A method for determining the fatigue index of cement concrete considering alternating tensile and compressive loads

Abstract

The present invention discloses a method for determining the fatigue index of cement concrete considering alternating tensile and compressive loads, including several steps such as conducting indoor tests, Weibull distribution test of test results, and determination of fatigue index. The present invention considers the influence of alternating tensile and compressive loads on the fatigue damage of cement concrete, proposes a method for establishing a more widely representative fatigue equation, probabilizes the fatigue index of cement concrete through Weibull distribution, and improves the reliability and scientificity of pavement structure design.

Description

Technical Field

[0001] The present invention belongs to the technical field of cement pavement design, and particularly relates to a method for determining the fatigue index of cement concrete considering alternating tensile and compressive loads. Background Art

[0002] The current cement pavement design code in China uses the comprehensive fatigue stress of temperature and load to check the ultimate state with the flexural tensile strength of cement concrete as the index. When calculating the load fatigue stress of the cement concrete pavement slab, the fatigue parameters of cement concrete are required, which are determined by fitting the S-N fatigue equation under double logarithm through fatigue test data. The fatigue parameters adopted in the current code are mainly determined by fatigue tests carried out by institutions and universities such as Zhejiang Provincial Institute, Tongji University, and Xi'an Highway and Transportation University (now Chang'an University) during the period from 1980 to 2000. The value of the fatigue parameter θ of the cement concrete pavement in the current Highway Cement Concrete Pavement Design Code (JTG D40-2011) is 0.057.

[0003] Existing research shows that the fatigue behavior of cement concrete under alternating tensile and compressive loads is different from that under conventional loads. However, the existing test data has a low-high stress ratio R value range of 0 to 0.5, and the case where R is less than 0 is not considered, that is, the stress state of alternating tensile and compressive of concrete is not considered. In fact, the stress state of alternating tensile and compressive exists when there is a specific temperature gradient, poor interface contact, or the coupling of slab bottom support and vehicle load. This indicates 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 for the mismatch between the designed life and the service life of existing cement pavements.

[0004] In summary, it is an urgent technical problem to be solved at present to improve the existing test method considering the stress state of alternating tensile and compressive of cement concrete, establish a widely representative fatigue bending equation for cement concrete, and thus determine the fatigue index of cement concrete materials to provide a theoretical basis for improving the service life of cement pavements. 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 alternating tensile and compressive loads. Based on the traditional method for establishing the fatigue equation of cement concrete, the present invention expands the range of fatigue test design parameters and improves the bending test fixture of cement concrete to form a method for establishing the bending fatigue equation of cement concrete considering alternating tensile and compressive loads, thereby determining the fatigue index of cement concrete.

[0006] To solve the above problems, the technical solution proposed by the present invention is as follows:

[0007] A method for determining the fatigue index of cement concrete considering alternating tensile and compressive loads, comprising the following steps:

[0008] S1. Conduct indoor tests

[0009] First, conduct parallel test designs and determine the value ranges and intervals of the stress ratio S and the low-to-high stress ratio R; among them, the lower limit of the value of R is less than 0;

[0010] Next, prepare specimens according to the test design;

[0011] Finally, use MTS with an eight-point bending fatigue test fixture to conduct fatigue tests to obtain the fatigue test data for each combination of S and R; among them, the fatigue tests are loaded in the form of a sine wave, and the maximum load is set to P max and the minimum load is P min , the maximum load P max and the minimum load P min The calculation formulas are as follows;

[0012] ;

[0013] Among them: h is the height of the specimen, in mm; b is the width of the specimen, in mm; L is the support spacing, in mm, f r is the flexural tensile strength, in Mpa;

[0014] S2. Weibull distribution test of fatigue test results

[0015] First, calculate the failure probability of each group of fatigue test data p , and the calculation formula is:

[0016]

[0017] Among them: n is the number of parallel tests; i is the serial number of the data;

[0018] Next, perform linear fitting on each group of fatigue test data for each combination of S and R to determine the parameters m and t0 in the Weibull distribution expression in double logarithmic form. Substitute the fitted parameters m and t0 into the Weibull distribution expression in double logarithmic form to obtain the Weibull probability formula for fatigue life; among them, the Weibull distribution expression in double logarithmic form is:

[0019]

[0020] Among them, m and t 0 are the shape parameter and the scale parameter respectively; N f is the fatigue life obtained from the test.

[0021] S3. Fatigue Index Determination

[0022] First, according to the fitted Weibull probability formula of fatigue life, determine the probabilistic fatigue life with a failure probability in the range of 0.05 - 0.5 for each combination of S and R;

[0023] Next, perform a linear fit of the double logarithmic fatigue equation based on the calculated probabilistic fatigue life to determine the double logarithmic fatigue equation at different failure probabilities. The expression of the double logarithmic fatigue equation is:

[0024]

[0025] where, a and b are both dimensionless parameters; N is the predicted fatigue life.

[0026] Finally, extract the parameters b of the fatigue equation at different failure probabilities. The b at different failure probabilities is the corresponding fatigue index.

[0027] Specifically, the expressions of S and R are:

[0028]

[0029] where: σ max and σ min are the maximum tensile stress and the minimum tensile stress respectively, in MPa; f r is the flexural tensile strength, in MPa.

[0030] Specifically, both S and R are variables during the experimental design. The value range of R is -1 to 1, and the value range of S is 0 to 1.

[0031] Specifically, the interval of the value of R is 0.25, and the interval of the value of S is 0.1.

[0032] Specifically, adopt the T0551 - 2020 test method in the "Test Regulations for Cement and Cement Concrete in Highway Engineering" (JTG 3420 - 2020) to form the cement concrete specimens.

[0033] Specifically, the size of the specimens is 150mm×150mm×550mm.

[0034] Specifically, adopt the T0558 - 2005 test method in the "Test Regulations for Cement and Cement Concrete in Highway Engineering" (JTG 3420 - 2020) to conduct the flexural tensile strength test and determine f r, and calculate the maximum and minimum loads required for the MTS loading program according to the calculation formula of T 0588-1 in T 0558-2005 and the test plan.

[0035] Specifically, during the fatigue test, the loading frequency is 10 Hz.

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] 1. The present invention takes into account the influence of alternating tensile and compressive loads on the fatigue damage of cement concrete. When designing the test, the value range of the parameter R in the double logarithmic fatigue equation of cement concrete is below 0, and the alternating tensile and compressive fatigue loading is realized through the MTS and the eight-point bending fatigue test fixture. The established fatigue equation has a more extensive representativeness and can cover most of the fatigue load characteristics of cement concrete pavements.

[0038] 2. The present invention introduces the probabilistic fatigue life through the Weibull distribution, thus probabilizing the fatigue index of cement concrete, adapting to the reliability-based design method of the current cement concrete pavement design code, taking values for the fatigue index according to different reliability requirements, conforming to the fatigue characteristics of concrete materials, and improving the reliability and scientificity of pavement structure design.

[0039] 3. The present invention gives a method for determining the fatigue index considering the influence of alternating tensile and compressive loads. Any new cement concrete material with an unknown fatigue index can adopt this method to determine its fatigue index, providing a solution to the lack of fatigue index when new materials are used in cement concrete pavement design.

[0040] 4. The determined fatigue equation is a probabilistic fatigue equation, and the predicted fatigue lives are different under different failure probabilities. The material fatigue index obtained according to the fatigue equation is also a probabilistic index, and the material fatigue indices are different under different failure probabilities, and can be taken according to the reliability requirements of the project. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is a schematic flow chart of the method for determining the fatigue index provided by the present invention;

[0042] Figure 2 is a physical diagram of the eight-point bending fatigue test on the specimen in the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0043] The present invention will be further described below with reference to the drawings and specific embodiments, but this does not limit the protection scope of the present invention.

[0044] See Figure 1 , a method for determining the fatigue index considering the alternating tensile and compressive loads of cement concrete, comprising the following steps:

[0045] S1. Conduct indoor tests;

[0046] First, conduct experimental design according to the key test parameters S (stress ratio) and R (low-to-high stress ratio). Design the value ranges and value intervals of S and R. When considering the influence of alternating tensile and compressive loads, the lower limit of the value 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 as follows:

[0047]

[0048] Where: σ max and σ min are the maximum and minimum tensile stresses, in MPa; f r is the flexural tensile strength, in MPa.

[0049] Next, refer to the test method T 0551-2020 in the "Code for Tests of Cement and Cement Concrete for Highway Engineering" (JTG 3420-2020) to form cement concrete specimens. The size of the specimens is 150mm×150mm×550mm.

[0050] Next, refer to the test method T 0558-2005 in the "Code for Tests of Cement and Cement Concrete for Highway Engineering" (JTG 3420-2020) to conduct flexural tensile strength tests and determine f r . Combine the calculation formula T 0588-1 in T 0558-2005 and the test plan to calculate the maximum and minimum loads ( P max and P min ), to prepare for setting the loading program of the MTS (universal material testing machine). Among them, the calculation formulas for the maximum and minimum loads ( P max and P min ) are as follows:

[0051]

[0052] Where: h is the height of the specimen, in mm; b is the width of the specimen, in mm; L is the support spacing, in mm.

[0053] Finally, as Figure 2 shown, use MTS with an eight-point bending fatigue test fixture to conduct fatigue tests to obtain the fatigue test data for each group under each combination of S and R. Use a sine wave form for loading, and set the maximum and minimum loads as ( P max and P min) with a loading frequency of 10 Hz.

[0054] S2. Weibull distribution test of test results;

[0055] First, calculate the failure probability of each group of data p , and the calculation formula is:

[0056]

[0057] where: n is the number of parallel tests; i is the serial number of the data.

[0058] Next, perform linear fitting on the data under each S and R combination to determine the parameters m and t0 in the Weibull distribution expression in double logarithmic form, R 2 (Coefficient of determination) greater than 0.6 is considered that the fitting result conforms to the Weibull distribution relatively well. The expression is:

[0059]

[0060] where, m and t 0 are the shape parameter and scale parameter respectively; N f is the fatigue life obtained from the test.

[0061] S3. Determination of fatigue index.

[0062] First, according to the fitted Weibull probability formula of fatigue life, determine the probabilistic fatigue life within the range of failure probability from 0.05 to 0.5 for each S and R combination.

[0063] Next, perform linear fitting of the double logarithmic fatigue equation based on the calculated probabilistic fatigue life to determine the double logarithmic fatigue equation under different failure probabilities. The expression of the double logarithmic fatigue equation is:

[0064]

[0065] where, a and b are both dimensionless parameters; N is the predicted fatigue life.

[0066] Finally, extract the parameters of the fatigue equation under different failure probabilities b . The b under different failure probabilities is the corresponding fatigue index.

[0067] The present invention will be further described below in conjunction with specific embodiments.

[0068] S1. Conduct indoor tests;

[0069] First, the experimental design was carried out. The value range of R was set as -0.5 to 0.5, and the value range of S was set as 0.5 to 0.9. The interval of R value was 0.25, and the interval of S value was 0.1. Considering the test duration comprehensively, the experimental design is shown in Table 1, where the numbers in the table represent the number of parallel tests.

[0070] Table 1 Experimental Design

[0071]

[0072] Next, according to the test method of T 0551-2020 in the "Test Regulations for Cement and Cement Concrete in Highway Engineering" (JTG 3420-2020), the cement concrete specimens were molded. Combining with the experimental design in Table 1, at least 52 specimens needed to be molded in total.

[0073] Next, referring to the test method of T 0558-2005 in the "Test Regulations for Cement and Cement Concrete in Highway Engineering" (JTG 3420-2020), the flexural tensile strength test was carried out to determine f r , the flexural tensile strength of three specimens was tested, the maximum failure load was read, and the flexural tensile strength was calculated through Equation T 0588-1, as shown in Table 2.

[0074] Table 2 Strength Test Results

[0075]

[0076] Calculate the P max and P min corresponding to the 19 groups of tests in Table 1. Taking R as -0.5 and S as 0.5 as an example, the calculation process is as follows:

[0077]

[0078] Calculate the P max and P min corresponding to all test groups according to the above calculation process, as shown in Table 3.

[0079] Table 3 P max and P min Calculate

[0080]

[0081] Finally, the fatigue test was carried out using MTS with an eight-point bending fatigue test fixture, as Figure 2As shown. Sine wave form is adopted for loading, and the maximum and minimum loads are set to ( P max and P min ), and the loading frequency is 10 Hz.

[0082] S2. Weibull distribution test of test results;

[0083] The test data with R being -0.25 are shown in Table 4.

[0084] Table 4 Partial fatigue life test results

[0085]

[0086] First, calculate the failure probability of each group of data p , taking the test data with R being -0.25 and S being 0.6 as an example, p the calculation process is as follows:

[0087]

[0088] Next, perform linear fitting on the data under each S and R combination to determine the parameters m and t0 in the Weibull distribution expression in double logarithmic form. Taking the data with R being -0.25 as an example, the fitting results are shown in Table 5.

[0089] Table 5 Parameter fitting results

[0090]

[0091] Then, the probability life calculation formula when R is -0.25 and S is 0.6 is:

[0092]

[0093] S3. Determination of fatigue index.

[0094] First, according to the fitted Weibull probability formula of fatigue life, determine the probability fatigue life within the range of failure probability from 0.05 to 0.5 for each S and R combination. Taking R being -0.25 and S being 0.6 as an example, calculate the probability fatigue life when the failure probabilities are 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.5. The calculation process when the failure probability is 0.05 is as follows:

[0095]

[0096] The calculation results for other failure probabilities when R is -0.25 are shown in Table 6.

[0097] Table 6 Fatigue life under different failure probabilities

[0098]

[0099] Calculate the fatigue life with different failure probabilities for all combinations of R and S according to the same method.

[0100] Next, perform a linear fit of the double-logarithmic fatigue equation based on the calculated probabilistic fatigue life to determine the double-logarithmic fatigue equation at different failure probabilities. The expression of the double-logarithmic fatigue equation is:

[0101]

[0102] The fatigue parameters obtained by fitting at different failure probabilities are shown in Table 7.

[0103] Table 7 Values of fatigue parameters at different failure probabilities

[0104]

[0105] Finally, according to Table 7, the material fatigue indices at different failure probabilities can be determined, that is, the b . In Article B.2.3 of the "Code for Design of Highway Cement Concrete Pavement" (JTG_D40 - 2011), relevant regulations on the values of the material fatigue indices of cement concrete are given. Except for steel fiber cement concrete, which gives the calculation method of the fatigue index under different steel fiber related parameters, the fatigue indices of other cement concrete materials are fixed values without giving the calculation method. For special concrete materials, when their fatigue performance is different from that of conventional cement concrete materials, the fatigue index of this material can be accurately determined by this method. In addition, the relevant regulations in Article B.2.3 do not consider the discreteness of cement concrete materials, and the material fatigue index is a fixed value, while the material fatigue index given by the present invention is a probabilistic value and can be taken according to the reliability requirements of the project.

[0106] The above are only the preferred embodiments of the present invention and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Therefore, any simple modifications, equivalent changes, and decorations made to the above embodiments based on the technical essence of the present invention without departing from 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 the fatigue index of cement concrete considering alternating tensile and compressive loads, characterized in that It includes the following steps: S1. Conduct indoor tests First, carry out parallel test design, and determine the value ranges and value intervals of the stress ratio S and the low-to-high stress ratio R; among them, the lower limit of the value of R is less than 0; Next, prepare specimens according to the test design; Finally, an MTS is used in conjunction with an eight-point bending fatigue test fixture to conduct fatigue tests, obtaining the fatigue test data for each group under each S and R combination; among them, the fatigue test is carried out with a sine wave form of loading, setting the maximum load to P max and the minimum load to P min , the maximum load P max and the minimum load P min are calculated as follows; ； Where: h is the height of the test piece, in mm; b is the width of the test piece, in mm; L is the span between supports, in mm, f r is the flexural tensile strength, in Mpa, S2. Weibull distribution test of fatigue test results First, calculate the failure probability of each group of fatigue test data p , and the calculation formula is as follows: ； Where: n is the number of parallel tests; i is the serial number of the data; Next, perform linear fitting on the fatigue test data of each group under each combination of S and R, determine the parameters m and t0 in the Weibull distribution expression in double logarithmic form, and substitute the obtained parameters m and t0 into the Weibull distribution expression in double logarithmic form to obtain the Weibull probability formula of fatigue life; among them, the Weibull distribution expression in double logarithmic form is: ； Among them, m and t 0 are the shape parameter and the scale parameter respectively; N f is the fatigue life obtained from the test; S ​ ​ ； Among them, a and b are both dimensionless parameters; N is the predicted fatigue life; Finally, extract the parameters of the fatigue equation under different failure probabilities b , and the b under different failure probabilities is the corresponding fatigue index.

2. The method for determining the fatigue index of cement concrete according to claim 1, wherein: ​ ； Wherein: ​ max and ​ min are the maximum tensile stress and the minimum tensile stress, respectively, in MPa; f r is the flexural tensile strength, in MPa.

3. The method for determining the fatigue index of cement concrete according to claim 1, characterized in that: ​ 4. The method for determining the fatigue index of cement concrete according to claim 1, characterized in that: ​ 5. The method for determining the fatigue index of cement concrete according to claim 1, characterized in that: ​ 6. The method for determining the fatigue index of cement concrete according to claim 1, wherein: ​

Images