A method for normalizing fatigue damage in asphalt mixtures

Abstract

This invention discloses a method for normalizing fatigue damage in asphalt mixtures, belonging to the field of road engineering technology. The method includes the following steps: conducting fatigue loading cyclic tests on asphalt mixtures; fitting a residual strength decay model using a power function based on the test results; constructing a cumulative fatigue damage model based on the residual strength decay model; characterizing the strength of the asphalt mixture under different test conditions along the tensile and compressive meridians using equivalent stress; calculating the fatigue stress ratio of the asphalt mixture under three-dimensional stress state based on the strength yield surface theory; constructing a fatigue normalization equation based on the fatigue stress ratio; and constructing a fatigue damage normalization model for asphalt mixtures based on the cumulative fatigue damage model and the fatigue normalization equation. This invention uses a fatigue damage normalization method to solve the problem of the difficulty in objectively characterizing the fatigue damage variation law of asphalt mixtures under three-dimensional stress state.

Description

Technical Field

[0001] This invention belongs to the field of road engineering technology, and specifically relates to a method for normalizing fatigue damage of asphalt mixtures. Background Technology

[0002] Asphalt pavement is a typical artificial, strip-shaped, three-dimensional structure that is exposed to complex and changing outdoor conditions for extended periods. Its service environment is harsh, and it is primarily composed of asphalt mixtures, which are viscoelastic-plastic materials made from asphalt and aggregates. These mixtures are extremely sensitive to changes in traffic loads and humid, hot environments. Under the coupled effects of vehicle loads and environmental factors, microcracks appear within the pavement, gradually evolving into macrocracks. The appearance of cracks leads to a decrease in pavement performance and affects its service life. Currently, scientific preventative maintenance techniques play a crucial role in extending pavement service life. The key to these techniques lies in understanding the evolution mechanism of pavement performance under multi-field coupling effects and its predictive model; that is, establishing a nonlinear damage evolution model of pavement materials throughout their entire life cycle under complex service conditions.

[0003] Existing research on fatigue damage of asphalt mixtures does not employ a unified experimental method for stress state and fatigue damage model. Furthermore, since any point within the asphalt mixture structure is under three-dimensional stress, it is difficult to objectively characterize the fatigue damage variation law of asphalt pavement under three-dimensional stress state using a linear fatigue damage model under simple experimental conditions. Summary of the Invention

[0004] The purpose of this invention is to provide a method for normalizing fatigue damage in asphalt mixtures, in order to solve the problem that it is currently difficult to objectively characterize the fatigue damage variation law of asphalt mixtures under three-dimensional stress.

[0005] The technical solution adopted in this invention is a method for normalizing fatigue damage in asphalt mixtures, comprising the following steps:

[0006] S1. Conduct fatigue loading cyclic tests on asphalt mixtures under different stress states, temperatures, loading frequencies, loading levels, and number of cycles. Based on the test results, use a power function to fit the residual strength decay model.

[0007] S2. Construct a cumulative fatigue damage model based on the residual strength decay model;

[0008] S3. The equivalent stress is used to characterize the strength of asphalt mixtures under different test conditions on the tensile and compressive meridians;

[0009] S4. Calculate the fatigue stress ratio of asphalt mixture under three-dimensional stress state based on the strength yield surface theory;

[0010] S5. Construct a fatigue normalization equation based on the fatigue stress ratio;

[0011] S6. Construct a fatigue damage normalization model for asphalt mixtures based on the cumulative fatigue damage model and the fatigue normalization equation.

[0012] Furthermore, in step S1, the stress state includes direct tension, uniaxial compression, and indirect tension.

[0013] Furthermore, in step S1, the residual intensity attenuation model is:

[0014]

[0015] In the formula, S N S0 is the residual strength of the asphalt mixture after N fatigue loading cycles; S0 is the initial strength of the asphalt mixture; N is the number of fatigue loading cycles; N0 f σ represents the fatigue life of the asphalt mixture, i.e., the maximum number of cycles without damage or fracture; σ represents the fatigue loading stress; γ1 and γ2 are model parameters that have no practical significance and are obtained by fitting a power function.

[0016] Furthermore, in step S2, the cumulative fatigue damage model is as follows:

[0017]

[0018] In the formula, D(N) represents the cumulative fatigue damage of the asphalt mixture.

[0019] Furthermore, in step S3, the equivalent stress on the tensile meridian and the compressive meridian is:

[0020]

[0021] In the formula, σ e t To determine the equivalent stress along the stretching meridian, σ e c To represent the equivalent stress along the compressive meridian, I1 is the first stress invariant, I1 = σ1 + σ2 + σ3, where σ1, σ2, and σ3 are the first, second, and third principal stresses at a point, respectively. R c Let be the uniaxial compressive strength of the asphalt mixture, where a, b, and m are simplified parameters with no practical significance.

[0022] k1, k2, and k3 are simplified parameters and have no practical significance. θ is the Lode angle, R T It is the direct tensile strength of asphalt mixture, R IT It is the indirect tensile strength of asphalt mixture.

[0023] Furthermore, in step S4, the fatigue stress ratio under the three-dimensional stress state is calculated as follows:

[0024]

[0025] In the formula, σ e (θ) represents the equivalent stress under three-dimensional stress, where α and θ are the Lode angles. σ1, σ2, and σ3 represent the first, second, and third principal stresses at a point, respectively, and Δ is the fatigue stress ratio of the asphalt mixture under three-dimensional stress. For fatigue cyclic loading equivalent stress,

[0026] Furthermore, in step S5, the fatigue normalization equation is:

[0027] N f =Δ -n

[0028] In the formula, n is a model parameter that has no practical meaning and is obtained by fitting a power function. Boundary conditions exist: Δ = 1, N f =1.

[0029] Furthermore, in step S6, the fatigue damage normalization model is:

[0030]

[0031] The beneficial effects of this invention are:

[0032] This invention establishes a residual strength decay model for asphalt mixtures, defining residual strength decay as a damage factor. It comprehensively considers the fatigue damage variation patterns of asphalt mixtures under various test conditions, establishing a fatigue damage model for asphalt mixtures. Based on the strength yield criterion of asphalt mixtures under three-dimensional stress, and combined with the fatigue normalization equation of asphalt mixtures, a normalized fatigue damage model for asphalt mixtures is derived. This model has a high correlation with actual test results, objectively characterizing the fatigue damage variation patterns of asphalt mixtures. It solves the problem of low correlation in the evaluation of fatigue damage of asphalt mixtures using a single test method under simple test conditions in existing technologies. Furthermore, by constructing the fatigue damage evolution law of asphalt mixtures under complex stress states, it objectively characterizes the actual stress state of asphalt pavements, achieving a scientific evaluation of fatigue damage in asphalt mixtures. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a schematic diagram of the equivalent stress envelope in the π-plane in Embodiment 1 of the present invention;

[0035] Figure 2 This is the fatigue damage curve under direct tensile stress in Embodiment 1 of the present invention;

[0036] Figure 3 This is the fatigue damage curve under uniaxial compressive stress state in Embodiment 1 of the present invention;

[0037] Figure 4 This is the fatigue damage curve under indirect tensile stress state in Embodiment 1 of the present invention;

[0038] Figure 5 It is the equivalent stress under direct tensile stress state in Embodiment 1 of the present invention;

[0039] Figure 6 It is the equivalent stress under uniaxial compressive stress state in Embodiment 1 of the present invention;

[0040] Figure 7 It is the equivalent stress under indirect tensile stress state in Embodiment 1 of the present invention;

[0041] Figure 8 This is the fatigue normalized curve of the asphalt mixture in Example 1 of the present invention;

[0042] Figure 9 This is the normalized fatigue damage curve of the asphalt mixture in Example 1 of the present invention. Detailed Implementation

[0043] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0044] This invention provides a method for normalizing fatigue damage in asphalt mixtures, comprising the following steps:

[0045] S1. Conduct fatigue loading cyclic tests on asphalt mixtures under different stress states, temperatures, loading frequencies, loading levels, and number of cycles. Based on the test results, use a power function to fit the residual strength decay model, which is:

[0046]

[0047] In the formula, S N S0 is the residual strength of the asphalt mixture after N fatigue loading cycles; S0 is the initial strength of the asphalt mixture; N is the number of fatigue loading cycles; N0 f σ represents the fatigue life of the asphalt mixture, i.e., the maximum number of cycles without damage or fracture; σ represents the fatigue loading stress; γ1 and γ2 are model parameters that have no practical significance and are obtained by fitting a power function.

[0048] The stress states include direct tension, uniaxial compression, and indirect tension.

[0049] S2. Construct a cumulative fatigue damage model based on the residual strength decay model, as follows:

[0050]

[0051] In the formula, D(N) represents the cumulative fatigue damage of the asphalt mixture.

[0052] S3. The equivalent stress characterization of asphalt mixtures under different test conditions along the tensile and compressive meridians is as follows:

[0053]

[0054] In the formula, σ e t To determine the equivalent stress along the stretching meridian, σ e c To represent the equivalent stress along the compressive meridian, I1 is the first stress invariant, I1 = σ1 + σ2 + σ3, where σ1, σ2, and σ3 are the first, second, and third principal stresses at a point, respectively. R c Let be the uniaxial compressive strength of the asphalt mixture, where a, b, and m are simplified parameters with no practical significance.

[0055] k1, k2, and k3 are simplified parameters and have no practical significance. θ is the Lode angle, R T It is the direct tensile strength of asphalt mixture, R IT It is the indirect tensile strength of asphalt mixture.

[0056] S4. The fatigue stress ratio of asphalt mixture under three-dimensional stress state is calculated based on the strength yield surface theory as follows:

[0057]

[0058] In the formula, σ e (θ) represents the equivalent stress under three-dimensional stress, where α and θ are the Lode angles. Δ represents the fatigue stress ratio of asphalt mixture under three-dimensional stress state. For fatigue cyclic loading equivalent stress,

[0059] S5. Based on the fatigue stress ratio, construct the fatigue normalization equation as follows:

[0060] N f =Δ -n

[0061] In the formula, n is a model parameter that has no practical meaning and is obtained by fitting a power function. Boundary conditions exist: Δ = 1, N f =1;

[0062] S6. Based on the cumulative fatigue damage model and the fatigue normalization equation, a fatigue damage normalization model for asphalt mixtures is constructed as follows:

[0063]

[0064] In the formula, σ eN The residual strength of the asphalt mixture after N fatigue loading cycles, characterized by equivalent stress.

[0065] Example 1

[0066] This embodiment conducts fatigue loading cyclic tests on SMA (stone matrix asphalt), setting the stress states as direct tension, uniaxial compression, and indirect tension; setting the temperatures as -15℃, 0℃, 15℃, and 25℃; setting the load frequencies as 0.1Hz, 1Hz, 10Hz, and 20Hz; setting the direct tension and uniaxial compression load levels as 0.2kN, 0.25kN, 0.5kN, 1kN, 1.5kN, 2kN, 2.5kN, and 3.5kN; setting the indirect tension load levels as 6kN, 9kN, 10kN, 12kN, 15kN, 21kN, 25kN, 31kN, 40kN, and 60kN; and setting the number of cycles as 0 and 20%N. f 50% N f 65% N f 80% N f ;

[0067] The residual strength of the asphalt mixture was tested under the above experimental conditions. Based on the residual strength, a residual strength attenuation model was fitted, and the results are as follows:

[0068] The direct tensile residual strength attenuation model is as follows:

[0069] The uniaxial compression residual strength decay model is as follows:

[0070] The indirect tensile residual strength attenuation model is as follows:

[0071] Based on the residual strength decay model, a cumulative fatigue damage model is constructed as follows:

[0072] The direct tensile cumulative fatigue damage model is as follows:

[0073] The uniaxial compression cumulative fatigue damage model is as follows:

[0074] The indirect tensile cumulative fatigue damage model is as follows:

[0075] Figure 2 The fatigue damage curve is under direct tensile stress. Figure 3 The fatigue damage curve is under uniaxial compressive stress. Figure 4 This is the fatigue damage curve under indirect tensile stress.

[0076] Equivalent stress characterizes the strength of asphalt mixtures along the tensile and compressive meridians. The equivalent stress envelope in the π-plane is as follows: Figure 1 As shown in Table 1, the calculation is performed based on the relationships shown in Table 1.

[0077] Table 1 Relationship between strength and equivalent stress under different stress states

[0078]

[0079] Figure 5 This is the equivalent stress under direct tensile stress. Figure 6 The equivalent stress under uniaxial compressive stress state, Figure 7 It is the equivalent stress under indirect tensile stress state.

[0080] The fatigue stress ratio of asphalt mixture under three-dimensional stress state, calculated based on the strength yield surface theory, is as follows:

[0081]

[0082] In the formula, Δ represents the fatigue stress ratio of the asphalt mixture under three-dimensional stress state. For fatigue cyclic loading equivalent stress,

[0083] The fatigue normalization equation is constructed based on the fatigue stress ratio as follows:

[0084] N f =Δ -4.22

[0085] Fatigue normalization curve as shown Figure 8 As shown, the correlation coefficient is 0.997.

[0086] The fatigue damage normalization model for asphalt mixtures is established based on the cumulative fatigue damage model and the fatigue normalization equation as follows:

[0087]

[0088] In the formula, σ eN The equivalent stress of asphalt mixture after N cycles of fatigue loading under stress;

[0089] Substituting the above results, we get:

[0090]

[0091] The fatigue damage normalization curve of asphalt mixture is as follows: Figure 9 As shown in the figure, the fitting results show that the fatigue damage normalization model of asphalt mixture in this invention has a high correlation with the experimental data, with a correlation coefficient of 0.992, which proves that the derived fatigue damage normalization model can better characterize the fatigue damage variation law of asphalt mixture.

[0092] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for normalizing fatigue damage in asphalt mixtures, characterized in that, Includes the following steps: S1. Conduct fatigue loading cyclic tests on asphalt mixtures under different stress states, temperatures, loading frequencies, loading levels, and number of cycles. Based on the test results, use a power function to fit the residual strength decay model. S2. Construct a cumulative fatigue damage model based on the residual strength decay model; S3. The equivalent stress is used to characterize the strength of asphalt mixtures under different test conditions on the tensile and compressive meridians; S4. Calculate the fatigue stress ratio of asphalt mixture under three-dimensional stress state based on the strength yield surface theory; S5. Construct a fatigue normalization equation based on the fatigue stress ratio; S6. Construct a fatigue damage normalization model for asphalt mixtures based on the cumulative fatigue damage model and the fatigue normalization equation. In step S4, the fatigue stress ratio under the three-dimensional stress state is calculated as follows: ； ； In the formula, The equivalent stress under three-dimensional stress state, To stretch the equivalent stress along the meridian, To compress the equivalent stress along the meridian, , For Cape Lord, , , , , These are the first, second, and third principal stresses at a given point. This represents the fatigue stress ratio of asphalt mixture under three-dimensional stress conditions. For fatigue cyclic loading equivalent stress, .

2. The method for normalizing fatigue damage of asphalt mixtures according to claim 1, characterized in that, In step S1, the stress state includes direct tension, uniaxial compression, and indirect tension.

3. The method for normalizing fatigue damage of asphalt mixtures according to claim 1, characterized in that, In step S1, the residual intensity attenuation model is: ； In the formula, The remaining strength of the asphalt mixture after N fatigue loading cycles; This represents the initial strength of the asphalt mixture. The number of fatigue loading cycles; The fatigue life of asphalt mixture is the maximum number of cycles without damage or fracture. For fatigue stress loading; , The model parameters are obtained by fitting a power function, since they have no practical meaning.

4. The method for normalizing fatigue damage of asphalt mixtures according to claim 1, characterized in that, In step S2, the cumulative fatigue damage model is as follows: ； In the formula, For asphalt mixtures to accumulate fatigue damage, The remaining strength of the asphalt mixture after N fatigue loading cycles. The initial strength of the asphalt mixture. For fatigue-loaded stress, The number of fatigue loading cycles, The fatigue life of asphalt mixtures. , The model parameters are obtained by fitting a power function, since they have no practical meaning.

5. The method for normalizing fatigue damage of asphalt mixtures according to claim 1, characterized in that, In step S3, the equivalent stress on the tensile meridian and the compressive meridian is: ； ； In the formula, To stretch the equivalent stress along the meridian, To compress the equivalent stress along the meridian, As the first stress invariant, , , , These are the first, second, and third principal stresses at a given point. , The uniaxial compressive strength of the asphalt mixture. , , m are simplified parameters and have no practical meaning. , , , , , Simplifying parameters is meaningless in practice. , , , For Cape Lord, It is the direct tensile strength of asphalt mixture. It is the indirect tensile strength of asphalt mixture.

6. The method for normalizing fatigue damage of asphalt mixtures according to claim 1, characterized in that, In step S5, the fatigue normalization equation is: ； In the formula, The fatigue life of asphalt mixtures. This represents the fatigue stress ratio of asphalt mixture under three-dimensional stress conditions. The model parameters are obtained by fitting a power function, which has no practical meaning, and there are boundary conditions: , =1.

7. The method for normalizing fatigue damage of asphalt mixtures according to claim 1, characterized in that, In step S6, the fatigue damage normalization model is: ； In the formula, For asphalt mixtures to accumulate fatigue damage, The number of fatigue loading cycles, For fatigue cyclic loading equivalent stress, The equivalent stress under three-dimensional stress state, The fatigue stress ratio of asphalt mixture. , , These are model parameters that have no practical significance.

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