A method and system for predicting the permeability coefficient of calcareous sand in an island reef underground fresh water lens model test
By using the permeability similarity criterion and the permeability coefficient prediction model, the problem of imperfect similarity design in island and reef model experiments was solved, and the permeability coefficient was accurately controlled and the experimental results were reliable, supporting the refined simulation of the freshwater lens formation process of islands and reefs.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- INST OF ROCK & SOIL MECHANICS CHINESE ACAD OF SCI
- Filing Date
- 2026-03-27
- Publication Date
- 2026-06-05
AI Technical Summary
Existing island and reef model tests suffer from imperfect similarity design, unreasonable material substitution, and difficulty in accurately controlling the permeability coefficient, making it difficult to reflect the seepage characteristics and seepage patterns of the prototype island and reef.
By establishing a permeability similarity criterion, determining the geometric similarity ratio and the permeability coefficient similarity ratio, a permeability coefficient prediction model is constructed with effective particle size, non-uniformity coefficient, and porosity as input parameters. Orthogonal experimental design is used to obtain gradation parameters and measured permeability coefficients, and the prediction model is solved to determine the sizing scheme of the model calcareous sand.
It achieves precise control of the permeability coefficient, improves the repeatability and comparability of experimental results, avoids the distortion of permeability patterns caused by terrigenous sand substitution, and provides refined simulation support for the formation process and mechanism of freshwater lenses on islands and reefs.
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Figure CN122157907A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the technical field of freshwater lens model testing for coral reef islands, and particularly relates to a method and system for predicting the permeability coefficient of calcareous sand in underground freshwater lens model testing for islands and reefs. Background Technology
[0002] Coral reef islands contain subsurface freshwater zones with a lower density than seawater, suspended above it, and thicker in the middle and thinner at the edges. These are commonly known as "freshwater lenses" and are a core element for vegetation supply and ecological maintenance on coral reef islands. The formation and development of freshwater lenses mainly depend on the infiltration of atmospheric precipitation into calcareous sand aquifers. Therefore, the permeability of calcareous sand aquifers is a key factor influencing the formation, evolution, morphological characteristics, and size of freshwater lenses.
[0003] Model tests have become a common approach for studying the formation process and mechanism of freshwater lenses due to their minimal environmental interference, controllable conditions, high reproducibility, and cost-effectiveness. However, current model tests still have the following shortcomings: First, island and reef model tests primarily use small sand tanks, typically less than 2 meters in size, resulting in a significant size effect and making it difficult to reflect the actual seepage characteristics of the prototype island or reef. Second, some tests use terrigenous sand instead of calcareous sand, making it difficult to characterize the seepage patterns caused by the unique dual-pore structure and particle morphology of calcareous sand. Third, scaled-down model test design and similarity processing are generally lacking, especially methods for preparing similar materials at specific similarity ratios, as well as precise control and prediction methods for permeability coefficients.
[0004] Therefore, it is urgent to establish a method for predicting the permeability coefficient of calcareous sand based on similarity theory, so as to solve the problems of imperfect similarity design, unreasonable material substitution, and difficulty in accurately controlling the permeability coefficient in existing model tests, and provide reliable technical support for the study of the formation mechanism of freshwater lenses in islands and reefs. Summary of the Invention
[0005] To address the aforementioned technical problems, this invention provides a method for predicting the permeability coefficient of calcareous sand in a model test of an underground freshwater lens on an island or reef, comprising the following steps: The geometric similarity ratio is determined based on the geometric scale of the prototype islands and reefs and the geometric scale of the model test. The permeability coefficient similarity ratio is determined based on the geometric similarity ratio and the seepage similarity relationship derived from dimensional analysis. Based on the permeability similarity ratio and the permeability of the prototype calcareous sand, the target permeability of the model calcareous sand is determined. A permeability coefficient prediction model was constructed using effective particle size, non-uniformity coefficient, and porosity as input parameters. The gradation parameters and measured permeability coefficients of calcareous sand samples with different mix proportions were obtained through orthogonal experimental design. Based on the gradation parameters and measured permeability coefficients, the undetermined coefficients in the prediction model are solved to obtain the calibrated permeability coefficient prediction model. Based on the target permeability coefficient and the calibrated permeability coefficient prediction model, determine the proportioning scheme for preparing the model calcareous sand.
[0006] Optionally, determining the geometric similarity ratio includes: The geometric scale of the model test is compared with that of the prototype island, and the ratio of the two is determined as the geometric similarity ratio.
[0007] Optionally, the permeability coefficient similarity ratio is determined based on the geometric similarity ratio and the seepage similarity relationship derived from dimensional analysis, including: Based on dimensional analysis, using density, geometric dimensions, and gravitational acceleration as the basic physical quantities, a dimensional relationship between the permeability coefficient and geometric dimensions is established. Based on dimensional relationships, the first power of the geometric similarity ratio is determined as the permeability coefficient similarity ratio.
[0008] Optionally, a permeability prediction model is constructed using effective particle size, non-uniformity coefficient, and porosity as input parameters, including: Based on the Hazen formula, an undetermined exponential term for the non-uniformity coefficient is introduced as a particle size distribution correction term. An undetermined exponential term of the porosity function based on the Kozeny-Carman equation is introduced as a pore structure correction term; The fixed exponent for effective particle size in the Hazen formula is adjusted to an adjustable parameter; A permeability coefficient prediction model was constructed, which includes a proportionality constant, an effective particle size adjustable index, an undetermined index of the non-uniformity coefficient, and an undetermined index of the porosity function.
[0009] Optionally, based on the gradation parameters and measured permeability coefficients, the undetermined coefficients in the prediction model are solved to obtain the calibrated permeability coefficient prediction model, including: Take the natural logarithm of both sides of the prediction model to transform it into a linear regression model; The effective particle size, non-uniformity coefficient, porosity, and measured permeability coefficient of the calcareous sand samples with different proportions were substituted into the linear regression model. The linear regression model was solved using the least squares method to obtain the specific values of the proportionality constant, the effective particle size adjustable index, the undetermined index of the non-uniformity coefficient, and the undetermined index of the porosity function.
[0010] Optionally, orthogonal experimental design can be used to obtain the gradation parameters and measured permeability coefficients of calcareous sand samples with different mix proportions, including: The calcareous sand was sieved into four particle size groups: coarse sand, medium sand, fine sand, and silt. Using the proportions of the four particle size components as factors, with at least two levels for each factor, an orthogonal experimental design was conducted to obtain multiple formulation schemes; Calcareous sand samples were prepared according to multiple mixing schemes, and the effective particle size, uniformity coefficient, porosity and permeability coefficient of each sample were measured.
[0011] Optionally, orthogonal experimental design may also include: Set proportion constraints, including that the sum of the proportions of coarse sand and medium sand is not equal to 100%, and the sum of the proportions of fine sand and silt is not equal to 100%.
[0012] This invention also provides a system for predicting the permeability coefficient of calcareous sand in a model test of an underground freshwater lens on an island or reef, comprising: The first determining module is used to determine the geometric similarity ratio based on the geometric scale of the prototype island and the geometric scale of the model test. The second determining module is used to determine the permeability coefficient similarity ratio based on the geometric similarity ratio and the seepage similarity relationship derived from dimensional analysis. The third determination module is used to determine the target permeability coefficient of the model calcareous sand based on the permeability coefficient similarity ratio and the permeability coefficient of the prototype calcareous sand. The model building module is used to build a permeability prediction model with effective particle size, non-uniformity coefficient, and porosity as input parameters; The test acquisition module is used to obtain the gradation parameters and measured permeability coefficients of calcareous sand samples with different mix proportions through orthogonal experimental design. The model solving module is used to solve for the undetermined coefficients in the prediction model based on the gradation parameters and the measured permeability coefficient, and obtain the calibrated permeability coefficient prediction model. The proportioning determination module is used to determine the proportioning scheme for preparing the model calcareous sand based on the target permeability coefficient and the calibrated permeability coefficient prediction model.
[0013] Compared with the prior art, the present invention has the following advantages and technical effects: This invention establishes a scientific permeability similarity criterion, clarifying the quantitative relationship between the geometric similarity ratio and the permeability coefficient similarity ratio between the model and the prototype. This provides a theoretical basis for the similarity design of model experiments and solves the core problem of the imperfections in existing experimental similarity designs. The constructed permeability coefficient prediction model comprehensively considers three key parameters: effective particle size, inhomogeneity coefficient, and porosity. By introducing a triple correction term (inhomogeneity coefficient correction term, porosity function correction term, and releasing the effective particle size index), it accurately characterizes the coupling effect of the dual-pore structure and particle size distribution of calcareous sand on permeability characteristics, achieving a prediction accuracy significantly higher than traditional empirical formulas. The proposed similar material proportioning design method, through orthogonal experiments and gradation constraints, achieves directional control of the permeability coefficient, enabling the permeability coefficient of the model calcareous sand to accurately match the target value, thus improving the repeatability and comparability of experimental results. This invention avoids the distortion of permeability patterns caused by the substitution of terrigenous sand, retains the original material properties of calcareous sand, and weakens the influence of size effect through similarity ratio design. It provides key technical support for the refined simulation of the formation process and mechanism of freshwater lenses on islands and reefs, and the experimental results can directly provide theoretical reference for the development and utilization of groundwater on islands and reefs. Attached Figure Description
[0014] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a physical simulation scenario of a freshwater lens on an island reef, according to an embodiment of the present invention. Detailed Implementation
[0015] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.
[0016] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.
[0017] Example 1 This embodiment addresses the problem of imperfect similarity design in existing island and reef freshwater lens model tests by establishing a scientific permeability similarity criterion, clarifying the similarity ratio of permeability coefficients between the model and the prototype, and ensuring the rationality and reliability of the model test. It constructs a targeted permeability coefficient prediction model based on the unique dual-pore structure and particle size distribution characteristics of calcareous sand; proposes specific design criteria for the proportioning of calcareous sand-like materials to achieve directional control of permeability coefficients, providing a standardized material preparation scheme for indoor physical model tests, and improving the repeatability and comparability of test results; and overcomes the limitations of existing tests such as unreasonable material substitution and significant size effects, providing key technical support for the refined simulation of the desalination process and mechanism of groundwater on islands and reefs.
[0018] like Figure 1 As shown in the figure, this embodiment provides a method for predicting the permeability coefficient of calcareous sand in an island reef underground freshwater lens model test, including the following steps: The geometric similarity ratio is determined based on the geometric scale of the prototype islands and reefs and the geometric scale of the model test. The permeability coefficient similarity ratio is determined based on the geometric similarity ratio and the seepage similarity relationship derived from dimensional analysis. Based on the permeability similarity ratio and the permeability of the prototype calcareous sand, the target permeability of the model calcareous sand is determined. A permeability coefficient prediction model was constructed using effective particle size, non-uniformity coefficient, and porosity as input parameters. The gradation parameters and measured permeability coefficients of calcareous sand samples with different mix proportions were obtained through orthogonal experimental design. Based on the gradation parameters and measured permeability coefficients, the undetermined coefficients in the prediction model are solved to obtain the calibrated permeability coefficient prediction model. Based on the target permeability coefficient and the calibrated permeability coefficient prediction model, determine the proportioning scheme for preparing the model calcareous sand.
[0019] Further, determining the geometric similarity ratio includes: The geometric scale of the model test is compared with that of the prototype island, and the ratio of the two is determined as the geometric similarity ratio.
[0020] Furthermore, based on the geometric similarity ratio and the seepage similarity relationship derived from dimensional analysis, the permeability coefficient similarity ratio is determined, including: Based on dimensional analysis, using density, geometric dimensions, and gravitational acceleration as the basic physical quantities, a dimensional relationship between the permeability coefficient and geometric dimensions is established. Based on dimensional relationships, the first power of the geometric similarity ratio is determined as the permeability coefficient similarity ratio.
[0021] Specifically, the fundamental physical quantities and their dimensions are analyzed as follows: Select density ρ (dimension[ ML −3 ]),size L (dimension[ L ]) Gravitational acceleration g (dimension[ LT −2 As a fundamental physical quantity, the core seepage parameters include the permeability coefficient. K (dimension[ LT −1 ]) Water storage coefficient μ (Dimensionless) Porosity n (Dimensionless). According to similarity theory, the physical quantities of the prototype and the model satisfy the similarity ratio relationship. C X = X m / X p ( C X physical quantity X similarity ratio X p prototype parameters X m (For model parameters).
[0022] The formula for the similarity ratio of permeability coefficients is derived as follows: The quantitative relationship between the permeability coefficient and the basic similarity ratio is derived through dimensional analysis: ; Combining the scale of the original island / reef (60-270m in diameter) with the size of the sand trough commonly used in indoor models (less than 2m), the geometric similarity ratio C is set. L =150, similarity ratio of gravitational acceleration C g =1, density similarity ratio C ρ =1, substituting into the calculation, we get: ; That is, the permeability coefficient of the model calcareous sand needs to be set to 1 / 12.24 of the permeability coefficient of the prototype calcareous sand. Based on the measured permeability coefficient K0 = 262 cm / d of the original calcareous sand sample, the ideal target permeability coefficient K≈21.42 cm / d of the model similar material is calculated.
[0023] Similarity ratio of other key parameters Similarity ratio of diffusion coefficient: ; Water storage coefficient μ and porosity n: the similarity ratio is 1, and the model is consistent with the prototype; Mechanical parameters (elastic modulus E, cohesion c): The similarity ratio is not considered in this embodiment and is only used as a reference parameter.
[0024] Furthermore, a permeability coefficient prediction model is constructed using effective particle size, non-uniformity coefficient, and porosity as input parameters, including: Based on the Hazen formula, an undetermined exponential term for the non-uniformity coefficient is introduced as a particle size distribution correction term. An undetermined exponential term of the porosity function based on the Kozeny-Carman equation is introduced as a pore structure correction term; The fixed exponent for effective particle size in the Hazen formula is adjusted to an adjustable parameter; A permeability coefficient prediction model was constructed, which includes a proportionality constant, an effective particle size adjustable index, an undetermined index of the non-uniformity coefficient, and an undetermined index of the porosity function.
[0025] Specifically, this embodiment uses the Hazen formula as its basic framework and makes three corrections to address its limitations: Introducing the non-uniformity coefficient C u Correction: C based on experimental data u The negative correlation with K, add C u α Multiplication terms characterize the effect of particle-level pairing permeability; a porosity function term is introduced: referring to the Kozeny-Carman equation, an n term is introduced. 3 / (1−n) 2 Characterize the effect of the dual-pore structure of calcareous sand on seepage; release the effective particle size index: release the fixed effective particle size index 2 in the classical Hazen formula as an adjustable parameter γ to adapt to the particle size characteristics of calcareous sand.
[0026] The improved prediction formula is as follows: ; Where A is the proportionality constant, γ is the effective particle size index, α is the non-uniformity coefficient index, μ is the porosity function index, K is the permeability coefficient (cm / d), and d 10 For the effective particle size (mm), C u is the non-uniformity coefficient (dimensionless), and n is the porosity (dimensionless).
[0027] The formula parameters are solved as follows: Taking the natural logarithm of both sides of the prediction formula transforms it into a linear model: ; Define variables: ; K, the permeability coefficient (cm / d), can be obtained through systematic permeability testing. 10 For the effective particle size (mm), C uThe coefficient of uniformity (dimensionless) is denoted by n, and the porosity (dimensionless) is denoted by n. A matrix equation is constructed using the obtained parameters. (X is the independent variable matrix, B is the parameter vector, and ε is the error term). Finally, the least squares method is used to solve for the proportionality constant A, which is the effective particle size index γ, the non-uniformity coefficient index α, and the porosity function index μ.
[0028] Furthermore, based on the gradation parameters and measured permeability coefficients, the undetermined coefficients in the prediction model are solved to obtain the calibrated permeability coefficient prediction model, including: Take the natural logarithm of both sides of the prediction model to transform it into a linear regression model; The effective particle size, non-uniformity coefficient, porosity, and measured permeability coefficient of the calcareous sand samples with different proportions were substituted into the linear regression model. The linear regression model was solved using the least squares method to obtain the specific values of the proportionality constant, the effective particle size adjustable index, the undetermined index of the non-uniformity coefficient, and the undetermined index of the porosity function.
[0029] Furthermore, through orthogonal experimental design, the gradation parameters and measured permeability coefficients of calcareous sand samples with different mix proportions were obtained, including: The calcareous sand was sieved into four particle size groups: coarse sand, medium sand, fine sand, and silt. Using the proportions of the four particle size components as factors, with at least two levels for each factor, an orthogonal experimental design was conducted to obtain multiple formulation schemes; Calcareous sand samples were prepared according to multiple mixing schemes, and the effective particle size, uniformity coefficient, porosity and permeability coefficient of each sample were measured.
[0030] Furthermore, orthogonal experimental design also includes: Set proportion constraints, including that the sum of the proportions of coarse sand and medium sand is not equal to 100%, and the sum of the proportions of fine sand and silt is not equal to 100%.
[0031] This embodiment also provides a system for predicting the permeability coefficient of calcareous sand in a model test of an underground freshwater lens on an island or reef, including: The first determining module is used to determine the geometric similarity ratio based on the geometric scale of the prototype island and the geometric scale of the model test. The second determining module is used to determine the permeability coefficient similarity ratio based on the geometric similarity ratio and the seepage similarity relationship derived from dimensional analysis. The third determination module is used to determine the target permeability coefficient of the model calcareous sand based on the permeability coefficient similarity ratio and the permeability coefficient of the prototype calcareous sand. The model building module is used to build a permeability prediction model with effective particle size, non-uniformity coefficient, and porosity as input parameters; The test acquisition module is used to obtain the gradation parameters and measured permeability coefficients of calcareous sand samples with different mix proportions through orthogonal experimental design. The model solving module is used to solve for the undetermined coefficients in the prediction model based on the gradation parameters and the measured permeability coefficient, and obtain the calibrated permeability coefficient prediction model. The proportioning determination module is used to determine the proportioning scheme for preparing the model calcareous sand based on the target permeability coefficient and the calibrated permeability coefficient prediction model.
[0032] The following experiments were also conducted in this embodiment: Scene setup, such as Figure 2 The diagram shown is a physical simulation scenario of a freshwater lens on an island reef, as described in this embodiment. This simulation scenario was set up in an indoor test environment.
[0033] 1. Experimental preparation: Prepare the calcareous sand material for the infiltration test and the relevant test equipment. The experimental design adopts a four-factor, three-level orthogonal experimental design. The factors are the proportions of coarse sand, medium sand, fine sand, and silt, and the levels are set to 0%, 25%, and 50%. A total of 17 mix proportion schemes are designed. An additional group of original calcareous sand natural gradation is added as a control group (sample 0), for a total of 18 test samples, as shown in Table 1-2.
[0034] Table 1 Table 2 2. Proportioning constraints: The proportions of coarse sand + medium sand ≠ 100% and fine sand + silt ≠ 100% are limited to avoid proportions with extremely high or low permeability.
[0035] Particle size composition selection: Four types of components are used: coarse sand (0.5~1mm), medium sand (0.25~0.5mm), fine sand (0.075~0.25mm), and silt (0~0.075mm). No external modification materials are introduced, and the original pore structure and particle morphology of calcareous sand are preserved. Effective particle size requirement: Effective particle size d 10 Within the range of <0.25mm, the formula prediction accuracy is relatively high.
[0036] 3. Parameter Determination: Based on the orthogonal experimental design, determine the permeability coefficient K and effective particle size d for each sample. 10 Inhomogeneity coefficient C u Porosity n.
[0037] 4. Derivation of the modified form of the Hazen formula: The original form of the Hazen formula is: ; Where C is the constant of the Hazen formula, d 10 Where is the effective particle size (mm), and K is the permeability coefficient (cm / s).
[0038] Introducing C into the Hazen formula u Corrected by raising the α power (α is an undetermined coefficient): ; Since the effect of porosity n is not reflected in the original Hazen formula, this study introduces a functional term from the Kozeny-Carman equation that characterizes the influence of pore structure to make corrections: ; In the classic Hazen formula, the effective particle size exponent is fixed at 2. Releasing this as an adjustable parameter γ yields a result considering the inhomogeneity coefficient C. u With the improved Hazen formula for porosity n: ; Where A is a proportionality constant (such as the constant C in the classical Hazen formula), γ is the effective particle size index (2 in the classical Hazen formula), α is the non-uniformity coefficient index, and μ is the porosity function index.
[0039] 5. Solving for model coefficients: To solve for the parameters in the model, we take the natural logarithm of both sides of the model: ; make: The linear regression model is obtained as follows: ; The specific values of A, γ, α, and μ were obtained by solving the least squares method. Table 3 shows the measured data and process calculation parameters of this scheme.
[0040] Table 3 The present invention has the following advantages: A scientific permeability similarity criterion was established, clarifying that the permeability coefficient similarity ratio is 12.24 under the condition of a geometric similarity ratio of 150, providing a quantitative basis for the permeability similarity between the model and the prototype, and solving the core problem of the imperfection of existing experimental similarity design; The constructed permeability coefficient prediction formula comprehensively considers three key parameters: effective particle size, non-uniformity coefficient, and porosity. It accurately characterizes the coupling effect of the dual pore structure and particle size distribution of calcareous sand. Within the applicable range (d10<0.25mm, K<1000cm / d), the determination coefficient R2 between the predicted and measured values is >0.96, and the average relative error is less than 8%, with a prediction accuracy significantly higher than that of the traditional formula. The proposed similar material ratio design criteria are specific and feasible. The permeability coefficient can be controlled in a directional manner by adjusting the proportion of each particle size component, so that the permeability coefficient of the model calcareous sand can be accurately matched with the target value, thereby improving the rationality and reliability of the test results. This method avoids the distortion of infiltration patterns caused by the substitution of terrigenous sand, preserves the original material properties of calcareous sand, and weakens the influence of size effect through similarity ratio design. It provides key technical support for the refined simulation of the formation process and mechanism of freshwater lenses on islands and reefs, and the experimental results can directly provide theoretical reference for the development and utilization of groundwater on islands and reefs.
[0041] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A method for predicting the permeability coefficient of calcareous sand in a model test of an underground freshwater lens on an island or reef, characterized in that, Includes the following steps: The geometric similarity ratio is determined based on the geometric scale of the prototype islands and reefs and the geometric scale of the model test. Based on the geometric similarity ratio and the seepage similarity relationship derived from dimensional analysis, the permeability coefficient similarity ratio is determined. Based on the permeability similarity ratio and the permeability of the prototype calcareous sand, the target permeability of the model calcareous sand is determined. A permeability coefficient prediction model was constructed using effective particle size, non-uniformity coefficient, and porosity as input parameters. The gradation parameters and measured permeability coefficients of calcareous sand samples with different mix proportions were obtained through orthogonal experimental design. Based on the gradation parameters and the measured permeability coefficient, the undetermined coefficients in the prediction model are solved to obtain the calibrated permeability coefficient prediction model; Based on the target permeability coefficient and the calibrated permeability coefficient prediction model, determine the mixing ratio scheme for preparing the model calcareous sand.
2. The method according to claim 1, characterized in that, Determining the geometric similarity ratio includes: The geometric scale of the model test is compared with the geometric scale of the prototype island, and the ratio of the two is determined as the geometric similarity ratio.
3. The method according to claim 1, characterized in that, Based on the geometric similarity ratio and the seepage similarity relationship derived from dimensional analysis, the permeability coefficient similarity ratio is determined, including: Based on dimensional analysis, using density, geometric dimensions, and gravitational acceleration as the basic physical quantities, a dimensional relationship between the permeability coefficient and geometric dimensions is established. Based on the dimensional relationship, the first power of the geometric similarity ratio is determined as the permeability coefficient similarity ratio.
4. The method according to claim 1, characterized in that, The construction of the permeability coefficient prediction model, using effective particle size, non-uniformity coefficient, and porosity as input parameters, includes: Based on the Hazen formula, an undetermined exponential term for the non-uniformity coefficient is introduced as a particle size distribution correction term. An undetermined exponential term of the porosity function based on the Kozeny-Carman equation is introduced as a pore structure correction term; The fixed exponent for effective particle size in the Hazen formula is adjusted to an adjustable parameter; A permeability coefficient prediction model was constructed, which includes a proportionality constant, an effective particle size adjustable index, an undetermined index of the non-uniformity coefficient, and an undetermined index of the porosity function.
5. The method according to claim 4, characterized in that, Based on the gradation parameters and the measured permeability coefficient, the undetermined coefficients in the prediction model are solved to obtain the calibrated permeability coefficient prediction model, including: Taking the natural logarithm of both sides of the prediction model transforms it into a linear regression model; The effective particle size, non-uniformity coefficient, porosity, and measured permeability coefficient of the calcareous sand samples with different proportions were substituted into the linear regression model. The linear regression model was solved using the least squares method to obtain the specific values of the proportionality constant, the effective particle size adjustable index, the undetermined index of the non-uniformity coefficient, and the undetermined index of the porosity function.
6. The method according to claim 1, characterized in that, The process of obtaining the gradation parameters and measured permeability coefficients of calcareous sand samples with different mix proportions through orthogonal experimental design includes: The calcareous sand was sieved into four particle size groups: coarse sand, medium sand, fine sand, and silt. Using the proportions of the four particle size components as factors, with at least two levels for each factor, an orthogonal experimental design was conducted to obtain multiple formulation schemes; Calcareous sand samples were prepared according to the multiple proportioning schemes, and the effective particle size, non-uniformity coefficient, porosity and permeability coefficient of each sample were measured.
7. The method according to claim 6, characterized in that, The orthogonal experimental design also includes: Set proportioning constraints, including that the sum of the proportions of coarse sand and medium sand is not equal to 100%, and the sum of the proportions of fine sand and silt is not equal to 100%.
8. A system for predicting the permeability coefficient of calcareous sand in a model test of an underground freshwater lens on an island or reef, characterized in that, include: The first determining module is used to determine the geometric similarity ratio based on the geometric scale of the prototype island and the geometric scale of the model test. The second determining module is used to determine the permeability coefficient similarity ratio based on the geometric similarity ratio and the seepage similarity relationship derived from dimensional analysis; The third determining module is used to determine the target permeability coefficient of the model calcareous sand based on the permeability coefficient similarity ratio and the permeability coefficient of the prototype calcareous sand. The model building module is used to build a permeability prediction model with effective particle size, non-uniformity coefficient, and porosity as input parameters; The test acquisition module is used to obtain the gradation parameters and measured permeability coefficients of calcareous sand samples with different mix proportions through orthogonal experimental design. The model solving module is used to solve for the undetermined coefficients in the prediction model based on the gradation parameters and the measured permeability coefficient, so as to obtain the calibrated permeability coefficient prediction model. The proportioning determination module is used to determine the proportioning scheme for preparing the model calcareous sand based on the target permeability coefficient and the calibrated permeability coefficient prediction model.