Method for calculating depth of ice body bearing working area under vertical concentrated load
By establishing an ice damage evolution model and an energy dissipation correlation model, the microscopic damage evolution of ice is simulated, and the depth of the bearing working zone is numerically iteratively solved. This solves the deviation caused by neglecting microscopic fragmentation behavior in traditional methods and improves the accuracy and safety of ice-based structure design.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- RES INST OF HIGHWAY MINIST OF TRANSPORT
- Filing Date
- 2026-02-27
- Publication Date
- 2026-06-05
Smart Images
Figure CN122154304A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of ice bearing capacity analysis technology, specifically a method for calculating the depth of the ice bearing working zone under vertical concentrated load. Background Technology
[0002] In polar engineering, cold-region architecture, and ice-related structural design, determining the depth of the load-bearing working zone of an ice body under concentrated vertical loads is a crucial fundamental task. This depth refers to the vertical extension of the area within the ice body that primarily bears and transmits the load, and its accurate estimation directly affects the safety and stability of the ice-based structure. Traditional analysis methods typically treat the ice body as a homogeneous continuous medium and approximate the working zone depth based on elasticity theory or empirical formulas. These methods can provide a certain degree of reference for engineering design.
[0003] However, existing computational methods generally rely on macroscopic mechanical responses while neglecting the control mechanism of the progressive fragmentation behavior of ice at the microscale on the formation of the working zone depth. Specifically, as a brittle material, the initiation and propagation of microcracks within ice under concentrated loads significantly affect the development depth and morphology of the actual load-bearing area. Current methods do not fully consider this damage evolution process related to loading rate and the brittleness of ice, resulting in a significant deviation between the theoretical calculated depth and the actual load-bearing range in actual high-speed or dynamic loading scenarios. Consequently, they cannot accurately reflect the actual working zone depth under the critical failure state of ice, limiting the applicability of computational methods in fine design and safety assessment. Summary of the Invention
[0004] To address the shortcomings of existing technologies, this invention provides a method for calculating the depth of the ice body's bearing capacity under vertical concentrated loads. This method solves the problem that traditional methods rely on macroscopic mechanical responses and neglect the microscopic progressive fragmentation behavior of ice bodies, leading to significant deviations between theoretical and actual bearing capacities in dynamic loading scenarios.
[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for calculating the depth of the ice-bearing working zone under vertical concentrated load, the method comprising: S1. Establishing an ice body damage evolution model. Specifically, S1 includes: S11. Introduce a damage variable D related to the stress state and loading rate of the ice body. The damage variable D ranges from 0 to 1, where 0 indicates that the ice material is undamaged and 1 indicates that the ice material completely loses its load-bearing capacity. S12. Determine the damage evolution rate of damage variable D. The damage evolution rate is jointly determined by the current stress level, the current loading rate, and the current damage state. The damage evolution rate is used to quantitatively describe the initiation and propagation process of microcracks in ice. S2. Determine the correlation model between energy dissipation and the depth of the bearing working area. Specifically, the correlation model in S2 includes: S21. Define the bearing working area as the ice body where the damage variable D is less than the critical damage value under vertical concentrated load. However, the area still participates in the main stress transfer; S22. Establish the energy balance relationship within the ice body. The energy balance relationship uses the total input energy, elastic strain energy, and damage dissipation energy as variables. The development depth of the bearing working area is directly related to the process by which the work done by the load is converted into the ice body's fractured new surface energy and other dissipated energy. S3. Calculate the depth of the critical load-bearing working zone, specifically including: S31. Couple the damage evolution model of S1 to the energy correlation model of S2; S32. Solve the coupled model through numerical iteration; S33. Under the given vertical concentrated load P and loading rate, simulate the spatiotemporal evolution of the damage field D inside the ice body under the load. S34. When the damage field tends to stabilize, determine the damage variable D by extending it downwards from the load-bearing surface to equal the critical damage value. The depth at which the ice body is located is determined, and this depth is used as the final calculated depth h of the ice body bearing working area.
[0006] Furthermore, the introduction of the damage variable D related to the ice stress state and loading rate in S11 specifically includes: Based on the brittle properties of ice, the damage variable D is determined as a dimensionless parameter characterizing the degree of damage to ice materials. Stress states include, but are not limited to, principal stress states, shear stress states, or equivalent stress states.
[0007] Furthermore, determining the damage evolution rate of the damage variable D in S12 specifically includes: Calculate the rate of change of damage variable D over time based on the current stress level, current loading rate, and current damage state; The mathematical expression for damage evolution rate takes into account stress intensity factor, crack propagation rate, and material toughness parameters.
[0008] Furthermore, the load-bearing working area defined in S21 is defined as the area where the damage variable D within the ice body is less than the critical damage value under a vertical concentrated load. However, the areas that still participate in the main stress transfer include: Determine the critical damage value A preset constant between 0 and 1, the critical damage value The damage threshold that indicates when macroscopic damage begins to occur in ice materials; The load-bearing working zone is defined as the area at the critical damage value. Below, the ice body can still maintain its main load-bearing function in the area.
[0009] Furthermore, establishing the energy balance within the ice body in S22 specifically includes: The total input energy is determined to be the work done on the ice body by the vertical concentrated load P during its operation; The elastic strain energy is defined as the energy stored in the ice body during the elastic deformation stage. Damage dissipation energy is defined as the energy dissipated by ice bodies during damage evolution through the initiation and propagation of microcracks.
[0010] Furthermore, the determination of the damage dissipation energy specifically includes: The newly formed surface energy of ice body breakage is calculated, and it is related to the total surface area and surface energy density of the microcracks. Calculate other dissipated energy, including plastic deformation energy, frictional energy, and thermal energy.
[0011] Furthermore, the step of S32, which involves solving the coupled model through numerical iteration, specifically includes: Set the initial time step and spatial grid, and discretize the interior of the ice body; Within each time step, the damage variable D of each discrete element inside the ice body is updated according to the loading rate and stress state; The update process is repeated until the change in the damage variable D is less than the preset threshold over consecutive time steps.
[0012] Furthermore, the simulation of the spatiotemporal evolution of the damage field D inside the ice body under the given vertical concentrated load P and loading rate in S33 specifically includes: A vertical concentrated load P is applied to the surface area of the ice body; Based on the finite element method or finite difference method, solve the coupled model to obtain the distribution of damage variable D at different locations and times inside the ice body; The simulation process takes into account the dynamic effects of the load and the nonlinear behavior of the ice material.
[0013] Furthermore, in S34, when the development of the damage field tends to stabilize, specifically: When no new significant damage is generated inside the ice body, or when the growth rate of the damage variable D inside the ice body is lower than the preset stability criterion, it is judged that the development of the damage field tends to be stable. Stability criteria can be determined based on the trend of changes in the average or maximum value of the damage variable D.
[0014] Furthermore, in step S34, the damage variable D is determined to extend downwards from the load-bearing surface to a value equal to the critical damage value. The depth at which the ice body is located is used as the final calculated depth h of the ice body bearing capacity working zone, specifically including: Scan the damage field D inside the ice body along the depth direction consistent with the direction of the vertical concentrated load; In the damage field D, the damage variable D first reaches or exceeds the critical damage value. The depth position; The depth position is taken as the working depth h of the ice body's bearing area.
[0015] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention establishes a damage evolution model related to the stress state and loading rate of ice, introduces damage variables and determines their evolution rate, quantitatively describes the microscopic progressive fracture behavior of microcrack initiation and propagation, and makes up for the shortcomings of traditional methods that ignore this behavior; then, it constructs a correlation model between energy dissipation and the depth of the bearing working zone, defines the bearing working zone and establishes a balance relationship between total input energy, elastic strain energy and damage dissipation energy, and realizes the coupling of macroscopic energy and microscopic damage; finally, it solves the coupling model numerically and iteratively to simulate the spatiotemporal evolution of the damage field, and takes the depth at which the damage variable reaches the critical value as the depth of the bearing working zone, effectively solving the problems of traditional methods relying on macroscopic mechanical response and significant deviations between theory and actual bearing range under dynamic loading, and improving the accuracy of calculation. 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 method for calculating the depth of the working zone of ice body under vertical concentrated load, the method comprising: S1. Establishing an ice body damage evolution model. Specifically, S1 includes: S11. Introduce damage variables related to the stress state and loading rate of the ice body. Damage variables The value range is from 0 to 1, where 0 indicates that the ice material is undamaged and 1 indicates that the ice material has completely lost its load-bearing capacity. S12. Determine damage variables The damage evolution rate is determined by the current stress level, current loading rate, and current damage state. The damage evolution rate is used to quantitatively describe the initiation and propagation process of microcracks in ice. S2. Determine the correlation model between energy dissipation and the depth of the bearing working area. Specifically, the correlation model in S2 includes: S21. Define the bearing working area as the damage variable within the ice body under vertical concentrated load. Less than the critical damage value However, the area still participates in the main stress transfer; S22. Establish the energy balance relationship within the ice body. The energy balance relationship uses the total input energy, elastic strain energy, and damage dissipation energy as variables. The development depth of the bearing working area is directly related to the process by which the work done by the load is converted into the ice body's fractured new surface energy and other dissipated energy. S3. Calculate the depth of the critical load-bearing working zone, specifically including: S31. Couple the damage evolution model of S1 to the energy correlation model of S2; S32. Solve the coupled model through numerical iteration; S33, under a given vertical concentrated load Simulated damage field inside ice body under loading conditions and loading rate. The spatiotemporal evolution; S34. When the damage field tends to stabilize, determine the damage variables. Extending downwards from the load-bearing surface to a value equal to the critical damage value. The depth at which the ice body is located is used as the final calculated depth of the ice body bearing capacity working area. .
[0019] Specifically, damage variables are introduced. At that time, taking into account the brittle nature of ice, Defined as a dimensionless parameter characterizing the influence of microcracks on load-bearing capacity, with a value ranging from 0 to 1. It relates to the microscopic mechanism based on microcrack density. Microcrack characteristic length and stress state construction The expression:
[0020] In the formula, The correction factor is set to, for example, 0.8 to 1.2; in this embodiment, it is set to 1.0 to match the brittleness characteristics of ice. Microcrack density, The characteristic length of the microcrack. This refers to the microcrack density parameter; The equivalent stress corresponding to the current stress state of the ice body can be represented by, for example, the von Mises equivalent stress can be used to characterize the stress state, or the principal stress or shear stress state can be selected according to the engineering scenario. This represents the uniaxial compressive strength of the ice body at a corresponding loading rate, for example, at a loading rate of 10 mm / s in an environment of -10℃. Take 8 MPa. This formula correlates the degree of damage with microscopic parameters, overcoming the limitation of traditional methods that only consider macroscopic responses.
[0021] When determining the damage evolution rate, it is necessary to reflect the influence of multiple factors on microcrack propagation, and the mathematical expression should include the stress intensity factor. Crack propagation rate and material toughness parameters : , In the formula, Damage evolution rate, characterizing Rate of change over time; For example, take the material characteristic constants. In this embodiment, ; This is a damage state correction term; the lower the damage level, the larger the correction term, which conforms to the nonlinear characteristics of damage accumulation. The stress intensity factor is calculated based on the microcrack geometry and stress distribution under the current stress state. To assess the fracture toughness of ice, for example, by taking samples at -15°C. ; This represents the current loading rate, for example, 520 mm / s in a dynamic loading scenario; For reference loading rate, for example, take 1 mm / s, to normalize the loading rate and ensure dimensionless; , The evolution index, Take 24, Take 1~2, in this embodiment Take 3, The value was set to 1.5, and the formula was calibrated through indoor testing. This formula quantitatively describes the dynamic process of microcracks, overcoming the deficiency of traditional methods that do not consider the correlation between loading rate and brittle damage.
[0022] When defining the load-bearing working area, it is considered that the ice body may still participate in stress transfer after damage, and it is defined as Less than the critical damage value However, it is in the area that participates in the main stress transfer. A preset constant between 0 and 1 represents the damage threshold at which the ice begins to macroscopically break down; for example, it is set to 0.2~0.4, and in this embodiment, it is set to 0.3. Less than When the elastic modulus of the ice element decreases by no more than 50%, it can still transmit more than 80% of the load stress, and is therefore judged to participate in the main stress transmission; when Reaching or exceeding At that time, obvious macroscopic cracks appeared in the unit, the load-bearing capacity was greatly reduced, and it was no longer included in the load-bearing working area.
[0023] When establishing an energy balance relationship, the total input energy For vertical concentrated loads Work done on ice, elastic strain energy Energy stored during the elastic deformation phase of ice, damage dissipation energy The energy dissipated for microcrack initiation and propagation satisfies the following three conditions: , In the formula, The total input energy is calculated as follows: , This represents the total displacement at the point of application of the load. For the displacement to reach Vertical concentrated load at that time; The elastic strain energy is calculated based on the elastic modulus under damage conditions, and its expression is as follows: , For stress tensor, For elastic strain tensor, The computational domain volume for the ice body; The energy dissipated due to damage is directly related to the depth of the working zone; the deeper the working zone, the larger the microcrack propagation range. The larger the value, the greater the relationship. This connection links macroscopic energy with microscopic damage dissipation, providing a theoretical basis for deep computing.
[0024] When constructing the coupling model, the damage evolution model of S1 is coupled to the energy correlation model of S2. Specifically, in the energy balance relationship, the elastic strain energy Introducing damage variables The effect of damage state elastic modulus , To maintain the elastic modulus of the ice body without damage, while simultaneously dissipating energy through damage. Through damage evolution rate Integral calculations enable dynamic coupling between damage and energy dissipation.
[0025] In numerical iterative solutions, the computational domain of the ice body is discretized using the finite element method, for example, by setting the initial time step to... In this embodiment, The spatial mesh uses hexahedral elements with an element size of 3-8 mm; in this embodiment, 5 mm is used. The ice computational domain size is set to 1m × 1m × 0.6m (length × width × height), covering the main damage area. The iteration process is as follows: Initial time... Ice body undamaged Apply an initial load increment; calculate the load displacement increment based on the loading rate within each time step. The stress state of each element is obtained by combining the stress-strain relationship; the damage evolution rate formula of S12 is used to update the stress state of each element. According to the new Adjusting the unit elastic modulus Recalculate the stress and energy distribution; repeat the above steps until all elements within three consecutive time steps are recalculated. The maximum change is less than The iteration is determined to be converged.
[0026] When simulating the spatiotemporal evolution of the damage field, a vertical concentrated load is given. and loading rate, for example In this embodiment, 50kN is used, and the loading rate is 8~15mm / s. In this embodiment, 10mm / s is used to simulate a dynamic loading scenario. The load is applied to the central region of the upper surface of the ice body, with an effective area of... Based on the coupled model, finite element software such as ABAQUS was used to solve the problem, obtaining results at different times (e.g., 0.02s, 0.05s, 0.1s) and different depths (e.g., 0mm, 30mm, 60mm). Distribution. The simulation incorporates an inertial force term to account for dynamic load effects, through... For elastic modulus The effect reflects the nonlinear behavior of ice bodies, and the damage can be clearly observed to extend downward from the load surface, solving the problem that traditional methods cannot simulate the spatiotemporal evolution of damage.
[0027] Determine the depth of the bearing working area When the damage field stabilizes, meaning no new significant damage is generated within the ice body (e.g., the proportion of newly added damaged units to the total number of units is less than 0.1% over five consecutive time steps), the damage field within the ice body is scanned vertically downwards along the direction of the concentrated vertical load. For example, starting from a depth of 0mm on the load-bearing surface, extract depths at 1mm intervals. Value, when scanning to a certain depth First time reaching This embodiment This depth is This method yields... It can accurately reflect the actual bearing capacity under the critical failure state of ice, and the calculation deviation is significantly reduced in dynamic loading scenarios, thus improving the applicability of the method in fine design and safety assessment.
[0028] In this embodiment, damage variables related to the ice stress state and loading rate are introduced in S11. Specifically, it includes: Determine damage variables based on the brittle properties of ice. A dimensionless parameter characterizing the degree of damage to ice materials; Stress states include, but are not limited to, principal stress states, shear stress states, or equivalent stress states.
[0029] Specifically, S11 introduces damage variables. At this time, further refinement is needed, taking into account the brittle characteristics of ice: damage variables As a characterization of the degree of damage to ice, its physical significance can be verified through microscopic experiments. For example, by observing the microcrack morphology of ice under different stresses and loading rates using cryogenic scanning electron microscopy, it can be discovered that... The area density of microcracks is positively correlated with the length of microcracks per unit area, therefore, this can be established through laboratory experiments. The relationship between the calibration and microscopic parameters.
[0030] The choice of stress state needs to be determined based on the engineering scenario. For example, in the design of polar ice-based pile foundations, when the ice body is subjected to a concentrated vertical load from the pile, the ice body around the pile experiences shear stress. The primary stress state can be selected as shear stress. In the ice-bearing capacity analysis of building foundations in cold regions, the ice body is mainly subjected to compressive stress, and the stress state can be selected as principal compressive stress. Regardless of the stress state chosen, normalization is required to ensure consistency with the damage variable. The expressions for shear stress have consistent dimensions, for example, shear stress. Divide by the shear strength of the ice body The dimensionless shear stress ratio is obtained. Substitute In the calculation formula.
[0031] In this embodiment, determining the damage variable in S12 The damage evolution rate specifically includes: Calculate the damage variables based on the current stress level, current loading rate, and current damage state. Rate of change over time; The mathematical expression for damage evolution rate takes into account stress intensity factor, crack propagation rate, and material toughness parameters.
[0032] Specifically, when determining the damage evolution rate, S12 needs to further clarify the physical meaning and value logic of each parameter in the mathematical expression based on the current stress level, current loading rate, and current damage state: Damage evolution rate The mathematical expression can be refined as follows: , In the formula, This is the stress intensity factor for Type I cracks, also known as open cracks. Ice bodies primarily develop this type of crack under vertical concentrated loads. Its calculation formula is: , This is half the length of the microcrack. The crack propagation rate is determined by indoor crack propagation tests, for example, at a stress intensity factor. hour, Pick ; For reference, take the crack propagation rate, for example... , is used for normalization; the meanings of the remaining parameters are the same as in the above implementation.
[0033] During the calculation process, it is necessary to first obtain the stress level corresponding to the current stress level through stress analysis. Combined with the experimental measurements and Relationship determination The value of is then substituted into the formula for calculation. For example, when , , , , , , ,current When, it can be calculated .
[0034] In this embodiment, the defined bearing working area in S21 is the damage variable within the ice body under vertical concentrated load. Less than the critical damage value However, the areas that still participate in the main stress transfer include: Determine the critical damage value A preset constant between 0 and 1, the critical damage value The damage threshold that indicates when macroscopic damage begins to occur in ice materials; The load-bearing working zone is defined as the area at the critical damage value. Below, the ice body can still maintain its main load-bearing function in the area.
[0035] Specifically, when defining the load-bearing working area in S21, the critical damage value needs to be further clarified. The method for determining the carrying work area and its functional characteristics: Critical damage value This needs to be calibrated through indoor mechanical testing. For example, vertical concentrated load tests can be conducted using ice samples of different sizes to monitor the stress-strain curves and microcrack development during the loading process. When the stress-strain curve shows the first obvious inflection point, i.e., the macroscopic yield point, the corresponding damage variable is... In this embodiment, it was determined through experiments. . A preset constant between 0 and 1, for different temperatures and ice densities. Individual calibration is required, for example, at -5°C the ice has a lower density and is less brittle. A value of 0.38 is acceptable; at -20℃, the ice has a higher density and is more brittle. 0.28 is acceptable.
[0036] The "participation in major stress transfer" of the bearing working area can be quantified through stress transfer efficiency, for example, when the ice element... Less than When the stress transfer efficiency of the element, i.e., the ratio of the actual stress transferred to the stress transferred under the undamaged state, is greater than 75%, it can be determined that it participates in the main stress transfer; when achieve When the stress transfer efficiency drops below 50%, the element loses its main load-bearing capacity.
[0037] In this embodiment, the establishment of the energy balance relationship within the ice body in S22 specifically includes: The total input energy is determined to be a vertical concentrated load. The work done on the ice during the process; The elastic strain energy is defined as the energy stored in the ice body during the elastic deformation stage. Damage dissipation energy is defined as the energy dissipated by ice bodies during damage evolution through the initiation and propagation of microcracks.
[0038] Specifically, when establishing the energy balance relationship in S22, the total input energy needs to be clearly defined. Elastic strain energy and damage dissipation energy Calculation details: Total input energy For vertical concentrated loads The work done on the ice body is considered if the load and displacement have a linear relationship during the loading process, such as in the initial stage of quasi-static loading. The calculation formula can be simplified to ,in, For the final applied vertical concentrated load, This corresponds to the total displacement; if it is dynamic loading, the load and displacement have a non-linear relationship, so it needs to be calculated by integration, for example, by using a displacement sensor to collect the displacement of the load application point in real time, combined with the data collected by the load sensor. The value is obtained through numerical integration, such as the trapezoidal integral method. .
[0039] elastic strain energy The calculation needs to consider the effect of damage on the elastic modulus, that is, the damaged elastic modulus should be used. ,in, The elastic modulus of the undamaged ice body, for example at -10°C. Take 9 GPa, therefore The expression can be refined to The total elastic strain energy is obtained by integrating over the entire computational domain. .
[0040] Damage dissipation energy Total input energy With elastic strain energy The difference, i.e. Its physical meaning is the energy used to generate microcracks and overcome crack propagation resistance during the work done by the load. It directly reflects the degree of ice damage and is used to determine the depth of the subsequent load-bearing working zone. Provides energy indicators.
[0041] In this embodiment, the determination of damage dissipation energy specifically includes: The newly formed surface energy of ice body breakage is calculated, and it is related to the total surface area and surface energy density of the microcracks. Calculate other dissipated energy, including plastic deformation energy, frictional energy, and thermal energy.
[0042] Specifically, damage dissipation energy The determination needs to be further subdivided into ice body breakup and newly formed surface energy. Other dissipated energy The calculation is as follows: Ice fragmentation and newly generated surface energy Total surface area of microcracks and surface energy density Related, its calculation formula is: , In the formula, The surface energy density of ice, for example at -15°C. Pick In this embodiment, ; The total surface area of the microcracks can be determined by damage variables. Calculated, for example, based on microscopic models, and The relationship is ,in The computational domain volume of the ice body. Let's take the average half-length of the microcrack, for example... In this embodiment, This formula can be used to represent macroscopic damage variables. Transformed into the surface area of microcracks at the microscopic level. .
[0043] Other dissipated energy Including plastic deformation energy Energy includes frictional energy and thermal energy, among which plastic deformation energy... It accounts for the largest proportion, and its calculation formula is: , In the formula, For plastic stress tensor, The plastic strain tensor is calculated using a damage-plastic constitutive model; frictional energy mainly arises from the relative sliding between microcrack surfaces and can be calculated by introducing a friction coefficient (e.g., 0.1~0.2) and sliding displacement; thermal energy accounts for a small proportion and can be approximately estimated using the energy conservation principle. .
[0044] In this embodiment, the numerical iteration solution of the coupled model in S32 specifically includes: Set the initial time step and spatial grid, and discretize the interior of the ice body; Within each time step, the damage variable of each discrete element inside the ice body is updated according to the loading rate and stress state. ; Repeat the update process until the damaged variable is removed. The change is less than a preset threshold within a continuous time step.
[0045] Specifically, when S32 solves the coupled model through numerical iteration, it is necessary to refine the discretization method and the iterative convergence criterion, as follows: When setting the initial time step and spatial grid, the time step needs to be based on the loading rate. Determine, for example, loading rate To ensure the capture of the dynamic evolution of damage at a speed of 10 mm / s, the initial time step is set to... If the damage changes gradually during the iteration process, the time step can be appropriately increased, such as not exceeding a maximum of The spatial grid uses a structured grid to discretize the ice body computational domain. For example, for a computational domain of 1m×1m×0.6m, 200 elements are divided along the length and width directions, and 120 elements are divided along the depth direction. The element size is 5mm. This ensures that the grid density in the load-bearing area and the damage concentration area is high enough. The grid density in the non-damaged area can be appropriately reduced to improve computational efficiency.
[0046] Update the damage variable at each time step. The process is as follows: First, based on the current loading rate Calculate the displacement increment within this time step. Combined with the damage elastic modulus Obtain stress increment Then Substituting into the damage evolution rate formula of S12, the damage increment within this time step is calculated. Finally, update each unit. Value And according to the new Value adjustment Then proceed to the next time step calculation.
[0047] The criterion for iterative convergence is that the damage variables of all elements within three consecutive time steps are equal. The maximum change is less than If within a certain time step Exceed If the time step is reduced, such as by halving, then the calculation needs to be repeated to ensure iterative stability.
[0048] In this embodiment, S33 refers to a given vertical concentrated load. Simulated damage field inside ice body under loading conditions and loading rate. The spatiotemporal evolution specifically includes: Vertical concentrated load Apply to the surface area of the ice body; Based on the finite element method or finite difference method, the coupled model is solved to obtain the damage variables at different locations and times inside the ice body. distributed; The simulation process takes into account the dynamic effects of the load and the nonlinear behavior of the ice material.
[0049] Specifically, when simulating the spatiotemporal evolution of the damage field in S33, it is necessary to clarify the load application method, numerical solution method, and consideration of key influencing factors, as follows: Vertical concentrated load When applying loads to the surface area of ice, it is necessary to simulate the load action in actual engineering, such as using a uniformly distributed load to equivalent vertical concentrated loads. The area of effect is circular, with its diameter determined based on the engineering scenario. For example, if the pile diameter of a polar ice-based pile foundation is 0.5m, then the diameter of the load-bearing area is taken as 0.5m, and the area of effect is... The load size is set according to design requirements, for example... .
[0050] When solving the coupled model based on the finite element method, an explicit dynamic solver such as ABAQUS / Explicit is used to adapt to the inertial effect under dynamic loading scenarios. The material constitutive model adopts the damage elastic constitutive model. The damage evolution model established by S1 is written as a user-defined material subroutine, namely UMAT, and embedded in the finite element software. The boundary conditions are set to a fixed displacement of 0 at the bottom of the ice body and free boundaries around it to simulate the constraint state of the actual ice body.
[0051] The dynamic effects of the load considered in the simulation are specifically addressed by introducing an inertial force term. ,in, For example, take the density of ice. , The acceleration at the point of application of the load is monitored in real time by an accelerometer and substituted into the calculation; the nonlinear behavior of the ice material is specifically manifested as a damage variable. When it increases, the elastic modulus The nonlinear decrease means that the stress-strain relationship no longer satisfies linear elasticity. Through this nonlinear description, the entire process of ice body from elastic deformation to damage propagation during loading can be accurately simulated.
[0052] In this embodiment, when the development of the damage field tends to stabilize in S34, specifically: When no new significant damage is generated inside the ice body, or the damage variables inside the ice body... The trend of the average or maximum value is used to make a judgment.
[0053] Specifically, when S34 determines that the damage field is stabilizing, the specific form and determination process of the stability criterion need to be clarified, as follows: Stability criteria can be based on damage variables average or maximum value The trend of change can be determined, for example, by using one of the following two criteria: Criterion 1: Based on The trend of maximum value change. Calculate the maximum value of all cells within the ice computational domain at each time step. Maximum value When within 5 consecutive time steps Change All less than At that time, it is determined that the damage field development tends to stabilize. For example... hour , hour , hour Within 5 consecutive time steps All less than The stability condition is met.
[0054] Criterion 2: Based on the proportion of newly added damage units. Newly added damage units are defined as those within the current time step. The value increased by more than [amount] compared to the previous time step. For each element, calculate the proportion of newly damaged elements to the total number of elements. When within 5 consecutive time steps When all values are less than 0.1%, the damage field is considered stable. For example, if the total number of elements is... The number of newly added damage units within a certain time step is 3200. If the value is less than 0.1%, and this condition is met for five consecutive time steps, the system can be considered stable.
[0055] In practical applications, two criteria can be used simultaneously. When either criterion is satisfied, the damage field can be considered stable, thereby improving the flexibility and reliability of the judgment.
[0056] In this embodiment, determining the damage variable in S34 Extending downwards from the load-bearing surface to a value equal to the critical damage value. The depth at which the ice body is located is used as the final calculated depth of the ice body bearing capacity working area. Specifically, it includes: Scan the damage field inside the ice body along the depth direction consistent with the direction of the vertical concentrated load. ; Identify damage field In the middle, damage variables The first time the critical damage value is reached or exceeded The depth position; The depth location is used as the working depth of the ice body's bearing area. .
[0057] Specifically, S34 determines the depth of the ice-bearing working zone. At this time, the depth scanning method and depth location recognition logic need to be refined, as follows: Scan the damage field inside the ice body along the depth direction consistent with the direction of the vertical concentrated load. During scanning, the scanning path must pass through the center of the load-bearing surface, i.e., coincide with the load axis, to ensure that the scanning results reflect the main path of load transfer. The scanning interval is determined based on the spatial grid size. For example, if the element size of the spatial grid along the depth direction is 5mm, then the scanning interval is 1mm. Linear interpolation is used to obtain the non-grid nodes. This increases the scanning accuracy.
[0058] Identify damage variables The first time the critical damage value is reached or exceeded When determining the depth position, linear interpolation is used to determine the precise depth. For example, in depth Place Less than In depth Place Greater than Then, it is calculated by linear interpolation. Depth of time : , Substituting the numerical values, we get This depth is the final working depth of the ice body bearing capacity. .
[0059] If local areas appear during the scan Value fluctuations, for example, at a certain depth Slightly more But at the depth below Smaller than Then it is necessary to use the first three consecutive scanning points below the load application surface. The values all reached or exceeded Depth as This avoids interference from localized micro-cracks in depth determination.
[0060] In summary, this invention establishes a damage evolution model related to the stress state and loading rate of the ice body, introduces damage variables and determines their evolution rate, quantitatively describing the microscopic progressive fracture behavior of microcrack initiation and propagation, thus overcoming the shortcomings of traditional methods that neglect this behavior. Furthermore, it constructs a correlation model between energy dissipation and the depth of the load-bearing working zone, defines the load-bearing working zone and establishes a balance relationship between total input energy, elastic strain energy, and damage dissipation energy, achieving coupling between macroscopic energy and microscopic damage. Finally, it numerically iterates and solves the coupled model to simulate the spatiotemporal evolution of the damage field, using the depth at which the damage variable reaches a critical value as the depth of the load-bearing working zone. This effectively solves the problems of traditional methods relying on macroscopic mechanical response and significant deviations between theoretical and actual load-bearing ranges under dynamic loading, thereby improving computational accuracy.
[0061] 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.
[0062] 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 method for calculating the depth of an ice body bearing working area under the action of a vertical concentrated load, characterized in that, The method includes: S1. Establishing an ice body damage evolution model. Specifically, S1 includes: S11. Introduce a damage variable D related to the stress state and loading rate of the ice body. The damage variable D ranges from 0 to 1, where 0 indicates that the ice material is undamaged and 1 indicates that the ice material completely loses its load-bearing capacity. S12. Determine the damage evolution rate of damage variable D. The damage evolution rate is jointly determined by the current stress level, the current loading rate, and the current damage state. The damage evolution rate is used to quantitatively describe the initiation and propagation process of microcracks in ice. S2. Determine the correlation model between energy dissipation and the depth of the bearing working area. Specifically, the correlation model in S2 includes: S21. Define the bearing working area as the ice body where the damage variable D is less than the critical damage value under vertical concentrated load. However, it still participates in the main stress transfer area; S22. Establish the energy balance relationship within the ice body. The energy balance relationship uses the total input energy, elastic strain energy, and damage dissipation energy as variables. The development depth of the bearing working area is directly related to the process by which the work done by the load is converted into the ice body's fractured new surface energy and other dissipated energy. S3. Calculate the depth of the critical load-bearing working zone, specifically including: S31. Couple the damage evolution model of S1 to the energy correlation model of S2; S32. Solve the coupled model through numerical iteration; S33. Under the given vertical concentrated load P and loading rate, simulate the spatiotemporal evolution of the damage field D inside the ice body under the load. S34. When the damage field tends to stabilize, determine the damage variable D by extending it downwards from the load-bearing surface to equal the critical damage value. The depth at which the ice body is located is determined, and this depth is used as the final calculated depth h of the ice body bearing working area.
2. The method for calculating the depth of the ice-bearing working zone under vertical concentrated load as described in claim 1, characterized in that, The introduction of the damage variable D related to the ice stress state and loading rate in S11 specifically includes: Based on the brittle properties of ice, the damage variable D is determined as a dimensionless parameter characterizing the degree of damage to ice materials. Stress states include, but are not limited to, principal stress states, shear stress states, or equivalent stress states.
3. The method for calculating the depth of the ice-bearing working zone under vertical concentrated load according to claim 2, characterized in that, Determining the damage evolution rate of the damage variable D in S12 specifically includes: Calculate the rate of change of damage variable D over time based on the current stress level, current loading rate, and current damage state; The mathematical expression for damage evolution rate takes into account stress intensity factor, crack propagation rate, and material toughness parameters.
4. The method for calculating the depth of the ice-bearing working zone under vertical concentrated load as described in claim 1, characterized in that, The load-bearing working area defined in S21 is when the damage variable D within the ice body is less than the critical damage value under vertical concentrated load. However, the areas that still participate in the main stress transfer include: Determine the critical damage value A preset constant between 0 and 1, the critical damage value The damage threshold that indicates when macroscopic damage begins to occur in ice materials; The load-bearing working zone is defined as the area at the critical damage value. Below, the ice body can still maintain its main load-bearing function in the area.
5. The method for calculating the depth of the ice-bearing working zone under vertical concentrated load according to claim 4, characterized in that, Establishing the energy balance within the ice body in S22 specifically includes: The total input energy is determined to be the work done on the ice body by the vertical concentrated load P during its operation; The elastic strain energy is defined as the energy stored in the ice body during the elastic deformation stage. Damage dissipation energy is defined as the energy dissipated by ice bodies during damage evolution through the initiation and propagation of microcracks.
6. The method for calculating the depth of the ice-bearing working zone under vertical concentrated load as described in claim 5, characterized in that, The determination of the damage dissipation energy specifically includes: The newly formed surface energy of ice body breakage is calculated, and it is related to the total surface area and surface energy density of the microcracks. Calculate other dissipated energy, including plastic deformation energy, frictional energy, and thermal energy.
7. The method for calculating the depth of the ice-bearing working zone under vertical concentrated load as described in claim 1, characterized in that, The numerical iteration method for solving the coupled model in S32 specifically includes: Set the initial time step and spatial grid, and discretize the interior of the ice body; Within each time step, the damage variable D of each discrete element inside the ice body is updated according to the loading rate and stress state; The update process is repeated until the change in the damage variable D is less than the preset threshold over consecutive time steps.
8. The method for calculating the depth of the ice-bearing working zone under vertical concentrated load according to claim 7, characterized in that, The spatiotemporal evolution of the damage field D inside the ice body under the given vertical concentrated load P and loading rate in S33 specifically includes: A vertical concentrated load P is applied to the surface area of the ice body; Based on the finite element method or finite difference method, solve the coupled model to obtain the distribution of damage variable D at different locations and times inside the ice body; The simulation process takes into account the dynamic effects of the load and the nonlinear behavior of the ice material.
9. The method for calculating the depth of the ice-bearing working zone under vertical concentrated load as described in claim 8, characterized in that, When the development of the damage field in S34 tends to stabilize, specifically: When no new significant damage is generated inside the ice body, or when the growth rate of the damage variable D inside the ice body is lower than the preset stability criterion, it is judged that the development of the damage field tends to be stable. Stability criteria can be determined based on the trend of changes in the average or maximum value of the damage variable D.
10. The method for calculating the depth of the ice-bearing working zone under vertical concentrated load according to claim 9, characterized in that, In step S34, the damage variable D is determined to extend downwards from the load-bearing surface to equal the critical damage value. The depth at which the ice body is located is used as the final calculated depth h of the ice body bearing capacity working zone, specifically including: Scan the damage field D inside the ice body along the depth direction consistent with the direction of the vertical concentrated load; In the damage field D, the damage variable D first reaches or exceeds the critical damage value. The depth position; The depth position is taken as the working depth h of the ice body's bearing area.