A safety assessment method for danger removal and reinforcement of concrete gravity dams

Abstract

The present invention discloses a safety assessment method for danger removal and reinforcement of concrete gravity dams, which includes constructing a calculation model for non-probabilistic reliability index of gravity dams based on interval variables and considering the influence of reinforcement measures and material aging on the service behavior of concrete gravity dams. First, the interval parameter boundaries of the gravity dam are obtained by using the original data of dam deformation, the results of physical models and calculation models. Secondly, the non-probabilistic reliability theory of time-varying is integrated to calculate the non-probabilistic reliability indexes of elements and systems, and a calculation method for non-probabilistic reliability indexes based on the response surface method is developed. Finally, the prediction of the service behavior of danger removal and reinforcement measures and material aging with the increase of the service life of concrete dams is analyzed from the failure modes of elements and systems. Applying this method overcomes factors such as the highly non-linear function of the traditional reliability analysis method, the strict randomness of uncertain parameters, and the sensitivity of calculation results to parameters.

Description

Technical Field

[0001] The present invention relates to the field of service reliability analysis of dams, and particularly to a method for evaluating the safety of a concrete gravity dam for danger removal and reinforcement. Background Art

[0002] Under the coupled action of multiple factors such as water level and temperature during the service period of a gravity dam, the problems of aging and damage are becoming increasingly prominent, seriously threatening the long-term healthy service of the gravity dam. Although various reinforcement measures can be implemented to repair the gravity dam, these reinforcement measures will inevitably affect the material properties and structural behavior of the gravity dam, resulting in changes in the service performance of the gravity dam. Evaluating the changes in the structural behavior and service performance of a concrete gravity dam for danger removal and reinforcement under the action of aging and reinforcement repair is of great significance for ensuring the safety of the dam.

[0003] The traditional research on the service safety of gravity dams is mainly based on the probability reliability theory. The probability reliability analysis method fully considers the uncertain factors of the gravity dam to comprehensively reflect the safety status of the structure under working conditions. However, this method requires a large amount of statistical data to determine the probability distribution function (PDF) of the uncertain parameters. Due to limited test and monitoring conditions, the statistical data of the uncertain parameters of most dams are extremely scarce, and a complete PDF cannot be determined. Moreover, many uncertain parameters are not strictly random (for example, the upstream water level of the dam). In addition, the calculation results of the probability reliability method are extremely sensitive to the uncertain parameters. The uncertain factors limit the application of the probability reliability analysis method in the field of dam engineering to a certain extent. In recent years, a non-probability theory based on the convex model has been developed in the structural field. Without knowing the probability distribution density of the uncertain parameters, only the upper and lower bounds of the set of uncertain parameters need to be known, and the safety degree of the structure is measured by a non-probability index, which has unique advantages and engineering adaptability in dealing with the reliability problems of structures with little information on uncertain parameters. Therefore, it is necessary to study the evolution law of the reinforcement efficiency of gravity dams under various reinforcement measures, and further study the influence of the time-varying evolution of dam reinforcement measures and materials on the service performance of gravity dams, so as to comprehensively evaluate and predict the evolution law of the service performance of the dam structure.

[0004] The advantage of the present invention is that, based on the analysis of the reinforcement efficiency and material aging effect of the gravity dam, a time-varying non-probability reliability index calculation model for the gravity dam element and system is established by combining time-varying non-probability reliability analysis and interval mathematics. The response surface method is used to efficiently calculate the non-probability reliability indices of the gravity dam element and system before and after reinforcement. Finally, the time-varying process and development trend of NR-η before and after the reinforcement of an existing reinforced gravity dam project are calculated and analyzed, and the evaluation and prediction of the reinforcement measures on improving the service reliability of the dam are carried out. Summary of the Invention

[0005] In order to overcome the deficiencies of existing methods and address the problem that the reliability of the structure changes with service due to the uncertainty of dam parameters caused by the coupling of multiple factors such as water level and temperature in the reinforcement efficiency of the concrete gravity dam for risk elimination and reinforcement, the present invention proposes a safety assessment method for the concrete gravity dam for risk elimination and reinforcement, which combines the RSM surrogate model to improve the calculation efficiency of the non-probabilistic reliability index of the gravity dam unit and system, providing a new method for the assessment and prediction of the service reliability of the gravity dam.

[0006] The present invention provides a safety assessment method for the concrete gravity dam for risk elimination and reinforcement, and its technical method includes the following steps:

[0007] Step 1: Adopt the method of collecting a large amount of monitoring data, and based on the interval hybrid monitoring model, invert the interval parameter boundaries of the gravity dam.

[0008] Under the coupling action of multiple factors such as water level and temperature, the structural parameters and material parameters of the gravity dam change greatly due to cumulative damage during the long-term service of the dam. Timely inversion of the main physical parameters of the dam body and foundation is conducive to accurately analyzing the true service state of the dam.

[0009] Fully utilize the monitoring data during the operation of the gravity dam, establish finite element models before and after reinforcement, and invert the uncertain parameter boundaries with the help of the interval hybrid monitoring model. Assume that all uncertain parameters are interval variables, where the upper and lower limits are x u and x l .

[0010] Step 2: Construct a non-probabilistic reliability index calculation model based on interval variables.

[0011] The performance function can be expressed as according to the failure criterion:

[0012] M = g(x) = g(x1, x2,..., x n ) (12)

[0013] Where g(x) is a continuous function of x i , and M is an interval variable. Furthermore, the non-probabilistic reliability index of the structure can be expressed as

[0014] η = M c / M r (13)

[0015] Where M c and M r are the mean value and deviation of M respectively.

[0016] When the performance function is a linear function of multiple interval variables, it is expressed as:

[0017]

[0018] where n is the number of structural resistance parameters, m is the number of structural load parameters, and A i and B j are constants. And and are independent interval variables, where and are the interval variables of the structural resistance and load parameters respectively.

[0019] The non - probabilistic reliability index of the structure can be expressed as:

[0020]

[0021] Step 3: Calculate the time - varying non - probabilistic reliability index of the gravity dam element by using the response surface method. The specific process is as follows:

[0022] Step 301: For the complex structure of the gravity dam, it is usually difficult to be expressed by an explicit expression. Use the response surface method surrogate model to represent the approximate limit state equation of the structure with a quadratic polynomial without cross - terms, that is:

[0023]

[0024] where x = [x1, x2,..., x n is the vector of parameter variables, and n is the number of parameter variables. The coefficients a, b = [b1, b2,..., b n T and c = [c1, c2,..., c n T constitute the solution of the above equation, and this equation should be determined by 2n + 1 sets of sampling point data. Use the RSM method to calculate the non - probabilistic reliability index of the gravity dam element.

[0025] Step 302: Combine the original detection data, physical model and mathematical model for analysis, and obtain the response surface function M = g(x) through regression fitting. According to the fitted response surface function M = g(x), use the mathematical programming method to obtain the maximum and minimum values of the fitted response surface function, regarded as the extreme value solution of the quadratic programming constraint problem, and calculate the minimum value M min and the maximum value M max , and the mathematical model is as follows:

[0026]

[0027] Step 4: Conduct non - probabilistic reliability analysis on the gravity dam element and system before and after the implementation of reinforcement measures, and finally search for failure modes. The specific process is as follows:

[0028] ​​Step 401. The main failure modes of the gravity dam are insufficient strength and sliding instability. Considering the strength failure of the gravity dam elements, the strength failure response function of the gravity dam elements in three-dimensional state is as follows:

[0029]

[0030] where g(x) is the function of the strength failure of the gravity dam elements; f t and f c are the tensile strength and compressive strength of the gravity dam respectively; σ1, σ2 and σ3 are the first, second and third principal stresses of the gravity dam elements (tension is positive and pressure is negative).

[0031] Step 402. Consider the sliding instability of the gravity dam along the surface of the dam foundation. According to the stresses of all elements on the dam body and the dam foundation on the sliding surface, the response function of the sliding instability along the dam foundation surface can be expressed as

[0032]

[0033] where g′(x) is the function of the sliding instability of the gravity dam along the dam foundation surface; m is the total number of elements on the dam foundation surface; f and c are the friction coefficient and cohesion of the dam foundation surface respectively; σ yi and τ xyi are the normal stress and shear stress of element i respectively; s i is the area of element i along the surface of the dam foundation.

[0034] Step 403. Search for the main failure modes of the gravity dam. To determine the failure modes, first calculate the gravity dam element η, select several possible first-failure elements as the initial failure elements in the dense area with lower η values of the gravity dam elements, and kill them and then search for the next adjacent failure element. Select element e1 as the initial failure element. In the finite element analysis, assume that element e1 is the first failure element (remove this element), then conduct non-probabilistic reliability calculation and analysis, and search for n possible failure elements near element e1. Then, combine the failure element e1 and the n possible failure elements in sequence to form n possible temporary failure paths respectively, and calculate the non-probabilistic reliability index of each group of possible temporary failure paths. Select the failure element of the temporary failure path with the minimum non-probabilistic reliability index as the next failure element e 2i . Finally, remove the failure element e 2i , and repeat the search process until the termination condition is met. The most dangerous failure path is determined by the failure elements (e1, e 2i ,..., e mk ).

[0035] Step 5. Prediction of the non-probabilistic reliability index of the gravity dam after the reinforcement measures with the service life. The specific process is as follows:

[0036] Step 501. Considering that during the service period of a gravity dam, due to the interaction of uncertain environmental factors, as well as the initial damage and defects of the dam body structure, it is inevitable that the material parameters and structural performance of the dam body will evolve over time. The boundary range of the uncertain parameters of the gravity dam changes dynamically as the dam is put into service. Therefore, the time-varying non-probabilistic reliability index of the gravity dam changes dynamically over time. At the same time, the comprehensive application of engineering and non-engineering reinforcement measures during the service period of the gravity dam plays an important role in maintaining and improving the service performance of the dam and extending the healthy service time of the dam.

[0037] Assume that the load and resistance of the gravity dam are interval variables that vary with time, and the performance function is expressed as follows:

[0038] M I (t) = R I (t) - S I (t) (20)

[0039] Where S I (t) and R I (t) are interval variables of the load and resistance that vary with time respectively; M I (t) is the interval variable of the performance function that varies with time. Assume that R u (0) and R l (0) are used to represent the upper and lower limits of the initial resistance R I (0) respectively. Similarly, S u (0) and S l (0) are used to represent the upper and lower limits of the initial electrical resistance S I (0) respectively. The time-varying evolution process of the mean values of the resistance and load of the gravity dam can be described as

[0040]

[0041] Where and are the mean values of the resistance and load of the gravity dam at time t respectively; and are the mean values of the resistance and load of the gravity dam at the initial time respectively; and are deterministic time functions. Combining equation (4), the time-varying NR-η of the gravity dam system can be expressed as

[0042]

[0043] Where

[0044] Step 502: To explore the effects of dam material aging and danger removal and reinforcement on the service performance and lifespan of gravity dams, the evolution of the post-reinforcement safety performance is analyzed according to the non-probabilistic time-varying theory, and the Weibull function is used to describe the time-varying process of material parameters. The attenuation functions of each parameter of the dam are determined as follows: the unit weight ρ of the dam body concrete c and the attenuation functions of the uplift pressure coefficient α are respectively taken as and The mechanical parameters E of the dam body concrete and rock mass C , f t , f c and E r , f t ′, f c ′, and the friction coefficient f and cohesion c of the dam foundation surface are all taken as The changes of other parameters with time can be ignored. Furthermore, the non-probabilistic reliability indices of the elements and systems after 10 years, 20 years, and 30 years of service after reinforcement are calculated, and the time-varying non-probabilistic indices of the gravity dam after implementing the reinforcement measures are predicted.

[0045] The beneficial effects of the present invention are as follows:

[0046] The present invention discloses a method for evaluating the safety of a danger-removing and reinforced concrete gravity dam, specifically a method for constructing a reliability analysis model of a danger-removing and reinforced concrete gravity dam before and after reinforcement from the aspects of dam element and system failure modes by combining interval analysis and non-probabilistic reliability theory; the method of the present invention utilizes the original data of dam deformation, samples the relevant parameters of the gravity dam through Latin hypercube sampling, combines interval mathematics theory, obtains the interval boundaries of the gravity dam parameters, and then integrates the time-varying non-probabilistic reliability theory, develops the NR calculation method based on the response surface method to ensure the calculation efficiency, analyzes the influence of the danger-removing and reinforcement measures on the service state of the concrete dam from the failure modes of the elements and systems, and obtains a method for analyzing the evolution law of the comprehensive effectiveness of the danger-removing and reinforcement measures and systematic evaluation, overcoming the factors such as the highly nonlinear function of the traditional reliability analysis method, the strict randomness of uncertain parameters, and the sensitivity of calculation results to parameters. At the same time, it provides a new method for the service reliability evaluation and prediction of gravity dams. Description of the Drawings

[0047] Figure 1 It is a flowchart of a method for analyzing the time-varying non-probabilistic reliability of a gravity dam according to the present invention;

[0048] Figure 2 Schematic diagram of failure mode search

[0049] Figure 3 Environmental detection curve

[0050] Figure 4 Finite element models of the gravity dam before and after reinforcement;

[0051] Figure 5 Contour map of the non - probabilistic reliability index of the gravity dam unit before reinforcement;

[0052] Figure 6 Contour map of the non - probabilistic reliability index of the gravity dam unit after reinforcement;

[0053] Figure 7 Statistical chart of the non - probabilistic reliability index of the dam body unit;

[0054] Figure 8 Each failure mode of the 35# dam section before reinforcement;

[0055] Figure 9 Each failure mode of the 35# dam section after reinforcement;

[0056] Figure 10 Non - probabilistic reliability index of the unit 10 years after reinforcement;

[0057] Figure 11 Non - probabilistic reliability index of the unit 20 years after reinforcement;

[0058] Figure 12 Non - probabilistic reliability index of the unit 30 years after reinforcement;

[0059] Figure 13 The most dangerous failure modes 10, 20 and 30 years after reinforcement. Specific implementation manner

[0060] The method for evaluating the safety of the concrete for danger removal and reinforcement of the present invention will be further described in detail with reference to the accompanying drawings.

[0061] Figure 1 This is the flow chart of a method for evaluating the safety of the concrete for danger removal and reinforcement of the present invention. In this embodiment, a 35# dam section of a certain concrete gravity dam is taken as the research object. The elevation of the dam crest of this dam section is 267.70m, the elevation of the dam foundation is 188.60m, the dam height is 79.1m, the total length of the dam section is 18.0m, the normal storage level of the upstream is 263.50m, and the downstream water level is 193.50m. A laser horizontal displacement D35 is arranged at the dam crest, and a laser horizontal displacement measuring point BJ35D is arranged at the dam foundation. In order to more accurately simulate the structural behavior of this dam section, according to the specific situation of this dam section, 1.5 times the dam height is taken upward and downstream from the heel and toe of the dam, and the depth of the dam foundation is taken as 120.0m, and a finite element model is established as Figure 2 shown. Two sets of finite element models of the 35# dam section before and after reinforcement are established. The model before reinforcement consists of 14,880 elements and 18,960 nodes, including 5,795 elements and 2,502 nodes of the dam body and 9,085 elements and 7,440 nodes of the dam foundation. The overlaid concrete of the model after reinforcement is composed of 1,380 elements and 2,502 nodes, and the prestressed anchor cable is meshed into 98 elements and 103 nodes.

[0062] Using the monitoring data of the measuring points during the period from 2000 to 2010, an interval hybrid monitoring model was established to invert the interval boundaries of parameters (taking the elastic modulus of the dam body and the dam foundation as an example). The upstream water level process line and the air temperature process line during this monitoring period are as Figure 3 shown. The physical and mechanical parameters of the gravity dam were inverted by using the interval inversion method, and the interval boundary values [x u , x l of the uncertain parameters were obtained. Combining the dam inspection data, test results and design data, all the parameters before and after the reinforcement of the 35th dam section are shown in Table 1.

[0063] Table 1 Statistical results of interval parameters before and after reinforcement

[0064]

[0065] Table 2 Statistical results of deterministic parameters

[0066]

[0067] According to the interval boundaries of the main parameters of the dam body and the dam foundation determined in Table 1 and Table 2, the Latin hypercube sampling method was used to select 2n + 1 interval parameter sample points (n = 10, where n is the number of interval parameters) for the 35th dam section before reinforcement. Considering the actions of three loads, namely the self-weight of the gravity dam, water load and seepage pressure, 21 groups of simulation analyses were carried out on the gravity dam elements of the model before reinforcement to obtain the stress response values of the gravity dam elements. To ensure the accuracy of the calculated response values, in the finite element analysis, before the dam body model and the load steps were applied, a geostress equilibrium step was carried out on the rock foundation, and then the non-probabilistic reliability index operation of the gravity dam elements was performed. Finally, the non-probabilistic reliability index distribution nephogram of the elements before reinforcement was obtained as Figure 5 , and the non-probabilistic reliability index distribution nephogram of the elements after reinforcement was obtained as Figure 6 .

[0068] According to Figure 5 and Figure 6 , it can be found that the distribution laws of the time-varying non-probabilistic reliability indexes of the elements before and after the reinforcement of the 35# dam section are similar. Failure elements with η < 1 appear near the heel and toe of the dam, and the η value at the contact surface between the dam body and the dam foundation is relatively low. After the reinforcement measures are implemented for the entire dam section, compared with before reinforcement, the number of failure elements is reduced to a certain extent, and the non-probabilistic reliability index η of the dam body and dam foundation elements is significantly improved. According to the definition of the non-probabilistic reliability index, the reinforcement measures can improve the safety of the dam elements. The specific quantities in different non-probabilistic reliability index η ranges before and after reinforcement are as Figure 7As shown, it can be obtained that the number of failed elements (η < 1) after implementing reinforcement measures decreased from 85 before reinforcement to 15, and the proportion of the number of elements with non-probabilistic reliability indices between 1 and 3 decreased from 2545 (43.9%) before reinforcement to 165 (2.8%) after reinforcement, and their distribution positions were mainly reduced near the heel and toe of the dam.

[0069] The gravity dam is a three-dimensional hyperstatic structure with an extremely complex failure mechanism and numerous failure paths. To describe the system safety of the gravity dam under multiple failure modes from the perspective of non-probabilistic theory, after analyzing the non-probabilistic reliability indices of the elements before and after the reinforcement of the gravity dam, the main failure modes need to be searched through the nonlinear finite element analysis of the gravity dam system and the identification of the system failure paths, so as to deeply analyze the effectiveness of the reinforcement in solving the problems and diseases of the gravity dam. For this purpose, the possible initial failed elements are selected and it is assumed that this element fails, and then the next failed element is searched for among the surrounding elements. As Figure 4 shown, when the failure mode constitutes the failure of the gravity dam system, then this failure mode is considered the main failure mode. Under the action of multiple external factors, the failure parts of the dam are mainly located in the dense areas with low non-probabilistic reliability indices of the elements. First of all, the failure positions are random, so there are multiple failure paths in the whole system. Considering the more prominent potential safety hazards near the heel and toe of the dam and the specific distribution of the non-probabilistic reliability indices, 4 and 2 elements with small non-probabilistic reliability indices and high sensitivity of calculation parameters are respectively selected from near the heel and toe of the dam as the initial failed elements, and the search for the failure mode is executed. The non-probabilistic reliability index of the gravity dam system is calculated according to the searched failure mode. Figure 8 and 9 respectively show the search results of 6 possible failure modes before and after reinforcement.

[0070] To study the comprehensive effects of the aging of the dam body materials and the reinforcement measures for hazard removal on the service safety and life of the gravity dam, according to the non-probabilistic time-varying theory, a time-varying analysis is carried out on the evolution law of the safety performance of the 35# dam section after reinforcement. The time-varying process of the material parameters is described by the Weibull function, and the attenuation functions of the relevant parameter intervals of the dam are as follows: the unit weight ρ of the dam concrete c and the attenuation function of the uplift pressure coefficient α are respectively taken as and The parameters f t , f c , f, c and f t ′, f c ′, f′, c′ have attenuation functions of The variations of other parameters with time are ignored. According to the decay functions of the geometric parameters of the gravity dam obtained from the parameter information, the non-probabilistic reliability indexes of the elements of this dam section during 10 years, 20 years, and 30 years of service after reinforcement measures are implemented are solved based on the time-varying non-probabilistic reliability analysis model of the gravity dam. The contour maps of the non-probabilistic reliability indexes of the elements at each moment of this dam section are as Figures 10 to 12 shown. It can be seen from the contour maps that the values of the non-probabilistic reliability indexes of the elements show a downward trend with the service life of the gravity dam, and the possible failure elements near the heel and toe of the dam gradually increase with the service life. The change of the non-probabilistic reliability index of the system after the dam body is reinforced and strengthened is analyzed by searching for the failure modes of different service years. Figure 13 The most dangerous failure modes during 10 years, 20 years, and 30 years of service are given.

[0071] The above-described embodiments are only specific implementation manners of the present invention and not limitations thereof. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the specific implementation manners of the present invention can still be modified or equivalently replaced. Any modification or equivalent replacement without departing from the spirit and scope of the present invention still falls within the protection scope of the technical solution of the present invention.

Claims

1. A safety assessment method for danger removal and reinforcement of a concrete gravity dam, characterized in that, The method includes the following steps: Step 1: Collect a large amount of monitoring data during the operation of the gravity dam, and inversely obtain the interval parameter boundaries of the gravity dam based on the interval hybrid monitoring model; Step 2: Construct a non-probabilistic reliability index calculation model based on interval variables; Step 3: Construct a non-probabilistic reliability index calculation model for gravity dam elements based on the response surface method; Step 4: Calculate the non-probabilistic reliability index of the gravity dam system and search for failure modes; Step 5: Predictive analysis of the time-varying non-probabilistic reliability index after the reinforcement and strengthening of the gravity dam; Specifically in Step 1: Using the monitoring data during the operation of the gravity dam, establish finite element models before and after reinforcement, and invert the bounds of uncertain parameters with the aid of the interval hybrid monitoring model; assume that all uncertain parameters x i are all interval variables, where i = 1, 2,..., n, and the upper and lower bounds are x u and x l respectively; X is the vector of uncertain parameter variables; The specific steps for constructing the non-probabilistic reliability index calculation model based on interval variables in Step 2 are as follows: (1) When the performance function is a linear function of a single interval variable, construct the performance function according to the failure criterion and express it as: M = g(x) = g(x1, x2,..., x n ) (1) where \(g(x)\) is a continuous function of \(x\) i and \(M\) is an interval variable; thus, the non - probabilistic reliability index of the gravity dam structure is calculated as follows: η = M c / M r (2) where M c and M r are the average value and deviation of M, respectively; (2) When the performance function is a linear function of multiple interval variables, it is expressed as: where n is the number of the gravity dam structural resistance parameters, m is the number of the gravity dam structural load parameters, A i and B j are constants, and and are independent interval variables, where and are the interval variables of the structural resistance and load parameters respectively; thus, the non-probabilistic reliability index of the gravity dam structure is calculated as follows: where is the mean value of the structural resistance, is the deviation of the structural resistance, is the mean value of the structural load, is the deviation of the structural load; In Step 3, the specific process of constructing the non-probabilistic reliability index calculation model for gravity dam elements based on the response surface method is as follows: Step 301: Use the response surface method surrogate model to represent the approximate limit state equation of the complex structure of the gravity dam using a quadratic polynomial without cross terms, that is: where X = [x1, x2,..., x n is a vector of parameter variables, and n is the number of parameter variables; the coefficients a, b = [b1, b2,..., b n T and c = [c1, c2,..., c n T constitute the solution of the above equation, which should be determined by 2n + 1 sets of sampling point data, and the non-probabilistic reliability index of the gravity dam element is calculated using the RSM method;​​ Step 302: Analyze by combining the original detection data, physical model, and mathematical model, and obtain the response surface function M = g(x) through regression fitting; according to the fitted response surface function M = g(x), use the mathematical programming method to obtain the maximum and minimum values of the fitted response surface function, regarded as the extreme value solution of the quadratic programming constraint problem, and calculate the minimum value M of the fitted response surface function through the optimization algorithm min and the maximum value M max , and the mathematical model is as follows:

2. The safety assessment method for the danger-removing and reinforcement concrete gravity dam according to claim 1, wherein Step 4 first conducts non-probabilistic reliability analysis on the gravity dam elements and the system before and after the implementation of reinforcement measures, and finally searches for failure modes. The main failure modes of the gravity dam are insufficient strength and sliding instability. The specific process is as follows: Step 401: Considering the strength failure of gravity dam elements, the strength failure response function of gravity dam elements in three-dimensional state is: where \(g(x)\) is the function of the strength failure of the gravity dam element; \(f\) t and \(f\) c are the tensile strength and compressive strength of the gravity dam respectively; \(\sigma_1\), \(\sigma_2\) and \(\sigma_3\) are the first, second and third principal stresses of the gravity dam element respectively, where tension is positive and pressure is negative; Step 402: Considering the sliding instability of the gravity dam along the surface of the dam foundation, according to the stresses of all elements on the dam body and the dam foundation on the sliding surface, the response function of sliding instability along the dam foundation surface can be expressed as Wherein, g′(x) is the function of the gravity dam sliding and losing stability along the dam foundation surface; m is the total number of elements on the dam foundation surface; f and c are the friction coefficient and cohesion of the dam foundation surface respectively; σ yi and τ xyi are the normal stress and shear stress of element i respectively; s i is the area of element i along the dam foundation surface; Step 403: Search for the main failure modes of the gravity dam, specifically: To determine the failure mode, first calculate the gravity dam element η. Select several possible first-failure elements as initial failure elements in the dense area with a lower η value of the gravity dam element, and kill them to search for the next adjacent failure element; Select element e1 as the initial failure element. In finite element analysis, assume that element e1 is the first failure element and remove this element, then conduct non-probabilistic reliability calculation analysis, and search for n possible failure elements near element e1; Then, the failed unit e1 and the n possible failed units are combined in sequence to form n possible temporary failure paths respectively, and the non-probabilistic reliability index of each group of possible temporary failure paths is calculated. The failed unit of the temporary failure path with the minimum non-probabilistic reliability index is selected as the next failed unit e 2i ; Finally, eliminate the failed element e 2i , and repeat the search process until the termination condition is met. The most dangerous failure path is then determined by the failed elements (e1, e 2i , …, e mk ).

3. A method for evaluating the safety of a risk-removing and reinforcement concrete gravity dam according to claim 1, characterized in that, Step 5 predicts the non-probabilistic reliability index of the gravity dam with the service life after the anti-risk reinforcement concrete measures. The specific process is as follows: Step 501: The boundary range of the uncertain parameters of the gravity dam changes dynamically with the commissioning of the dam. Therefore, the time-varying non-probabilistic reliability index of the gravity dam changes dynamically with time; Assume that the load and resistance of the gravity dam are interval variables that change with time, and the performance function is expressed as follows: M I R(t) I - S(t) I (9) where S I (t) and R I (t) are interval variables of the load and the resistance varying with time respectively; M I (t) is an interval variable of the performance function varying with time; assume that R u (0) and R l (0) are used to represent the upper limit and the lower limit of the initial resistance R I (0) respectively. Similarly, S u (0) and S l (0) are used to represent the upper limit and the lower limit of the initial electrical resistance S I (0); The time-varying evolution process of the mean values of the resistance and load of the gravity dam is described as: where and are the average values of the resistance and load of the gravity dam at time t, and are respectively the average values of the resistance and load of the gravity dam at the initial stage; and are deterministic time functions; The time-varying of the gravity dam system in combination with the above equation (4) is expressed as: Step 502: Analyze the evolution of the safety performance after reinforcement according to the non-probabilistic time-varying theory. Use the Weibull function to describe the time-varying process of material parameters to deduce the influence of dam material aging and anti-risk reinforcement on the service performance and life of the gravity dam; Determine the attenuation functions of each parameter of the gravity dam, including: Unit weight ρ of dam concrete c The attenuation functions of the uplift pressure coefficient α are respectively taken as and The mechanical parameters E of the dam concrete and rock mass C , f t , f c , and E r , f t ′, f c ′s attenuation function, the friction coefficient f and cohesion c of the dam foundation surface are all taken as The variations of other parameters with time can be ignored; Furthermore, the non-probabilistic reliability indices of the elements and systems after 10 years, 20 years, and 30 years of service after reinforcement are calculated, and the time-varying non-probabilistic indices of the gravity dam after reinforcement are predicted.

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