A method and system for calculating the fracture toughness of a reinforced beam of ultra-high performance concrete

Abstract

The application discloses a kind of super high performance concrete reinforced beam fracture toughness calculation method and system, belong to concrete structure finite element analysis technical field, including: in UHPC reinforced crack concrete beam model Double-line type Cohesive element is added, and the extended finite element model considering interface bonding performance is obtained;Based on the extended finite element model, the three-point bending simulation of UHPC reinforced crack concrete beam is carried out, and the F-CMOD curve data of UHPC reinforced crack concrete beam is obtained;F-CMOD curve data is input to the improved double K fracture model, and the crack initiation toughness and instability toughness of UHPC reinforced crack concrete beam are obtained.The application adopts fracture mechanics theory and carries out UHPC+B fracture toughness research by numerical simulation, uses extended finite element to solve the high-density grid section in crack tip high stress and deformation concentration area of existing method, and the calculation amount is huge, it is difficult to accurately capture the real crack propagation process and other problems.

Description

Technical Field

[0001] This invention belongs to the field of finite element analysis technology for concrete structures, and particularly relates to a method and system for calculating the fracture toughness of ultra-high performance concrete reinforced beams. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Over time, concrete structures are affected by human activities and the deterioration of the natural environment, leading to reduced concrete durability, decreased load-bearing capacity, and a series of safety problems such as damage, delamination, and deterioration. Therefore, for buildings and structures that have fallen into disrepair or no longer meet the requirements for use, a series of assessments and evaluations should be carried out, followed by reinforcement and renovation to ensure that they meet the structural safety requirements under existing codes.

[0004] Traditional glass / carbon fiber cloth and repair mortar reinforcement materials have various problems in the application of reinforced concrete structures. In recent years, ultra-high performance concrete (UHPC) has become an ideal reinforcement and repair material due to its high strength, high toughness and good bonding durability.

[0005] The fracture toughness of concrete is a key parameter in the design of hydraulic fracturing of reinforced structures. Determining the fracture toughness of concrete in advance can quantitatively evaluate the reliability of reinforced structures and provide important reference for the fracture morphology during concrete hydraulic fracturing.

[0006] Currently, the Extended Finite Element Method (XFEM) is used to simulate the fracture process of UHPC-reinforced beams and then calculate their fracture toughness. However, this method is not perfect: on the one hand, the influence of the interfacial bond performance between the UHPC reinforcement layer and the deteriorated concrete beam is not considered when establishing the beam model; on the other hand, the closing effect of the UHPC reinforcement layer on the damaged concrete is ignored when calculating the fracture toughness of the reinforced beam. Summary of the Invention

[0007] To overcome the shortcomings of the prior art, the present invention provides a method and system for calculating the fracture toughness of ultra-high performance concrete reinforced beams.

[0008] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0009] The first aspect of this invention provides a method for calculating the fracture toughness of ultra-high performance concrete-reinforced beams, comprising:

[0010] Based on the physical and geometric parameters of UHPC and concrete, a model of UHPC-reinforced cracked concrete beam is established.

[0011] Bilinear cohesive elements are added to the UHPC-reinforced cracked concrete beam model. The traction force rule in the bilinear cohesive elements is used to represent the interfacial bond-slip relationship between UHPC and concrete, resulting in an extended finite element model that considers interfacial bond performance.

[0012] Based on the extended finite element model, a three-point bending simulation was performed on a UHPC-reinforced cracked concrete beam to obtain the F-CMOD curve data of the UHPC-reinforced cracked concrete beam.

[0013] The F-CMOD curve data were input into the improved double-K fracture model to obtain the crack initiation toughness and instability toughness of the UHPC-reinforced cracked concrete beam.

[0014] A second aspect of the present invention provides a system for calculating the fracture toughness of ultra-high performance concrete-reinforced beams, comprising:

[0015] The model building module is configured to: build a UHPC-reinforced cracked concrete beam model based on the physical performance parameters and geometric parameters of UHPC and concrete.

[0016] The bilinear cohesive element addition module is configured to add bilinear cohesive elements to the UHPC-reinforced cracked concrete beam model, and use the traction force law in the bilinear cohesive element to represent the interfacial bond-slip relationship between UHPC and concrete, thereby obtaining an extended finite element model that considers the interfacial bond performance.

[0017] The three-point bending simulation module is configured to: perform three-point bending simulation on UHPC-reinforced cracked concrete beams based on the extended finite element model, and obtain the F-CMOD curve data of UHPC-reinforced cracked concrete beams.

[0018] The fracture toughness calculation module is configured to input F-CMOD curve data into the improved double-K fracture model to obtain the crack initiation toughness and instability toughness of UHPC-reinforced cracked concrete beams.

[0019] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps in the method for calculating the fracture toughness of an ultra-high performance concrete-reinforced beam as described in the first aspect of the present invention.

[0020] The fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the method for calculating the fracture toughness of an ultra-high performance concrete reinforced beam as described in the first aspect of the present invention.

[0021] The above one or more technical solutions have the following beneficial effects:

[0022] (1) The present invention is based on the extended finite element method for simulating the fracture toughness of UHPC+B. It adopts fracture mechanics theory and conducts numerical simulation to study the fracture toughness of UHPC+B. The extended finite element method solves the problems of existing methods, such as high-density meshing in high stress and deformation concentration areas such as crack tip, and the need to re-mesh the mesh to adapt to crack direction during crack initiation and propagation, resulting in huge computational load and difficulty in accurately capturing the real crack propagation process. The invention achieves accurate calculation of crack propagation path and fracture toughness value.

[0023] (2) The interfacial relationship between UHPC and concrete was characterized using cohesive elements, which intuitively introduced the bond strength between UHPC and concrete, ensuring the reliability of the experimental results.

[0024] (3) Based on existing fracture mechanics theory, the closing effect of UHPC on concrete beams is considered. Fracture toughness calculation parameters applicable to reinforced concrete are introduced, and the improved toughness index is used to characterize the reinforcement effect of UHPC on concrete beams. This aims to provide theoretical and technical support for the analysis of crack propagation and fracture performance of UHPC+B.

[0025] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0026] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0027] Figure 1 The flowchart shows a method for calculating the fracture toughness of an ultra-high performance concrete reinforced beam according to the first embodiment.

[0028] Figure 2 This is a structural diagram of the UHPC+B model of the first embodiment.

[0029] Figure 3 The image shows the F-CMOC curve of the UHPC-reinforced beam under the joint height ratio a / h in the first embodiment.

[0030] Figure 4 The image shows the F-CMOC curves of the UHPC-reinforced beams with different UHPC thicknesses in the first embodiment.

[0031] Figure 5The image shows the F-CMOC curves of the UHPC-strengthened beams under different concrete strength grades in the first embodiment.

[0032] Figure 6 (a), (b), and (c) in the diagrams are schematic diagrams of the UHPC starting to fracture, the UHPC completely fractured, and the UHPC reinforcement beam completely fractured, respectively, in the first embodiment. Detailed Implementation

[0033] Example 1

[0034] like Figure 1 As shown in the figure, this embodiment discloses a method for calculating the fracture toughness of ultra-high performance concrete-reinforced beams, including:

[0035] Step 1: Based on the physical property parameters and geometric parameters of UHPC and concrete, establish a UHPC-reinforced cracked concrete beam model;

[0036] Step 2: Add bilinear cohesive elements to the UHPC-reinforced cracked concrete beam model, and use the traction force rule in the bilinear cohesive elements to represent the interfacial bond-slip relationship between UHPC and concrete, thus obtaining an extended finite element model considering interfacial bond performance.

[0037] Step 3: Based on the extended finite element model, a three-point bending simulation was performed on the UHPC-reinforced cracked concrete beam to obtain the F-CMOD curve data of the UHPC-reinforced cracked concrete beam.

[0038] Step 4: Input the F-CMOD curve data into the improved double-K fracture model to obtain the crack initiation toughness and instability toughness of the UHPC-reinforced cracked concrete beam.

[0039] Step 1 includes establishing a UHPC-reinforced cracked concrete beam model based on the physical property parameters and geometric parameters of UHPC and concrete; wherein, the concrete beam sample size is 1000mm×200mm×120mm, and the basic performance parameters of the UHPC-reinforced cracked concrete beam are shown in Table 1.

[0040] This invention establishes a numerical model for simulating the fracture toughness of UHPC+B based on the physical property parameters of UHPC and concrete, and the geometric parameters of experimental specimens, using the cohesive interface and extended finite element method. The test follows the specifications of the standard "Test Procedure for Fracture of Hydraulic Concrete" (DL / T 5332-2005), and a three-point bend simulation of UHPC+B is performed using the extended finite element method.

[0041] Table 1 Basic performance parameters of UHPC-reinforced cracked concrete beams

[0042]

[0043] In step 2, bilinear cohesive elements are added to the UHPC-reinforced cracked concrete beam model. This bilinear cohesive model is used as the constitutive model for the interface elements between the UHPC reinforcement layer and the concrete in the UHPC-reinforced structure. An extended finite element model considering interfacial bonding performance is then established, as follows: Figure 2 As shown, the model consists of four parts: UHPC, concrete, cracks, and pad blocks, with cohesive elements added between the UHPC and concrete.

[0044] The bond performance between the UHPC reinforcement layer and the deteriorated concrete is represented by the constitutive relationship of the cohesion between the interfaces and the relative displacement of the interfaces. The bond strength between the interfaces varies with the relative distance between the material interfaces. A bilinear cohesive model is established to characterize the bond-slip relationship between UHPC and concrete (as shown in Equation 1).

[0045]

[0046] Where: σ max δ represents the maximum stress in the interface normal direction, and δ0 represents the initial damage separation amount; δ c To completely destroy the separation quantity.

[0047] This invention utilizes a bilinear cohesive model to characterize the interfacial relationship between UHPC and concrete, assuming that the interfacial properties change with the relative displacement between the materials. The parameters of the bilinear cohesive model used are shown in Table 2.

[0048] Table 2 Performance parameters of the interface between UHPC reinforcement layer and concrete

[0049]

[0050] In Table 2, K n K S and K t These are the normal and tangential stiffness components related to the normal and shear separation through the interface before damage begins. The contact stress at the interface (t) n t s and t t The normal stress and two other shear stresses correspond to deformations perpendicular to the interface and are parallel to the first and second shear directions, respectively. Contact stress (t) n t s and t t They have the same assumed value, which is equal to the direct tensile strength obtained from the direct tensile test.

[0051] In step 3, a three-point bending simulation is performed on the UHPC-strengthened concrete beam based on the extended finite element model. This includes applying displacement loads of different magnitudes to the extended finite element model, changing the concrete strength, UHPC thickness, joint height ratio a / h, and the interfacial bond relationship between the UHPC and the concrete matrix, to simulate the fracture process of the UHPC-strengthened concrete beam. Specifically:

[0052] (1) Apply a displacement load of 1 mm / s to the extended finite element model, fix the interface bonding relationship (i.e. cohesion parameter) between UHPC and concrete matrix, UHPC thickness of 20 mm and concrete strength, change the value of joint height ratio a / h, observe the crack initiation load and peak load of UHPC-reinforced concrete beam, and obtain the F-CMOD curve data of the beam.

[0053] (2) Apply a displacement load of 1 mm / s to the extended finite element model, fix the interfacial bonding relationship (i.e., cohesion parameter), a / h and concrete strength between UHPC and concrete matrix, change the value of UHPC thickness, observe the crack initiation load and peak load of UHPC-reinforced concrete beam, and obtain the F-CMOD curve data of the beam.

[0054] (3) Apply a displacement load of 1 mm / s to the extended finite element model, fix the interface bonding relationship between UHPC and concrete matrix, a / h and UHPC thickness of 20 mm, change the concrete strength grade, observe the crack initiation load and peak load of UHPC-reinforced concrete beam, and obtain the F-CMOD curve data of the beam.

[0055] In step 4, a double-K fracture model is constructed to calculate the UHPC-strengthened concrete beam. Considering the confinement effect of UHPC on the concrete beam, the following assumptions are made for the UHPC-strengthened beam: 1) the crack surface is linear; 2) the interface crack between UHPC and concrete is not considered; 3) the force of UHPC on the concrete beam is equivalent to the concentrated force acting on the bottom of the beam.

[0056] The obtained experimental data were input into the improved double-K fracture model to obtain the crack initiation toughness and instability toughness of UHPC+B, and a data comparison chart was constructed.

[0057] By increasing the stress intensity factor to take into account the closing effect of UHPC on concrete, a double-K fracture calculation model for UHPC-reinforced cracked concrete was further developed. The crack initiation toughness and instability toughness of the UHPC-reinforced beam were obtained, and the reinforcement effect of UHPC on the beam was analyzed.

[0058] Among them, fracture toughness at initiation The fracture toughness of UHPC+B under the initial crack initiation state is defined as the stress intensity factor at the time of crack initiation. The applied load at this time is defined as the initiation load F. iniThe crack length is the initial crack length a0; the instability fracture toughness This represents the fracture toughness corresponding to the instability of UHPC+B, i.e., the stress intensity corresponding to the crack instability propagation. The applied load at this time is the instability load F. max The instability load is also the maximum load, and the crack length is the critical effective crack length a. c The crack opening displacement is the critical crack opening displacement (CMOD). c The schematic diagrams of UHPC starting to fracture, UHPC completely fracture, and UHPC reinforced beam completely fracture are shown below. Figure 6 As shown in (a), (b), and (c).

[0059] The fracture toughness calculation process is as follows:

[0060]

[0061] in:

[0062] In the formula, F is the load borne by the concrete beam, kN; m is the mass of the specimen between supports, kg; and g is the acceleration due to gravity, taken as 9.81 m / s². 2 S is the span between the two supports of the specimen, m; t is the thickness of the specimen, m; h is the height of the specimen, m;

[0063] When F = F ini When α=α0=a / h, Among them, F ini denoted as the initiation load of the beam, kN; that is, the load corresponding to the inflection point where the F-CMOD curve of the specimen transitions from a straight line to a curve; a is the initial crack length of the concrete; h is the height of the concrete beam.

[0064] When F = F max , α=α c =a c / h, at this time Among them, F max The maximum load on the beam is kN; a c The effective crack length is in meters (m).

[0065] Among them, a c It should be calculated using the following formula:

[0066]

[0067] In the formula: h0 is the thickness of the thin steel plate of the clamp-type drawing blade, in meters (m). For finite element analysis, h0 = 0. CMOD c is the critical value of crack opening displacement, μm; E is the calculated elastic modulus, GPa;

[0068] The elastic modulus E can be determined based on the given F-CMOD relationship, expressed as:

[0069]

[0070] in:

[0071]

[0072] In the formula, k i =F i / CMOD I Let be the initial stiffness of the specimen. Calculate the stiffness at any point on the linear elastic segment of the F-CMOD curve. To reduce error, multiple points can be selected to calculate the average value of the elastic modulus.

[0073] The formula for calculating the fracture toughness generated by UHPC during crack propagation is as follows:

[0074]

[0075] in:

[0076]

[0077] In the formula: d is the thickness of the UHPC reinforcement layer.

[0078] When σ=σ ini When α=α0=a / h, Where, σ ini The tensile stress in UHPC-B beam when the initial crack begins to initiate; This represents the stress intensity factor at the initial crack location in a UHPC-reinforced concrete beam when the crack has just begun to propagate, caused by the action of the UHPC. Since the force exerted by the UHPC has a crack-closing effect, therefore... It is a negative value.

[0079] When σ=σ ini , α=α c =a c / h time, Where, σ max It is the tensile stress in the UHPC when the crack in the UHPC-B beam begins to cause instability; This represents the stress intensity factor at the crack tip caused by the action of the UHPC when the crack begins to propagate unstably. Since the force of the UHPC has a closure effect on the crack, therefore... It is also a negative value. To make the calculation results more accurate, the α value used in this invention for UHPC-strengthened concrete beams is... c The critical effective crack length corresponding to the peak load was extracted and calculated using a Python secondary development program for Abaqus.

[0080] By adding a stress intensity factor characterizing the closing effect of UHPC on concrete to the double-K fracture model, an improved double-K fracture model is obtained, including a crack initiation toughness calculation model and a buckling toughness calculation model. The crack initiation toughness and buckling toughness of UHPC-strengthened concrete beams can be obtained using the following formula:

[0081]

[0082]

[0083] in: Strengthen the crack initiation toughness of UHPC reinforced concrete beams; To enhance the instability toughness of UHPC reinforced concrete beams. This represents the crack initiation toughness corresponding to the crack initiation load of the concrete beam. This represents the instability toughness corresponding to the maximum load on the concrete beam.

[0084] Experimental example: (1) A displacement load of 1 mm / s was applied to the three-point bending numerical model of a C30 concrete beam reinforced with UHPC. The cohesion parameter and the thickness of UHPC were fixed, and the crack initiation load and peak load of the beam under different a / h were obtained, as shown in Table 3. The results show that the crack initiation load and peak load of the reinforced beam decrease with the increase of a / h.

[0085] The experimental data obtained in (1) were input into the improved double-K fracture model to obtain the crack initiation toughness and instability toughness of UHPC+B, and a data comparison chart was constructed, as shown in the figure. Figure 3 As shown.

[0086] Table 3. Fracture toughness of UHPC-reinforced concrete beams at different a / h.

[0087]

[0088] Experimental Example: (2) A displacement load of 1 mm / s was applied to the three-point bending numerical model of a C30 concrete beam reinforced with UHPC. The cohesion parameter and a / h were fixed, and the crack initiation load and peak load of the reinforced beam under different UHPC thicknesses were obtained, as shown in Table 4. The results show that the crack initiation load and peak load of UHPC+B gradually increase with the increase of the UHPC protective layer thickness.

[0089] The experimental data obtained in (2) were input into the improved double-K fracture model to obtain the crack initiation toughness and instability toughness of the UHPC-strengthened beam, and a data comparison chart was constructed, see... Figure 4 See Table 4. The results show that the fracture toughness of UHPC+B improves with increasing UHPC thickness.

[0090] Table 4 Fracture toughness of UHPC-B beams with different UHPC layer thicknesses

[0091]

[0092] Experimental Example: (3) A displacement load of 1 mm / s was applied to the numerical model of the three-point bending of the UHPC-reinforced C20-C40 concrete beam. The cohesion parameters, a / h, and UHPC thickness were fixed, and the F-CMOC curve of the beam under the concrete strength grade was obtained. The results show that the cracking load and peak load of UHPC+B gradually increase with the increase of concrete strength grade.

[0093] The experimental data obtained in (3) were input into the improved double-K fracture model to obtain the crack initiation toughness and instability toughness of UHPC+B, and a data comparison chart was constructed, see Figure 5 See Table 5. The results show that the fracture toughness of UHPC+B improves with increasing concrete strength grade.

[0094] Table 5 Fracture toughness of UHPC-strengthened concrete beams under different concrete strength grades

[0095]

[0096] Example 2

[0097] This embodiment discloses a fracture toughness calculation system for ultra-high performance concrete-strengthened beams, including:

[0098] The model building module is configured to: build a UHPC-reinforced cracked concrete beam model based on the physical performance parameters and geometric parameters of UHPC and concrete.

[0099] The bilinear cohesive element addition module is configured to add bilinear cohesive elements to the UHPC-reinforced cracked concrete beam model, and use the traction force law in the bilinear cohesive element to represent the interfacial bond-slip relationship between UHPC and concrete, thereby obtaining an extended finite element model that considers the interfacial bond performance.

[0100] The three-point bending simulation module is configured to: perform three-point bending simulation on UHPC-reinforced cracked concrete beams based on the extended finite element model, and obtain the F-CMOD curve data of UHPC-reinforced cracked concrete beams.

[0101] The fracture toughness calculation module is configured to input F-CMOD curve data into the improved double-K fracture model to obtain the crack initiation toughness and instability toughness of UHPC-reinforced cracked concrete beams.

[0102] Example 3

[0103] The purpose of this embodiment is to provide a computer-readable storage medium.

[0104] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the method for calculating the fracture toughness of an ultra-high performance concrete-reinforced beam as described in Embodiment 1 of this disclosure.

[0105] Example 4

[0106] The purpose of this embodiment is to provide an electronic device.

[0107] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the method for calculating the fracture toughness of an ultra-high performance concrete-reinforced beam as described in Embodiment 1 of this disclosure.

[0108] The steps and methods involved in the apparatuses of Embodiments 2, 3, and 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0109] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0110] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for calculating the fracture toughness of ultra-high performance concrete-reinforced beams, characterized in that, include: Based on the physical property parameters of UHPC and concrete and the geometric parameters of the experimental specimens, a model of UHPC-reinforced cracked concrete beam was established. Bilinear cohesive elements are added to the UHPC-reinforced cracked concrete beam model. The traction force rule in the bilinear cohesive elements is used to represent the interfacial bond-slip relationship between UHPC and concrete, resulting in an extended finite element model that considers interfacial bond performance. Based on the extended finite element model, a three-point bending simulation was performed on a UHPC-reinforced cracked concrete beam to obtain the F-CMOD curve data of the UHPC-reinforced cracked concrete beam. The F-CMOD curve data were input into the improved double-K fracture model to obtain the crack initiation toughness and instability toughness of the UHPC-reinforced cracked concrete beam. An improved double-K fracture model is obtained by adding a stress intensity factor characterizing the closing effect of UHPC on concrete to the double-K fracture model, including a crack initiation toughness calculation model and an instability toughness calculation model. The crack initiation toughness calculation model for: In the formula, The stress intensity factor at the initial crack location of the UHPC-reinforced cracked concrete beam when the crack just begins to propagate is the stress intensity factor generated by the action of UHPC. Fracture toughness corresponding to the crack initiation load for UHPC-reinforced cracked concrete beams; The thickness of the UHPC reinforcement layer; The tensile stress in UHPC-B beam when the initial crack begins to initiate; The stress intensity factor at the initial crack location of the UHPC-reinforced concrete beam when the crack just begins to propagate is the stress intensity factor generated by the action of UHPC. h is the initial crack length in the concrete; h is the height of the concrete beam. ; The instability toughness calculation model for: In the formula, The stress intensity factor generated at the crack tip by the action of UHPC when the crack begins to unstablely propagate; This is the stress intensity factor corresponding to the maximum load on the concrete beam.

2. The method for calculating the fracture toughness of ultra-high performance concrete-reinforced beams as described in claim 1, characterized in that, The bilinear cohesive unit is: In the formula, The maximum stress in the interface normal direction, This represents the initial damage separation amount; To completely destroy the separation quantity.

3. The method for calculating the fracture toughness of ultra-high performance concrete-reinforced beams as described in claim 1, characterized in that, The extended finite element model includes: UHPC, concrete, cracks, pad blocks, and bilinear cohesive elements added between UHPC and concrete.

4. The method for calculating the fracture toughness of ultra-high performance concrete reinforced beams as described in claim 1, characterized in that, The three-point bending simulation of the UHPC-reinforced cracked concrete beam based on the extended finite element model includes: By applying displacement loads of different magnitudes to the extended finite element model, and changing the concrete strength, UHPC thickness, joint height ratio, and interfacial bond relationship between UHPC and the concrete matrix, the fracture process of UHPC-reinforced cracked concrete beams was simulated, and the crack initiation load and peak load of the reinforced cracked concrete beams were obtained.

5. A system for calculating the fracture toughness of ultra-high performance concrete-reinforced beams, characterized in that, A method for calculating the fracture toughness of ultra-high performance concrete-reinforced beams according to any one of claims 1-4 includes: The model building module is configured to: build a UHPC-reinforced cracked concrete beam model based on the physical performance parameters of UHPC and concrete and the geometric parameters of the experimental specimens; The bilinear cohesive element addition module is configured to add bilinear cohesive elements to the UHPC-reinforced cracked concrete beam model, and use the traction force law in the bilinear cohesive element to represent the interfacial bond-slip relationship between UHPC and concrete, thereby obtaining an extended finite element model that considers the interfacial bond performance. The three-point bending simulation module is configured to: perform three-point bending simulation on UHPC-reinforced cracked concrete beams based on the extended finite element model, and obtain the F-CMOD curve data of UHPC-reinforced cracked concrete beams. The fracture toughness calculation module is configured to input F-CMOD curve data into the improved double-K fracture model to obtain the crack initiation toughness and instability toughness of UHPC-reinforced cracked concrete beams.

6. A computer-readable storage medium having a program stored thereon, characterized in that, When executed by the processor, the program implements the steps in the method for calculating the fracture toughness of an ultra-high performance concrete reinforced beam as described in any one of claims 1-4.

7. An electronic device, comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the method for calculating the fracture toughness of an ultra-high performance concrete reinforced beam as described in any one of claims 1-4.

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