

[0051] Obtaining the slope safety factor Based on the probability density function and its time-varying evolution, through the analysis of... The probability of <1 is used for integral calculation to achieve the overall time-varying reliability index of the tailings dam. and failure probability Quantitative assessment.

[0052] Specifically, in some embodiments of this application, the process of solving for the failure probability and reliability index includes: defining and solving... , yes The failure probability at time t is obtained and the constraint condition expressed by equation (12) is satisfied: Equation (12).

[0053] That is, failure probability This refers to the probability that the safety factor is less than 1.

[0054] Define and solve the reliability index Reliability index It is an important parameter used in structural engineering and geotechnical engineering to measure the safety of a system, and is defined as a standard normal distribution.

[0055] For a standard normal distribution, it is expressed as equation (13): Equation (13); in, It is the cumulative distribution function of the standard normal distribution, expressed as equation (14): Equation (14); It is the inverse function of the standard normal distribution.

[0056] That is, time-varying reliability index This refers to the inverse function of the standard normal distribution in (1- The value at ().

[0057] Depend on Figure 1 It can be seen that the time-varying reliability analysis method for tailings dams that takes into account freeze-thaw degradation and seismic randomness provided in this application has significant advantages and effectively improves the accuracy and efficiency of tailings dam reliability assessment.

[0058] First, it achieves innovative breakthroughs in modeling. It couples the uncertainty of tailings parameters under freeze-thaw conditions, the random parameters of the physical model of random ground motion in engineering, and the unsaturated seepage of rainfall infiltration into the model. This changes the limitations of traditional methods that only consider static parameters or single disaster factors, and can more comprehensively and realistically reflect the actual situation of tailings dams in complex environments.

[0059] Secondly, it performs excellently in sample generation. It uses a probability space partitioning method based on GF bias to generate random samples, which not only solves the problem of low computational efficiency of traditional Monte Carlo methods in high-dimensional spaces, but also controls the sample coverage of low-probability regions more accurately than traditional Latin hypercube sampling methods, and optimizes the assignment probability of sample points, making the samples more representative and accurate.

[0060] Furthermore, earthquake motion simulation is more scientific. Using a physical model of engineering random earthquake motion instead of traditional earthquake time history superposition preserves the non-stationary frequency domain characteristics of earthquake motion, and can better simulate the impact of earthquakes on tailings dams.

[0061] Finally, it is highly efficient and convenient in probability density calculation. Based on the theory of probability density evolution, the time-varying probability density function of the slope safety factor can be directly obtained by solving the generalized probability density evolution equation, without relying on large-scale sampling of Monte Carlo simulation, which greatly improves the computational efficiency.

[0062] In summary, this method has been optimized and innovated in several key aspects, and can effectively realize the overall time-varying reliability assessment of tailings dams, providing strong support for the safety management of tailings dams.

[0063] Figure 2 A schematic diagram of a time-varying reliability analysis device for tailings dams considering freeze-thaw degradation and seismic randomness according to an embodiment of this application is shown. Figure 2 It can be seen that the time-varying reliability analysis device 200 for tailings dams, which considers freeze-thaw degradation and seismic randomness, includes: The first acquisition unit 210 is used to acquire the shear strength parameters and permeability coefficient statistical characteristics of tailings materials under freeze-thaw conditions; The second acquisition unit 220 is used to construct a physical random ground motion model and acquire multiple random ground motion parameters; The sample generation unit 230 is used to generate random samples and corresponding assigned probabilities by taking the shear strength parameter, the statistical characteristics of the permeability coefficient and the random ground motion parameter as random variables and using a probability space partitioning method based on grouping-fractional deviation. The first model constructs a solution element 240, which is used to establish a finite element model of the tailings dam, and calculates the slope safety factor corresponding to each sample based on unsaturated seepage analysis and slope stability analysis. The second model constructs a solution unit 250, which is used to establish and solve the generalized probability density evolution equation based on the probability density evolution theory, and obtain the probability density function of the slope safety factor and its time-varying evolution process. The result output unit 260 is used to solve the failure probability and reliability index of the tailings dam at different times, so as to realize the overall time-varying reliability assessment of the tailings dam.

[0064] Since the aforementioned time-varying reliability analysis device for tailings dams that considers freeze-thaw degradation and seismic randomness can implement the aforementioned time-varying reliability analysis method for tailings dams that consider freeze-thaw degradation and seismic randomness, it will not be elaborated further.

[0065] In one embodiment, a computer device is provided. The computer device includes a processor, memory, a network interface, and a database connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile and / or volatile storage media and internal memory. The non-volatile storage media stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface is used to communicate with external clients via a network connection. When the computer program is executed by the processor, it implements the functions or steps of a time-varying reliability analysis method for tailings dams that considers freeze-thaw degradation and seismic randomness.

[0066] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the time-varying reliability analysis method for tailings dams that takes into account freeze-thaw degradation and seismic randomness of this application.

[0067] It should be noted that the functions or steps that can be implemented by the computer-readable storage medium or computer device described above can be referred to the relevant descriptions in the foregoing method embodiments. To avoid repetition, they will not be described one by one here.

[0068] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0069] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is used as an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above.

[0070] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A time-varying reliability analysis method for tailings dams considering freeze-thaw degradation and seismic randomness, characterized in that, The method includes: Statistical characteristics of shear strength parameters and permeability coefficient of tailings materials under freeze-thaw conditions were obtained; Construct a physical random ground motion model and obtain multiple random ground motion parameters; Based on the shear strength parameter, the statistical characteristics of the permeability coefficient, and the random ground motion parameter, random samples and their corresponding assigned probabilities are generated using a probability space partitioning method based on grouping-fractional deviation. A finite element model of the tailings dam was established, and the slope safety factor for each sample group was calculated based on unsaturated seepage analysis and slope stability analysis. Based on the probability density evolution theory, the generalized probability density evolution equation is established and solved to obtain the probability density function of the slope safety factor and its time-varying evolution process. Solve for the failure probability and reliability index of tailings dam at different times to achieve overall time-varying reliability assessment of tailings dam.

2. The method according to claim 1, characterized in that, The acquisition of shear strength parameters and permeability coefficient statistical characteristics of tailings materials under freeze-thaw conditions includes: Through indoor freeze-thaw cycle tests, triaxial shear tests, and permeability coefficient tests, the shear strength parameters and permeability coefficient statistical characteristics of tailings materials under multiple freeze-thaw cycles were obtained. The shear strength includes cohesion c and internal friction angle φ. The permeability coefficient statistical characteristics include mean, standard deviation, value range, and probability distribution model.

3. The method according to claim 1, characterized in that, The physical random ground motion model is expressed as equation (1): Equation (1); In equation (1), For seismic acceleration, and epicenter distance The time history amplitude and phase spectra of ground motion acceleration at the location; and These are the random parameter vectors of the amplitude spectrum and the deterministic parameter vectors of the phase spectrum, respectively. The amplitude spectrum and phase spectrum of the physical random ground motion model are respectively expressed as Equation (2) and Equation (3): Equation (2); Equation (3); In equations (2) and (3), The parameter representing the dielectric attenuation effect is empirically taken to be 10. -5 s / km, amplitude spectrum random parameter vector , It reflects the intensity of the earthquake source. The Brune focal coefficient, and These are the equivalent damping ratio and equivalent dominant circular frequency of the local site, respectively. , , , For random parameters, epicentral distance It is a random variable.

4. The method according to claim 1, characterized in that, The establishment of a finite element model of the tailings dam, and the calculation of the slope safety factor for each sample group based on unsaturated seepage analysis and slope stability analysis, include: Using the Geostudio SEEP / W module, based on the water-air two-phase flow control equation and the van Genuchten-Mualem constitutive relation model, we conducted an analysis of unsaturated seepage under rainfall infiltration conditions. Input the random sample and the corresponding assigned probability to simulate the seepage field changes of the tailings dam under different freeze-thaw deterioration and seismic action; Based on the obtained seepage field change information, slope stability analysis is performed using the rigid body limit equilibrium method, and the safety factor of the tailings dam slope corresponding to each group of random samples is calculated.

5. The method according to claim 4, characterized in that, The analysis of unsaturated seepage under rainfall infiltration conditions, using the Geostudio SEEP / W module and based on the water-air two-phase flow governing equations and constitutive models, includes: The governing equations for the water-air two-phase flow are constructed, wherein the governing equation for the water phase is expressed as equation (4): Equation (4); The relative control equation for the gas phase is expressed as equation (5): Equation (5); In equations (4) and (5), Saturation; , Pore ​​water pressure, Pore ​​gas pressure, ; The intrinsic permeability coefficient, ; The relative permeability coefficient of the aqueous phase. The relative permeability coefficient of the gas phase; It is the acceleration due to gravity. The density of the aqueous phase, The density is in the gas phase, kg / m³ 3 ; The viscosity coefficient of the liquid phase. This is the gas phase viscosity coefficient; For liquid phase intrinsic terms, For gas-phase endogenous terms, kg s); A constitutive model is introduced to solve the governing equations for the water-air two-phase flow, including: soil-water characteristic curves, water phase relative permeability coefficient curves, and air phase relative permeability curves; wherein, the soil-water characteristic curves adopt the van Genuchten model and are expressed as equation (6): Equation (6); In equation (6), The matrix suction is calculated to be ( ), This is the intake air value. Residual saturation, These are parameters related to the model's materials; The relative permeability coefficient curve relationship of the aqueous phase is expressed by the van Genuchten-Mualem model, as shown in equation (7): Equation (7); In equation (7), The relative permeability coefficient of the aqueous phase; The relative permeability curve relationship of the gas phase is adopted using the Brooks-Corey model and is expressed as Equation (8): Equation (8); In equation (8), The matrix suction is calculated to be ( ), This is the intake air value. Residual saturation, These are parameters related to the model's materials.

6. The method according to claim 5, characterized in that, Slope stability analysis is performed using the rigid body limit equilibrium models shown in equations (9) and (10): Equation (9); Equation (10); In equations (9) and (10), For the slope safety factor, For the first The remaining sliding force of the soil strip, i.e. the pushing force on the next strip; For the first The effective cohesion of the bottom sliding surface of the soil strip, For the first The effective internal friction angle of the bottom sliding surface of the soil strip, For the first Length of the soil strip slip surface For the first The weight of the soil strip, For the first The internal friction angle of the bottom sliding surface of the soil strip. and For the first The pore air pressure and pore water pressure of the soil strip This represents the rate at which shear strength increases with matrix suction. No. Transmission coefficient of earth strip thrust.

7. The method according to claim 1, characterized in that, The process of establishing and solving the generalized probability density evolution equation based on probability density evolution theory to obtain the probability density function of the slope safety factor and its time-varying evolution process includes: Based on the probability density evolution theory, a generalized probability density evolution equation for the slope safety factor as a function of time or working conditions is established, expressed as equation (11): Equation (11); In equation (11), the slope safety factor Its evolution is influenced by random variables, denoted as ; vector Their joint probability density is ; The generalized probability density evolution equation is numerically solved using the finite difference method based on the TVD scheme to obtain the probability density function of the slope safety factor and its time-varying evolution process.

8. The method according to claim 1, characterized in that, The method of solving for the failure probability and reliability index of the tailings dam at different times to achieve the overall time-varying reliability assessment of the tailings dam includes: Define and solve , yes The failure probability at time t is obtained and the constraint condition expressed by equation (12) is satisfied: Equation (12); Define and solve the reliability index , For a standard normal distribution, it is expressed as equation (13): Equation (13); in, It is the cumulative distribution function of the standard normal distribution, expressed as equation (14): Equation (14); It is the inverse function of the standard normal distribution.

9. A time-varying reliability analysis device for tailings dams considering freeze-thaw degradation and seismic randomness, characterized in that, The device includes: The first acquisition unit is used to acquire the shear strength parameters and permeability coefficient statistical characteristics of tailings materials under freeze-thaw conditions; The second acquisition unit is used to construct a physical random ground motion model and acquire multiple random ground motion parameters; The sample generation unit is used to take the shear strength parameter, the statistical characteristics of the permeability coefficient and the random ground motion parameter as random variables, and generate random samples and corresponding assigned probabilities using a probability space partitioning method based on grouping-fractional deviation. The first model constructs a solution unit to establish a finite element model of the tailings dam, and calculates the slope safety factor corresponding to each sample based on unsaturated seepage analysis and slope stability analysis. The second model constructs a solution unit, which is used to establish and solve the generalized probability density evolution equation based on the probability density evolution theory, and obtain the probability density function of the slope safety factor and its time-varying evolution process. The result output unit is used to solve the failure probability and reliability index of the tailings dam at different times, so as to realize the overall time-varying reliability assessment of the tailings dam.

10. A computer-readable storage medium storing a computer program, characterized in that, When a computer program is executed by a processor, it implements the steps of the method described in any one of claims 1-8.

Images