Method for analyzing bearing performance of prestressed hollow square pile based on model fusion

Abstract

The invention discloses a method for analyzing the bearing performance of a prestressed hollow square pile based on model fusion, and relates to the technical field of geotechnical engineering analysis. The method comprises the following steps: establishing a pre-stressed hollow square pile-soil system unified analysis model fusing a physical mechanism and data driving, constructing a parameterized input space containing geometric parameters, material parameters, soil body parameters and load conditions of the pre-stressed hollow square pile, establishing a composite loss function, and taking variables in the parameterized input space as input; taking at least one physical field response of the pile-soil system as an output deep neural network, taking minimization of a composite loss function as an optimization target, training the deep neural network, and obtaining a trained physical information deep neural network model, and engineering parameters of the prestressed hollow square pile to be analyzed are input into the trained physical information deep neural network model, and a bearing performance prediction result is output.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering analysis technology, and in particular to a method for analyzing the bearing capacity of prestressed hollow square piles based on model fusion. Background Technology

[0002] Prestressed concrete hollow square piles, as an important type of pile foundation, are widely used in buildings, bridges, ports, and other engineering projects due to their advantages such as high bearing capacity, convenient construction, and stable quality. Accurately predicting their bearing capacity is crucial for ensuring project safety and economic optimization. However, the bearing mechanism of prestressed hollow square piles is complex, involving multi-physics coupling problems such as the nonlinearity of the pile concrete material, the prestress effect, the nonlinear contact between the pile and soil interface, and the spatial variability of the soil. Traditional analysis methods face numerous challenges.

[0003] Currently, the main traditional analysis methods used in engineering practice include: empirical formula methods based on standards, finite element methods based on numerical simulation, and experimental methods based on field tests. However, traditional analysis methods struggle to balance accuracy, efficiency, reliability, and interpretability: standard methods are efficient but have low accuracy and unclear mechanisms; finite element methods have clear mechanisms but are inefficient and sensitive to parameters; experimental methods are reliable but costly and cannot predict the future; and purely data-driven methods are efficient but have poor interpretability and rely on large datasets.

[0004] In recent years, with the development of artificial intelligence technology, purely data-driven machine learning methods (such as support vector machines, random forests, and neural networks) have begun to be used for predicting the bearing capacity of pile foundations. These methods achieve rapid prediction by learning the mapping relationship between inputs (pile parameters, soil parameters) and outputs (bearing capacity) in historical experimental data. However, existing models are mostly "black boxes," lacking physical interpretability in their predictions, making them difficult for engineers to trust and use to guide design. Furthermore, the performance of existing models heavily depends on the quantity and quality of training data, while high-quality experimental data for pile foundations is scarce and costly to obtain, making them prone to overfitting or insufficient generalization under small sample conditions. Moreover, existing models cannot guarantee that the prediction results satisfy basic physical laws (such as stress balance), potentially leading to physically unreasonable predictions in sparse data regions. Therefore, the engineering community urgently needs an analytical method that can quickly, accurately, and mechanistically clearly predict the bearing capacity of prestressed hollow square piles during the design phase. To this end, a model fusion-based method for analyzing the bearing capacity of prestressed hollow square piles is proposed. Summary of the Invention

[0005] The main objective of this invention is to provide a model-fusion-based method for analyzing the bearing capacity of prestressed hollow square piles. This method enables rapid, accurate, and mechanistic prediction of the bearing capacity of prestressed hollow square piles during the design phase. Furthermore, it allows for model calibration and inversion using limited monitoring data, thus providing core technical support for the intelligent design, construction, and safety assessment of pile foundations. This effectively addresses the problems in the background technology.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: The bearing capacity analysis method for prestressed hollow square piles based on model fusion includes the following steps: Establish a unified analysis model for the prestressed hollow square pile-soil system that integrates physical mechanisms and data-driven approaches; Construct a parameterized input space that includes the geometric parameters, material parameters, soil parameters, and load conditions of prestressed hollow square piles; Based on the unified analysis model, the parameterized input space is sampled to obtain multi-source training data. The multi-source training data includes at least the first physical field data generated by numerical simulation, the second physical field data obtained by physical experiments, and the unlabeled coordinate point data randomly sampled in the computational domain. Construct a deep neural network that takes the variables in the parameterized input space as input and the physical field response of at least one of the pile-soil systems as output; Construct a composite loss function, which includes at least: a data loss term for measuring the difference between the neural network output and the second physical field data, a physical residual loss term for forcing the neural network output to satisfy a preset set of control equations, and a constraint loss term for forcing the satisfaction of boundary conditions and pile-soil interface contact conditions. The deep neural network is trained with the goal of minimizing the composite loss function, resulting in a trained physical information deep neural network model. The engineering parameters of the prestressed hollow square pile to be analyzed are input into the trained physical information deep neural network model, which directly outputs the predicted results of its bearing capacity.

[0007] Furthermore, the physical mechanism of the unified analysis model is established based on the following set of governing equations, which includes: Static equilibrium equations are used to ensure that the infinitesimal elements of a structural system are in a state of force equilibrium at any location. The constitutive equation of concrete is used to describe the elastic-plastic or damage behavior of concrete. The soil constitutive equation is used to describe the nonlinear behavior of soil. Geometric equations are used to link the macroscopically measurable displacement field with the strain state of the internal material elements to ensure that deformation is continuous and consistent.

[0008] Furthermore, the deep neural network employs a domain decomposition architecture, including: Pile subnetworks used to simulate the pile domain; And, soil subnetworks used to simulate the surrounding soil domain; The pile subnetwork and the soil subnetwork are coupled at the shared pile-soil interface through physical continuity conditions or contact laws, and the coupling conditions are components of the composite loss function.

[0009] Furthermore, the step of training the deep neural network employs a course learning strategy, specifically including: In the first stage, the deep neural network is initially trained under the assumption of linear elastic materials. In the second stage, based on the fixed weights of the network, a nonlinear constitutive relationship between the soil and concrete is introduced for training. In the third stage, nonlinear contact conditions at the pile-soil interface are further introduced for refined training.

[0010] Furthermore, the composite loss function is expressed as: = + + + ;in, For data loss items, These are the weighting coefficients for the data loss terms. This is the physical residual loss term. The weighting coefficients for the physical residual loss term. For boundary condition loss terms, These are the weighting coefficients for the boundary condition loss term. For interface condition loss terms, These are the weight coefficients for the interface condition loss term; during training, each weight coefficient is adaptively adjusted according to the gradient statistics or changing trends of each loss component to ensure that each loss decreases in a balanced manner during the optimization process.

[0011] Furthermore, the load-bearing capacity prediction results include at least one of the following: Load-settlement curve throughout the entire process; Distribution of axial force, side friction and end resistance in the pile body; Stress and strain fields of the pile cross section; Stress and displacement fields of the soil surrounding the pile; The ultimate bearing capacity is determined based on a preset settlement standard.

[0012] Furthermore, the method also includes a parameter inversion step: The weights of the trained physical information deep neural network model are fixed; The unknown soil or interface parameters to be inverted are used as trainable variables to construct the inversion loss function; By optimizing the inversion loss function and updating the trainable variables, the parameter values ​​identified by the inversion are obtained.

[0013] Furthermore, the inversion loss function, used to describe the difference between the pile top response predicted by the neural network and the actual monitored pile top response, is defined as: = ;in, The inversion loss function is... For the measured response data of the i-th monitoring point, For inversion parameters, To use the current inversion parameters The deep learning model, along with known parameters, is input into the frozen physical information to calculate the predicted response at the i-th monitoring point. The number of monitoring data points.

[0014] A model fusion-based bearing capacity analysis system for prestressed hollow square piles includes: The data acquisition module is used to acquire the engineering parameters of the prestressed hollow square pile. The engineering parameters include at least the geometric parameters, material parameters, soil parameters and load conditions of the prestressed hollow square pile. The parameterized input space construction module is used to construct the parameterized input space for the engineering parameters of prestressed hollow square piles; The analysis model building module is used to establish a unified analysis model of the prestressed hollow square pile-soil system that integrates physical mechanisms and data-driven approaches. The spatial sampling module is used to sample the parameterized input space based on the unified analysis model to obtain multi-source training data, wherein the multi-source training data includes at least first physical field data generated by numerical simulation, second physical field data obtained by physical experiments, and unlabeled coordinate point data randomly sampled in the computational domain. A neural network module is used to construct a deep neural network that takes variables in the parameterized input space as input and at least one physical field response of the pile-soil system as output. The loss function construction module is used to construct the composite loss function of the deep neural network, wherein the composite loss function includes at least a data loss term for measuring the difference between the neural network output and the second physical field data, a physical residual loss term for forcing the neural network output to satisfy a preset set of control equations, and a constraint loss term for forcing the satisfaction of boundary conditions and pile-soil interface contact conditions. The neural network training module is used to train the deep neural network with the goal of minimizing the composite loss function, so as to obtain a trained physical information deep neural network model. The result output module is used to input the engineering parameters of the prestressed hollow square pile to be analyzed into the trained physical information deep neural network model and directly output its bearing capacity prediction results. The parameter inversion module is used to invert the trained physical information deep neural network model by using the difference between the monitoring data and the model prediction as a driving force to obtain the parameter values ​​identified by the inversion.

[0015] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the model fusion-based prestressed hollow square pile bearing performance analysis method.

[0016] The present invention has the following beneficial effects: Compared to existing technologies, this scheme constructs a physical information deep neural network by embedding physical laws such as static equilibrium equations, geometric equations, and material constitutive equations into the neural network training in the form of differentiable residual losses. This model achieves an intrinsic fusion of prior physical knowledge and measured data during the learning process. The network's predicted solutions not only fit the limited experimental data but also strictly satisfy universal physical conservation laws. Compared to purely data-driven models, this scheme's model can still provide reasonable predictions based on physical laws in data-sparse regions, significantly improving generalization ability and extrapolation accuracy, overcoming the problem of uncontrolled predictions in "black box models" when data is insufficient. Compared to the traditional finite element method, this invention's model avoids numerical errors caused by mesh discretization and iterative convergence through physical constraints, theoretically providing continuous, smooth, and strictly satisfied physical field solutions that satisfy the governing equations.

[0017] Compared with existing technologies, this solution constructs an efficient inversion framework that can use a small amount of field monitoring data (such as pile top settlement) to inversely identify equivalent soil mechanical parameters or interface parameters in a short time. Compared with traditional inversion methods (such as those combined with finite element method), this solution transforms the inverse problem into a gradient optimization process, enabling the model to be quickly calibrated based on specific site data, improving the pertinence and reliability of predictions, and providing a core tool for information-based monitoring and dynamic design adjustment during construction. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the bearing capacity analysis method for prestressed hollow square piles based on model fusion according to the present invention. Figure 2 This is a schematic diagram of the bearing capacity analysis system for prestressed hollow square piles based on model fusion, as described in this invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0020] Example 1: See Figure 1 The flowchart shown is a method for analyzing the bearing capacity of prestressed hollow square piles based on model fusion according to the present invention, which includes the following steps: Establish a unified analysis model for the prestressed hollow square pile-soil system that integrates physical mechanisms and data-driven approaches; Construct a parameterized input space that includes the geometric parameters, material parameters, soil parameters, and load conditions of prestressed hollow square piles; Based on a unified analysis model, the parameterized input space is sampled to obtain multi-source training data. The multi-source training data includes at least the first physical field data generated by numerical simulation, the second physical field data obtained by physical experiments, and the unlabeled coordinate point data randomly sampled in the computational domain. Construct a deep neural network that takes variables in a parameterized input space as input and at least one physical field response of the pile-soil system as output; Construct a composite loss function, which includes at least: a data loss term for measuring the difference between the neural network output and the second physical field data, a physical residual loss term for forcing the neural network output to satisfy the preset control equation set, and a constraint loss term for forcing the boundary conditions and pile-soil interface contact conditions to be satisfied. The deep neural network is trained with the goal of minimizing the composite loss function, resulting in a trained physical information deep neural network model. The engineering parameters of the prestressed hollow square pile to be analyzed are input into the trained physical information deep neural network model, and its bearing capacity prediction results are directly output. It also includes a parameter inversion step: The weights of the physical information deep neural network model are fixed after training. The unknown soil or interface parameters to be inverted are used as trainable variables to construct the inversion loss function; By optimizing the inversion loss function and updating the trainable variables, the parameter values ​​identified by the inversion are obtained.

[0021] The following are the complete implementation steps of the present invention, including: Step 1: Problem Definition and Physical Modeling Step 1.1: Define the analysis objectives and scope Define the forecast target: The predicted bearing capacity results can be of the following types: load-settlement curves throughout the entire process; distribution of axial force, side friction, and end resistance in the pile; stress and strain fields of the pile cross-section; stress and displacement fields of the soil surrounding the pile; and ultimate bearing capacity determined based on a preset settlement standard. Specifically, the ultimate bearing capacity, load-settlement curves, pile stress distribution, and pile-soil interaction mechanisms can be used as prediction targets for analysis.

[0022] Define the analysis scale: determine whether to use a two-dimensional axisymmetric model or a three-dimensional full model, and whether to consider time effects (creep, dynamic loading).

[0023] Define the input variable space: clarify all parameters that affect bearing capacity and their reasonable range of variation (e.g., B=300-500mm, L=10-30m, soil internal friction angle φ=15-35°, etc.).

[0024] Step 1.2: Establish the governing physical equations The physical mechanism of the unified analysis model is established based on the following set of governing equations, which include: 1) Static equilibrium equations This principle ensures that the infinitesimal elements of a structural system are in equilibrium at any location; it is a fundamental physical law that all structural analyses must satisfy. For pile-soil systems, it requires that the variation (divergence) of the internal stress in every infinitesimal volume element within the pile and surrounding soil must cancel out the body forces (such as gravity) acting on that element. This determines the stress transmission path. For example, the load applied at the pile top is transmitted downwards through the internal stresses of the pile material, including the axial force σ. zz and shear stress τ in the x and y directions xz ,τ yz .

[0025] The static equilibrium equations relate the interaction between the pile and the soil. Pile stress is transferred to soil stress through the pile-soil interface, and continues to diffuse and redistribute within the soil according to the equilibrium equations. It also reveals the load transfer mechanism: the exertion of pile side skin friction is precisely due to the pile shear stress τ. xz ,τ yz The result of varying depth to balance the changes in axial force within the pile body. This is the strongest and most universal constraint in the physical information loss function of the physical information deep learning model.

[0026] In one possible implementation, the expression for the static equilibrium equations can be defined as: In quasi-static analysis, neglecting the inertia term, the divergence of the stress tensor σ is in equilibrium with the body force b.

[0027] Tensor form: ∇×σ+b=0; where: σ is the Cauchy stress tensor, σ=[σ ij](i,j=x,y,z); b is the body force vector, usually b=ρ×g×ez, where ρ is the material density, g is the gravitational acceleration, and ez is the vertical unit vector. ∇ is the divergence operator.

[0028] Its component form in a three-dimensional rectangular coordinate system (used for residual calculation) is as follows: ∂σ xx / ∂x+∂τ xy / ∂y+∂τ xz / ∂z+b x =0; ∂τ yx / ∂x+∂σ yy / ∂y+∂τ yz / ∂z+b y =0; ∂τ zx / ∂x+∂τ zy / ∂y+∂σ zz / ∂z+b z =0; Due to the symmetry of the stress tensor (τ) xy =τ yx ,τ xz =τ zx ,τ yz =τ zy Therefore, it is usually abbreviated as: The residual R of the static equilibrium equation in the x-direction x,balance =σ xx,x +τ xy,y +τ xz,z =0; The residual R of the static equilibrium equation in the Y direction y,balance =τ xy,x +σ yy,y +τ yz,z =0; The residual R of the static equilibrium equation in the z-direction z,balance =τ xz,x +τ yz,y +σ zz,z +ρg=0 (Let bz=-ρg); In this context, the comma subscript indicates a partial derivative, such as σ. xx,x =∂σ xx / ∂x.

[0029] Its role in deep learning models of physical information: the stress field σ predicted by the network. pred The residual R should be minimized at all points within the computational domain. balance =(R x,balance ,R y,balance ,R z,balance It is close to zero.

[0030] 2) Geometric equations It is used to link macroscopically measurable displacement fields with the strain state of internal material elements to ensure continuous and consistent deformation. It defines strain as a measure of displacement gradient. Under small deformation theory, it guarantees that no cracks or overlaps will appear in the object after deformation (satisfying the compatibility condition from the perspective of continuum mechanics). In analysis, this is specifically reflected in: The easily monitorable "displacement" (such as pile top settlement w, horizontal displacement u at different depths of the pile) is transformed into a key input for analyzing material response—"strain" (ε). zz ,γ xz (etc.). Bearing capacity is essentially a manifestation of material stress, and stress needs to be calculated through strain. The compression zone and bending zone of the pile body, as well as the shear zone and plastic zone of the soil, can be clearly identified through the strain field.

[0031] Connecting different components: This ensures that the displacement of the pile is geometrically compatible with the displacement of the adjacent soil, providing a basis for defining the relative slip (displacement difference) of the pile-soil interface.

[0032] Its key role in deep learning models of physical information is bridging the gap between automatic differentiation and physical reasoning. The neural network directly outputs the displacement field u, while the strain field ε is obtained by automatically differentiating u. This avoids the incompatible strain fields that may occur in traditional finite element methods due to discretization, and eliminates the need for the network to learn strain additionally or worry about strain-displacement mismatch. The constitutive equations and equilibrium equations are directly established on a reliable strain field.

[0033] The tensor form of its equation is: ε = (1 / 2)*[∇u + (∇u)] T ]; where: ε is the small strain tensor, ε=[ε ij ]; u is the displacement vector, u=(u,v,w)=(u x ,u y ,u z ∇u is the displacement gradient tensor, (∇u) T It is its transpose.

[0034] The component form of its equation is: ε xx =∂u / ∂x; ε yy =∂v / ∂y; ε zz =∂w / ∂z; γ xy =2×ε xy =∂u / ∂y+∂v / ∂x; γ xz =2×ε xz =∂u / ∂z+∂w / ∂x; γ yz =2×ε yz =∂v / ∂z+∂w / ∂y; It should be noted that the relationship between engineering shear strain γ and tensor shear strain ε is γ = 2ε.

[0035] 3) Concrete constitutive equation Used to describe the elastoplastic or damage behavior of concrete, it describes the quantitative relationship between internal stress and strain of the concrete material in the prestressed hollow square pile body when it is under stress, and reflects its key nonlinear mechanical properties.

[0036] Key characteristics specifically demonstrated in the analysis: Initial stiffness and elasticity: The linear behavior of concrete at low stress levels is defined by the elastic tensor Ce.

[0037] The effect of prestressing: The prestressing effect applied to the concrete by the prestressing tendons is equivalently characterized by the initial strain ε0. This is the core difference between prestressed piles and ordinary piles, as it actively improves the stress state of the pile body and enhances crack resistance and stiffness.

[0038] Nonlinearity and strength softening: The damage variable D is used to characterize the microcrack development, stiffness degradation, and strength softening process of concrete as it approaches and reaches its ultimate load. This determines the initiation and evolution of pile failure.

[0039] Plastic deformation: The permanent deformation that cannot be recovered after the load is removed is described by plastic strain εp.

[0040] Its key role in physical information deep learning models is to provide differentiable physical transformation rules from strain (a geometric quantity) to stress (a mechanical quantity). This constrains the concrete stress predicted by the neural network to conform to the known mechanical behavior of the material, which is derived from the strain state (through geometric equations from displacement).

[0041] Specifically, the constitutive equation of concrete can be described using a differentiable, simplified combinatorial model, as follows: a) Total strain decomposition and effective stress The total strain ε is decomposed into elastic strain ε e and plastic strain ε p Meanwhile, considering the initial prestress strain ε0 (caused by the tensioning of the prestressing tendons, which is a known field): ε = ε e +εp+ε0; Define effective stress σ eff Its effect on the concrete skeleton: σ eff =C e :ε e =C e :(ε-εp-ε0); where Ce It is a fourth-order isotropic elastic stiffness tensor, determined by the initial elastic modulus E0 and Poisson's ratio ν.

[0042] b) Damage and apparent stress A scalar damage variable D (0 ≤ D < 1) is introduced to describe the material stiffness degradation. The actual, macroscopically measured apparent stress σ is: σ = (1 - D) * σ eff .

[0043] c) Damage evolution and yield function (plasticity) Damage D and plastic strain ε p The evolution needs to be associated with a yield / damage surface to ensure differentiability. The following smooth form is commonly used: Form 1: Definition of Equivalent Variable Define a positive scalar strain measure, such as the elastic strain energy density equivalent strain: ε eq =sqrt(ε e :C e :ε e ) / E0; where sqrt() is the square root function.

[0044] Form 2: Plastic Yield Function To clearly distinguish between plasticity and damage, a differentiable plastic yield function F can be used, such as the smooth Drucker-Prager criterion based on effective stress: F(σ eff ,K p )=q eff -(AB×p eff )*[1-α×tanh(γ×K p )]≤0; where p eff It is the effective mean stress, q eff It is the effective generalized shear stress, where A, B, α, and γ are material constants, and K is the effective generalized shear stress. p It is a plastic internal variable. The constraint F≤0 introduces a loss function through the penalty function method or the Lagrange multiplier method.

[0045] 4) Soil constitutive equation Used to describe the nonlinear behavior of soil, it quantitatively describes the stress-strain-strength relationship of the complex medium of soil around and at the pile tip, and is the key to accurately simulating the load transfer from the pile to the soil and the resulting soil response.

[0046] The key characteristics specifically reflected in the analysis include: Characteristic 1: Nonlinearity and stress dependence The soil modulus increases with increasing confining pressure (p). η in the Drucker-Prager criterion... pThis reflects the characteristic that the strength of frictional soil increases linearly with confining pressure, which is one of the most fundamental differences between soil and materials such as metal.

[0047] Characteristic 2: Shear Failure Criterion The yield function F=0 defines the failure envelope of soil under combined stresses (p and q). It determines the theoretical maximum values ​​of the ultimate skin friction and ultimate end bearing of the pile.

[0048] Characteristic 3: Plastic flow and hardening / softening The flow law defines the direction of deformation (whether or not the soil expands) after yielding; the hardening law describes the changes in strength parameters (such as φ and c) after yielding, simulating the process of soil from peak strength to residual strength. This affects the hardening or softening morphology of the pile load-settlement curve.

[0049] Its key role in deep learning models of physical information: Similar to the constitutive equation of concrete, it is the physical law for calculating soil stress. However, its importance is even more prominent because the bearing capacity of a pile is ultimately provided entirely by the soil. The equation is: The load transfer function is determined by the shear stress (i.e., side friction) at a point on the side of the pile, which depends on the relative displacement (slippage) between the pile and the soil at that point, as well as the current stress state and strength of the soil at that point. All of these are controlled by the soil constitutive equation.

[0050] Predicting soil failure modes: The yield function can be used to determine whether the soil around the pile has entered a plastic state, thereby predicting whether the pile will fail first or the soil will fail first, as well as the extent of the expansion of the plastic zone of the soil.

[0051] Achieving nonlinear coupling of the system: The nonlinear response of the soil is strongly coupled with the displacement field of the pile (through the equilibrium equation and interface conditions) through the constitutive equation, which together determine the nonlinear bearing behavior of the entire system.

[0052] Specifically, to balance accuracy and differentiability, a smoothed Drucker-Prager (DP) elastoplastic model is used to define the soil constitutive equations: a) Stress and strain The total strain of the soil is entirely composed of the elastoplastic component: ε = ε e +ε p .

[0053] b) Elastic part The elastic stress-strain relationship is similar to that of concrete, but the parameters are different: σ e =C es :ε e =C es :(ε-ε p ); where C es It is determined by the soil's elastic modulus Es and Poisson's ratio νs.

[0054] c) Plastic part: Smooth DP model Stress invariants: The average stress p = tr(σ) / 3; where tr is the trace of the matrix, which is a linear function acting on the matrix. For an n×n matrix A, the trace tr(A) is defined as the sum of all elements on the main diagonal of the matrix.

[0055] The generalized shear stress q = sqrt(3*J2) = sqrt[(3 / 2)s:s], where s = σ - pI is the deviatoric stress tensor.

[0056] Yield function (smoothed): The standard DP yield function is: F = q - η × p - ξ × c; where η and ξ are constants related to the friction angle φ (e.g., η = 6sinφ / (3-sinφ), ξ = 6cosφ / (3-sinφ)), and c is the cohesion.

[0057] Plastic flow laws and hardening: The flow rules can be correlated (Q=F) or uncorrelated. The direction of the plastic strain rate is given by the gradient of the plastic potential function Q. The hardening law can be expressed by the friction angle φ or the cohesion c as a function of the plastic shear strain ε. pq It is reflected by changes, for example: φ(ε) pq )=φ0+(φ peak -φ0)*[1-exp(-k*ε pq )).

[0058] The above four equations constitute a complete and closed mathematical-physical system, which together describe the bearing mechanism of prestressed hollow square piles: Given the load and boundary conditions, the system begins to deform, generating a displacement field (u).

[0059] The total strain (ε) is calculated from the displacement field based on the geometric equations.

[0060] The current stress (σ) of the pile body and the soil is calculated from the strain history based on their respective constitutive equations.

[0061] The calculated stress field must satisfy the static equilibrium equation everywhere. If it is not satisfied at first, the equilibrium equation will force the displacement field and material state to be adjusted through iteration (in the physical information deep learning model, it is through backpropagation of the loss function) until it is satisfied.

[0062] The adjusted displacement field then influences strain through geometric equations, which in turn influences stress through constitutive equations… This cycle continues until all equations are satisfied simultaneously. The solution obtained at this point is the true response of the system under a given load.

[0063] Within the framework of deep learning models for physical information, neural networks are trained to directly approximate the solutions (displacement field and state variable field) of this coupled system. All the residuals of the above equations are used as the source of training signals, powerfully "instilling" physical laws into the network, thereby obtaining an intelligent proxy model that both fits the data and strictly adheres to physical laws.

[0064] Step 1.3: Constructing the computational domain and coordinate system Define the pile domain Ω pile and soil domain Ω soil The geometric shape.

[0065] Establish an overall coordinate system and determine the definition of each physical field (displacement, stress) within the domain.

[0066] Step 2: Data Preparation and Sampling Strategy Step 2.1: Multi-source data collection and fusion High-fidelity data (sparse but accurate): collects key data from laboratory model tests and field static load tests (pile top load-settlement data, strain data of specific sections of the pile body).

[0067] Low-fidelity data (rich but approximate): Run parametric finite element analysis (FEA) to generate a large amount of "virtual test" data covering the entire input variable space and obtain full-field information (stress and strain contour plots).

[0068] Physical knowledge data (unlabeled): A large number of points randomly generated on the computational domain and boundaries, requiring no measurements and used solely for calculating physical residuals.

[0069] Step 2.2: Training Point Sampling Design Internal residual point sampling: in Ω pile and Ω soil Internally, a point set is generated using Latin hypercube sampling or an adaptive method to evaluate the PDE loss.

[0070] Boundary / interface point sampling: Special sampling is performed at displacement boundaries, load boundaries, and pile-soil interfaces to assess boundary losses and contact losses.

[0071] Data point sampling: Sampling is performed at the actual measurement locations (pile top, strain gauge location) to calculate data loss.

[0072] Increase sampling density in key areas: Actively increase sampling density in the pile tip and near the interface area on the pile side.

[0073] Step 3: Construction of the network architecture and loss function for the deep learning model of physical information Step 3.1: Neural Network Structure Design Backbone network selection: Design a deep feedforward neural network (e.g., 8-10 layers, 256 neurons per layer), with inputs of (x, y, z, material parameters, load parameters) and outputs of all physical field components (u, v, w, σ). xx ,σ yy ,...).

[0074] Feature embedding: Fourier feature maps or sinusoidal activation functions are added after the input layer to better learn high-frequency features.

[0075] Domain decomposition strategy (optional but recommended): Establish sub-networks (Sub-physical information deep learning models) for the pile domain and soil domain respectively, and achieve strong coupling at the shared interface through physical continuity conditions.

[0076] Step 3.2: Formalization of the composite loss function The composite loss function is expressed as: = + + + ;in, For data loss items, These are the weighting coefficients for the data loss terms. This is the physical residual loss term. The weighting coefficients for the physical residual loss term. For boundary condition loss terms, These are the weighting coefficients for the boundary condition loss term. For interface condition loss terms, These are the weighting coefficients for the interface condition loss term. During training, each weighting coefficient is adaptively adjusted based on the gradient statistics or trends of each loss component to ensure a balanced decrease in each loss during optimization. Specifically, 1) Data loss L data Used to ensure that the model's predictions match actual engineering observation data, this loss serves as the "anchor point" for model calibration in the real world. This loss measures the difference between the neural network's predicted and measured values ​​at known measurement points (i.e., locations with real data). It forces the network's learning process to remain grounded in reality, prioritizing high accuracy at locations where data is available.

[0077] In one possible implementation, it can be specifically defined as: L data =(1 / N d )Σ||NN output(Xi) -Measured datai || 2 ; where N dX represents the total number of data points. i This is the coordinates and state vector of the i-th data point. It is a multi-dimensional input that includes not only the spatial location (x, y) but also the state vector. i ,y i ,z i This usually includes the corresponding load step number or load value, as well as the material identifier for that point (to distinguish between piles and soil); NN output(Xi) For neural networks, input X i The output is a vector of predicted physical quantities. The specific content depends on the network's output design. For example, for pile top settlement data points, the output is the predicted vertical displacement w. pred For the pile strain gauge data points, the output may be the predicted axial strain εzz. pred ;Measured datai For position / state X i The corresponding measured physical quantity vector. For example, the measured value s of the pile top settlement under the k-th level load in a static load test. measured，k ; or the reading ε of a certain depth strain gauge under the k-th level load. measured .

[0078] Project counterpart: Pile top load-settlement curve (Qs curve): The core result of the static load test. L_data penalizes the deviation between predicted settlement and measured settlement.

[0079] Pile strain / stress distribution: Strain data along the pile depth obtained through embedded sensors or optical fibers. L_data penalizes the deviation between predicted strain and measured strain.

[0080] Soil displacement monitoring data: such as the deep horizontal displacement of the soil around the pile (inclinometer data).

[0081] Its role in training is to provide strong supervisory signals. It is the only part of the loss function that directly utilizes the "answer" (labeled data), responsible for quickly pulling the neural network from a randomly initialized state to a solution space consistent with the experimental data. Without this, the model might converge to a solution that mathematically satisfies the physical equations but is inconsistent with reality.

[0082] 2. Physical residual loss L pde This loss function, used to force the neural network to obey fundamental physical conservation laws (governing equations) at all points within the computational domain, is core to the model's "physical common sense" and generalization ability. This loss is not based on data, but on physical principles. A large number of points are randomly or strategically selected throughout the computational domain (piles and soil), and the physical quantities (such as stress and strain) predicted by the neural network at these points are calculated to satisfy the static equilibrium equations and constitutive relations. The residuals approach zero.

[0083] In one possible implementation, it can be specifically defined as: L pde =(1 / N p )Σ||Residual_of_Governi(∇NN output(Xj) )|| 2 ; where X j This represents the coordinates and state vector of the j-th placement point. It typically includes spatial coordinates (x, y). j ,y j ,z j Material parameters (such as the c and φ values ​​of the soil layer to which this point belongs), body force information, etc.; ∇NN output(Xj) The gradient of the neural network output with respect to the input coordinates (calculated via automatic differentiation): If the network outputs a displacement field u=[u,v,w], then ∇u is the displacement gradient tensor, from which the strain tensor ε=0.5*(∇u+∇u) can be calculated. T ); If the network directly or indirectly outputs the stress field σ, then ∇·σ is the stress divergence (used in the equilibrium equations).

[0084] `Residual_of_Governing(...)` is the residual vector of the governing equations. It is a mathematical function whose input is the neural network output and its gradient. The output is the residual value that measures the degree to which the equations are satisfied. It mainly includes two parts: the equilibrium equation residual and the constitutive relation residual. Specifically: Equilibrium equation residual: R balance =∇·σ pred +b (three-dimensional vector); Constitutive relation residual: R constitutive =σ pred -fc onstitutive .

[0085] Therefore, ||Residual_of_Governing|| 2 Usually ||R balance || 2 +λ||R constitutive || 2 The weighted sum.

[0086] Project counterpart: Static equilibrium equation residuals: ensure that the pile and soil elements do not violate Newton's laws (resultant force is zero) at any location. For example, it automatically guarantees that the rate of change of the axial force of the pile along the depth is equal to the sum of the side friction at that depth.

[0087] Constitutive residuals ensure that the stress-strain relationship of the material conforms to a given concrete damage model and soil elastoplastic model. For example, it prevents the network from predicting soil stress states that violate the Mohr-Coulomb yield criterion.

[0088] Its role in training: to provide physical regularization and interpolation / extrapolation capabilities.

[0089] Regularization: In regions where data is sparse or absent (such as inside the pile or deep in the soil), L_pde is the primary training guide signal to prevent the model from making absurd predictions in these regions.

[0090] Interpolation and extrapolation: Due to the universality of physical laws, the laws learned by the model can be extended to parameter ranges not covered by the training data (such as different pile lengths and soil types), which is difficult for purely data-driven models to achieve.

[0091] Acting as "unlimited free data": The location and number of configuration points can be generated arbitrarily, which is equivalent to providing the network with a massive amount of training samples that, although unlabeled, contain physical rules.

[0092] 3. Boundary condition loss L bc This loss term, used to ensure that the model's predicted solutions satisfy the specific boundary constraints set by the engineering problem, is key to defining a specific boundary value problem. It forces the neural network to ensure that its predictions at the boundaries of the computational domain are equal to known values ​​given in the engineering context.

[0093] In one possible implementation, it can be specifically defined as: L bc =(1 / N b )Σ||NN output(Xk) -BCv alue || 2 ; where NN output(Xk) For the neural network at this boundary point X k Predicted output at; BCv alue For the boundary point X k The specified boundary condition values, in their specific form, depend on the boundary type. Specifically: When it is a displacement boundary: BCv alue It is a specified displacement vector. For example, at the bottom of a fixed pile: BCv alue = [0, 0, 0]. The loss function penalizes the deviation between the predicted displacement and the specified displacement.

[0094] When at the stress boundary: BCv alue It is the specified boundary traction force vector t prescribed At this time, NN output(Xk) What is needed is the projection of the predicted stress vector onto the boundary normal, i.e., σpred •n. The loss function penalizes the deviation between the predicted surface force and the specified surface force.

[0095] When at a mixed / elastic boundary: BCv alue It could be an equation that relates displacement to stress.

[0096] This loss term encodes the specific settings of the engineering problem (such as how loads are applied and support conditions) into the model.

[0097] Project counterpart: Displacement boundary conditions: Pile bottom constraint: If the simulated pile tip is placed in a hard rock layer, the displacement loss term requires the pile bottom displacement (u,v,w)=(0,0,0).

[0098] Symmetrical boundary: When simplifying the model using symmetry, it is required that the normal displacement on the symmetry plane is zero and the tangential direction is free.

[0099] Stress / force boundary conditions: Pile top loading: requires the pile top surface to withstand a specified uniform pressure or concentrated force.

[0100] Far-field boundary: The outer boundary of the soil model is required to be in a state of static earth pressure (σ=K0*σ_v) or have zero displacement.

[0101] Free surface: requires that the normal stress and shear stress on the surface be zero.

[0102] The role of training: to identify a unique solution to the problem. The Physical Governing Equations (PDEs) themselves may have infinitely many general solutions. Boundary conditions are used to select the solution that best fits the specific engineering scenario from among the many possible solutions. bc Guide the network to find the correct solution that satisfies specific boundary constraints.

[0103] 4) Interface condition loss L interface This loss is used to accurately describe and enforce the complex interaction mechanism between the pile and the surrounding soil. It specifically acts on the pile-soil contact surface, forcing the kinematic and dynamic constraints of the contact surface to be met.

[0104] In one possible implementation, it can be specifically defined as: L interface =(1 / N i )Σ[Contact condition (NN output，pile(Xl) ,NN output，soil(Xl) )] 2 ; where N i X represents the total number of sampling points placed on the pile-soil interface; lHere are the coordinates of the l-th interface sampling point, which is precisely located at the interface between the outer surface of the pile body and the soil; NN output，pile(Xl) Indicates that X l The output obtained from the input pile subnet (such as the pile side displacement u) p Stress σ p ); NN output，soil(Xl) Indicates that X l The output obtained from the input soil subnet (such as the displacement u of the soil side) s Stress σ s Contact condition This is the interface contact condition residual function, used to measure whether the predicted pile and soil physical quantities at the interface point satisfy the contact law. It returns a scalar residual value (squared and included in the loss), which includes two parts: normal contact residual and tangential friction residual. Normal contact residual R n = Penalty(g,σ n Where, g = (u s - u p ) · n is the normal clearance (negative values ​​indicate penetration), σ n This is the normal contact stress. This function penalizes penetration (g<0) and tensile stress (σ). n <0), and encourages satisfying the complementarity condition (g * σ) n = 0).

[0105] Tangential friction residual R t = || τ - Friction Law (σ n , relative slip , c, φ) || 2 Where τ is the predicted interfacial shear stress, relative slip = (u s - u p )_t is the tangential relative displacement. Friction Law It is a differentiable approximation of Coulomb's friction law (e.g., smoothed using the tanh function).

[0106] Interface contact condition residual function Contact condition Usually R n + β* R t β is the weight.

[0107] It should be noted that NN output，pile(Xl) With NN output，soil(Xl)This is a key design feature in the implementation of the deep learning model for physical information in this invention. Since piles and soil are two materials with drastically different physical properties, a "domain decomposition" strategy is often adopted, which uses two sub-networks: one specifically predicting the pile body domain (Ω). pile The physical field of Ω, another predictor of the soil domain (Ω) soil The physical field of ).

[0108] Interface condition loss L interface The mechanism by which loads are transferred from the pile to the soil (side friction and end resistance) is directly defined. This is the part of the analysis that best reflects the working characteristics of the pile foundation, forcing the network to learn a physically real pile-soil coupling behavior.

[0109] Project counterpart: Normal contact condition: Non-penetration: Soil nodes cannot be embedded into the pile body, and pile nodes cannot detach from the soil (unless uplift occurs). This simulates the geometric compatibility of pile-soil contact.

[0110] Unidirectional contact pressure: The contact surface can only transmit pressure, not tension. This simulates the physical fact that the pile and soil may separate.

[0111] Tangential contact conditions (friction): Coulomb's law of friction states that the interfacial shear stress cannot exceed its shear strength (τ≤c+σ_n*tanφ), and the direction of the shear stress is opposite to the direction of the relative slip tendency. This precisely describes the mechanism of lateral friction resistance—the nonlinear process from elastic bonding to complete sliding.

[0112] Its role in training: to provide a physical channel for load transfer. The load on the pile top is transferred through L. interface The constrained interface is transmitted to the soil in the form of lateral friction and end resistance.

[0113] It defines the load transfer function: the interface loss term is essentially learning or enforcing a complex, nonlinear "spring-slip" relationship that determines the efficiency of load transfer.

[0114] It distinguishes between different working stages: through the constraints of friction conditions, the model can automatically identify whether a certain section of the pile is in the state of "elastic bonding" (small slip) or "plastic sliding" (the ultimate frictional resistance has been exerted).

[0115] It is the source of nonlinear coupling: the strong nonlinearity of the interface conditions is one of the main reasons for the nonlinear response of the entire pile-soil system, and accurate simulation of it is crucial for predicting the ultimate bearing capacity.

[0116] Step 3.3: Design of Adaptive Loss Balancing Mechanism Implement learning rate annealing or gradient statistics to dynamically adjust the weights λ during training, so that the gradient magnitudes of various losses are at the same level, avoiding any one factor from dominating the training.

[0117] Step 4: Model Training and Optimization Step 4.1: Training Strategy Formulation The training steps employ a course-based learning strategy, including: The first stage involves preliminary training of the deep neural network under the assumption of linear elastic materials. In the second stage, based on the fixed weights of the network, a nonlinear constitutive relationship between the soil and concrete is introduced for training. In the third stage, nonlinear contact conditions at the pile-soil interface are further introduced for refined training. Specifically: Phase 1 (Linear Elastic Preheating): Set all materials to linear elasticity and train the network to initially meet equilibrium and boundary conditions.

[0118] Phase Two (Introduction of Nonlinearity): Gradually switch the constitutive relations of soil and concrete to a nonlinear / elastoplastic model.

[0119] Phase 3 (Introduction of Contact): Finally, nonlinear constraints on the pile-soil interface contact are added.

[0120] Transfer learning initialization: If there is a pre-trained model with a similar problem, use its weights as initial values ​​to accelerate convergence.

[0121] Step 4.2: Optimization Process Execution Optimizer selection: In one possible implementation, the Adam optimizer is used for rapid descent in the early stages, and then switched to the L-BFGS optimizer for fine-tuning to obtain a more accurate physics analysis.

[0122] Batch training: Divide the sampling points into small batches and perform iterative training. Monitor the decrease in various losses and validation set error.

[0123] Convergence criterion: Training is stopped when the total loss decreases to a stable plateau and all losses reach the preset threshold.

[0124] Step 5: Model Validation, Interpretation and Application Step 5.1: Multi-dimensional verification Physical consistency verification: Check whether the displacement field and stress field predicted by the model conform to intuitive physical laws (e.g., stress is concentrated at the pile end and displacement decreases from top to bottom).

[0125] Comparative verification: Comparison with high-fidelity FEM: For a set of complex benchmark cases that were not trained, the results (bearing capacity, settlement, stress path) of the physical information deep learning model are compared with those of high-precision commercial FEM software.

[0126] Comparison with field tests: The engineering prediction accuracy of the model was verified using independent full-scale field test data.

[0127] Extrapolation capability test: Apply the model to "extreme conditions" at the edge of the input parameter space to test its generalization and robustness.

[0128] Step 5.2: Model Interpretation and Visualization Field visualization: Generate and analyze displacement cloud maps, stress contour maps, and plastic zone distribution maps predicted by the deep learning model of physical information to intuitively understand the working mechanism of the pile-soil system.

[0129] Sensitivity analysis: Utilizing the differentiability of neural networks, the gradient of bearing capacity with respect to various input parameters (such as soil c and φ values) is calculated to quantitatively assess the influence of these parameters.

[0130] Step 5.3: Deployment of Engineering Application Scenarios Step 5.31: Forward high-performance prediction: Encapsulate the trained model, input new engineering parameters, and output complete load-settlement curves and ultimate bearing capacity in seconds.

[0131] Step 5.32: Uncertainty Quantification: Combining the Bayesian framework, network weights and input parameters are treated as random variables, Monte Carlo sampling is performed, and the probability distribution of bearing capacity (such as failure probability) is output.

[0132] Step 5.33: Parameter Inversion Identification: With fixed network weights, the unknown soil parameters are set as trainable variables. The measured pile top response data is input, and the equivalent soil parameters are identified through reverse optimization. The parameter inversion steps include: The weights of the physical information deep neural network model are fixed after training. The unknown soil or interface parameters to be inverted are used as trainable variables to construct the inversion loss function; By optimizing the inversion loss function and updating the trainable variables, the parameter values ​​identified by the inversion are obtained.

[0133] Specifically, Inversion Steps: Principles and Procedures Step a: Lock the forward model All weights and bias parameters θ of the trained physical information deep neural network (physical information deep learning model) networkSetting it to untrainable (frozen) preserves the complex, high-dimensional, nonlinear mapping between the input parameters and the overall physical response that the network has already learned. In this case, the network is equivalent to a differentiable and incredibly fast "forward simulator".

[0134] Step b: Define inversion variables The unknown engineering parameters to be inverted are defined as new, independent, trainable variables. Let the set of these parameters be φ. inverse The typical inversion parameter φ_inverse includes: Equivalent mechanical parameters of soil: internal friction angle φ, cohesion c, elastic modulus E of soil layer s Poisson's ratio ν; Interface characteristic parameters: friction coefficient μ (or equivalent tanδ) of the pile-soil interface, adhesion force c a .

[0135] Initial geostress coefficient: lateral pressure coefficient K0.

[0136] Input Recombination: For a new inversion case, the input consists of known fixed parameters (such as pile size and concrete strength) and the variable to be inverted, φ. inverse Together they form a deep learning model that feeds in the frozen physical information.

[0137] Step c: Construct the inversion loss function The inversion loss function describes the difference between the pile top response predicted by the neural network and the actual monitored pile top response. It uses the difference between the monitoring data and the model prediction to drive the inversion process. The inversion loss function is defined as follows: = ;in, The inversion loss function is... For the measured response data of the i-th monitoring point, For inversion parameters, To use the current inversion parameters The deep learning model, along with known parameters, is input into the frozen physical information to calculate the predicted response at the i-th monitoring point. The number of monitoring data points; where, the monitoring data y measured Typical forms include: 1) Pile top load-settlement curve: the most commonly used and core inversion data source. y can be different load levels P j The settlement below j .

[0138] 2) Axial force distribution in the pile body: Strain / axial force data along the depth can be collected by sensors.

[0139] 3) Stress field and strain field of the pile cross section: such as inclinometer data, which can be used for inversion of horizontally loaded piles.

[0140] 4) Stress and displacement fields of the soil surrounding the pile; 5) The ultimate bearing capacity determined based on the preset settlement standard.

[0141] Step d: Optimize the solution of inversion parameters To minimize the inversion loss function L inverse To achieve the goal, gradient descent-type optimization algorithms (such as Adam and L-BFGS) are used to update only the inversion variable φ. inverse And the network parameter θ network It remains unchanged.

[0142] The optimization process is as follows: Forward propagation: Given a set of φ inverse The full-field prediction is calculated using a deep learning model based on the frozen physical information, and the predicted response y of the monitoring points is extracted. pred .

[0143] Calculate the loss: compare y pred With y measured Calculate L inverse .

[0144] Backpropagation: Calculating L inverse For the inversion variable φ inverse Since the physical information deep learning model itself is completely differentiable, the gradient can be obtained accurately and efficiently through automatic differentiation without the need for finite differences.

[0145] Update parameters: Update φ according to gradient direction inverse This is to adjust it in a way that makes the predicted response closer to the measured response.

[0146] Convergence criterion: When L inverse Less than the preset threshold, or φ inverse When the change in φ is very small, the iteration stops. inverse *This represents the optimal parameter estimate obtained through inversion.

[0147] Step 6: Iterative Improvement and Knowledge Accumulation Step 6.1: Performance Evaluation and Bottleneck Analysis The system evaluates the model's performance under different working conditions, identifies its failure modes (e.g., inaccurate prediction of deep soft soil), and analyzes the causes of bottlenecks (e.g., limitations imposed by physical constraints, sampling strategies, or network capacity).

[0148] Step 6.2: Model Iteration and Upgrade Physical upgrades: Introduce more accurate constitutive models (such as boundary surface models), or consider fluid-solid coupling (for saturated soils).

[0149] Data upgrade: Integrate new experimental or monitoring data to incrementally train the model.

[0150] Step 6.3: Develop an expert knowledge base The trained optimal model, its applicable parameter range, performance boundaries, and typical prediction cases are compiled into a knowledge base for intelligent analysis of the bearing capacity of prestressed hollow square piles, providing the industry with standardized and reusable analysis tools.

[0151] The above-described process of the present invention enables a rigorous systems engineering approach, from abstracting physical principles to mathematical formalization, then to algorithm implementation, and finally to engineering verification, forming a closed loop. It emphasizes the guiding role of physical a priori knowledge, the balance between data and mechanisms, and interpretability and reliability for engineering practicality. It serves as a systematic roadmap for advancing pile foundation engineering analysis towards intelligence and high fidelity.

[0152] Example 2: This invention also provides a bearing capacity analysis system for prestressed hollow square piles based on model fusion, see [link to relevant documentation]. Figure 2 The system architecture diagram shown includes: The data acquisition module is used to acquire the engineering parameters of the prestressed hollow square pile. The engineering parameters include at least the geometric parameters, material parameters, soil parameters and load conditions of the prestressed hollow square pile. The parameterized input space construction module is used to construct the parameterized input space for the engineering parameters of prestressed hollow square piles; The analysis model building module is used to establish a unified analysis model of the prestressed hollow square pile-soil system that integrates physical mechanisms and data-driven approaches. The spatial sampling module is used to sample the parameterized input space based on the unified analysis model to obtain multi-source training data. The multi-source training data includes at least the first physical field data generated by numerical simulation, the second physical field data obtained by physical experiments, and the unlabeled coordinate point data randomly sampled in the computational domain. The neural network module is used to construct a deep neural network that takes variables in the parameterized input space as input and at least one physical field response of the pile-soil system as output. The loss function construction module is used to construct a composite loss function for a deep neural network. The composite loss function includes at least a data loss term for measuring the difference between the neural network output and the second physical field data, a physical residual loss term for forcing the neural network output to satisfy a preset set of control equations, and a constraint loss term for forcing the boundary conditions and pile-soil interface contact conditions to be satisfied. The neural network training module is used to train a deep neural network with the goal of minimizing the composite loss function, so as to obtain a trained physical information deep neural network model. The results output module is used to input the engineering parameters of the prestressed hollow square pile to be analyzed into the trained physical information deep neural network model and directly output its bearing capacity prediction results. The parameter inversion module is used to invert the trained physical information deep neural network model by using the difference between the monitoring data and the model prediction as the driving force, and obtain the parameter values ​​identified by the inversion.

[0153] Example 3: The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method for analyzing the bearing capacity of prestressed hollow square piles based on model fusion.

[0154] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for analyzing the bearing capacity of prestressed hollow square piles based on model fusion, characterized in that, Includes the following steps: Establish a unified analysis model for the prestressed hollow square pile-soil system that integrates physical mechanisms and data-driven approaches; Construct a parameterized input space that includes the geometric parameters, material parameters, soil parameters, and load conditions of prestressed hollow square piles; Based on the unified analysis model, the parameterized input space is sampled to obtain multi-source training data. The multi-source training data includes at least the first physical field data generated by numerical simulation, the second physical field data obtained by physical experiments, and the unlabeled coordinate point data randomly sampled in the computational domain. Construct a deep neural network that takes the variables in the parameterized input space as input and the physical field response of at least one of the pile-soil systems as output; Construct a composite loss function, which includes at least: a data loss term for measuring the difference between the neural network output and the second physical field data, a physical residual loss term for forcing the neural network output to satisfy a preset set of control equations, and a constraint loss term for forcing the satisfaction of boundary conditions and pile-soil interface contact conditions. The deep neural network is trained with the goal of minimizing the composite loss function, resulting in a trained physical information deep neural network model. The engineering parameters of the prestressed hollow square pile to be analyzed are input into the trained physical information deep neural network model, which directly outputs the predicted results of its bearing capacity.

2. The method for analyzing the bearing capacity of prestressed hollow square piles based on model fusion according to claim 1, characterized in that, The physical mechanism of the unified analysis model is established based on the following set of governing equations, which include: Static equilibrium equations are used to ensure that the infinitesimal elements of a structural system are in a state of force equilibrium at any location. The constitutive equation of concrete is used to describe the elastic-plastic or damage behavior of concrete. The soil constitutive equation is used to describe the nonlinear behavior of soil. Geometric equations are used to link the macroscopically measurable displacement field with the strain state of the internal material elements to ensure that deformation is continuous and consistent.

3. The method for analyzing the bearing capacity of prestressed hollow square piles based on model fusion according to claim 1, characterized in that, The deep neural network adopts a domain decomposition architecture, including: Pile subnetworks used to simulate the pile domain; And, soil subnetworks used to simulate the surrounding soil domain; The pile subnetwork and the soil subnetwork are coupled at the shared pile-soil interface through physical continuity conditions or contact laws, and the coupling conditions are components of the composite loss function.

4. The method for analyzing the bearing capacity of prestressed hollow square piles based on model fusion according to claim 1, characterized in that, The step of training the deep neural network employs a course-based learning strategy, specifically including: In the first stage, the deep neural network is initially trained under the assumption of linear elastic materials. In the second stage, based on the fixed weights of the network, a nonlinear constitutive relationship between the soil and concrete is introduced for training. In the third stage, nonlinear contact conditions at the pile-soil interface are further introduced for refined training.

5. The method for analyzing the bearing capacity of prestressed hollow square piles based on model fusion according to claim 1, characterized in that, The composite loss function is expressed as follows: = + + + ;in, For data loss items, These are the weighting coefficients for the data loss terms. This is the physical residual loss term. The weighting coefficients for the physical residual loss term. For boundary condition loss terms, These are the weighting coefficients for the boundary condition loss term. For interface condition loss terms, These are the weight coefficients for the interface condition loss term; during training, each weight coefficient is adaptively adjusted according to the gradient statistics or changing trends of each loss component to ensure that each loss decreases in a balanced manner during the optimization process.

6. The method for analyzing the bearing capacity of prestressed hollow square piles based on model fusion according to claim 1, characterized in that, The load-bearing capacity prediction results include at least one of the following: Load-settlement curve throughout the entire process; Distribution of axial force, side friction and end resistance in the pile body; Stress and strain fields of the pile cross section; Stress and displacement fields of the soil surrounding the pile; The ultimate bearing capacity is determined based on a preset settlement standard.

7. The method for analyzing the bearing capacity of prestressed hollow square piles based on model fusion according to claim 1, characterized in that, The method also includes a parameter inversion step: The weights of the trained physical information deep neural network model are fixed; The unknown soil or interface parameters to be inverted are used as trainable variables to construct the inversion loss function; By optimizing the inversion loss function and updating the trainable variables, the parameter values ​​identified by the inversion are obtained.

8. The method for analyzing the bearing capacity of prestressed hollow square piles based on model fusion according to claim 7, characterized in that, The inversion loss function is used to describe the difference between the pile top response predicted by the neural network and the actual monitored pile top response, and is defined as follows: = ;in, The inversion loss function is... For the measured response data of the i-th monitoring point, For inversion parameters, To use the current inversion parameters The deep learning model, along with known parameters, is input into the frozen physical information to calculate the predicted response at the i-th monitoring point. The number of monitoring data points.

9. A model-fusion-based bearing capacity analysis system for prestressed hollow square piles, used to implement the model-fusion-based bearing capacity analysis method for prestressed hollow square piles as described in any one of claims 1-8, characterized in that, include: The data acquisition module is used to acquire the engineering parameters of the prestressed hollow square pile. The engineering parameters include at least the geometric parameters, material parameters, soil parameters and load conditions of the prestressed hollow square pile. The parameterized input space construction module is used to construct the parameterized input space for the engineering parameters of prestressed hollow square piles; The analysis model building module is used to establish a unified analysis model of the prestressed hollow square pile-soil system that integrates physical mechanisms and data-driven approaches. The spatial sampling module is used to sample the parameterized input space based on the unified analysis model to obtain multi-source training data, wherein the multi-source training data includes at least first physical field data generated by numerical simulation, second physical field data obtained by physical experiments, and unlabeled coordinate point data randomly sampled in the computational domain. A neural network module is used to construct a deep neural network that takes variables in the parameterized input space as input and at least one physical field response of the pile-soil system as output. The loss function construction module is used to construct the composite loss function of the deep neural network, wherein the composite loss function includes at least a data loss term for measuring the difference between the neural network output and the second physical field data, a physical residual loss term for forcing the neural network output to satisfy a preset set of control equations, and a constraint loss term for forcing the satisfaction of boundary conditions and pile-soil interface contact conditions. The neural network training module is used to train the deep neural network with the goal of minimizing the composite loss function, so as to obtain a trained physical information deep neural network model. The result output module is used to input the engineering parameters of the prestressed hollow square pile to be analyzed into the trained physical information deep neural network model and directly output its bearing capacity prediction results. The parameter inversion module is used to invert the trained physical information deep neural network model by using the difference between the monitoring data and the model prediction as a driving force to obtain the parameter values ​​identified by the inversion.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the bearing capacity analysis method for prestressed hollow square piles based on model fusion as described in any one of claims 1 to 7.

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