Reinforcing steel bar-solid waste concrete bonding strength prediction method based on improved failure criterion
By improving the failure criterion and residual network model, the complexity of predicting the bond strength of reinforced concrete-solid waste was solved, enabling accurate prediction and engineering applications under multi-parameter conditions, and improving prediction accuracy and robustness.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2026-03-27
- Publication Date
- 2026-04-28
AI Technical Summary
Existing methods for predicting the bond strength of reinforced concrete with solid waste have poor universality when considering complex and variable influencing factors. Traditional empirical models are simple, finite element analysis has high computational costs, and machine learning models lack sufficient physical constraints, making it difficult to accurately predict bond strength under complex working conditions.
A residual network model based on an improved failure criterion is constructed. The cross section is simplified by the minimum constraint equivalence principle. The model combines elastoplastic state partitioning, extended Mohr-Coulomb criterion and particle swarm optimization algorithm, and embeds a physically constrained residual network to achieve nonlinear mapping and accurate prediction of bond strength.
It enables refined characterization of bond strength under multi-parameter coupling conditions, improves prediction accuracy and extrapolation robustness, is applicable to complex working conditions and novel solid waste materials, and provides a theoretical basis for engineering design.
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Figure CN121936307A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of mechanical modeling of reinforced concrete-solid waste concrete, and specifically relates to a method for predicting the bond strength of reinforced concrete-solid waste concrete based on an improved failure criterion. Background Technology
[0002] Solid waste concrete, an aluminosilicate cementitious material formed from alkali-activated industrial byproducts (such as fly ash and slag), has the potential to replace traditional silicate solid waste concrete due to its high early strength, excellent high-temperature resistance, strong resistance to acid and alkali corrosion, and extremely low carbon footprint. Especially in marine structures operating in harsh environments such as cross-sea bridges, large seaport terminals, subsea tunnels, and underground utility tunnels, solid waste concrete can significantly improve the durability and life-cycle benefits of these structures.
[0003] In reinforced concrete structures, the bond performance between the steel reinforcement and the concrete is the mechanical basis for their interaction. The strength of the bond directly determines the stress transfer efficiency, load-bearing capacity, and crack control level within the structure. However, due to its significantly different cementitious system compared to traditional concrete, reinforced concrete exhibits higher brittleness, different shrinkage characteristics, and a denser interfacial transition zone. These material-level differences lead to significant changes in the bond failure mechanism and force transfer mechanism between reinforced concrete and steel reinforcement compared to traditional concrete, making it difficult to directly extrapolate existing mechanical specifications and empirical formulas based on traditional concrete.
[0004] Currently, methods for predicting the bond strength between solid waste concrete and steel reinforcement are mainly divided into three categories: empirical models, finite element analysis (FEM), and basic machine learning models. Traditional empirical models are mostly based on limited experimental data and often only consider single physical quantities such as solid waste concrete strength and anchorage length. They struggle to encompass complex and variable influencing factors such as the ratio of fly ash to slag, alkali activator concentration, and the degree of lateral constraint, resulting in poor generalizability of prediction results. While FEM can simulate from a mechanical mechanism perspective, it is highly dependent on the accuracy of the interface constitutive relationship. In the field of solid waste concrete, accurate bond-slip constitutive relationships are still in the exploratory stage, and FEM has extremely high computational costs when dealing with nonlinear failure processes, making it difficult to meet the needs of rapid engineering design. Finally, while machine learning models, which have emerged in recent years, can handle nonlinear mappings, they exhibit significant black-box properties. These models often ignore physical constraints in the mechanical field, leading to prediction results that may violate basic mechanical laws. Furthermore, traditional networks are prone to gradient vanishing or degradation problems when handling multi-parameter, deep feature extraction, resulting in bottlenecks in prediction accuracy. Especially under the specific condition of "sufficient lateral constraint," the stress state inside solid waste concrete is under complex triaxial stress. Its interface failure is no longer a simple shear failure, but a composite failure regulated by lateral constraint forces. Existing failure criteria often suffer from insufficient accuracy or difficulty in obtaining parameters when describing solid waste concrete, a material with obvious brittle characteristics. How to embed improved mechanical failure criteria as physical constraints into deep learning algorithms to construct a predictive model that has both physical interpretability and strong nonlinear fitting capabilities has become a key technical problem that urgently needs to be solved in the current scientific research on solid waste concrete structures.
[0005] Therefore, developing a predictive model that combines the powerful feature extraction capabilities of residual networks and introduces improved failure criteria as a novel physical constraint is of great scientific research value and engineering significance for accurately assessing the interfacial bond strength between solid waste concrete and steel reinforcement, and ensuring the safety and reliability of marine engineering structures. Summary of the Invention
[0006] The purpose of this invention is to overcome the shortcomings of existing technologies, specifically addressing the difficulty in accurately predicting the bond strength of reinforced concrete-solid-waste concrete, and to provide a method for predicting the bond strength of reinforced concrete-solid-waste concrete based on an improved failure criterion. This invention constructs a residual network model guided by the improved failure criterion. This model reflects the nonlinear mapping relationship between radial constraint stress and bond stress, and can predict the evolution of the bond strength of the reinforced concrete-solid-waste concrete interface under different structural and material parameters within a unified computational framework.
[0007] The specific technical solution adopted in this invention is as follows:
[0008] This invention provides a method for predicting the bond strength of reinforced concrete based on an improved failure criterion, as detailed below:
[0009] S1: According to the principle of minimum constraint equivalence, the cross section of a general rectangular steel-reinforced solid waste concrete member is equivalent to a simplified circular cross section with uniform constraints.
[0010] S2: The simplified circular cross section is divided into a plastic internal cracked region and an elastic external uncracked region according to the elastic-plastic state. Based on the force balance condition and deformation coordination condition, the calculation equations of the radial stress provided by solid waste concrete in the two regions are determined respectively.
[0011] S3: Based on the simplified circular cross section, the calculation equation for the radial stress provided by the passive constraint component is determined according to the force balance condition and deformation compatibility condition.
[0012] S4: An extended Mohr-Coulomb criterion is proposed, defining the yield line of the interfacial shear behavior determined by the calculation results of S2 and the sliding behavior determined by the calculation results of S3 under fully constrained conditions, characterizing the nonlinear mapping between radial stress and bond stress.
[0013] S5: Considering crack kinematics, a crack expansion factor is introduced to correlate the crackability of solid waste concrete matrix with the material strength degradation property of solid waste concrete during loading. The value of the parameter to be optimized is searched through particle swarm optimization algorithm.
[0014] S6: Based on S4 and S5, construct the existing physical model calculation framework, embed the results obtained from the existing physical model calculation framework into the residual network loss function term, construct a residual network model that integrates physical constraints, and improve the accuracy of bond strength prediction.
[0015] Preferably, in S2, the calculation equations for the radial stress provided by the solid waste concrete in the internally cracked region and the externally uncracked region are as follows:
[0016] ;
[0017] ;
[0018] Where, r cr r is the virtual radial crack radius. s Let r be the radius of the reinforcing bar. e f is the radius of the solid waste concrete section. tp To account for the tensile strength of solid waste concrete in terms of crack kinematics, This refers to the bridging stress between cracks in solid waste concrete. Radial stress provided to the uncracked external area of solid waste concrete. Radial stress provided for the cracked areas inside solid waste concrete.
[0019] Preferably, in S3, the passive constraint component is FRP or stirrup constraint.
[0020] Preferably, in step S3, the equation for calculating the radial stress provided by the passive constraint component is:
[0021] ;
[0022] ;
[0023] ;
[0024] ;
[0025] ;
[0026] ;
[0027] ;
[0028] in, Total radial constraint force provided for the constrained components. The radial constraint force provided for a single constrained component. The radial restraint force provided to the stirrups, The radial constraint force provided for FRP The elastic modulus of the stirrup is... The elastic modulus of FRP, This represents the tensile strain of the stirrup. For the tensile strain of FRP, The radial stress provided by the passively constrained component is represented by N, which represents the number of virtual cracks, and w is the number of virtual cracks. st and w f They represent r=r st and r=r e The width of the solid waste concrete crack at the location. A represents the tensile strain of solid waste concrete in the plastic region. st and A f A represents the total cross-sectional area of the stirrups and FRP, respectively. st 'and A f 'Represents the bond area between the stirrups and FRP and the solid waste concrete, respectively. and r represents the interfacial bond strength between the stirrups and FRP and the solid waste concrete, respectively. st The radius of the stirrup constraint; The angle between the radial stress and the axial direction; r sLet be the radius of the reinforcing bar, and l be the anchorage length of the reinforcing bar.
[0029] Preferably, in S4, the yield line expressions for the interface shear behavior determined by the calculation results of S2 and the sliding behavior determined by the calculation results of S3 under fully constrained conditions are as follows:
[0030] ;
[0031] ;
[0032] in, Additional shear stress provided to the constrained components. For undetermined coefficients, Additional sliding stress provided to the constrained components This is the critical internal friction angle.
[0033] Preferably, S5 is as follows:
[0034] Correction factor for the mechanical properties of solid waste concrete, considering crack kinematics. ;
[0035] Among them, f c Represents the compressive strength of solid waste concrete; The efficiency factor for the strength of solid waste concrete is given by the formula: ;w max d represents the maximum crack width. r It is the surface roughness parameter of cracked solid waste concrete; The parameters to be optimized for the performance of solid waste concrete materials are determined based on the particle swarm optimization algorithm, as follows:
[0036] ;
[0037] ;
[0038] in, Let represent the velocity of particle i in the d-th dimension at the next iteration (t+1); Let represent the velocity of particle i in the d-th dimension at this iteration (t); This represents the particle's best historical position. This is the global optimal position for the particle. and x is a random number in (0,1); z1 and z2 are acceleration constants, where z1 represents the weight that adjusts the particle's tendency to move closer to its own best historical position, and z2 represents the weight that adjusts the particle's tendency to move closer to the group's best historical position; x i t Indicates the current position of the particle, x it+1 This indicates the particle's new position in the next iteration. This represents the velocity of particle i in the next iteration (t+1), and u is the inertia weight.
[0039] Preferably, in the particle swarm optimization algorithm of S5, the number of particles and the dimension of the input data are 30 and 3, respectively, and the upper limit of the iteration is set to 100 times.
[0040] Preferably, in step S6, the construction and calculation of both the existing physical model calculation framework and the residual network model are implemented using Matlab.
[0041] Preferably, in step S6, the loss function of the constructed residual network model that incorporates physical constraints is as follows:
[0042] ;
[0043] in, Adjust parameters based on the importance of calculating frame term errors in existing physical models, MSE res and MSE phy These represent the mean square errors between the predicted ultimate bond strength and the experimental and physical model predictions, respectively.
[0044] Preferably, in step S6, the forward propagation consists of two residual blocks with the activation function tanh(x) and the dropout rate of the dropout layer is set to 10%.
[0045] Compared with the prior art, the present invention has the following advantages:
[0046] The method of this invention innovatively constructs a generalized predictive model for the interfacial bond performance of reinforced concrete and solid waste. This model overcomes the limitations of traditional empirical formulas, which have narrow applicability and ambiguous physical meaning, and possesses the following core advantages:
[0047] (1) The theoretical framework is unified and the physical meaning is clear: Based on the theory of damage mechanics and interface fracture mechanics, the model parameters are no longer simple fitting coefficients, but are directly related to the concrete matrix strength, interface friction coefficient, chemical bonding force and aggregate interlocking, etc., which are clear physical mechanisms, realizing the essential expression of the interface bonding failure mechanism.
[0048] (2) Refined characterization under multi-parameter coupling: It can quantitatively analyze the nonlinear influence of key material and structural parameters such as solid waste concrete strength grade, steel bar diameter, protective layer thickness and anchorage length on bond strength, and accurately capture the whole process characteristics of bond stress evolution with slip.
[0049] (3) Excellent prediction accuracy and extrapolation robustness: Through a large amount of experimental data verification, the model not only has high fitting accuracy under normal working conditions, but also shows strong extrapolation prediction ability in extreme working conditions or new solid waste material applications where experimental data is lacking, effectively overcoming the defects of overfitting in traditional models.
[0050] (4) Significant engineering application value: This achievement can directly serve the design calculation of anchorage length and the evaluation of mechanical performance during service life of reinforced concrete-solid waste structures, providing a solid theoretical basis and design tool for promoting the safe application of green building materials in load-bearing structures. Attached Figure Description
[0051] Figure 1 This is a method for simplifying the cross-sectional shape of reinforced concrete in the embodiments;
[0052] Figure 2 This illustrates the relationship between the FRP and stirrup constraint positions and the virtual crack radius in the embodiment.
[0053] Figure 3 The yield line is defined for the extended Mohr-Coulomb in the embodiments; where (a) is the yield line; (b) is the yield line evolution controlled by shear behavior; and (c) is the yield line evolution controlled by sliding behavior.
[0054] Figure 4 This is a schematic diagram of the residual block in the embodiment;
[0055] Figure 5 This is a diagram showing the calculation results of the residual network in the embodiment. Detailed Implementation
[0056] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. Technical features in various embodiments of the present invention can be combined accordingly without mutual conflict.
[0057] This invention provides a method for predicting the bond strength of reinforced concrete-solid waste based on an improved failure criterion. The model constructed by this method can reflect the nonlinear mapping relationship between radial constraint stress and bond stress, and can predict the evolution of the bond strength of reinforced concrete-solid waste interface under different structural and material parameters within a unified calculation framework.
[0058] The method of the present invention specifically includes the following steps:
[0059] S1, Simplified method for reinforced concrete-solid waste section:
[0060] According to the principle of minimum constraint equivalence, the cross-section of a general rectangular reinforced concrete-reinforced concrete member is equivalent to a simplified circular cross-section with uniform constraints. That is, if the cross-section of the reinforced concrete-reinforced concrete member is rectangular, it is modified into a circumferentially uniform circular cross-section according to the principle of minimum constraint equivalence.
[0061] In a preferred embodiment of the present invention, the reinforcing steel used is ordinary deformed reinforcing steel, and the constraint form is FRP / stirrup constraint.
[0062] In practical applications, the mechanical state of a single main reinforcement bar on a rectangular cross-section is determined based on a simplified circular cross-section model subjected to uniform circumferential constraints. The radius r of the reinforcement bar in the simplified cross-section is specified. s and stirrup radius R st Keeping constant, the stirrup constraint radius r st It equals the distance from the center of the stirrup to the center of the main reinforcement. The radius r of the simplified section. e It is equal to the distance from the center of the reinforcing bar to the edge of the solid waste concrete or the center-to-center spacing of adjacent reinforcing bars, and is determined by the minimum of the two:
[0063] ;
[0064] in, denoted as , where c is the spacing between two adjacent longitudinal reinforcement bars, and c is the thickness of the concrete cover.
[0065] S2, Calculation of radial stress:
[0066] The simplified circular cross section is divided into a plastic internal cracked region and an elastic external uncracked region according to the elastic-plastic state. Based on the force balance condition and deformation compatibility condition, the calculation equations for the radial stress provided by solid waste concrete in the two regions are determined respectively.
[0067] In a preferred embodiment of the present invention, the radial stress calculation provided by the plastic region needs to consider the tensile-cracking index constitutive model of solid waste concrete. The bridging stress between cracks in solid waste concrete is determined according to the tensile-cracking index constitutive model of solid waste concrete.
[0068] In a preferred embodiment of the present invention, the radial stress contributions of the two regions to the bonding interface are as follows:
[0069] (1);
[0070] (2);
[0071] Where, r cr r is the virtual radial crack radius. s Let r be the radius of the reinforcing bar.e f is the radius of the solid waste concrete section. tp To account for the tensile strength of solid waste concrete in terms of crack kinematics, This refers to the bridging stress between cracks in solid waste concrete. The radial stress provided to the elastic zone of solid waste concrete (i.e., the external, uncracked area). Radial stress provided to the plastic zone (i.e., the internal cracked zone) of solid waste concrete.
[0072] S3: Based on the simplified circular cross section, the calculation equation for the radial stress provided by the passively constrained component is determined according to the force equilibrium condition and deformation compatibility condition.
[0073] As a preferred embodiment of the present invention, the deformation coordination conditions of the passive restraint component (FRP or stirrup) vary depending on the relationship between the virtual crack development radius and the stirrup restraint radius.
[0074] In a preferred embodiment of the present invention, the interfacial bond strength between solid waste concrete and stirrups is determined by the bond-slip test of plain round steel bars-solid waste concrete, and the interfacial bond strength between solid waste concrete and FRP is determined by the single shear test of FRP-solid waste concrete.
[0075] In a preferred embodiment of the present invention, in this step, the radial stress contribution of the passively constrained component to the bonding interface is determined according to the deformation compatibility condition:
[0076] (3);
[0077] (4);
[0078] (5);
[0079] (6);
[0080] (7);
[0081] (8);
[0082] (9);
[0083] in, Total radial constraint force provided for the constrained components. The radial constraint force provided for a single constrained component. The radial restraint force provided to the stirrups, The radial constraint force provided for FRP The elastic modulus of the stirrup is... The elastic modulus of FRP, This represents the tensile strain of the stirrup. For the tensile strain of FRP, The radial stress provided by the passively constrained component is represented by N, which represents the number of virtual cracks, and w is the number of virtual cracks. st and w f They represent r=r st and r=r e The width of the solid waste concrete crack at the location. A represents the tensile strain of solid waste concrete in the plastic region. st and A f A represents the total cross-sectional area of the stirrups and FRP, respectively. st 'and A f 'Represents the bond area between the stirrups and FRP and the solid waste concrete, respectively. and r represents the interfacial bond strength between the stirrups and FRP and the solid waste concrete, respectively. st The radius of the stirrup constraint; The angle between the radial stress and the axial direction; r s Let be the radius of the reinforcing bar, and l be the anchorage length of the reinforcing bar.
[0084] In practical applications, the constitutive model of the tensile-crack index of solid waste concrete is used in the calculation of radial stress.
[0085] ;
[0086] in, For the bridging stress between cracks in solid waste concrete, f tp denoted as σ0, where σ0 represents the tensile strength of solid waste concrete, w represents the crack width of solid waste concrete, w0 represents the crack width of solid waste concrete when the bridging stress is 0, and c1 and c2 are constant coefficients.
[0087] Debonding of reinforcing bars causes expansion of the solid concrete, promoting tensile deformation of stirrups or FRPs, thus inducing their passive confinement effect on the core solid concrete. The confinement effect of stirrups and FRPs is determined by crack evolution, and they independently contribute to enhanced bond strength. The enhanced confinement force can be viewed as a linear superposition of contributions from multiple confinement components. According to the force balance relationship, the enhanced confinement force provided by stirrups or FRPs is contributed by the normal tensile force borne on their transverse sections and the bond force between them and the solid concrete interface.
[0088] The bond strength between the stirrups and the solid waste concrete was determined by the bond-slip test of plain round steel bars and solid waste concrete.
[0089] ;
[0090] The interfacial bond strength between FRP and solid waste concrete was determined by a single shear test.
[0091] ;
[0092] The development of cracks will alter the deformation compatibility between the stirrups or FRP and the solid concrete, resulting in different tensile strain evolutions. When the solid concrete in contact with the stirrups or FRP is elastic, its strain is determined by the elastic deformation of the solid concrete. When the solid concrete in contact with the stirrups or FRP is plastic, the circumferential deformation of the solid concrete in the cracked area includes not only tensile deformation but also the total crack width.
[0093] S4, Improved Mohr-Coulomb Criterion:
[0094] An extended Mohr-Coulomb criterion is proposed, defining yield lines for the interfacial shear behavior determined by S2 calculations and the sliding behavior determined by S3 calculations under fully constrained conditions, characterizing the nonlinear mapping between radial stress and bond stress.
[0095] As a preferred embodiment of the present invention, the extended Mohr-Coulomb criterion applies only to the incremental portion of the bond stress under the constraint mechanism.
[0096] As a preferred embodiment of the present invention, the undetermined coefficients defined by the extended Mohr-Coulomb criterion are determined by the critical internal friction angle, so that the yield line function added under the constraint mechanism remains continuous with the yield line defined by the traditional Mohr-Coulomb criterion under the unconstrained mechanism.
[0097] In a preferred embodiment of the present invention, this step extends the Mohr-Coulomb criterion to construct a nonlinear mapping between radial stress and bond stress. The yield line under unconstrained conditions is defined by the traditional Mohr-Coulomb criterion.
[0098] (10);
[0099] (11);
[0100] in, and These represent the radial stress and shear stress at the bond interface under an unconstrained mechanism, respectively. The compressive strength of solid waste concrete considering crack kinematics. This represents the critical internal friction angle.
[0101] The yield line under the additional constraint mechanism is defined by the improved Mohr-Coulomb criterion and divided into two branches according to shear behavior and sliding behavior.
[0102] (12);
[0103] (13);
[0104] in, Additional shear stress provided to the constrained components. For undetermined coefficients, Additional sliding stress provided to the constrained components This is the critical internal friction angle.
[0105] In practical applications, deformation behavior is considered to evolve within a plastic band of a certain thickness, and the macroscopic motion comprises multiple strain increment fields of pure separation or pure sliding. It is assumed that all deformation within the solid waste concrete member can be concentrated within the plastic band, and the evolution characteristics of the plastic band are consistent with the kinematic characteristics of cracked solid waste concrete. The thickness of the plastic band can be adjusted and, based on a two-dimensional problem, can be represented in the form of a yield line.
[0106] For the bond behavior of reinforced concrete and solid waste, the yield line of the member under debonding conditions manifests as the shear failure surface of the solid waste concrete. The mechanical evolution along the yield line is a hybrid separation-slip mode, which can be characterized by a given coordinate system. The horizontal axis represents the normal stress, i.e., the radial stress provided to the bond interface by the solid waste concrete and the constrained member, and the vertical axis represents the tangential stress, i.e., the bond stress at the reinforced concrete and solid waste concrete interface. When the internal friction angle is greater than the critical value, the yield line is still defined by the Mohr-Coulomb criterion. When external constraints are applied, a stiffness decay function is proposed to quantify the yield line controlled by shear behavior under the constraint mechanism, and a linear function is proposed to quantify the yield line controlled by slip behavior under the constraint mechanism.
[0107] S5, Calibration of mechanical property parameters of solid waste concrete:
[0108] Considering crack kinematics, a crack propagation factor is introduced to correlate the crackability of solid waste concrete matrix with the material strength degradation property of solid waste concrete during loading. The particle swarm optimization algorithm is used to search for the value of the parameter to be optimized.
[0109] As a preferred embodiment of the present invention, the strength correction of reinforced concrete-solid waste concrete needs to take into account the dynamic changes in the maximum crack opening of the solid waste concrete.
[0110] In a preferred embodiment of the present invention, in this step, considering crack kinematics, the mechanical property correction factor for solid waste concrete is:
[0111] (14);
[0112] (15);
[0113] Among them, f c w represents the compressive strength of solid waste concrete. max d represents the maximum crack width. r These are surface roughness parameters of cracked solid waste concrete. The strength efficiency factor for solid waste concrete. These are the parameters to be optimized.
[0114] Based on the particle swarm optimization algorithm, determine the parameters to be optimized in the correction coefficient of solid waste concrete. :
[0115] (16);
[0116] (17);
[0117] in, Let represent the velocity of particle i in the d-th dimension at the next iteration (t+1); Let represent the velocity of particle i in the d-th dimension at this iteration (t); This represents the particle's best historical position. This is the global optimal position for the particle. and x is a random number in (0,1); z1 and z2 are acceleration constants, where z1 represents the weight that adjusts the particle's tendency to move closer to its own best historical position, and z2 represents the weight that adjusts the particle's tendency to move closer to the group's best historical position; x i t Indicates the current position of the particle, x i t+1 This indicates the particle's new position in the next iteration. This represents the velocity of particle i in the next iteration (t+1), and u is the inertia weight.
[0118] In this embodiment, the constant coefficients to be optimized are determined using the particle swarm optimization algorithm. The optimal motion pattern of the particles within a certain range is obtained by setting the objective function or the number of iterations. During the iteration process, the i-th particle continuously adjusts its speed and position, striving towards its historical optimal position P. i and the global optimal position P g The number of particles and the dimension of the input data are 30 and 3, respectively, and the upper limit of iteration is set to 100 times.
[0119] S6, Physically Constrained Embedding and Residual Network Training:
[0120] Based on S4 and S5, an existing physical model calculation framework is constructed. The results obtained from the existing physical model calculation framework are embedded into the residual network loss function term to construct a residual network model that integrates physical constraints, thereby improving the accuracy of bond strength prediction.
[0121] As a preferred embodiment of the present invention, the residual network model uses the aforementioned existing analytical process as a physical constraint to limit the neural network output to a reasonable range.
[0122] In a preferred embodiment of the present invention, the loss function of the residual network model that incorporates physical constraints constructed in this step is as follows:
[0123] (18);
[0124] in, Adjusting parameters to assess the importance of errors in the physical model terms, MSE res and MSE phy These represent the mean square errors between the predicted ultimate bond strength and the experimental and physical model predictions, respectively.
[0125] In this embodiment, the basic components of the physical information-based residual network model include forward propagation and backward propagation. The input to the residual block is passed to the additional layer through both residual mapping and identity mapping, with the sum of these two methods serving as the output of the residual block. Neurons input to the residual block pass through a dropout layer, a fully connected layer, and an activation function layer to obtain the residual part, where the activation function is tanh(x). To improve the model's generalization ability, the dropout rate of the dropout layer is set to 10%. The loss function consists of the mean square error between the predicted ultimate bond strength and the experimental result, as well as the mean square error between the predicted ultimate bond strength and the physical model's prediction result. The overall backpropagation law of the residual physical network is determined using the chain rule. After backpropagation, the update values of the corresponding parameters are determined based on the derivative of the loss function with respect to each training parameter, and the above operation is iterated repeatedly. Model training is completed when the loss function is less than a predetermined value or the number of iterations reaches a predetermined value. The physical process calculations of the model and the training of the residual network are performed using Matlab software.
[0126] The methods and effects of the present invention will be specifically illustrated below through examples.
[0127] Example
[0128] This embodiment takes a reinforced concrete-solid waste concrete member as the research object and uses a method for predicting the bond strength of reinforced concrete-solid waste concrete based on an improved failure criterion proposed in this invention to predict the interfacial bond strength. The working conditions of the member used in this embodiment are as follows: the member shape is rectangular, the protective layer thickness is 61 mm; the diameter of the main reinforcement is 28 mm; the spacing between adjacent main reinforcements is 160 mm; the compressive strength of solid waste concrete is 37.32 MPa; there is one transverse stirrup with a diameter of 8 mm, an elastic modulus of 200 GPa, and a confinement radius of 55 mm; there are three layers of external FRP, with a single layer thickness of 1.67 mm, an FRP confinement radius of 75 mm, and an elastic modulus of 245 GPa.
[0129] The specific method is as follows:
[0130] 1. Simplification of reinforced concrete-solid waste section
[0131] By applying the principle of minimum constraint equivalence, rectangular cross-section reinforced concrete-reinforced concrete members are simplified to circular members, such as... Figure 1 As shown, the simplified component parameters are as follows: r e =75 mm, r s =14 mm, r st =55 mm.
[0132] 2. Calculation of radial stress
[0133] The input virtual crack radius variation range is [14 mm, 75 mm], and the increment step of the virtual crack radius is set to 1 mm. When the solid concrete in contact with stirrups or FRP is elastic, their strain is determined based on the elastic deformation of the solid concrete. When the solid concrete in contact with stirrups or FRP is plastic, the circumferential deformation of the solid concrete in the cracked area includes not only tensile deformation but also the total crack width, such as... Figure 2 As shown.
[0134] The physical model iteration calculation stops when the radial stress output by the current virtual crack is less than the radial stress output by the previous virtual crack.
[0135] For the component in the embodiment, the virtual crack radius is input as 17 mm. The virtual crack radius is smaller than the stirrup constraint radius. The radial stress calculation results are as follows: =2.93 MPa, =0.57 MPa = 0.56 MPa, total radial stress 4.06 MPa.
[0136] …
[0137] For the component in the embodiment, the input virtual crack radius is 63 mm. The virtual crack radius is larger than the stirrup constraint radius. The radial stress calculation results are as follows: =2.75 MPa =7.50 MPa = 4.69 MPa, total radial stress 14.94 MPa.
[0138] For the component in the embodiment, the input virtual crack radius is 64 mm. The virtual crack radius is larger than the stirrup constraint radius. The radial stress calculation results are as follows: =1.89 MPa =8.39 MPa = 4.77 MPa, total radial stress 15.05 MPa.
[0139] For the component in the embodiment, the input virtual crack radius is 65 mm. The virtual crack radius is larger than the stirrup constraint radius. The radial stress calculation results are as follows: =1.08 MPa =9.12 MPa = 4.81 MPa, total radial stress 15.01 MPa.
[0140] The limiting condition is determined to be a virtual crack radius of 64 mm.
[0141] 3. Radial stress-bond stress nonlinear mapping
[0142] like Figure 3 As shown, the critical internal friction angle is determined by the bond stress and radial stress under an unconstrained mechanism. Using the critical internal friction angle as a boundary condition, the undetermined coefficients of the extended Mohr-Coulomb yield line are determined, with a = 0.197.
[0143] ;
[0144] Based on the extended Mohr-Coulomb, the bond stress calculation results are as follows: =18.31 MPa =0.54 MPa, =0.94 MPa, total adhesion strength 19.79 MPa.
[0145] 4. Correction of mechanical parameters of solid waste concrete
[0146] The optimal motion pattern of a particle within a certain range is obtained by setting an objective function or the number of iterations. During the iteration process, the i-th particle continuously adjusts its speed and position, striving towards its historical optimal position P. i and the global optimal position P gThe number of particles and the dimension of the input data are 30 and 3, respectively, and the iteration limit is set to 100 times. Optimized parameters are obtained by training on 165 sets of solid waste concrete components from a database. =100, with a goodness of fit of 0.99. After optimizing the mechanical parameters of solid waste concrete by considering crack kinematics, the conservative prediction result of bond strength is 18.45 MPa.
[0147] 5. Residual Network Training
[0148] The residual block structure diagram is as follows Figure 4 As shown, the input is passed to the additional layer through both its residual mapping and identity mapping, and the sum of the two is used as the output of the residual block.
[0149] ;
[0150] The neurons input to the residual block pass through a dropout layer, a fully connected layer, and an activation function layer to obtain the residual part.
[0151] ;
[0152] The activation function tanh(x) is expressed in the following form:
[0153] ;
[0154] To improve the model's generalization ability, the dropout rate of the dropout layer was set to 10%.
[0155] Considering that too few residual blocks would prevent the learning of nonlinear relationships in the solution and hinder the reduction of physical residuals, while too many residual blocks would lead to high computational costs and the risk of overfitting, it is recommended that the forward propagation consist of two residual blocks, resulting in better model performance.
[0156] By employing a residual block structure to connect the input and output, the network can directly propagate to earlier layers during backpropagation, effectively mitigating network degradation. Based on the backpropagation of the weight vector of the i-th fully connected layer, the overall backpropagation law of the residual physical network is as follows:
[0157] ;
[0158] The backpropagation law in the residual block is as follows:
[0159] ;
[0160] After backpropagation is completed, the update values of the corresponding parameters are determined based on the derivative of the loss function with respect to each training parameter. The above operation is iterated repeatedly until the loss function is less than a predetermined value or the number of iterations reaches a predetermined value, thus completing the training of the model.
[0161] Hyperparameters were selected using a grid search method, with parameters set to a discrete grid to systematically achieve combinations of all parameters. The dataset was randomly divided into a training set of 135 samples and a test set of 30 samples. Figure 5 The dataset prediction results are shown, and it can be seen that the prediction error of the test set is within 15%, proving that the model has high accuracy and robustness.
[0162] As demonstrated by the above embodiments, the residual network model based on the improved failure criterion proposed in this invention defines an existing computational framework and can effectively predict the bond strength at the steel-solid waste concrete interface. The prediction results and computational efficiency verify the effectiveness and engineering applicability of the model of this invention.
[0163] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.
Claims
1. A method for predicting the bond strength of reinforced concrete based on an improved failure criterion, characterized in that, Specifically as follows: S1: According to the principle of minimum constraint equivalence, the cross section of a general rectangular steel-reinforced solid waste concrete member is equivalent to a simplified circular cross section with uniform constraints. S2: The simplified circular cross section is divided into a plastic internal cracked region and an elastic external uncracked region according to the elastic-plastic state. Based on the force balance condition and deformation coordination condition, the calculation equations for the radial stress provided by solid waste concrete in the two regions are determined respectively. S3: Based on the simplified circular cross section, the calculation equation for the radial stress provided by the passive constraint component is determined according to the force balance condition and deformation compatibility condition. S4: An extended Mohr-Coulomb criterion is proposed, defining the yield line of the interfacial shear behavior determined by the calculation results of S2 and the sliding behavior determined by the calculation results of S3 under fully constrained conditions, characterizing the nonlinear mapping between radial stress and bond stress. S5: Considering crack kinematics, a crack expansion factor is introduced to correlate the crackability of solid waste concrete matrix with the material strength degradation property of solid waste concrete during loading. The value of the parameter to be optimized is searched through particle swarm optimization algorithm. S6: Based on S4 and S5, construct the existing physical model calculation framework, embed the results obtained from the existing physical model calculation framework into the residual network loss function term, construct a residual network model that integrates physical constraints, and improve the accuracy of bond strength prediction.
2. The method for predicting the bond strength of reinforced concrete based on an improved failure criterion according to claim 1, characterized in that, In S2, the calculation equations for the radial stress provided by the solid waste concrete in the internally cracked region and the externally uncracked region are as follows: ； ； Where, r cr r is the virtual radial crack radius. s Let r be the radius of the reinforcing bar. e f is the radius of the solid waste concrete section. tp To account for the tensile strength of solid waste concrete in terms of crack kinematics, This refers to the bridging stress between cracks in solid waste concrete. Radial stress provided to the uncracked external area of solid waste concrete. Radial stress provided for the cracked areas inside solid waste concrete.
3. The method for predicting the bond strength of reinforced concrete based on an improved failure criterion according to claim 1, characterized in that, In S3, the passive constraint component is FRP or stirrup constraint.
4. The method for predicting the bond strength of reinforced concrete based on an improved failure criterion according to claim 1, characterized in that, In S3, the equation for calculating the radial stress provided by the passively constrained component is: ； ； ； ； ； ； ； in, The total radial constraint force provided to the constrained components. The radial constraint force provided for a single constrained component. The radial restraint force provided to the stirrups, The radial constraint force provided for FRP The elastic modulus of the stirrup is... The elastic modulus of FRP, This represents the tensile strain of the stirrup. For the tensile strain of FRP, The radial stress provided by the passively constrained component is represented by N, which represents the number of virtual cracks, and w st and w f They represent r=r st and r=r e The width of the solid waste concrete crack at the location. A represents the tensile strain of solid waste concrete in the plastic region. st and A f A represents the total cross-sectional area of the stirrups and FRP, respectively. st 'and A f 'Represents the bond area between the stirrups and FRP and the solid waste concrete, respectively. and r represents the interfacial bond strength between the stirrups and FRP and the solid waste concrete, respectively. st The radius of the stirrup constraint; The angle between the radial stress and the axial direction; r s Let be the radius of the reinforcing bar, and l be the anchorage length of the reinforcing bar.
5. The method for predicting the bond strength of reinforced concrete based on an improved failure criterion according to claim 1, characterized in that, In S4, the yield line expressions for the interface shear behavior determined by the calculation results of S2 and the sliding behavior determined by the calculation results of S3 under fully constrained conditions are as follows: ； ； in, Additional shear stress provided to the constrained components. For undetermined coefficients, Additional sliding stress provided to the constrained components This is the critical internal friction angle.
6. The method for predicting the bond strength of reinforced concrete based on an improved failure criterion according to claim 1, characterized in that, S5 is specifically as follows: Correction factor for the mechanical properties of solid waste concrete, considering crack kinematics. ; Among them, f c Represents the compressive strength of solid waste concrete; The efficiency factor for the strength of solid waste concrete is given by the formula: ;w max d represents the maximum crack width. r It is the surface roughness parameter of cracked solid waste concrete; The parameters to be optimized for the performance of solid waste concrete materials are determined based on the particle swarm optimization algorithm, as follows: ； ； in, Let represent the velocity of particle i in the d-th dimension at the next iteration (t+1); Let represent the velocity of particle i in the d-th dimension at time t in this iteration; This represents the particle's best historical position. This is the global optimal position for the particle. and z1 and z2 are random numbers in the interval (0,1); z1 and z2 are acceleration constants, where z1 represents the weight that adjusts the particle's tendency to move closer to its own historical best position, and z2 represents the weight that adjusts the particle's tendency to move closer to the group's historical best position; x i t Indicates the current position of the particle, x i t+1 This indicates the particle's new position in the next iteration. This represents the velocity of particle i in the next iteration (t+1), and u is the inertia weight.
7. The method for predicting the bond strength of reinforced concrete based on an improved failure criterion according to claim 1, characterized in that, In the particle swarm optimization algorithm of S5, the number of particles and the dimension of the input data are 30 and 3, respectively, and the upper limit of the iteration is set to 100 times.
8. The method for predicting the bond strength of reinforced concrete based on an improved failure criterion according to claim 1, characterized in that, In S6, the construction and calculation of the existing physical model calculation framework and the residual network model are both implemented using Matlab.
9. The method for predicting the bond strength of reinforced concrete based on an improved failure criterion according to claim 1, characterized in that, In step S6, the loss function of the constructed residual network model that incorporates physical constraints is as follows: ； in, Adjust parameters based on the importance of calculating frame term errors in existing physical models, MSE res and MSE phy These represent the mean square errors between the predicted ultimate bond strength and the experimental and physical model predictions, respectively.
10. The method for predicting the bond strength of reinforced concrete based on an improved failure criterion according to claim 1, characterized in that, In S6, the forward propagation consists of two residual blocks with the activation function tanh(x) and the drop rate of the drop layer is set to 10%.