A method for determining the wall thickness of a disengaged concrete pipeline CIPP under complex load coupling

Abstract

This invention discloses a method for determining the wall thickness of disjointed concrete pipes (CIPP) under complex load coupling conditions. The method includes: constructing a pipe maximum bending moment prediction model to characterize the nonlinear mapping relationship between various variables and the pipe's maximum bending moment; extracting an explicit prediction formula through symbolic regression; establishing bending bearing capacity models for the composite section of the non-disjointed zone and the CIPP bridging section of the disjointed joint, respectively, using preset structural parameters, material parameters, and load parameters as modeling inputs; calculating the allowable bending moment of the composite section of the non-disjointed zone and the allowable bending moment of the bridging lining of the disjointed joint, and selecting the minimum value between the two as the overall allowable bending moment; calculating the actual maximum bending moment requirement of the pipe based on the explicit prediction formula; and obtaining the minimum design wall thickness of the CIPP lining based on the actual maximum bending moment requirement and the overall allowable bending moment. This invention can meet the requirements for safe, economical, and accurate CIPP lining wall thickness design for disjointed pipes under complex load coupling conditions.

Description

Technical Field

[0001] This invention relates to the field of pipe wall thickness design, and in particular to a method for determining the wall thickness of CIPP (concrete composite pipe) under complex load coupling. Background Technology

[0002] As the service life of underground pipe networks in Chinese cities continues to increase, a large number of existing concrete drainage pipes are exposed to complex service environments for extended periods. Under the combined effects of multiple factors such as vehicle traffic loads, overlying soil pressure, groundwater erosion, and uneven foundation deformation, various structural defects commonly occur, including joint disconnection, pipe misalignment, pipe wall cracking, and localized leakage. Among these, pipe joint disconnection is the most prominent defect. This defect directly disrupts the axial structural continuity of adjacent pipe sections, causing abrupt changes in structural stiffness and localized moment concentration at the pipe joint location. This significantly reduces the overall load-bearing capacity and long-term service safety of the pipeline. If not repaired promptly and effectively, it can easily lead to soil erosion around the pipe, pipe hollowing, and ultimately, municipal safety accidents such as road subsidence and collapse, seriously threatening the safety of urban road traffic and the stability of underground drainage networks.

[0003] Compared to traditional open-cut repair techniques, which suffer from drawbacks such as significant construction disturbance, long construction period, high cost, and disruption to citizens' travel, CIPP in-situ curing lining repair technology boasts significant advantages, including minimal construction disturbance, high repair efficiency, wide applicability to various pipe diameters and damage scenarios, and excellent overall pipeline integrity after repair. It has now become the mainstream technology for trenchless repair of urban drainage pipelines. This technology forms an integrated continuous lining by curing the existing pipe wall, effectively repairing damaged pipe bodies, reconstructing pipeline structural continuity, and optimizing the overall stress state of the pipeline. For pipelines with disconnected joints, the CIPP lining not only needs to bear the bending load of conventional non-disconnected pipe sections but also needs to play a crucial bridging and force transmission role at the disconnected joint location. Therefore, the wall thickness parameter of the CIPP lining is the core key factor determining the bending resistance, structural safety reserve, and engineering economy of the repaired disconnected pipeline, directly affecting the overall quality and service life of the repair project.

[0004] Currently, the design work for CIPP lining wall thickness in the industry mainly relies on existing technical specifications and engineering experience formulas. The conventional design approach divides the pipeline into two states: partially deteriorated and completely deteriorated. It focuses on calculating the wall thickness based on single or a few working parameters such as external water pressure, soil pressure, surface live load, and pipeline circumferential stability. This traditional design method has certain applicability in the repair of conventionally damaged pipe sections with intact structures and no joint defects, but it has significant technical limitations. First, the theoretical basis of the traditional design method is based on ideal circular pipes, complete and continuous pipe sections, and simplified boundary conditions. It cannot accurately characterize the local structural discontinuities caused by joint disconnection, the stress mechanism of the lining bridge, and the dynamic changes in pipe-soil interaction, resulting in a large deviation from the actual stress conditions of disconnected pipelines. Secondly, traditional design systems struggle to perform coupled analysis of multiple key parameters such as traffic load, soil cover depth, groundwater level, joint disconnection length, pipe diameter, lining thickness, and material elastic modulus. They cannot take into account the complex stress state under the combined effect of multiple factors, which can easily lead to problems such as overly conservative lining wall thickness design, wasted engineering costs, or insufficient wall thickness, inadequate structural safety reserves, and easy secondary damage to the pipeline after repair.

[0005] To address the shortcomings of traditional design methods, existing technologies have incorporated two auxiliary design tools: finite element analysis (FEM) and machine learning. FEM can accurately simulate the stress response of CIPP (concrete composite pipe) repair structures under complex conditions, offering high computational accuracy. However, it suffers from complex modeling processes, long computation times, and poor adaptability to various working conditions, failing to meet the rapid wall thickness design requirements for large-scale engineering projects and thus limiting its practical engineering applicability. While traditional machine learning methods can significantly improve the prediction efficiency of wall thickness and stress parameters, existing models are mostly black-box models, outputting only single prediction results and failing to derive explicit calculation formulas directly applicable to engineering design. Furthermore, relying solely on maximum bending moment predictions cannot accurately determine the reasonable wall thickness of the lining, establish a matching relationship between bending moment requirements and allowable resistance of the repair structure, or form a complete closed-loop design system, making it difficult to guide actual engineering construction design. Therefore, a method for determining the wall thickness of CIPP under complex load coupling is urgently needed to solve these problems. Summary of the Invention

[0006] To address the aforementioned problems, the present invention aims to provide a method for determining the wall thickness of disjointed concrete pipes (CIPP) under complex load coupling conditions. This method can meet the design requirements for safe, economical, and accurate CIPP lining wall thickness of disjointed pipes under complex load coupling conditions.

[0007] Based on this, the present invention provides a method for determining the wall thickness of CIPP (concrete composite pipe) under complex load coupling, the method comprising:

[0008] Based on pre-defined standardized model variables, a pipeline maximum bending moment prediction model is constructed to characterize the nonlinear mapping relationship between each variable and the pipeline maximum bending moment.

[0009] Sign regression was performed on the maximum bending moment prediction model to extract the explicit prediction formula for the maximum bending moment demand of the pipeline.

[0010] Using existing structural mechanics modeling methods, bending bearing capacity models of the composite section of the non-disconnected zone of the pipeline and the CIPP bridging section of the disconnected joint are established respectively. Pre-set structural parameters, material parameters and load parameters are used as modeling inputs. The allowable bending moment of the composite section of the non-disconnected zone and the allowable bending moment of the bridging lining of the disconnected joint are calculated respectively, and the minimum value between the two is selected as the overall allowable bending moment of the repair structure.

[0011] The actual maximum bending moment requirement of the pipeline is calculated based on the explicit prediction formula, and the minimum design wall thickness of the CIPP lining is obtained based on the actual maximum bending moment requirement and the overall allowable bending moment.

[0012] The process of obtaining the standardized model variables includes:

[0013] A finite element model of CIPP (concrete composite pipe) repair structure was established, with traffic load, soil cover depth, groundwater level, disconnection length, pipe diameter, CIPP lining thickness, and elastic modulus as input variables. By changing the values ​​of each variable parameter, multiple sets of combined working conditions were formed. The maximum bending moment response data of the pipe corresponding to each working condition were calculated in batches to obtain the original sample data used to construct the dataset. The maximum bending moment response data refers to the maximum circumferential bending moment or control section bending moment of the CIPP repaired disconnected concrete pipe under the corresponding working condition.

[0014] Establish a one-to-one correspondence between input variables and the maximum bending moment response under the corresponding working conditions, construct a sample dataset, and perform dimensionless preprocessing on the dataset to obtain the standardized model variables.

[0015] The dimensionless input variables obtained by performing dimensionless preprocessing on the input variables in the dataset include:

[0016] Load stiffness ratio, soil cover depth ratio, disjoint length ratio, groundwater level ratio, and CIPP lining thickness ratio.

[0017] Wherein, when the maximum bending moment response data is the bending moment of the control section, its dimensionless maximum bending moment response data is expressed as:

[0018] ;

[0019] Among them, the The inner diameter of the pipe, the The elastic modulus of the CIPP liner is... For the maximum bending moment response data, the These are dimensionless maximum bending moment response data.

[0020] The allowable bending moment of the composite section in the non-disconnected zone is the minimum of the stress limit of the concrete duct and the stress limit of the CIPP lining.

[0021] The stress limit of the concrete pipe is expressed as follows:

[0022] ;

[0023] in, The The elastic modulus of the concrete pipe, the The elastic modulus of the CIPP liner is... The second moment of the concrete pipe section is... The second moment of the CIPP liner section, the The design stress limit for concrete, the The outer radius of the concrete pipe.

[0024] The stress limit value of the CIPP lining is expressed as follows:

[0025] ;

[0026] in, The The elastic modulus of the concrete pipe, the The elastic modulus of the CIPP liner is... The second moment of the concrete pipe section is... The second moment of the CIPP liner section, the The design stress limit for CIPP lining, the The inner radius of the concrete pipe.

[0027] The stress limit value of the CIPP lining is expressed as follows:

[0028] ;

[0029] Wherein, DN is the diameter of the concrete pipe, t is the thickness of the CIPP lining, and f is the diameter of the concrete pipe. l,d The design stress limit for CIPP lining.

[0030] The minimum design wall thickness of the CIPP liner is obtained based on the actual maximum bending moment requirement and the overall allowable bending moment, including:

[0031] A wall thickness inversion equation is constructed based on the critical safety state where the actual maximum bending moment requirement equals the overall allowable bending moment. The minimum design wall thickness of the CIPP lining is obtained by solving the equation.

[0032] The maximum bending moment prediction model is constructed using the KAN algorithm.

[0033] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for determining the wall thickness of CIPP (Concrete Integrated Plumbing) repairs for disconnected concrete pipes under complex load coupling conditions. This method solves the problems of existing design methods failing to accurately characterize the stress characteristics of disconnected pipes, lacking multi-factor coupling analysis, resulting in large design deviations, and hindering rapid and accurate closed-loop design. By integrating multiple technical steps, including multi-factor bending moment prediction, explicit formula extraction, composite section resistance calculation in the non-disconnected zone, and bridging resistance verification of disconnected joints, a complete closed-loop design system is constructed, from predicting the stress response under complex working conditions to accurately determining the minimum safe wall thickness of CIPP. This effectively balances the accuracy, efficiency, safety, and economy of wall thickness design, while ensuring the interpretability and verifiability of the design results. It significantly improves the design standardization and engineering applicability of CIPP repair projects for disconnected concrete drainage pipes, providing reliable technical support for related pipeline repair projects. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 This is a schematic diagram of the method for determining the wall thickness of CIPP (concrete composite pipe) under complex load coupling provided in an embodiment of the present invention;

[0036] Figure 2 This is a schematic diagram of the finite element model for repairing disconnected concrete pipes using CIPP (Compact Injection Polymerization) according to an embodiment of the present invention.

[0037] Figure 3 This is a schematic diagram of the bending analysis of the CIPP bridge at the non-disconnection zone composite section and the disconnection joint provided in an embodiment of the present invention;

[0038] Figure 4 A bending moment demand-resistance relationship diagram provided for embodiments of the present invention;

[0039] Figure 5 This is a schematic diagram illustrating the inversion solution of the minimum wall thickness of CIPP provided in an embodiment of the present invention. Detailed Implementation

[0040] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] Figure 1 This is a schematic diagram of a method for determining the wall thickness of a disjointed concrete pipe (CIPP) under complex load coupling provided in an embodiment of the present invention. The method includes:

[0042] S101. Based on the preset standardized model variables, construct a pipeline maximum bending moment prediction model to characterize the nonlinear mapping relationship between each variable and the pipeline maximum bending moment;

[0043] The process of obtaining the standardized model variables includes:

[0044] A finite element model of CIPP (concrete composite pipe) repair structure was established, with traffic load, soil cover depth, groundwater level, disconnection length, pipe diameter, CIPP lining thickness, and elastic modulus as input variables. By changing the values ​​of each variable parameter, multiple sets of combined working conditions were formed. The maximum bending moment response data of the pipe corresponding to each working condition were calculated in batches to obtain the original sample data used to construct the dataset. The maximum bending moment response data refers to the maximum circumferential bending moment or control section bending moment of the CIPP repaired disconnected concrete pipe under the corresponding working condition.

[0045] Establish a one-to-one correspondence between input variables and the maximum bending moment response under the corresponding working conditions, construct a sample dataset, and perform dimensionless preprocessing on the dataset to obtain the standardized model variables.

[0046] The dimensionless input variables obtained by performing dimensionless preprocessing on the input variables in the dataset include:

[0047] Load stiffness ratio, soil cover depth ratio, disjoint length ratio, groundwater level ratio, and CIPP lining thickness ratio.

[0048] Wherein, when the maximum bending moment response data is the bending moment of the control section, its dimensionless maximum bending moment response data is expressed as:

[0049] ;

[0050] Among them, the The inner diameter of the pipe, the The elastic modulus of the CIPP liner is... For the maximum bending moment response data, the These are dimensionless maximum bending moment response data.

[0051] A three-dimensional finite element model for CIPP repair of disconnected concrete pipes was established. Figure 2 This is a schematic diagram of the finite element model for repairing disconnected concrete pipes using CIPP (Compact Integrated Plumbing Repair) according to an embodiment of the present invention. Please refer to [the diagram]. Figure 2 The model includes a concrete pipe, a CIPP liner, a disjoint joint area, and the surrounding soil area. The CIPP liner is continuously installed along the inner wall of the concrete pipe. The disjoint joint area is characterized by the axial gap between adjacent concrete pipe sections, and the disjoint length is denoted as _____. The soil area around the pipe is used to simulate the soil constraints around the buried pipeline and the interaction between the pipe and the soil.

[0052] In this embodiment, the concrete pipe is simulated using C30 concrete material parameters, the CIPP lining is simulated using linear elastic material parameters, and the surrounding soil is simulated using the Mohr-Coulomb elastoplastic constitutive model. An interface connection is established between the CIPP lining and the inner wall of the concrete pipe to characterize the coordinated stress between the two after lining repair; a contact relationship is established between the concrete pipe and the surrounding soil to characterize the load transfer and deformation coordination between the pipe and the soil under buried conditions.

[0053] The main effects considered in the three-dimensional finite element model of the disjointed concrete pipe include: (1) ground traffic load; (2) overburden pressure; (3) groundwater action; and (4) pipe-soil interaction. Traffic load is applied through the surface loading area; overburden pressure is formed by the self-weight of the soil above the pipe; and groundwater action is simulated by setting different groundwater level conditions.

[0054] The main parameters of the finite element model include: traffic load. , soil covering depth Groundwater level Length of joint disconnection Pipe diameter CIPP liner thickness and CIPP liner elastic modulus The above parameter ranges were determined based on the actual operating conditions of the drainage pipeline, CIPP repair design parameters, and finite element parameter analysis requirements. 635 sets of physical variables were generated using random sampling, and the value ranges for each parameter are shown in the table below:

[0055] parameter Range of values Traffic load 0.50~1.00 MPa Burial depth 0.5～3.0 m <![CDATA[groundwater level a > 0.5～5.0 m Joint disconnection length 0.10～0.50 m Pipe diameter 0.30～1.20 m CIPP liner thickness 2–10 mm CIPP lining elastic modulus 4000~18000 MPa

[0056] a Distance from the Earth's surface.

[0057] The finite element method was used to analyze the stress on CIPP repair disconnected concrete pipes under different parameter combinations, and the maximum bending moment response of the pipe control section was extracted. The control section can be a section near the disengagement joint, a section at the top of the pipe, a section at the bottom of the pipe, or other critical sections with large bending moment responses.

[0058] This establishes the initial sample database:

[0059] ;

[0060] In the formula, This serves as the initial sample database. Number the sample; The total number of samples; , , , , , , The first Traffic load, soil cover depth, groundwater level, joint disconnection length, pipe diameter, CIPP lining thickness and CIPP lining elastic modulus under the following working conditions; For the first The maximum bending moment response obtained by finite element analysis under the combined working conditions.

[0061] Extracting the maximum bending moment response of CIPP repaired disconnected concrete pipes under different working conditions Traffic load, soil cover depth, groundwater level, joint disconnection length, pipe diameter, CIPP lining thickness, and CIPP lining elastic modulus are used as corresponding input parameters to form sample data of "physical factors - maximum bending moment response".

[0062] Due to differences in the dimensions and orders of magnitude of the input parameters, dimensionless processing is performed on the finite element sample data to improve the training stability and generalization ability of the subsequent pipeline maximum bending moment prediction model. In this embodiment, the elastic modulus of the CIPP lining is selected. and pipe diameter As a fundamental physical quantity, a dimensionless input variable is constructed.

[0063] The load stiffness ratio is expressed as:

[0064] ;

[0065] The ratio of soil cover depth to burial depth is expressed as:

[0066] ;

[0067] The joint disconnection length ratio is expressed as:

[0068] ;

[0069] The groundwater level ratio is expressed as:

[0070] ;

[0071] The thickness ratio of CIPP lining is expressed as:

[0072] ;

[0073] When the maximum bending moment When controlling the total bending moment of the section, the dimensionless maximum bending moment response is expressed as:

[0074] ;

[0075] Therefore, the initial sample database is transformed into a dimensionless maximum bending moment prediction sample set:

[0076] ;

[0077] in, This is a sample set for predicting dimensionless maximum bending moment. , , , , The first The load stiffness ratio, soil cover depth ratio, joint disengagement length ratio, groundwater level ratio, and CIPP lining thickness ratio corresponding to the group of working conditions. For the first The dimensionless maximum bending moment response corresponding to the set of working conditions. The total number of samples.

[0078] The dimensionless maximum bending moment prediction sample set That is, the sample set to which the standardized model variables belong serves as the training and testing data basis for the subsequent maximum bending moment prediction model.

[0079] Based on the sample set for predicting dimensionless maximum bending moment A maximum bending moment prediction model is established. This model is constructed using the KAN algorithm.

[0080] The maximum bending moment prediction model uses the load stiffness ratio , soil cover depth ratio , Joint disconnection length ratio groundwater level ratio Compared with CIPP liner thickness As an input variable, the dimensionless maximum bending moment response As an output variable, it is used to characterize the nonlinear mapping relationship between various physical factors and the maximum bending moment response of CIPP repaired disconnected concrete pipes under complex load coupling conditions.

[0081] For the The input vector of the sample group is represented as:

[0082] ;

[0083] The maximum bending moment prediction model is expressed as:

[0084] ;

[0085] In the formula, This is the dimensionless maximum bending moment response predicted by the maximum bending moment prediction model for the i-th group of samples. The nonlinear mapping function established for the maximum bending moment prediction model.

[0086] In specific calculations, The trained maximum bending moment prediction model is input, and it transforms, combines, and propagates each input variable through a trained univariate nonlinear function, ultimately outputting the corresponding dimensionless maximum bending moment prediction value. .therefore, This represents the predictive calculation process from dimensionless input parameters to the dimensionless maximum bending moment response.

[0087] During model training, the dimensionless maximum bending moment prediction sample set will be used. Divided into training set and test set The training set is used to optimize the parameters of the maximum bending moment prediction model, while the test set is used to evaluate the model's predictive ability on samples not included in the training. The model training objective is to minimize the error between the predicted values ​​of the maximum bending moment prediction model and the finite element calculation values, using the mean squared error as the loss function.

[0088] ;

[0089] In the formula, Let the mean squared error loss function be used. The number of samples used in training or evaluation; For the first The finite element dimensionless maximum bending moment response corresponding to the sample group.

[0090] After the model training is completed, the accuracy of the maximum bending moment prediction model is evaluated using a test set. The evaluation metrics include the coefficient of determination. The mean square error (MSE) and mean absolute error (MAE) are used to predict the maximum bending moment. Once the model's prediction accuracy meets the preset requirements, the trained maximum bending moment prediction model is used as the prediction model for the maximum bending moment requirement of CIPP repair disconnected concrete pipes under complex load coupling, and is subsequently used for the extraction of the explicit prediction formula for the maximum bending moment.

[0091] S102. Perform symbolic regression on the maximum bending moment prediction model to extract the explicit prediction formula for the maximum bending moment demand of the pipeline;

[0092] Based on the trained maximum bending moment prediction model, symbolic regression is performed on its prediction results to extract an explicit prediction formula for the maximum bending moment that can be used for engineering calculations. The symbolic regression uses the dimensionless maximum bending moment response output by the maximum bending moment prediction model as the fitting object, converting the nonlinear mapping relationship in the maximum bending moment prediction model into an explicit analytical expression, thereby improving the interpretability and engineering verifiability of the maximum bending moment prediction model.

[0093] Substitute the dimensionless input variables into the trained maximum bending moment prediction model to obtain the corresponding prediction results, and construct a symbolic regression sample set:

[0094] ;

[0095] In the formula, The sample set used for symbolic regression; To train the completed maximum bending moment prediction model for the first... The dimensionless maximum bending moment response predicted from the sample group.

[0096] Dimensionless maximum bending moment response predicted by the maximum bending moment prediction model A symbolic regression model is established as the fitting target. The predicted value of the symbolic regression model for the i-th sample group is expressed as:

[0097] ;

[0098] In the formula, For the symbolic regression model on the 1st The dimensionless maximum bending moment response predicted from a set of samples; This is the explicit analytic function obtained from symbolic regression.

[0099] The goal of symbolic regression is to make the predicted values ​​of the symbolic regression model as close as possible to the predicted values ​​of the maximum bending moment prediction model. Its optimization problem is expressed as:

[0100] ;

[0101] In the formula, This is the optimal explicit analytic function obtained after optimization; This is the space of candidate functions for symbolic regression; This represents the number of samples used for symbolic regression.

[0102] In this embodiment, the candidate function space for symbolic regression consists of linear functions, square functions, exponential functions, logarithmic functions, absolute value functions, and their combinations. The general expression for the symbolic regression model can be written as:

[0103] ;

[0104] In the formula, For constant terms; For the first The regression coefficients of the basis function terms; For the first One basis function; This represents the number of basis function terms in the explicit analytic function.

[0105] To evaluate how well the symbolic regression model approximates the prediction results of the maximum bending moment prediction model, a fitting error function is constructed:

[0106] ;

[0107] In the formula, This represents the sign regression fitting error.

[0108] when After meeting the preset accuracy requirements, the optimal explicit analytical function will be used. As an explicit prediction function for dimensionless maximum bending moment:

[0109] ;

[0110] According to the definition of dimensionless maximum bending moment response, the actual maximum bending moment demand is expressed as:

[0111] ;

[0112] Substituting the dimensionless explicit prediction function for the maximum bending moment into the above equation, we obtain the maximum bending moment demand function for repairing disconnected concrete pipes in CIPP under complex load coupling:

[0113] ;

[0114] In the formula, The thickness of the CIPP liner is The maximum bending moment requirement at that time.

[0115] Given traffic load, soil cover depth, groundwater level, joint disconnection length, pipe diameter, and CIPP lining elastic modulus, except for the CIPP lining thickness... All other parameters are known. Therefore, the maximum bending moment requirement can be expressed as a function of the CIPP liner thickness. This is used as the input for bending moment requirements in the subsequent inversion calculation of the minimum wall thickness of the CIPP lining.

[0116] S103. Using existing structural mechanics modeling methods, establish bending bearing capacity models for the composite section of the non-disconnected zone of the pipeline and the CIPP bridging section of the disconnected joint, respectively. Use preset structural parameters, material parameters and load parameters as modeling inputs, calculate the allowable bending moment of the composite section of the non-disconnected zone and the allowable bending moment of the bridging lining of the disconnected joint, and select the minimum value between the two as the overall allowable bending moment of the repair structure.

[0117] After obtaining the maximum bending moment demand function, the bending capacity of the CIPP repair structure in the non-disconnection zone was further calculated in order to check the structural resistance. Figure 3 For a schematic diagram of the bending analysis of the CIPP bridge at the non-disconnected composite section and the disconnected joint provided in this embodiment of the invention, please refer to... Figure 3 In the non-disconnected zone, the concrete pipe and CIPP lining maintain a good interfacial connection, and they can be analyzed as a concentric annular composite section subjected to bending. This step is used to determine the allowable bending moment of the concrete pipe-CIPP lining composite section in the non-disconnected zone. .

[0118] Let the inner radius of the concrete pipe be... The outer radius is The wall thickness of the concrete pipe is ,in:

[0119] ;

[0120] ;

[0121] The second moment of the concrete pipe section is:

[0122] ;

[0123] The CIPP lining is located inside the concrete pipe, and its outer radius is... Inner radius is Therefore, the second moment of the CIPP liner section is:

[0124] ;

[0125] In the formula, The second moment of the concrete pipe section. The second moment of the CIPP lining section. This refers to the thickness of the CIPP liner.

[0126] Under conditions of combined bending, the concrete duct and the CIPP lining have the same curvature, and the equivalent bending stiffness of the composite section is expressed as:

[0127] ;

[0128] In the formula, The equivalent bending stiffness of the composite section in the non-disconnected region. The elastic modulus of concrete pipes; The elastic modulus of CIPP lining.

[0129] When the composite section is subjected to bending moment When the stress at the outermost edge of the concrete duct and the stress within the CIPP lining are respectively expressed as:

[0130] ;

[0131] ;

[0132] To ensure that the composite section in the non-disconnected zone meets the strength requirements, the stress at the outermost edge of the concrete duct should not exceed the design stress limit of the concrete. The stress of the control fibers in the CIPP liner should not exceed the design stress limit of the CIPP liner. Therefore, the allowable bending moment controlled by the main concrete pipe can be obtained. and allowable bending moment controlled by CIPP lining :

[0133] ;

[0134] ;

[0135] Therefore, the allowable bending moment of the composite section in the non-disconnected zone is taken as the smaller of the two values ​​mentioned above:

[0136] ;

[0137] Right now:

[0138] ;

[0139] The above calculations can be used to obtain the thickness of different CIPP liners. The bending bearing capacity of the composite section in the non-disconnected zone provides resistance input for subsequent comparison with the allowable bending moment of the CIPP bridging lining at the disconnected joint.

[0140] At the disjoint joint, there is an axial gap between adjacent concrete pipe sections, weakening the structural continuity of the concrete pipeline at the joint location. The bending moment at the joint is mainly borne by the CIPP lining bridging section that spans the disjoint area. Therefore, this step treats the CIPP lining bridging section at the disjoint joint as an independent annular section bending member for bending capacity calculation.

[0141] Since the CIPP lining is attached to the inner wall of the concrete pipe, the outer diameter of its bridging section is approximately equal to the pipe diameter. The inner diameter is Therefore, the second moment of the section of the CIPP lining bridging segment. for:

[0142] ;

[0143] The corresponding section modulus is:

[0144] ;

[0145] Will Substituting into the above equation, we get:

[0146] ;

[0147] In the formula, The section modulus of the CIPP lining bridging section at the disjoint joint.

[0148] When the CIPP bridging section at the joint is subjected to bending moment At that time, its maximum bending normal stress is:

[0149] ;

[0150] To ensure that the CIPP lining bridging section at the disjoint joint meets the strength requirements, its maximum bending normal stress should not exceed the design stress limit of the CIPP lining. ,Right now:

[0151] ;

[0152] Therefore, the allowable bending moment of the CIPP bridging liner at the disjointed joint is obtained:

[0153] ;

[0154] Will Substituting into the above equation, we get:

[0155] ;

[0156] In the formula, Allowable bending moment for CIPP bridging liner at disjoint joint; The design stress limit for CIPP lining.

[0157] The above calculations can be used to obtain the bending resistance of the CIPP bridging section at the disjoint joint under different CIPP liner thicknesses t, providing the resistance input of the joint control section for subsequent determination of the overall allowable bending moment of the repair structure.

[0158] Allowable bending moment based on composite section in non-disconnected region Allowable bending moment of CIPP bridging liner at disjoint joint The overall allowable bending moment for CIPP repair of disconnected concrete pipes was determined.

[0159] Since the control section for CIPP repair of disconnected concrete pipes may be located in the non-disconnected zone or at the disconnected joint, the overall allowable bending moment of the repair structure should consider the bending capacity of both types of sections. To ensure that the repair structure meets the strength requirements at different control locations, the smaller value between the allowable bending moment of the composite section in the non-disconnected zone and the allowable bending moment of the CIPP bridging lining at the disconnected joint is taken as the overall allowable bending moment.

[0160] ;

[0161] When satisfied When the bending resistance of the composite section in the non-disconnected zone is relatively small, the overall allowable bending moment of the repaired structure is controlled by the composite section in the non-disconnected zone. At this point, we have:

[0162] ;

[0163] When satisfied When this occurs, it indicates that the CIPP bridging liner at the disjointed joint has relatively low bending resistance. The overall allowable bending moment of the repaired structure is controlled by the bridging section at the disjointed joint. At this point, we have:

[0164] ;

[0165] When satisfied This indicates that the composite section in the non-disconnected zone and the CIPP bridging section at the disconnected joint simultaneously reach the same allowable bending moment level, and the two together control the overall bending resistance of the repaired structure.

[0166] The above comparisons can determine the thickness of different CIPP liners. Overall allowable bending moment of the lower repair structure The control areas were clearly identified, providing structural resistance input for the subsequent inversion of the minimum wall thickness of the CIPP lining.

[0167] S104. Calculate the actual maximum bending moment requirement of the pipeline based on the explicit prediction formula, and obtain the minimum design wall thickness of the CIPP lining based on the actual maximum bending moment requirement and the overall allowable bending moment.

[0168] The minimum design wall thickness of the CIPP liner is obtained based on the actual maximum bending moment requirement and the overall allowable bending moment, including:

[0169] A wall thickness inversion equation is constructed based on the critical safety state where the actual maximum bending moment requirement equals the overall allowable bending moment. The minimum design wall thickness of the CIPP lining is obtained by solving the equation.

[0170] Specifically, based on the maximum bending moment demand function and the overall allowable bending moment of the repair structure An inversion equation for the minimum wall thickness of the CIPP liner was established. Taking the maximum bending moment requirement not exceeding the overall allowable bending moment of the repaired structure as the design criterion, the CIPP liner thickness should meet the following requirements:

[0171] ;

[0172] In the formula, The maximum bending moment requirement for repairing disconnected concrete pipes using CIPP under complex load coupling conditions; To repair the overall allowable bending moment of the structure; This refers to the thickness of the CIPP liner.

[0173] Figure 4 For the bending moment demand-resistance relationship diagram provided in the embodiments of the present invention, please refer to... Figure 4 The minimum wall thickness of CIPP lining is defined as the minimum positive thickness that meets safety requirements, and its expression is:

[0174] ;

[0175] In the formula, Minimum wall thickness for CIPP liner; and These represent the lower and upper limits of the CIPP wall thickness range, respectively.

[0176] To facilitate the solution, a safety margin function is constructed:

[0177] ;

[0178] when When, it means that under the current CIPP liner thickness, the overall allowable bending moment of the repaired structure is not less than the maximum bending moment requirement, and the wall thickness meets the design requirements; when When the thickness of the CIPP lining is increased, it indicates that the structural resistance is insufficient and the thickness of the CIPP lining needs to be increased.

[0179] Figure 5 This is a schematic diagram of the CIPP minimum wall thickness inversion solution provided in an embodiment of the present invention. Please refer to it. Figure 5 In this embodiment, the minimum wall thickness of the CIPP liner is determined using the bisection method.

[0180] Set the wall thickness search range And make it satisfy:

[0181] ;

[0182] ;

[0183] No. In the next iteration, the intermediate wall thickness is taken as:

[0184] ;

[0185] If the intermediate wall thickness meets the safety requirements, that is:

[0186] ;

[0187] This indicates that the current intermediate thickness meets the safety requirements, and the upper limit of the search interval is updated to:

[0188] ;

[0189] Meanwhile, the lower limit of the search interval remains unchanged:

[0190] ;

[0191] If the intermediate wall thickness does not meet the safety requirements, that is:

[0192] ;

[0193] Then the lower limit of the search range will be updated to:

[0194] ;

[0195] Meanwhile, the upper limit of the search interval remains unchanged:

[0196] ;

[0197] Repeat the above iterative process until the preset convergence condition is met:

[0198] ;

[0199] Or it satisfies the convergence condition of the safety margin function:

[0200] ;

[0201] In the formula, For wall thickness convergence tolerance, This is the convergence tolerance for the safety margin function.

[0202] When the iteration satisfies the convergence condition, let the final iteration step be... The upper limit of the current search interval that meets the safety requirements is taken as the minimum wall thickness of the CIPP liner:

[0203] ;

[0204] Furthermore, the allowable bending moment of the CIPP bridging liner at the disjoint joint is controlled, and the CIPP liner meets the thin-wall condition. When this is the case, an explicit approximation formula can be used for rapid estimation. If the maximum bending moment demand function can be approximated as:

[0205] ;

[0206] Furthermore, the allowable bending moment of the CIPP bridging liner at the disjoint joint can be approximately expressed as:

[0207] ;

[0208] Then, in the critical state, we have:

[0209] ;

[0210] After substituting, we get:

[0211] ;

[0212] Therefore, an explicit approximate expression for the minimum wall thickness of the CIPP liner can be obtained:

[0213] ;

[0214] In the formula, This is a basic bending moment requirement that is independent of the thickness of the CIPP liner. This is the influence coefficient of CIPP lining thickness.

[0215] The explicit approximation formula can be used for preliminary engineering estimation and initial value determination in numerical iteration. The initial estimated wall thickness is obtained using the explicit approximation formula. Afterwards, Substituting into the aforementioned complete safety margin function Perform a review. If This indicates that the initial estimated wall thickness meets the design requirement that the maximum bending moment does not exceed the overall allowable bending moment; if This indicates that the structural resistance is insufficient under the initial estimated wall thickness, and should be adjusted accordingly. As the initial value or lower bound of the search, the thickness of the CIPP liner is increased using the aforementioned bisection method, stepwise search method, or Newton's iteration method until the desired result is met. The final determined minimum wall thickness of the CIPP liner should be based on the verification results of the aforementioned complete safety margin function.

[0216] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for determining the wall thickness of CIPP (Concrete Integrated Plumbing) repairs for disconnected concrete pipes under complex load coupling conditions. This method solves the problems of existing design methods failing to accurately characterize the stress characteristics of disconnected pipes, lacking multi-factor coupling analysis, resulting in large design deviations, and hindering rapid and accurate closed-loop design. By integrating multiple technical steps, including multi-factor bending moment prediction, explicit formula extraction, composite section resistance calculation in the non-disconnected zone, and bridging resistance verification of disconnected joints, a complete closed-loop design system is constructed, from predicting the stress response under complex working conditions to accurately determining the minimum safe wall thickness of CIPP. This effectively balances the accuracy, efficiency, safety, and economy of wall thickness design, while ensuring the interpretability and verifiability of the design results. It significantly improves the design standardization and engineering applicability of CIPP repair projects for disconnected concrete drainage pipes, providing reliable technical support for related pipeline repair projects.

[0217] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and substitutions can be made without departing from the technical principles of the present invention, and these improvements and substitutions should also be considered within the scope of protection of the present invention.

Claims

1. A method for determining the wall thickness of CIPP (concrete composite pipe) under complex load coupling, characterized in that, include: Based on pre-defined standardized model variables, a pipeline maximum bending moment prediction model is constructed to characterize the nonlinear mapping relationship between each variable and the pipeline maximum bending moment. Sign regression was performed on the maximum bending moment prediction model to extract the explicit prediction formula for the maximum bending moment demand of the pipeline. Using existing structural mechanics modeling methods, bending bearing capacity models of the composite section of the non-disconnected zone of the pipeline and the CIPP bridging section of the disconnected joint are established respectively. Pre-set structural parameters, material parameters and load parameters are used as modeling inputs. The allowable bending moment of the composite section of the non-disconnected zone and the allowable bending moment of the bridging lining of the disconnected joint are calculated respectively, and the minimum value between the two is selected as the overall allowable bending moment of the repair structure. The actual maximum bending moment requirement of the pipeline is calculated based on the explicit prediction formula, and the minimum design wall thickness of the CIPP lining is obtained based on the actual maximum bending moment requirement and the overall allowable bending moment.

2. The method for determining the wall thickness of CIPP (concrete composite pipe) under complex load coupling as described in claim 1, characterized in that, The process of obtaining the standardized model variables includes: A finite element model of CIPP (concrete composite pipe) repair structure was established, with traffic load, soil cover depth, groundwater level, disconnection length, pipe diameter, CIPP lining thickness, and elastic modulus as input variables. By changing the values ​​of each variable parameter, multiple sets of combined working conditions were formed. The maximum bending moment response data of the pipe corresponding to each working condition were calculated in batches to obtain the original sample data used to construct the dataset. The maximum bending moment response data refers to the maximum circumferential bending moment or control section bending moment of the CIPP repaired disconnected concrete pipe under the corresponding working condition. Establish a one-to-one correspondence between input variables and the maximum bending moment response under the corresponding working conditions, construct a sample dataset, and perform dimensionless preprocessing on the dataset to obtain the standardized model variables.

3. The method for determining the wall thickness of CIPP (concrete composite pipe) under complex load coupling as described in claim 2, characterized in that, The dimensionless input variables obtained by performing dimensionless preprocessing on the input variables in the dataset include: Load stiffness ratio, soil cover depth ratio, disjoint length ratio, groundwater level ratio, and CIPP lining thickness ratio.

4. The method for determining the wall thickness of CIPP (concrete composite pipe) under complex load coupling as described in claim 2, characterized in that, When the maximum bending moment response data is the bending moment of the control section, its dimensionless maximum bending moment response data is expressed as follows: ； Among them, the The inner diameter of the pipe, the The elastic modulus of the CIPP liner is... For the maximum bending moment response data, the These are dimensionless maximum bending moment response data.

5. The method for determining the wall thickness of CIPP (concrete composite pipe) under complex load coupling as described in claim 1, characterized in that, The allowable bending moment of the composite section in the non-disconnected zone is the minimum value between the stress limit of the concrete duct and the stress limit of the CIPP lining.

6. The method for determining the wall thickness of CIPP (concrete composite pipe) under complex load coupling as described in claim 5, characterized in that, The stress limit for the concrete pipe is expressed as follows: ； in, The The elastic modulus of the concrete pipe, the The elastic modulus of the CIPP liner is... The second moment of the concrete pipe section is... The second moment of the CIPP liner section, the The design stress limit for concrete, the The outer radius of the concrete pipe.

7. The method for determining the wall thickness of CIPP (concrete composite pipe) under complex load coupling as described in claim 5, characterized in that, The stress limit value of the CIPP lining is expressed as follows: ； in, The The elastic modulus of the concrete pipe, the The elastic modulus of the CIPP liner is... The second moment of the concrete pipe section is... The second moment of the CIPP liner section, the The design stress limit for CIPP lining, the The inner radius of the concrete pipe.

8. The method for determining the wall thickness of CIPP (concrete composite pipe) under complex load coupling as described in claim 5, characterized in that, The stress limit value of the CIPP lining is expressed as follows: ； Wherein, DN is the diameter of the concrete pipe, t is the thickness of the CIPP lining, and f is the diameter of the concrete pipe. l,d The design stress limit for CIPP lining.

9. The method for determining the wall thickness of CIPP (concrete composite pipe) under complex load coupling as described in claim 1, characterized in that, The minimum design wall thickness of the CIPP liner is obtained based on the actual maximum bending moment requirement and the overall allowable bending moment, including: A wall thickness inversion equation is constructed based on the critical safety state where the actual maximum bending moment requirement equals the overall allowable bending moment. The minimum design wall thickness of the CIPP lining is obtained by solving the equation.

10. The method for determining the wall thickness of CIPP (concrete composite pipe) under complex load coupling as described in claim 1, characterized in that, The maximum bending moment prediction model is constructed using the KAN algorithm.

Images