A method and system for calculating the load proportion of each arch ring in the process of dividing the arch ring of a concrete arch bridge

Abstract

The application discloses a kind of concrete arch bridge ring arch process each arch ring load sharing ratio calculation method and system. It is related to bridge engineering structural calculation technical field, including the accurate calculation method based on relative stiffness, the simplified calculation method based on displacement increment, and the load sharing ratio comprehensive optimization calculation method of fusion neural network;The accurate calculation method deduces the load sharing accurate formula based on the virtual work principle, the simplified calculation method deduces the engineering practical formula based on displacement increment, the neural network fusion method takes the result of two kinds of calculation methods as core input, model training and prediction are carried out in combination with construction measured characteristic parameter, and the comprehensive optimization output of load sharing ratio is realized.The application clarifies the load sharing mechanism of arch bridge ring arch, further improves the fitting degree of load sharing ratio calculation result and engineering practice after fusion intelligent algorithm, and can provide more accurate theory and data basis for structural safety prevention and control, design optimization and construction improvement.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering structural calculation technology, and more specifically to a method and system for calculating the load distribution ratio of each arch ring during the process of forming a concrete arch bridge. Background Technology

[0002] The cross-sectional stiffness of the main arch ring of a rigid-frame concrete arch bridge develops asynchronously with each construction stage. Before the concrete poured later reaches its full strength, its self-weight load is often borne by the arch rings that have already been joined in the earlier stages. Due to the different material properties and cross-sectional parameters of each arch ring, their stiffness varies significantly, and the proportion of load they bear also differs.

[0003] Clarifying the load-sharing mechanism of each arch ring is crucial for predicting and preventing safety hazards during structural construction. It also provides data and theoretical basis for designers to optimize arch bridge design, reduce steel and concrete usage, and lower project costs. Furthermore, it can guide designers to develop new construction methods or processes, adjust the pouring sequence, adopt new support systems, and improve construction efficiency and safety.

[0004] In the existing technology, there is a lack of a dedicated method for calculating the load distribution ratio of the arch rings during the arch formation process of reinforced concrete arch bridges. Conventional structural stiffness calculation methods require repeated consideration of the changes in the neutral axis of the composite section, making the calculation process complex and cumbersome. The calculation of the bending moment of inertia is difficult and cannot meet the needs of rapid calculation on the engineering site. On the other hand, simple estimation methods have insufficient accuracy and cannot provide accurate support for construction safety and design optimization.

[0005] Therefore, how to propose a method and system for calculating the load distribution ratio of each arch ring in the process of forming a concrete arch bridge, which is both accurate and practical, and overcomes the shortcomings of existing technologies, is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a method and system for calculating the load-sharing ratio of each arch ring during the segmented arch formation process of a concrete arch bridge. It constructs both an accurate calculation method and a simplified calculation method. The accurate calculation method achieves high-precision solution of the load-sharing ratio, while the simplified calculation method offers convenient calculation and meets engineering requirements in terms of accuracy. This effectively solves the problems of complexity and difficulty in balancing accuracy and practicality in existing calculation methods. To achieve the above objectives, the present invention adopts the following technical solution: A method for calculating the load-sharing ratio of each arch ring during the segmented arch construction process of a concrete arch bridge includes: Based on the principle of virtual work, the calculation method for the elastic displacement of the arch structure is determined, and the elastic displacement of the arch structure is calculated. Assumptions are made for a rigid frame concrete arch bridge with segmented casting to simplify the elastic displacement of the arch structure. Assuming the load acts on the arch structure, calculate the load shared by the stiffening frame and each closed arch ring, as well as the displacement of each arch ring, derive the load sharing relationship, and calculate the accurate formula for the load sharing ratio of the arch ring based on the load sharing relationship. The accurate formula for load sharing ratio is simplified, and the load sharing ratio of the arch ring is calculated using the simplified formula.

[0007] Optionally, the step of determining the calculation method for the elastic displacement of the arch structure based on the principle of virtual work, and calculating the elastic displacement of the arch structure, includes: For the main arch ring of a reinforced concrete arch bridge with a multi-ring casting structure, neglecting the influence of axial force deformation, the elastic displacement of the arch structure is calculated according to the formula... Calculate, where, This refers to the elastic displacement of the arch structure. To simulate the structural bending moment caused by a unit load, The structural bending moment caused by the actual load. The elastic modulus of the material. The moment of inertia of the arch section is the bending moment. This is a micro-element segment of the arch axis.

[0008] Optionally, the assumptions made for the rigid frame concrete arch bridge cast in rings include: material homogeneity assumption: the concrete and steel are uniform in the longitudinal direction and are both isotropic materials; small deformation assumption: the arch structure does not undergo large deformation during construction and the stress-strain relationship of the materials is within the linear elastic range; and displacement compatibility assumption: there is no relative displacement between the rigid frame and the concrete of each ring.

[0009] Optionally, the simplified arch structure's elastic displacement includes: Based on the assumption that the difference in arch axis length between the stiffening frame and each ring of concrete is ignored, the arch axis of the two are assumed to have the same shape and equal length, with only vertical distance offset. The rigid frame and all the joined rings of concrete are simplified as an arch structure. Assuming that the rotational moment of inertia of the cross-section of the structure along the arch axis remains constant, the elastic displacement of the arch structure is simplified as follows: ,in, .

[0010] Optionally, the calculation of the loads acting on the arch structure, the loads shared by the stiffening frame and each closed arch ring, and the displacements of each arch ring, includes: Assume load The loads acting on the arch structure, the stiffening frame, and each closed arch ring are respectively... ,satisfy , This represents the number of completed arch rings. The displacements of each arch are respectively The displacements of each arch ring satisfy ,in For the first The elastic modulus of the arch material For the first The moment of inertia of each arch ring relative to the neutral axis of the composite section. , for The resulting structural bending moment.

[0011] Optionally, the derivation of the load sharing relationship includes: Based on the fact that all the arch rings have the same structural form, we obtain The derivation is as follows Combined with the coordination relationship of the displacement of each arch ring , deduced .

[0012] Optionally, the step of calculating the precise formula for the load-sharing ratio of the arch ring based on the load-sharing relationship includes: Based on the load sharing relationship, the first... The precise formula for the load-sharing ratio of each arch is: ,in For the first The load sharing ratio of each arch ring.

[0013] Optionally, the simplification of the precise formula for load sharing ratio includes: S201. Define the arch deformation parameters: Let... The deformation of the rigid frame arch under a unit load before concrete pouring; For the first The increase in arch crown deformation of the main arch structure under a unit load immediately after the ring concrete is poured. , This represents the total number of arches; S202, Based on precise formula , combined Derivation This yields a simplified relationship for the load sharing ratio, expressed as an increment in the arch displacement. S203. Calculate the load-sharing ratio during the pouring of a single-ring concrete: When pouring the first ring of concrete, the concrete of the first ring has not yet reached its full strength, and its self-weight is entirely borne by the stiffening frame, i.e. , The load distribution ratio of the rigid frame ; pouring the first When using ring concrete, the front The first arch has been formed as a whole, the second The circumferential concrete has not yet participated in the combined action, the first The first arch bears the first The proportion of the self-weight of the ring concrete is , ; S204. Calculate the proportion of the total load borne by each arch ring: Let the first... The proportion of the weight of the ring concrete to the total weight of the arch box is Then the first The proportion of the total load borne by each arch ring in the arch box is: ,in, For the first The first arch bears the first The proportion of the self-weight of the ring concrete.

[0014] Optionally, for the main arch ring of a rigid-frame concrete arch bridge cast in multiple rings, when the pressure line of the arch structure is close to the arch axis, the calculation of the elastic displacement of the arch structure needs to consider both bending deformation and axial deformation, according to the formula. Calculate, where, To simulate the axial force caused by a unit load, The axial force caused by the actual load. This represents the cross-sectional area of ​​the arch.

[0015] Optionally, a system for calculating the load-sharing ratio of each arch ring during the segmented arch formation process of a concrete arch bridge includes: Arch structure elastic displacement calculation module: used to determine the calculation method of arch structure elastic displacement based on the principle of virtual work, and to calculate the elastic displacement of arch structure; Assumption module: Used to make assumptions about the rigid frame concrete arch bridge with segmented casting, simplifying the elastic displacement of the arch structure; Precise Calculation Module: Used to set loads acting on the arch structure, calculate the loads shared by the stiffening frame and each closed arch ring, the displacement of each arch ring, derive the load sharing relationship, and calculate the precise formula for the load sharing ratio of the arch rings based on the load sharing relationship. Simplified Calculation Module: This module simplifies the precise formula for load sharing ratio, and calculates the load sharing ratio of the arch ring using the simplified formula.

[0016] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method and system for calculating the load distribution ratio of each arch ring in the process of constructing a concrete arch bridge, which has the following beneficial effects: This invention proposes a precise calculation method based on relative stiffness. Based on the principle of virtual work, it clarifies the load-sharing mechanism between the stiffening frame and the concrete of each ring through three fundamental assumptions. The derived precise formula accurately reflects the load-sharing pattern of each arch ring, providing precise theoretical data for refined bridge structural design and safety control. Addressing the complexity of the precise formula calculation, a simplified calculation method based on displacement increments is proposed. By replacing stiffness parameters with the displacement increment at the arch crown, the calculation process is significantly simplified. Engineering field tests have verified that the calculation error of the simplified formula is within an acceptable range, adapting to the rapid calculation needs of engineering sites. This invention's calculation method clarifies the load-sharing pattern of the ring-to-arch structure in a stiffened frame concrete arch bridge, providing guidance for predicting and preventing structural safety hazards during construction. It also provides data support for designers to optimize the use of steel and concrete in arch bridges, reducing engineering costs. Furthermore, it guides designers to adjust the pouring sequence and develop new support systems, improving construction efficiency and safety. Attached Figure Description

[0017] 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 embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 This invention provides a schematic flowchart for calculating the load-sharing ratio of each arch ring during the process of constructing a concrete arch bridge.

[0019] Figure 2 This is a diagram illustrating the ring-splitting method of the arch ring provided by the present invention. Detailed Implementation

[0020] 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.

[0021] This invention discloses a method for calculating the load-sharing ratio of each arch ring during the segmented arch formation process of a concrete arch bridge, such as... Figure 1 As shown, it includes: Based on the principle of virtual work, the calculation method for the elastic displacement of the arch structure is determined, and the elastic displacement of the arch structure is calculated. Assumptions are made for a rigid frame concrete arch bridge with segmented casting to simplify the elastic displacement of the arch structure. Assuming the load acts on the arch structure, calculate the load shared by the stiffening frame and each closed arch ring, as well as the displacement of each arch ring, derive the load sharing relationship, and calculate the accurate formula for the load sharing ratio of the arch ring based on the load sharing relationship. The accurate formula for load sharing ratio is simplified, and the load sharing ratio of the arch ring is calculated using the simplified formula.

[0022] In specific implementations, the cross-sectional stiffness of the main arch ring of a rigid-frame concrete arch bridge is asynchronously formed during the construction stages. Before the later-poured concrete reaches its full strength, its self-weight load is often borne by the previously joined arch rings. Due to the significant differences in stiffness among the arch rings, the proportion of load they bear also varies. Clarifying the load-sharing mechanism of each arch ring can provide guidance for predicting and preventing potential structural safety hazards. Simultaneously, it can provide designers with data and theoretical basis to optimize arch bridge design, such as reducing the use of steel or concrete, thereby reducing costs while ensuring structural safety. Furthermore, it can guide designers in developing new construction methods or processes, such as adjusting the pouring sequence or adopting new support systems to improve construction efficiency and safety. Based on this, a method for calculating the load-sharing ratio of each arch ring during the segmented arch formation process of a concrete arch bridge is constructed as follows: (1) Calculation method of load distribution ratio of arch ring based on relative stiffness According to the principle of virtual work, the displacement of an arch structure can be calculated using the following formula: ; In the formula, This represents the displacement of the arch structure under a unit load. This represents the reaction force generated at point K under external load. The displacement at point K and the deformation corresponding to the internal forces of the structure can be calculated using the following formula: ; ; ; In the formula, E and G are the elastic modulus and shear modulus of the material, respectively; A and I are the area of ​​the arch section and the moment of inertia, respectively; k is a coefficient related to the shape of the section.

[0023] Thus, the formula for calculating the elastic displacement of a structure under load is derived: ; In the formula, , and These are the internal forces of the structure caused by the actual load; , and These are the internal forces in the structure caused by a hypothetical unit load.

[0024] For arch structures, when the pressure line and the arch axis are close, both bending deformation and axial deformation should be considered simultaneously, i.e.: ; When the pressure line and the arch axis are not close, the axial force deformation is much smaller than the bending deformation. In this case, the effect of the former can be ignored, and we have: ; For the main arch ring of a rigid frame concrete arch bridge that is cast in sections, the pressure line changes repeatedly during construction and is often difficult to rejoin the arch axis. In this case, the elastic deformation should be calculated according to the above formula.

[0025] To derive the load-bearing ratio of the stiffening frame and the concrete of each ring, the following assumptions are made: (1) Assumption of material homogeneity: Concrete and steel are homogeneous in the longitudinal direction and are both isotropic materials; (2) Small deformation assumption: During construction, the arch structure does not undergo large deformation, and the stress-strain relationship of the material is within the linear elastic range; (3) Displacement compatibility assumption: There is no relative displacement between the stiffening frame and the concrete of each ring.

[0026] Based on the above assumptions, the stiffening frame and the concrete of each ring can be simplified into a common arch structure in the longitudinal direction. The arch axes of each arch are approximately the same in shape, but their lengths differ slightly. Taking the stiffening frame and the concrete base slab as an example, if we assume the difference in length between one side of the two arches is... Then we have: ; In the formula, The distance between the two arches is the distance between the axis of the concrete arch in the base slab and the axis of the rigid frame arch; f is the rise of the arch; and l is the span of the arch.

[0027] because The value of is often small, and it is related to the span of the arch structure. The ratio is even smaller; for long-span arch bridges, the rise-to-span ratio is... The value is also very small, so it can be ignored. The calculation assumes that the arch axes of the stiffening frame and each ring of concrete are not only the same in shape, but also equal in length, with only a certain distance offset in the vertical direction.

[0028] When a load P is applied to an arch structure, the formula is... It can be simplified to: ; Assuming the moment of inertia of the cross-section of the structure along the arch axis remains constant, the above equation can be rewritten as: ; in, .

[0029] Under load P, the loads shared by the stiffening frame and the concrete of each ring are respectively Then there is The displacement of each arch ring is denoted as According to the formula have: ; In the formula, Regarding the material modulus of each arch ring, it should be specifically noted that... This refers to the moment of inertia of each arch ring relative to the neutral axis of the composite section, rather than the moment of inertia relative to the neutral axis of the individual arch ring sections. This represents the number of arches that have already been joined together.

[0030] Although the elastic modulus and bending moment of inertia of the materials of each arch ring are different, since the structural form of each arch ring is the same, within the elastic range of the materials, let them be respectively composed of The bending moments at any cross section caused by the load are respectively Then we have: ; For the same structural form They are the same, therefore: ; Because the main arch ring is constructed symmetrically from left to right, the various arch rings do not experience lateral relative displacement, nor do they separate vertically. Therefore: ; Summarized as follows: ; Therefore, the first The load proportion borne by each arch ring is: .

[0031] (2) Calculation method of load distribution ratio of arch ring based on displacement increment

[0032] formula This provides an accurate calculation formula for the proportion of external loads borne by each arch ring of a rigid-frame concrete arch bridge. However, as the concrete is poured, the neutral axis of the cross section in the composite structure changes continuously, making the calculation of the bending moment of inertia complex and requiring repeated calculations based on the number of construction stages. Therefore, in order to better serve the needs of the project, it is necessary to propose a simplified calculation formula with an accuracy acceptable to the project.

[0033] set up The deformation of the rigid frame arch under a unit load before concrete pouring; Indicates the first When the ring concrete is just poured, the increase in arch crown deformation of the main arch structure under a unit load can be expressed as: The proportion of the weight of the first ring concrete borne by the stiffening frame can be expressed as: ; Since the concrete of the first ring has just been poured and has not yet reached its full strength, its self-weight load is entirely borne by the stiffening frame, and there is Therefore, , .

[0034] formula and formula The biggest difference is that the former obtains the proportion of external load borne by each arch ring by solving for stiffness, while the latter obtains the load distribution proportion by solving for displacement.

[0035] Now consider the proportion of the self-weight of the second ring concrete borne by each arch ring after the second ring concrete is poured. This is the increase in deformation of the arch crown under a unit load immediately after the second ring of concrete is poured. At this point, the first ring of concrete has already formed an integral part with the stiffening frame, and the second ring of concrete has not yet participated in the joint action. Therefore, the proportion of the self-weight load of the second ring of concrete borne by the stiffening frame and the first ring of concrete is: ; And so on, It was before When the three arches work together, the first The first arch bears the first +1 ring concrete self-weight ratio, if the first ring concrete self-weight ratio is increased by 1 / 2, if the first ring concrete The proportion of the weight of the +1 ring concrete to the weight of the arch box is denoted as: Then the first The proportion of load borne by each arch ring is: .

[0036] In specific implementation methods, both the precise calculation method based on relative stiffness and the simplified calculation method based on displacement increment are derived from theoretical assumptions and engineering simplifications. However, in actual engineering, the ring-casting process of stiffened frame concrete arch bridges is affected by on-site conditions such as environmental factors, construction technology, and material performance dispersion. As a result, there is a certain systematic deviation between the theoretical calculation results and the actual load-sharing ratio.

[0037] To overcome the limitations of purely theoretical calculations, this invention introduces a neural network algorithm. Leveraging its powerful nonlinear fitting and feature learning capabilities, and using the results of two theoretical calculation methods as the core, it integrates multi-dimensional feature parameters from the construction site to construct a comprehensive optimization and prediction model for the load-sharing ratio. This achieves deep coupling between theoretical calculation results and actual engineering conditions, outputting a load-sharing ratio for the arch ring that better reflects the actual site conditions. The specific steps are as follows: (1) Construct a feature dataset for calculating load sharing ratio The dataset serves as the training foundation for the neural network model and must include input features that reflect the influence of the load-sharing ratio on the arch and labels that characterize the actual load-sharing results. The specific breakdown is as follows: 1) Input feature set The input feature set is divided into core calculation features and construction site features. The core calculation features are the calculation results of two theoretical methods and are the core factors that determine the load distribution ratio. The construction site features are the external working condition parameters that affect the actual load distribution and are used to correct the deviation between theoretical calculations and engineering reality.

[0038] Core computational feature: accurate calculation results based on relative stiffness (Load distribution ratio of the i-th arch ring), simplified calculation results based on displacement increments ; Construction site characteristics: Select measurable parameters directly related to concrete forming and arch structure deformation, including but not limited to: ambient temperature (T, ℃) during arch ring pouring, concrete curing humidity (RH, %), concrete age (t, d), measured stress values ​​(σ, MPa) at key sections of the stiffening frame, measured displacement values ​​at the arch crown (δ, mm), construction deviation values ​​for the arch span (Δl, mm), and construction deviation values ​​for the arch rise (Δf, mm). These site characteristic parameters can be added or removed based on actual monitoring conditions to ensure their measurability and relevance.

[0039] 2) Tag set

[0040] The label set consists of the actual load distribution ratio values ​​of each arch ring obtained through on-site stress monitoring, displacement monitoring, and other means. These are the target values ​​for model training, and it is necessary to ensure the accuracy and completeness of the measured data to provide a reliable basis for model fitting.

[0041] The dataset needs to cover the entire construction phase of the arch bridge (from the first ring to the nth ring) and can collect measured data from similar arch bridge projects to expand the sample size and improve the model's generalization ability.

[0042] (2) Build the neural network model and complete the initialization.

[0043] Based on the nonlinear mapping characteristics of the load-sharing ratio of the arch ring, a neural network model suitable for small sample and nonlinear regression prediction is selected. An LSTM (Long Short-Term Memory) network is chosen, and the basic model structure includes an input layer, hidden layers, and an output layer. Input layer: The number of neurons equals the total number of feature dimensions in the input feature set. If the input features are... , If the seven parameters are ambient temperature, curing humidity, concrete age, stiffening frame stress, and arch displacement, then the number of neurons in the input layer is 7. Hidden layers: 1-3 hidden layers are used, and the number of neurons in each layer is determined by calculation (generally 2-5 times the number of neurons in the input layer). They are used to learn the non-linear relationship between input features and load sharing ratio. Output layer: The number of neurons is equal to the number of arcs to be predicted, and the output value is the comprehensive optimized load sharing ratio of each arc.

[0044] The model initialization settings need to specify the core training parameters, as follows: Activation functions: The hidden layer preferentially uses the ReLU function to solve the gradient vanishing problem and improve the model training efficiency; the output layer uses the Sigmoid function to map the output value to the [0,1] interval, which matches the numerical range of the load sharing ratio. Optimizer: The Adam optimizer is used to adaptively adjust the learning rate and accelerate model convergence. Loss function: Mean squared error (MSE) is used to characterize the deviation between the model's predicted values ​​and the measured label values. The formula is: ; Where N is the sample size. To predict the load sharing ratio for the model, This represents the measured load distribution ratio; Learning rate: Initially set to 0.001-0.01, and adaptively adjusted during training; Training iterations (Epoch): Initially set to 100-500 epochs to prevent underfitting or overfitting of the model.

[0045] (3) Feature dataset preprocessing

[0046] The original dataset contains issues such as dimensional discrepancies, outliers, and missing values. Direct input will lead to low model training efficiency and poor prediction accuracy. Therefore, preprocessing is necessary. The specific steps are as follows: Outlier removal: The 3σ criterion is used to identify and remove outlier samples. That is, when the deviation of the sample data from the mean exceeds 3 times the standard deviation, it is judged as an outlier and deleted. Missing value completion: For a small number of missing feature parameters, the mean, median or linear interpolation of samples from the same construction stage is used to complete the missing values. Data normalization: The min-max normalization method is used to map all input features and label data to the [0,1] interval to eliminate the influence of dimensional differences. The formula is: ; in, Here, x represents the normalized data, and x represents the original data. , These are the minimum and maximum values ​​of the feature parameter, respectively.

[0047] After preprocessing, the dataset is randomly divided into a training set (for model training), a validation set (for adjusting hyperparameters), and a test set (for verifying the final accuracy of the model) in a ratio of 7:2:1.

[0048] (4) Training, validation and testing of neural network models

[0049] Model training: The preprocessed training set is input into the initialized neural network model, and iterative training is carried out according to the process of forward propagation to calculate the predicted value, back propagation to calculate the loss value, and updating the model weights and biases, so as to gradually reduce the deviation between the model's predicted value and the measured label value. Model validation: After each training round, the validation set is input into the model. The model hyperparameters (such as the number of hidden layer neurons, learning rate, and number of iterations) are adjusted based on the loss function value of the validation set. If the loss value of the validation set does not decrease for 10-20 consecutive rounds, the training is stopped using the early stopping method to prevent the model from overfitting. Model testing: Input the test set into the trained model, calculate the evaluation metrics of the model's prediction results and the measured label values, and verify the model's generalization ability and prediction accuracy. The core evaluation metrics selected include: Coefficient of determination R 2 R represents the degree to which the model fits the data. 2 The closer the result is to 1, the better the fit. The formula is: ; in, This represents the average of the measured load distribution ratios; Mean Absolute Percentage Error (MAPE): Characterizes the relative deviation of the predicted values. The smaller the MAPE, the higher the prediction accuracy. The formula is: ; When the model satisfies R²≥0.9 and MAPE≤5%, the prediction accuracy of the model is determined to meet the requirements of engineering applications, and the trained model parameters are saved.

[0050] (5) Comprehensive optimization prediction of load sharing ratio in actual projects

[0051] When applying the integrated optimization calculation method incorporating neural networks to the actual rigid frame concrete arch bridge segmented arch engineering, the following steps should be performed: For the construction phase of actual projects, two methods were employed: a precise calculation method based on relative stiffness and a simplified calculation method based on displacement increments, to obtain the load distribution ratio of each arch ring. , ; On-site measurements were taken of environmental temperature, curing humidity, concrete age, stiffening frame stress, arch displacement, and other on-site characteristic parameters during this construction phase to ensure that the parameters were synchronized with the construction conditions. Will , The on-site characteristic parameters were normalized according to the preprocessing rules; The normalized input data is fed into the trained neural network model, and the model outputs the normalized comprehensive optimized load sharing ratio. The model output is denormalized to restore the load distribution ratio of the arch ring to the actual engineering scale, which is the final load distribution ratio result that comprehensively considers the theoretical calculation and the actual engineering situation.

[0052] If the actual project is an arch bridge with a new span and a new cross section, and there is no similar measured data to support model training, the model can be pre-trained using a dataset of similar arch bridges, and then fine-tuned using a small amount of measured data from this project to quickly adapt to the construction conditions of this project.

[0053] The comprehensive optimization calculation method integrating neural networks proposed in this invention does not replace the precise calculation method based on relative stiffness and the simplified calculation method based on displacement increment, but rather intelligently optimizes and corrects the results of the two theoretical calculations. Using the results of the two theoretical calculations as core inputs ensures the theoretical rationality of the load-sharing ratio. Simultaneously, it integrates multi-dimensional characteristic parameters from the field to correct theoretical deviations caused by environmental, construction, and material factors, making the calculation results more closely aligned with engineering realities. The neural network model can be continuously trained and fine-tuned by adding new measured data, adapting to arch bridge projects with different spans, cross-sectional forms, and construction environments, demonstrating strong generalization ability. After the model training is complete, actual projects only need to input a small amount of calculation results and on-site measured parameters to quickly output the optimized load-sharing ratio, balancing calculation accuracy with the rapid calculation needs of engineering sites.

[0054] In a specific embodiment, for a reinforced concrete structure with a span of 138m, the proportion of the load borne by the arch ring during the segmented pouring of the main arch ring concrete of the hingeless arch was calculated.

[0055] The main arch of the bridge has a single-box, three-cell cross-section, and the main arch concrete was poured using a four-ring, six-working-face method, with the rings arranged as follows: Figure 2As shown. The first ring consists of 1.5m high concrete for the bottom slab and web of the side chamber; the second ring consists of the top slab of the side chamber and the remaining 1.3m high concrete for the web; the third ring consists of the bottom slab of the intermediate chamber; and the last ring consists of the top slab of the intermediate chamber. The first and second rings are poured using six working faces, while the third and fourth rings are poured continuously in one go.

[0056] When using this invention to solve the proportion of the load on the unreinforced concrete self-weight of each arch ring, the bending moment of inertia of each arch ring can be obtained through the knowledge of structural mechanics, and the final arch ring load distribution ratio is shown in Table 1.

[0057] Table 1. Results of Load Distribution Ratio for Each Arch Ring

[0058] As shown in Table 1, the maximum error between the load distribution ratio of the arch rings calculated using the present invention at different construction stages and the measured results is 4.5%, which is within the acceptable error range in engineering, verifying the correctness of the load distribution ratio calculation of each arch ring of the stiffened frame concrete arch bridge.

[0059] This invention addresses the main arch ring of a rigid frame arch bridge constructed with segmented cast concrete. Based on the principle of virtual work and the relative stiffness of the structure, it derives an accurate calculation formula for the load-sharing ratio of each arch ring. To address the complexity of this formula, a simplified calculation formula for the load-sharing ratio of the arch rings is derived from the perspective of structural displacement increment. This invention integrates a comprehensive optimization calculation method using neural networks. It does not replace the accurate calculation method based on relative stiffness or the simplified calculation method based on displacement increment, but rather intelligently optimizes and corrects the results of both theoretical calculations. Using measured data from a 138m main span reinforced concrete arch bridge and its construction process, the calculated arch frame load-sharing ratios were compared. The results show that the maximum relative error between the two is 4.5%, verifying the correctness of the calculations in this invention.

[0060] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0061] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calculating the load-sharing ratio of each arch ring during the segmented arch formation process of a concrete arch bridge, characterized in that, include: Based on the principle of virtual work, the calculation method for the elastic displacement of the arch structure is determined, and the elastic displacement of the arch structure is calculated. Assumptions are made for a rigid frame concrete arch bridge with segmented casting to simplify the elastic displacement of the arch structure. Assuming the load acts on the arch structure, calculate the load shared by the stiffening frame and each closed arch ring, as well as the displacement of each arch ring, derive the load sharing relationship, and calculate the accurate formula for the load sharing ratio of the arch ring based on the load sharing relationship. The accurate formula for load sharing ratio is simplified, and the load sharing ratio of the arch ring is calculated using the simplified formula.

2. The method for calculating the load-sharing ratio of each arch ring during the segmented arch formation process of a concrete arch bridge according to claim 1, characterized in that, The method for calculating the elastic displacement of an arch structure based on the principle of virtual work includes: For the main arch ring of a reinforced concrete arch bridge with a multi-ring casting structure, neglecting the influence of axial force deformation, the elastic displacement of the arch structure is calculated according to the formula... Calculate, where, This refers to the elastic displacement of the arch structure. To simulate the structural bending moment caused by a unit load, The structural bending moment caused by the actual load. The elastic modulus of the material. The moment of inertia of the arch section is the bending moment. This is a micro-element segment of the arch axis.

3. The method for calculating the load-sharing ratio of each arch ring during the segmented arch formation process of a concrete arch bridge according to claim 1, characterized in that, The assumptions made for the rigid frame concrete arch bridge cast in sections include: material homogeneity assumption: the concrete and steel are uniform in the longitudinal direction and are both isotropic materials; small deformation assumption: the arch structure does not undergo large deformation during construction and the stress-strain relationship of the materials is within the linear elastic range; and displacement compatibility assumption: there is no relative displacement between the rigid frame and the concrete of each ring.

4. The method for calculating the load-sharing ratio of each arch ring during the segmented arch formation process of a concrete arch bridge according to claim 1, characterized in that, The simplified arch structure elastic displacement includes: Based on the assumption that the difference in arch axis length between the stiffening frame and each ring of concrete is ignored, the arch axis of the two are assumed to have the same shape and equal length, with only a vertical distance offset. The rigid frame and all the joined rings of concrete are simplified as an arch structure. Assuming that the rotational moment of inertia of the cross-section of the structure along the arch axis remains constant, the elastic displacement of the arch structure is simplified as follows: ,in, .

5. The method for calculating the load-sharing ratio of each arch ring during the segmented arch formation process of a concrete arch bridge according to claim 1, characterized in that, The load is applied to the arch structure. The calculation of the load shared by the stiffening frame and each closed arch ring, as well as the displacement of each arch ring, includes: Assume load The loads acting on the arch structure, the stiffening frame, and each closed arch ring are respectively... ,satisfy , This represents the number of completed arch rings. The displacements of each arch are respectively The displacements of each arch ring satisfy ,in For the first The elastic modulus of the arch material For the first The moment of inertia of each arch ring relative to the neutral axis of the composite section. , for The resulting structural bending moment.

6. The method for calculating the load-sharing ratio of each arch ring during the segmented arch formation process of a concrete arch bridge according to claim 1, characterized in that, The derived load sharing relationship includes: Based on the fact that all the arch rings have the same structural form, we obtain The derivation is as follows Combined with the coordination relationship of the displacement of each arch ring , deduced .

7. The method for calculating the load-sharing ratio of each arch ring during the segmented arch formation process of a concrete arch bridge according to claim 1, characterized in that, The precise formula for calculating the load-sharing ratio of the arch ring based on the load-sharing relationship includes: Based on the load sharing relationship, the first... The precise formula for the load-sharing ratio of each arch is: ,in For the first The load sharing ratio of each arch ring.

8. The method for calculating the load-sharing ratio of each arch ring during the segmented arch formation process of a concrete arch bridge according to claim 1, characterized in that, The simplification of the precise formula for load sharing ratio includes: S201. Define the arch deformation parameters: Let... The deformation of the rigid frame arch under a unit load before concrete pouring; For the first The increase in arch crown deformation of the main arch structure under a unit load immediately after the ring concrete is poured. , This represents the total number of arches; S202, Based on precise formula , combined Derivation This yields a simplified relationship for the load sharing ratio, expressed as an increment in the arch displacement. S203. Calculate the load-sharing ratio during the pouring of a single-ring concrete: When pouring the first ring of concrete, the concrete of the first ring has not yet reached its full strength, and its self-weight is entirely borne by the stiffening frame, i.e. , The load distribution ratio of the rigid frame ; pouring the first When using ring concrete, the front The first arch has been formed as a whole, the second The circumferential concrete has not yet participated in the combined action, the first The first arch bears the first The proportion of the self-weight of the ring concrete is , ; S204. Calculate the proportion of the total load borne by each arch ring: Let the first... The proportion of the weight of the ring concrete to the total weight of the arch box is Then the first The proportion of the total load borne by each arch ring in the arch box is: ,in, For the first The first arch bears the first The proportion of the self-weight of the ring concrete.

9. The method for calculating the load-sharing ratio of each arch ring during the segmented arch formation process of a concrete arch bridge according to claim 2, characterized in that, This also includes, for the main arch ring of a rigid-frame concrete arch bridge cast in multiple rings, when the pressure line of the arch structure is close to the arch axis, the calculation of the elastic displacement of the arch structure needs to consider both bending deformation and axial deformation, according to the formula... Calculate, where, To simulate the axial force caused by a unit load, The axial force caused by the actual load. This represents the cross-sectional area of ​​the arch.

10. A system for calculating the load-sharing ratio of each arch ring during the segmented arch formation process of a concrete arch bridge, characterized in that, include: Arch structure elastic displacement calculation module: used to determine the calculation method of arch structure elastic displacement based on the principle of virtual work, and to calculate the elastic displacement of arch structure; Assumption module: Used to make assumptions about the rigid frame concrete arch bridge with segmented casting, simplifying the elastic displacement of the arch structure; Precise Calculation Module: Used to set loads acting on the arch structure, calculate the loads shared by the stiffening frame and each closed arch ring, the displacement of each arch ring, derive the load sharing relationship, and calculate the precise formula for the load sharing ratio of the arch rings based on the load sharing relationship. Simplified Calculation Module: This module simplifies the precise formula for load sharing ratio, and calculates the load sharing ratio of the arch ring using the simplified formula.

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