Cement concrete fatigue index determination method considering tension-compression alternating load

Abstract

The invention discloses a cement concrete fatigue index determination method considering tension-compression alternating load. The cement concrete fatigue index determination method comprises the steps of indoor test development, test result Weibull distribution test and fatigue index determination. According to the method, the influence of the tension-compression alternating load on the fatigue damage of the cement concrete is considered, a wider representative fatigue equation establishment method is provided, the fatigue index of the cement concrete is probabilized through Weibull distribution, and the reliability and scientificity of pavement structure design are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of cement pavement design, and in particular relates to a method for determining a cement concrete fatigue index taking into account tension-compression alternating loads. Background Art

[0002] The current cement pavement design specification in my country uses temperature and load comprehensive fatigue stress to check the limit state with cement concrete flexural tensile strength as an indicator. The fatigue parameters of cement concrete are required to calculate the load fatigue stress of cement pavement panels, which are determined by fitting the SN fatigue equation under double logarithms with fatigue test data. The fatigue parameters used in the current specification are mainly determined by fatigue tests conducted by institutions and universities such as Zhejiang Provincial Academy, Tongji University, and Xi'an University of Highways and Transportation (now Chang'an University) from 1980 to 2000. The value of the fatigue parameter θ of cement concrete pavement in the current highway cement concrete pavement design specification (JTG D40-2011) is 0.057.

[0003] Existing studies have shown that the fatigue behavior of cement concrete under alternating tension and compression loads is different from that under conventional loads. However, the low-to-high stress ratio R of existing test data ranges from 0 to 0.5, and does not consider the case where R is less than 0, that is, the stress state of alternating tension and compression of concrete is not considered. In fact, the stress state of alternating tension and compression exists under certain temperature gradients, poor interlayer contact, or coupling of slab bottom support and vehicle loads. This shows that the existing fatigue equation is not representative of the fatigue behavior of concrete materials under specific stress states, which may be one of the reasons why the design life of existing cement pavements does not correspond to the service life.

[0004] In summary, it is a technical problem that needs to be solved urgently to improve the existing test method by considering the alternating tension and compression stress state of cement concrete and establish a fatigue bending equation of cement concrete with broad representativeness, so as to determine the fatigue index of cement concrete materials and provide a theoretical basis for improving the service life of cement pavement. Summary of the invention

[0005] The main purpose of the present invention is to provide a method for determining the fatigue index of cement concrete considering the alternating tension and compression loads. The present invention is based on the traditional cement concrete fatigue equation establishment method, expands the range of fatigue test design parameters, improves the cement concrete bending test fixture, and forms a method for establishing the cement concrete bending fatigue equation considering the alternating tension and compression loads, thereby determining the fatigue index of cement concrete.

[0006] To solve the above problems, the technical solutions proposed by the present invention are as follows: A method for determining fatigue index of cement concrete considering alternating tension and compression loads comprises the following steps: S1. Conduct indoor experiments Firstly, a parallel test design is carried out, and the value range and value interval of the stress ratio S and the low-high stress ratio R are proposed; among which, the lower limit of R is less than 0; Next, the test specimens were prepared according to the experimental design; Finally, the fatigue test was carried out using MTS in combination with an eight-point bending fatigue test fixture to obtain fatigue test data for each group under each combination of S and R. The fatigue test was loaded in the form of a sine wave, and the maximum load was set to P max and the minimum load is P min , maximum load P max and minimum load P min The calculation formula is as follows; ;

[0007] Where: h is the specimen height, mm; b is the specimen width, mm; L is the support spacing, mm, f r is the bending tensile strength, MPa; S2. Weibull distribution test of fatigue test results First, calculate the failure probability of each group of fatigue test data p , the calculation formula is:

[0008] Where: n is the number of parallel experiments; i is the sequence number of the data; Next, a linear fit is performed on each group of fatigue test data under each combination of S and R to determine the parameters m and t in the double logarithmic Weibull distribution expression. 0 , the fitted parameters m and t 0 Substituting into the double logarithmic Weibull distribution expression, the fatigue life Weibull probability formula is obtained; among which, the double logarithmic Weibull distribution expression is:

[0009] in, m and t 0 are shape parameter and scale parameter respectively; N f is the fatigue life obtained from the test.

[0010] S3. Fatigue index determination Firstly, according to the fitted Weibull probability formula of fatigue life, the probabilistic fatigue life with failure probability ranging from 0.05 to 0.5 under each combination of S and R is determined; Next, a linear fit of the double logarithmic fatigue equation is performed based on the calculated probabilistic fatigue life to determine the double logarithmic fatigue equation under different failure probabilities. The double logarithmic fatigue equation is expressed as:

[0011] in, a and b All are dimensionless parameters; N is the predicted fatigue life.

[0012] Finally, extract the parameters of the fatigue equation at different failure probabilities b , under different failure probabilities b This is the corresponding fatigue index.

[0013] Specifically, the expressions of S and R are:

[0014] in: σ max , σ min are the maximum tensile stress and the minimum tensile stress, MPa, respectively; f r is the flexural strength, MPa.

[0015] Specifically, when designing the experiment, S and R are both variables, the value range of R is -1~1, and the value range of S is 0~1.

[0016] Specifically, the interval of R value is 0.25, and the interval of S value is 0.1.

[0017] Specifically, the T0511-2020 test method in the "Test Code for Cement and Cement Concrete for Highway Engineering" (JTG 3420-2020) is used to form cement concrete specimens.

[0018] Specifically, the size of the test piece is 150 mm×150 mm×550 mm.

[0019] Specifically, the flexural strength test was carried out using the T0558-2005 test method in the "Test Code for Cement and Cement Concrete for Highway Engineering" (JTG 3420-2020) to determine the f r , and calculate the maximum and minimum loads required for the MTS loading procedure based on the T 0588-1 calculation formula and test plan in T 0558-2005.

[0020] Specifically, during the fatigue test, the loading frequency is 10 Hz.

[0021] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention takes into account the influence of alternating tension and compression loads on fatigue damage of cement concrete. When designing the test, the value range of parameter R in the double logarithmic fatigue equation of cement concrete is set below 0, and alternating tension and compression fatigue loading is achieved through MTS and eight-point bending fatigue test fixture. The established fatigue equation has a wider range of representativeness and can cover most fatigue load characteristics of cement concrete pavements.

[0022] 2. The present invention introduces probabilistic fatigue life through Weibull distribution, thereby probabilizing the fatigue index of cement concrete, which is compatible with the reliability-based design method of the current cement concrete pavement design specification. The fatigue index is determined according to different reliability requirements, which conforms to the fatigue characteristics of concrete materials and improves the reliability and scientificity of pavement structure design.

[0023] 3. The present invention provides a method for determining fatigue index that takes into account the influence of alternating tension and compression loads. The fatigue index of any new cement concrete material with an unknown fatigue index can be determined by this method, and a solution to the lack of fatigue index when new materials are used in cement concrete pavement design is provided.

[0024] 4. The fatigue equation is determined to be a probabilistic fatigue equation. The fatigue life predicted under different failure probabilities is different. The material fatigue index obtained according to the fatigue equation is also a probabilistic index. The material fatigue index under different failure probabilities is different and can be determined according to the reliability requirements of the project. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a schematic flow chart of the fatigue index determination method provided by the present invention; Figure 2 This is a real picture of the eight-point bending fatigue test performed on the specimen in the present invention. DETAILED DESCRIPTION

[0026] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited thereby.

[0027] See also Figure 1 , a method for determining fatigue index of cement concrete considering alternating tension and compression loads, comprising the following steps: S1. Conduct indoor experiments; First, the test design is carried out based on the key test parameters S (stress ratio) and R (low-high stress ratio). The value range and value interval of S and R are designed. When considering the influence of alternating tension and compression loads, the lower limit of R should be less than 0, and the value intervals of S and R should be uniform. The expressions of S and R are:

[0028] in: σmax and σ min is the maximum and minimum tensile stress, MPa; f r is the flexural strength, MPa.

[0029] Next, the cement concrete specimens were formed according to the T 0511-2020 test method in the "Testing Procedures for Cement and Cement Concrete in Highway Engineering" (JTG 3420-2020). The size of the specimens was 150 mm × 150 mm × 550 mm.

[0030] Next, the bending tensile strength test was carried out according to the T 0558-2005 test method in the "Test Code for Cement and Cement Concrete for Highway Engineering" (JTG 3420-2020), and the f r . Combine the calculation formula and test scheme of T 0588-1 in T 0558-2005 to calculate the maximum and minimum loads ( P max and P min ) to prepare for setting up the MTS (universal testing machine) loading program. Among them, the maximum and minimum loads ( P max and P min ) is calculated as follows:

[0031] Where: h is the specimen height, mm; b is the specimen width, mm; L is the support spacing, mm.

[0032] Finally, if Figure 2 As shown, fatigue tests were performed using MTS with an eight-point bending fatigue test fixture to obtain fatigue test data for each group under each S and R combination. Sine wave loading was used, and the maximum and minimum loads were set to ( P max and P min ), the loading frequency is 10Hz.

[0033] S2. Weibull distribution test of test results; First, calculate the failure probability of each group of data p , the calculation formula is:

[0034] Where: n is the number of parallel experiments; i is the sequence number of the data.

[0035] Next, a linear fit is performed on the data under each combination of S and R to determine the parameters m and t in the double logarithmic Weibull distribution expression. 0 , R 2 (Determination coefficient) greater than 0.6 is considered to be highly consistent with the Weibull distribution. The expression is:

[0036] in, m and t 0 are shape parameter and scale parameter respectively; N f is the fatigue life obtained from the test.

[0037] S3. Fatigue index determination.

[0038] Firstly, according to the fitted Weibull probability formula of fatigue life, the probabilistic fatigue life with failure probability ranging from 0.05 to 0.5 under each combination of S and R is determined.

[0039] Next, a linear fit of the double logarithmic fatigue equation is performed based on the calculated probabilistic fatigue life to determine the double logarithmic fatigue equation under different failure probabilities. The double logarithmic fatigue equation is expressed as:

[0040] in, a and b All are dimensionless parameters; N is the predicted fatigue life.

[0041] Finally, extract the parameters of the fatigue equation at different failure probabilities b . b This is the corresponding fatigue index.

[0042] The present invention will be further described below in conjunction with specific embodiments.

[0043] S1. Conduct indoor experiments; First, the experimental design was carried out, and the R value range was proposed to be -0.5~0.5, the S value range was 0.5~0.9, the R value interval was 0.25, and the S value interval was 0.1. Taking the experimental duration into consideration, the experimental design is shown in Table 1. The numbers in the table represent the number of parallel experiments.

[0044] Table 1 Experimental design

[0045] Next, the cement concrete specimens were formed according to the T 0511-2020 test method in the "Test Code for Cement and Cement Concrete for Highway Engineering" (JTG 3420-2020). Combined with the test design in Table 1, a total of at least 52 specimens needed to be formed.

[0046] Next, the bending tensile strength test was carried out according to the T 0558-2005 test method in the "Test Code for Cement and Cement Concrete for Highway Engineering" (JTG 3420-2020) f r The flexural strength of three specimens was tested, the maximum failure load was read and the flexural strength was calculated by formula T 0588-1, as shown in Table 2.

[0047] Table 2 Strength test results

[0048] Calculate the corresponding values ​​of the 19 groups of tests in Table 1 P max and P min , taking R as -0.5 and S as 0.5 as an example, the calculation process is as follows:

[0049] Calculate the above calculation process for all test groups P max and P min , as shown in Table 3.

[0050] Table 3 P max and P min calculate

[0051] Finally, the fatigue test was carried out using MTS with an eight-point bending fatigue test fixture, such as Figure 2 As shown. Use sine wave to load, set the maximum and minimum loads to ( P max and P min ), the loading frequency is 10Hz.

[0052] S2. Weibull distribution test of test results; The experimental data with R=-0.25 are shown in Table 4.

[0053] Table 4 Some fatigue life test results

[0054] First, calculate the failure probability of each group of data p , taking the test data of R = -0.25 and S = 0.6 as an example, p The calculation process is:

[0055] Next, a linear fit is performed on the data under each combination of S and R to determine the parameters m and t in the double logarithmic Weibull distribution expression. 0 , taking the data with R=-0.25 as an example, the fitting results are shown in Table 5.

[0056] Table 5 Parameter fitting results

[0057] Then, the probability life calculation formula when R is -0.25 and S is 0.6 is:

[0058] S3. Fatigue index determination.

[0059] First, according to the fitted Weibull probability formula of fatigue life, the probabilistic fatigue life with a failure probability range of 0.05~0.5 is determined for each combination of S and R. Taking R as -0.25 and S as 0.6 as an example, the probabilistic fatigue life with a failure probability of 0.05, 0.1, 0.15, 0.2, 025, 0.3, 0.35, 0.4, and 0.5 is calculated. The calculation process when the failure probability is 0.05 is as follows:

[0060] The calculation results under other failure probabilities when R is -0.25 are shown in Table 6.

[0061] Table 6 Fatigue life under different failure probabilities

[0062] The fatigue life of all R and S combinations with different failure probabilities is calculated using the same method.

[0063] Next, a linear fit of the double logarithmic fatigue equation is performed based on the calculated probabilistic fatigue life to determine the double logarithmic fatigue equation under different failure probabilities. The double logarithmic fatigue equation is expressed as:

[0064] The fatigue parameters under different failure probabilities obtained by fitting are shown in Table 7.

[0065] Table 7 Values ​​of fatigue parameters under different failure probabilities

[0066] Finally, the material fatigue index under different failure probabilities can be determined according to Table 7, that is, b . Article B.2.3 of the "Highway Cement Concrete Pavement Design Code" (JTG_D40-2011) provides relevant provisions for the value of the material fatigue index of cement concrete. Except for steel fiber cement concrete, which provides a method for calculating the fatigue index under different steel fiber related parameters, the fatigue index of other cement concrete materials are fixed values ​​and no calculation method is given. For special concrete materials, when their fatigue properties are different from those of conventional cement concrete materials, this method can accurately determine the fatigue index of the material. In addition, the relevant provisions of Article B.2.3 do not take into account the discreteness of cement concrete materials, and the material fatigue index is a fixed value, while the material fatigue index given in the present invention is a probability value, which can be taken according to the reliability requirements of the project.

[0067] The above is only a preferred embodiment of the present invention, and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment, it is not intended to limit the present invention. Therefore, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the scope of protection of the technical solution of the present invention.

Claims

1. A method for determining fatigue index of cement concrete considering alternating tension and compression loads, characterized in that: The steps include: S1. Conduct indoor experiments Firstly, a parallel test design is carried out, and the value range and value interval of the stress ratio S and the low-high stress ratio R are proposed; among which, the lower limit of R is less than 0; Next, the test specimens were prepared according to the experimental design; Finally, the fatigue test was carried out using MTS in combination with an eight-point bending fatigue test fixture to obtain fatigue test data for each group under each combination of S and R. The fatigue test was loaded in the form of a sine wave, and the maximum load was set to P max and the minimum load is P min , maximum load P max and minimum load P min The calculation formula is as follows; ； Where: h is the specimen height, mm; b is the specimen width, mm; L is the support spacing, mm, f r is the bending tensile strength, MPa, S2. Weibull distribution test of fatigue test results First, calculate the failure probability of each group of fatigue test data p , the calculation formula is: ； Where: n is the number of parallel experiments; i is the sequence number of the data; Next, linear fitting is performed on each group of fatigue test data under each combination of S and R to determine the parameters m and t0 in the double logarithmic Weibull distribution expression. The fitted parameters m and t0 are substituted into the double logarithmic Weibull distribution expression to obtain the fatigue life Weibull probability formula; wherein, the double logarithmic Weibull distribution expression is: ； in, m and t 0 are shape parameter and scale parameter respectively; N f is the fatigue life obtained from the test; S3. Fatigue index determination Firstly, according to the fitted Weibull probability formula of fatigue life, the probabilistic fatigue life with failure probability ranging from 0.05 to 0.5 under each combination of S and R is determined; Next, a linear fit of the double logarithmic fatigue equation is performed based on the calculated probabilistic fatigue life to determine the double logarithmic fatigue equation under different failure probabilities. The double logarithmic fatigue equation is expressed as: ； in, a and b All are dimensionless parameters; N is the predicted fatigue life; Finally, extract the parameters of the fatigue equation at different failure probabilities b , under different failure probabilities b This is the corresponding fatigue index.

2. The method for determining the fatigue index of cement concrete according to claim 1, characterized in that: The expressions for S and R are: ； in: σ max , σ min are the maximum tensile stress and the minimum tensile stress, MPa, respectively; f r is the flexural strength, MPa.

3. The method for determining the fatigue index of cement concrete according to claim 1, characterized in that: When designing the experiment, S and R are both variables, the value range of R is -1~1, and the value range of S is 0~1.

4. The method for determining the fatigue index of cement concrete according to claim 1, characterized in that: The size of the specimen is 150mm×150mm×550mm.

5. The method for determining the fatigue index of cement concrete according to claim 1, characterized in that: During fatigue testing, the loading frequency was 10 Hz.

6. The method for determining the fatigue index of cement concrete according to claim 1, characterized in that: At least three parallel experiments were designed for each combination of S and R, and the test results were subjected to Weibull distribution test.

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