Parameter random field modeling method and system considering unloading effect of gravel soil foundation

Abstract

The application discloses a parameter random field modeling method and system considering unloading effect of gravel foundation, and the method comprises the following steps: establishing an initial numerical model; determining a probability model and statistical characteristics of spatial variability of rock and soil parameters; performing regularization processing and discretization on an irregular site; constructing an initial random field model of reference compression modulus based on a covariance matrix decomposition method; establishing a correlation between deformation parameters of an HS model through an indoor test; mapping and assigning initial random field parameters to the numerical model; and removing elements that do not satisfy the yield criterion by comparing the spatial relationship between the random points of the grid elements and the yield surface of the HS model, thereby generating a final parameter random field numerical model. The application realizes deep integration of HS model parameters and random field theory, ensures the mechanical rationality of parameter combinations through a yield criterion screening mechanism, effectively represents the excavation unloading effect of the gravel foundation, and significantly improves the accuracy and reliability of foundation deformation prediction.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, specifically to a parametric random field modeling method and system that considers the unloading effect of gravelly soil foundations. Background Technology

[0002] As products of natural geological processes, soil and rock masses undergo complex formation processes, exhibiting significant differences in mineral composition, stress history, and other conditions. This results in marked variations in their physical and mechanical parameters across space, a characteristic known as "spatial variability." This variability is one of the main sources of uncertainty in geotechnical engineering, directly impacting the safety and economy of engineering design. Traditional geotechnical engineering design methods typically simplify soil masses as horizontally layered "homogeneous" materials. While this facilitates calculations, it fails to accurately reflect the spatial variability characteristics of natural soil masses.

[0003] In recent years, the international geotechnical engineering field has increasingly emphasized the importance of parameter uncertainty. Eurocode 7, the European geotechnical engineering design standard, explicitly states that the selection of soil parameter characteristic values ​​must consider their uncertainty, and requires that the probability of the system reaching its limit state under unfavorable parameter combinations not exceed 5%. The International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE) has also established a dedicated working group to promote research on geotechnical engineering reliability design methods based on spatial variability analysis.

[0004] Furthermore, with the development of numerical simulation technology, an increasing number of studies have shown that linear elastic or traditional elastoplastic models are insufficient to accurately describe the deformation characteristics of gravelly soil foundations during excavation. Especially under unloading conditions, the unloading modulus of the soil is much greater than the loading modulus, exhibiting a significant "unloading effect." Therefore, the constitutive model reflecting the hardening characteristics of soil—the hardened soil model (HS model)—has been proposed and widely applied. However, how to reasonably incorporate the HS model parameters into random field modeling while considering the variability of parameter space remains a challenge in current research.

[0005] Although existing research has made some progress in random field modeling of geotechnical parameters, the following shortcomings still exist:

[0006] Single-parameter modeling has strong limitations: existing random field modeling methods mostly focus on single soil parameters (such as compression modulus), failing to fully consider the intrinsic mechanical relationships between multiple deformation parameters in complex constitutive models (such as the HS model), making it difficult to comprehensively reflect the mechanical behavior of soil.

[0007] Lack of mechanical rationality in parameter combination: In traditional random field modeling, parameters are often generated independently without considering whether the parameters conform to the yield criterion of the constitutive model. This may result in mechanically unreasonable parameter combinations, affecting the reliability of subsequent numerical simulations.

[0008] Unloading effect and spatial variability are not effectively coupled: Current numerical simulation methods have difficulty in simultaneously considering the spatial variability of soil parameters and the unloading effect during excavation. In particular, within the HS model framework, there is a lack of systematic parametric random field modeling methods, which limits the accuracy and reliability of foundation excavation deformation prediction.

[0009] The modeling process lacks systematicity and operability: existing methods lack clear data transfer and logical connection between parameter selection, random field generation, and model assignment, making it difficult to embed them into mainstream numerical simulation software for widespread application. Summary of the Invention

[0010] This invention aims to overcome the shortcomings of existing technologies and provide a random field modeling method and system that can simultaneously consider the spatial variability of parameters in gravelly soil foundations and the excavation unloading effect. Based on the covariance matrix decomposition method and combined with the mechanical correlation between parameters in the HS model, this invention constructs a random field model that satisfies the yield criterion, thereby achieving a unified representation of parameter spatial variability and constitutive behavior.

[0011] A parametric random field modeling method considering the unloading effect of gravelly soil foundations includes the following steps:

[0012] Step S1: Establish an initial numerical model corresponding to the size of the region to be simulated;

[0013] Step S2: Determine the probabilistic model and statistical characteristics that characterize the spatial variability of the parameters of the soil and rock mass to be simulated. The statistical characteristics include mean, variance, coefficient of variation, probability distribution type, autocorrelation function, horizontal autocorrelation distance, and vertical autocorrelation distance.

[0014] Step S3: Determine the dimensions and scale of the site to be simulated, and normalize irregular sites.

[0015] Step S4: Discretize the site after the normalization process in step S3 using regularly arranged grid cells of the same size to generate discrete grid cells.

[0016] Step S5: Based on the covariance matrix decomposition method, according to the statistical characteristics determined in step S2 and the discrete grid cells generated in step S4, construct an initial random field model of the reference compression modulus.

[0017] Step S6: Obtain the basic parameters of the HS model of gravelly hardened soil through indoor tests, and establish the correlation between the deformation parameters in the HS model. The deformation parameters include the reference compression modulus, the reference loading and unloading modulus, and the reference secant modulus.

[0018] Step S7: Based on the correlation between the initial random field model of the reference compression modulus constructed in step S5 and the deformation parameters established in step S6, the parameters in the initial random field model are mapped to the grid cells of the initial numerical model established in step S1 according to the principle of coordinate proximity through the built-in programming language of the numerical simulation software. The parameters of the initial numerical model are assigned to obtain the numerical model after assigning the values ​​of each key parameter of the HS model.

[0019] Step S8: By comparing the spatial relationship between the random points of each grid cell in the numerical model after assignment obtained in step S7 and the yield surface of the HS model, grid cells that do not meet the yield criterion are identified and removed, and only grid cells within or on the yield surface are retained, thereby generating a final parametric random field numerical model that meets the yield criterion of the HS model and can reflect the unloading effect of excavation of gravelly soil foundation.

[0020] Furthermore, the probability distribution type mentioned in step S2 is a normal distribution or a log-normal distribution, the autocorrelation function is an exponential autocorrelation function, and the ratio of the horizontal autocorrelation distance to the vertical autocorrelation distance constitutes the anisotropy coefficient.

[0021] Furthermore, the size of the grid cell in step S4 is between 1 / 5 and 1 / 10 of the vertical autocorrelation distance.

[0022] Furthermore, the covariance matrix decomposition method described in step S5 specifically includes: constructing a covariance matrix between discrete points, performing Cholesky decomposition on the covariance matrix to obtain a lower triangular matrix, multiplying mutually independent standard normal random column vectors with the lower triangular matrix to obtain a standard normal random field that satisfies a specified correlation structure, and then obtaining a random field model with a reference compression modulus through log-normal transformation.

[0023] Furthermore, the correlation between the deformation parameters established in step S6 is as follows: ;in, For reference loading and unloading modulus, For reference secant modulus, For reference compression modulus, , This is the proportionality coefficient calibrated through indoor testing.

[0024] A parametric random field modeling method and system considering the unloading effect of gravelly soil foundations, used to implement the method described above, includes:

[0025] The initial numerical model establishment module is used to establish an initial numerical model corresponding to the size of the region to be simulated;

[0026] The statistical feature determination module is used to determine the probabilistic model and statistical features that characterize the spatial variability of the parameters of the soil and rock mass to be simulated;

[0027] The site regularization module is used to determine the dimensions and scale of the site to be simulated and to regularize irregular sites.

[0028] The grid discretization module is used to discretize the regularized site using regularly arranged grid cells of the same size, generating discrete grid cells.

[0029] An initial random field generation module is used to construct an initial random field model with a reference compression modulus based on the covariance matrix decomposition method, according to the statistical characteristics and discrete grid cells.

[0030] The parameter relationship establishment module is used to obtain the basic parameters of the gravelly soil HS model through indoor tests and establish the correlation between various deformation parameters in the HS model. The deformation parameters include the reference compression modulus, the reference loading and unloading modulus, and the reference secant modulus.

[0031] The parameter mapping and assignment module is used to map the parameters in the initial random field model to the grid cells of the initial numerical model according to the principle of coordinate proximity, based on the correlation between the initial random field model and the deformation parameters, and to assign parameter values ​​to the initial numerical model to obtain the numerical model after assigning the values ​​of each key parameter of the HS model.

[0032] The yield criterion screening module is used to identify and remove grid cells that do not meet the yield criterion by comparing the spatial relationship between the random points of each grid cell in the numerical model after assignment and the yield surface of the HS model, and only retaining grid cells within or on the yield surface, thereby generating a final parametric random field numerical model that meets the yield criterion of the HS model and can reflect the unloading effect of excavation on the gravelly soil foundation.

[0033] Furthermore, the probability distribution type determined in the statistical feature determination module is a normal distribution or a log-normal distribution, the autocorrelation function is an exponential autocorrelation function, and the ratio of the horizontal autocorrelation distance to the vertical autocorrelation distance constitutes the anisotropy coefficient.

[0034] Furthermore, the grid cell size used in the grid discretization module is between 1 / 5 and 1 / 10 of the vertical autocorrelation distance.

[0035] Furthermore, the implementation of the covariance matrix decomposition method in the initial random field generation module includes: constructing a covariance matrix between discrete points, performing Cholesky decomposition on the covariance matrix to obtain a lower triangular matrix, multiplying mutually independent standard normal random column vectors with the lower triangular matrix to obtain a standard normal random field that satisfies a specified correlation structure, and then obtaining a random field model with a reference compression modulus through log-normal transformation.

[0036] Furthermore, the correlation between the deformation parameters established in the parameter relationship establishment module is as follows: ;in, For reference loading and unloading modulus, For reference secant modulus, For reference compression modulus, , This is the proportionality coefficient calibrated through indoor testing.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] First, this invention achieves a deep integration of HS model parameters and random field theory. Addressing the shortcomings of existing random field modeling methods that primarily focus on single soil parameters and struggle to reflect the spatial variability of parameters in complex constitutive models, this invention establishes a reference compression modulus in the gravelly soil HS model. Reference loading and unloading modulus and reference secant modulus The correlation between them was determined, and a covariance matrix decomposition method was used to construct the model. The initial random field model is obtained, and then the random fields of each key parameter of the HS model are obtained by inversion. This method not only preserves the spatial variability of the parameters, but also ensures the mechanical correlation between the deformation parameters, providing more realistic material parameter inputs for the reliability analysis of crushed stone foundation engineering.

[0039] Second, this invention proposes a parametric random field screening mechanism based on the yield criterion of the HS model. Addressing the problem that traditional random field modeling may generate parameter combinations that do not satisfy the mechanical constitutive relations, this invention identifies and removes grid cells that do not satisfy the yield criterion by comparing the spatial relationships between the random points of each grid cell in the numerical model after assignment and the yield surface of the HS model, retaining only grid cells within or on the yield surface. This screening mechanism ensures that the final generated parametric random field numerical model strictly satisfies the yield criterion of the HS model, fundamentally solving the problem of the mechanical rationality of parameter combinations in random field models.

[0040] Third, this invention achieves a parameterized characterization of the excavation unloading effect in gravelly soil foundations. Addressing the technical bottleneck of existing geotechnical engineering numerical simulations that struggle to simultaneously consider the spatial variability of soil parameters and the excavation unloading effect, this invention constructs a parametric random field satisfying the yield criterion within the HS model framework. This enables the generated numerical model to accurately reflect the unloading response characteristics of gravelly soil foundations during excavation. This method organically unifies the spatial variability of soil with its mechanical constitutive behavior, significantly improving the accuracy and reliability of foundation excavation deformation prediction.

[0041] Fourth, this invention constructs a complete parametric random field modeling process, with clear logic and explicit data transfer between each step. From the initial numerical model establishment, statistical feature determination, site regularization, and grid discretization, to the initial random field generation, HS model parameter relationship establishment, parameter mapping assignment, and finally yield surface selection, the processing results of each step serve as inputs for subsequent steps, forming a complete closed-loop technical solution. This method can be directly embedded into FLAC. 3D It has good engineering practicality and promotional value in commercial numerical simulation software. Attached Figure Description

[0042] Figure 1 This is a flowchart of a parametric random field modeling method for considering the unloading effect of gravelly soil foundations in an embodiment of the present invention;

[0043] Figure 2 For FLAC 3D A schematic diagram of the numerical model in the diagram;

[0044] Figure 3 A schematic diagram of a first-order implementation of a reference compression modulus random field;

[0045] Figure 4 A schematic diagram of a random field screening method for crushed stone soil parameters considering unloading effects;

[0046] Figure 5 Reference loading / unloading modulus in the HS model A schematic diagram of a random field model;

[0047] Figure 6 Reference secant modulus in the HS model A schematic diagram of a random field model. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0049] like Figure 1 As shown, embodiments of the present invention provide a parametric random field modeling method and system that considers the unloading effect of gravelly soil foundations, including the following steps:

[0050] The first step is to establish an initial numerical model corresponding to the size of the region to be simulated.

[0051] For a specific simulated area of ​​150m × 63m, this embodiment utilizes FLAC. 3D An initial numerical model of the corresponding size is established;

[0052] The second step is to determine the probabilistic model and statistical characteristics that characterize the spatial variability of the parameters of the soil and rock mass to be simulated.

[0053] The statistical characteristics of the probabilistic model of soil and rock parameters described are: mean, variance, coefficient of variation, probability distribution type, autocorrelation function, horizontal autocorrelation distance, and vertical autocorrelation distance.

[0054] Based on literature review and statistics, it was found that the probability distribution of soil and rock parameters is mostly normal or log-normal; the autocorrelation function is often used to characterize the autocorrelation of soil and rock parameters; generally, sedimentary strata show obvious "transverse isotropic" correlation structure, and the vertical fluctuation distance of soil and rock parameters is generally 0.5~6.0m, and the horizontal fluctuation distance is 30.0~80.0m;

[0055] The third step is to determine the dimensions and scale of the site to be simulated, and to normalize irregular sites.

[0056] For two-dimensional random fields, the field is typically rectangular or square, while for three-dimensional random fields it is cuboid or cube. When the field to be simulated is irregularly shaped, this invention suggests normalizing the irregular field. Specifically, the direction containing the longest length of the irregular field is selected as any principal axis in the two-dimensional (three-dimensional) Cartesian coordinate system (here, denoted by the x-axis), and the longest length value is the length of the normalized field. Then, the length values ​​of the irregular field on the other principal axes (y-axis and z-axis) of the coordinate system are determined. Therefore, random field modeling can be performed on the normalized field, and data points can be selectively extracted from the regular random field model according to actual needs during application.

[0057] Step 4: Discretize the site to be simulated using a grid.

[0058] The aforementioned mesh discretization refers to discretizing the simulated site using regularly arranged mesh elements of the same size. For two-dimensional and three-dimensional site conditions, quadrilateral and hexahedral elements are used for mesh discretization, respectively. For example, the coordinates of the center point of a quadrilateral element after discretization can be expressed as (x... i , y j ), i = 1, 2, …, N x ; i, j = 1, 2,…, N y N x and N y These represent the number of elements in the x and y directions, respectively. The discretized mesh elements are numbered, denoted by N, where N = 1, 2, ..., N. x×N y Literature review revealed that, given a fixed autocorrelation distance, the grid size used in the calculation significantly impacts the accuracy. Generally, a smaller grid size results in higher accuracy, but also longer computation time. Considering all factors, a grid size between 1 / 5 and 1 / 10 of the autocorrelation distance is recommended.

[0059] Step 5: Establishing the initial random field model based on the covariance matrix decomposition method

[0060] The constructed initial random field model has the same dimensions as the initial numerical model. The covariance matrix decomposition method simulates the autocorrelation of parameter random fields by constructing the covariance matrix, exhibiting high computational efficiency. Assume x... i and x j (i, j=1, 2, …, n) are discrete points in a random field, τ ij For any two points x i and x j The relative distance between them, C is the nth-order covariance matrix composed of the covariances between n points. This matrix is ​​a positive definite symmetric matrix, and any element of matrix C contains C. ij x represents i and x j The covariance between them, C ij =C (τ ij The covariance matrix C is decomposed using Cholesky method to obtain upper and lower triangular matrices:

[0061] (1)

[0062] In the formula: L is a lower triangular matrix, U is an upper triangular matrix, and L T Let Y be the transpose of matrix L. Let Y be a column vector consisting of n independent random numbers following a standard normal distribution. Then the nth-order random field matrix Z can be expressed as:

[0063] (2)

[0064] Where: Z is any point in the random field matrix Z. ij It follows a standard normal distribution, and its covariance matrix E(ZZ) T )=E(LYY T L T )=E(LL T Since C satisfies the correlation requirement, matrix Z can be used as a realization of a random field. Figure 3 A schematic diagram of a single implementation of a reference compression modulus random field is given.

[0065] Based on the initial random field model, using FLAC 3DThe system incorporates the FISH programming language and identifies the cell positions based on the proximity principle between the finite difference grid coordinates and the random field cell coordinates. It then maps the parameters in the initial random field model one-to-one to the finite difference grid cells, thus realizing the conversion from the random field model to the numerical analysis model.

[0066] Step 6: Establishing the correlation of parameters in the HS model for gravelly soil

[0067] Sampling was conducted at a gravelly soil foundation project site, followed by density tests, one-dimensional standard consolidation tests, triaxial consolidated drained shear tests, and triaxial consolidated drained loading and unloading tests to obtain the basic parameters of the gravelly soil HS model. Based on this, the correlation between the parameters was established, especially the deformation parameter reference compression modulus. Reference loading and unloading modulus Reference secant modulus The relationship between them.

[0068] Step 7: Parameter Random Field Inversion Method for HS Model Based on Correlation

[0069] Based on random field theory, a Matlab program was written using the covariance matrix decomposition method to construct a gravelly soil model. The spatial variability model was then developed. Subsequently, based on the established correlation between deformation parameters, secondary development was carried out using the FISH language built into FLAC to realize the random field assignment and modeling of key parameters of the HS model.

[0070] Step 8: Random Field Screening Method for Gravelly Soil Parameters Considering Unloading Effect

[0071] Within the HS model framework, a random field of soil parameters satisfying the corresponding yield criterion is generated. To achieve this, a three-dimensional stress space function of the soil parameters needs to be established, and the spatial relationship between random points and the yield surface (e.g., ...) is compared. Figure 4 The generated random numbers can be categorized into three types: those within the yield surface (e.g., point A, satisfying the yield criterion), those on the yield surface (e.g., point B, satisfying the yield criterion), and those outside the yield surface (e.g., point C, not satisfying the yield criterion). In this random field modeling, unreasonable random points are removed as the selection criterion for the HS model's parameter random field. Specifically, random point C outside the yield surface is removed, and only random points A and B within or on the yield surface are retained. The generated parameter random field then satisfies the yield criterion of the HS model and can reflect the unloading effect of excavation on gravelly soil foundations.

[0072] Example: Based on a domestic gravel soil foundation project, given the inherent variability of gravel soil layer parameters and the coupling effect of excavation unloading, traditional deterministic methods are difficult to accurately predict foundation deformation, which may lead to the risk of uncontrolled deformation or excessive prediction deviation in later construction.

[0073] The first step is to establish a numerical model.

[0074] Using FLAC 3D The software was used to create an initial numerical model with dimensions of 150m × 63m, such as... Figure 2 As shown.

[0075] The second step is to determine the probabilistic model and statistical characteristics that characterize the spatial variability of the parameters of the soil and rock mass to be simulated.

[0076] The reference compression modulus of gravelly soil was selected as the physical and mechanical parameter for random simulation, as shown in Table 1. Its mean was determined through subsequent indoor tests, with a coefficient of variation of 0.3 and a log-normal probability distribution model. Without loss of generality, the autocorrelation of soil parameters was described using a "transversely isotropic" correlation structure, and an exponential correlation function was selected. The horizontal autocorrelation distance was 48 m, and the vertical autocorrelation distance was 3 m, meaning the anisotropy coefficient of the soil parameters was 16.

[0077] Table 1 Spatial variability characteristics of parameters in gravelly soil

[0078]

[0079] Reference compression modulus Follows a log-normal distribution Then it follows a normal distribution. The mean and variance can be expressed as:

[0080] (4)

[0081] (5)

[0082] In the formula, and These are the mean and standard deviation of the reference compression modulus, respectively.

[0083] Characterizing the reference compressive modulus A Gaussian random field with spatial variability can be represented as:

[0084] (6)

[0085] In the formula, X is the standard normal random field matrix, X N The reference compression modulus random field matrix.

[0086] The third step is to determine the dimensions and scale of the site to be simulated, and to normalize irregular sites.

[0087] The geological model established in this case study, reflecting the spatial variability of soil parameters, can be used for subsequent numerical analysis. A two-dimensional random field model, measuring 150m × 63m, is used to simulate a rectangular site, with the x-axis at 150m and the y-axis at 63m.

[0088] Step 4: Discretize the site to be simulated using a grid.

[0089] In this case, the discretized grid is taken as 1 / 5 of the vertical autocorrelation distance, that is, the size is 0.6m×0.6m.

[0090] Step 5: Establishing a random field model based on covariance matrix decomposition.

[0091] According to formula (2), any Gaussian random field can be obtained. In this invention, the above modeling process is implemented using the MATLAB platform.

[0092] Based on this, using FLAC 3D The system incorporates the FISH programming language and identifies the cell positions based on the proximity principle between the finite difference grid coordinates and the random field cell coordinates. It then maps the parameters in the random field model to the finite difference grid cells one-to-one, thus realizing the conversion from the random field model to the numerical analysis model.

[0093] Step 6: Establishing the correlation of parameters in the HS model for gravelly soil

[0094] Samples were taken at the site of a gravelly soil foundation project, and then density tests, one-dimensional standard consolidation tests, triaxial consolidation drained shear tests, and triaxial consolidation drained loading and unloading tests were carried out to obtain the basic parameters of the gravelly soil HS model, as shown in Table 2. The average value of the reference compression modulus can be obtained as 34.8 MPa.

[0095] Table 2 Parameters of the HS Model for Gravelly Soil

[0096]

[0097] Based on this, an approximate relationship between deformation parameters can be established:

[0098]

[0099] Step 7: HSS Model Parameter Random Field Inversion Method Based on Correlation

[0100] Based on the empirical relationship between the random field model of the reference compression modulus of gravelly soil and other deformation parameters of the HS model, the random field model of each parameter of the HS model of gravelly soil is obtained by inverting using FLAC and its built-in HS model and deformation Fish code.

[0101] Step 8: Random Field Screening Method for Gravelly Soil Parameters Considering Unloading Effect

[0102] Within the HS model framework, a parametric random field model for gravelly soil satisfying the corresponding yield criterion is generated. By comparing the spatial relationship between random points and the yield surface, removing unreasonable random points is used as the screening criterion for considering the unloading effect of foundation excavation in the parametric random field. Figure 4 This involves removing random points C outside the yield surface and retaining only random points A and B within or on the yield surface. The resulting parametric random field satisfies the yield criterion of the HS model and reflects the excavation unloading effect of the gravelly soil foundation. Figure 5 The reference loading and unloading modulus in the final generated HS model A schematic diagram of a random field model; Figure 6 The reference secant modulus in the final generated HS model A schematic diagram of a random field model.

[0103] In summary, this invention provides a stochastic field modeling method for excavation deformation analysis and reliability design of gravelly soil foundation engineering that can comprehensively consider the spatial variability of parameters and the unloading effect. It can be widely applied to numerical simulation and risk assessment in fields such as foundation pit engineering, slope engineering, and tunnel engineering.

[0104] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A parametric random field modeling method considering the unloading effect of gravelly soil foundations, characterized in that, Includes the following steps: Step S1: Establish an initial numerical model corresponding to the size of the region to be simulated; Step S2: Determine the probabilistic model and statistical characteristics that characterize the spatial variability of the parameters of the soil and rock mass to be simulated. The statistical characteristics include mean, variance, coefficient of variation, probability distribution type, autocorrelation function, horizontal autocorrelation distance, and vertical autocorrelation distance. Step S3: Determine the dimensions and scale of the site to be simulated, and normalize irregular sites. Step S4: Discretize the site after the normalization process in step S3 using regularly arranged grid cells of the same size to generate discrete grid cells. Step S5: Based on the covariance matrix decomposition method, according to the statistical characteristics determined in step S2 and the discrete grid cells generated in step S4, construct an initial random field model of the reference compression modulus. Step S6: Obtain the basic parameters of the HS model of gravelly hardened soil through indoor tests, and establish the correlation between the deformation parameters in the HS model. The deformation parameters include the reference compression modulus, the reference loading and unloading modulus, and the reference secant modulus. Step S7: Based on the correlation between the initial random field model of the reference compression modulus constructed in step S5 and the deformation parameters established in step S6, the parameters in the initial random field model are mapped to the grid cells of the initial numerical model established in step S1 according to the principle of coordinate proximity through the built-in programming language of the numerical simulation software. The parameters of the initial numerical model are assigned to obtain the numerical model after assigning the values ​​of each key parameter of the HS model. Step S8: By comparing the spatial relationship between the random points of each grid cell in the numerical model after assignment obtained in step S7 and the yield surface of the HS model, grid cells that do not meet the yield criterion are identified and removed, and only grid cells within or on the yield surface are retained, thereby generating a final parametric random field numerical model that meets the yield criterion of the HS model and can reflect the unloading effect of excavation of gravelly soil foundation.

2. The parametric random field modeling method considering the unloading effect of gravelly soil foundation according to claim 1, characterized in that, The probability distribution type mentioned in step S2 is a normal distribution or a log-normal distribution, the autocorrelation function is an exponential autocorrelation function, and the ratio of the horizontal autocorrelation distance to the vertical autocorrelation distance constitutes the anisotropy coefficient. 3.The method of claim 1, wherein, The size of the grid cell in step S4 is between 1 / 5 and 1 / 10 of the vertical autocorrelation distance.

4. The parameter random field modeling method for considering unloading effect of a gravel ground according to claim 1, characterized in that, The covariance matrix decomposition method described in step S5 specifically includes: constructing a covariance matrix between discrete points, performing Cholesky decomposition on the covariance matrix to obtain a lower triangular matrix, multiplying mutually independent standard normal random column vectors with the lower triangular matrix to obtain a standard normal random field that satisfies a specified correlation structure, and then obtaining a random field model with a reference compression modulus through log-normal transformation.

5. The parametric random field modeling method considering the unloading effect of gravelly soil foundation according to claim 1, characterized in that, The correlation between the deformation parameters established in step S6 is: ; wherein, is the reference loading and unloading modulus, is the reference secant modulus, is the reference compression modulus, , is a scale factor calibrated by indoor tests.

6. A parameter random field modeling system for taking into account the unloading effect of a gravel ground, for implementing the method according to any one of claims 1 to 5, characterized in that, include: The initial numerical model establishment module is used to establish an initial numerical model corresponding to the size of the region to be simulated; The statistical feature determination module is used to determine the probabilistic model and statistical features that characterize the spatial variability of the parameters of the soil and rock mass to be simulated; The site regularization module is used to determine the dimensions and scale of the site to be simulated and to regularize irregular sites. The grid discretization module is used to discretize the regularized site using regularly arranged grid cells of the same size, generating discrete grid cells. An initial random field generation module is used to construct an initial random field model with a reference compression modulus based on the covariance matrix decomposition method, according to the statistical characteristics and discrete grid cells. The parameter relationship establishment module is used to obtain the basic parameters of the gravelly soil HS model through indoor tests and establish the correlation between various deformation parameters in the HS model. The deformation parameters include the reference compression modulus, the reference loading and unloading modulus, and the reference secant modulus. The parameter mapping and assignment module is used to map the parameters in the initial random field model to the grid cells of the initial numerical model according to the principle of coordinate proximity, based on the correlation between the initial random field model and the deformation parameters, and to assign parameter values ​​to the initial numerical model to obtain the numerical model after assigning the values ​​of each key parameter of the HS model. The yield criterion screening module is used to identify and remove grid cells that do not meet the yield criterion by comparing the spatial relationship between the random points of each grid cell in the numerical model after assignment and the yield surface of the HS model, and only retaining grid cells within or on the yield surface, thereby generating a final parametric random field numerical model that meets the yield criterion of the HS model and can reflect the unloading effect of excavation on the gravelly soil foundation.

7. The parameter random field modeling system for considering unloading effect of crushed stone ground according to claim 6, wherein, The probability distribution type determined in the statistical feature determination module is a normal distribution or a log-normal distribution, the autocorrelation function is an exponential autocorrelation function, and the ratio of the horizontal autocorrelation distance to the vertical autocorrelation distance constitutes the anisotropy coefficient.

8. The parametric random field modeling system considering the unloading effect of gravelly soil foundations according to claim 6, characterized in that, The grid cell size used in the grid discretization module is between 1 / 5 and 1 / 10 of the vertical autocorrelation distance.

9. The parametric random field modeling system considering the unloading effect of gravelly soil foundations according to claim 6, characterized in that, The implementation of the covariance matrix decomposition method in the initial random field generation module includes: constructing a covariance matrix between discrete points, performing Cholesky decomposition on the covariance matrix to obtain a lower triangular matrix, multiplying mutually independent standard normal random column vectors with the lower triangular matrix to obtain a standard normal random field that satisfies a specified correlation structure, and then obtaining a random field model with a reference compression modulus through log-normal transformation.

10. The parameter random field modeling system for considering unloading effect of crushed stone ground according to claim 6, wherein, The correlation between the deformation parameters established in the parameter relationship establishment module is as follows: ;in, For reference loading and unloading modulus, For reference secant modulus, For reference compression modulus, , This is the proportionality coefficient calibrated through indoor testing.

Images