Method for predicting fatigue cracking damage of unsaturated solidified soil based on energy-mechanical method

Abstract

The application discloses a kind of non-saturated solidified soil fatigue cracking damage prediction methods based on energy-mechanics method.The application introduces the effective stress formula proposed by Lytton and gives the solution method of relevant parameters in combination with energy-mechanics method, obtains the damage density evolution trend of non-saturated solidified soil material, finally based on the theory of fracture mechanics and continuous damage mechanics, on the basis of Paris equation, introduce damage density function, and based on dissipation strain energy DSE, the expression form of J integral is obtained, so as to establish the damage evolution prediction model capable of characterizing the multi-crack cracking process.The application solves the problem that the previous solidified soil fatigue cracking model cannot effectively reflect the influence of unsaturated characteristics on soil material cracking, and the model is based on the basis of mechanics theory, can better predict the multi-crack fatigue cracking damage evolution process from the mechanism level of non-saturated solidified soil material fatigue cracking, and provides basis and guidance for the design of solidified soil material and solidified soil road structure.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of road material performance evaluation and prediction, in particular to the analysis and damage prediction of the fatigue cracking performance of unsaturated solidified soil base material. BACKGROUND

[0002] Traditional road construction materials such as gravel and slag are in short supply and their prices are rising, so more and more highways and municipal roads use solidified soil material as the filling material for road subgrade or base. With the large-scale application of solidified soil material, the performance of solidified soil material has attracted more and more attention in terms of its impact on road structure, especially when it is used as base or subbase material. The cracking performance of solidified soil material under tensile fatigue load has a significant impact on the service life of road structure, so it is particularly important to effectively predict the fatigue cracking behavior of solidified soil material, which is of great significance to guide the design and application of solidified soil road structure.

[0003] At present, the prediction method of the fatigue cracking performance of solidified soil material in China mostly uses empirical models, and some scholars have given some fatigue cracking models of solidified soil material based on the fatigue cracking models of traditional stable gravel and other semi-rigid materials based on mechanical theory, but most of them do not pay attention to the unsaturated characteristics of solidified soil material. Unlike stable gravel, solidified soil is still a soil material, and it is greatly affected by matrix suction in the unsaturated state, so it is still insufficient to directly use the fatigue cracking model of traditional semi-rigid base material to characterize the fatigue cracking behavior of solidified soil material. Moreover, in most areas of China, solidified soil base material is in an unsaturated state, so it is of great importance to establish a fatigue cracking model that takes into account the unsaturated characteristics of solidified soil for the practical application of solidified soil in engineering. SUMMARY

[0004] The purpose of the present application is to propose a cracking damage model that can effectively predict the cracking damage of unsaturated solidified soil material under tensile fatigue load, and to give a set of methods that can effectively solve the fatigue cracking damage density and related parameters based on energy-mechanical theory, and then be used for the fatigue cracking damage prediction of unsaturated solidified soil. The problem of previous solidified soil fatigue cracking models being based on regression analysis and not being able to effectively reflect the fatigue damage process of solidified soil material from the theoretical and mechanism level is solved, and the establishment and prediction of the fatigue cracking damage model of unsaturated solidified soil material are effectively realized.

[0005] The technical solution adopted by the present application is:

[0006] A fatigue cracking damage prediction method for unsaturated solidified soil based on energy-mechanical method, comprising:

[0007] The direct tensile cyclic test is performed on the unsaturated solidified soil material to obtain parameters of the direct tensile cyclic test, including apparent effective stress amplitudes under different strain loading periods absolute value of downward offset of a standard half-sine wave in apparent effective stress apparent strain phase angle in apparent strain

[0008] The unsaturated solidified soil fatigue cracking damage model based on the energy-mechanical method is used to predict the fatigue cracking damage process of the unsaturated solidified soil material

[0009] The unsaturated solidified soil fatigue cracking damage model based on the energy-mechanical method is established based on Paris' Law equation and a damage density function, and is expressed as follows:

[0010]

[0011] where N is a loading period; is a damage density function, J R is a J integral calculated based on dissipated strain energy DSE; A', n' are fatigue cracking parameters:

[0012]

[0013] In the formula: A is the entire cross-sectional area of the test piece; a, b, e, g are related fitting parameters, which are obtained based on the obtained parameters of the direct tensile cyclic test and based on the energy-mechanical method, and are specifically as follows:

[0014] a, b are parameters related to the damage density development trend of the material, which are obtained by fitting through the following formula:

[0015]

[0016] e, g are parameters related to the cumulative dissipated strain energy DSE of the material, and the cumulative dissipated strain energy DSE of the material u and N can be fitted through the following formula:

[0017] DSE u = eN g

[0018] where the damage density corresponding to each loading period is an apparent effective stress amplitude, is a true effective stress amplitude, for a lossless state, S c is a pore and crack area of a cross section of the solidified soil test piece, and is equal to an initial porosity of the material in a lossless state; for a damaged state, V is an apparent volume of the solidified soil test piece; Vt is the volume occupied by the skeleton structure of soil particles inside the cured soil specimen, is the phase angle in true strain, according to is obtained by solving, is the apparent dissipated strain energy is the apparent recoverable strain energy, is the absolute value of the downward shift of the standard half-sine wave in the apparent effective stress; is the real complex modulus of the material, and for the same strain level loading condition, the real complex modulus of the material in different loading cycles is the same, so for the loss state, the real effective stress amplitude of the material at the beginning of the damage test, i.e. N = 0, is used is obtained by calculation:

[0019] S c is the pore and crack area of the cross section of the cured soil specimen, S c is the initial porosity of the material; is the apparent effective stress amplitude at N = 0.

[0020] Further, the apparent effective stress amplitude is the absolute value of the downward shift of the standard half-sine wave in the apparent effective stress is obtained by collecting the parameters of the direct tension cycle test combined with the expression of the effective stress:

[0021]

[0022] h m0 is the matrix suction amplitude; h mc is the absolute value of the downward shift of the standard half-sine wave in the matrix suction; θ represents the volume water content, f is the saturation influence factor, σ0 represents the total stress amplitude, σ c represents the absolute value of the downward shift of the standard half-sine wave in the total stress. σ0, σ c is obtained by fitting the experimental data using formulas 1 and 2.

[0023] Further, in the parameter solving process of e and g, the real cumulative dissipated strain energy is solved in relation to N, which can be obtained by solving the energy-mechanical method, and its expression is

[0024] Further, under the loss state, the real complex modulus of the material The solving process is as follows:

[0025] Based on the obtained parameters of the direct tension cycle test under the loss state, including the apparent effective stress amplitude under different loading cycles absolute value of downward shift of standard half-sine wave in apparent effective stress phase angle in apparent strain apparent effective stress amplitude in lossy state is obtained by fitting with power function respectively fitting curve, absolute value of downward shift of standard half-sine wave in apparent effective stress fitting curve, and phase angle in apparent strain fitting curve

[0026] apparent effective stress amplitude when N=0 in lossy state is obtained based on the obtained fitting curve absolute value of downward shift of standard half-sine wave in apparent effective stress phase angle in apparent strain

[0027] real effective stress amplitude when N=0 is calculated apparent dissipated strain energy and apparent recoverable strain energy phase angle in real strain

[0028]

[0029] material real complex modulus when N=0 is finally calculated, which represents material real complex modulus under different loading cycles in lossy state

[0030]

[0031] The present application has the following beneficial effects:

[0032] The present application provides a model capable of effectively predicting fatigue cracking damage evolution of unsaturated solidified soil material under direct tensile fatigue load, and a damage prediction method based on model analysis and solution. The method first gives a solution method of fatigue cracking damage density of unsaturated solidified soil material based on energy-mechanical method, so as to obtain performance parameters and damage density of unsaturated solidified soil material, then based on analysis result of damage density, combines fracture mechanics and continuous damage mechanics theory, introduces damage density function into equation based on Paris' Law criterion, and gives specific solution process of fatigue cracking model parameters, finally obtains damage evolution model and method capable of predicting unsaturated solidified soil material under multi-crack cracking condition. This is different from previous analysis model based on statistical significance, can better reflect damage and failure process of unsaturated solidified soil material under direct tensile fatigue load from fatigue cracking mechanism level, and provides effective guidance for base solidified soil material matching and road structure design. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 is a schematic diagram of the stress curve of the loading process of the present application;

[0034] Figure 2 is a schematic diagram of the strain loading curve of the loading process of the present application, wherein the solid line is the strain curve and the dashed line is the stress curve;

[0035] Figure 3 is an evolution diagram of the damage density of the material in the fatigue cracking process of the present application.

[0036] Figure 4 is an evolution diagram of the real dissipation cumulative strain energy of the material in the fatigue cracking process of the present application. DETAILED DESCRIPTION

[0037] The present application provides a non-saturated solidified soil base fatigue cracking damage model prediction and method based on energy-mechanical method, comprising:

[0038] Direct tensile cycle test is performed on the non-saturated solidified soil material to obtain parameters of the direct tensile cycle test, including apparent effective stress apparent effective stress amplitude apparent strain phase angle in the apparent strain

[0039] and the damage evolution model established based on Paris' Law equation and damage density function and the solving and analysis method established based on energy-mechanical method are used to predict the fatigue cracking damage of the non-saturated solidified soil material.

[0040] The present application is to effectively characterize the fatigue cracking damage process of the solidified soil material under the non-saturated condition, considers the influence of the effective stress on the stress state of the soil body, establishes the stress-strain expression of the non-saturated solidified soil material by introducing the effective stress formula proposed by Lytton et al. for the non-saturated foundation and roadbed soil, and gives the solving method of the related parameters through the establishment of the energy balance equation and the mechanical balance equation, and obtains the change trend of the damage density of the non-saturated solidified soil material in the fatigue cracking process. Finally, based on the theoretical basis of fracture mechanics and continuous damage mechanics, the damage density function is introduced on the basis of Paris equation, and the expression form of J integral is obtained based on dissipation strain energy DSE, so as to establish the damage evolution equation which can characterize the multi-crack cracking process. The damage evolution equation established based on the energy-mechanical method comprises the following steps:

[0041] (1) test process;

[0042] (2) stress-strain expression;

[0043] ​(3) Damage state determination;

[0044] (4) Energy solution formula determination;

[0045] (5) Establishment of energy balance equation;

[0046] (6) Expression of true stress and strain;

[0047] (7) Solution of true stress and strain under non-destructive condition;

[0048] (8) Solution of material true performance parameters;

[0049] (9) Solution of material true stress and strain under destructive condition;

[0050] (10) Determination of damage density;

[0051] (11) Establishment of base fatigue cracking damage model based on Paris equation.

[0052] The present application is based on tensile test data combined with theoretical derivation, and the first step is to obtain tensile data. In step (1), the test tensile method adopts direct tensile test method, and the test piece is a cylindrical test piece with a height-diameter ratio of 2:1. In order to study the fatigue cracking behavior of the cured soil base, a group of direct tensile cycle tests (RDT) with controlled strain are designed, in which the strain loading adopts sinusoidal wave mode, which is the tensile strain level, and the loading frequency is 1Hz. A plurality of strain levels are used to test the same test piece by RDT, the time interval between every two continuous strain levels is 20 minutes, the strain level is gradually increased from low to high, and the initial loading strain level is ensured to be in the non-destructive state of the material.

[0053] In step (2):

[0054] Non-saturated solidified soil is a basic structure composed of three-phase materials, including porous soil skeleton structure composed of solid particles with different arrangements and different connection strengths, and gas and liquid fluids filled in the pores in different forms. Due to the presence of gas, the properties of non-saturated solidified soil are much more complex than those of saturated solidified soil. In order to effectively describe the cracking damage law of non-saturated solidified soil material under tensile fatigue load, the effective stress principle in non-saturated soil mechanics needs to be used. After nearly 80 years of development, the research on the effective stress principle of non-saturated soil has made certain progress. According to the types of the effective stress principle, there are mainly three types: the first type is to use single stress variable effective stress, the second type is to use double stress variable theory, and the third type is to determine the effective stress from the expression of work. Some other research theories are further developed based on the three types of effective stress principles. In the invention, considering the non-saturated characteristics of the solidified soil material, the effective stress formula proposed by Lytton et al. in 1996 for non-saturated foundation and subgrade soil is selected for parameter solving analysis.

[0055] In the RDT test of controlled strain, the axial strain is controlled as a standard sinusoidal waveform (the axial strain is positive), and the stress applied is also a biased sinusoidal wave load, so that a mathematical model can be used to represent the stress-strain change process of the material, wherein the total stress σ is expressed as formula 1, the strain ε is expressed as formula 2, and the matrix suction is expressed as formula 3:

[0056] σ=σ0[1-cos(ωt)]-σ c (1)

[0057]

[0058] h m =h m0 [1-cos(ωt)]-h mc (3)

[0059] In the formula, σ0 represents the total stress amplitude, σ c represents the absolute value of the downward shift of the standard half-sine wave in the total stress, ω represents the angular velocity, which is related to the loading frequency, ε0 represents the strain amplitude, represents the phase angle in the strain.

[0060] According to the non-saturated soil effective stress formula proposed by Lytton et al., the following can be derived:

[0061] σ′=σ-θfh m =σ0[1-cos(ωt)]-σ c -θf[h m0 [1-cos(ωt)]-hmc ] = (σ0- θfh m0 )[1-

[0062] cos(ωt)] - σ c - θfh mc ) = σ'0[1 - cos(ωt)] - σ' c (4)

[0063] Therefore, the expression of the effective stress of the unsaturated soil in the RDT test under the controlled strain can be obtained as follows:

[0064] σ' = σ'0[1 - cos(ωt)] - σ' c (5)

[0065] wherein:

[0066] σ'0= σ0- θfh m0 (6)

[0067] σ' c = σ c - θfh mc (7)

[0068] In the formula, h m is the matrix suction inside the material at time t; h m0 is the amplitude of the matrix suction; h mc is the absolute value of the downward shift of the standard half-sine wave in the matrix suction; σ' is the effective stress inside the material of the unsaturated solidified soil at time t, σ'0is the amplitude of the effective stress; σ' c is the absolute value of the downward shift of the standard half-sine wave in the effective stress; is the phase angle in the strain, wherein the subscript u represents the parameter meaning related to the unsaturated soil. θ represents the volumetric water content, and f represents the non-saturation influence factor.

[0069] After the test data are obtained, the fitting analysis can be performed to obtain the complex modulus size under different strain levels or different cycle conditions. The complex modulus size can be calculated according to formula 8.

[0070]

[0071] In the step (3), the step (3) is characterized in that:

[0072] In the process of the RDT test under the controlled strain, with the increase of the strain level, the deformation of the material can be in the undamaged region or the damaged region. The division of the damage stage and the undamaged stage of the solidified soil material can be determined by analyzing the change of the complex modulus under each strain level according to formula 8, and the specific determination method is as follows:

[0073] Judgment of the damage-free zone: when the material is in the damage-free zone, the material's will not change, but the material's will change as the strain level increases.

[0074] Judgment of the damage zone: when the material is in the damage stage, the material's will change as the number of load cycles increases.

[0075] Determination of the damage critical point: the boundary point A between the damage-free zone and the damage zone is defined as the damage critical point. Before the critical point, the material's deformation at any stress level can be fully recovered, but after the critical point, damage occurs inside the material, resulting in irreversible plastic deformation, i.e. permanent deformation.

[0076] In the step (4):

[0077] When the material is subjected to force, the internal energy of the material will change accordingly. In the fatigue cracking analysis based on the energy-mechanical method, the solution of energy is very important for the establishment of the later model, so it is necessary to solve the energy change of the material during the RDT test by a certain method, which includes the cumulative dissipated strain energy (DSE) and the recoverable strain energy (RSE). The formulas for calculating DSE and RSE can be expressed as follows:

[0078]

[0079] In the formula, DSE u is the cumulative dissipated strain energy; RSE u is the recoverable strain energy; π is the circular constant.

[0080] In the step (5):

[0081] The energy balance equation is a key step in the energy-mechanical method. Through the establishment of the energy balance equation, the apparent stress, energy and other related parameters can be related to the real stress, energy and other related parameters inside the material, which is the theoretical basis for solving the change of damage density of solidified soil material in the later period. The energy balance equation includes the dissipated strain energy balance equation and the recoverable strain energy balance equation, which are shown in formulas 11 and 12:

[0082]

[0083] In the formula: is the apparent dissipated strain energy; is the real dissipated strain energy; is the apparent recoverable strain energy; is the real recoverable strain energy; V is the apparent volume of the solidified soil specimen; V tis the volume occupied by the skeleton structure of soil particles in the cured soil specimen.

[0084] In the step (6), the step (7) is performed.

[0085] When the cured soil material is subjected to a certain load, the true stress-strain and the apparent stress-strain are in the same form, that is, in the RDT test of controlled strain, the mathematical expressions of the true stress, the true strain and the apparent stress, the apparent strain satisfy the formula 5 and the formula 2. Therefore, the mathematical expressions of the true stress and the true strain inside the cured soil material are as shown in the formula 13 and the formula 14:

[0086]

[0087] In the formula, σ

[0088]

[0089] In the formula, σ T ′ is the true effective stress corresponding to the time t under the action of the load; is the true effective stress amplitude; is the absolute value of the downward shift of the standard half-sine wave in the true effective stress. ε T ′ is the true strain corresponding to the time t under the action of the load; is the true strain amplitude; is the phase angle in the true strain. is the true complex modulus of the material.

[0090] In the step (7), the step (8) is performed.

[0091] The apparent stress and the apparent strain can be directly fitted and analyzed by the test results of the RDT test, but for the solution of the true stress and the true strain, since there are variables such as pores and crack areas, certain methods need to be used to solve them step by step. Therefore, on the basis of the energy balance equation, the mechanical balance equation of the material is further introduced, so as to develop the solution method of the related parameters of the true stress and the true strain of the material and the damage density based on the energy-mechanical method.

[0092] When the material is subjected to external force, there is a certain relationship between the apparent effective stress and the true effective stress, which can be expressed by the balance equation 16:

[0093]

[0094] σ A ′ is the true effective stress corresponding to the time t under the action of the load; is the true effective stress amplitude; is the absolute value of the downward shift of the standard half-sine wave in the true effective stress. ε

[0095] According to equation 16, equation 17 and equation 18 can be obtained:

[0096]

[0097] From equation 17 and equation 18, the related parameters of real effective stress can be solved and as shown in the following equation:

[0098]

[0099] In the equation, A is the total area of the cross section of the solidified soil sample; S c is the pore and crack area of the cross section of the solidified soil sample.

[0100] When the material is in a damage-free state, S c is the initial porosity of the material, so the related parameters of the real effective stress of the material can be directly solved by the apparent effective stress related parameters.

[0101] In the step (8):

[0102] In order to further solve the real stress and strain parameters of the material under the damaged condition, the real performance parameters of the material need to be obtained. The solution of the real performance of the material needs to use two energy balance equations of equation 11 and equation 12. In these two energy balance equations, the expressions of apparent / real dissipation strain energy and apparent / real recoverable strain energy are shown in equation 9 and equation 10, and the specific expressions are as follows:

[0103]

[0104] Substituting equation 23 and equation 24 into equation 11 and equation 12 respectively can obtain:

[0105]

[0106] Dividing equation 25 and equation 26 on the left and right respectively can obtain equation 27:

[0107]

[0108] Further substituting equation 19 and equation 20 into equation 27 can obtain equation 28:

[0109]

[0110] In equation 28, and are the quantities related to the apparent stress, which can be obtained by processing and analyzing the RDT test data of the controlled strain. Therefore, the only unknown quantity can be obtained by inverse calculation of equation 28.

[0111] Seek Further calculation of the complex modulus of the real material is required. The process is as follows:

[0112] Substituting Equation 15 into Equation 25 yields Equation 29:

[0113]

[0114] Substituting Equation 19 into Equation 29 and solving for the complex modulus, we obtain the complex modulus.

[0115]

[0116] The true performance parameters of solidified soil materials under non-destructive conditions can be directly obtained using equations 28 and 30. However, for destructive conditions, due to S... c This includes the area of ​​material damage and cracking, and is therefore an unknown quantity. To obtain the true performance parameters of the material under damaged conditions, further solutions are needed. The specific process is as follows:

[0117] 1) Using Equations 5 and 2, the stress-strain terms in the RDT test results under damaged conditions are fitted and analyzed to obtain the apparent stress-strain related parameters corresponding to different periods: Apparent strain Phase angle in apparent strain

[0118] 2) Draw the corresponding periods on the graph. And use power functions The optimal fitting curve is obtained by fitting the data points, thus yielding the relevant fitting equation. N represents the loading period, and x1, x2, and x3 are the fitting parameters.

[0119] 3) When N = 0, the apparent effective stress amplitude of the material at the start of the damage test. This can be obtained by fitting the equation in the previous step. When N = 0, it indicates that the material has not yet been damaged, so the internal crack area of ​​the solidified soil is 0, i.e., S. c Let be the initial pore area of ​​the material, and be a known parameter.

[0120] 4) Repeat steps 2)-3) to obtain the result. When N=0, the corresponding The value is then calculated according to Equations 21 and 22 to obtain the corresponding equivalent apparent energy. and The true damage phase angle of the material can then be calculated according to Equation 28.

[0121] 5) Substituting the numerical value into Equation 19, the true effective stress amplitude at the start of the damage test can be calculated. Then Substituting into Equation 30, the true complex modulus of material damage of the solidified soil at this strain level can be obtained.

[0122] In step (9):

[0123] The methods described above can be used to indirectly obtain the true performance parameters of the material under damage. and Furthermore, based on the characteristics of the material's true performance parameters, it can be known that under the same strain level loading conditions, the material's true performance parameters are the same for different periods. Therefore, the obtained material performance parameters can be used... and The true stress magnitude corresponding to different periods under the strain level load can be further calculated. and The specific solution process is as follows:

[0124] Will and Substituting into equation 30, we can obtain

[0125]

[0126] Then, based on equations 19 and 20, we can obtain...

[0127]

[0128] In step (10):

[0129] Stabilized soil specimens undergo fatigue damage under fatigue loading, and the degree of fatigue cracking damage in the stabilized soil base layer changes after cracking occurs. To characterize the damage degree of stabilized soil materials under direct tensile fatigue loading, the fatigue cracking damage density of the stabilized soil base layer is given. Definition of damage density It can be represented as follows:

[0130]

[0131] In the formula Damage density is a descriptive index of the degree of damage to a solidified soil sample; A t S is the area of ​​the solidified soil mass on the cross-section of the specimen; A is the total cross-sectional area of ​​the specimen; S c The area of ​​pores and cracks on the cross-section of the specimen is denoted as .

[0132] In the step (11) :

[0133] The present application attempts to combine the methods of fracture mechanics and damage mechanics, on the basis of Paris criterion, by introducing damage density function, to establish damage evolution model, so as to effectively characterize the multi-crack fatigue cracking of solidified soil material. The improved Paris' Law method is as follows:

[0134]

[0135] Where A' and n' are fatigue cracking parameters, J R J is calculated based on the dissipated strain energy DSE, which can be used to simulate the growth of material cracks, and its calculation formula is as follows:

[0136]

[0137] The cracking area can be obtained by multiplying the damage density by the cross-sectional area of the specimen, and the calculation formula is as follows:

[0138]

[0139] DSE represents the rate of change of dissipated energy, and the relationship between DSE and N can be obtained by fitting formula 37:

[0140]

[0141] e, g are related fitting parameters;

[0142] Substituting formula 35, formula 36 and formula 37 into formula 34 can obtain:

[0143]

[0144] Solving:

[0145]

[0146] Integrating both sides to obtain:

[0147]

[0148] Obtained by formula 40:

[0149]

[0150] On the other hand: the damage factor change trend of the material can be obtained by the method in step (10), which can be fitted by the following formula:

[0151] a, b, c are fitting parameters.

[0152] Comparing formula 41 and formula 42 can obtain:

[0153]

[0154] Therefore, the following can be solved:

[0155]

[0156] Therefore, through the above solving process, the fatigue cracking parameters A' and n' of the solidified soil material under the action of direct tensile fatigue load can be obtained, so as to determine the damage evolution model and its parameters of the solidified soil material under the action of direct tensile fatigue load, which can be used for the prediction of the damage evolution process of the solidified soil material.

[0157] In the following, specific embodiments of the non-saturated solidified soil fatigue cracking damage prediction model and method based on the above energy-mechanical method are used to predict the direct tensile fatigue cracking performance of the solidified soil material:

[0158] Cement soil direct tensile fatigue cracking test: In this embodiment, the soil source is soft soil obtained by subway excavation, the cement content is 9%, and the compaction degree is controlled at 95%. The specimen is made by using static pressure forming method under the condition of optimum moisture content of 18%. The specific test steps are as follows:

[0159] (1) Specimen preparation: cylindrical specimens with a diameter of Φ70mm and a height of 140mm are used, which are rolled into shape through a certain process, and are taken out for tensile fatigue test after curing for 28 days. Before the direct tensile fatigue test, the solidified soil specimen needs to be centered and bonded with the tensile device for a series of treatments, and then installed on the UTM universal pressure testing machine, set the related programs and parameters, and then test.

[0160] (2) Direct tensile cycle test of non-saturated solidified soil material to obtain the parameters of direct tensile cycle test:

[0161] (2.1) Stress-strain data fitting analysis: after obtaining the relevant test data, post-processing is carried out, and the stress-strain data at each strain level or each cycle are fitted and analyzed by formula (1) and (2) to obtain the related parameters of stress-strain, and the matrix suction data output by the external pore pressure sensor are fitted and analyzed by formula (3). Referring to Figure 1 、 2 , the loading program in this embodiment is set to control the strain type cycle loading. Figure 1 is the expression form of stress, the stress is sinusoidal mode, wherein the loading cycle is T, σ is the stress suffered by the material inside at time t; σ0 is the stress amplitude; σ cis the absolute value of the downward shift of the standard half-sine wave; t is the loading time. In order to ensure that the strain is a tensile strain, the stress will appear in both tension and compression, and the stress and strain are not completely synchronized, but there is a certain lag relationship, which can be seen in detail from Figure 2 . It can be seen from Figure 2 that there is a certain lag between strain and stress, which can be represented by the phase angle . In which Figure 2 , ε is the strain size of the material at t time; ε0is the strain amplitude. Figure 1 and Figure 2 The stress and strain curves in and (2) can be mathematically expressed by the stress-strain expression, which can be seen in detail from formula (1) and formula (2).

[0162] (2.2) Damage critical point determination: the size of the complex modulus at each strain level or under each cycle condition is calculated by formula (8), and the damage critical point A of the material is determined according to the damage determination method of step (3) of the specific embodiment of the present application.

[0163] (2.3) Loading test under damaged condition: after determining the damage critical point, the strain level loading under the damaged condition is carried out, and the loading cycle is 5000 times.

[0164] (3) Fatigue cracking damage density solution: the related mechanical parameters and performance parameters of the material are determined according to the solving method and process based on the energy-mechanical method proposed in steps (2)-(10) of the specific embodiment of the present application, and finally the size of the damage density changes with the cycle according to formula (33). Referring to Figure 3 , after obtaining the related test data, the fatigue cracking damage density solving method of unsaturated solidified soil based on the energy-mechanical method can obtain the damage degree of the material, which can be characterized by the damage density , and the development trend of the damage density is shown in Figure 3 . Further, the fatigue cracking damage density solving method of unsaturated solidified soil based on the energy-mechanical method can obtain the real dissipation cumulative strain energy evolution process of the material, and the fitting result is shown in Figure 4 .

[0165] (4) Fatigue cracking damage model establishment and solution, and fatigue cracking damage prediction of unsaturated solidified soil material: based on the Paris equation and the damage density function, the fatigue cracking damage evolution model of unsaturated solidified soil material is established, and the sizes of the related fatigue cracking characterization parameters A' and n' are obtained according to the model parameter solving method proposed in step (11) of the present application. Further, the fatigue cracking damage process of unsaturated solidified soil material is predicted according to the fatigue cracking damage model.

[0166] Obviously, the above embodiments are merely exemplary but not restrictive. Based on the above description, those skilled in the art can make other different forms of changes or modifications. All the embodiments are not required to be exhaustive. The obvious changes or modifications derived therefrom are still within the protection scope of the present application.

Claims

1. A method for predicting fatigue cracking damage of unsaturated solidified soil based on energy-mechanical method, characterized in that, Comprise: direct tensile cyclic tests are carried out on unsaturated solidified soil materials, and parameters of the direct tensile cyclic tests are obtained, including apparent effective stress amplitudes under different strain loading periods absolute value of downward shift of standard half-sine wave in apparent effective stress apparent strain phase angle in apparent strain The energy-mechanical method based unsaturated solidified soil fatigue cracking damage model predicts the fatigue cracking damage process of unsaturated solidified soil material; The energy-mechanical method based unsaturated solidified soil fatigue cracking damage model is obtained based on Paris' Law equation and damage density function, and is expressed as follows: where N is the loading cycle; is the damage density function, J R is the J integral calculated based on the dissipated strain energy, DSE; A ′ , n ′ is the fatigue cracking parameter: In the formula, A is the entire cross-sectional area of the test piece; a, b, e, and g are related fitting parameters, which are obtained based on the parameters of the obtained direct tensile cycle test and based on the energy-mechanical method solution, and are specifically as follows: a and b are parameters related to the damage density development trend of the material, which are obtained by fitting through the following formula: e, g are parameters related to the accumulated dissipated strain energy of the material, which accumulated dissipated strain energy DSE u The relationship with N was fitted by the following equation: DSE u = eN g wherein each loading cycle corresponds to a damage density is the apparent effective stress amplitude, is the true effective stress amplitude, for the undamaged state, S c is the cross-sectional area of the cured soil specimen, which equals the initial porosity of the material in the undamaged state; for the damaged state, V is the apparent volume of the cured soil specimen; V t is the volume occupied by the internal soil particle skeleton structure of the cured soil specimen, is the phase angle in the true strain, obtained according to is the phase angle in the true strain, obtained according to is the apparent dissipated strain energy is the apparent recoverable strain energy, is the absolute value of the downward offset of the standard half-sine wave in the apparent effective stress; is the true complex modulus of the material, for the same strain level loading condition, the true complex modulus of the material in different loading cycles is the same, therefore, for the damaged state, the true effective stress amplitude corresponding to N = 0 is used is calculated as follows: S c is the area of pores and cracks in the cross section of the cured soil specimen, S c is the initial porosity of the material; is the apparent effective stress amplitude for N = 0.

2. The method of claim 1, wherein, the apparent effective stress amplitude the absolute value of the downward shift of the standard half-sine wave in the apparent effective stress is calculated by acquiring parameters of the direct tension cycle test in combination with the expression of the effective stress h m0 is the amplitude of the matrix suction; h mc is the absolute value of the downward shift of the standard half-sine wave in the matrix suction; θ represents the volumetric water content, f is the saturation influence factor, σ0represents the total stress amplitude, σ c represents the absolute value of the downward shift of the standard half-sine wave in the total stress.

3. The method of claim 1, wherein, In the parameter solving process of the e and g, the real cumulative dissipation strain energy The relationship with N is solved, The expression is obtained by energy-mechanical method, and is 4. The method of claim 1, wherein, Real complex modulus of a material in a lossy state The solution process is as follows: Based on the obtained parameters of direct tension cycle test under the lossy state, including the apparent effective stress amplitude under different loading cycles The absolute value of the downward shift of the standard half-sine wave in the apparent effective stress The phase angle in the apparent strain The apparent effective stress amplitude under the lossy state is obtained by fitting with a power function respectively The fitting curve, the absolute value of the downward shift of the standard half-sine wave in the apparent effective stress The fitting curve, and the phase angle in the apparent strain The fitting curve; Based on the obtained fitting curve, the apparent effective stress amplitude at N=0 in the lossy state is obtained The absolute value of the downward shift of the standard half-sine wave in the apparent effective stress The phase angle in the apparent strain Compute the true effective stress amplitude for N=0 apparent dissipated strain energy and apparent recoverable strain energy phase angle in true strain : Finally, the real complex modulus of the material at N=0 is calculated, which represents the real complex modulus of the material at different loading cycles in the damaged state:

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