Shield lateral penetrating existing pile foundation deformation calculation method based on physical information neural network
By using a physical information neural network-based approach, combined with numerical simulation and theoretical calculation, a deformation prediction model for shield tunneling side-penetrating pile foundations was established. This solved the problems of prediction lag and high computational cost in existing technologies, achieving efficient and accurate pile foundation deformation analysis and ensuring construction safety and efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- WUHAN MUNICIPAL CONSTR GROUP
- Filing Date
- 2025-12-30
- Publication Date
- 2026-04-24
AI Technical Summary
Existing technologies for analyzing the deformation of adjacent pile foundations during shield tunnel construction suffer from problems such as prediction lag, high calculation costs, and limited applicability. They are difficult to accurately assess the stress and deformation response of pile foundations, thus affecting construction safety and efficiency.
A recurrent neural network prediction model based on physical information neural networks is established by combining numerical simulation and theoretical calculation. The theoretical calculation values are used as physical constraints and incorporated into the loss function to construct a database of shield tunnel side-penetrating pile foundation deformation. Accurate prediction is then achieved by combining multiple influencing factors.
This method improves the accuracy and calculation efficiency of pile foundation deformation prediction during shield tunneling, expands the scope of application, ensures that the prediction results are consistent with the actual engineering situation, and provides reliable guidance for construction plans.
Smart Images
Figure CN121919954A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the technical field of tunnel engineering, and specifically to a method for calculating the deformation of shield tunneling through existing pile foundations based on a physical information neural network. Background Technology
[0002] With the rapid development of urban rail transit, the shield tunneling method has become the mainstream construction method for underground engineering projects such as urban subways and tunnels due to its advantages such as high construction efficiency, minimal ground disturbance, and good safety. However, shield tunnel excavation can cause deformation of the surrounding strata, leading to lateral horizontal displacement of the pile foundations of adjacent buildings, bridges, and other infrastructure. This can significantly impact the normal operation of nearby underground pile foundations, thereby affecting the stability of the superstructure. Therefore, accurately assessing the stress and deformation response of existing pile foundations during the excavation of adjacent shield tunnels is of significant engineering importance and research value for ensuring the operational safety of urban infrastructure and developing reasonable construction plans.
[0003] In the study of the impact of shield tunnel construction on adjacent pile foundations, the main methods currently used include the measured analysis method, the numerical simulation method, and the theoretical analysis method. The measured analysis method has a time lag in the results and cannot provide timely warnings to guide the shield tunnel construction on site. The numerical simulation model makes simplified assumptions and is difficult to fully simulate the real construction environment. Different scenarios require multiple modeling, resulting in high computational costs. The theoretical analysis method is mostly based on certain assumptions, which leads to relatively conservative calculation results. It also does not consider the dynamic process of shield tunnel construction and has limited applicability.
[0004] In summary, existing methods have limitations to varying degrees in analyzing the deformation of pile foundations crossing the sides of shield tunnels. There is an urgent need for a method that can ensure prediction accuracy while also taking into account computational efficiency and physical rationality, in order to improve the assessment and control capabilities of the impact on adjacent pile foundations during shield tunneling. Summary of the Invention
[0005] The purpose of this invention is to overcome the shortcomings of the above-mentioned background technology and provide a method for calculating the deformation of shield tunneling through existing pile foundations based on physical information neural networks.
[0006] To achieve the above objectives, the present invention provides a method for calculating the deformation of existing pile foundations during shield tunneling based on a physical information neural network, comprising the following steps: Step S1: Based on the Mindlin and Loganathan solutions, calculate the horizontal displacement of the ground caused by shield tunneling parameters and ground losses; Step S2: Treat the existing pile foundation as an elastic foundation beam placed on the Pasternak two-parameter foundation. Based on the horizontal displacement of the strata, solve for the horizontal deformation of the existing pile foundation to obtain the theoretical calculation value. Step S3: Use finite element simulation software to establish multiple three-dimensional models of shield tunneling side-penetrating pile foundations, calculate the deformation of the shield tunneling side-penetrating pile foundations under different influencing factors, and obtain numerical simulation calculation results; Step S4: Based on the numerical simulation results, construct a database and establish a prediction model for the horizontal deformation of the shield tunneling through the existing pile foundation based on a recurrent neural network. Step S5: Build a calculation model for the horizontal deformation of the shield tunneling through the existing pile foundation based on the physical information neural network, and incorporate the theoretical calculation value as a physical constraint into the loss function of the prediction model. The loss function includes the difference between the predicted value of the recurrent neural network and the numerical simulation calculation result, as well as the difference between the predicted value of the recurrent neural network and the theoretical calculation value.
[0007] In a preferred embodiment, in step S1, the horizontal displacement of the strata caused by the additional thrust of the shield, the friction of the shield shell, and the grouting pressure at the tail of the shield is calculated based on the Mindlin solution.
[0008] In a preferred embodiment, in step S1, the horizontal displacement of the soil caused by the ground loss during shield tunneling is calculated based on the Loganathan solution.
[0009] In a preferred embodiment, in step S1, the horizontal displacement of the stratum is the sum of the horizontal displacement of the stratum caused by the shield tunneling parameters and the horizontal displacement of the soil caused by the stratum loss.
[0010] In a preferred embodiment, in step S2, the horizontal deformation of the existing pile foundation is obtained by solving the control equation for the horizontal deformation of the elastic foundation beam.
[0011] In a preferred embodiment, the horizontal deformation control equation is solved using the finite difference method combined with the free boundary conditions at the pile end and pile top.
[0012] In a preferred embodiment, the horizontal deformation control equation includes the horizontal bending stiffness of the pile foundation, the shear layer stiffness of the soil along the pile, and the spring stiffness of the soil along the pile.
[0013] In a preferred embodiment, the horizontal deformation control equation is: ;
[0014] In the formula: The horizontal bending stiffness of the pile foundation; This refers to the horizontal displacement of the pile foundation; D is the shear stiffness of the soil lateral to the pile; D is the pile diameter. U represents the spring stiffness of the soil around the pile; U represents the horizontal displacement of the ground at the pile location caused by the tunnel boring machine.
[0015] In a preferred embodiment, the different influencing factors in step S3 include geological conditions, the distance between the tunnel and the pile foundation, and the pile embedment depth.
[0016] In a preferred embodiment, the loss function in step S5 is: ; In the formula: The predicted value is from a recurrent neural network; The results of numerical simulation calculations in the database; These are theoretically calculated values. These are the weighting coefficients.
[0017] Compared with the prior art, the present invention has the following advantages: Firstly, this invention establishes multiple models of shield tunneling through existing pile foundations using numerical simulation. The model calculation results are then used to build a neural network database predicting the deformation of existing pile foundations during shield tunneling. The calculated values, obtained through a two-stage theoretical formula, are added as physical constraints to the loss function of the neural network model, thereby accurately calculating the deformation of existing pile foundations during shield tunneling. This method constructs a representative database, providing a large amount of sample data for subsequent deep learning training. Furthermore, by introducing physical constraints into the neural network model and using a two-stage method to accurately describe the soil-pile coupling response, the model can capture the complex nonlinear characteristics of the data while ensuring that the prediction results conform to physical laws, thus improving the model's accuracy and expanding its applicability.
[0018] Secondly, this invention significantly improves prediction accuracy by integrating numerical simulation data and theoretical calculation results, fully utilizing data characteristics and physical laws. Physical constraints enhance the model's stability and robustness when facing unknown conditions. Accurate pile foundation deformation prediction provides a reliable basis for safe shield tunneling construction, aiding in the development of reasonable construction plans and risk assessments, and ensuring the safety of existing structures. This invention, through multi-model data construction, utilizing deep learning to capture complex nonlinear characteristics, and integrating physical information, provides an efficient, accurate, and promising method for calculating the deformation of existing pile foundations during shield tunneling.
[0019] Third, this invention calculates the horizontal displacement of the strata caused by the additional thrust of the shield, the friction of the shield shell, and the grouting pressure at the tail of the shield based on the Mindlin solution, and calculates the horizontal displacement of the soil caused by the strata loss during shield excavation based on the Loganathan solution. The two are superimposed to obtain the total horizontal displacement field of the strata. This invention comprehensively considers the influence of two types of factors on the surrounding soil during shield tunneling: mechanical action and strata loss. This ensures accurate assessment of the horizontal displacement of the strata caused by shield construction and provides reliable input data for subsequent pile foundation deformation analysis.
[0020] Fourth, this invention establishes the governing equations for the horizontal deformation of the pile foundation, employing the finite difference method combined with the free boundary conditions at the pile tip and top to ensure that the calculation process conforms to the actual stress boundary of the pile foundation, thus improving the reliability of the theoretical solution. The governing equations incorporate parameters such as the bending stiffness of the pile foundation, the shear layer stiffness of the soil along the pile, and the spring stiffness of the soil along the pile, comprehensively reflecting the mechanical properties of the pile-soil system and making the calculation results more accurate and reliable.
[0021] Fifth, this invention utilizes finite element simulation software to establish multiple three-dimensional models of shield tunneling pile foundations, calculating pile foundation deformation under various influencing factors (geological conditions, tunnel-pile distance, pile depth, etc.), and obtaining a large amount of high-precision numerical simulation results. The abundant simulation data covers various geological conditions and construction scenarios, comprehensively characterizing the impact of shield tunneling on pile foundations, and providing a reliable training database for subsequent prediction models. Modeling and analysis are performed separately considering different geological conditions, tunnel-pile distance, and pile length and depth, ensuring the diversity and representativeness of the samples in the established database.
[0022] Sixth, this invention constructs a database based on a large number of numerical simulation results, and then builds a recurrent neural network prediction model. It utilizes deep learning to automatically extract the complex nonlinear relationship between shield tunneling parameters and pile foundation deformation, achieving rapid prediction of pile foundation deformation. The establishment of a large-scale database ensures the richness and diversity of model training data, giving the neural network model good generalization ability and making it applicable to the prediction of shield tunneling deformation in different scenarios, significantly improving computational efficiency. Introducing a recurrent neural network model leverages its advantages in modeling sequential data, further considering the impact of the phased and continuous nature of the shield tunneling process on pile foundation deformation, thus improving the predictive model's adaptability to dynamic construction conditions from a data perspective.
[0023] Seventh, this invention constructs a calculation model for the horizontal deformation of existing pile foundations during shield tunneling based on a physical information neural network. The obtained theoretical calculation values are incorporated as physical constraints into the loss function of the recurrent neural network model. By simultaneously considering the differences between the predicted values, numerical simulation results, and theoretical calculation values in the loss function, the data-driven model and the physical model are organically integrated, ensuring that the network training process follows basic mechanical laws while pursuing accuracy, and the output results are more consistent with engineering practice.
[0024] Eighth, this invention employs a loss function incorporating physical constraints, composed of the differences between recurrent neural network predictions and numerical simulation results from the database, as well as the differences between predicted and theoretically calculated values, combined with appropriate weighting coefficients. This loss function design balances data fitting accuracy and physical consistency during training, preventing the model from over-relying on data and producing predictions that contradict actual mechanics. By adjusting the weighting coefficients, the strength of physical constraints can be flexibly controlled, fully learning the nonlinear characteristics in the numerical simulation data while ensuring that the prediction results do not violate inherent mechanical laws. Ultimately, the established physical information neural network model possesses high-precision prediction capabilities and good physical interpretability, significantly improving the accuracy of deformation calculations for shield tunneling through existing pile foundations and expanding the applicability of the method. Attached Figure Description
[0025] Figure 1 This is a flowchart of the shield tunneling deformation calculation method for existing pile foundations based on physical information neural networks, according to an embodiment of the present invention. Figure 2 This is a schematic diagram of a shield tunnel passing through a pile foundation. Figure 3 A simplified mechanical model diagram for shield tunneling construction; In the diagram: 1-Shield tunnel; 2-Pile foundation; x-Horizontal distance from the center of the tunnel to the pile foundation; D-Pile foundation diameter; h-Depth of the shield tunnel axis; R-Depth of the shield tunnel. Detailed Implementation
[0026] The following examples illustrate the implementation of the present invention in detail, but they do not constitute a limitation on the invention and are merely illustrative. Furthermore, the advantages of the present invention will become clearer and easier to understand by explaining them.
[0027] This invention proposes a method for calculating the deformation of existing pile foundations when a shield tunnel passes through them, based on a physical information neural network, including the following methods: Step S1: Two-stage theoretical analytical solution for the horizontal displacement of adjacent pile foundations caused by ground movement due to tunnel excavation. The first stage is based on the Mindlin and Loganathan solutions to calculate the horizontal displacement of the ground caused by shield tunneling parameters and ground loss, respectively. According to the Mindlin solution, it can be seen that vertical and horizontal point loads acting on a semi-infinite space at any point... The horizontal deformation at the point of application. x is the longitudinal horizontal distance from the point of application, positive along the shield excavation direction; y is the transverse horizontal distance from the point of application, i.e., the direction of the shield tunnel cross-section; z is the vertical distance from the ground surface, positive downwards. ρ is the Poisson's ratio of the soil; h is the depth of the shield tunnel axis; G is the shear modulus of the soil. M and N are the distances from the point of application of the concentrated force and the point of symmetry to any point in space. distance, , .
[0028] Select a point on the circular cross-section of the shield cutterhead. For differential area The additional thrust of the tunnel boring machine is obtained by integration. Caused horizontal displacement of strata: ; ; In the formula: q To add thrust to the tunnel boring machine; x 1 ,y 1 ,z 1 This refers to the spatial distance between the desired horizontal displacement of the strata and the location of the selected additional thrust of the shield tunneling machine. h 1 The depth at which the selected shield tunneling machine applies additional thrust. h The depth of the shield tunnel axis. r The distance from the center of the cross-section to apply additional thrust to the selected shield. θ 1 The angle between the selected shield additional thrust point and the horizontal y-axis within the circular cross-section.
[0029] Select a point on the surface of the tunnel boring machine its differential area Integrating the forces yields the shield friction. Caused horizontal displacement of strata: ; ; In the formula: f For the friction of the shield shell; x 2 ,y 2 ,z 2 This is the distance in space between the desired horizontal displacement of the stratum and the selected point of friction of the shield shell. h 2 The depth at the selected point of friction on the shield shell; h This refers to the depth of the shield tunnel axis. R The diameter of the shield tunnel; L The shield length; θ 2 The angle between the selected friction point on the shield and the horizontal y-axis within the circular cross-section is given.
[0030] Select a point along the grouting length its differential area Integrating the components yields the tail grouting pressure. Caused horizontal displacement of strata: ; ; In the formula: p This refers to the grouting pressure at the shield tail. x 3 ,y 3 ,z 3 This is the distance in space between the desired horizontal displacement of the stratum and the selected shield tail grouting pressure. h 3 The depth at the selected point of friction on the shield shell; h This refers to the depth of the shield tunnel axis. R The diameter of the shield tunnel; This refers to the grouting length; θ 3 The angle between the selected tail grouting pressure point and the horizontal y-axis within the circular cross-section.
[0031] According to the Loganathan analytical solution, the horizontal displacement of soil caused by ground loss during shield tunneling is as follows: ; In the formula: denoted as stratum loss ratio; x is the longitudinal horizontal distance from the point of action, positive along the shield excavation direction; y is the transverse horizontal distance from the point of action, i.e., the direction of the shield tunnel cross-section; z is the vertical distance from the ground surface, positive downwards. denoted as Poisson's ratio of the soil; h is the depth of the shield tunnel axis; and R is the diameter of the shield tunnel.
[0032] Considering the shield tunneling parameters and ground losses, the solution for the horizontal ground displacement caused by shield excavation is as follows: ; In the formula: This refers to the horizontal displacement of the strata under the combined influence of multiple factors. The horizontal displacement of the strata caused by the additional thrust of the tunnel boring machine; This refers to the horizontal displacement of the strata caused by the friction of the shield shell. This refers to the horizontal displacement of the formation caused by the grouting pressure at the shield tail. This refers to the horizontal displacement of the formation caused by the formation loss rate.
[0033] Step S2: Two-stage theoretical analytical solution for the horizontal displacement of adjacent pile foundations caused by ground movement due to tunnel excavation. In the second stage, the existing pile foundation is regarded as an elastic foundation beam placed on the Pasternak two-parameter foundation, and the horizontal deformation control equation of the existing pile foundation caused by the horizontal displacement of the soil layer due to the tunnel excavation is obtained: ; In the formula: The horizontal bending stiffness of the pile foundation; This refers to the horizontal displacement of the pile foundation; D is the shear stiffness of the soil lateral to the pile; D is the pile diameter. b represents the spring stiffness of the soil around the pile; b represents the horizontal displacement of the ground at the pile location caused by the tunnel boring machine.
[0034] Using the finite difference method combined with the free boundary conditions at the pile tip and pile top, the equation for the horizontal displacement of the pile foundation caused by shield tunnel excavation is as follows: ; In the formula: Here is the stiffness matrix of the pile foundation; Here is the soil shear stiffness matrix; The stiffness matrix of the formation; This represents the horizontal displacement vector of the pile foundation. This is the ground displacement vector at the pile location caused by the tunnel boring machine excavation.
[0035] Step S3: Using finite element simulation software, consider various factors affecting pile foundation deformation, such as geological conditions, distance between the tunnel and the pile foundation, and pile depth, to establish multiple three-dimensional models of shield tunnel side-penetration pile foundations and calculate the deformation of shield tunnel side-penetration pile foundations under different influencing factors.
[0036] Step S4: Construct a database based on massive simulation data and establish a prediction model for the horizontal deformation of existing pile foundations by shield tunneling based on recurrent neural networks.
[0037] Step S5: Construct a calculation model for the horizontal deformation of an existing pile foundation during shield tunneling based on a physical information neural network. The calculated values from the two-stage theoretical formulas are incorporated as physical constraints into the loss function of the prediction model. The loss function is then designed as follows: ; In the formula: The predicted value is from a recurrent neural network; The results of numerical simulation calculations in the database; These are theoretically calculated values. These are the weighting coefficients.
[0038] In one specific embodiment, a three-dimensional numerical model of a shield tunnel passing through pile foundations was established using ABAQUS finite element software to generate a training dataset. The model's geometric parameters were set as follows: shield tunnel diameter 6m, burial depth 10m, adjacent pile diameter 1m, pile length 20m, and horizontal clearance between the tunnel axis and the pile foundation 5m. Typical sandy soil parameters were used, and reasonable boundary ranges were set to avoid boundary effects. By changing the stratum conditions (e.g., soft clay, dense sand), the distance between the tunnel and the pile foundation (e.g., 3m, 5m, 8m), and the pile length and burial depth (e.g., 10m, 20m), 50 different working condition models were established to obtain the corresponding numerical simulation results of the pile foundation's horizontal displacement, constructing a database with a large number of samples. Based on this, a pile foundation deformation prediction model based on a physical information neural network was constructed. This model uses a two-layer long short-term memory (LSTM) network structure with 50 hidden units in each layer to capture the temporal characteristics of the shield tunneling process. The model input is a sequence of construction parameters arranged in the tunneling cycle, and the output is the predicted value of the corresponding pile foundation's horizontal displacement. During model training, the Adam optimization algorithm is used for parameter updates, with a learning rate of 0.001 and 10,000 iterations. The loss function consists of data term loss and physical constraint term, where the weighting coefficient λ = 0.5, used to balance the accuracy of data fitting with the degree of satisfaction of physical constraints. With the above settings, those skilled in the art can train a prediction model that meets the accuracy requirements, thereby realizing the pile foundation deformation calculation method of the present invention.
[0039] The above are merely specific embodiments of the present invention. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the protection scope of the present invention. All other details not described in detail belong to the prior art.
Claims
1. A method for calculating the deformation of existing pile foundations during shield tunneling based on a physical information neural network, characterized in that, Includes the following steps: Step S1: Based on the Mindlin and Loganathan solutions, calculate the horizontal displacement of the ground caused by shield tunneling parameters and ground losses; Step S2: Treat the existing pile foundation as an elastic foundation beam placed on the Pasternak two-parameter foundation, and solve the horizontal deformation of the existing pile foundation based on the horizontal displacement of the stratum to obtain the theoretical calculation value; Step S3: Use finite element simulation software to establish multiple three-dimensional models of shield tunneling side-penetrating pile foundations, calculate the deformation of the shield tunneling side-penetrating pile foundations under different influencing factors, and obtain numerical simulation calculation results; Step S4: Based on the numerical simulation results, construct a database and establish a prediction model for the horizontal deformation of the shield tunneling through the existing pile foundation based on a recurrent neural network. Step S5: Build a calculation model for the horizontal deformation of the shield tunneling through the existing pile foundation based on the physical information neural network, and incorporate the theoretical calculation value as a physical constraint into the loss function of the prediction model. The loss function includes the difference between the predicted value of the recurrent neural network and the numerical simulation calculation result, as well as the difference between the predicted value of the recurrent neural network and the theoretical calculation value.
2. The method according to claim 1, characterized in that, In step S1, the horizontal displacement of the strata caused by the additional thrust of the shield, the friction of the shield shell, and the grouting pressure at the tail of the shield is calculated based on the Mindlin solution.
3. The method according to claim 1, characterized in that, In step S1, the horizontal displacement of the soil caused by the ground loss during shield tunneling is calculated based on the Loganathan solution.
4. The method according to claim 1, 2 or 3, characterized in that, In step S1, the horizontal displacement of the stratum is the sum of the horizontal displacement of the stratum caused by the shield tunneling construction parameters and the horizontal displacement of the soil caused by the stratum loss.
5. The method according to claim 1, characterized in that, In step S2, the horizontal deformation of the existing pile foundation is obtained by solving the control equation of the horizontal deformation of the elastic foundation beam.
6. The method according to claim 5, characterized in that, The horizontal deformation control equation is solved using the finite difference method combined with the free boundary conditions at the pile end and pile top.
7. The method according to claim 5, characterized in that, The horizontal deformation control equation includes the horizontal bending stiffness of the pile foundation, the shear layer stiffness of the soil along the pile, and the spring stiffness of the soil along the pile.
8. The method according to claim 5, characterized in that, The horizontal deformation control equation: In the formula: The horizontal bending stiffness of the pile foundation; This refers to the horizontal displacement of the pile foundation; D is the shear stiffness of the soil lateral to the pile; D is the pile diameter. b represents the spring stiffness of the soil around the pile; b represents the horizontal displacement of the ground at the pile location caused by the tunnel boring machine.
9. The method according to claim 1, characterized in that, In step S3, the different influencing factors include geological conditions, the distance between the tunnel and the pile foundation, and the pile embedment depth.
10. The method according to claim 1, characterized in that, In step S5, the loss function is: In the formula: The predicted value is from a recurrent neural network; The results of numerical simulation calculations in the database; These are theoretically calculated values. These are the weighting coefficients.