A method and system for predicting displacement probability of foundation pit excavation under the condition of non-homogeneous multi-layer soil body

Abstract

The present application belongs to the technical field of foundation pit excavation simulation, and discloses a method and system for predicting the displacement probability of foundation pit excavation under the condition of non-homogeneous multi-layer soil, comprising: dividing the multi-layer soil according to the engineering survey data, independently selecting key random parameters and their statistical characteristics for each layer; proposing a stratified differentiated KL expansion method, performing K-L expansion on each layer to generate a random field, and introducing a distance-weighted continuity constraint transition zone treatment at the interface between layers to ensure smooth transition of the parameters of the random field of adjacent soil layers at the interface; establishing a two-dimensional finite element model of the foundation pit in COMSOL Multiphysics software, and importing the stratified generated random field into the material parameters of the model; solving by MATLAB cyclic call to obtain the horizontal displacement of the wall after the foundation pit is excavated; finally, the probability prediction and uncertainty quantification of the horizontal displacement of the retaining wall are carried out based on statistical analysis.

Description

Technical Field

[0001] This invention belongs to the field of foundation pit excavation simulation technology, specifically relating to a method and system for predicting the probability of foundation pit excavation displacement under heterogeneous multi-layered soil conditions. Background Technology

[0002] Retaining structures are widely used in infrastructure construction such as railways, highways, and water conservancy projects. Their stability requirements are increasingly stringent, necessitating the comprehensive consideration of various influencing factors. The main method for stability analysis of retaining wall structures is the safety factor method based on Rankine's earth pressure theory or Coulomb's earth pressure theory. This method is simple and practical, but it does not consider the uncertainties in the calculation parameters, resulting in inaccurate calculations of retaining wall displacement and a high risk of structural failure in practical applications.

[0003] In recent years, the stochastic finite element method has been gradually introduced into foundation pit engineering analysis, using stochastic field theory to characterize the spatial variability of soil parameters. Among these methods, the Karhunen-Loève (KL) expansion is one of the most commonly used methods for generating stochastic fields. However, existing foundation pit displacement prediction methods based on KL expansion typically treat the entire computational domain as a single homogeneous stochastic field, applying uniform statistical parameters (mean, coefficient of variation, correlation length) across the entire domain. This approach fails to reflect the inherent spatial variability between multiple soil layers in actual engineering—the mean, dispersion, and spatial correlation of mechanical parameters in different soil layers often differ significantly. Furthermore, simply superimposing multiple independent stochastic fields can lead to discontinuous jumps in parameters at interlayer interfaces, causing instability or even non-convergence in numerical calculations.

[0004] To address the aforementioned technical problems, this invention proposes a method for predicting the probability of excavation displacement in heterogeneous multi-layered soil. By employing layered differential KL expansion and interlayer continuity constraint transition zone processing, it achieves accurate characterization of the differential spatial variability of multi-layered soil while ensuring a smooth transition of interlayer parameters. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method and system for predicting the probability of excavation displacement in heterogeneous multi-layered soil conditions. It innovatively proposes a layered differentiated KL expansion method, which independently performs KL expansion on each soil layer to preserve the differentiated statistical characteristics of each layer. Furthermore, a distance-weighted continuity constraint transition zone processing mechanism is introduced at the interlayer interface. By defining the transition zone width criterion and the linear weighted interpolation function, a smooth transition of the random field of adjacent soil layers at the interface is achieved, avoiding numerical instability caused by parameter jumps.

[0006] To achieve the above objectives, the present invention provides the following solution: A method for predicting the probability of excavation displacement in heterogeneous multi-layered soil conditions, the method comprising: Step 1: Divide the soil into multiple layers according to the engineering survey report, and independently select key soil random parameters and their statistical characteristics for each layer; Step 2: Use COMSOL Multiphysics to establish a two-dimensional finite element excavation model of soil-structure interaction; Step 3: Based on the key soil random parameters and their statistical characteristics, generate random fields for each soil layer using the layered differential Karhunen-Loève expansion method, and apply a continuity constraint transition zone at the interlayer interface to generate a global continuous random field. Step 4: Input the global continuous random field into the two-dimensional soil-structure interaction finite element excavation model, and use MATLAB to call the two-dimensional soil-structure interaction finite element excavation model to calculate the wall displacement under different random fields; Step 5: Based on the wall displacement under different random fields, quantitatively evaluate the impact of the spatial variability of multi-layer soil on the foundation pit displacement.

[0007] The preferred method for independently selecting random parameters of multi-layered soil is as follows: The strata within the impact area of ​​the foundation pit are divided into: L Layers, each layer l , l =1, 2, ..., L Select key soil parameters independently, including but not limited to the internal friction angle. f l Cohesion c l and elastic modulus E l Each layer of parameters is assumed to be independent and follows a given probability distribution function, where the mean of each parameter is... m l Data was taken from engineering survey reports at each level, and the coefficient of variation (COV) was determined independently for each level. l Spatial related length i l This is to reflect the differentiated statistical characteristics of different soil layers.

[0008] Preferred methods for establishing a two-dimensional finite element excavation model of soil-structure interaction using COMSOL Multiphysics include: An elastoplastic constitutive model is constructed using the Drucker-Prager strength criterion: ; In the formula, I 1 and J 2 represents the first invariant of stress and the second invariant of deviatoric stress, respectively.α , k These are material constants; When simulating foundation pit excavation in COMSOL Multiphysics software, a two-dimensional plane strain model is used. In the two-dimensional plane strain analysis, the Drucker-Prager criterion and the Mohr-Coulomb criterion are matched. ; in, , These are the internal friction angle of the soil and the cohesion of the soil, respectively. During the excavation of the foundation pit, the displacement of the retaining wall is described by the fundamental governing equations of solid mechanics. Assuming it is a quasi-static problem, the governing equations are: ; in, For divergence operators, s Let f be the stress tensor and f be the body force; under the assumption of small deformation, the relationship between strain and displacement is: ; In the formula, It is a displacement matrix, and ε is the strain tensor; in the elastic stage, stress and strain satisfy the generalized Hooke's law σ=D:ε, where D is the constitutive stiffness tensor, which depends on Young's modulus. E Compared with Poisson n Once the stress exceeds the yield strength, it enters the plastic stage and follows the specified yield criterion.

[0009] Preferably, the method for generating a global continuous random field by using the layered differential Karhunen-Loève expansion method to generate random fields for each soil layer and applying a continuity constraint transition zone treatment at the interlayer interface includes: For each soil layer l In its occupied spatial domain Ω l Each layer independently performs a KL expansion to obtain random fields. By solving the independent second-type Fredholm homogeneous integral equations for each layer, the eigenvalues ​​and eigenfunctions of each layer are obtained. A continuous transition zone with interlayer continuity constraints is applied to two independent KL expansion random fields to construct a global continuous random field covering the entire computational domain.

[0010] Preferably, for each soil layer l In its occupied spatial domain Ω l Methods for independently performing KL expansions to obtain random fields for each layer include: ; In the formula, As coordinates, μl For the first l Mean values ​​of parameters in a layered random field. For uncorrelated random variables that conform to a standard normal distribution, and The first l Layer covariance function Cl The corresponding eigenvalues ​​and eigenfunctions; Ml For the first l The truncation order of the layer KL expansion; The covariance function for each layer adopts the exponential form: ; In the formula, , These are the coordinates of two points, 1 and 2, in space. sl = COV l × μl For the first l Layer standard deviation, θl For the first l Layer space related length.

[0011] Preferably, the method for obtaining the eigenvalues ​​and eigenfunctions of each layer by solving the independent second-kind Fredholm homogeneous integral equations for each layer includes: ; For exponential covariance functions, analytical solutions are used to obtain the eigenvalues ​​and eigenfunctions of each layer, and the one-dimensional form is extended to two dimensions: ; ; in, It is the first One eigenvalue or eigenfunction It is the x-direction of the first One eigenvalue or eigenfunction It is the y-direction first 1 eigenvalues ​​or eigenfunctions, where the superscript 1 represents eigenvalues ​​or eigenfunctions. x Direction, 2 represents z The spatial lengths of each layer differ in each direction.

[0012] Preferably, the method for handling the interlayer continuity constraint transition zone of two independent KL expansion random fields includes: In adjacent soil layers l and l At the +1 interface, the width is defined as d transition zone region T {l,l+1} The transition zone is located at the top and bottom of the interface. d Within the range of / 2; In the transition zone T {l,l+1} Internally, a distance-weighted smooth interpolation function is used to fuse the random field values ​​of the upper and lower layers. The fusion formula is as follows: ; in, d To calculate the signed distance from a point to the interlayer interface, d >0 indicates that it is on the upper side. d <0 indicates that it is on the lower side; and The distance weighting function is specifically defined as: d ∈[ -d / 2, d / 2]; d ∈[ -d / 2, d / 2]; Outside the transition zone, i.e. | d |> d For the region of / 2, the random field value is directly taken from the KL expansion result of the corresponding layer; transition band width d Determined as: d = b · min( i l , θ l+1 ); in β This is the transition zone width coefficient, with a value ranging from 0.1 to 0.5. i l and i l+1 These represent the spatial correlation lengths of two adjacent floors.

[0013] Preferably, the constructed global continuous random field covering the entire computational domain is: H ( x ) = H l ( x ), when x ∈Ω l and |z - z {l,l+1} |>d / 2; H ( x ) = H T ( x ), when |z - z {l,l+1} | ≤ δ / 2.

[0014] Preferably, the method of inputting a global continuous random field into a two-dimensional soil-structure interaction finite element excavation model, and calculating the wall displacement under different random fields by calling the two-dimensional soil-structure interaction finite element excavation model through MATLAB includes: Create an interpolation function under the global definition node in the COMSOL Multiphysics software; Configure the data source of the interpolation function to come from an external file, which is a text file generated by MATLAB and storing global continuous random field data, wherein the data format includes spatial coordinate dimensions and corresponding soil parameter values ​​for each layer. In the physics settings or material properties of COMSOL Multiphysics, the interpolation function is referenced to assign and call global continuous random field data as spatially varying material parameters; A connection is established through the LiveLink for MATLAB interface provided by COMSOL Multiphysics. In MATLAB, a loop control structure is set up with the number of loops matching the number of samples in the global continuous random field. COMSOL is then driven to load each random field sample file sequentially, call the solver to complete the calculation, and extract the displacement results data to a specified file for saving.

[0015] The present invention also provides a system for predicting the probability of excavation displacement in heterogeneous multi-layered soil conditions. The system is used to implement the aforementioned method. The system includes: a soil layer division and parameter statistics module, a finite element model construction module, a layered random field generation module, a random finite element calculation module, and a variability impact assessment module. The soil layer division and parameter statistics module is used to divide the soil into multiple layers according to the engineering survey report, and to independently select key soil random parameters and their statistical characteristics for each layer. The finite element model building module is used to establish a two-dimensional finite element excavation model of soil-structure interaction using COMSOL Multiphysics. The layered random field generation module is used to generate random fields for each soil layer based on key soil random parameters and their statistical characteristics using the layered differentiated Karhunen-Loève expansion method, and to apply a continuity constraint transition zone at the interlayer interface to generate a global continuous random field. The stochastic finite element calculation module is used to input a global continuous random field into a two-dimensional soil-structure interaction finite element excavation model, and to calculate the wall displacement under different random fields by calling the two-dimensional soil-structure interaction finite element excavation model through MATLAB. The variability impact assessment module is used to quantitatively assess the impact of multi-layer soil spatial variability on foundation pit displacement based on wall displacement under different random fields.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) It can accurately characterize the differentiated spatial variability of multi-layered soil. Unlike existing methods that treat the entire field as a single random field, this invention performs KL expansion independently on each layer. Each layer can use different mean, coefficient of variation and spatial correlation length, which is more in line with actual engineering geological conditions.

[0017] (2) By using the interlayer continuity constraint transition zone processing mechanism, the problem of discontinuous parameter jump at the interface of multilayer independent random fields is solved, ensuring the numerical stability and convergence of finite element calculation.

[0018] (3) The transition zone width criterion is adaptively determined based on the spatial correlation length of adjacent layers, which has the advantages of clear physical meaning and well-founded parameter selection.

[0019] (4) This method can be used for foundation pit deformation risk analysis and construction decision optimization under complex multi-layer geological conditions. It has high precision, high applicability and scalability. Attached Figure Description

[0020] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is an example diagram of a random field in soil layers according to an embodiment of the present invention; Figure 2 This is a model mesh partitioning diagram according to an embodiment of the present invention; Figure 3 This is a model boundary definition diagram according to an embodiment of the present invention; Figure 4 This is a diagram showing the horizontal displacement distribution of the retaining wall according to an embodiment of the present invention. Figure 5 This is a distribution diagram of the average maximum wall displacement in an embodiment of the present invention; Figure 6 This is a distribution diagram of the maximum wall displacement standard deviation in an embodiment of the present invention; Figure 7This is a probability distribution diagram of wall deformation failure according to an embodiment of the present invention; Figure 8 This is a schematic diagram of a method for predicting the probability of excavation displacement in a heterogeneous multi-layered soil condition according to an embodiment of the present invention. Detailed Implementation

[0022] 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.

[0023] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0024] Example 1 like Figure 1-Figure 8 As shown, this invention provides a method for predicting the probability of excavation displacement in heterogeneous multi-layered soil conditions. This method can be used for deformation risk analysis and construction decision optimization in complex multi-layered geological conditions, overcoming the shortcomings of existing single random fields that cannot reflect the differentiated spatial variability of multi-layered soil. The process includes the following steps: Step 1: Divide the soil into multiple layers according to the engineering survey report, and independently select key soil random parameters and their statistical characteristics for each layer.

[0025] Step 2: Use COMSOL Multiphysics to establish a two-dimensional finite element excavation model of soil-structure interaction.

[0026] Step 3: Generate random fields for each soil layer based on the hierarchical differentiated Karhunen-Loève expansion method, and apply continuity constraint transition zone treatment at the interlayer interface to generate a global continuous random field.

[0027] Step 4: MATLAB calls COMSOL Multiphysics to calculate the wall displacement under different random fields.

[0028] Step 5: Construction of a set of random simulated responses based on simulated samples and quantification of uncertainty.

[0029] Furthermore, the method for selecting random parameters for multi-layered soil in step 1: The strata within the impact area of ​​the foundation pit are divided into: L Layers, each layer l ( l =1, 2, ..., LIndependently select key soil parameters (including but not limited to the internal friction angle). f l Cohesion c l and elastic modulus E l And assume that it follows a given probability distribution function (such as a normal distribution or a log-normal distribution). The mean of each parameter. m l Data were taken from engineering survey reports, laboratory tests, or empirical standards at each level. To characterize the dispersion and spatial variability of parameters at each level, a coefficient of variation (COV) was independently introduced for each level. l Spatial related length i l (Different coefficients of variation result in different ranges of parameter values. A short correlation length indicates that two spatially close points are correlated, while those far apart are not. A long correlation length indicates that even two spatially distant points are correlated.) Statistical parameters can be completely different across different layers to accurately reflect the differentiated spatial variability of multi-layered soil.

[0030] Further, step 2, finite element model analysis: An elastoplastic constitutive model is constructed using the Drucker-Prager strength criterion: In the formula, I 1 and J 2 represents the first invariant of stress and the second invariant of deviatoric stress, respectively. α , k Here, represents a material constant. A two-dimensional plane strain model is used to simulate foundation pit excavation in COMSOL Multiphysics software. In the two-dimensional plane strain analysis, the matching relationship between the Drucker-Prager criterion and the Mohr-Coulomb criterion is as follows: in, , These are the internal friction angle of the soil and the cohesion of the soil, respectively.

[0031] During the excavation of the foundation pit, the displacement of the retaining wall is described by the quasi-static governing equations of solid mechanics: in, For divergence operators, s Let be the stress tensor, and f be the volume force. Under the assumption of small deformation (usually considered as the ratio of displacement deformation to structural characteristic lengths (such as span, side length, etc.) less than 5%), the strain-displacement relationship is: in, It is a displacement matrix.

[0032] The elastic stage satisfies the generalized Hooke's law σ=D:ε, while the plastic stage follows a specified yield criterion (determined based on the selected yield criterion). For multi-layered soil models, each layer is assigned a different material parameter domain in the finite element model according to the actual stratum distribution.

[0033] Furthermore, step 3, the method for handling the hierarchical differentiated KL expansion and the interlayer continuity constraint transition zone, includes the following sub-steps: (3.1) Layered Differentiated KL Deployment For each soil layer l ( l =1, 2, ..., L ), in its occupied spatial domain Ω l The KL (Karhunen-Loève) expansion is performed independently within the unit. l The random field of the layer is represented as: In the formula, As coordinates, μl For the first l Mean values ​​of parameters in a layered random field. For uncorrelated random variables that conform to a standard normal distribution, and The first l Layer covariance function Cl The corresponding eigenvalues ​​and eigenfunctions; Ml For the first l The truncation order of the layer KL expansion. The covariance function for each layer is exponential. in, , These are the coordinates of two points, 1 and 2, in space. s l = COV l × m l For the first l Layer standard deviation, i l For the first l The length of the soil layer is related to the spatial dimensions. The key difference lies in the different soil layers. s l , i l and m l As different values ​​are taken, the eigenvalue spectrum and eigenfunction of each layer are also different, thus reflecting the spatial variation characteristics of the differences in each layer.

[0034] (3.2) Solving for eigenvalues ​​and eigenfunctions of each layer The eigenvalues ​​and eigenfunctions are obtained by solving the independent second-kind Fredholm homogeneous integral equations for each layer: For exponential covariance functions, analytical solutions exist. The eigenvalues ​​and eigensols of the function are as follows: in, . The characteristic frequency to be determined can be determined by solving the following transcendental equation, which has infinitely many positive roots. Arrange them in ascending order, thus obtaining a descending order. .

[0035] Extending the one-dimensional form to two dimensions: The superscript 1 represents x Direction, 2 represents z direction, It is the first One eigenvalue or eigenfunction yes x Direction One eigenvalue or eigenfunction yes y Direction Each eigenvalue or eigenfunction. Note that due to the different Ω values ​​in each layer... l The geometric ranges are different (especially) z Even if the correlation length is the same in the same direction (the thickness varies in different directions), the eigenvalue spectrum and eigenfunction shape of each layer will be different.

[0036] (3.3) Treatment of interlayer continuity constraint transition zone In adjacent soil layers l and l +1 interface location z = z {l,l+1} If two independent KL expansion random fields are directly spliced ​​together, the parameter values ​​will exhibit discontinuous jumps at the interface. To address this issue, this invention introduces a transition band processing mechanism.

[0037] Transition zone definition: in the interface z {l,l+1} Up and down d Define a transition zone area within / 2.T {l,l+1} ,Right now z ∈[ z {l,l+1} - d / 2, z {l,l+1} + d / 2]. The transition band width δ is determined by the following criteria: d = b · min( i l , θ l+1 ) in β The transition band width coefficient ranges from 0.1 to 0.5, with 0.2 being preferred. Selecting the smaller of the correlation lengths of the two layers as a benchmark ensures that the transition band width does not exceed the effective correlation range of either layer, maintaining physical rationality.

[0038] Transition zone fusion formula: In the transition zone T {l,l+1} Within, for the same spatial point x The random field values ​​are obtained using distance-weighted linear interpolation: in d = z - z {l,l+1} To calculate the distance from a point to the interlayer interface, the distance weighting function is defined as: , , d ∈ [ -d / 2 , d / 2] The weighting function satisfies the following properties: (a) at the interface ( d =0), (a) The upper and lower layers each contribute half; (b) at the boundary of the transition zone ( d = d / 2), , (c) at the lower boundary of the transition zone ( d =- d / 2), , It completely degenerates into a lower-level random field; (d) This ensures the physical validity of the merged random field values.

[0039] (3.4) Construction of global continuous random fields Through the above processing, a global continuous random field covering the entire computational domain is constructed.H ( x ): H ( x ) = H l ( x ), when x ∈Ω l and |z - z {l,l+1} |>d / 2 H ( x ) = H T ( x ), when |z - z {l,l+1} | ≤ δ / 2 The global continuous random field has the following characteristics: (1) it retains the independent statistical characteristics of each soil layer; (2) it achieves smooth parameter transition through the transition zone at the interlayer interface; and (3) it avoids the numerical instability of the finite element caused by parameter jumps.

[0040] In the MATLAB programming environment, the above-described layer generation and transition band splicing operations are performed on each random field sample to generate... N Output a global continuous random field sample in text file (.txt) or matrix format.

[0041] Furthermore, in step 4, the specific steps for MATLAB to call COMSOL Multiphysics for calculation are as follows: Step A1: In the COMSOL Multiphysics software, create an interpolation function under the global definition node.

[0042] Step A2: Configure the data source of the interpolation function to be an external file, which is a text file generated by MATLAB and storing global continuous random field data, wherein the data format includes spatial coordinate dimensions and corresponding soil parameter values ​​for each layer.

[0043] Step A3: In the physics settings or material properties of COMSOL Multiphysics, reference the interpolation function name to assign and call the global continuous random field data as a spatially varying physical quantity or material parameter.

[0044] Step A4: Establish a connection with a COMSOL model file through the LiveLink for MATLAB interface provided by COMSOL Multiphysics. Set up a loop control structure in MATLAB, with the number of iterations matching the number of global continuous random field samples generated. Drive COMSOL to load each random field sample file sequentially, call the solver to complete the calculation, and extract the displacement results data to a specified file for saving.

[0045] Furthermore, step 5 involves constructing a set of random simulated responses based on simulated samples and quantifying the uncertainty: The calculated displacement results of retaining walls corresponding to each global continuous random field sample were imported into the MATLAB environment in text format for post-processing analysis. The mean and standard deviation of each response quantity were calculated using statistical methods, and their probability density functions were plotted based on the sample data. The Monte Carlo method was used to fit the distribution characteristics of the response variables and identify their most likely distribution type (e.g., normal, log-normal, or skewed distribution). Based on the obtained probability distribution curves, the failure probability of the structure under different control indices (e.g., when the maximum wall displacement exceeds the allowable limit) was calculated to quantitatively assess the impact of the spatial variability of multi-layered soil on the foundation pit displacement.

[0046] Example 2 The present invention discloses a method for predicting the probability of excavation displacement in heterogeneous multi-layered soil conditions, which specifically includes the following process: 1. Setting parameters for multi-layered soil and generating random fields This example uses a three-layer foundation pit as an example. According to the engineering survey report, the strata within the influence area of ​​the foundation pit are divided into three layers from top to bottom: the first layer is a fill layer (10m thick), the second layer is a silty clay layer (25m thick), and the third layer is a sandy soil layer (25m thick). The soil parameters of each layer are shown in the table below: Table 1 Statistical parameters of soil layers KL expansion is performed on each layer to generate independent two-dimensional Gaussian random fields for each layer. At the interface between layers 1 and 2 ( z Set the transition zone width at 10m (point) d 12 = 0.2 × min(2, 5) = 0.4m; at the interface of layer 2-3 ( z (At a distance of 35m) Set the width of the transition zone d 23 = 0.2 × min(5, 10) = 1.0m. Within the transition zone, adjacent random fields are fused using distance-weighted interpolation to ultimately construct a global continuous random field. Each set of parameters generates 500 random field samples.

[0047] 2. Model dimensions and boundary conditions The geometry and boundary conditions of the excavation pit are as follows: the total length of the calculation area is 90m, the height is 60m, and the excavation depth is 30m. The concrete retaining wall is 30m high and 0.8m wide. Supports are installed promptly after excavation, with three supports located at 4.8m, 9.3m, and 14.35m below the initial surface, respectively. Fixed constraints are applied to the bottom boundary, and horizontal constraints are applied to the left and right vertical boundaries, allowing only vertical displacement.

[0048] 3. Finite element modeling Excavation is simulated using parametric scanning. For portions of the wall exceeding the actual excavation depth, a boundary load is applied to the uncracked side of the retaining wall, equal to the in-situ stress on the excavated side. Boolean expressions enable or disable supports based on the soil excavation depth. A mapped mesh is applied to the retaining wall domain, while the soil portion uses a structured uniform mesh with four-node elements of 1m x 1m size. The finite element model assigns different material parameter domains based on three soil strata, and a global continuous random field is mapped to each mesh node via an interpolation function.

[0049] 4. Import and numerical solution of random fields In this embodiment, the generated global continuous random field file is imported into COMSOL Multiphysics software. First, an interpolation function is created under the global definition node, and the independent variable of the interpolation function is defined as spatial coordinates (…). x , y The function values ​​are the corresponding global continuous random field parameter values. Then, a loop structure is set up in MATLAB to control the automatic repeated calculation of COMSOLMultiphysics. Each loop loads a global continuous random field file and performs a finite element solution once. When the number of loops reaches... N The calculation will automatically end when the value reaches 500.

[0050] 5. Statistical Analysis After excavation, wall displacement was directly extracted using MATLAB software. The maximum horizontal displacement of each displacement curve was extracted from 500 random simulations, forming a maximum wall displacement sample set. Further probabilistic statistical analysis was performed on this sample to obtain the probability distribution of the maximum displacement. Based on the distribution of the maximum wall deflection, if the deflection exceeds a set limit, it is considered a failure. The failure probability was calculated to quantitatively assess the impact of the spatial variability of multi-layered soil on the foundation pit displacement.

[0051] Comparative analysis with traditional single random field methods shows that the layered differentiated KL expansion method proposed in this invention can more accurately reflect the displacement distribution characteristics under multi-layered strata conditions. In particular, when there are significant differences in mechanical parameters between layers, traditional methods may underestimate or overestimate displacement risk, while the probability predictions given by the method of this invention are more reliable.

[0052] Example 3 This invention provides a system for predicting the probability of excavation displacement in heterogeneous multi-layered soil conditions. The system is used to implement the method described in Embodiment 1. The system includes: a soil layer division and parameter statistics module, a finite element model construction module, a layered random field generation module, a random finite element calculation module, and a variability impact assessment module. The soil layer division and parameter statistics module is used to divide the soil into multiple layers according to the engineering survey report, and to independently select key soil random parameters and their statistical characteristics for each layer. The finite element model building module is used to build a two-dimensional finite element excavation model of soil-structure interaction using COMSOL Multiphysics. The layered random field generation module is used to generate random fields for each soil layer based on key soil random parameters and their statistical characteristics using the layered differentiated Karhunen-Loève expansion method, and to apply a continuity constraint transition zone at the interlayer interface to generate a global continuous random field. The stochastic finite element calculation module is used to input a global continuous stochastic field into a two-dimensional soil-structure interaction finite element excavation model, and to calculate the wall displacement under different stochastic fields by calling the two-dimensional soil-structure interaction finite element excavation model through MATLAB. The variability impact assessment module is used to quantitatively assess the impact of spatial variability of multi-layer soil on foundation pit displacement based on wall displacement under different random fields.

[0053] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for predicting the probability of excavation displacement in heterogeneous multi-layered soil conditions, characterized in that, The method includes: Step 1: Divide the soil into multiple layers according to the engineering survey report, and independently select key soil random parameters and their statistical characteristics for each layer; Step 2: Use COMSOL Multiphysics to establish a two-dimensional finite element excavation model of soil-structure interaction; Step 3: Based on the key soil random parameters and their statistical characteristics, generate random fields for each soil layer using the layered differential Karhunen-Loève expansion method, and apply a continuity constraint transition zone at the interlayer interface to generate a global continuous random field. Step 4: Input the global continuous random field into the two-dimensional soil-structure interaction finite element excavation model, and use MATLAB to call the two-dimensional soil-structure interaction finite element excavation model to calculate the wall displacement under different random fields; Step 5: Based on the wall displacement under different random fields, quantitatively evaluate the impact of the spatial variability of multi-layer soil on the foundation pit displacement.

2. The method according to claim 1, characterized in that, The independent selection method for random parameters of multi-layered soil is as follows: The strata within the impact area of ​​the foundation pit are divided into: L Layers, each layer l , l =1, 2, ..., L Select key soil parameters independently, including but not limited to the internal friction angle. φ l Cohesion c l and elastic modulus E l Each layer of parameters is assumed to be independent and follows a given probability distribution function, where the mean of each parameter is... μ l Data was taken from engineering survey reports at each level, and the coefficient of variation (COV) was determined independently for each level. l Spatial related length θ l This is to reflect the differentiated statistical characteristics of different soil layers.

3. The method according to claim 2, characterized in that, Methods for establishing two-dimensional soil-structure interaction finite element excavation models using COMSOL Multiphysics include: An elastoplastic constitutive model is constructed using the Drucker-Prager strength criterion: ； In the formula, I 1 and J 2 represents the first invariant of stress and the second invariant of deviatoric stress, respectively. α , k These are material constants; When simulating foundation pit excavation in COMSOL Multiphysics software, a two-dimensional plane strain model is used. In the two-dimensional plane strain analysis, the Drucker-Prager criterion and the Mohr-Coulomb criterion are matched. ； in, , These are the internal friction angle of the soil and the cohesion of the soil, respectively. During the excavation of the foundation pit, the displacement of the retaining wall is described by the fundamental governing equations of solid mechanics. Assuming it is a quasi-static problem, the governing equations are: ； in, For divergence operators, σ Let f be the stress tensor and f be the body force; under the assumption of small deformation, the relationship between strain and displacement is: ； In the formula, It is a displacement matrix, and ε is the strain tensor; in the elastic stage, stress and strain satisfy the generalized Hooke's law σ = D:ε, where D is the constitutive stiffness tensor, which depends on Young's modulus. E Compared with Poisson ν Once the stress exceeds the yield strength, it enters the plastic stage and follows the specified yield criterion.

4. The method according to claim 3, characterized in that, Methods for generating a global continuous random field include: using the hierarchical differential Karhunen-Loève expansion method to generate random fields for each soil layer, and applying continuity constraint transition zones at the interlayer interfaces. For each soil layer l In its occupied spatial domain Ω l Each layer independently performs a KL expansion to obtain random fields. By solving the independent second-type Fredholm homogeneous integral equations for each layer, the eigenvalues ​​and eigenfunctions of each layer are obtained. A continuous transition zone with interlayer continuity constraints is applied to two independent KL expansion random fields to construct a global continuous random field covering the entire computational domain.

5. The method according to claim 4, characterized in that, For each soil layer l In its occupied spatial domain Ω l Methods for independently performing KL expansions to obtain random fields for each layer include: ； In the formula, As coordinates, μl For the first l Mean values ​​of parameters in a layered random field. For uncorrelated random variables that conform to a standard normal distribution, and The first l Layer covariance function Cl The corresponding eigenvalues ​​and eigenfunctions; Ml For the first l The truncation order of the layer KL expansion; The covariance function for each layer adopts the exponential form: ； In the formula, , These are the coordinates of two points, 1 and 2, in space. σl = COV l × μl For the first l Layer standard deviation, θl For the first l Layer space related length.

6. The method according to claim 5, characterized in that, Methods for obtaining eigenvalues ​​and eigenfunctions of each layer by solving the independent second-kind Fredholm homogeneous integral equations for each layer include: ； For exponential covariance functions, analytical solutions are used to obtain the eigenvalues ​​and eigenfunctions of each layer, and the one-dimensional form is extended to two dimensions: ； ； in, It is the first One eigenvalue or eigenfunction It is the x-direction of the first One eigenvalue or eigenfunction It is the y-direction first 1 eigenvalues ​​or eigenfunctions, where the superscript 1 represents eigenvalues ​​or eigen x Direction, 2 represents z The spatial lengths of each layer differ in each direction.

7. The method according to claim 6, characterized in that, Methods for handling the interlayer continuity constraint transition zone of two independent KL expansion random fields include: In adjacent soil layers l and l At the +1 interface, the width is defined as δ transition zone region T {l,l+1} The transition zone is located at the top and bottom of the interface. δ Within the range of / 2; In the transition zone T {l,l+1} Internally, a distance-weighted smooth interpolation function is used to fuse the random field values ​​of the upper and lower layers. The fusion formula is as follows: ； in, d To calculate the signed distance from a point to the interlayer interface, d >0 indicates that it is on the upper side. d <0 indicates that it is on the lower side; and The distance-weighted function is specifically defined as: d ∈[ -δ / 2, δ / 2]； d ∈[ -δ / 2, δ / 2]； Outside the transition zone, i.e. | d | > δ For the region of / 2, the random field value is directly taken from the KL expansion result of the corresponding layer; transition band width δ Determined as: δ = β · min( θ l , θ l+1 ); in β This is the transition zone width coefficient, with a value ranging from 0.1 to 0.

5. θ l and θ l+1 These represent the spatial correlation lengths of two adjacent floors.

8. The method according to claim 7, characterized in that, The constructed global continuous random field covering the entire computational domain is as follows: H ( x ) = H l ( x ),when x ∈Ω l and |z - z {l,l+1} | > δ / 2; H ( x ) = H T ( x ),when |z - z {l,l+1} | ≤ δ / 2.

9. The method according to claim 1, characterized in that, Methods for calculating wall displacements under different random fields by inputting a global continuous random field into a two-dimensional soil-structure interaction finite element excavation model and then using MATLAB to call the two-dimensional soil-structure interaction finite element excavation model include: Create an interpolation function under the global definition node in the COMSOL Multiphysics software; Configure the data source of the interpolation function to come from an external file, which is a text file generated by MATLAB and storing global continuous random field data, wherein the data format includes spatial coordinate dimensions and corresponding soil parameter values ​​for each layer. In the physics settings or material properties of COMSOL Multiphysics, the interpolation function is referenced to assign and call global continuous random field data as spatially varying material parameters; A connection is established through the LiveLink for MATLAB interface provided by COMSOL Multiphysics. In MATLAB, a loop control structure is set up with the number of loops matching the number of samples in the global continuous random field. COMSOL is then driven to load each random field sample file sequentially, call the solver to complete the calculation, and extract the displacement results data to a specified file for saving.

10. A system for predicting the probability of excavation displacement in heterogeneous multi-layered soil conditions, the system being used to implement the method described in any one of claims 1-9, characterized in that, The system includes: a soil layer division and parameter statistics module, a finite element model construction module, a layered random field generation module, a random finite element calculation module, and a variability impact assessment module; The soil layer division and parameter statistics module is used to divide the soil into multiple layers according to the engineering survey report, and to independently select key soil random parameters and their statistical characteristics for each layer. The finite element model building module is used to establish a two-dimensional finite element excavation model of soil-structure interaction using COMSOL Multiphysics. The layered random field generation module is used to generate random fields for each soil layer based on key soil random parameters and their statistical characteristics using the layered differentiated Karhunen-Loève expansion method, and to apply a continuity constraint transition zone at the interlayer interface to generate a global continuous random field. The stochastic finite element calculation module is used to input a global continuous random field into a two-dimensional soil-structure interaction finite element excavation model, and to calculate the wall displacement under different random fields by calling the two-dimensional soil-structure interaction finite element excavation model through MATLAB. The variability impact assessment module is used to quantitatively assess the impact of multi-layer soil spatial variability on foundation pit displacement based on wall displacement under different random fields.

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