Snow surface overlay layering design method for ice structure bearing

Abstract

This invention discloses a layered design method for snow surface overlay on ice-structured load-bearing structures, relating to the field of ice and snow engineering technology. The method includes the following steps: S1, determining the design constraints and performance indicators of the snow surface overlay based on target working conditions and environmental data; S2, obtaining the microstructural parameters of the snow material to be laid, including initial porosity, ice crystal size distribution, coordination number, and contact geometry. This invention establishes a cross-scale mechanical performance evolution model to accurately capture the microscopic mechanisms of ice crystal sintering, particle creep, and fatigue damage of snow material under long-term load and temperature, solving the problem of performance prediction deviations caused by the inability of existing macroscopic models to reflect microscopic evolution. By constructing a quantitative mapping relationship between microstructural parameters and macroscopic mechanical properties, combined with thermo-coupling load history simulation, accurate performance evolution data of the overlay can be obtained.

Description

Technical Field

[0001] This invention relates to the field of ice and snow engineering technology, specifically to a layered design method for snow surface layering for ice structure load-bearing bodies. Background Technology

[0002] In cold-region engineering and the construction of ice and snow sports facilities, ice structural load-bearing structures often require the addition of snow to enhance their functionality. As a porous medium, the mechanical properties of snow are significantly affected by temperature, humidity, and load history; therefore, precise design is crucial for ensuring the long-term stability of the structure. The snow overlay layer must simultaneously meet the requirements of load-bearing capacity and deformation coordination, and the rationality of its layered structure directly affects the overall performance of the ice-snow composite system.

[0003] Existing design methods largely rely on macroscopic mechanical models, simplifying the snow layer as a homogeneous continuum for analysis. However, under long-term loading and alternating temperature cycles, the snow layer undergoes microstructural evolution, including ice crystal sintering, particle creep, and fatigue damage. These microscopic changes gradually accumulate and affect the macroscopic mechanical response. Because macroscopic models cannot capture these microscopic mechanisms, predictions of the overlay's mechanical properties are biased, leading to discrepancies between the load-bearing capacity assessment and actual operating conditions, making it difficult to meet engineering reliability requirements. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a layered design method for snow surface overlay on ice structure load-bearing structures. This method solves the problem that existing technologies, when compared in comparison, cannot capture microscopic mechanisms in macroscopic models, leading to deviations in the prediction of the mechanical properties of the overlay.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a layered design method for snow surface layering for ice structure load-bearing bodies, comprising: S1. Based on the target working conditions and environmental data, determine the design constraints and performance indicators of the snow surface overlay layer; S2. Obtain the microstructure parameters of the snow material to be laid, including initial porosity, ice crystal size distribution, coordination number and contact geometry. S3. Establish a cross-scale mechanical performance evolution model for the snow surface overlay, wherein the model is used to establish a quantitative mapping relationship between the microstructure parameters and the macroscopic mechanical performance parameters; S4. Based on the cross-scale mechanical performance evolution model, input the thermo-mechanical coupling load history corresponding to the target working condition, perform numerical simulation on the long-term macroscopic mechanical response of the snow surface overlay layer, and obtain its performance evolution data. S5. Based on the performance evolution data, with the performance index as the objective function and the design constraints as the boundary, iteratively optimize the layering scheme of the snow surface overlay layer to determine the thickness and initial density configuration of each layer. The establishment of the cross-scale mechanical performance evolution model of the snow surface overlay also includes: Construct representative volumetric units that can characterize the microscopic geometric features of snow material; Within the representative volume unit, a micromechanical behavior model considering ice crystal sintering, particle creep, and fatigue damage is established. By applying a macroscopic strain field to the representative volume element and performing numerical homogenization calculations, the macroscopic equivalent constitutive relation of the snow surface overlay is obtained.

[0006] Furthermore, obtaining the microstructure parameters of the snow material to be laid specifically includes: Industrial computed tomography was performed on samples of the snow to be laid to obtain three-dimensional digital image data. The three-dimensional digital image data is binarized and geometrically reconstructed to generate a refined three-dimensional digital model of the snow material. Based on the three-dimensional digital model, image analysis algorithms are used to extract the initial porosity, ice crystal size distribution function, average coordination number between ice crystal particles, and contact neck radius distribution.

[0007] Furthermore, the establishment of a micromechanical behavior model considering ice crystal sintering specifically includes: Based on temperature and stress state, determine the sintering driving force at the contact point of ice crystal particles; A governing equation for the evolution of the contact neck radius over time was established, which is related to surface energy, grain boundary energy, and water vapor diffusion coefficient. The connection relationship and contact stiffness between particles within the representative volume unit are updated in real time to reflect the enhanced mechanical properties caused by ice crystal sintering.

[0008] Furthermore, the governing equation for the evolution of the contact neck radius over time is specifically as follows: , Where x represents the contact neck radius at time t. The initial contact neck radius is represented by , n is the sintering mechanism exponent, which ranges from 2 to 5; K is the material-related sintering rate constant. denoted as , where is the apparent activation energy of the sintering process; R is the ideal gas constant; t' is the integral time variable of the sintering process, and dt' is the differential element corresponding to the time variable; T(t') is the absolute temperature that varies with time.

[0009] Furthermore, the establishment of the micromechanical behavior model considering particle creep specifically includes: In the ice crystal particle contact model of the representative volume element, normal and tangential contact force components based on power-law creep constitutive model are introduced; The normal and tangential contact force components are used to describe the irreversible deformation of the contact area caused by dislocation motion and diffusion flow under sustained load. Based on the load history and temperature history of the target working condition, the creep displacement at each contact point is calculated cumulatively, and the overall geometric configuration of the representative volume element is updated.

[0010] Furthermore, the strain rate corresponding to the power-law creep constitutive model Obtain it using the following formula: , Where A is the creep coefficient. The equivalent stress is given by m, which is the stress exponent and ranges from 1 to 4. R is the activation energy of the creep process; T is the ideal gas constant; and T is the absolute temperature. Based on the strain rate, calculate at the time step The creep strain increment within the particle is applied to the relative displacement of the particle contact.

[0011] Furthermore, the establishment of the micromechanical behavior model considering fatigue damage specifically includes: A damage state variable D is defined at the contact point of the ice crystal particles in the representative volume unit; Based on the stress amplitude and loading number of cyclic loads, the evolution rule of the damage state variable D is established; When the accumulated damage state variable D at any contact point reaches the preset critical damage threshold, it is determined that the contact point has fractured, and the contact connection is disconnected in the model to reflect the degradation of material stiffness.

[0012] Furthermore, the evolution rule of the damage state variable D is specifically as follows: For the Nth load cycle, the damage increment Obtain it using the following formula: , in, This represents the cumulative damage at the end of the previous cycle; This represents the stress amplitude of the current cycle; is the fatigue strength coefficient of the material; p is the fatigue damage index, which ranges from 2 to 8; The critical damage threshold is set to 1.

[0013] Furthermore, the iterative optimization of the layering scheme for the snow surface overlay specifically includes: Define a multi-objective optimization function that includes load-bearing capacity deviation, deformation compatibility, and cumulative damage level; A multi-objective genetic algorithm was used, with the thickness and initial density of each layer as optimization variables; In each iteration, the cross-scale mechanical performance evolution model is invoked for simulation calculation to obtain the performance index under the current combination of optimization variables; The fitness value of the multi-objective optimization function is calculated, and new combinations of optimization variables are generated through selection, crossover, and mutation operations. When the change in the fitness value converges to within the preset convergence tolerance, the iteration terminates, and the current optimal combination of optimization variables is determined as the final hierarchical design scheme.

[0014] Furthermore, it also includes establishing a database of snow performance parameters, the establishment of which includes: For different types of snow and snow materials in their initial compaction state, the modeling and simulation process described above is performed offline; Structured storage of data on different microstructural parameters, thermo-mechanical coupled load history, and their corresponding macroscopic mechanical performance evolution. When performing a new hierarchical design, firstly, case data similar to the current target working condition is retrieved from the database, and the retrieved hierarchical scheme is used as the initial solution for the iterative optimization described above, so as to improve optimization efficiency. Beneficial effects

[0015] This invention establishes a cross-scale mechanical property evolution model to accurately capture the microscopic mechanisms of ice crystal sintering, particle creep, and fatigue damage of snow materials under long-term load and temperature, solving the problem of performance prediction deviations caused by the inability of existing macroscopic models to reflect microscopic evolution. By constructing a quantitative mapping relationship between microscopic structural parameters and macroscopic mechanical properties, combined with thermo-coupling load history simulation, the performance evolution data of the overlay can be accurately obtained. Based on multi-objective optimization, iterative optimization of the layering scheme can determine the reasonable configuration of the thickness and initial density of each layer, ensuring the load-bearing capacity and deformation coordination of the ice-snow composite system. The establishment of a snow material performance parameter database can also improve design efficiency, ultimately enhancing the long-term stability and engineering reliability of the snow surface overlay of the ice structure load-bearing body, meeting the functional requirements of cold-region engineering and ice and snow facilities. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Please see Figure 1 This invention provides a layered design method for snow surface layering on ice structure load-bearing bodies, comprising: S1. Based on the target working conditions and environmental data, determine the design constraints and performance indicators of the snow surface overlay layer; S2. Obtain the microstructure parameters of the snow material to be laid. The microstructure parameters include initial porosity, ice crystal size distribution, coordination number and contact geometry. S3. Establish a cross-scale mechanical property evolution model for snow surface overlays. The model is used to establish a quantitative mapping relationship between microstructural parameters and macroscopic mechanical property parameters. S4. Based on the cross-scale mechanical performance evolution model, input the thermo-mechanical coupling load history corresponding to the target working condition, perform numerical simulation on the long-term macroscopic mechanical response of the snow surface overlay layer, and obtain its performance evolution data. S5. Based on the performance evolution data, with the performance index as the objective function and the design constraints as the boundary, iteratively optimize the layering scheme of the snow surface overlay to determine the thickness and initial density configuration of each layer. Establishing a cross-scale mechanical property evolution model for snow surface overlays also includes: Construct representative volumetric units that can characterize the microscopic geometric features of snow material; Within a representative volume element, a micromechanical behavior model considering ice crystal sintering, particle creep, and fatigue damage is established. By applying a macroscopic strain field to representative volume elements and performing numerical homogenization calculations, the macroscopic equivalent constitutive relation of the snow surface overlay is obtained.

[0019] Specifically, when obtaining the microstructural parameters of the snow mix to be laid, samples are taken, for example, from different locations and depths. Industrial computed tomography (CT) equipment is used to scan the samples, with a scanning resolution set to 50 μm, to obtain clear three-dimensional digital image data. The three-dimensional digital image data is then binarized, and an appropriate grayscale threshold is set to distinguish the snow mix from the pores. A refined three-dimensional digital model of the snow mix is ​​then generated using a geometric reconstruction algorithm. Based on this model, image analysis algorithms are used to extract the initial porosity, i.e., the ratio of pore volume to total volume; the ice crystal particle size distribution is obtained by measuring the diameter of different ice crystal particles and statistically analyzing their distribution; the coordination number is the average number of contacts between each ice crystal particle and surrounding particles; and the contact geometry includes the shape and size of the contact neck, etc.

[0020] When establishing a cross-scale mechanical property evolution model, a representative volume element can be selected as a cubic region containing a certain number of ice crystal particles, such as 500-1000 ice crystal particles, to characterize the microscopic geometric features of the snow material. Within the representative volume element, a microscopic mechanical behavior model considering ice crystal sintering, particle creep, and fatigue damage is established. For ice crystal sintering, the sintering driving force is determined based on temperature and stress state, and an equation for the evolution of the contact neck radius over time is established. For particle creep, the normal and tangential contact force components of the power-law creep constitutive model are introduced. For fatigue damage, damage state variables are defined and their evolution rules are established. By applying a macroscopic strain field, such as axial tensile or compressive strain, to the representative volume element and performing numerical homogenization calculations, the mechanical response at the microscopic scale is averaged, yielding a macroscopic equivalent constitutive relation. This relation reflects the quantitative mapping between microscopic structural parameters and macroscopic mechanical property parameters, solving the problem that existing macroscopic models cannot capture microscopic mechanisms.

[0021] Based on the cross-scale mechanical performance evolution model, the thermo-mechanical coupling load history corresponding to the target working condition is input, such as temperature changes and load magnitude at different time periods. The long-term macroscopic mechanical response of the snow surface overlay is numerically simulated to obtain performance evolution data, such as bearing capacity and deformation at different time points.

[0022] Based on performance evolution data, and using performance indicators as objective functions (e.g., maximizing load-bearing capacity retention) as the goal, and design constraints as boundaries (e.g., deformation not exceeding a limit), a multi-objective optimization algorithm is employed to iteratively optimize the layering scheme of the snow overlay. For example, the overlay can be divided into 3-5 layers, with the thickness and initial density of each layer as optimization variables. Through multiple iterative calculations, the optimal layering design scheme is determined. This method enables the designed snow overlay to better meet the overall performance requirements of the ice-snow composite system, improving engineering reliability.

[0023] In this embodiment, obtaining the microstructure parameters of the snow material to be laid specifically includes: Industrial computed tomography was performed on samples of the snow to be laid to obtain three-dimensional digital image data. Binarization and geometric reconstruction are performed on the three-dimensional digital image data to generate a refined three-dimensional digital model of the snow material; Based on a three-dimensional digital model, an image analysis algorithm was used to extract the initial porosity, ice crystal size distribution function, average coordination number between ice crystal particles, and contact neck radius distribution.

[0024] Specifically, when performing industrial computed tomography (CT) scans on samples of snow to be laid, a representative snow sample is selected, with a sample volume set to 10mm × 10mm × 10mm. The sample is placed on the scanning stage, and the scanning parameters are adjusted, such as setting the tube voltage to 100kV, the tube current to 100μA, and the scanning step size to 0.05mm, to obtain clear three-dimensional digital image data that accurately reflects the microstructure inside the snow.

[0025] When binarizing 3D digital image data, an appropriate threshold is determined by analyzing the grayscale distribution of the image. For example, areas with grayscale values ​​greater than 150 are identified as snow particles, and areas with grayscale values ​​less than or equal to 150 are identified as pores, thus dividing the image into two parts: snow particles and pores. Next, geometric reconstruction is performed, using a 3D reconstruction algorithm to combine the 2D sliced ​​images into a 3D model, generating a refined 3D digital model of the snow particles. This model clearly shows the spatial distribution and morphology of ice crystal particles.

[0026] Based on a three-dimensional digital model, image analysis algorithms were used to extract relevant parameters. The initial porosity was obtained by statistically analyzing the ratio of the total pore volume to the total model volume. The ice crystal size distribution function was obtained by measuring the equivalent diameter of each ice crystal particle and then performing statistical analysis to determine the proportion of particles in different size ranges. The average coordination number between ice crystal particles was obtained by statistically analyzing the number of contacts between each particle and surrounding particles and then averaging the results. The contact neck radius distribution was obtained by measuring and statistically analyzing the radius of the contact neck at each contact point. These steps accurately obtain the microstructural parameters of the snow material, providing reliable data support for the subsequent establishment of a cross-scale mechanical property evolution model and improving the accuracy of the model.

[0027] In this embodiment, a micromechanical behavior model considering ice crystal sintering is established, specifically including: Based on temperature and stress state, determine the sintering driving force at the contact point of ice crystal particles; The governing equation for the evolution of the contact neck radius over time was established, and the governing equation is related to surface energy, grain boundary energy and water vapor diffusion coefficient. The connection relationship and contact stiffness between particles within a representative volume unit are updated in real time to reflect the enhanced mechanical properties caused by ice crystal sintering.

[0028] Specifically, when determining the sintering driving force at the contact point of ice crystal particles based on temperature and stress state, the temperature is monitored in real time by sensors to detect changes in the temperature of the snow surface overlay, and the stress state is calculated based on the applied load. For example, when the temperature rises, the surface energy of the ice crystal particles increases, and the stress promotes a closer contact between the particles. The magnitude of the sintering driving force is determined by combining these two factors; the greater the driving force, the easier the sintering process is.

[0029] When establishing the governing equation for the evolution of the contact neck radius over time, the equation comprehensively considers the effects of surface energy, grain boundary energy, and water vapor diffusion coefficient. Surface energy tends to increase the contact neck size, grain boundary energy affects atomic diffusion, and the water vapor diffusion coefficient is temperature-dependent; the higher the temperature, the larger the diffusion coefficient, and the faster the contact neck grows. This governing equation can accurately describe the change in the contact neck radius over time.

[0030] When updating the connectivity and contact stiffness between particles within a representative volume element in real time, as the sintering process progresses, the contact neck radius increases, and the connection between particles becomes stronger, potentially changing from point contact to surface contact. The contact stiffness is updated based on the size of the contact neck and the mechanical properties of the particles; a larger contact neck results in greater contact stiffness. This real-time updating accurately reflects the enhanced mechanical properties caused by ice crystal sintering in the model, making the calculation results closer to reality and improving the accuracy of predicting the mechanical properties of snow overlays.

[0031] In this embodiment, the governing equation for the evolution of the contact neck radius over time is as follows: , Where x represents the contact neck radius at time t, in meters; The initial contact neck radius is represented in meters (m); n is the sintering mechanism exponent, ranging from 2 to 5, with n taking the value of 3 when surface diffusion is dominant and 5 when volume diffusion is dominant; K is the material-related sintering rate constant, in cubic meters (m). ; denoted as Δt(t'), which is the apparent activation energy of the sintering process, in J / mol; R is the ideal gas constant, with a value of 8.314 J / (mol·K); t' is the integral time variable of the sintering process, and dt' is the differential element corresponding to the time variable; T(t') is the absolute temperature as a function of time, in K.

[0032] Specifically, when applying the governing equation for the evolution of the contact neck radius over time, the specific values ​​of each parameter are first determined. For example, the initial contact neck radius... This can be obtained through observation of the microstructure of the snow material, assumed to be 1×10^-6 m; based on the sintering mechanism of the snow material, the value of n is selected, and if surface diffusion is the main process, n is taken as 3; the value of K is determined experimentally, and for a certain type of snow material, it may be 2×10^-15. ; Also obtained experimentally, assumed to be 60000 J / mol; T(t) is measured in real time by a temperature sensor and converted into absolute temperature.

[0033] Substituting these parameters into the equation, the contact neck radius x at different times t can be obtained through integration. For example, at a certain temperature T(t') = 263K, i.e. -10℃, the contact neck radius x can be obtained after integration at t = 3600s. This equation can accurately describe the evolution of the contact neck radius over time, providing a quantitative basis for establishing a micromechanical behavior model considering ice crystal sintering. This allows the model to accurately reflect the changes in the microstructure of snow material caused by sintering, thereby improving the accuracy of predicting the macroscopic mechanical properties of snow surface overlays.

[0034] In this embodiment, a micromechanical behavior model considering particle creep is established, specifically including: In the ice crystal particle contact model of the representative volume element, the normal and tangential contact force components based on the power-law creep constitutive model are introduced; The normal and tangential contact force components are used to describe the irreversible deformation of the contact area caused by dislocation motion and diffusion flow under sustained load. Based on the load and temperature history of the target working condition, the creep displacement at each contact point is calculated cumulatively, and the overall geometry of the representative volume element is updated.

[0035] Specifically, when introducing normal and tangential contact force components based on power-law creep constitutive model into the contact model of ice crystal particles in a representative volume element, the normal contact force component is perpendicular to the contact surface of the particles, while the tangential contact force component is parallel to the contact surface. For example, for two contacting ice crystal particles, the normal contact force causes the particles to creep in the vertical direction, while the tangential contact force causes the particles to creep with relative sliding in the horizontal direction.

[0036] The normal and tangential contact force components are calculated using a power-law creep constitutive relation, which reflects the irreversible deformation in the contact region caused by dislocation motion and diffusion flow under sustained load. Dislocation motion refers to the deformation caused by the misalignment of atoms in the crystal, while diffusion flow is the deformation caused by the movement of atoms under the influence of a concentration gradient. The combined effect of these two mechanisms produces particle creep.

[0037] Based on the load and temperature history of the target working condition, for example, the load gradually increases from 100N to 500N, and the temperature changes from -15℃ to -5℃, the creep displacement at each contact point is calculated sequentially according to the time step. Within each time step, the strain rate is calculated using a power-law creep constitutive model based on the current load and temperature, and then the creep strain increment is obtained by combining it with the time step, thereby calculating the creep displacement. The creep displacements of each time step are accumulated, and the overall geometry of the representative volume element is updated based on these displacements, such as changes in the position and shape of the particles. In this way, the model can accurately simulate the creep behavior of particles under long-term loads, making the prediction of the mechanical properties of snow overlays more consistent with reality and providing a more reliable basis for layered design.

[0038] In this embodiment, the strain rate corresponding to the power-law creep constitutive model It can be obtained through the following formula: , Where A is the creep coefficient, and the unit is  ; The equivalent stress is expressed in Pa; m is the stress exponent, which ranges from 1 to 4. When creep is mainly caused by diffusion, m is 1; when creep is mainly caused by dislocation climb, m is 4. ν is the activation energy of the creep process, in J / mol; R is the ideal gas constant, with a value of 8.314 J / (mol·K); T is the absolute temperature, in K. Based on strain rate, calculations are performed at the time step. The creep strain increment within the particle is applied to the relative displacement of the particle contact.

[0039] Specifically, in calculating the strain rate corresponding to the power-law creep constitutive model... First, determine the values ​​of each parameter. For example, for a certain type of snow material, the value of A is experimentally measured to be 5 × 10^-20. Equivalent stress The load at the contact point is calculated and assumed to be 2 × 10^6 Pa; based on the creep mechanism of the snow, m is taken as 3. The experimentally obtained value is 40000 J / mol; T is the current absolute temperature, assumed to be 260 K, i.e., -13 °C.

[0040] Substituting these parameters into the formula, the strain rate can be calculated. .For example: , Calculation yields The specific value.

[0041] Based on this strain rate, the calculation at the time step is performed. ,like Incremental creep strain The creep strain increment is applied to the relative displacement of the particle contact, that is, the change in relative displacement is calculated based on the strain increment and particle size, and the positional relationship of the particle contact is updated. This formula can accurately calculate the creep strain rate and strain increment of the particles, enabling the model to accurately simulate the creep behavior of the particles, thereby improving the accuracy of predicting the long-term mechanical response of snow overlays.

[0042] In this embodiment, a micromechanical behavior model considering fatigue damage is established, specifically including: A damage state variable D is defined at the contact point of ice crystal particles in a representative volume element; Based on the stress amplitude and loading number of cyclic loads, an evolution rule for the damage state variable D is established. When the accumulated damage state variable D at any contact point reaches the preset critical damage threshold, it is determined that the contact point has fractured, and the contact connection is disconnected in the model to reflect the degradation of material stiffness.

[0043] Specifically, a damage state variable D is defined at the contact point of ice crystal particles in a representative volume element. The initial value of D is 0, indicating that there is no damage at the contact point. As the number of load cycles increases, the value of D gradually increases. When D reaches a critical value, it indicates that the contact point has fractured. For example, for a new contact point, the initial D=0.

[0044] When establishing the evolution rule for the damage state variable D based on the stress amplitude and loading number of cyclic loads, the stress amplitude is the difference between the maximum and minimum stress in each cycle, and the loading number is the number of load cycles. For example, if the stress amplitude of the cyclic load is 5 × 10^5 Pa, after 100 cycles, the increment of D is calculated according to the evolution rule, increasing the value of D from 0 to 0.2.

[0045] The preset critical damage threshold can be set to 1. When the accumulated damage state variable D at any contact point reaches 1, the contact point is considered to have fractured. The contact connection is then disconnected in the model, meaning the force transmission at that contact point is no longer considered, thus reflecting the degradation of material stiffness. For example, if the value of D reaches 1 after 500 cycles of loading, the connection at that contact point is disconnected in the model, and the stiffness at that point becomes 0. In this way, the model can simulate the fatigue damage process of snow material under cyclic loading, making the analysis of the mechanical properties of snow overlays more comprehensive and improving the reliability of the design.

[0046] In this embodiment, the evolution rule of the damage state variable D is as follows: For the Nth load cycle, the damage increment Obtain it using the following formula: , in, This represents the cumulative damage at the end of the previous cycle; This represents the stress amplitude for the current cycle, in Pa. is the fatigue strength coefficient of the material, in Pa; p is the fatigue damage index, which ranges from 2 to 8, with a larger value for brittle snow materials. The critical damage threshold is set to 1.

[0047] Specifically, in calculating the damage increment of the Nth load cycle At this time, it is necessary to determine the values ​​of each parameter. For example, the cumulative damage at the end of the previous cycle. Stress amplitude of the current cycle fatigue strength coefficient of the material Based on the brittleness of the snow, p is set to 5.

[0048] Substituting these parameters into the formula, we get: , Calculation yields Let's assume the specific value is 0.02, then the cumulative damage at the end of the Nth cycle... .

[0049] When the cumulative damage D reaches the critical damage threshold of 1, the contact point is considered to have fractured. For example, after multiple cycles, the D value of a certain contact point reaches 1, at which point the contact point fractures. This formula can quantitatively calculate the damage increment of each cycle, accurately describe the evolution process of the damage state variable D, and enable the model to accurately simulate the fatigue damage behavior of snow material, providing a reliable basis for assessing the service life of snow overlay layers.

[0050] In this embodiment, the layering scheme for snow surface overlay is iteratively optimized, specifically including: Define a multi-objective optimization function that includes load-bearing capacity deviation, deformation compatibility, and cumulative damage level; A multi-objective genetic algorithm was used, with the thickness and initial density of each layer as optimization variables; In each iteration, a cross-scale mechanical performance evolution model is invoked for simulation calculations to obtain performance indicators under the current combination of optimization variables; Calculate the fitness value of the multi-objective optimization function, and generate new combinations of optimization variables through selection, crossover, and mutation operations; When the change in fitness value converges to within the preset convergence tolerance, the iteration terminates, and the current optimal combination of optimization variables is determined as the final hierarchical design scheme.

[0051] Specifically, when defining a multi-objective optimization function, the bearing capacity deviation is the ratio of the difference between the actual bearing capacity and the design bearing capacity to the design bearing capacity; the deformation compatibility is the degree of deformation difference between each layer; and the cumulative damage level is the total damage of the overlay within its design service life. For example, the optimization function can be set to minimize the bearing capacity deviation, maximize the deformation compatibility, and minimize the cumulative damage level.

[0052] When using a multi-objective genetic algorithm, the thickness and initial density of each overlay layer are used as optimization variables. For example, the overlay layer consists of three layers. The thickness of the first layer ranges from 5 to 15 cm, and the initial density ranges from 200 to 300 kg / m³. The second and third layers also have corresponding value ranges set.

[0053] In each iteration, the cross-scale mechanical performance evolution model is invoked to simulate and calculate the current combination of optimization variables, and the performance indicators such as bearing capacity, deformation of each layer, and damage under this combination are obtained.

[0054] The fitness value of the multi-objective optimization function is calculated based on performance indicators. A higher fitness value indicates a better combination of optimization variables. The selection operation chooses individuals with high fitness values; the crossover operation combines the optimization variables of two individuals to generate new individuals; and the mutation operation randomly changes some of the optimization variables of an individual to increase diversity. For example, individuals with the top 30% fitness values ​​are selected for crossover and mutation to generate new combinations of optimization variables.

[0055] The preset convergence tolerance can be set to 0.01. When the change in fitness value is less than 0.01 in consecutive iterations, the iteration is terminated, and the current optimal combination of optimization variables is determined as the final layer design scheme. For example, after 50 iterations, the change in fitness value converges to 0.008, and the determined layer thickness and initial density at this point are the optimal scheme. Using this iterative optimization method can obtain a more reasonable layer scheme, enabling the snow surface overlay layer to achieve a better performance level while meeting design constraints.

[0056] In this embodiment, a snow performance parameter database is established. The establishment of the database includes: The modeling and simulation process is performed offline for different types of snow and snow materials in their initial compaction state. Structured storage of data on different microstructural parameters, thermo-mechanical coupled load history, and their corresponding macroscopic mechanical performance evolution. When implementing a new hierarchical design, we first retrieve case data similar to the current target working condition from the database, and use the retrieved hierarchical scheme as the initial solution for iterative optimization to improve optimization efficiency.

[0057] Specifically, when establishing the snow performance parameter database, offline modeling and simulation processes are performed for different snow types, such as dry snow, wet snow, and powder snow, and for different initial compaction states, such as snow with a compaction degree of 50%, 70%, and 90%. For example, for dry snow with an initial compaction degree of 70%, microstructural parameters are obtained through industrial computed tomography, a cross-scale mechanical property evolution model is established, and simulation calculations are performed.

[0058] The system stores structured data on various microstructural parameters, such as initial porosity and ice crystal size distribution; thermo-coupled load histories, such as temperature change curves and load application methods; and their corresponding macroscopic mechanical property evolution data, such as changes in load-bearing capacity over time and the development of deformation. A database management system can be used to classify, organize, and index the data for easy retrieval.

[0059] When conducting new layered design, similar case data is retrieved from the database based on characteristics such as snow type, initial compaction state, temperature range, and load magnitude of the current target working condition. For example, if the current design uses dry snow, has an initial compaction degree of 75%, a temperature range of -20℃ to -5℃, and a load of 200N, similar cases can be retrieved with dry snow, an initial compaction degree of 70%, a temperature range of -18℃ to -6℃, and a load of 180N.

[0060] The retrieved layering schemes are used as initial solutions for iterative optimization, such as the layer thickness and initial density configuration in this case, and substituted into the optimization process. Since the initial solution is close to the optimal solution, the number of iterations can be reduced, optimization efficiency can be improved, and the design cycle can be shortened. Furthermore, the more data accumulated in the database, the greater the likelihood of finding similar cases, and the more significant the improvement in optimization efficiency.

[0061] In summary, by establishing a cross-scale mechanical property evolution model, the microscopic mechanisms of ice crystal sintering, particle creep, and fatigue damage of snow materials under long-term load and temperature are accurately captured, solving the problem of performance prediction deviations caused by the inability of existing macroscopic models to reflect microscopic evolution. By constructing a quantitative mapping relationship between microscopic structural parameters and macroscopic mechanical properties, combined with thermo-coupling load history simulation, the performance evolution data of the overlay can be accurately obtained. Based on multi-objective optimization, iterative optimization of the layering scheme can determine the reasonable configuration of the thickness and initial density of each layer, ensuring the load-bearing capacity and deformation coordination of the ice-snow composite system. The establishment of a snow material performance parameter database can also improve design efficiency, ultimately enhancing the long-term stability and engineering reliability of the snow surface overlay of the ice structure load-bearing body, meeting the functional requirements of cold-region engineering and ice and snow facilities.

[0062] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0063] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A layered design method for snow surface layering on ice-supported structures, characterized in that, include: S1. Based on the target working conditions and environmental data, determine the design constraints and performance indicators of the snow surface overlay layer; S2. Obtain the microstructure parameters of the snow material to be laid, including initial porosity, ice crystal size distribution, coordination number and contact geometry. S3. Establish a cross-scale mechanical performance evolution model for the snow surface overlay, wherein the model is used to establish a quantitative mapping relationship between the microstructure parameters and the macroscopic mechanical performance parameters; S4. Based on the cross-scale mechanical performance evolution model, input the thermo-mechanical coupling load history corresponding to the target working condition, perform numerical simulation on the long-term macroscopic mechanical response of the snow surface overlay layer, and obtain its performance evolution data. S5. Based on the performance evolution data, with the performance index as the objective function and the design constraints as the boundary, iteratively optimize the layering scheme of the snow surface overlay layer to determine the thickness and initial density configuration of each layer. The establishment of the cross-scale mechanical performance evolution model of the snow surface overlay also includes: Construct representative volumetric units that can characterize the microscopic geometric features of snow material; Within the representative volume unit, a micromechanical behavior model considering ice crystal sintering, particle creep, and fatigue damage is established. By applying a macroscopic strain field to the representative volume element and performing numerical homogenization calculations, the macroscopic equivalent constitutive relation of the snow surface overlay is obtained.

2. The snow surface layering design method for ice structure load-bearing bodies as described in claim 1, characterized in that, The acquisition of the microstructure parameters of the snow to be laid specifically includes: Industrial computed tomography was performed on samples of the snow to be laid to obtain three-dimensional digital image data. The three-dimensional digital image data is binarized and geometrically reconstructed to generate a refined three-dimensional digital model of the snow material. Based on the three-dimensional digital model, image analysis algorithms are used to extract the initial porosity, ice crystal size distribution function, average coordination number between ice crystal particles, and contact neck radius distribution.

3. The snow surface layering design method for ice structure load-bearing bodies as described in claim 1, characterized in that, The establishment of a micromechanical behavior model considering ice crystal sintering specifically includes: Based on temperature and stress state, determine the sintering driving force at the contact point of ice crystal particles; A governing equation for the evolution of the contact neck radius over time was established, which is related to surface energy, grain boundary energy, and water vapor diffusion coefficient. The connection relationship and contact stiffness between particles within the representative volume unit are updated in real time to reflect the enhanced mechanical properties caused by ice crystal sintering.

4. The snow surface layering design method for ice structure load-bearing bodies as described in claim 3, characterized in that, The governing equation for the evolution of the contact neck radius over time is as follows: , Where x represents the contact neck radius at time t. The initial contact neck radius is represented by , n is the sintering mechanism exponent, which ranges from 2 to 5; K is the material-related sintering rate constant. denoted as , where is the apparent activation energy of the sintering process; R is the ideal gas constant; t' is the integral time variable of the sintering process, and dt' is the differential element corresponding to the time variable; T(t') is the absolute temperature that varies with time.

5. The snow surface layering design method for ice structure load-bearing bodies as described in claim 1, characterized in that, The establishment of the micromechanical behavior model considering particle creep specifically includes: In the ice crystal particle contact model of the representative volume element, normal and tangential contact force components based on power-law creep constitutive model are introduced; The normal and tangential contact force components are used to describe the irreversible deformation of the contact area caused by dislocation motion and diffusion flow under sustained load. Based on the load history and temperature history of the target working condition, the creep displacement at each contact point is calculated cumulatively, and the overall geometric configuration of the representative volume element is updated.

6. The snow surface layering design method for ice structure load-bearing bodies as described in claim 5, characterized in that, The strain rate corresponding to the power-law creep constitutive model Obtain it using the following formula: , Where A is the creep coefficient. The equivalent stress is given by m, which is the stress exponent and ranges from 1 to 4. R is the activation energy of the creep process; T is the ideal gas constant; and T is the absolute temperature. Based on the strain rate, calculate at the time step The creep strain increment within the particle is applied to the relative displacement of the particle contact.

7. The snow surface layering design method for ice structure load-bearing bodies as described in claim 1, characterized in that, The establishment of the micromechanical behavior model considering fatigue damage specifically includes: A damage state variable D is defined at the contact point of the ice crystal particles in the representative volume unit; Based on the stress amplitude and loading number of cyclic loads, the evolution rule of the damage state variable D is established; When the accumulated damage state variable D at any contact point reaches the preset critical damage threshold, it is determined that the contact point has fractured, and the contact connection is disconnected in the model to reflect the degradation of material stiffness.

8. The snow surface layering design method for ice structure load-bearing bodies as described in claim 7, characterized in that, The evolution rule of the damage state variable D is as follows: For the Nth load cycle, the damage increment Obtain it using the following formula: , in, This represents the cumulative damage at the end of the previous cycle; This represents the stress amplitude of the current cycle; is the fatigue strength coefficient of the material; p is the fatigue damage index, which ranges from 2 to 8; The critical damage threshold is set to 1.

9. The snow surface layering design method for ice structure load-bearing bodies as described in claim 1, characterized in that, The iterative optimization of the layering scheme for the snow surface overlay specifically includes: Define a multi-objective optimization function that includes load-bearing capacity deviation, deformation compatibility, and cumulative damage level; A multi-objective genetic algorithm was used, with the thickness and initial density of each layer as optimization variables; In each iteration, the cross-scale mechanical performance evolution model is invoked for simulation calculation to obtain the performance index under the current combination of optimization variables; The fitness value of the multi-objective optimization function is calculated, and new combinations of optimization variables are generated through selection, crossover, and mutation operations. When the change in the fitness value converges to within the preset convergence tolerance, the iteration terminates, and the current optimal combination of optimization variables is determined as the final hierarchical design scheme.

10. The snow surface layering design method for ice structure load-bearing bodies as described in claim 1, characterized in that, It also includes establishing a database of snow performance parameters, the establishment of which includes: For different types of snow and snow materials in their initial compaction state, the process of establishing a cross-scale mechanical property evolution model of the snow surface overlay and numerically simulating the long-term macroscopic mechanical response of the snow surface overlay is performed offline, as described in any one of claims 1 to 8. Structured storage of data on different microstructural parameters, thermo-mechanical coupled load history, and their corresponding macroscopic mechanical performance evolution. When performing a new hierarchical design, firstly, case data similar to the current target working condition is retrieved from the database, and the retrieved hierarchical scheme is used as the initial solution for the iterative optimization described in claim 9, so as to improve the optimization efficiency.

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