Dam slope equivalent stress analysis method and system based on finite elements

Abstract

The application relates to the technical field of structural safety evaluation, in particular to a dam slope equivalent stress analysis method and system based on finite elements. The method comprises the following steps: presetting a water pressure level, carrying out grid division, and obtaining the equivalent stress of the grid; calculating the similarity of the equivalent stresses of adjacent water pressure levels; determining a first stability index based on the fitting degree of the corresponding relationship between the water pressure level and the equivalent stress and the fluctuation of the similarity; obtaining a quantile sequence of the equivalent stress, determining a relative relationship based on the equivalent stress difference of the same quantile, determining the equivalent stress distribution characteristics based on the adjacent relative relationship difference and the relative relationship offset; determining the overall flatness through the first stability index, and then determining the equivalent stress imbalance coefficient by combining the equivalent stress distribution characteristics; and performing stability analysis through the equivalent stress imbalance coefficient. The application improves the accuracy of dam slope equivalent stress analysis.

Description

Technical Field

[0001] This application relates to the field of structural safety assessment technology, specifically to a method and system for equivalent stress analysis of dam slopes based on the finite element method. Background Technology

[0002] Earth-rock dams, including both upstream and downstream slopes, are one of the most important dam types in water conservancy projects. Their safety directly affects the lives and property of downstream residents and the normal operation of the water conservancy project. Therefore, stability analysis of the dam slope based on equivalent stress is not only a core issue in earth-rock dam design but also a crucial step in ensuring the long-term safe operation of the project.

[0003] Existing methods for equivalent stress analysis of dam slopes typically employ the finite element method (FEM), which involves applying loads, such as water pressure, to obtain the stress distribution within the dam body and then performing equivalent stress analysis based on equivalence criteria, such as the Drucker-Prag equivalent stress. However, in actual engineering projects, upstream and downstream stresses on the dam slope often exhibit asynchronous changes, especially under different load increments. The differences in stress response amplitudes between upstream and downstream sections mean that existing equivalent stress analysis methods fail to adequately consider the relative changes in stress between the upstream and downstream sections and neglect deviations between local stresses, thus affecting the assessment of the true stability state of the dam slope. Summary of the Invention

[0004] To address the technical problem of low accuracy in stress analysis, this application provides a finite element method and system for equivalent stress analysis of dam slopes. The specific technical solution adopted is as follows: Firstly, this application proposes a finite element method for equivalent stress analysis of dam slopes, which includes the following steps: Preset water pressure levels; divide the dam slope into upstream and downstream dam slope regions through finite element simulation, and divide the regions into grids to obtain the equivalent stress of the grid at each water pressure level; For each water pressure level, the equivalent stress of the upstream and downstream dam slope grids are respectively constructed into equivalent stress sequences; the similarity of the equivalent stress sequences of adjacent water pressure levels is calculated, and the instability characteristics of the dam slope area are determined based on the similarity fluctuation; the stability characteristics are determined based on the fitting degree of the curve of the correspondence between water pressure level and equivalent stress; and the first stability index is determined through the stability characteristics and instability characteristics. The equivalent stress sequences of the upstream and downstream dam slopes are processed by quantile processing to obtain their quantile sequences; the relative relationship is determined by the difference in equivalent stress at the same quantile between the upstream and downstream dam slopes, which is used to represent the degree of difference in equivalent stress distribution; the characteristics of equivalent stress distribution are determined by the difference in the relative relationship between adjacent water pressure levels and the offset of the relative relationship from the benchmark relative relationship. The harmonic mean of the first stability index of the upstream and downstream dam slopes is used as the overall stability. The equivalent stress imbalance coefficient is determined based on the overall stability of the dam slopes and the characteristics of equivalent stress distribution. Stability analysis is performed using the equivalent stress imbalance coefficient.

[0005] In the aforementioned scheme, this application, through the analysis of the equivalent stress sequence of upstream and downstream dam slopes, highlights the spatial order and variation characteristics of stress distribution during load increment, reflecting the continuous influence of water pressure on the stress of upstream and downstream dam slopes. Furthermore, through the analysis of the quantile sequence of equivalent stress, it highlights the magnitude of the shift in the relationship between upstream and downstream stress responses, reflecting the influence of water pressure increment on the coordination of equivalent stress in the upstream and downstream dam bodies, and characterizing the degree of change in the relative relationship between upstream and downstream stresses. In addition, combining the stability and distribution characteristics of the equivalent stress of upstream and downstream dam slopes, an equivalent stress imbalance coefficient index is constructed. This index reflects the overall balance of the dam body under progressively increasing water pressure, accurately reflecting the overall balance of the dam body under progressively increasing water pressure, as well as the coordination of upstream and downstream stress responses. This solves the problem in existing dam slope equivalent stress analysis methods that ignore the differences in stress variation between upstream and downstream under different load increments, which affects the evaluation results, and improves the accuracy of dam slope equivalent stress analysis.

[0006] In one embodiment, the method for constructing equivalent stress sequences from the upstream and downstream dam slope grids for each water pressure level is as follows: Under different water pressure levels, the equivalent stresses of all grids in the upstream and downstream grid sets are combined into corresponding equivalent stress sequences according to the order of each grid from left to right and from top to bottom.

[0007] In one embodiment, the method for calculating the similarity of equivalent stress sequences of adjacent water pressure levels and determining the instability characteristics of the dam slope region based on similarity fluctuations is as follows: For the dam slope, the similarity between two equivalent stress sequences of adjacent water pressure levels is calculated, and all similarities are combined into a similarity sequence. The first-order difference sequence of the similarity sequence is obtained, and the standard deviation of the elements in the first-order difference sequence is calculated as the instability feature of the dam slope region.

[0008] In one embodiment, the method for determining the stability characteristics based on the fitting degree of the curve relating water pressure level and equivalent stress is as follows: For each dam slope region, the mean value of all equivalent stresses of the dam slope under each water pressure level is calculated and used as the dependent variable, with the water pressure level as the independent variable, and linear fitting is performed using the least squares method; the determination coefficient of the fitted curve is used as the stability feature.

[0009] In one embodiment, the first stability index is positively correlated with stability features and negatively correlated with instability features.

[0010] In one embodiment, the method for determining the relative relationship through the equivalent stress difference at the same quantile of the upstream and downstream dam slopes is as follows: The relative difference of equivalent stress at the same quantile in the quantile sequence of the upstream and downstream dam slopes is denoted as the stress relative difference; the relative difference is the ratio of the absolute value of the difference of equivalent stress at the same quantile to the global maximum value of equivalent stress in the quantile sequence of the upstream and downstream dam slopes. The mean of the relative stress difference for each quantile sequence is calculated as the relative relationship at different water pressure levels.

[0011] In one embodiment, the equivalent stress distribution characteristics are positively correlated with the relative relationship difference and the relationship offset magnitude, respectively.

[0012] In one embodiment, the relative relationship difference is the difference in the relative relationship between adjacent water pressure levels; the relationship offset amplitude is the difference between the relative relationship at the water pressure level and the benchmark relative relationship; the benchmark relative relationship is the relative relationship when the water pressure level is at its minimum.

[0013] In one embodiment, the equivalent stress imbalance coefficient is positively correlated with the overall stability and negatively correlated with the equivalent stress distribution characteristics.

[0014] On the other hand, this application also provides a finite element-based dam slope equivalent stress analysis system, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the steps of any of the above-described finite element-based dam slope equivalent stress analysis methods.

[0015] The beneficial effects of this application are as follows: This application, through the analysis of the equivalent stress sequence of upstream and downstream dam slopes, highlights the spatial order and variation characteristics of stress distribution during load increment, reflecting the continuous influence of water pressure on the stress of upstream and downstream dam slopes. Furthermore, by analyzing the quantile sequence of equivalent stress, it highlights the magnitude of the shift in the relationship between upstream and downstream stress responses, reflecting the influence of water pressure increment on the coordination of equivalent stress in the upstream and downstream dam bodies, and characterizing the degree of change in the relative relationship of upstream and downstream stresses. In addition, combining the stability and distribution characteristics of equivalent stress in upstream and downstream dam slopes, an equivalent stress imbalance coefficient index is constructed. This index reflects the overall balance of the dam body under progressively increasing water pressure, accurately reflecting the overall balance of the dam body under progressively increasing water pressure, as well as the coordination of upstream and downstream stress responses. This solves the problem in existing dam slope equivalent stress analysis methods that ignore the differences in stress variation between upstream and downstream under different load increments, which affects the evaluation results, thus improving the accuracy of dam slope equivalent stress analysis. Attached Figure Description

[0016] To more clearly illustrate the technical solutions and advantages in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art 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 This is a flowchart of a dam slope equivalent stress analysis method based on finite element method provided in one embodiment of this application. Detailed Implementation

[0018] To further illustrate the technical means and effects adopted by this application to achieve the intended inventive purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of the finite element-based dam slope equivalent stress analysis method and system proposed in this application. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0019] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0020] A Finite Element-Based Method and System Implementation for Equivalent Stress Analysis of Dam Slopes: The following, in conjunction with the accompanying drawings, details the specific scheme of the finite element-based dam slope equivalent stress analysis method and system provided in this application.

[0021] Please see Figure 1 The diagram illustrates a flowchart of a dam slope equivalent stress analysis method based on the finite element method according to an embodiment of this application. The method includes the following steps: Step S001: Preset water pressure level and perform mesh generation to obtain the equivalent stress of the mesh.

[0022] To analyze the imbalance of equivalent stress between the upstream and downstream regions of a dam slope under different increments of water pressure, this application first obtains the two-dimensional geometric model of the dam slope from the CAD model and uses it as input to the MIDASGTS software. The Duncan-Chang EB model in the software is then used to perform a finite element simulation of the dam slope, obtaining stress data for all meshes of the dam slope. One embodiment of this application specifies the following: the dam body material is gravel, with a modulus coefficient set to 800, a modulus exponent set to 0.45, a failure ratio set to 0.78, an initial friction angle set to 44°, a friction angle increment set to 7.5°, a cohesion set to 0 kPa, a bulk modulus coefficient set to 400, a bulk modulus exponent set to 0.35, an unloading-reloading modulus coefficient set to 800, and a standard atmospheric pressure set to 101.325 kPa.

[0023] Water pressure is achieved by applying nodal head to the upstream dam face. The water level starts from the dam base elevation (empty) and increases at equal intervals to the check flood level, with a total of 9 increments. In this embodiment, taking a dam height of 50m as an example, the dam base elevation is set to 0m, the normal storage level is set to 35m, and the flood level is set to 45m, with each increment increasing the water level by 5m. This yields multiple water pressure levels.

[0024] To divide the dam slope into upstream and downstream regions, the geometric segmentation function in the MIDASGTS software was used to divide the dam body into an upstream region, a core wall region, and a downstream region. Then, the element set creation function in the software was used to select all the meshes in the upstream and downstream regions respectively to obtain the upstream and downstream mesh sets of the dam slope. The MIDASGTS software and the Duncan-Chang EB model are well-known technologies in this field, and the specific processing procedures will not be described in detail.

[0025] Furthermore, due to the significant frictional properties of gravel materials in earth-rock dams, the higher the hydrostatic pressure, the more intense the frictional interlocking between material particles, requiring a larger deviatoric stress to induce a yield state. Therefore, for each mesh, its stress data is used as input to the Drucker-Prag equivalent formula to calculate the equivalent stress of the mesh under all water pressures. The Drucker-Prag criterion incorporates the combined effect of principal stress difference and hydrostatic pressure; the Drucker-Prag equivalent stress formula is a well-known technique in the field, and its specific calculation method will not be elaborated further.

[0026] At this point, the equivalent stress of each grid cell has been obtained.

[0027] Step S002: Calculate the similarity of equivalent stress between adjacent water pressure levels; determine the first stability index based on the fitting degree of the correspondence between water pressure levels and equivalent stress and the fluctuation of similarity.

[0028] The stress on the upstream dam slope originates from water pressure and its own weight, while the stress on the downstream dam slope originates from its own weight. When the water pressure on the upstream dam slope increases, the stress on the upstream dam slope increases synchronously. When the stress on the upstream dam slope acts on the downstream dam slope, the stress on the downstream dam slope changes compared to when there is no water pressure. Theoretically, the stress distribution between the upstream and downstream dam slopes should maintain a balance that adapts to the water pressure; that is, when the water pressure on the upstream dam slope is transmitted to the downstream dam slope through the internal stress of the dam body, the overall stress field of the upstream and downstream dam slopes should be continuous. If this balance is broken (for example, a surge in stress on the upstream dam slope while the stress response on the downstream dam slope lags behind), it indicates an abnormal stress change within the dam body.

[0029] Based on this, this application combines the equivalent stresses of all grids in the upstream and downstream grid sets into corresponding equivalent stress sequences according to the order of each grid from left to right and from top to bottom under different water pressure levels; and analyzes the stability of the equivalent stress sequences of the upstream or downstream dam slopes under different water pressures and the relative stability of the upstream and downstream dam slopes under the same water pressure compared to when the water pressure is 0, and further constructs the equivalent stress imbalance coefficient of the upstream and downstream dam slopes.

[0030] Specifically, the degree of change in equivalent stress in a single region under different water pressures can characterize the region's sensitivity to water pressure. To analyze the degree of change in equivalent stress on the upstream and downstream dam slopes under different water pressures, for each water pressure level, the equivalent stress of all grids on the upstream and downstream dam slopes is used to construct an equivalent stress sequence; that is, for each water pressure level, an equivalent stress sequence is obtained for the upstream dam slope and another for the downstream dam slope. In this embodiment, the water pressure levels are 1 to 10, divided into 10 levels; when the water pressure level is 1, the water pressure is 0.

[0031] For each type of dam slope region, the similarity between its two adjacent equivalent stress sequences is calculated, and all similarities are combined into a similarity sequence. In this embodiment, the similarity is calculated using Euclidean distance. The similarity sequence is used as input to a first-order difference algorithm, and the first-order difference sequence of this sequence is output. The standard deviation of the first-order difference sequence is used as the instability characteristic of the dam slope region. The instability characteristic reflects the oscillation amplitude of the similarity sequence; the larger the instability characteristic, the worse the stability of the stress field of the dam slope during the incremental process.

[0032] Furthermore, for each dam slope region, the mean of all equivalent stresses at each water pressure level was calculated and used as the dependent variable, with the water pressure level as the independent variable. Linear fitting was performed using the least squares method. Theoretically, the higher the water pressure, the larger the mean of the equivalent stress, and the better the fit curve. Therefore, the coefficient of determination of this fitted curve was used as a stability characteristic. The stability characteristic reflects the degree of linear response of the overall stress level of the dam slope to the increase of load. The larger the stability characteristic, the more stable the linear growth trend of the overall stress level of the dam slope with the increase of water pressure, and the more regular and stable the stress response.

[0033] The first stability index of the dam slope is calculated based on the stability and instability characteristics of the dam slope.

[0034] The first stability index is positively correlated with stability characteristics and negatively correlated with instability characteristics.

[0035] It should be noted that positive correlation means that when one variable increases, the other variable also increases, and the two variables change in the same direction. When one variable changes from large to small or from small to large, the other variable also changes from large to small or from small to large. The specific relationship is determined by the actual application, and this application does not impose any special restrictions.

[0036] It should be noted that negative correlation means that when one variable increases, the other variable decreases accordingly, and the two variables change in opposite directions. When one variable changes from large to small or from small to large, the other variable also changes from small to large or from large to small. The specific relationship is determined by practical application, and this application does not impose any special restrictions.

[0037] Preferably, taking the upstream dam slope as an example, the expression for the first stability index is: , This indicates the instability characteristics of the upstream dam slope. This indicates the stability characteristics of the upstream dam slope. Represents the denominator constant. This represents the first stability index of the upstream dam slope. In this embodiment, the denominator constant is 0.01.

[0038] The first stability index reflects the overall stability characteristics of the equivalent stress change of the dam slope under the action of progressively increasing water pressure. The larger the first stability index, the more stable the linear growth trend of the overall stress level of the first stability index with the increase of water pressure, the smaller the stress field fluctuation between adjacent increments, that is, the more regular and stable the stress response with the increase of load, and the more controllable the structural safety of the dam slope.

[0039] In this application, the first-order difference standard deviation of the similarity sequence of equivalent stress under different increments of the dam slope is used to characterize the intensity of local fluctuations in the stress field, and the linear fitting determination coefficient of the mean equivalent stress of the dam slope under different increments and the water pressure level is used to characterize the stability of the overall growth law of the stress field. The two are combined in the form of a ratio to obtain the first stability index, which provides a basis for judgment for subsequent comparison and evaluation of the stability of upstream and downstream dam slopes.

[0040] Using the methods described above, the first stability index of the upstream and downstream dam slopes is calculated respectively.

[0041] Thus, the first stability indicators for the upstream and downstream dam slopes were obtained.

[0042] Step S003: Obtain the quantile sequence of equivalent stress, determine the relative relationship based on the difference of equivalent stress at the same quantile, and determine the distribution characteristics of equivalent stress based on the difference of adjacent relative relationships and the offset of relative relationships.

[0043] Under no water pressure, stress is primarily generated by the weight of the dam slope itself, and the relative relationship between the equivalent stresses of the upstream and downstream dam slopes should be the baseline relative relationship. Theoretically, when water pressure occurs, the stress increase on the upstream dam slope will be higher than that on the downstream dam slope. Therefore, under normal water pressure, the difference between the baseline relative relationships of the equivalent stresses of the upstream and downstream dam slopes at the same water pressure can characterize the distribution characteristics of the equivalent stresses of the upstream and downstream dam slopes during the water pressure increment process. Therefore, for each water pressure level, the baseline relative relationship of the equivalent stress sequence of the upstream and downstream dam slopes is calculated, and the distribution characteristics of the baseline relative relationship at different water pressure levels are analyzed.

[0044] Because the number of grids formed by the upstream and downstream dam slopes may differ, the length of the equivalent stress sequence corresponding to the same water pressure level will be different. Therefore, each equivalent stress sequence is first sorted in ascending order based on all equivalent stress values. Then, according to the principle of quantiles, the length of each equivalent stress sequence is unified to obtain its quantile sequence. Each element in the quantile sequence is the equivalent stress value corresponding to each quantile. In this embodiment, the initial and final values ​​are set to 0 and 1 respectively, with a step size of 0.1, meaning the quantile sequence length is 11. A quantile of 0 represents the minimum equivalent stress, a quantile of 0.1 represents 10% of the equivalent stress, and a quantile of 1 represents the maximum equivalent stress.

[0045] This yielded the quantile sequence of the upstream and downstream dam slopes. To analyze the baseline relative relationship of equivalent stress under different water pressure levels, the relative difference of equivalent stress values ​​at the same quantile in the quantile sequence of the upstream and downstream dam slopes was calculated and denoted as the stress relative difference. The relative difference is the ratio of the absolute value of the difference of equivalent stress values ​​at the same quantile to the global maximum value of equivalent stress in the quantile sequence of the upstream and downstream dam slopes. If the denominator is 0, the relative difference is set to 0.

[0046] The relative stress difference of all quantiles of the upstream and downstream dam slopes is calculated separately. For each quantile sequence, the mean of the relative stress difference is calculated as the relative relationship at that water pressure level. The relative relationship at the lowest water pressure level is recorded as the benchmark relative relationship. The benchmark relative relationship can reflect the benchmark difference in the equivalent stress distribution of the upstream and downstream dam slopes at different water pressure levels. The larger the benchmark relative relationship, the more obvious the difference in the equivalent stress distribution of the upstream and downstream dam slopes when there is no water pressure.

[0047] For the upstream and downstream dam slopes, the difference in the relative relationship between adjacent water pressure levels is recorded as the relative relationship difference. This difference characterizes the instantaneous change in the relative stress relationship between upstream and downstream slopes when the water pressure increases by one level, reflecting the intensity of the disturbance of the incremental load on the stress coordination of the dam body. The larger the relative relationship difference, the more abrupt the stress distribution between upstream and downstream slopes has changed under the current water pressure level. The difference between the relative relationship and the benchmark relative relationship at each water pressure level is calculated and used as the relationship offset amplitude. This characterizes the offset amplitude of the relative stress relationship between upstream and downstream slopes relative to the initial state without water pressure under the current water pressure level, reflecting the degree of stress imbalance caused by the long-term action of water pressure. The larger the relationship offset amplitude, the more the stress difference between upstream and downstream slopes deviates from the state when there is no water pressure as the water level rises, and the overall coordination of the dam body decreases.

[0048] The relative relationship difference and the relationship offset amplitude reflect the distribution characteristics of the relative stress relationship between upstream and downstream during the process of increasing water pressure level. The equivalent stress distribution characteristics are calculated by the relative relationship difference and relationship offset amplitude under all water pressure levels.

[0049] The equivalent stress distribution characteristics are positively correlated with the relative relationship difference and the relationship offset amplitude, respectively.

[0050] Preferably, in this embodiment, the expression for the equivalent stress distribution characteristics is: , This indicates the relative relationship of the j-th water pressure level. This indicates the relative relationship of the (j-1)th water pressure level. This indicates the relative relationship of the first water pressure level. Indicates the number of water pressure levels. Indicates the characteristics of equivalent stress distribution. This represents a positive number and serves to prevent the denominator from being 0; in this embodiment, the value is 0.0011. Indicates a poor relative relationship. Indicates the magnitude of the relationship offset.

[0051] The equivalent stress distribution characteristics reflect the overall degree of incoordination in the stress response of the upstream and downstream dam slopes as the water pressure level increases. A larger value indicates a more drastic change in the relative relationship of equivalent stress between the upstream and downstream slopes as the water pressure increases; a greater range of stress distribution variation between adjacent levels; and a more significant deviation of the current stress state from the baseline state without water pressure. This value reflects the overall degree of incoordination in the equivalent stress response of the upstream and downstream dam slopes, providing a more accurate basis for subsequently constructing the equivalent stress imbalance coefficient.

[0052] Thus, the equivalent stress distribution characteristics of the upstream and downstream dam slopes were obtained.

[0053] Step S004: Determine the overall stability through the first stability index, and then determine the equivalent stress imbalance coefficient by combining the equivalent stress distribution characteristics.

[0054] The above steps yielded the first stability indices and equivalent stress distribution characteristics of the upstream and downstream dam slopes. Each of these first stability indices characterizes the average stability of the equivalent stress on the upstream and downstream dam slopes. Since both indices are associated with greater stability and either being too small would disrupt the overall equilibrium, this embodiment combines the two first stability indices using a harmonic mean. This highlights the constraining effect of the less stable upstream and downstream dam slope on the overall equilibrium, and this is denoted as the overall stability. A higher overall stability indicates better overall stability of the equivalent stress on the upstream and downstream dam slopes, and that the stress responses in both regions are relatively regular and stable.

[0055] Therefore, the equivalent stress imbalance coefficient of the dam slope is determined based on the equivalent stress distribution characteristics of the upstream and downstream slopes and the overall stability. This provides a basis for subsequent evaluation of the overall compatibility analysis of the dam slope under different water pressure levels.

[0056] The equivalent stress imbalance coefficient is positively correlated with the overall stability and negatively correlated with the equivalent stress distribution characteristics.

[0057] Preferably, in this embodiment, the expression for the equivalent stress imbalance coefficient is: , This indicates the equivalent stress distribution characteristics of the upstream and downstream dam slopes. This indicates the overall stability of the upstream and downstream dam slopes. Represents a very small positive number. This represents the equivalent stress imbalance coefficient between the upstream and downstream dam slopes. In this embodiment, The value is 0.01.

[0058] because It can characterize the degree of incoordination relative to , The ratio of stationarity, which may be 0 (perfectly coordinated) or tend to infinity (extremely incompatible), may cause the balance coefficient to be affected when used directly as the denominator. When reconciling, a denominator of zero or an unbounded range fails to reflect the degree of balance. Therefore, adding 1 avoids the problem of a zero denominator and can also... Normalization is performed when the degree of incoordination of equivalent stress on the upstream and downstream dam slopes is zero. The value is 1 (perfect balance). As the degree of incoordination increases, It monotonically decreases and approaches 0 (extreme imbalance).

[0059] Thus, the equivalent stress imbalance coefficient of the dam slope was obtained.

[0060] Step S005: Perform stability analysis using the equivalent stress imbalance coefficient.

[0061] Based on the calculation results of the Drucker-Prag equivalent stress, the maximum Drucker-Prag equivalent stress of each unit of the dam body is compared with the allowable equivalent stress of the soil and rock materials: if the maximum Drucker-Prag equivalent stress is less than the allowable equivalent stress of the soil and rock materials, it indicates that the dam slope meets the stability requirements in terms of strength, and the stress has not exceeded the yield limit of the materials; if the maximum Drucker-Prag equivalent stress is greater than or equal to the allowable equivalent stress of the soil and rock materials, it indicates that the dam slope has the risk of local yielding or failure, and the stability is poor.

[0062] However, the Drucker-Prag equivalent stress only reflects the strength margin at a single point or overall, and cannot reflect the stress coordination between upstream and downstream dam slopes. Therefore, the equivalent stress imbalance coefficient is further used for stability analysis. The closer the coefficient is to 1, the more coordinated the changes in equivalent stress between upstream and downstream dam slopes with increasing water pressure, the more balanced the stress distribution, and the better the overall stability of the dam slope. Conversely, the closer the coefficient is to 0, the more asynchronous the stress responses are (e.g., a surge in upstream stress followed by a lag in downstream stress). Even if the maximum Drucker-Prag equivalent stress has not exceeded the limit, the dam body may still experience uneven deformation or localized failure due to stress imbalance, resulting in poor stability. Further protective measures or reinforcement designs should be implemented, such as adding downstream counterweights, strengthening upstream dam face seepage prevention, or optimizing the dam drainage system, to improve the stress coordination between upstream and downstream and reduce the risk of dam slope instability.

[0063] Based on the same inventive concept as the above method, this embodiment of the invention also provides a dam slope equivalent stress analysis system based on finite element method, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the steps of any one of the above-described dam slope equivalent stress analysis methods based on finite element method.

[0064] It should be noted that the above 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 scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

[0065] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

Claims

1. A finite element method for analyzing equivalent stress in dam slopes, characterized in that, The method includes the following steps: Preset water pressure levels; divide the dam slope into upstream and downstream dam slope regions through finite element simulation, and divide the regions into grids to obtain the equivalent stress of the grid at each water pressure level; For each water pressure level, the equivalent stress of the upstream and downstream dam slope grids are respectively constructed into equivalent stress sequences; the similarity of the equivalent stress sequences of adjacent water pressure levels is calculated, and the instability characteristics of the dam slope area are determined based on the similarity fluctuation; the stability characteristics are determined based on the fitting degree of the curve of the correspondence between water pressure level and equivalent stress; and the first stability index is determined through the stability characteristics and instability characteristics. The equivalent stress sequences of the upstream and downstream dam slopes are processed by quantile processing to obtain their quantile sequences; the relative relationship is determined by the difference in equivalent stress at the same quantile between the upstream and downstream dam slopes, which is used to represent the degree of difference in equivalent stress distribution; the characteristics of equivalent stress distribution are determined by the difference in the relative relationship between adjacent water pressure levels and the offset of the relative relationship from the benchmark relative relationship. The harmonic mean of the first stability index of the upstream and downstream dam slopes is used as the overall stability. The equivalent stress imbalance coefficient is determined based on the overall stability of the dam slopes and the characteristics of equivalent stress distribution. Stability analysis is performed using the equivalent stress imbalance coefficient.

2. The finite element method for analyzing equivalent stress in dam slopes as described in claim 1, characterized in that, The method for constructing equivalent stress sequences from the upstream and downstream dam slope grids for each water pressure level is as follows: Under different water pressure levels, the equivalent stresses of all grids in the upstream and downstream grid sets are combined into corresponding equivalent stress sequences according to the order of each grid from left to right and from top to bottom.

3. The finite element method for analyzing equivalent stress in dam slopes as described in claim 1, characterized in that, The method for calculating the similarity of equivalent stress sequences of adjacent water pressure levels and determining the instability characteristics of the dam slope area based on similarity fluctuations is as follows: For the dam slope, the similarity between two equivalent stress sequences of adjacent water pressure levels is calculated, and all similarities are combined into a similarity sequence. The first-order difference sequence of the similarity sequence is obtained, and the standard deviation of the elements in the first-order difference sequence is calculated as the instability feature of the dam slope region.

4. The finite element method for analyzing equivalent stress in dam slopes as described in claim 1, characterized in that, The method for determining the stability characteristics based on the fitting degree of the curve corresponding to the water pressure level and equivalent stress is as follows: For each dam slope region, the mean value of all equivalent stresses of the dam slope under each water pressure level is calculated and used as the dependent variable, with the water pressure level as the independent variable, and linear fitting is performed using the least squares method; the determination coefficient of the fitted curve is used as the stability feature.

5. The finite element method for analyzing equivalent stress in dam slopes as described in claim 1, characterized in that, The first stability index is positively correlated with stability characteristics and negatively correlated with instability characteristics.

6. The finite element method for analyzing equivalent stress in dam slopes as described in claim 1, characterized in that, The method for determining the relative relationship by the equivalent stress difference at the same quantile of the upstream and downstream dam slopes is as follows: The relative difference of equivalent stress at the same quantile in the quantile sequence of the upstream and downstream dam slopes is denoted as the stress relative difference; the relative difference is the ratio of the absolute value of the difference of equivalent stress at the same quantile to the global maximum value of equivalent stress in the quantile sequence of the upstream and downstream dam slopes. The mean of the relative stress difference for each quantile sequence is calculated as the relative relationship at different water pressure levels.

7. The finite element method for analyzing equivalent stress in dam slopes as described in claim 1, characterized in that, The equivalent stress distribution characteristics are positively correlated with the relative relationship difference and the relationship offset amplitude, respectively.

8. The finite element method for analyzing equivalent stress in dam slopes as described in claim 7, characterized in that, The relative relationship difference is the difference in the relative relationship between adjacent water pressure levels; the relationship offset is the difference between the relative relationship at the water pressure level and the benchmark relative relationship; the benchmark relative relationship is the relative relationship when the water pressure level is at its minimum.

9. The finite element method for analyzing equivalent stress in dam slopes as described in claim 1, characterized in that, The equivalent stress imbalance coefficient is positively correlated with the overall stability and negatively correlated with the equivalent stress distribution characteristics.

10. A finite element method-based dam slope equivalent stress analysis system, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the finite element-based dam slope equivalent stress analysis method as described in any one of claims 1-9.

Images