Shield tunneling process pipe-soil void prediction method and system based on nonlinear ground stiffness

Abstract

This application discloses a method and system for predicting pipe-soil voids during shield tunneling based on nonlinear foundation stiffness, belonging to the field of construction safety monitoring technology. The method involves: firstly, obtaining the load-displacement relationship between the upper and lower foundations; then constructing a double-layer hyperbolic foundation model based on this relationship; secondly, performing initial linear elastic analysis on the Winkler foundation model based on pipeline parameters and foundation parameters to obtain iterative initial conditions; and thirdly, simulating the free displacement field of the soil during shield tunneling construction; and finally, iteratively updating the foundation flexibility matrix of the hyperbolic foundation model based on the simulation results. The iterative update results are then detected to obtain the distribution of pipe-soil voids in the underground pipeline. Therefore, by implementing this application, the problem of significant errors in predicting pipe-soil void distribution caused by the difficulty in accurately constructing the relationship between foundation stiffness and factors such as relative displacement between pipe and soil, differences in bearing capacity between upper and lower foundations, and the contact state between pipe and soil can be solved in existing technologies.

Description

Technical Field

[0001] This application belongs to the field of construction safety detection technology, specifically relating to a method and system for predicting soil-tube separation during shield tunneling based on nonlinear foundation stiffness. Background Technology

[0002] Shield tunneling is an underground construction method that involves advancing a tunnel boring machine (TBM) underground. The TBM's outer shell and segments support the surrounding rock to prevent tunnel collapse, while simultaneously excavating the soil and removing it from the tunnel, thus forming the tunnel structure. In subway TBM construction, the ability of the TBM to safely pass through existing underground pipelines is primarily determined by detecting whether any gaps occur between the tunnel and the surrounding soil.

[0003] Pipe-soil separation refers to the partial or complete detachment of underground pipelines from the surrounding foundation soil due to various reasons. This results in the pipeline losing soil support, significantly altering its stress state and service performance, potentially leading to deformation or even rupture. The engineering community typically uses a bilinear soil-spring model to calculate the interaction between underground pipelines and the soil. This model predicts the soil load on the pipeline based on foundation stiffness, thereby predicting the occurrence of pipe-soil separation. This method assumes the soil surrounding the pipeline is a series of independent springs with a "bilinear" constitutive relationship. Before the applied load reaches the ultimate bearing capacity of the foundation, the foundation stiffness K is assumed to be constant, exhibiting linear elasticity. Once the applied load reaches the ultimate bearing capacity, the stiffness abruptly drops to zero, and the soil enters a plastic flow state. However, this method fails to consider the significant nonlinear characteristics of actual sandy soil materials. Therefore, the foundation stiffness gradually decreases with increasing displacement (relative displacement between the pipeline and the soil), rather than remaining constant before yielding and undergoing a sudden change after reaching the ultimate bearing capacity. Furthermore, the ultimate bearing capacity of the foundation is finite, not infinite as assumed by current technology. Therefore, using this method makes it difficult to accurately determine which locations of pipe-soil separation occur during tunnel boring by predicting the forces borne by underground pipelines, and it is impossible to detect potential safety hazards in a timely manner during construction. Summary of the Invention

[0004] This application proposes a method and system for predicting tunnel-soil voids during shield tunneling based on nonlinear foundation stiffness. This method can solve the problem that existing technologies have difficulty accurately constructing the relationship between foundation stiffness and factors such as relative displacement between the tunnel and soil, differences in bearing capacity between the upper and lower foundations, and the contact state between the tunnel and soil, which leads to large errors in the prediction of tunnel-soil void distribution.

[0005] The first aspect of this application provides a method for predicting tunnel-to-soil voids during shield tunneling based on nonlinear foundation stiffness, the method comprising: The foundation soil on both sides of the underground pipeline is discretized into two independent nonlinear spring systems. The load-displacement relationship of the overlying foundation and the underlying foundation is obtained respectively. The load-displacement relationship is hyperbolic fitted to obtain the initial foundation stiffness and the ultimate bearing capacity of the foundation, so as to construct a double-layer hyperbolic foundation model. The nonlinear spring system includes several soil elements. Based on preset pipeline parameters and foundation parameters, an initial linear elastic analysis of the pipeline is performed on the preset Winkler foundation model to obtain the iterative initial conditions; wherein, when performing the initial linear elastic analysis of the pipeline, the underground pipeline is discretized into several pipeline nodes; Based on the initial conditions of the iteration, the shield tunneling construction simulation is performed on the preset free displacement field of the soil with the preset spatial step size and shield tunneling construction parameters. The foundation flexibility matrix of the double-layer hyperbolic foundation model is iteratively updated based on the simulation results corresponding to each spatial step size. The distribution of soil-pipe voids in underground pipelines is obtained by detecting the iterative update results using a preset soil-pipe void judgment criterion.

[0006] The above scheme introduces a nonlinear spring system to characterize the foundation soil around underground pipelines, transforming the change in foundation stiffness into a more realistic nonlinear representation. This results in a double-layer hyperbolic foundation model with excellent response prediction capabilities. Furthermore, by obtaining the ultimate bearing capacity of the foundation, it can describe the nonlinear evolution of the foundation reaction force from an initial approximately linear increase to approaching the ultimate bearing capacity. This more reasonably reflects the stiffness weakening characteristics of sandy soil foundations under large deformation conditions and improves the accuracy of identifying pipe-soil separation nodes, enabling more precise identification of pipeline nodes exhibiting such separation. Then, through initial linear elastic analysis of the pipeline, coupled analysis of the pipeline nodes and soil elements is performed, enhancing the ability to describe the stress and deformation response of the pipeline during shield tunneling and providing a more accurate initial mechanical state for subsequent shield simulation. Finally, shield simulation is conducted on a preset soil free displacement field to simulate the tunneling process of the shield machine, recording the displacement data during this process to obtain the relative displacement between the pipe and the soil. The foundation flexibility matrix of the double-layer hyperbolic foundation model is updated based on the relative displacement between the pipe and the soil. The pipeline displacement, pipeline bending moment, and foundation reaction force are re-solved using the updated foundation flexibility matrix. Based on the relative displacement between the pipe and the soil and the foundation reaction force state after iterative convergence, the contact state between the pipeline node and the soil element is determined. If a pipe-soil separation occurs, the pipeline node and the soil element are processed to mark the location of the pipe-soil separation, thus obtaining a pipe-soil separation distribution that conforms to reality and providing a more reliable basis for construction safety assessment.

[0007] In one possible implementation of the first aspect, the load-displacement relationship between the underground pipeline and the soil element is hyperbolic fitted to obtain the initial foundation stiffness and ultimate bearing capacity, thereby constructing a two-layer hyperbolic foundation model, specifically: Based on the pipeline node and the nonlinear spring system, the foundation bearing response results of the soil above and below the underground pipeline are obtained by conducting foundation bearing tests. The load-displacement relationship corresponding to the foundation bearing response results is then fitted with a hyperbola to obtain the upper nonlinear spring load-displacement curve and the lower nonlinear spring load-displacement curve corresponding to the pipeline node. The initial foundation stiffness and ultimate bearing capacity of the foundation on both sides above and below the underground pipeline are derived by using hyperbolic fitting results. Based on the fitting results, the initial foundation stiffness, and the ultimate bearing capacity of the foundation, corresponding nonlinear variation curves are constructed for the foundation stiffness on both sides above and below the underground pipeline, thus obtaining the double-layer hyperbolic foundation model.

[0008] The above scheme takes into account the different resistances encountered by the pipeline when moving upwards or downwards relative to the soil. Therefore, the soil on the upper and lower sides is treated as an independent nonlinear spring system to characterize the difference in the force response of the pipeline on the upper and lower soil sides, thus improving the model accuracy. Then, by conducting foundation bearing capacity tests, the load-displacement relationship between the underground pipeline and the soil elements on the upper and lower sides is fitted hyperbolically. The initial foundation stiffness and ultimate bearing capacity of the foundation on the upper and lower sides of the underground pipeline are derived from the fitting results. Because the foundation stiffness on the upper and lower sides of the underground pipeline changes nonlinearly when pipeline displacement occurs, the nonlinear mechanical relationship between the pipeline and the soil is further refined by modeling a more realistic nonlinear double-layer hyperbolic foundation model to characterize the stiffness changes of the foundation on the upper and lower sides of the pipeline, providing a basis for subsequent foundation stiffness change analysis.

[0009] In one possible implementation of the first aspect, based on preset pipeline parameters and foundation parameters, an initial linear elastic analysis of the pipeline is performed on a preset Winkler foundation model to obtain iterative initial conditions, specifically: In the Winkler foundation model, the foundation reaction forces on each pipeline node are discretized into nodal forces acting on the geometric center point of each pipeline node, and the foundation reaction force vector of the pipeline node is defined; wherein, the foundation reaction force is obtained through the foundation parameters; Based on the pipeline parameters and the foundation reaction vector, initial linear elastic analysis and pipeline stiffness matrix calculation are performed on the pipeline nodes to obtain the iterative initial conditions.

[0010] The above scheme simplifies the handling of foundation reaction forces by using a discretization method, reducing the computational complexity. Linear elastic analysis is used to assess the deformation of underground pipelines under load, providing more accurate initial conditions for subsequent tunnel boring simulations.

[0011] In one possible implementation of the first aspect, the load-displacement variation curve of the double-layer hyperbolic foundation model is used to describe the relationship between the foundation reaction vector and the relative displacement of the pipe-soil.

[0012] In one possible implementation of the first aspect, the pipeline node is subjected to initial linear elastic analysis and pipeline stiffness matrix calculation based on the pipeline parameters and the foundation reaction vector to obtain the iterative initial conditions, specifically: The pipeline parameters include the outer diameter, burial depth, and bending stiffness of the underground pipelines; Based on the Winkler foundation model and Euler-Bernouli beam theory, the bending behavior equation of underground pipelines is constructed according to the bending stiffness. By using the bending behavior equation and the foundation reaction vector, a stress analysis is performed at the pipeline node to obtain the pipeline bending moment control equation. Obtain the free displacement of the soil caused by the tunnel boring machine during construction, and construct the pipeline deflection control equation based on the free displacement of the soil, the pipeline bending moment control equation, and the foundation reaction vector; The foundation reaction force vector, pipeline bending moment control equation, and pipeline deflection control equation are integrated to obtain the iterative initial conditions.

[0013] The above scheme organically combines the mechanical properties of the pipeline itself with the foundation reaction force, realizing the coupled analysis of the pipeline-soil system, improving the model's ability to describe the stress and deformation response of the pipeline, and providing a more accurate mechanical state for subsequent construction simulation.

[0014] In one possible implementation of the first aspect, a shield tunneling simulation is performed on a preset free displacement field of soil using a preset spatial step size and shield tunneling parameters. The foundation compliance matrix of the double-layer hyperbolic foundation model is iteratively updated based on the simulation results corresponding to each spatial step size. Specifically: Based on the initial conditions of the iteration, the free displacement field of the soil is simulated using the shield tunneling construction parameters. Each time the shield machine moves the spatial step, the free displacement field of the soil is updated according to the current position of the shield machine to obtain the pipeline displacement of the soil unit and the free displacement of the soil caused by tunnel excavation. The iterative initial conditions provide initial state quantities for the iterative update of the double-layer hyperbolic foundation model, including initial pipeline displacement, initial pipeline bending moment, and initial foundation reaction force vector; The difference between the pipeline displacement and the free displacement of the soil is taken as the relative displacement between the pipeline and the soil.

[0015] The above scheme advances the shield tunneling simulation step by step in spatial increments, more accurately simulating the tunneling process of the tunnel boring machine. By recording the soil displacement and pipeline displacement in the free displacement field of the soil during the shield simulation, the spatiotemporal evolution characteristics of the pipe-soil interaction are characterized, providing data support for subsequent judgment of the contact between the pipeline and the soil.

[0016] In one possible implementation of the first aspect, the distribution of pipe-soil voids in underground pipelines is obtained by detecting the iterative update results through a preset pipe-soil void judgment criterion, specifically as follows: The foundation flexibility matrix of the double-layer hyperbolic foundation model is iteratively updated based on the relative displacement between the pipe and the soil. The output of each iterative update result is checked using the pipe-soil void determination criterion, and the pipeline nodes and soil elements are processed based on the detection results. When the preset iteration termination condition is met, the distribution of soil voids in the underground pipeline is output.

[0017] In one possible implementation of the first aspect, the foundation compliance matrix of the bilayer hyperbolic foundation model is iteratively updated based on the relative displacement of the pipe and soil, specifically as follows: The direction of the relative displacement between the pipe and the soil is determined based on the magnitude of the relative displacement. The foundation flexibility matrix is ​​updated based on the direction of the relative displacement between the pipe and the soil, the upper soil parameters, and the lower soil parameters. Based on the updated foundation compliance matrix, the relative displacement of the pipe and soil is recalculated to obtain the iterative update result.

[0018] The above scheme determines the direction of movement of the pipeline unit relative to the soil by measuring the relative displacement between the pipe and the soil, thereby dynamically updating the foundation flexibility matrix of the soil on both the upper and lower sides, making the updated foundation flexibility matrix more consistent with the actual mechanical mechanism. Through the iterative cycle of "displacement-stiffness-displacement", the location of pipe-soil separation during shield tunneling is continuously identified.

[0019] In one possible implementation of the first aspect, the pipeline node and the soil unit are processed based on the detection results, specifically as follows: When the test results meet the criteria for determining pipe-soil separation, it indicates that pipe-soil separation has occurred. The foundation spring unit corresponding to the pipeline node is set to invalid, and the foundation reaction force at the pipeline node is set to 0, in order to characterize the contact separation phenomenon between the pipeline node and the soil unit.

[0020] If the above scheme fails to meet the criteria for determining pipe-soil void, the connection between the pipeline node and the soil node is physically disconnected. That is, the foundation spring unit corresponding to the pipeline node is set to invalid, and the foundation reaction force at the pipeline node is set to 0. This simulates the physical phenomenon of "soil cracking / voiding" in digital space and obtains a pipe-soil void distribution that conforms to reality.

[0021] The second aspect of this application provides a tunnel boring machine (TBM) process pipe-soil void prediction system based on nonlinear foundation stiffness. The system includes: a foundation model construction module, a linear elastic analysis module, a TBM tunneling simulation module, and a pipe-soil void detection module. The foundation model construction module is used to discretize the foundation soil on both sides of the underground pipeline into two independent nonlinear spring systems, obtain the load-displacement relationship of the overlying foundation and the underlying foundation respectively, and perform hyperbolic fitting on the load-displacement relationship to obtain the initial foundation stiffness and the ultimate bearing capacity of the foundation, so as to construct a double-layer hyperbolic foundation model; wherein, the nonlinear spring system includes several soil elements; The linear elasticity analysis module is used to perform initial linear elasticity analysis of pipelines on a preset Winkler foundation model based on preset pipeline parameters and foundation parameters, so as to obtain the initial conditions for iteration; wherein, when performing initial linear elasticity analysis of pipelines, the underground pipelines are discretized into several pipeline nodes; The shield tunneling simulation module is used to simulate the shield tunneling construction of a preset soil free displacement field based on the preset spatial step size and shield construction parameters according to the initial conditions of the iteration, and to iteratively update the foundation flexibility matrix of the double-layer hyperbolic foundation model according to the simulation results corresponding to each spatial step size. The pipe-soil void detection module is used to detect the iterative update results through preset pipe-soil void judgment criteria, and obtain the distribution of pipe-soil voids in underground pipelines. Attached Figure Description

[0022] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0023] Figure 1 This is a schematic diagram of the specific process of a method for predicting soil-tube separation in shield tunneling based on nonlinear foundation stiffness, provided in an embodiment of this application. Figure 2 This is a pipeline-soil model diagram of a method for predicting pipe-soil voids in a shield tunneling process based on nonlinear foundation stiffness, provided in an embodiment of this application. Figure 3This is a comparison of two curves for a method for predicting soil-tube voids in a shield tunneling process based on nonlinear foundation stiffness, provided in an embodiment of this application. Figure 4 This is a schematic diagram of pipeline discretization of a method for predicting pipe-soil separation during shield tunneling based on nonlinear foundation stiffness, provided in an embodiment of this application. Figure 5 This is a pipeline node stress analysis diagram of a method for predicting pipe-soil separation during shield tunneling based on nonlinear foundation stiffness, provided in an embodiment of this application. Figure 6 This is a schematic diagram of a tunnel under a pipeline, based on a method for predicting the separation of pipe and soil during shield tunneling, provided in an embodiment of this application, using nonlinear foundation stiffness. Figure 7 This is a structural diagram of a shield tunneling process soil-tube void prediction system based on nonlinear foundation stiffness, provided in one embodiment of this application. Detailed Implementation

[0024] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0025] It should be understood that the step numbers used in the text are for ease of description only and are not intended to limit the order in which the steps are performed.

[0026] First Embodiment Pipe-soil separation significantly alters the interaction mechanism between underground pipelines and the foundation soil, thereby affecting the pipeline's stress state and structural safety. Existing pipe-soil separation detection technologies are mostly based on linearly changing foundation stiffness. This approach clearly ignores the stiffness degradation of the soil during construction, from "small strain" to "failure." Furthermore, when shield tunneling disturbances are significant, the soil around the pipe is often in a transitional state of "semi-yield" or "sharply decreased stiffness." Existing technologies either overestimate soil constraints (using only initial foundation stiffness for calculations), leading to underestimation of pipeline displacement calculations, or underestimate soil constraints (using secant foundation stiffness). This makes it difficult to accurately characterize the influence of foundation stiffness on relative pipe-soil displacement, differences in bearing capacity between upper and lower foundations, and the pipe-soil contact state. Consequently, they cannot accurately predict changes in foundation stiffness during shield tunneling, resulting in significant errors between predicted pipe-soil separation and actual conditions.

[0027] To address the aforementioned issues, this application introduces a non-linearly varying foundation stiffness and analyzes the soil on both sides of the underground pipeline as two independent systems, thereby enabling accurate prediction of soil-pipe separation.

[0028] like Figure 1 As shown, to address the problem in existing technologies where the calculation of the actual load exerted by the foundation soil on underground pipelines leads to significant errors in the predicted pipe-soil separation, the first embodiment of this application provides a detailed flowchart of a method for predicting pipe-soil separation during shield tunneling based on nonlinear foundation stiffness. This embodiment's method includes steps S1 to S4, detailed below: Step S1: Discretize the foundation soil on both sides of the underground pipeline into two independent nonlinear spring systems, obtain the load-displacement relationship of the overlying foundation and the underlying foundation respectively, and perform hyperbolic fitting on the load-displacement relationship to obtain the initial foundation stiffness and ultimate bearing capacity of the foundation, so as to construct a double-layer hyperbolic foundation model.

[0029] Existing technologies always assume that the foundation stiffness is constant when the foundation reaction force reaches its limit. However, in reality, sandy soil materials have significant nonlinear characteristics. Therefore, the embodiments of this application discretize the underground pipeline and the soil around the pipeline into multiple points to perform more accurate modeling.

[0030] To simplify mathematical calculations, since the resistance encountered by underground pipelines when moving upward and downward relative to the foundation soil is different, the foundation soil cannot be regarded as a whole, but rather as two different systems on the upper and lower sides. Therefore, the foundation soil on the upper and lower sides of the underground pipeline (i.e., the upper soil and the lower soil, also known as the overlying foundation and the underlying foundation) is discretized into two independent nonlinear spring systems, each containing multiple soil elements.

[0031] On the model composed of the nonlinear spring system, the load-displacement relationship between the underground pipeline and the soil element (i.e., the load-displacement relationship between the underground pipeline and the overlying foundation and the underlying foundation, respectively) is obtained through foundation bearing capacity tests, and load-displacement variation curves of the soil element on the upper and lower soil sides are constructed. Then, hyperbolic fitting is performed on the load-displacement variation curves for the upper and lower soil sides respectively, and the initial foundation stiffness and ultimate bearing capacity of the foundation on both sides above and below the underground pipeline are derived from the hyperbolic fitting results. Based on the fitting results, the initial foundation stiffness, and the ultimate bearing capacity of the foundation, corresponding nonlinear variation curves are constructed for the foundation stiffness on both sides above and below the underground pipeline, resulting in a double-layer hyperbolic foundation model.

[0032] The load-displacement variation curve of the double-layer hyperbolic foundation model is used to describe the relationship between the foundation reaction vector of the pipeline node and the relative displacement between the pipe and the soil.

[0033] The initial foundation stiffness is the initial stiffness of the foundation soil in the initial stage of stress; the ultimate bearing capacity of the foundation is the maximum compressive stress that the foundation soil can provide when it reaches the state of shear failure or complete plastic flow during the stress process.

[0034] Figure 2 The provided pipeline-soil model diagram shows underground pipelines with thick black lines. The overlying foundation and the underlying foundation are located on either side of the pipelines. Both foundation systems are discretized as nonlinear spring systems. Figure 2 The provided curve is the foundation stiffness variation curve, and the formula is: , u ( x ) represents the vertical deformation of the foundation. p ( x The force is the interaction force between the soil and the pipe. a , b These are the parameters for the interaction between the soil and the pipe.

[0035] when hour, ;when hour, .in, k 0 represents the initial foundation stiffness. p u1 Let be the ultimate bearing capacity of the foundation. Substituting back into the formula... The expression for the foundation stiffness of the hyperbolic nonlinear Winkler model can be obtained as follows: Since the upper and lower soil masses are two independent systems, the upper and lower sides of the underground pipeline should each have their own specific foundation stiffness expressions, the specific expressions of which are: ; ; In the formula, k u0 and k d0 These represent the first initial stiffness above the underground pipeline and the second initial stiffness below it. q u and q d These are the ultimate bearing capacities of the foundation on both sides above and below the underground pipeline. k u The first stiffness on the upper side of the underground pipeline, k d This is the second stiffness on the underside of the underground pipe.

[0036] The curve corresponding to the load-displacement relationship is: ; in, p / D p The average load intensity applied to the soil by the underground pipeline. s This represents the vertical displacement of the foundation soil.

[0037] Specifically, the ultimate bearing capacity of the foundation can be obtained from the results of the foundation load test, and the specific expression is as follows: ; ; in, q u and q d These represent the ultimate bearing capacity of the foundation on both sides above and below the underground pipeline. D p The diameter of the underground pipeline. a , b These are parameters of the soil-pipe interaction, used to determine the soil-pipe interaction... p - s Curve shape.

[0038] The initial foundation stiffness can be obtained from the results of the foundation load test, and its specific expression is as follows: ; ; in, k u0 and k d0 These represent the initial foundation stiffness on both the upper and lower sides of the underground pipeline.

[0039] The expressions for the first and second stiffness obtained above are respectively introduced into the load-displacement variation curves, resulting in two different curves. These two curves are fitted, and the initial foundation stiffness and ultimate bearing capacity of the foundation on both sides above and below the underground pipeline are inferred from the hyperbolic fitting results. This constructs a double-layer hyperbolic foundation model containing two load-displacement variation curves. Compared with existing technologies, the constructed hyperbola can reflect the nonlinear displacement development of sandy soil under upward and downward compressive loads.

[0040] As a supplement to the above scheme, the embodiments of this application are based on the results of local bearing capacity tests on sandy soil foundations under non-plane strain conditions (hereinafter referred to as the results of foundation load tests). Existing empirical formulas for the ultimate bearing capacity of sandy soil foundations are modified to propose pull-out correction factors and compressive correction factors. These two correction factors are used to correct the ultimate bearing capacity of the foundation calculated by existing empirical formulas, thereby reducing the deviation between the empirical formulas and the actual soil-to-basic interaction behavior. When the measured load-displacement relationship cannot be obtained, the modified empirical formulas can be used to determine the ultimate bearing capacity parameters required for a double-layer hyperbolic foundation model, and a double-layer hyperbolic foundation model can be constructed.

[0041] By comparing the ultimate bearing capacity of the foundation obtained through foundation load tests with the relevant content proposed in existing formulas, the pull-out correction factor and the compressive correction factor can be obtained. If test results are unavailable, the pull-out correction factor and the compressive correction factor can be obtained using the following formulas, where the pull-out correction factor is 2.0 and the compressive correction factor is 1 / 3: ; ; in, q u and q d These represent the ultimate bearing capacity of the foundation on the upper and lower sides, respectively. N q and N r These are all parameters related to compressive bearing capacity. N v This is the uplift bearing capacity coefficient. r Z represents the effective unit weight of the soil. p The depth of the pipeline axis.

[0042] Figure 3 The blue dashed line in the embodiment of this application represents a double-layer curve comparison diagram. It represents a double-layer ideal elastoplastic model, which ignores the plastic deformation and stiffness decay of sand during the stress process. It assumes that a constant foundation stiffness is used before reaching the ultimate bearing capacity of the foundation. After the foundation reaction reaches the ultimate bearing capacity, the foundation reaction remains at the limit value, and the corresponding tangential stiffness drops to zero. Although this model considers the ultimate bearing capacity and plastic stage of the foundation, it fails to continuously describe the process of the foundation stiffness gradually weakening with the development of displacement. The orange dashed line represents a double-layer hyperbolic model, which is a double-layer hyperbolic foundation model that considers nonlinear characteristics. It introduces the initial foundation stiffness and the ultimate bearing capacity of the foundation. Through the continuous hyperbolic relationship, it can describe the nonlinear evolution process of the foundation reaction gradually approaching the ultimate bearing capacity from the initial approximately linear growth. As the relative displacement of the pipe and soil increases, the slope of the hyperbola gradually decreases, which characterizes the continuous weakening process of the foundation stiffness. z uThis represents the displacement of the upper foundation soil when it reaches the ultimate bearing capacity of the foundation. z d This represents the displacement of the underlying foundation soil when it reaches the ultimate bearing capacity of the foundation. z p This is the distance from the top / side soil to the center of the pipeline, i.e., the burial depth of the pipeline axis.

[0043] Figure 3 The essential difference between the two models lies in whether or not they consider the nonlinear physical and mechanical behavior (stiffness decay) of the foundation soil. The two-layer ideal elastoplastic model employs constant foundation stiffness before reaching the ultimate bearing capacity and then uses ideal plasticity treatment after reaching the ultimate bearing capacity. The two-layer hyperbolic foundation model, on the other hand, uses a continuous function to describe the nonlinear evolution process of foundation stiffness gradually weakening with the relative displacement of the soil and the foundation reaction gradually approaching the ultimate bearing capacity. Because the two-layer hyperbolic foundation model considers this behavior, it has higher computational accuracy and engineering safety under soft soil or large deformation conditions.

[0044] Step S2: Based on the preset pipeline parameters and foundation parameters, perform initial linear elastic analysis of the pipeline on the preset Winkler foundation model to obtain the initial conditions for iteration.

[0045] To obtain the initial input for the iterative model of the bilayer hyperbolic foundation, this step performs an initial linear elastic analysis on the underground pipelines. Pipeline and foundation parameters are provided prior to the elastic analysis.

[0046] First, the underground pipeline of length L is discretized into multiple pipeline units based on the finite difference method.

[0047] The pipeline parameters include the outer diameter, burial depth, wall thickness, and bending stiffness of the underground pipeline. The bending stiffness is determined by the elastic modulus and the moment of inertia of the section, and is used to characterize the pipeline's ability to resist bending deformation; the moment of inertia of the section is calculated from the outer diameter and wall thickness of the pipeline; the burial depth is used to determine the weight of the soil above the pipeline, the range of pull-out failure, and the geometric parameters in the calculation of the ultimate bearing capacity of the foundation. The foundation parameters include the effective unit weight of the soil, the effective internal friction angle, the initial foundation stiffness of the upper soil (i.e., the first initial stiffness), the initial foundation stiffness of the lower soil (i.e., the second initial stiffness), and the ultimate bearing capacity of the upper and lower soils. The initial foundation stiffness and ultimate bearing capacity are preferably obtained by fitting the load-displacement curves from local bearing tests; when test data is lacking, they can be calculated based on existing empirical formulas combined with pull-out and compressive strength correction factors.

[0048] According to the Euler-Bernoulli beam theory, the governing differential equation for pipeline bending behavior (referred to as the bending behavior equation) can be obtained as follows: ; in, E p For the pipeline's Young's modulus, I p The moment of inertia of the cross section is... w ( x ( ) represents pipeline deflection. x The coordinates are along the pipeline axis. M It represents the bending moment.

[0049] First, the foundation reaction vector of the pipeline nodes is constructed. The foundation reaction force at each pipeline node is discretized into nodal forces acting at the geometric center point of each pipeline node. The foundation reaction vector of the pipeline node is obtained through these nodal forces, specifically as follows: Figure 4 As shown.

[0050] Figure 4 The difference nodes in the diagram are discrete pipeline nodes. P i To act on nodes i The ground reaction force at a given location is composed of the ground reaction forces at each node, forming the ground reaction force vector {P}. L For pipeline length, n This represents the number of nodes.

[0051] When the nodal force is downward, the foundation reaction vector is negative.

[0052] Set the axial coordinate of the pipeline as follows: x Because pipeline deflection affects any pipeline node on the pipeline cross-section. x If it is continuously and twice differentiable, then the central difference method can be used to obtain the equation: ; in, w i-1 , w i , w i+1 The first i -1, i , i +1 pipeline deflection at pipeline node.

[0053] like Figure 5 The diagram shows the stress analysis of the pipeline node. M i For the first i The internal bending moment of each pipeline node is directed upwards in the diagram.

[0054] Based on the static equilibrium condition of underground pipelines, the first... i Internal bending moment of each pipeline node Mi The specific expression is: ; Solving the above equations simultaneously, we can obtain the following pipeline bending moment control equations: ; To solve the above equations, this application introduces the equilibrium condition of the entire underground pipeline and the boundary condition that the bending moment at the right end of the pipeline is 0. The specific expressions are as follows: ; ; Based on the introduced boundary conditions, the following formula in matrix form is obtained: ; In the formula, [ K p [ ] is the pipeline stiffness matrix, and the elements in this matrix are... k p = E p I p ; Let [ be the pipeline deflection vector] C ] is the coefficient matrix, Let be the foundation reaction force vector.

[0055] Based on the deformation compatibility criterion of the pipe-soil interface, for pipeline nodes and soil units in a state of compressive contact, the free displacement of soil caused by the tunnel boring machine during construction... s ( x The relative displacement of the pipe and soil caused by the interaction between the pipe and the soil u ( x The specific expression is: ; ; In the formula, Let [ be the pipeline deflection vector] λ [ ] represents the foundation compliance matrix, and the elements in the matrix are... λ ij Represented in soil unit j Soil elements caused by unit load i Soil displacement at the location; F} represents the force vector exerted by the pipeline on the soil, which is related to... These are interaction forces.

[0056] By combining the above displacement formula, pipeline bending moment control equation, and foundation reaction vector, the pipeline deflection control equation can be constructed, the specific expression of which is: ; Therefore, the pipeline bending moment control equation can be transformed. and the governing equations of the foundation reaction vector : ; ; When using the Winkler foundation model for initial linear elastic analysis, the foundation compliance matrix [λ] is a diagonal matrix: In the initial linear elastic analysis, the foundation stiffness is represented by the foundation compliance matrix [λ]. k s It can be seen as a combined manifestation of the stiffness of the foundation above and below the pipeline.

[0057] q d This refers to the ultimate compressive bearing capacity of the soil at the bottom of the pipeline. z d This represents the displacement when the bottom foundation reaches its bearing capacity limit. q u This refers to the ultimate compressive bearing capacity of the soil above the pipeline. z u Displacement when the superstructure reaches its bearing limit Finally, by integrating the foundation reaction vector, pipeline bending moment control equation, and pipeline deflection control equation, the iterative initial conditions for the bilayer hyperbolic foundation model are obtained. These initial iterative conditions provide initial state variables for the iterative update of the bilayer hyperbolic foundation model, including initial pipeline displacement, initial pipeline bending moment, and initial foundation reaction vector.

[0058] This step organically combines the mechanical properties of the pipeline itself with the foundation reaction force, realizing the coupled analysis of the pipeline-soil system, improving the model's ability to describe the stress and deformation response of the pipeline, and providing a more accurate mechanical state for subsequent construction simulation of the double-layer hyperbolic foundation model.

[0059] Step S3: Based on the initial iteration conditions, perform shield tunneling simulation on the preset free displacement field of the soil using a preset spatial step size and shield tunneling construction parameters, and iteratively update the foundation flexibility matrix of the double-layer hyperbolic foundation model based on the simulation results corresponding to each spatial step size.

[0060] Figure 6A schematic diagram of a tunnel passing under a pipeline is provided. Blue represents the tunnel, and horizontal lines represent underground pipelines containing multiple pipeline nodes. Using the pipeline direction as the horizontal axis, the free displacement vector of the soil can be obtained. s The expression for}: ; In the formula, θ p The angle between the tunnel and the pipeline; when the tunnel passes perpendicularly under the pipeline, the tunnel-pipe angle is... θ p =90°; x i For the first i The coordinates of the geometric center point of each pipeline node; R Where is the tunnel radius. V 1 represents the formation loss rate. z 0 represents the burial depth of the tunnel axis. z p For the burial depth of the pipeline axis, K ( z ) is the burial depth z Settlement trough width parameters, s i for{ s The first in} i Each element.

[0061] Based on the above expression for the free displacement vector of soil, it can be used to calculate the soil displacement of the soil element under each movement of the tunnel boring machine during shield tunneling construction simulation.

[0062] Therefore, after inputting the iterative initial conditions into the double-layer hyperbolic foundation model, shield tunneling simulation is performed on the double-layer hyperbolic foundation model based on the iterative initial conditions, initial foundation stiffness, and ultimate bearing capacity of the foundation, using the set shield tunneling construction parameters. During the simulation, each time the shield machine moves a preset spatial step, the soil free displacement field under the current construction step is updated according to the current position of the shield machine, obtaining the pipeline node displacement and the corresponding soil free displacement vector.

[0063] Then, based on the difference between the pipeline displacement and the free displacement of the soil, the relative displacement between the pipeline node and the soil unit is obtained. The specific calculation formula is as follows: ; in, The relative displacement between the pipe and the soil. w ( x The displacement of the pipeline is the pipeline deflection. s ( x ) represents the displacement of the soil.

[0064] If the relative displacement between the pipe and the soil is less than 0, it indicates that the pipeline displacement caused by tunnel construction is less than the soil displacement, and the pipeline node moves upward relative to the soil. If the relative displacement between the pipe and the soil is greater than 0, it indicates that the pipeline displacement caused by tunnel construction is greater than the soil displacement, and the pipeline node moves downward relative to the soil.

[0065] Step S4: The iterative update results are detected by using the preset pipe-soil void judgment criteria to obtain the distribution of pipe-soil voids in underground pipelines.

[0066] Therefore, based on the magnitude or sign of the relative displacement between the pipeline and the soil, the direction of movement of the pipeline relative to the soil can be determined.

[0067] Each time the relative displacement between the pipe and the soil is obtained, the foundation flexibility matrix of the double-layer hyperbolic foundation model is updated. Then, the update result is detected by the preset pipe-soil void judgment criterion to determine which pipeline nodes have pipe-soil void phenomena.

[0068] During the continuous updating process, the foundation flexibility matrix is ​​continuously corrected until the pipeline displacement and foundation reaction force vector meet the preset nonlinear coordination conditions or the preset iteration termination conditions. At this point, the iteration ends, and the distribution of the underground pipeline's soil-pipe separation is output.

[0069] In each iteration, the direction of the relative displacement between the pipe and the soil, i.e., the direction of movement of the pipeline node, is first determined. Then, based on the direction of the relative displacement between the pipe and the soil, the upper soil parameters, and the lower soil parameters, the foundation flexibility coefficients at each pipeline node in the double-layer hyperbolic foundation model are updated to form an updated foundation flexibility matrix. Based on the updated foundation flexibility matrix, the relative displacement between the pipe and the soil is recalculated in the double-layer hyperbolic foundation model to obtain the iterative update result. The contact state between the pipeline and the soil is determined using the pipe-soil separation criterion. When the relative displacement between the pipe and the soil exceeds the preset soil contact limit, the detection result is determined to meet the pipe-soil separation criterion, indicating that pipe-soil separation has occurred. The foundation spring unit corresponding to the pipeline node is set to invalid, and the foundation reaction force at the pipeline node is set to 0 to characterize the contact separation phenomenon between the pipeline node and the soil unit.

[0070] For example, the upward movement of the pipeline is determined by the direction of the relative displacement between the pipe and the soil. If the upward displacement of the pipeline exceeds the soil contact limit, the physical connection between the pipeline node and the soil unit is forcibly broken. For example, the foundation stiffness of the corresponding soil unit is set to 0, and the foundation reaction force at the corresponding pipeline node is set to 0 to simulate pipe-soil separation. Ultimately, the contact separation phenomenon between the pipeline and the surrounding soil is simulated in digital space.

[0071] Optionally, the iteration termination condition is that the difference in pipeline displacement between two adjacent iterations is less than or equal to a set threshold, which is considered as iteration convergence. In this embodiment, the threshold is set to 10. -6 m.

[0072] Substituting the pipeline displacement vector obtained from the last iteration into the pipeline bending moment control equation, and combining it with the finally updated foundation compliance matrix to calculate the foundation reaction vector, the final bending moment vector and foundation reaction vector can be obtained.

[0073] Then, based on the distribution of soil-pipe separation of underground pipelines, it can be determined which pipeline locations experienced soil-pipe separation during the shield tunneling process. Combined with the final bending moment vector and geographical reaction force vector, data support is provided for assessing construction safety.

[0074] Implementing the embodiments of this application has the following beneficial effects: This application introduces a nonlinear spring system to characterize the foundation soil surrounding underground pipelines. Based on the load-displacement relationship between the overlying and underlying foundations and the underground pipelines, the foundation stiffness at each pipeline node can continuously change nonlinearly with the local relative displacement between the pipe and the soil. This overcomes the limitation of traditional linear elastic foundation models that use constant foundation stiffness (i.e., linearly changing foundation stiffness), improving the ability to describe the nonlinear stress and deformation response of underground pipelines. The resulting foundation stiffness variation is more consistent with reality and more reasonable. Furthermore, by setting an ultimate bearing capacity, the nonlinear evolution process of the foundation reaction force, from an initial approximately linear increase to gradually approaching the ultimate bearing capacity, is described, thereby improving the accuracy of calculating the foundation reaction force and pipeline response at different deformation stages. Based on this, the pipe-soil contact state at each pipeline node is detected according to the relative displacement between the pipe and the soil and the foundation reaction state, thereby identifying pipeline nodes where pipe-soil separation has occurred. This allows for more accurate identification of pipeline nodes where pipe-soil separation has occurred. Then, through initial linear elastic analysis of the pipeline, coupled analysis of the pipeline nodes and soil elements is performed to improve the ability of the double-layer hyperbolic foundation model to describe the stress and deformation response of the pipeline, providing a more accurate initial mechanical state for subsequent shield tunneling simulation. During the shield tunneling simulation, the free displacement field of the soil at the pipeline location is calculated based on the shield construction parameters and the shield machine's advancement position, and the relative displacement between the pipe and soil is calculated in conjunction with the pipeline node displacement of the current iteration. The foundation flexibility matrix is ​​updated based on the relative displacement between the pipe and soil, and the pipeline response is re-solved using the updated foundation flexibility matrix, thereby improving the ability to describe the stress and deformation response of the pipeline. The contact state between the pipeline node and the soil element is detected based on the relative displacement between the pipe and soil and the foundation reaction state. The foundation spring element corresponding to the side where contact separation occurs is set to invalid, and the foundation reaction force on the corresponding side is set to zero. The working state of the foundation spring element on the other side is determined according to the corresponding pipe-soil contact state and the load-displacement relationship to characterize the contact failure between the pipeline node and the separated soil. After identifying pipe-soil separation (pipe-soil contact failure), the pipeline support conditions can be dynamically changed as the separation occurs by using the foundation spring on the failed separation side, updating the foundation flexibility matrix, and resolving the pipeline response. This allows the prediction of the location and evolution of the pipe-soil separation.

[0075] Second Embodiment Furthermore, in order to implement the shield tunneling process soil-tube void prediction system based on nonlinear foundation stiffness corresponding to the above method embodiments, and to achieve the corresponding functions and technical effects, Figure 2 A structural diagram of a shield tunneling process soil-tube separation prediction system based on nonlinear foundation stiffness is provided. For ease of explanation, only the parts relevant to this embodiment are shown. The shield tunneling process soil-tube separation prediction system based on nonlinear foundation stiffness provided in this application embodiment includes: The foundation model construction module 201 is used to discretize the foundation soil on both sides of the underground pipeline into two independent nonlinear spring systems, obtain the load-displacement relationship of the overlying foundation and the underlying foundation respectively, and perform hyperbolic fitting on the load-displacement relationship to obtain the initial foundation stiffness and the ultimate bearing capacity of the foundation, so as to construct a double-layer hyperbolic foundation model; wherein, the nonlinear spring system includes several soil elements.

[0076] Based on the pipeline node and the nonlinear spring system, the foundation bearing response results of the soil above and below the underground pipeline are obtained by conducting foundation bearing tests. The load-displacement relationship corresponding to the foundation bearing response results is then fitted with a hyperbola to obtain the upper nonlinear spring load-displacement curve and the lower nonlinear spring load-displacement curve corresponding to the pipeline node.

[0077] The initial foundation stiffness and ultimate bearing capacity of the foundation on both sides above and below the underground pipeline are derived by using hyperbolic fitting results. Based on the fitting results, the initial foundation stiffness, and the ultimate bearing capacity of the foundation, corresponding nonlinear variation curves are constructed for the foundation stiffness on both sides above and below the underground pipeline, thus obtaining the double-layer hyperbolic foundation model.

[0078] The pipeline initial linear elasticity analysis module 202 is used to perform pipeline initial linear elasticity analysis on a preset Winkler foundation model based on preset pipeline parameters and foundation parameters to obtain iterative initial conditions; wherein, when performing pipeline initial linear elasticity analysis, the underground pipeline is discretized into several pipeline nodes.

[0079] In the Winkler foundation model, the foundation reaction forces on each pipeline node are discretized into nodal forces acting on the geometric center point of each pipeline node, and the foundation reaction force vector of the pipeline node is defined; wherein, the forces are obtained through the foundation parameters; Based on the pipeline parameters and the foundation reaction vector, initial linear elastic analysis and pipeline stiffness matrix calculation are performed on the pipeline nodes to obtain the iterative initial conditions.

[0080] The shield tunneling simulation module 203 is used to simulate the shield tunneling construction of a preset soil free displacement field based on the preset spatial step size and shield construction parameters according to the initial iteration conditions, and to iteratively update the foundation flexibility matrix of the double-layer hyperbolic foundation model according to the simulation results corresponding to each spatial step size.

[0081] Based on the initial conditions of the iteration, the free displacement field of the soil is simulated using the shield tunneling construction parameters. Each time the shield machine moves the spatial step, the free displacement field of the soil is updated according to the current position of the shield machine to obtain the pipeline displacement of the soil unit and the free displacement of the soil caused by tunnel excavation. The iterative initial conditions provide initial state quantities for the iterative update of the double-layer hyperbolic foundation model, including initial pipeline displacement, initial pipeline bending moment, and initial foundation reaction force vector; The difference between the pipeline displacement and the free displacement of the soil is taken as the relative displacement between the pipeline and the soil.

[0082] The pipe-soil void detection module 204 is used to detect the iterative update results through preset pipe-soil void judgment criteria to obtain the distribution of pipe-soil voids in underground pipelines.

[0083] The pipeline node and the soil unit are processed based on the pipeline-soil void determination criteria for each iteration update. When the preset iteration termination condition is met, the distribution of soil voids in the underground pipeline is output.

[0084] When the relative displacement between the pipe and the soil exceeds the preset soil contact limit, the detection result is determined to meet the pipe-soil separation judgment criterion, and the pipe-soil separation between the pipeline node and the corresponding soil unit is determined. When the test results meet the criteria for determining pipe-soil separation, it indicates that pipe-soil separation has occurred. The foundation spring unit corresponding to the pipeline node is set to invalid, and the foundation reaction force at the pipeline node is set to 0, in order to characterize the contact separation phenomenon between the pipeline node and the soil unit.

[0085] Implementing the embodiments of this application has the following beneficial effects: This application introduces a nonlinear spring system to characterize the foundation soil surrounding underground pipelines, transforming the change in foundation stiffness into a nonlinear process. This results in a well-predicted response from the constructed double-layer hyperbolic foundation model. Furthermore, by setting an ultimate bearing capacity, the model can describe the nonlinear evolution of foundation reaction forces from an initial approximately linear increase to approaching the ultimate bearing capacity, enabling more accurate identification of pipeline nodes where pipe-soil separation occurs. Then, through initial linear elastic analysis of the pipeline, coupled analysis of the pipeline nodes and soil elements is performed, enhancing the double-layer hyperbolic foundation model's ability to describe the pipeline's stress and deformation responses, providing a more accurate initial mechanical state for subsequent shield tunneling simulations. During shield tunneling simulation, the free displacement field of the soil at the pipeline location is calculated based on shield construction parameters and the shield machine's advancement position. The relative displacement between the pipe and soil is then calculated using the pipeline node displacements from the current iteration. The foundation flexibility matrix is ​​updated based on this relative displacement, and the pipeline response is re-solved using the updated foundation flexibility matrix, thereby improving the ability to describe the pipeline's stress and deformation responses. The contact state between the pipeline node and the soil unit is detected based on the relative displacement of the pipe and the foundation reaction state. When the detection result meets the pipe-soil separation judgment criterion, it indicates that the pipe-soil separation phenomenon has occurred. The foundation spring unit corresponding to the pipeline node is set to invalid, and the foundation reaction force at the pipeline node is set to 0, so as to characterize the contact separation phenomenon between the pipeline node and the soil unit.

[0086] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of this application. It should be understood that the above descriptions are merely specific embodiments of this application and are not intended to limit the scope of protection of this application. In particular, it should be noted that any modifications, equivalent substitutions, or improvements made by those skilled in the art within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for predicting soil-tube separation during shield tunneling based on nonlinear foundation stiffness, characterized in that, include: The foundation soil on both sides of the underground pipeline is discretized into two independent nonlinear spring systems. The load-displacement relationship of the overlying foundation and the underlying foundation is obtained respectively. The load-displacement relationship is hyperbolic fitted to obtain the initial foundation stiffness and the ultimate bearing capacity of the foundation, so as to construct a double-layer hyperbolic foundation model. The nonlinear spring system includes several soil elements. Based on preset pipeline parameters and foundation parameters, an initial linear elastic analysis of the pipeline is performed on the preset Winkler foundation model to obtain the iterative initial conditions; wherein, when performing the initial linear elastic analysis of the pipeline, the underground pipeline is discretized into several pipeline nodes; Based on the initial conditions of the iteration, the shield tunneling construction simulation is performed on the preset free displacement field of the soil with the preset spatial step size and shield tunneling construction parameters. The foundation flexibility matrix of the double-layer hyperbolic foundation model is iteratively updated based on the simulation results corresponding to each spatial step size. The distribution of soil-pipe voids in underground pipelines is obtained by detecting the iterative update results using a preset soil-pipe void judgment criterion.

2. The method for predicting tunnel-to-soil voids based on nonlinear foundation stiffness in shield tunneling as described in claim 1, characterized in that, Hyperbolic fitting is performed on the load-displacement relationship to obtain the initial foundation stiffness and ultimate bearing capacity, in order to construct a two-layer hyperbolic foundation model, specifically: Based on the pipeline node and the nonlinear spring system, the foundation bearing response results of the soil above and below the underground pipeline are obtained by conducting foundation bearing tests. The load-displacement relationship corresponding to the foundation bearing response results is then fitted with a hyperbola to obtain the upper nonlinear spring load-displacement curve and the lower nonlinear spring load-displacement curve corresponding to the pipeline node. The initial foundation stiffness and ultimate bearing capacity of the foundation on both sides above and below the underground pipeline are derived by using hyperbolic fitting results. Based on the fitting results, the initial foundation stiffness, and the ultimate bearing capacity of the foundation, corresponding nonlinear variation curves are constructed for the foundation stiffness on both sides above and below the underground pipeline, thus obtaining the double-layer hyperbolic foundation model.

3. The method for predicting tunnel-to-soil separation based on nonlinear foundation stiffness in shield tunneling as described in claim 1, characterized in that, Based on preset pipeline parameters and foundation parameters, an initial linear elastic analysis of the pipeline is performed on a preset Winkler foundation model to obtain the iterative initial conditions, specifically: In the Winkler foundation model, the foundation reaction forces on each pipeline node are discretized into nodal forces acting on the geometric center point of each pipeline node, and the foundation reaction force vector of the pipeline node is defined; wherein, the foundation reaction force is obtained through the foundation parameters; Based on the pipeline parameters and the foundation reaction vector, initial linear elastic analysis and pipeline stiffness matrix calculation are performed on the pipeline nodes to obtain the iterative initial conditions.

4. The method for predicting tunnel-to-soil separation based on nonlinear foundation stiffness according to claim 3, characterized in that, The load-displacement variation curve of the double-layer hyperbolic foundation model is used to describe the relationship between the foundation reaction vector and the relative displacement of the pipe and soil.

5. The method for predicting tunnel-to-soil voids based on nonlinear foundation stiffness in shield tunneling as described in claim 3, characterized in that, The initial conditions for the iteration are obtained by performing initial linear elastic analysis and calculating the pipeline stiffness matrix on the pipeline nodes based on the pipeline parameters and the foundation reaction vector, specifically: The pipeline parameters include the outer diameter, burial depth, and bending stiffness of the underground pipelines; Based on the Winkler foundation model and Euler-Bernouli beam theory, the bending behavior equation of underground pipelines is constructed according to the bending stiffness. By using the bending behavior equation and the foundation reaction vector, a stress analysis is performed at the pipeline node to obtain the pipeline bending moment control equation. Obtain the free displacement of the soil caused by the tunnel boring machine during construction, and construct the pipeline deflection control equation based on the free displacement of the soil, the pipeline bending moment control equation, and the foundation reaction vector; The foundation reaction force vector, pipeline bending moment control equation, and pipeline deflection control equation are integrated to obtain the iterative initial conditions.

6. The method for predicting tunnel-to-soil voids based on nonlinear foundation stiffness in shield tunneling as described in claim 1, characterized in that, A shield tunneling simulation is performed on a preset free displacement field of soil using a preset spatial step size and shield tunneling parameters. The foundation compliance matrix of the double-layer hyperbolic foundation model is iteratively updated based on the simulation results corresponding to each spatial step size. Specifically: Based on the initial conditions of the iteration, the free displacement field of the soil is simulated using the shield tunneling construction parameters. Each time the shield machine moves the spatial step, the free displacement field of the soil is updated according to the current position of the shield machine to obtain the pipeline displacement of the soil unit and the free displacement of the soil caused by tunnel excavation. The iterative initial conditions provide initial state quantities for the iterative update of the double-layer hyperbolic foundation model, including initial pipeline displacement, initial pipeline bending moment, and initial foundation reaction force vector; The difference between the pipeline displacement and the free displacement of the soil is taken as the relative displacement between the pipe and the soil.

7. The method for predicting tunnel-to-soil voids based on nonlinear foundation stiffness in shield tunneling as described in claim 6, characterized in that, The distribution of pipe-soil voids in underground pipelines is obtained by detecting the iterative update results using a preset criterion for determining pipe-soil voids. Specifically: The foundation flexibility matrix of the double-layer hyperbolic foundation model is iteratively updated based on the relative displacement between the pipe and the soil; the output iteration update result is detected by the pipe-soil void judgment criterion, and the pipeline node and the soil unit are processed according to the detection result; When the preset iteration termination condition is met, the distribution of soil voids in the underground pipeline is output.

8. The method for predicting soil-tube separation during shield tunneling based on nonlinear foundation stiffness according to claim 7, characterized in that, The iterative update of the foundation compliance matrix of the double-layer hyperbolic foundation model based on the relative displacement of the soil and pipe is specifically as follows: The direction of the relative displacement between the pipe and the soil is determined based on the magnitude of the relative displacement. Update the foundation flexibility matrix based on the direction of the relative displacement of the soil-to-pipe structure, the upper soil parameters, and the lower soil parameters. Based on the updated foundation compliance matrix, the relative displacement between the pipe and the soil is recalculated to obtain the iterative update result.

9. The method for predicting tunnel-to-soil voids based on nonlinear foundation stiffness in shield tunneling as described in claim 7, characterized in that, The specific steps for processing the pipeline node and the soil unit based on the detection results are as follows: When the test results meet the criteria for determining pipe-soil separation, it indicates that pipe-soil separation has occurred. The foundation spring unit corresponding to the pipeline node is set to invalid, and the foundation reaction force at the pipeline node is set to 0, in order to characterize the contact separation phenomenon between the pipeline node and the soil unit.

10. A shield tunneling process soil-tube void prediction system based on nonlinear foundation stiffness, characterized in that, include: The module includes a foundation model construction module, a linear elastic analysis module, a shield tunneling simulation module, and a soil-to-tube void detection module. The foundation model construction module is used to discretize the foundation soil on both sides of the underground pipeline into two independent nonlinear spring systems, obtain the load-displacement relationship of the overlying foundation and the underlying foundation respectively, and perform hyperbolic fitting on the load-displacement relationship to obtain the initial foundation stiffness and the ultimate bearing capacity of the foundation, so as to construct a double-layer hyperbolic foundation model; wherein, the nonlinear spring system includes several soil elements; The linear elasticity analysis module is used to perform initial linear elasticity analysis of pipelines on a preset Winkler foundation model based on preset pipeline parameters and foundation parameters, so as to obtain the initial conditions for iteration; wherein, when performing initial linear elasticity analysis of pipelines, the underground pipelines are discretized into several pipeline nodes; The shield tunneling simulation module is used to simulate the shield tunneling construction of a preset soil free displacement field based on the preset spatial step size and shield construction parameters according to the initial conditions of the iteration, and to iteratively update the foundation flexibility matrix of the double-layer hyperbolic foundation model according to the simulation results corresponding to each spatial step size. The pipe-soil void detection module is used to detect the iterative update results through preset pipe-soil void judgment criteria, and obtain the distribution of pipe-soil voids in underground pipelines.

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