UHPC reinforced RC arch bridge stress performance analysis method

Abstract

The invention relates to the technical field of stress performance analysis, and discloses a UHPC reinforced RC arch bridge stress performance analysis method, which comprises the following steps: establishing a UHPC hoop constraint reinforced RC arch bridge finite element model: adopting a C3D8R unit to simulate a UHPC material and a common concrete material, adopting a truss T3D2 unit to simulate a reinforcing steel bar, and adopting a UHPC hoop constraint reinforced RC arch bridge finite element model to establish a UHPC hoop constraint reinforced RC arch bridge finite element model; a UHPC reinforcing layer is annularly additionally arranged on the outer layer of the original RC arch ring to form a composite arch ring structure; the method aims at solving the problems that in an existing UHPC reinforced RC arch bridge stress performance analysis method, a confined concrete constitutive model is imperfect, parameter influence rule analysis is not systematic, interface connection simulation is inaccurate, and the accuracy of an analysis result is insufficient due to the fact that the initial stress state of an original arch ring is not fully considered.

Description

Technical Field

[0001] This invention relates to the field of stress performance analysis technology, specifically a method for stress performance analysis of UHPC-reinforced RC arch bridges. Background Technology

[0002] Reinforced concrete arch bridges occupy an important position in my country's highway bridges, but many early-built RC arch bridges have experienced varying degrees of damage and insufficient load-bearing capacity after long-term use. Traditional hoop reinforcement methods improve load-bearing capacity by adding a concrete reinforcement layer to the outside of the original arch ring. However, ordinary concrete hoop reinforcement significantly increases the structural dead load, which is usually borne by the original arch ring, negatively impacting the original structure's stress distribution. Ultra-high performance concrete (UHPC), due to its high strength, high toughness, and high durability, has been applied to the reinforcement of RC arch bridges. Using UHPC hoop confinement reinforcement in the negative bending moment section at the arch foot can effectively improve the structural load-bearing capacity. However, the analytical methods for the stress performance of UHPC-reinforced RC arch bridges directly affect the rationality and safety of the reinforcement design. Accurately predicting the load-bearing capacity performance of the reinforced composite arch ring has become an urgent need in engineering practice.

[0003] However, in finite element modeling, constitutive models of confined concrete often neglect the influence of the descending section on the simulation results, leading to an inaccurate reflection of material softening characteristics. Furthermore, the parameter analysis lacks a systematic study of multiple factors such as the thickness of the UHPC reinforcement layer, stirrup ratio, longitudinal reinforcement ratio, longitudinal reinforcement diameter, and the original concrete strength grade, making it difficult to reveal the influence of each parameter on bearing capacity performance. The simulation of the collaborative working mechanism between the UHPC reinforcement layer and the original RC arch ring in the interface connection settings is not precise enough. More importantly, existing methods do not fully consider the changes in the initial stress state caused by damage to the RC arch bridge during its service phase, failing to truly reflect the actual stress state of the original arch ring before reinforcement. This directly affects the accuracy of the finite element analysis results and the applicability of the bearing capacity calculation formula, hindering the widespread application of UHPC reinforcement technology in RC arch bridge engineering. Summary of the Invention

[0004] The purpose of this invention is to address the problems in existing methods for analyzing the stress performance of UHPC-strengthened RC arch bridges, such as imperfect constitutive models of confined concrete, unsystematic analysis of parameter influence laws, inaccurate simulation of interface connections, and insufficient accuracy of analysis results due to inadequate consideration of the initial stress state of the original arch ring. Therefore, this invention proposes a new method for analyzing the stress performance of UHPC-strengthened RC arch bridges.

[0005] The technical solution of the present invention to solve the above-mentioned technical problems is as follows:

[0006] A method for analyzing the stress performance of a UHPC-reinforced RC arch bridge includes the following steps:

[0007] S1. Establish the finite element model of the UHPC hoop-constrained and reinforced RC arch bridge: C3D8R elements are used to simulate UHPC material and ordinary concrete material, and truss T3D2 elements are used to simulate steel bars. A UHPC reinforcement layer is added in a ring shape on the outer layer of the original RC arch ring to form a composite arch ring structure.

[0008] S2. Define material constitutive relations: Establish constitutive models for constrained ordinary concrete and constrained UHPC, where the constrained concrete constitutive model includes a descending segment;

[0009] S3. Set interface connection and boundary conditions: The interface between the UHPC reinforcement layer and the original RC arch ring is connected by tie. The steel bars are embedded in the concrete model in the Embedded manner, and a shim is set at the bottom and coupled to the midpoint of the structural surface.

[0010] S4. Apply load and perform parametric analysis: Perform parametric analysis on the thickness of the UHPC reinforcement layer, the stirrup ratio of the UHPC, the longitudinal reinforcement ratio of the UHPC layer, the diameter of the longitudinal reinforcement and the strength grade of ordinary concrete to obtain the bearing capacity performance data of the composite arch ring.

[0011] S5. Verify the bearing capacity calculation formula: Verify the rationality of the bearing capacity calculation formula of the UHPC hoop-constrained RC arch bridge based on finite element simulation data.

[0012] Based on the above technical solution, the present invention can be further improved as follows.

[0013] Furthermore, the specific process of establishing the finite element model of the UHPC-enclosed reinforced RC arch bridge in S1 is as follows: a UHPC reinforcement layer is added in a cast-in-place ring outside the original RC arch ring in the negative bending moment section at the arch foot. The UHPC reinforcement layer includes a UHPC concrete matrix, longitudinal steel bars, and stirrups, forming a composite main arch ring structure. The UHPC reinforcement layer deforms in coordination with the original arch ring and shares the load, thereby increasing the structural bearing capacity by increasing the strength and stiffness of the main arch ring. The internal forces borne by the original RC arch ring before reinforcement are expressed as follows:

[0014] N 原 =N 1恒 +N 2恒 +N 活

[0015] M 原 =M 1恒 +M 2恒 +M 活

[0016] Where: N 1恒 M 1恒 To reinforce the axial force and bending moment generated by the pre-existing structural dead load on the original arch ring; n 2恒 M 2恒The axial force and bending moment generated by the newly added dead load on the original arch ring after reinforcement; N 活 M 活 This refers to the axial force and bending moment generated by the live load on the original arch ring after reinforcement.

[0017] Furthermore, in S1, C3D8R elements are used to simulate the mechanical properties of UHPC materials and ordinary concrete materials under axial loads and low-cycle repeated loads. The C3D8R element is an eight-node linear hexahedral reduced integral solid element, which can effectively capture the nonlinear stress characteristics of concrete materials. The truss T3D2 element is used to simulate the uniaxial stress performance of steel bars. The T3D2 element is a two-node three-dimensional truss element, which does not consider the bond slip effect between steel bars and concrete. The accurate simulation of the stress process of the composite structure is achieved through element selection.

[0018] Furthermore, when establishing the constitutive model of the confined concrete in S2, a complete stress-strain relationship curve including both the ascending and descending segments is used, with a focus on the influence of the descending segment on the finite element simulation results, in order to accurately reflect the softening characteristics of concrete materials after peak stress; the edge stress of the original RC arch section is expressed as:

[0019]

[0020] In the formula: Aoriginal is the cross-sectional area of ​​the original arch ring; Woriginal is the bending geometric modulus of the original arch ring cross-section; by using this stress calculation formula, the stress state of the original arch ring before reinforcement can be determined, providing a theoretical basis for the design of reinforcement schemes.

[0021] Furthermore, in S3, when setting the interface connection, the UHPC reinforcement layer and the original RC arch ring interface are rigidly connected by a tie connection to simulate the complete collaborative working state between the two, so that the reinforced composite section has no shear deformation and follows the plane section assumption; the steel bars are embedded in the UHPC concrete and ordinary concrete matrix respectively by the Embedded embedding technology to achieve displacement coordination between the steel bars and concrete, and ensure the overall stress performance of the composite structure.

[0022] Furthermore, the parametric analysis in S4 employs the controlled variable method. By keeping other variables constant and changing only one variable, the influence of the following parameters on the bearing capacity performance of the UHPC hoop-constrained reinforced RC arch bridge is systematically analyzed: the thickness of the UHPC reinforcement layer ranges from 10mm to 200mm, with a gradient of 10mm or 20mm; the UHPC stirrup ratio ranges from 0.2% to 2.0%, with a gradient of 0.2% or 0.3%; the longitudinal reinforcement ratio of the UHPC layer ranges from 0.5% to 4.0%, with a gradient of 0.5%; the longitudinal reinforcement diameter ranges from 10mm to 32mm, including commonly used specifications such as 10mm, 12mm, 16mm, 20mm, 25mm, and 32mm; and the ordinary concrete strength grades include five levels: C30, C35, C40, C45, and C50.

[0023] Furthermore, when applying loads in S4, the changes in the initial stress state caused by varying degrees of damage suffered by the RC arch bridge during long-term use are fully considered. In the finite element model, the initial horizontal stress or initial strain is set by a predefined field to truly reflect the actual stress state and damage degree of the original RC arch ring before reinforcement. By introducing the initial stress state, the joint stress process of the reinforcement layer and the original structure is simulated to obtain load-bearing capacity analysis results that are more in line with engineering reality.

[0024] Furthermore, it also includes a simulation of the graded reinforcement construction process: the step-by-step clamping method is used to simulate the actual reinforcement construction process, dividing the entire bridge longitudinally into multiple pouring sections, each with a length of 2m to 5m; the entire bridge is divided into two levels of reinforcement, the first level being the section from the arch foot to L / 4, and the second level being the section from L / 4 to the arch crown, where L is the span of the arch bridge; in the finite element analysis, the birth and death element technology is used to simulate the construction process of activating the next pouring section after the concrete of each pouring section reaches 75% of the design strength, and the step-by-step construction simulation truly reflects the stress accumulation of the reinforcement layer and the redistribution of internal forces in the structure.

[0025] Furthermore, the parametric analysis also includes an analysis of the impact of the spatial arrangement of the UHPC reinforcement layer. The reinforcement layer arrangement schemes include four arrangements: reinforcement only in the negative bending moment section at the arch foot, reinforcement from the arch foot to L / 4 section, reinforcement from the arch foot to L / 2 section, and full-span closed reinforcement. By comparing the improvement in structural bearing capacity, material consumption, construction difficulty, and economy under different arrangement positions, the reinforcement effect of each scheme is comprehensively evaluated, the optimal reinforcement range and arrangement form are determined, and a design reference is provided for practical engineering applications.

[0026] Furthermore, in S5, when verifying the bearing capacity calculation formula, based on the large amount of parametric analysis data obtained in S4, and combined with the basic principles of arch bridge bearing capacity calculation in the current bridge design specifications and the theoretical derivation conclusions in existing literature, the bearing capacity calculation formula for UHPC hoop-constrained reinforced RC arch bridge is modified and improved. By comparing and analyzing the ultimate bearing capacity value obtained from finite element simulation with the theoretical formula calculation value, error analysis and regression analysis methods are used to verify the accuracy, applicability and engineering practicality of the modified formula, providing a reliable theoretical calculation method for future engineering design.

[0027] Compared with the prior art, the technical solution of this application has the following beneficial technical effects:

[0028] The constitutive model of confined concrete established in this invention explicitly includes a descending segment, accurately reflecting the softening characteristics and bearing capacity degradation process of concrete after peak stress. Secondly, it uses C3D8R eight-node linear hexahedral reduced integral solid elements to simulate UHPC and ordinary concrete, and truss T3D2 elements to simulate reinforcing steel. Through reasonable element selection, it achieves accurate simulation of the stress process of the composite arch structure, laying a solid foundation for subsequent parameter analysis. The interface between the UHPC reinforcement layer and the original RC arch is set using a tie connection method, and the connection relationship between the reinforcing steel and concrete is set using an embedded method, accurately simulating the synergy between the reinforcement layer and the original structure. In addition to the working mechanism and displacement coordination relationship, the study systematically conducted parametric analysis on five key parameters: UHPC reinforcement layer thickness, stirrup ratio, longitudinal reinforcement ratio, longitudinal reinforcement diameter, and ordinary concrete strength grade. This comprehensively revealed the influence of each parameter on the bearing capacity performance of the composite arch ring, making up for the lack of systematic parameter research in existing technologies. At the same time, the study considered the changes in the initial stress state caused by damage to the RC arch bridge during the service stage. By setting the initial stress in the finite element model, the study realistically reflected the actual stress state of the original arch ring before reinforcement. Finally, the rationality of the bearing capacity calculation formula was verified based on a large amount of parametric analysis data, forming a complete technical system from finite element simulation to theoretical calculation. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the UHPC hoop reinforcement of the main arch ring of the present invention;

[0030] Figure 2 This is a schematic diagram of the UHPC-reinforced rib arch bridge of the present invention;

[0031] Figure 3 This is a schematic diagram of the bearing capacity of the main arch ring before reinforcement according to the present invention. Detailed Implementation

[0032] 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.

[0033] Combination Figures 1-3 As shown, the present invention provides a method for analyzing the stress performance of a UHPC-reinforced RC arch bridge, comprising the following steps:

[0034] S1. Establish the finite element model of the UHPC hoop-constrained and reinforced RC arch bridge: C3D8R elements are used to simulate UHPC material and ordinary concrete material, and truss T3D2 elements are used to simulate steel bars. A UHPC reinforcement layer is added in a ring shape on the outer layer of the original RC arch ring to form a composite arch ring structure.

[0035] S2. Define material constitutive relations: Establish constitutive models for constrained ordinary concrete and constrained UHPC, where the constrained concrete constitutive model includes a descending segment;

[0036] S3. Set interface connection and boundary conditions: The interface between the UHPC reinforcement layer and the original RC arch ring is connected by tie. The steel bars are embedded in the concrete model in the Embedded manner, and a shim is set at the bottom and coupled to the midpoint of the structural surface.

[0037] S4. Apply load and perform parametric analysis: Perform parametric analysis on the thickness of the UHPC reinforcement layer, the stirrup ratio of the UHPC, the longitudinal reinforcement ratio of the UHPC layer, the diameter of the longitudinal reinforcement and the strength grade of ordinary concrete to obtain the bearing capacity performance data of the composite arch ring.

[0038] S5. Verify the bearing capacity calculation formula: Verify the rationality of the bearing capacity calculation formula of the UHPC hoop-constrained RC arch bridge based on finite element simulation data.

[0039] The specific process of establishing the finite element model of the UHPC-reinforced RC arch bridge in S1 is as follows: A UHPC reinforcement layer is added in a cast-in-place annular shape to the outer layer of the original RC arch ring in the negative bending moment section at the arch foot. The UHPC reinforcement layer includes a UHPC concrete matrix, longitudinal reinforcement, and stirrups, forming a composite main arch ring structure. The UHPC reinforcement layer deforms in coordination with the original arch ring and shares the load, thereby increasing the structural bearing capacity by increasing the strength and stiffness of the main arch ring. The internal forces borne by the original RC arch ring before reinforcement are expressed as follows:

[0040] N 原 =N 1恒 +N 2恒 +N 活

[0041] M原 =M 1恒 +M 2恒 +M 活

[0042] Where: N 1恒 M 1恒 To reinforce the axial force and bending moment generated by the pre-existing structural dead load on the original arch ring; n 2恒 M 2恒 The axial force and bending moment generated by the newly added dead load on the original arch ring after reinforcement; N 活 M 活 To account for the axial force and bending moment generated by the live load on the original arch ring after reinforcement, when establishing the finite element model of the UHPC hoop-constrained reinforced RC arch bridge, the negative bending moment section at the arch foot is the most unfavorable part of the stress. This area is often the first to show defects such as cracks and insufficient bearing capacity during long-term use.

[0043] like Figure 1 The diagram shows a UHPC-reinforced main arch ring. Before reinforcement, the main arch ring had a rectangular solid cross-section. After reinforcement, a UHPC reinforcement layer was added in a ring around the original main arch ring, forming a composite main arch ring structure. The UHPC reinforcement layer consists of a UHPC concrete matrix, longitudinal steel bars, and stirrups. By configuring a steel mesh, the high strength characteristics of UHPC can be fully utilized, while the restraining effect of the steel bars significantly improves the ductility of UHPC.

[0044] like Figure 2 The diagram shown is a schematic of a ribbed arch bridge reinforced with UHPC (Ultra-High-Pressure Polymer) hoop reinforcement. The elevation view of the reinforced structure illustrates the location of the reinforcement layer in the negative bending moment section at the arch foot, while the detailed diagram shows the configuration of the longitudinal reinforcement and stirrups within the UHPC reinforcement layer. In actual engineering, the internal forces borne by the original RC arch ring before reinforcement consist of three parts: the axial force N generated by the dead load of the structure before reinforcement... 1恒 and bending moment M 1恒 The axial force N generated by the additional dead load after reinforcement 2恒 and bending moment M 2恒 And the axial force N generated by the live load after reinforcement. 活 and bending moment M 活 .

[0045] During construction, the original structure bears the original dead load while sharing the dead load of the reinforcement layer with the construction support. After construction is completed, the newly added reinforcement layer bears part of the new dead load and part of the live load. This phased stress mechanism achieves the unloading effect on the original arch ring.

[0046] As can be seen from the internal force calculation formula, minimizing the structural dead load before reinforcement is beneficial to reducing the internal force of the original arch ring. Compared with ordinary concrete, UHPC material has a higher strength-to-weight ratio, which can effectively control the new dead load while enhancing the bearing capacity. This is the key advantage of UHPC reinforcement over traditional ordinary concrete hoop reinforcement.

[0047] In S1, C3D8R elements are used to simulate the mechanical properties of UHPC and ordinary concrete under axial loads and low-cycle cyclic loading. The C3D8R element is an eight-node linear hexahedral reduced-integral solid element, which effectively captures the nonlinear stress characteristics of concrete. T3D2 truss elements are used to simulate the uniaxial stress performance of reinforcing steel. The T3D2 element is a two-node three-dimensional truss element that does not consider the bond-slip effect between the steel and concrete. Accurate simulation of the stress process of the composite structure is achieved through element selection. In finite element simulation, the choice of element type directly affects the accuracy of the simulation results. The C3D8R element is an eight-node linear hexahedral reduced-integral solid element in ABAQUS software. This element uses reduced integration technology to effectively avoid shear locking and accurately captures the nonlinear mechanical behavior of concrete under compression, making it particularly suitable for simulating the complex stress characteristics of UHPC and ordinary concrete under axial loads and low-cycle cyclic loading. For the simulation of reinforcing bars, the T3D2 truss element is used. This element is a two-node three-dimensional truss element that only considers the axial tensile and compressive properties of the reinforcing bars, which is consistent with the actual working state of the reinforcing bars in concrete structures, which mainly bear axial forces.

[0048] In this invention, the bond-slip effect between the reinforcing steel and concrete is not considered. This is based on the excellent bond performance between UHPC material and reinforcing steel, and it also simplifies the complexity of the model and improves computational efficiency. By combining C3D8R solid elements and T3D2 truss elements, accurate numerical simulation of the stress process of UHPC-strengthened RC arch bridge composite structures is achieved, providing a reliable technical foundation for subsequent parametric analysis.

[0049] When establishing the constitutive model of confined concrete in S2, a complete stress-strain relationship curve including both the ascending and descending segments is used, with a focus on the influence of the descending segment on the finite element simulation results to accurately reflect the softening characteristics of concrete after peak stress; the edge stress of the original RC arch section is expressed as:

[0050]

[0051] In the formula: Aoriginal represents the cross-sectional area of ​​the original arch ring; Woriginal represents the flexural geometric modulus of the original arch ring cross-section. This stress calculation formula is used to determine the stress state of the original arch ring before reinforcement, providing a theoretical basis for reinforcement scheme design. Establishing a constitutive model of constrained concrete is the core content of finite element analysis. Traditional concrete constitutive models often only consider the ascending segment while ignoring the descending segment, which leads to simulation results that cannot accurately reflect the structural bearing capacity degradation process after peak load.

[0052] The constitutive model of confined concrete established in this invention employs a complete stress-strain relationship curve including an ascending segment and a descending segment. The ascending segment reflects the strengthening process of concrete material from the elastic stage to the plastic stage, while the descending segment accurately describes the softening characteristics and bearing capacity degradation law of concrete after reaching peak stress. By introducing the descending segment, the failure process of concrete material under ultimate state can be realistically simulated, which is of great significance for predicting the ultimate bearing capacity and failure mode of structures.

[0053] Before carrying out reinforcement design, it is necessary to evaluate the stress state of the original RC arch ring. The edge stress of the original arch ring section is generated by the combined action of axial force and bending moment, where Aoriginal is the cross-sectional area of ​​the original arch ring, and Woriginal is the flexural geometric modulus of the original arch ring section. Through this stress calculation, it can be determined whether the original arch ring is under tension or whether the compressive stress exceeds the compressive strength of concrete before reinforcement, providing a theoretical basis for determining the necessity and rationality of the reinforcement scheme.

[0054] For sections with insufficient load-bearing capacity, it is necessary to use UHPC hoop restraint reinforcement to increase the cross-sectional area and stiffness, thereby reducing the stress level and improving the load-bearing capacity.

[0055] When setting the interface connection in S3, the UHPC reinforcement layer and the original RC arch ring interface are rigidly connected using a tie connection to simulate a completely coordinated working state between the two. This ensures that the reinforced composite section has no shear deformation and follows the plane section assumption. The reinforcing bars are embedded using an embedded technology, with longitudinal reinforcing bars and stirrups respectively embedded into the UHPC concrete and ordinary concrete matrix. This achieves displacement coordination between the reinforcing bars and concrete, ensuring the overall load-bearing performance of the composite structure. The interface connection method directly affects the coordinated working performance between the reinforcement layer and the original structure. In the ABAQUS finite element software, the tie connection method is used to define the rigid constraint relationship between the two contact surfaces. After adopting this connection method, no relative slippage or shear deformation occurs between the UHPC reinforcement layer and the original RC arch ring interface; both deform completely coordinatedly and share the external load.

[0056] This rigid connection simulates the reliable connection effect achieved in actual engineering through interface treatment and rebar anchoring technology, ensuring that the reinforced composite section follows the plane section assumption, that is, the section remains planar after deformation, and the strain is linearly distributed along the section height.

[0057] For the connection between steel bars and concrete, the Embedded technology is an efficient modeling method. This technology embeds steel bar elements into concrete solid elements, automatically establishing a displacement coordination relationship between the two, so that the displacement of the steel bar node is consistent with the displacement of the concrete at its location.

[0058] Longitudinal reinforcement bars are embedded in the UHPC concrete matrix, and stirrups are similarly embedded in both the UHPC and ordinary concrete matrices. This embedding method achieves overall synergistic work between the reinforcement and concrete, ensuring that the composite structure can fully utilize the mechanical properties of each component material. When setting the bottom boundary conditions, shims are set and coupled with the midpoint of the structural surface to simulate the support constraint conditions in actual tests, providing the necessary support and displacement constraints for the structure.

[0059] In S4, the parametric analysis employs the controlled variable method. By keeping other variables constant and changing only one variable, it systematically analyzes the influence of the following parameters on the bearing capacity performance of UHPC-reinforced RC arch bridges: the thickness of the UHPC reinforcement layer ranges from 10mm to 200mm, with a gradient of 10mm or 20mm; the UHPC stirrup ratio ranges from 0.2% to 2.0%, with a gradient of 0.2% or 0.3%; the longitudinal reinforcement ratio of the UHPC layer ranges from 0.5% to 4.0%, with a gradient of 0.5%; the longitudinal reinforcement diameter ranges from 10mm to 32mm, including commonly used specifications such as 10mm, 12mm, 16mm, 20mm, 25mm, and 32mm; and the ordinary concrete strength grades include five levels: C30, C35, C40, C45, and C50. Parametric analysis is a key step in revealing the influence of various factors on the bearing capacity performance of UHPC-reinforced RC arch bridges. Parametric studies are conducted using the controlled variable method, which involves keeping other parameters constant while analyzing the influence of a certain parameter. By systematically changing the value of the parameter, a series of finite element analysis results are obtained, thereby quantitatively assessing the degree and trend of the parameter's influence on the structural bearing capacity.

[0060] For the UHPC reinforcement layer thickness parameter, the value range is set to 10mm to 200mm. This is based on the commonly used range of reinforcement layer thickness in actual engineering. A reinforcement layer that is too thin will not provide sufficient load-bearing capacity improvement, while a reinforcement layer that is too thick will significantly increase the structural dead load and construction difficulty.

[0061] In parameter analysis, a gradient of 10mm or 20mm is used for incremental increases. By plotting the relationship curve between bearing capacity and reinforcement layer thickness, the optimal range of reinforcement layer thickness can be determined. For the stirrup ratio of UHPC, the value ranges from 0.2% to 2.0%, with a gradient of 0.2% or 0.3%. The main function of stirrups is to provide lateral restraint to UHPC concrete, improving its ductility and bearing capacity. If the stirrup ratio is too low, the restraint effect is not obvious; if the stirrup ratio is too high, it will increase construction difficulty and material costs. The longitudinal reinforcement ratio of the UHPC layer ranges from 0.5% to 4.0%, with a gradient of 0.5%. The longitudinal reinforcement mainly bears the tensile stress generated by bending moment, and the change in the reinforcement ratio directly affects the flexural bearing capacity of the composite section.

[0062] The longitudinal reinforcement diameter parameters are selected from commonly used steel bar specifications in engineering, such as 10mm, 12mm, 16mm, 20mm, 25mm, and 32mm. Different diameter steel bars correspond to different reinforcement areas and bond performance. Ordinary concrete strength grades cover five levels: C30, C35, C40, C45, and C50, representing the typical range of original arch ring concrete strength in existing RC arch bridges in my country. By analyzing the reinforcement effects under different original concrete strength grades, a reference basis can be provided for the reinforcement design of arch bridges with different technical conditions.

[0063] like Figure 3 The table showing the bearing capacity of the main arch ring before reinforcement lists the bearing capacity verification results of each control section in a real engineering case. All sections do not meet the bearing capacity requirements and need to be reinforced. This provides a real engineering background for parametric analysis.

[0064] When applying loads in S4, the changes in the initial stress state caused by varying degrees of damage to the RC arch bridge during long-term use are fully considered. In the finite element model, the initial horizontal stress or initial strain is set by predefined fields to truly reflect the actual stress state and damage degree of the original RC arch ring before reinforcement. By introducing the initial stress state, the joint stress process of the reinforcement layer and the original structure is simulated to obtain load-bearing capacity analysis results that are more in line with engineering reality. During long-term use, the RC arch bridge is affected by various factors such as repeated vehicle loads, temperature changes, material aging and environmental erosion, which will cause varying degrees of damage, resulting in an initial stress state inside the original arch ring.

[0065] The existence of this initial stress state significantly affects the stress performance and load-bearing capacity improvement of the reinforced structure. Therefore, this actual working condition must be fully considered in finite element analysis.

[0066] In ABAQUS software, the predefined field function allows setting initial stress or initial strain in the model. Specifically, before simulating the reinforcement layer construction, the original RC arch ring is subjected to the dead load and partial live load it experiences during its service phase. This yields the stress state of the original arch ring, which is then saved as the initial condition. When applying the reinforcement layer and analyzing the ultimate bearing capacity, the original arch ring continues to be stressed from this initial stress state. This method realistically reflects the joint stress process of the reinforcement layer and the original structure; that is, the original arch ring, with its initial stress state, works collaboratively with the newly added UHPC reinforcement layer to resist the subsequently applied loads.

[0067] The bearing capacity analysis results obtained after considering the initial stress state are more in line with the actual engineering situation. Compared with the idealized analysis without considering the initial stress, the ultimate bearing capacity value is often lower after considering the initial stress, which provides a safer and more reliable basis for reinforcement design.

[0068] Parametric analysis allows setting different levels of initial stress states to simulate the reinforcement effects of arch bridges with varying degrees of damage, providing technical support for developing targeted reinforcement solutions.

[0069] The invention also includes a simulation of the graded reinforcement construction process: a step-by-step clamping method is used to simulate the actual reinforcement construction process, dividing the entire bridge longitudinally into multiple pouring sections, each ranging from 2m to 5m in length; the entire bridge is divided into two levels of reinforcement: the first level is the section from the arch foot to L / 4, and the second level is the section from L / 4 to the arch crown, where L is the arch span; in the finite element analysis, the birth and death element technique is used to simulate the construction process of activating the next pouring section after the concrete in each pouring section reaches 75% of its design strength. This step-by-step construction simulation realistically reflects the stress accumulation of the reinforcement layer and the redistribution of internal forces within the structure. The graded reinforcement construction process simulation is a key innovation of this invention, accurately reflecting the impact of construction techniques on the structural performance in actual engineering projects. In actual engineering projects, due to limitations in construction conditions and concrete curing requirements, the UHPC reinforcement layer cannot be poured in one go; instead, a step-by-step clamping method is used for segmented and graded construction.

[0070] The specific construction process is as follows: determine the length of the section of the hoop enlargement section according to the actual stress condition of the arch bridge, calculate the thickness of the reinforcement layer in accordance with the specifications, demolish part of the superstructure of the arch to facilitate construction, plant reinforcement bars on the surface of the original arch ring and tie longitudinal reinforcement bars and stirrups, install the formwork and pour UHPC material to form the hoop enlargement section, and restore the superstructure of the arch after the UHPC has been cured to the design strength.

[0071] In the tiered construction process, the entire bridge is divided into multiple pouring sections along its longitudinal direction. The length of each pouring section is determined according to the construction organization design, generally ranging from 2m to 5m. After each pouring section is completed, it needs to be cured until the concrete reaches 75% of its design strength before the next stage of pouring can begin. This is to ensure that the poured parts have sufficient strength to withstand the subsequent construction loads. The entire bridge is reinforced in two levels. The first level is the section from the arch foot to L / 4, which is the area with the largest negative bending moment and is the key area for reinforcement. The second level is the section from L / 4 to the arch crown, where L is the span of the arch bridge.

[0072] In finite element analysis, the birth and death element technique is used to simulate this step-by-step construction process. In the initial state, all reinforcement layer elements are set to an inactive state. As the construction process progresses, the elements corresponding to each pouring segment are gradually activated. After each pouring segment is activated, a static analysis is performed to obtain the stress and deformation state of that stage, which is then used as the initial conditions for the next stage of analysis.

[0073] This step-by-step construction simulation can realistically reflect the stress accumulation process of the reinforcement layer and the redistribution law of the internal forces of the structure. Due to the different construction times, the internal stress states of different pouring sections are also different. The first pouring section bears part of the load of the subsequent construction stage, while the later pouring section mainly bears the load of the service stage. This stress distribution characteristic cannot be reflected in the simplified model of one-time pouring.

[0074] Parametric analysis also includes the impact analysis of the spatial arrangement of the UHPC reinforcement layer. The reinforcement layer arrangement schemes include four arrangements: reinforcement only in the negative bending moment section of the arch foot, reinforcement from the arch foot to L / 4 section, reinforcement from the arch foot to L / 2 section, and full-span closed reinforcement. By comparing the improvement in structural bearing capacity, material consumption, construction difficulty, and economy under different arrangement positions, the reinforcement effect of each scheme is comprehensively evaluated to determine the optimal reinforcement range and arrangement form, providing design reference for practical engineering applications. The spatial arrangement of the UHPC reinforcement layer has a significant impact on the reinforcement effect and engineering economy, and the optimal arrangement scheme needs to be determined through parametric analysis. This invention presents four typical reinforcement layer placement schemes for comparative analysis: The first scheme involves reinforcement only in the negative bending moment section at the arch foot. This scheme is highly targeted, uses the least amount of material, and is suitable for situations where the local bearing capacity at the arch foot is insufficient while the bearing capacity of other sections meets the requirements. The second scheme involves reinforcement from the arch foot to the L / 4 section, which covers the main negative bending moment area of ​​the arch bridge, resulting in good reinforcement effect and moderate material usage. The third scheme involves reinforcement from the arch foot to the L / 2 section, further expanding the reinforcement range and significantly improving the overall stiffness and bearing capacity of the structure, but correspondingly increasing the material usage and construction workload. The fourth scheme involves full-span closed reinforcement, that is, full-range reinforcement of the entire arch ring from the arch foot to the arch crown. This scheme has the best reinforcement effect, but uses the most material, and is also the most difficult and costly to construct.

[0075] In parametric analysis, a corresponding finite element model is established for each layout scheme, and the same load conditions are applied. Key indicators such as the ultimate bearing capacity, material consumption, and bearing capacity improvement of each scheme are obtained through comparative analysis. Taking into account the construction difficulty and economic factors in conjunction with the actual project, the technical and economic indicators of each scheme are comprehensively evaluated, and the optimal reinforcement range is recommended.

[0076] Generally, the reinforcement scheme for the section from the arch foot to L / 4 can achieve a good balance between the load-bearing capacity improvement effect, material consumption and construction difficulty, and is a commonly used reinforcement range in engineering. However, for arch bridges with different technical conditions and load-bearing capacity defects, it is necessary to select the appropriate reinforcement range according to the specific circumstances.

[0077] In S5, when verifying the bearing capacity calculation formula, based on a large amount of parametric analysis data obtained in S4, and combined with the basic principles of arch bridge bearing capacity calculation in current bridge design codes and theoretical derivations in existing literature, the bearing capacity calculation formula for UHPC hoop-constrained reinforced RC arch bridges was modified and improved. By comparing the ultimate bearing capacity values ​​obtained from finite element simulation with the theoretically calculated values, error analysis and regression analysis methods were used to verify the accuracy, applicability, and engineering practicality of the modified formula. This provides a reliable theoretical calculation method for future engineering designs. Verifying the bearing capacity calculation formula is a crucial step in transforming finite element simulation results into engineering design methods. Based on the large amount of finite element simulation data obtained from the aforementioned parametric analysis, including ultimate bearing capacity values ​​under different combinations of UHPC reinforcement layer thickness, hoop ratio, longitudinal reinforcement ratio, longitudinal reinforcement diameter, and original concrete strength grade, a complete database was formed. Based on the basic principles of arch bridge bearing capacity calculation in the current highway bridge design specifications, including the basic assumptions for cross-sectional bearing capacity calculation, the method for determining material strength and the principle for determining the safety factor, as well as the theoretical derivation conclusions of UHPC confined concrete bearing capacity in existing literature, the bearing capacity calculation formula for UHPC hoop-confined reinforced RC arch bridges is systematically revised and improved.

[0078] The key to the correction lies in determining critical parameters such as the UHPC constraint effect coefficient, stress reduction coefficient, and bearing capacity enhancement coefficient, which need to be extracted from the finite element simulation data through regression analysis.

[0079] The specific verification process is as follows: First, the ultimate bearing capacity value obtained from finite element simulation is used as the actual value. Then, the theoretical bearing capacity value under the same parameter combination is calculated using the modified theoretical formula. The difference between the two is compared, and the relative error is calculated. When the relative error is within a reasonable range, the formula is considered accurate and reliable. Error analysis is used to statistically analyze the error distribution characteristics of all working conditions. Regression analysis is used to establish the correlation between the calculated value and the finite element simulation value. The fitting accuracy of the formula is evaluated through the correlation coefficient. After repeated revisions and verifications, the final bearing capacity calculation formula should meet the requirements of accuracy, applicability, and engineering practicality. It should be able to accurately predict the ultimate bearing capacity of UHPC-strengthened RC arch bridges, be easy for engineering designers to use, and provide reliable theoretical calculation methods and technical guidance for the design and construction of similar projects in the future.

[0080] This invention first addresses the problem of insufficient bearing capacity in the negative bending moment section of the arch foot of RC arch bridges by establishing a UHPC hoop-constrained finite element model. It uses C3D8R eight-node linear hexahedral reduced integral solid elements to simulate the three-dimensional stress characteristics of UHPC and ordinary concrete materials, and T3D2 two-node three-dimensional truss elements to simulate the uniaxial stress performance of the reinforcing steel. A UHPC reinforcement layer is added in a ring shape to the outer layer of the original RC arch ring to form a composite arch ring structure. Reasonable element selection lays the foundation for subsequent analysis.

[0081] Then, the material constitutive relation is defined, and the constitutive model of constrained concrete containing the rising and falling segments is established to accurately reflect the softening characteristics and bearing capacity degradation law of concrete material after peak stress, and to provide theoretical support for capturing the failure process of structure under ultimate limit state.

[0082] Next, interface connections and boundary conditions were set. The interface between the UHPC reinforcement layer and the original RC arch ring was rigidly constrained by a tie connection, ensuring that the composite section deformed in accordance with the plane section assumption. The reinforcing bars were embedded using the embedded technology to achieve displacement coordination with the concrete, ensuring the overall load-bearing performance of the composite structure. After the model was established, the control variable method was used to systematically analyze key parameters such as the thickness of the UHPC reinforcement layer, the stirrup ratio, the longitudinal reinforcement ratio, the longitudinal reinforcement diameter, and the strength grade of ordinary concrete. When applying loads, the initial stress state caused by damage to the RC arch bridge during long-term use was fully considered. The initial stress was set by a predefined field to truly reflect the actual stress state of the original arch ring before reinforcement, obtaining a large amount of composite arch ring bearing capacity performance data.

[0083] Finally, based on the finite element simulation data obtained from parametric analysis, combined with bridge design specifications and theoretical derivation conclusions, the calculation formula for the bearing capacity of UHPC hoop-constrained reinforced RC arch bridges was revised and improved. The accuracy and applicability of the formula were verified through error analysis and regression analysis, forming a complete technical system from numerical simulation to theoretical calculation, providing reliable analysis methods and calculation basis for the engineering design of UHPC reinforced RC arch bridges.

[0084] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0085] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for analyzing the stress performance of a UHPC-reinforced RC arch bridge, characterized in that, Includes the following steps: S1. Establish the finite element model of the UHPC hoop-constrained and reinforced RC arch bridge: C3D8R elements are used to simulate UHPC material and ordinary concrete material, and truss T3D2 elements are used to simulate steel bars. A UHPC reinforcement layer is added in a ring shape on the outer layer of the original RC arch ring to form a composite arch ring structure. S2. Define material constitutive relations: Establish constitutive models for constrained ordinary concrete and constrained UHPC, where the constrained concrete constitutive model includes a descending segment; S3. Set interface connection and boundary conditions: The interface between the UHPC reinforcement layer and the original RC arch ring is connected by tie. The steel bars are embedded in the concrete model in the Embedded manner, and a shim is set at the bottom and coupled to the midpoint of the structural surface. S4. Apply load and perform parametric analysis: Perform parametric analysis on the thickness of the UHPC reinforcement layer, the stirrup ratio of the UHPC, the longitudinal reinforcement ratio of the UHPC layer, the diameter of the longitudinal reinforcement and the strength grade of ordinary concrete to obtain the bearing capacity performance data of the composite arch ring. S5. Verify the bearing capacity calculation formula: Verify the rationality of the bearing capacity calculation formula of the UHPC hoop-constrained RC arch bridge based on finite element simulation data.

2. The method for analyzing the stress performance of a UHPC-reinforced RC arch bridge according to claim 1, characterized in that, The specific process of establishing the finite element model of the UHPC-enclosed reinforced RC arch bridge in S1 is as follows: A UHPC reinforcement layer is added in a cast-in-place annular shape to the outer layer of the original RC arch ring in the negative bending moment section at the arch foot. The UHPC reinforcement layer includes a UHPC concrete matrix, longitudinal reinforcement bars, and stirrups, forming a composite main arch ring structure. The UHPC reinforcement layer deforms in coordination with the original arch ring and shares the load, thereby increasing the structural bearing capacity by increasing the strength and stiffness of the main arch ring. The internal forces borne by the original RC arch ring before reinforcement are expressed as follows: N 原 =N 1恒 +N 2恒 +N 活 M 原 =M 1恒 +M 2恒 +M 活 Where: N 1恒 M 1恒 To reinforce the axial force and bending moment generated by the pre-existing dead load on the original arch ring; N 2恒 M 2恒 The axial force and bending moment generated by the newly added dead load on the original arch ring after reinforcement; N 活 M 活 This refers to the axial force and bending moment generated by the live load on the original arch ring after reinforcement.

3. The method for analyzing the stress performance of a UHPC-reinforced RC arch bridge according to claim 2, characterized in that, In S1, C3D8R elements are used to simulate the mechanical properties of UHPC materials and ordinary concrete materials under axial loads and low-cycle repeated loads. The C3D8R element is an eight-node linear hexahedral reduced integral solid element, which can effectively capture the nonlinear stress characteristics of concrete materials. The truss T3D2 element is used to simulate the uniaxial stress performance of steel bars. The T3D2 element is a two-node three-dimensional truss element, which does not consider the bond slip effect between steel bars and concrete. The accurate simulation of the stress process of composite structures is achieved through element selection.

4. The method for analyzing the stress performance of a UHPC-reinforced RC arch bridge according to claim 1, characterized in that, When establishing the constitutive model of the confined concrete in S2, a complete stress-strain relationship curve including the rising and falling segments is used, with a focus on the influence of the falling segment on the finite element simulation results to accurately reflect the softening characteristics of concrete materials after peak stress; the edge stress of the original RC arch section is expressed as: In the formula: Aoriginal is the cross-sectional area of ​​the original arch ring; Woriginal is the bending geometric modulus of the original arch ring cross-section; by using this stress calculation formula, the stress state of the original arch ring before reinforcement can be determined, providing a theoretical basis for the design of reinforcement schemes.

5. The method for analyzing the stress performance of a UHPC-reinforced RC arch bridge according to claim 1, characterized in that, When setting the interface connection in S3, the UHPC reinforcement layer and the original RC arch ring interface are rigidly connected by a tie connection to simulate the complete collaborative working state between the two, so that the reinforced composite section has no shear deformation and follows the plane section assumption; the steel bars are embedded in the UHPC concrete and ordinary concrete matrix respectively by the Embedded embedding technology to achieve displacement coordination between the steel bars and concrete and ensure the overall stress performance of the composite structure.

6. The method for analyzing the stress performance of a UHPC-reinforced RC arch bridge according to claim 1, characterized in that, The parametric analysis in S4 employs the controlled variable method, systematically analyzing the influence of the following parameters on the bearing capacity performance of UHPC-reinforced RC arch bridges by keeping other variables constant while changing only one variable: the thickness of the UHPC reinforcement layer ranges from 10mm to 200mm, with a gradient of 10mm or 20mm; the UHPC stirrup ratio ranges from 0.2% to 2.0%, with a gradient of 0.2% or 0.3%; the longitudinal reinforcement ratio of the UHPC layer ranges from 0.5% to 4.0%, with a gradient of 0.5%; the longitudinal reinforcement diameter ranges from 10mm to 32mm, including commonly used specifications such as 10mm, 12mm, 16mm, 20mm, 25mm, and 32mm; and the ordinary concrete strength grades include five levels: C30, C35, C40, C45, and C50.

7. The method for analyzing the stress performance of a UHPC-reinforced RC arch bridge according to claim 6, characterized in that, When applying loads in S4, the changes in initial stress state caused by varying degrees of damage to the RC arch bridge during long-term use are fully considered. In the finite element model, initial horizontal stress or initial strain is set by predefined fields to truly reflect the actual stress state and damage degree of the original RC arch ring before reinforcement. By introducing the initial stress state, the joint stress process of the reinforcement layer and the original structure is simulated to obtain load-bearing capacity analysis results that are more in line with engineering reality.

8. The method for analyzing the stress performance of a UHPC-reinforced RC arch bridge according to claim 1, characterized in that, It also includes a simulation of the graded reinforcement construction process: the step-by-step clamping method is used to simulate the actual reinforcement construction process, dividing the entire bridge longitudinally into multiple pouring sections, each with a length of 2m to 5m; the entire bridge is divided into two levels of reinforcement, the first level being the section from the arch foot to L / 4, and the second level being the section from L / 4 to the arch crown, where L is the span of the arch bridge; in the finite element analysis, the birth and death element technology is used to simulate the construction process of activating the next pouring section after the concrete of each pouring section reaches 75% of the design strength, and the step-by-step construction simulation truly reflects the stress accumulation of the reinforcement layer and the redistribution of internal forces in the structure.

9. The method for analyzing the stress performance of a UHPC-reinforced RC arch bridge according to claim 6, characterized in that, The parametric analysis also includes the influence analysis of the spatial arrangement of the UHPC reinforcement layer. The reinforcement layer arrangement schemes include four arrangements: reinforcement only in the negative bending moment section of the arch foot, reinforcement from the arch foot to L / 4 section, reinforcement from the arch foot to L / 2 section, and full-span closed reinforcement. By comparing the structural bearing capacity improvement, material consumption, construction difficulty, and economy under different arrangement positions, the reinforcement effect of each scheme is comprehensively evaluated, the optimal reinforcement range and arrangement form are determined, and design reference is provided for practical engineering applications.

10. The method for analyzing the stress performance of a UHPC-reinforced RC arch bridge according to claim 1, characterized in that, In S5, when verifying the bearing capacity calculation formula, based on the large amount of parametric analysis data obtained in S4, and combined with the basic principles of arch bridge bearing capacity calculation in the current bridge design code and the theoretical derivation conclusions in existing literature, the bearing capacity calculation formula of UHPC hoop-constrained RC arch bridge is modified and improved. By comparing and analyzing the ultimate bearing capacity value obtained by finite element simulation with the theoretical formula calculation value, error analysis and regression analysis methods are used to verify the accuracy, applicability and engineering practicality of the modified formula, providing a reliable theoretical calculation method for future engineering design.

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