A Method for Predicting Concrete Cracking Load Based on a Nonlinear Fracture Model

Abstract

This invention belongs to the technical field of concrete fracture performance evaluation in bridges, hydraulic engineering, and marine engineering, specifically involving a method for predicting concrete cracking load based on a nonlinear fracture model. The method defines the parameter system for the target concrete and its corresponding precast mortar notched beam in a three-point bending test; prepares precast mortar notched beam specimens, and obtains the ultimate load at fracture of the mortar specimen through a three-point bending fracture test, determining the tensile strength of the mortar specimen unaffected by size effects; establishes a nonlinear fracture model under the concrete cracking state, and establishes equilibrium equations based on the cross-sectional force equilibrium conditions under the concrete cracking state, solving for the concrete cracking load, which is the predicted value of the target concrete cracking load. Compared with existing technologies, this invention can be completed under ordinary test conditions, and has advantages such as simple operation, low equipment requirements, low test costs, and ease of implementation and promotion.

Description

Technical Field

[0001] This invention belongs to the technical field of concrete fracture performance evaluation in bridges, water conservancy and marine engineering, and specifically relates to a method for predicting concrete crack initiation load based on a nonlinear fracture model. Background Technology

[0002] During service, concrete is subjected to the coupled effects of static loads, dynamic loads, fatigue loads, and environmental factors. Once cracks initiate and propagate, they lead to structural stiffness degradation, reduced load-bearing capacity, and shortened service life. Crack propagation in concrete fracture typically occurs in three stages: crack initiation, stable propagation, and unstable propagation. Accurately determining the crack initiation load of concrete is crucial for crack resistance evaluation, fracture parameter determination, and structural safety analysis.

[0003] Currently, the main methods for determining the concrete cracking load include load-crack opening displacement (…). F Methods include the CMOD curve inflection point method, the local strain method at the crack tip, and optical and acoustic methods. F The CMOD curve method typically uses the load corresponding to the inflection point where the curve transitions from an approximately linear to a nonlinear stage as the crack initiation load. However, for concrete containing coarse aggregates, the inflection point on the curve is often unclear due to significant microscopic heterogeneity near the crack tip, making it susceptible to human interpretation. The crack tip local strain method, on the other hand, usually determines the crack initiation time by placing strain gauges near the precast crack tip and observing the abrupt changes, hysteresis, or inflection points in the local strain response before and after crack initiation. This method can directly reflect the local mechanical response in the crack tip region, but crack initiation usually occurs when the strain gauge retraction is observed, and the test requires high precision in terms of measuring point placement, measurement accuracy, and test stability. Sometimes, it is even difficult to capture the strain gauge retraction phenomenon. Furthermore, while optical or acoustic methods can identify the crack initiation process through full-field deformation, local crack evolution, or fluctuation signal changes, they suffer from high equipment costs, complex testing procedures, and high barriers to data processing. Therefore, it is necessary to propose a concrete crack initiation load prediction method with clearly defined physical meanings and a simple testing process.

[0004] The information disclosed in this background section is intended only to enhance the understanding of the overall background of the present invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method for predicting concrete crack initiation load based on a nonlinear fracture model.

[0006] The technical solution adopted by this invention to solve its technical problem is as follows: a method for predicting concrete crack initiation load based on a nonlinear fracture model, comprising the following steps: S1. Define the parameter system for the target concrete and its corresponding mortar precast notched beam in a three-point bending test. The parameters of the target concrete specimen include the concrete beam height. , width of concrete beam Initial notch length of concrete beam , concrete beam span and the self-weight of concrete beams The corresponding mortar specimen parameters include the height of the mortar beam. mortar beam width Initial notch length of mortar beam mortar beam span and the self-weight of the mortar beam ; S2. Prepare precast mortar notched beam specimens according to the composition of the target concrete formula after removing coarse aggregate. Conduct three-point bending fracture tests on the precast mortar notched beam specimens to obtain the ultimate load at fracture of the mortar specimens. The tensile strength of the mortar specimen, unaffected by size effects, is determined according to the following formula. : ; in, It is the coefficient of variation that reflects the discontinuous characteristics of mortar. The average aggregate particle size in the mortar. The joint height ratio of the mortar; It is a shape function; S3. Establish a nonlinear fracture model for concrete under crack initiation conditions, assuming that when the concrete specimen reaches the crack initiation load... At that time, the strength of the mortar matrix had fully developed, and the initial notch tip formation length was... The fracture process zone, wherein the tensile stress in the fracture process zone is taken as the mortar tensile strength. ,in, The coefficient of variation is used to reflect the discontinuous characteristics of concrete. The average coarse aggregate particle size in concrete; S4. Establish the equilibrium equation based on the section force equilibrium condition under the concrete cracking state, and solve for the concrete cracking load according to the following formula. : ; This is the predicted value of the target concrete cracking load.

[0007] Preferably, it also includes according to Determine the reasonable fluctuation range of the target concrete crack initiation load. The statistically obtained mortar tensile strength mean and its standard deviation Substituting into the equilibrium equation, the upper and lower limits of the reasonable fluctuation range satisfy: .

[0008] Preferably, the reasonable fluctuation range is the 95% guarantee range of the concrete cracking load.

[0009] Preferably, the ratio of the initial notch to the beam height of the mortar or concrete specimen is 0.1 to 0.5.

[0010] Preferably, the method is applicable to composite materials that contain at least a mortar phase and a coarse aggregate phase.

[0011] Preferably, the method can be used for predicting the crack initiation load, evaluating crack resistance, and performing related numerical simulation analysis on precast concrete notched beam specimens of different sizes.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. Compared with existing methods for determining crack initiation load, this invention does not require complex testing methods such as optical, acoustic, or local strain at the crack tip, nor does it require manual interpretation of characteristic points of the P-CMOD curve. It only requires measuring the ultimate load through a three-point bending test of the corresponding precast mortar notched beam, and combining it with the model proposed by the boundary effect to determine the crack initiation load of concrete. This invention does not require additional special equipment or complex data acquisition and post-processing systems, and can be completed under ordinary test conditions. It has the advantages of simple operation, low equipment requirements, low test cost, and easy implementation and promotion.

[0013] 2. This invention starts from the microstructure of concrete and measures the tensile strength of mortar corresponding to the target concrete. A method for determining the initiation load is introduced, giving the initiation control parameters a clear physical meaning. The entire model is based on nonlinear fracture mechanics theory, fully considering the heterogeneity and discontinuity of concrete itself, which can reduce the influence of size effect on strength assessment. It is used to evaluate the initiation load of concrete structures of different sizes, and the maximum error with the initiation load measured by traditional strain gauges does not exceed 10%. 3. The concrete crack initiation load prediction method established in this invention is a macroscopic fracture performance determination method based on microscopic characteristics. It can provide input parameters with clear physical meaning for relevant finite element numerical simulations, which facilitates the crack initiation analysis, crack resistance evaluation and fracture process simulation of concrete components in relevant numerical analysis software, and has good engineering practical value. Attached Figure Description

[0014] Figure 1 This is a damage cloud map showing the distribution of microcracks within the fracture process zone at the initial crack tip of a three-point bending specimen.

[0015] Figure 2 This is a diagram showing the stress distribution at the critical section of a mortar specimen under ultimate load.

[0016] Figure 3 This is a model diagram of crack propagation from crack initiation to failure in concrete. Among them, (a) is a macroscopic crack propagation morphology diagram of the crack initiation stage; (b) is a macroscopic crack propagation morphology diagram of the early stage of stable crack propagation; (c) is a macroscopic crack propagation morphology diagram of the late stage of stable crack propagation; (d) is a macroscopic crack propagation morphology diagram of the unstable crack propagation stage; (e) is a microscopic crack development morphology diagram of the crack initiation stage; (f) is a microscopic crack development morphology diagram of the early stage of stable crack propagation; (g) is a microscopic crack development morphology diagram of the late stage of stable crack propagation; and (h) is a microscopic crack development morphology diagram of the unstable crack propagation stage.

[0017] Figure 4 This is a stress diagram of a three-point bending section under the crack initiation state of concrete.

[0018] Figure 5 Comparison of predicted and measured crack initiation loads for a 40mm high concrete beam (crack height ratio of 0.2).

[0019] Figure 6 The image shows a comparison between the predicted and measured crack initiation loads for a 40mm high concrete beam (crack height ratio of 0.3).

[0020] Figure 7 This is a comparison chart of the predicted and measured crack initiation loads for a 100mm high concrete beam (crack height ratio of 0.2).

[0021] Figure 8 This is a comparison chart of the predicted and measured crack initiation loads for a 100mm high concrete beam (crack height ratio of 0.3). Detailed Implementation

[0022] To facilitate understanding of the present invention, it will be described in more detail below with reference to the accompanying drawings and specific embodiments. However, the present invention can be implemented in many different forms and is not limited to the embodiments described in this specification. Rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of the present invention.

[0023] A method for predicting concrete crack initiation load based on a nonlinear fracture model first determines the tensile strength of the mortar corresponding to the target concrete. Then the above As the controlling tensile stress in the fracture zone during concrete cracking, an equilibrium equation is established under the concrete cracking state to obtain the concrete cracking load value. This includes the following steps: S1. Define the parameter system for the precast notched beam prepared with the target concrete and corresponding mortar in the three-point bending test. Define the relevant parameters of the target concrete specimen as: concrete beam height. , width of concrete beam Initial notch length of concrete beam , concrete beam span Self-weight of concrete beams The relevant parameters of the mortar specimens after removing coarse aggregate, corresponding to the target concrete mix proportion, are defined as: mortar beam height. mortar beam width Initial notch length of mortar beam mortar beam span , self-weight of mortar beam ; S2. Prepare precast mortar notched beam specimens according to the composition after removing coarse aggregate from the target concrete mix proportion. Conduct three-point bending fracture tests on the precast mortar notched beam specimens to obtain the ultimate load at fracture of the mortar specimens. .like Figure 1 As shown, once the specimen enters the cracking state, due to the material's heterogeneity, the initial crack tip will form many discrete microcracks, rather than the single crack obtained under the assumption of continuous homogeneity. Therefore, for heterogeneous materials, nonlinear fracture mechanics theory needs to be introduced for analysis. Figure 2 As shown, the critical crack propagation length when the ultimate load is reached... With the average aggregate particle size in the mortar Closely related, it can be expressed as the dispersion coefficient reflecting the discontinuous characteristics of mortar. Multiply by to reflect the unevenness of the mortar ,Right now .

[0024] Within an extremely limited critical crack propagation length, the nominal strength considering the presence of an initial notch is considered. Assuming it remains constant, its magnitude is affected by the distance from the initial crack tip to the specimen boundary, and can be expressed as: ; Among them, the equivalent crack length This reflects the distance from the initial crack tip to the front and rear boundaries, and can be expressed as the crack height ratio of the mortar. express, Shape function: .

[0025] Finally, by combining the above equations and the critical section equilibrium condition, the tensile strength of the mortar specimen unaffected by size effects can be obtained and determined according to the following formula. : ; The above formula is based on nonlinear fracture mechanics and takes into account the influence of boundary effects on the evaluation of mortar fracture performance. Therefore, the results obtained from the three-point bending fracture test are... The size-effect-free tensile strength of mortar can be derived. This allows for the reasonable prediction of crack initiation loads in concrete specimens of different sizes.

[0026] S3. Establish a nonlinear fracture model of concrete under crack initiation state and solve for the crack initiation load. .like Figure 3 As shown, when concrete specimens progress from the crack initiation stage (as shown in (a) and (e)) to the stable crack propagation stage (as shown in (b) and (f), (c) and (g), and then to the unstable crack propagation stage (as shown in (d) and (h), at the microscopic level, it can be seen that the cracks gradually develop by passing through or bypassing the aggregate, and the aggregate gradually plays a bridging and crack-preventing role. When in the crack initiation state, the bridging role of the aggregate has not yet been fully utilized. For precast notched concrete three-point bending beams, at the microscopic level, it can be assumed that the strength of the mortar matrix has been fully developed when the concrete reaches the crack initiation load. That is, it is assumed that when the concrete is subjected to... At that time, the initial notch tip appeared at a length of 100 mm. The fracture zone (FPZ) is where the tensile stress reaches the tensile strength of the mortar. And it remains constant. Among them... The coefficient of variation is used to reflect the discontinuous characteristics of concrete. This represents the average coarse aggregate particle size in concrete. For example... Figure 4 As shown, based on the section force equilibrium condition under the concrete cracking state, we can obtain: ; ; in For the self-weight of the concrete beam, Let x be the compressive stress at the top of the beam, and y be the lengths of the tension and compression zones of the uncracked portion of the beam along the beam height, respectively. Combining these with the above formula, the concrete cracking load can be obtained. The prediction formula: .

[0027] S4. Solve for the concrete cracking load value. The upper and lower limits of the mortar tensile strength obtained statistically. mean and its standard deviation By substituting the values, we can obtain the reasonable fluctuation range of the target concrete cracking load.

[0028] .

[0029] In one embodiment, the ratio of the span between the two supports of the beam to the beam height in a three-point bending fracture test can be selected as 4, corresponding to the shape function. .

[0030] In one embodiment, the ratio of the initial notch to the beam height of the concrete or mortar specimen is 0.1 to 0.5.

[0031] In one embodiment, the method is applicable to composite materials that contain at least two phases: a mortar phase and a coarse aggregate phase.

[0032] In one embodiment, the concrete to be measured includes, but is not limited to, ordinary concrete, alkali-activated concrete, high-performance concrete, marine concrete, and their corresponding mortars.

[0033] In one embodiment, this method can eliminate the size effect of concrete strength and accurately determine the crack initiation load of concrete specimens of different sizes. The method described in this application can be used for predicting the crack initiation load, evaluating crack resistance, and conducting related numerical simulation analyses of precast notched concrete beam specimens of different sizes.

[0034] The concrete raw materials used in the following examples include: P·O42.5 ordinary Portland cement, F-grade fly ash, ordinary tap water, polycarboxylate superplasticizer with a water reduction rate of 27%, ordinary river sand, and granite coarse aggregate. The fineness modulus of the ordinary river sand is 3.6; the maximum particle size of the granite aggregate is 10 mm.

[0035] This invention determines the tensile strength of the mortar specimen, unaffected by size effects, by first testing the three-point bending fracture limit load of the mortar specimen corresponding to the target concrete, and then using the formula described in this invention. Then the statistics obtained Substituting the mean and standard deviation into the concrete crack initiation load prediction formula, the predicted value of the crack initiation load of the target concrete specimen and its reasonable fluctuation range with a 95% guarantee rate are obtained. Finally, the crack initiation load of the concrete specimen is measured by the traditional crack tip local strain method, and the predicted results are compared with the predicted results to verify the rationality and accuracy of the method of the present invention.

[0036] Example 1: This example is used to predict the crack initiation load of small-sized concrete specimens and is compared and verified with the results obtained by the traditional crack tip local strain method.

[0037] (1) First, precast notched mortar beam specimens were prepared according to the corresponding mortar after removing coarse aggregate in the target concrete mix proportion. The specimen size was 50mm×50mm×300mm, the span-to-depth ratio was 4, and the joint height ratio was [missing information]. The values ​​were 0.2 and 0.3 respectively, and 5 parallel specimens were set for each group of seam height ratios.

[0038] but: =50mm, =50mm, =200mm, =10mm or 15mm.

[0039] when =0.2 ， =10mm, =0.99; when =0.3 ， =15mm, =1.04.

[0040] The fine aggregate in the mortar specimens was ordinary river sand with an average particle size of 2.5 mm. Mortar tensile strength... The calculation process is as follows: .

[0041] After testing, this embodiment =2.5mm, =1.5, The load was 15.9 N. The mortar specimen was subjected to a three-point bending fracture test at a loading rate of 0.02 mm / min to obtain the ultimate load of the mortar at fracture failure. The value is 1072N. Substituting the above data into the mortar tensile strength calculation formula yields the mortar... mean and its standard deviation The values ​​are 4.66 MPa and 0.39 MPa, respectively.

[0042] (2) Then the obtained Substituting the mean and standard deviation into the concrete crack initiation load prediction formula described in this invention, the crack initiation load of small-sized concrete specimens can be predicted. The concrete specimen to be tested is a precast notched three-point bending beam with dimensions of 40mm × 40mm × 160mm and a span-to-depth ratio of 2.5. Then: =40mm, =40mm, =100mm, =8mm or 12mm.

[0043] This example has been tested. =6.7mm, =1.5.

[0044] .

[0045] When the concrete specimen joint height ratio When it is 0.2, =8mm, self-weight of concrete beam The mortar is 7.5N. Substituting the mean into the above formula, we can obtain the predicted crack initiation load of the concrete specimen as 1250N.

[0046] .

[0047] The statistically obtained average tensile strength of mortar and standard deviation Substituting into the above formula, we can obtain the concrete specimen of this size. A reasonable fluctuation range with a 95% guarantee rate has upper and lower limits of 1460N and 1040N, respectively. Similarly, when the joint height ratio of the concrete specimen is 0.3, =12mm, W c The crack initiation load is 7.3N, and the predicted value of the crack initiation load obtained according to the method of the present invention is 1099N, with a corresponding 95% guarantee rate range of 914N to 1284N.

[0048] (3) The traditional crack tip local strain method was used to test the crack initiation load of a group of five concrete specimens of the same size and crack height ratio. By placing strain gauges at the crack tip, the measured crack initiation loads of each specimen with a crack height ratio of 0.2 were 1343N, 1269N, 1399N, 1342N, and 1322N, respectively. Therefore, the measured average value was 1335N, and the predicted value obtained by this invention differed from the measured average value by only 85N, with a relative error of approximately 6.4%. The measured crack initiation loads of each specimen with a crack height ratio of 0.3 were 1057N, 1154N, 1011N, 1243N, and 1217N, respectively. Therefore, the measured average value was 1136N, and the predicted value obtained by this invention differed from the measured average value by approximately 37N, with a relative error of only 3.3%. Furthermore, as... Figure 5 and Figure 6 As shown, the above measured results are all within the prediction range with a 95% guarantee rate, indicating that the method of the present invention has a relatively reliable predictive ability for the crack initiation load of small-sized concrete specimens under different initial crack conditions.

[0049] Example 2: This example is used to predict the crack initiation load of large-sized concrete specimens and is compared and verified with the results obtained by the traditional crack tip local strain method.

[0050] (1) The concrete and mortar materials used in this embodiment have the same composition as those in Embodiment 1. Since this invention establishes a mortar tensile strength evaluation method without size effect based on nonlinear fracture mechanics theory, the mortar in this embodiment... The testing process was the same as in Example 1. After obtaining the ultimate load of the mortar through the three-point bending fracture test, the mean tensile strength of the corresponding mortar specimen was determined to be 4.66 MPa, and the standard deviation was 0.39 MPa.

[0051] (2) Unlike Example 1, the concrete specimen predicted in this example is a precast three-point curved beam with a larger size, measuring 100mm × 100mm × 515mm, with a span-to-depth ratio of 4. Therefore: =100mm, =100mm, =400mm, =20mm or 30mm. (The above...) Substituting the mean and standard deviation into the concrete crack initiation load prediction formula described in this invention, the results are recorded as follows. When the crack height ratio of the concrete specimen is 0.2, =20mm, W c The value is 118.8N, and the predicted crack initiation load is 6182N, with a corresponding 95% guarantee rate range of 5138N to 7227N. When the joint height ratio of the concrete specimen is 0.3, =30mm, The crack initiation load is 117.1N, and the crack initiation load predicted by this invention is 4833N, with a corresponding 95% guarantee rate range of 4014N to 5651N.

[0052] (3) Using the traditional crack tip local strain method, the initiation loads of the five specimens in the same group when the crack height ratio was 0.2 were 5786N, 6632N, 6415N, 7107N, and 6100N, respectively. The calculated mean value was 6408N, and the predicted value of this invention differed from the measured mean value by 226N, with a relative error of only about 3.5%. When the crack height ratio was 0.3, the initiation loads of the five specimens were 4765N, 5013N, 4908N, 4839N, and 5135N, respectively. The calculated mean value was 4932N, and the predicted value of this invention differed from the measured mean value by 99N, with a relative error of about 2.01%. Meanwhile, as... Figure 7 and Figure 8 As shown, all measured results are reasonably covered by the predicted ranges of 5138–7227 N and 4014–5651 N, indicating that the method of the present invention also has good applicability to larger concrete specimens.

[0053] The predicted values, measured values, and relative error results for Examples 1-2 are shown in Table 1. As can be seen from Table 1, the concrete cracking load predicted using the method of this invention is quite close to the measured results of the traditional local strain method at the crack tip. For the four working conditions involved in the above examples, the relative errors between the predicted values ​​and the measured average values ​​are 6.4%, 3.3%, 3.5%, and 2.0%, respectively, all at a low level, indicating that the method of this invention has good prediction accuracy. Meanwhile, the measured cracking loads of each group of specimens all fall within the 95% guarantee rate prediction range given by this invention, indicating that the prediction method established by this invention can not only reasonably reflect the stress characteristics of concrete cracking, but also better reflect the dispersion and fluctuation range of the cracking load of concrete as a multiphase composite material with a complex internal structure, demonstrating good reliability and stability.

[0054] Furthermore, from the smaller specimens in Example 1 to the larger specimens in Example 2, the method of the present invention demonstrates good applicability under different sizes and crack height ratios, indicating that the method can be used to predict and evaluate the crack initiation load of concrete specimens of different sizes. In summary, the method of the present invention has a clear mechanical basis and good engineering practical value, and can provide a reliable basis for concrete crack initiation load analysis, crack resistance performance evaluation, and related numerical simulations.

[0055] Table 1. Summary of comparison between predicted values ​​of concrete cracking load and measured values ​​using traditional methods in Examples 1-2 In summary, this invention, by measuring the three-point bending fracture ultimate load of mortar specimens corresponding to the target concrete and combining it with a nonlinear fracture mechanics model, can accurately predict the crack initiation load of concrete specimens of different sizes and crack height ratios. Compared with the traditional local strain method at the crack tip, this invention does not require precise placement of strain gauges near the crack tip, nor does it rely on local strain abrupt changes or retraction phenomena to determine the crack initiation moment. This avoids the shortcomings of traditional methods, such as high requirements for measuring point placement, high requirements for the stability of the testing process, and sometimes difficulty in accurately capturing the crack initiation moment. Furthermore, the predicted results of this invention agree well with the measured results and can provide a reasonable prediction range with a 95% guarantee rate. Therefore, the method of this invention for determining the concrete crack initiation load is not only reliable and effective, but also simpler and more convenient to test, and can be implemented under ordinary test conditions.

[0056] Those skilled in the art should recognize that the above embodiments are only used to illustrate this application and are not intended to limit this application. Any appropriate changes and variations made to the above embodiments within the essential spirit and scope of this application fall within the scope of protection claimed in this application.

Claims

1. A method for predicting concrete crack initiation load based on a nonlinear fracture model, characterized in that, Includes the following steps: S1. Define the parameter system for the target concrete and its corresponding mortar precast notched beam in a three-point bending test. The parameters of the target concrete specimen include the concrete beam height. , width of concrete beam Initial notch length of concrete beam , concrete beam span and the self-weight of concrete beams The corresponding mortar specimen parameters include the height of the mortar beam. mortar beam width Initial notch length of mortar beam mortar beam span and the self-weight of the mortar beam ; S2. Prepare precast mortar notched beam specimens according to the composition after removing coarse aggregate from the target concrete mix proportion. Conduct three-point bending fracture tests on the precast mortar notched beam specimens to obtain the ultimate load at fracture of the mortar specimens. The tensile strength of the mortar specimen, unaffected by size effects, is determined according to the following formula. : ； in, It is the coefficient of variation that reflects the discontinuous characteristics of mortar. The average aggregate particle size in the mortar. The joint height ratio of the mortar; It is a shape function; S3. Establish a nonlinear fracture model for concrete under crack initiation conditions, assuming that when the concrete specimen reaches the crack initiation load... At that time, the strength of the mortar matrix had fully developed, and the initial notch tip formation length was... The fracture process zone, wherein the tensile stress in the fracture process zone is taken as the mortar tensile strength. ,in, The coefficient of variation is used to reflect the discontinuous characteristics of concrete. The average coarse aggregate particle size in concrete; S4. Establish the equilibrium equation based on the section force equilibrium condition under the concrete cracking state, and solve for the concrete cracking load according to the following formula. : ； This is the predicted value of the target concrete cracking load.

2. The method for predicting concrete cracking load according to claim 1, characterized in that, Also includes according to Determine the reasonable fluctuation range of the target concrete crack initiation load. The statistically obtained mortar tensile strength mean and its standard deviation Substituting into the equilibrium equation, the upper and lower limits of the reasonable fluctuation range satisfy: 。 3. The method for predicting concrete cracking load according to claim 2, characterized in that, The reasonable fluctuation range is the 95% guarantee range of the concrete cracking load.

4. The method for predicting concrete cracking load according to claim 1, characterized in that, The initial notch to beam height ratio of the mortar or concrete specimen is 0.1 to 0.

5.

5. The method for predicting concrete cracking load according to any one of claims 1-4, characterized in that, The method is applicable to composite materials that contain at least a mortar phase and a coarse aggregate phase.

6. The method for predicting concrete cracking load according to any one of claims 1-4, characterized in that, The method can be used to predict the crack initiation load, evaluate crack resistance, and perform related numerical simulation analysis on precast concrete notched beam specimens of different sizes.

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