CN115527639B - Asphalt mixture fatigue life prediction method considering loading order - Google Patents
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Abstract
The invention discloses a fatigue life prediction method of an asphalt mixture considering a loading order, which comprises the steps of carrying out constant amplitude and amplitude-variable loading fatigue tests on the asphalt mixture, and establishing a fatigue life prediction model considering the loading order by determining the relation between a second-stage loading life fraction and a first-stage loading life fraction under amplitude-variable loading. The prediction method can reflect the influence of the running sequence of the vehicle on the fatigue damage of the road surface structure, improves the prediction precision of the service life of the road surface under variable amplitude loading, provides a basis for scientific management of the asphalt road surface, and has good economical efficiency and operability.
Description
Technical Field
The invention relates to the field of road engineering, in particular to a fatigue life prediction method of asphalt mixture considering loading order.
Background
Asphalt pavement is easy to generate fatigue damage under the cyclic action of vehicle load, and fatigue damage occurs when the fatigue damage is accumulated to a failure threshold value, and the fatigue damage is one of main diseases of the asphalt pavement. The fatigue damage characteristics of the asphalt mixture are researched by virtue of a fatigue test, and a fatigue life prediction model of the asphalt mixture is provided, so that the service life of the asphalt pavement structure can be predicted, and theoretical basis is provided for prolonging the service life, reducing the construction cost and improving the economic benefit.
Aiming at the problem of predicting the fatigue life of asphalt mixture under the action of cyclic load, a great deal of researches exist at present, such as: patent CN202110335280.1 discloses a method for predicting fatigue life of asphalt mixture based on a stable value of cumulative dissipation energy relative change rate, which comprises: determining a relative rate of change of the cumulative dissipation energy and a plateau thereof; determining the relation between the accumulated dissipation energy relative change rate stable value and the fatigue life; and (5) establishing a fatigue model to predict the fatigue life. Patent CN103630450 discloses a method for predicting the lifetime of an asphalt mixture taking into account the fatigue-creep interaction damage, comprising: determining complex modulus of asphalt mixture under the action of periodic load; determining damage variables of the asphalt mixture; respectively establishing an asphalt mixture creep damage equation and a fatigue damage equation; and establishing an asphalt mixture life prediction model under the combined action of creep damage and fatigue damage. However, the existing research on fatigue life prediction of asphalt mixture has the following defects when applied to solving fatigue cracking diseases of asphalt pavement:
(1) The vehicle load with the variable load amplitude is regarded as the load amplitude with constant amplitude, the influence of the vehicle running sequence on the load amplitude change is ignored, and the load amplitude is not in accordance with the actual stress state of the asphalt mixture bearing variable amplitude load in the asphalt pavement structure;
(2) The fatigue damage accumulation process of the asphalt mixture under constant amplitude loading can be represented, and the fatigue damage accumulation process under variable amplitude loading cannot be represented accurately, so that the predicted fatigue life has theoretical difference from the actual service fatigue life of an actual pavement.
Disclosure of Invention
The invention aims to: aiming at the defects of the prior art, the invention provides a fatigue life prediction method for asphalt mixture taking the loading sequence into consideration, which solves the problem that the operability, the accuracy and the economy in the prior art cannot be well ensured.
The technical scheme is as follows: the invention relates to a load order considered asphalt mixture fatigue life prediction method, which comprises the following steps:
s1, establishing an asphalt mixture secondary loading life fraction prediction model under variable amplitude loading:
carrying out constant amplitude and amplitude-variable load fatigue tests on the asphalt mixture, determining an asphalt mixture fatigue damage model under constant amplitude load and asphalt mixture fatigue damage equivalence under amplitude-variable load, and establishing an asphalt mixture secondary load life fraction prediction model considering a load order based on damage equivalence criteria;
s2, building an asphalt mixture fatigue life prediction model considering a loading sequence:
and fitting a secondary loading life fraction prediction model to determine loading order parameters, determining an asphalt mixture fatigue life prediction model under constant amplitude loading, and finally establishing an asphalt mixture fatigue life prediction model considering the loading order according to the obtained loading order parameters and the asphalt mixture fatigue life prediction model under constant amplitude loading, so as to predict the asphalt mixture fatigue life.
The further preferable technical scheme of the invention is that the specific method for determining the asphalt mixture fatigue damage model under constant amplitude loading in the step S1 is as follows:
respectively selecting high load amplitude sigma high And low load amplitude sigma low As a constant load amplitude sigma, performing a constant load fatigue test; selecting a Chaboche damage model, and representing an evolution rule of asphalt mixture fatigue damage under constant amplitude loading, wherein the evolution rule is shown as a formula (1):
D＝1-[1-(N/N f ) 1/(1-α) ] 1/(1+β) (1)；
wherein D is an asphalt mixture damage variable; n is the load cycle number; n (N) f Is fatigue life; alpha is a model parameter dependent on temperature and load amplitude; beta is a temperature dependent model parameter.
Preferably, the specific method for equivalent fatigue damage of the asphalt mixture under variable amplitude loading in the step S1 is as follows:
selecting a low-high loading order and a high-low loading order, and carrying out an amplitude-variable loading fatigue test;
the test procedure includes the use of a first order stress amplitude sigma 1 N is carried out 1 The next stage of loading; then adopts the second-level stress amplitude sigma 2 N is carried out 2 Secondary loading to fatigue failure;
sigma is calculated based on damage equivalent criteria 1 Action N 1 The fatigue damage caused by the second generation is equivalent to sigma 2 Action N 2 ' secondary damage, as shown in formula (2):
D(σ 1 ,N 1 /N f1 )＝D(σ 2 ,N' 2 /N f2 ) (2)；
wherein N is f1 Is the load amplitude sigma 1 The fatigue life of the corresponding constant amplitude loading fatigue test; n (N) f2 Is the load amplitude sigma 2 Fatigue life of corresponding constant amplitude loading fatigue test and satisfies N f2 ＝N 2 +N 2 ’。
Preferably, in step S1, the specific method for establishing the asphalt mixture secondary loading life fraction prediction model considering the loading order is as follows:
substituting the formula (1) into the formula (2) according to the damage equivalence, and making the loading order parameter gamma= (1-alpha) 2 )/(1-α 1 ) Obtaining a secondary loading life fraction prediction model, wherein the secondary loading life fraction prediction model is shown as a formula (3):
wherein alpha is 1 For a load amplitude sigma 1 α of constant amplitude loading fatigue test; alpha 2 For a load amplitude sigma 2 α of constant amplitude loading fatigue test; n (N) 1 /N f1 And N 2 /N f2 The primary loading life fraction and the secondary loading life fraction are respectively.
Preferably, the specific method for determining the loading order parameter γ in step S2 is as follows:
fitting N by adopting (3) 1 /N f1 -N 2 /N f2 Curve, gamma in no load order:
wherein, gamma low-high And gamma high-low Load order parameters for the low-high and high-low load orders, respectively.
Preferably, the specific method for determining the asphalt mixture fatigue life prediction model under constant amplitude loading in the step S2 is as follows:
fitting test data by adopting a common fatigue equation shown in the formula (6) to obtain a fatigue life prediction model under constant amplitude loading, wherein the fatigue life prediction model is shown in the formula (7):
lgN f ＝a+blgσ (6)；
N f ＝10exp(a+blgσ) (7)；
wherein N is f Is fatigue life; a and b are model parameters; sigma is the stress amplitude.
Preferably, the specific method for establishing the asphalt mixture fatigue life prediction model considering the loading sequence in the step S2 is as follows:
establishing a fatigue life prediction model of the asphalt mixture under the low-high and high-low loading sequences, wherein the fatigue life prediction model is shown as a formula (8) and a formula (9):
wherein N is 1 The number of cycles for the first level loading; sigma (sigma) low Sum sigma high The low load amplitude and the high load amplitude are respectively;
and (3) predicting the fatigue life of the asphalt mixture according to the formula (8) and the formula (9).
The beneficial effects are that: (1) According to the invention, a two-stage loading amplitude variation fatigue test is carried out on the asphalt mixture, a load order considered fatigue life prediction model of the asphalt mixture is established, the influence of the vehicle running order on the vehicle cyclic load amplitude born by the asphalt pavement structure can be reflected to a certain extent, and the problem that the operability, accuracy and economy of the existing research on fatigue life prediction of the asphalt mixture cannot be well ensured is solved.
(2) Compared with the existing prediction method, the method can more accurately represent the nonlinear fatigue damage accumulation process of the asphalt pavement structure, realize the fatigue life prediction under variable amplitude loading, and improve the prediction precision of the service fatigue life of the asphalt pavement.
(3) The invention can provide reasonable theoretical basis for scientific management of asphalt pavement and can create good economic benefit.
Drawings
FIG. 1 is a schematic illustration of the preparation of a test piece in example 1;
FIG. 2 is a schematic loading diagram of the SCB constant amplitude fatigue test in example 1;
FIG. 3 is a schematic illustration of the luffing load fatigue test of example 1;
FIG. 4 is a graph of N1/Nf1-N2/Nf2 at different loading orders in example 1.
Detailed Description
The technical scheme of the invention is described in detail below through the drawings, but the protection scope of the invention is not limited to the embodiments.
Examples: according to the method for predicting the fatigue life of the asphalt mixture by considering the loading sequence through the semicircular bending (SCB) test, the semicircular bending (SCB) test can accurately simulate the mechanical response of the asphalt mixture under repeated load, and the test piece is relatively simple in preparation process and good in repeatability. The test temperature is 25 ℃ medium temperature, the heat preservation time is 2h, and the test equipment is a multifunctional hydraulic servo pavement material dynamic test system (DTS-30) loading device. The number of parallel test pieces is 3, and the corresponding results are averaged.
S1, performing semicircular bending fatigue test
1) Material and test piece preparation
Asphalt was selected as SBS modified asphalt, and its technical index was tested according to the procedure of Highway engineering asphalt and asphalt mixture test procedure, and the results are shown in Table 1. The aggregate and grading were granite and SMA, respectively, as shown in table 2. The asphalt content and void fraction were 6% and 4%, respectively. And forming a cylindrical asphalt mixture test piece with the diameter and the height of 150mm by adopting a rotary compaction instrument. As shown in fig. 1 (a), the test piece cutting process comprises the following steps: 1) Cutting off two ends with the height of 25mm along the horizontal direction to obtain a cylindrical test piece A; 2) Centering and cutting the test piece A along the horizontal direction to obtain a cylindrical test piece B with the diameter and the height of 150mm and 50mm respectively; 3) The test piece B was cut in a centered manner in the vertical direction to obtain SCB test pieces having diameters and thicknesses of 150mm and 50mm, respectively.
Table 1 asphalt technical index
| Index (I) | Results |
| Penetration (25 ℃ C.)/0.1 mm | 46 |
| Softening point/. Degree.C | 93 |
| Rotational viscosity (135 ℃ C.)/mPa.s | 2450 |
TABLE 2 aggregate grading
2) Constant amplitude load fatigue test
In order to minimize the friction between the loading mold and the test piece and to ensure that the crack propagates upward from the center of the bottom of the test piece, the mold support at the bottom of the test piece is designed as a horizontally slidable cylinder for supporting the test piece, and the fulcrum spacing satisfies 0.8 times the diameter of the test piece, and a load is applied to the top of the test piece, as shown in fig. 1 (b).
And (3) loading the test piece to fracture at a speed of 50mm/min, wherein a transverse tensile stress analysis solution of the SCB test piece is shown in a formula (1), and determining the strength of the test piece according to the formula (1). The breaking load of the test piece is recorded as sigma max Selecting two stress ratios (0.190 and 0.135) with moderate fatigue life to obtain a high load amplitude (sigma) of a fatigue test high ) And low load amplitude (sigma) low ) I.e. sigma high ＝0.190σ max ，σ low ＝0.135σ max 。σ max 、σ high 、σ low The results of (2) and the constant amplitude load fatigue life are shown in Table 3. FIG. 2 is a schematic loading diagram of SCB constant amplitude fatigue test. Starting the repeated loading program of the DTS-30, and selecting sigma respectively high Sum sigma low As a load amplitude, a semi-positive vector cyclic load with a frequency of 10Hz was applied until the SCB test piece was broken. Fatigue life of test piece (N) f ) The results are shown in Table 3.
Wherein: sigma is a transverse tensile stress analytical solution, kPa; l is the distance between fulcrums, mm; f is force, N; t is thickness, mm; omega is diameter, mm.
TABLE 3 fatigue life under constant amplitude loading
3) Amplitude-variable loading fatigue test
Select high-low (sigma high -σ low ) And low-high (sigma low -σ high ) The two loading orders are subjected to amplitude-variable loading fatigue test, and the loading steps of the load waveform and the frequency are consistent with those of constant amplitude loading fatigue test: the first-order fatigue life score (N) 1 /N f1 ) Setting the values to be 0, 0.15, 0.3, 0.6 and 1, and determining the first-stage loading times N of the luffing fatigue test 1 (＝N 1 /N f1 *N f1 ) The method comprises the steps of carrying out a first treatment on the surface of the Using primary load amplitude (sigma) 1 ) N is carried out on the test piece 1 The next stage of loading; then the first-order load amplitude (sigma) 2 ) N is carried out 2 The secondary load was subjected to fatigue failure and the primary load life fraction (N 1 /N f1 ) Second order load life score (N) 2 /N f2 ) Fatigue life (N) 1 +N 2 )。σ high -σ low The corresponding primary and secondary load amplitudes of the loading order are sigma respectively high Sum sigma low ，σ low -σ high The corresponding primary and secondary load amplitudes of the loading order are sigma respectively low Sum sigma high 。
(2) Establishing an asphalt mixture secondary loading life fraction prediction model under variable amplitude loading
1) Selecting asphalt mixture fatigue damage model under constant amplitude loading
And selecting a Chaboche damage model to represent the evolution rule of the fatigue damage of the asphalt mixture under constant amplitude loading, wherein the evolution rule is shown in a formula (2).
D＝1-[1-(N/N f ) 1/(1-α) ] 1/(1+β) (2)；
Wherein D is an asphalt mixture damage variable; n is the load cycle number; n (N) f Is fatigue life; beta is a temperature dependent model parameter; alpha is a model parameter that depends on temperature and load amplitude.
2) Asphalt mixture fatigue damage equivalence under variable amplitude loading:
sigma in the primary loading process is based on damage equivalent criterion 1 Action N 1 Secondarily produced leachingGreen mixture fatigue damage equivalent to sigma 2 Action N 2 ' the secondary damage is as shown in formula (3).
D(σ 1 ,N 1 /N f1 )＝D(σ 2 ,N' 2 /N f2 ) (3)；
In sigma 1 Sum sigma 2 The load amplitude values of the primary loading and the secondary loading are respectively; n (N) f1 For a load amplitude sigma 1 Fatigue life of a constant amplitude loading fatigue test; n (N) f2 For a load amplitude sigma 2 Fatigue life of a constant amplitude loading fatigue test; n (N) 1 /N f1 The life score is loaded for the first stage.
3) Establishing an asphalt mixture secondary loading life fraction prediction model considering a loading order:
substituting the formula (2) into the formula (3) according to the damage equivalence, so that the loading order parameter gamma= (1-alpha) 2 )/(1-α 1 ) And obtaining a secondary loading life fraction prediction model as shown in a formula (4).
Wherein alpha is 1 For a load amplitude sigma 1 α of constant amplitude loading fatigue test; alpha 2 For a load amplitude sigma 2 α of constant amplitude loading fatigue test; n (N) 1 /N f1 And N 2 /N f2 The primary loading life fraction and the secondary loading life fraction are respectively.
(3) Establishing an asphalt mixture fatigue life prediction model considering loading order under variable amplitude loading
1) Determining a loading order parameter gamma:
n of low-high and high-low load orders 1 /N f1 -N 2 /N f2 The curve is shown in fig. 4. Fitting N by adopting (4) 1 /N f1 -N 2 /N f2 Curve, gamma in no load order is determined. Load order parameters (gamma) resulting in a low-high load order low-high ) Load of 3.569, load order high-lowOrder parameter (gamma) high-low ) 0.794.
Wherein, gamma low-high And gamma high-low Load order parameters for the low-high and high-low load orders, respectively.
2) Determining an asphalt mixture fatigue life prediction model under constant amplitude loading:
fitting the load amplitude (sigma) using a common fatigue equation as shown in equation (7) high ) And low load amplitude (sigma) low ) And obtaining a fatigue life prediction model under constant amplitude loading according to the corresponding fatigue life under constant amplitude loading, wherein the fatigue life prediction model is shown in a formula (7).
lgN f ＝a+blgσ (7)；
N f ＝10exp(1.525-3.716lσ) (8)；
Wherein a and b are model parameters; sigma is the stress amplitude.
3) Establishing an asphalt mixture fatigue life prediction model considering loading order under variable amplitude loading
And (3) establishing fatigue life prediction models of the asphalt mixture in low-high and high-low loading sequences, namely a formula (9) and a formula (10), and performing fatigue life prediction of the asphalt mixture by the formula (9) and the formula (10).
N f ＝N 1 +10exp(1.525-3.716)lgσ high [1-(N 1 /N f1 ) 3.569 ] (9)；
N f ＝N 1 +10exp(1.525-3.716)lgσ low [1-(N 1 /N f1 ) 0.794 ] (10)。
4) Asphalt mixture fatigue life prediction model verification
In order to verify the effectiveness of the built model, other working conditions are kept unchanged, and an amplitude-variable loading fatigue test with the primary loading life score of 0.4 is carried out in a complementary mode. Comparing the test result of the variable amplitude loading fatigue life with the prediction result, the comparison result is shown in table 4, and the relative errors are 6.083% and 2.601%, which shows that the constructed model can accurately predict the fatigue life of the asphalt mixture under different loading orders.
TABLE 4 comparison of fatigue life prediction results
As described above, although the present invention has been shown and described with reference to certain preferred embodiments, it is not to be construed as limiting the invention itself. Various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (1)
1. The fatigue life prediction method for the asphalt mixture taking the loading sequence into consideration is characterized by comprising the following steps of:
s1, establishing an asphalt mixture secondary loading life fraction prediction model under variable amplitude loading:
carrying out constant amplitude and amplitude-variable load fatigue tests on the asphalt mixture, determining an asphalt mixture fatigue damage model under constant amplitude load and asphalt mixture fatigue damage equivalence under amplitude-variable load, and establishing an asphalt mixture secondary load life fraction prediction model considering a load order based on damage equivalence criteria;
the specific method for determining the asphalt mixture fatigue damage model under constant amplitude loading comprises the following steps:
respectively selecting high load amplitude sigma high And low load amplitude sigma low As a constant load amplitude sigma, performing a constant load fatigue test; selecting a Chaboche damage model, and representing an evolution rule of asphalt mixture fatigue damage under constant amplitude loading, wherein the evolution rule is shown as a formula (1):
D＝1-[1-(N/N f ) 1/(1 - a) ] 1/(1+β) (1)；
wherein D is an asphalt mixture damage variable; n is the load cycle number; n (N) f Is fatigue life; alpha is a model parameter dependent on temperature and load amplitude; beta is a temperature dependent model parameter;
the specific method for equivalent fatigue damage of the asphalt mixture under variable amplitude loading comprises the following steps:
selecting a low-high loading order and a high-low loading order, and carrying out an amplitude-variable loading fatigue test;
the test procedure includes the use of a first order stress amplitude sigma 1 N is carried out 1 The next stage of loading; then adopts the second-level stress amplitude sigma 2 N is carried out 2 Secondary loading to fatigue failure;
sigma is calculated based on damage equivalent criteria 1 Action N 1 The fatigue damage caused by the second generation is equivalent to sigma 2 Action N 2 ' secondary damage, as shown in formula (2):
D(σ 1 ,N 1 /N f1 )＝D(σ 2 ,N’ 2 /N f2 ) (2)；
wherein N is f1 Is the load amplitude sigma 1 The fatigue life of the corresponding constant amplitude loading fatigue test; n (N) f2 Is the load amplitude sigma 2 Fatigue life of corresponding constant amplitude loading fatigue test and satisfies N f2 ＝N 2 +N 2 ’；
The specific method for establishing the asphalt mixture secondary loading life fraction prediction model considering the loading order comprises the following steps:
substituting the formula (1) into the formula (2) according to the damage equivalence, and making the loading order parameter gamma= (1-alpha) 2 )/(1-α 1 ) Obtaining a secondary loading life fraction prediction model, wherein the secondary loading life fraction prediction model is shown as a formula (3):
wherein alpha is 1 For a load amplitude sigma 1 α of constant amplitude loading fatigue test; alpha 2 For a load amplitude sigma 2 α of constant amplitude loading fatigue test; n (N) 1 /N f1 And N 2 /N f2 The first-stage loading life fraction and the second-stage loading life fraction are respectively;
s2, building an asphalt mixture fatigue life prediction model considering a loading sequence:
fitting a secondary loading life fraction prediction model to determine loading order parameters, determining an asphalt mixture fatigue life prediction model under constant amplitude loading, and finally establishing an asphalt mixture fatigue life prediction model considering the loading order according to the obtained loading order parameters and the asphalt mixture fatigue life prediction model under constant amplitude loading, so as to predict the asphalt mixture fatigue life;
the specific method for determining the loading order parameter gamma comprises the following steps:
fitting N by adopting (3) 1 /N f1 -N 2 /N f2 Curve, gamma corresponding to low-high and high-low loading order is determined:
N 2 /N f2 low-high ＝1-(N 1 /N f1 ) γlow-high (4)；
N 2 /N f2 high-low ＝1-(N 1 /N f1 ) γhigh-low (5)；
wherein, gamma low-high And gamma high-low Load order parameters for the low-high and high-low load orders, respectively;
the specific method for determining the asphalt mixture fatigue life prediction model under constant amplitude loading comprises the following steps:
fitting test data by adopting a common fatigue equation shown in the formula (6) to obtain a fatigue life prediction model under constant amplitude loading, wherein the fatigue life prediction model is shown in the formula (7):
lgN f ＝a+blgσ (6)；
N f ＝10exp(a+blgσ) (7)；
wherein N is f Is fatigue life; a and b are model parameters; sigma is the stress amplitude;
the specific method for establishing the asphalt mixture fatigue life prediction model considering the loading sequence comprises the following steps:
establishing a fatigue life prediction model of the asphalt mixture under the low-high and high-low loading sequences, wherein the fatigue life prediction model is shown as a formula (8) and a formula (9):
N f low-high ＝N 1 +10exp(a+blgσ high [ 1- (N 1 / N f1 ) γlow-high ] (8)；
N f high-low ＝N 1 +10exp(a+blgσ low )[ 1- (N 1 / N f1 ) γhigh-low ] (9)；
wherein N is 1 The number of cycles for the first level loading; sigma (sigma) low Sum sigma high The low load amplitude and the high load amplitude are respectively;
and (3) predicting the fatigue life of the asphalt mixture according to the formula (8) and the formula (9).
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