In order to investigate the creep performance of cement asphalt mortar (CA mortar), the field sampling of CA mortar cylinder samples was produced, and all samples were tested on WDW series electric universal testing machine by using uniaxial static creep test at 25°C, and the load stress levels were 0.05 MPa, 0.1 MPa, 0.3 MPa, and 0.5 MPa. The greater the load is, the bigger the creep deformation is. The creep performance was simulated by using Burgers model, and the correlation coefficients between fitting results of Burgers model and experimental results are all greater than 0.9. Based on the requirements of finite element software, the Prony series of Burgers model was obtained, and the short-term creep process of CA mortar was simulated by the finite element software ANSYS. The relative error between simulation results and experimental data is not more than 2.5%, which indicates that the short-creep process of CA mortar can be simulated by ANSYS software. The study results can improve the structural design theory of slab track.
1. Introduction
The nonballast slab track consists of concrete roadbed, reinforced concrete track slab, and cement asphalt mortar (CA mortar) injected between the roadbed and track slab [1]. With the rapid development of high-speed railway, cement and asphalt mortar (CA mortar) which is the key material of the cushion layer of ballastless slab track is widely used in high-speed railways in Japan [2, 3], Germany, France, and China [4], and it consists of cement, emulsified asphalt, fine aggregates, water, and admixtures and is an organic–inorganic composite material formed by mechanical mixing, whose main functions are supporting and adjustment, buffer and load transfer, blocking cracking, and providing elasticity and resistance for track structure [5]. CA mortar is very important for the safety, stability, and comfortable degree of high-speed railway [6].
As a viscoelastic material and in order to meet its service environment and construction conditions, the physical and chemical properties of CA mortar and mechanical properties have been studied extensively [7–13]. Wang et al. [7] investigated the compressive strength developing process and the microstructure of CA mortar. Yutaka et al. [8] introduce the CA mortar used in cold weather, and Kazuyosi and Yosio [9] and Wang et al. [10] studied the compressive strength of CA mortar and its temperature susceptibility. Liu et al. [11] studied the static and dynamic mechanical properties of CA mortar. Qiu et al. [12] studied the fatigue behavior of CA mortar and proposed the fatigue equation. Xu et al. [13] investigated the dynamic compression damage properties of CA mortar under different strain rates. These research results play a useful guiding role in actual projects. Creep property is an important index for evaluating the viscoelastic behavior of CA mortar, and according to survey, after the high-speed railway has been operated for 3–5 years, the CA mortar layer will have unrecoverable deformation. Therefore, the study on the creep properties of CA mortar is very necessary.
Creep is the case that the deformation of material increases with the growth of time at constant load. Uniaxial static load creep test is one of the principal methods of studying material viscoelastic properties. Xie et al. [5] studied the long-term deformation properties and creep properties of CA mortar. Li and Jiang [14] conducted uniaxial creep test of asphaltic sand under 6 loading stresses at 20°C, and the results showed that the Burgers model can reflect asphaltic sand’s viscoelasticity well. Guo and Zhao [15] studied the effects of fiber content on the creep performance of fiber reinforced asphalt concrete by using uniaxial creep test, and the reasonable fiber content is 0.2%.
As the buffer, damping structural layer of slab track, CA mortar is mainly under the vertical load and in dynamic loading process [16], so the short-term creep properties are also needed to be researched. In this work, the relationship between deformation of CA mortar and time was measured under uniaxial static load through uniaxial compression creep test. The creep properties of CA mortar under different stress level were studied, and the test curve was fitted, which could provide an experimental basis for the optimization of CA mortar and design of slab track.
2. Experimental2.1. Raw Materials and Specimen Fabricating
In order to reflect the mechanical properties of CA mortar in field CRTS I type slab track, the CA mortar specimens used in this experiment were sampled in the construction field. The lift plate test of field CA mortar layer of CRTS I type slab track was conducted firstly. And then, core samples were taken on the CA mortar layer. Specimens are cylinder specimens with the size of φ50 × 50 mm. Sampling process and part specimens of CA mortar layer are shown in Figure 1.
Sampling process and part specimens.
The raw materials of CA mortar field specimens come from Anhui Engineering Material Technology Co., Ltd., of CTCE Group. The 24 h volume expansion rate of these cement emulsified asphalt mortar special dry ingredients is 2.1%, whose 7 d line expansion rate is 0.1% and the 1 d compressive strength is 6.89 MPa. The asphalt emulsion is the special emulsified asphalt of CA mortar on CRTS I type slab ballastless track, whose solid mass fraction is 62.1%. Average strength of CA mortar specimens is 2.63 MPa and the elasticity modulus is 269.58 MPa. Other properties meet the Chinese regulation [17] put in references. The mix proportion of CA mortar is m(dry ingredients) : m(asphalt) : m(water) = 1000 : 500 : 60. Mixing water is tap water. The age of CA mortar used in the creep test is 180 d.
2.2. Experimental Method
The experiment was conducted by WDW series microcomputer electronic universal testing machine, and this machine was controlled by computer, driven by a servomotor, and loaded by precision ball screw machine. There is load sensor in the compressive direction. The displacement was measured by high precision displacement sensor. The accuracy of this experiment machine can reach to 10^{−3 }mm. This machine has the advantages of stable loading, accurate measurement, and the machine can collect load and displacement data automatically.
The creep test of CA mortar is conducted by uniaxial compressive creep test. According to the stress of CA mortar in actual engineering which is 0.1 MPa [18], considering the deterioration of track irregularity and the disease of CA mortar, when the debonding length of CA mortar varies from 0.0 m to 1.0 m, the stress of CA mortar varies from 0.057 MPa to 0.53 MPa [19]. Short-creep properties of CRTS I type slab ballastless track were studied, respectively, at 4 load levels (0.05 MPa, 0.1 MPa, 0.3 MPa, and 0.5 MPa). The experimental temperature was controlled in 23±2°C. The experimental process is first preload (0.005 MPa) 10 min and then applied to the required load moment and kept in 60 min, and then the experiment is ended. The deformation measurement is the key point in a creep test. The creep deformation was collected automatically by the electronic universal testing machine, which can ensure the reliability and accuracy of data to measure. There were 3 specimens in each group, and the final result was the average deformation of 3 specimens. Two loading surfaces were coated with French chalk to reduce the surface restraint effect and three samples were used for each test as duplication. If test results are discrete, the number of specimens should be increased in order to ensure the validity of test data.
3. Results and Analysis
According to test results, the average values of the test results are listed in the same coordinate system. Creep curves of CA mortar under different load level are shown in Figure 2.
Creep curves of CA mortar under different load level.
As shown in Figure 2, the shapes of creep curves of CA mortar are similar under different load level. CA mortar can be seen as three-phase system: asphalt, cement gel, and fine aggregates. In the beginning of the three-phase system of CA mortar bearing the load together, with the passage of time, the asphalt gradually unloads due to viscous flow, and the cement gel and fine aggregates bear more load and have elastic deformation [5]. Under the action of instantaneous load, CA mortar produces the instantaneous deformation, and the deformation increases sharply. With the sustaining action of a constant load, the deformation of CA mortar increases, and the final incremental deformation is gradually stabilized. This stage of deformation is called delayed elastic deformation, and then CA mortar shows a viscous flow gradually. The higher the load level is, the larger the creep deformation of CA mortar is. When the load stress is 0.05 MPa, the creep deformation of CA mortar is 0.074 mm. When the load stress is 0.5 MPa, the creep deformation is 0.431 mm. The creep deformation of CA mortar increases by 5.82 times when the load stress varies from 0.05 MPa to 0.5 MPa.
4. Creep Model
Viscoelasticity material can be described by an appropriate mathematical model, and the basic components used to describe the viscoelastic properties are hook springs and Newton sticky pot. There are viscoelastic models: Maxwell model, Kelvin model, Burgers model, and generalized Maxwell model used in engineering, and the Burgers model could reflect the creep and relaxation properties. In this paper, the Burgers model was selected to describe the creep property of CA mortar.
4.1. Creep Model and Constitutive Equations
Burgers model consists of two hook springs and two Newton sticky pots. The Burgers model was shown in Figure 3.
Schematic diagram of Burgers model.
Burgers model is four-parameter fluid model and its constitutive relation can be expressed as(1)σ+p1σ˙+p2σ¨=q1ε˙+q2ε¨.Here, p1=η1/E1+η1+η2/E2, p2=η1η2/E1E2, q1=η1, and q2=η1η2/E2.
The creep compliance can be obtained by formula (1), which can be expressed as(2)Jt=1E1+tη1+1E21-e-E2t/η2.For the Burgers model, the total deformation of CA mortar under stress of σ=σ0H(t) is(3)εt=σ01E1+tη1+1E21-e-E2t/η2.Here, E1, η1, η2, and E2 are model parameters, t is the experiment time, and σ0 is the loading stress.
4.2. Parameters Calculation of Creep Model
The viscoelastic parameters of the model are determined by mathematical iteration method. According to the creep test data, the nonlinear fitting method was provided by Origin software. The initial parameters are assumed and the parameters of the model are obtained by the given function expression.
It is assumed that the initial values of Burgers model parameters E1, η1, E2, and η2 are 120, 5e5, 60, and 7e3, the fitted parameters of CA mortar under different stress level are shown in Table 1, and the fitted results are shown in Figure 4.
Parameters of Burgers model.
Load level/MPa
Model parameters
Correlation coefficient
E1/MPa
η1/(10^{5} MPa⋅s)
E_{2}/MPa
η_{2}/(10^{4} MPa⋅s)
0.05
31.957
9.289
163.123
1.782
0.981
0.1
33.326
13.68
172.126
1.958
0.974
0.3
58.862
13.295
168.315
1.638
0.987
0.5
84.549
16.691
215.809
2.09
0.989
Fitting curves of Burgers model and experimental curves of CA mortar.
As shown in Table 1 and Figure 4, the Burgers model can effectively predict the short-term creep of CA mortar under different load level.
For the Burgers model, elastic parameter E1 determines the initial position in the creep process, which reflects the ability to resist deformation of CA mortar. Elastic parameter E2 determines the value of delayed elastic deformation of CA mortar, viscosity parameter η1 influences the curve slope of viscous flow deformation, and viscosity parameter η2 controls the bending extent of the delayed elastic deformation curve.
4.3. Simulation of CA Mortar Creep Process
The mechanical parameters of material are required by the Prony series when calculating the viscoelastic mechanics using the ANSYS finite element software. According to [20], the shear modulus of the Burgers model can be expressed as Prony series as follows:(4)Gt=G∞+G0g1e-t/τ1+g2e-t/τ2.Here, G∞=0, G0=G1, g1=1/α-β(G2/n2-β), g2=1/α-β(α-G2/n2), τ1=1/β, τ2=1/α, and n2=η2/3, where g1, g2, τ1, and τ2 are the coefficients needed to be entered, which correspond to the ANSYS software in the specified Prony series, respectively. And E1, μ are the initial elastic modulus and Poisson’s ratio.
Since the stress of CA mortar is 0.1 MPa in actual engineering [18], the Burgers model parameters under 0.1 MPa were put into the formula above, and the Prony series g1, g2, τ1, and τ2 of Burgers model needed to be entered in ANSYS software are shown in Table 2.
The Prony series of Burgers model parameters.
Load stress/MPa
Prony series of Burgers model
g1
g2
τ1
τ2
0.1
0.1628
0.8371
95.303
49016.136
In order to calculate simply, the model is a rectangle with size 1 m × 2 m × 1 m, and the size of an element is 1 m × 1 m × 1 m. The calculation model of ANSYS software is shown in Figure 5. The calculation model was simulated by solid 185, which has the properties of super elasticity, stress toughened, creep, large deformation, and large strain. The model has two elements, and the axial uniformly distributed load p=100 kN/m^{2}. According to the element area, the stress of each unit is 0.1 MPa, and the load time is 3600 s. The axial strain of unit 1 was chosen as a comparative data. Creep test data, fitting data, and ANSYS calculation results are compared in Table 3.
Compared with the result of creep test, fitting data, and ANSYS calculated.
Time/s
Test data (strain)
Fitting data of Burgers model
Calculation results of ANSYS
Total strain
Relative error
Total strain
Relative error
10
0.00307
0.00305
0.651%
0.00308
−0.326%
20
0.00314
0.003096
1.40%
0.00312
0.637%
30
0.00319
0.003137
1.66%
0.00315
1.25%
40
0.00323
0.003176
1.67%
0.00319
1.24%
50
0.00326
0.003211
1.50%
0.00322
1.22%
100
0.00337
0.003348
0.653%
0.00333
1.18%
150
0.00342
0.003437
−0.497%
0.00341
0.292%
200
0.00347
0.003496
−0.749%
0.00345
0.576%
500
0.00359
0.003611
−0.585%
0.00355
1.11%
1000
0.00367
0.003655
0.408%
0.00359
2.18%
1500
0.0037
0.003691
0.243%
0.00362
2.16%
2000
0.00374
0.003728
0.321%
0.00365
2.40%
2600
0.00377
0.003772
0.053%
0.00369
2.12%
3600
0.0038
0.003801
0.026%
0.00375
1.31%
Calculation model of ANSYS.
As shown in Table 3, the relative error of creep experimental data of CA mortar and fitting data is less than 1.7%, and the relative error and ANSYS calculation results are below 2.5%. The short-term creep process of viscoelastic material can be simulated using ANSYS software. The differences between test data, fitting data, and ANSYS calculation results are mainly due to the error of fitting and viscoelastic parameters transform to Prony series.
5. Conclusions
The short-term creep properties of CA mortar were studied by the independently uniaxial static creep experiment, the creep properties of CA mortar were fitted by Burgers model, and the short-term creep process was simulated by ANSYS software. The following conclusions can be drawn:
CA mortar as a typical viscoelastic material has obvious creep characteristics, the shapes of creep curves of CA mortar are similar under different load level, and the higher the load level is, the larger the creep deformation of CA mortar is. When the load level reaches 0.5 MPa, the creep deformation is 0.431 mm; compared to the creep deformation under the load level 0.05 MPa, the creep deformation of CA mortar increases by 5.82 times.
A creep constitutive model of CA mortar based on the Burgers model is established. The model has a simple form and can predict the short-term creep deformation of CA mortar, and the correlation coefficients of the creep constitutive model of CA mortar are more than 0.9.
The short-term creep process of viscoelastic material can be simulated using ANSYS software. And the differences between test data, fitting data, and ANSYS calculation results are mainly due to the error of fitting and viscoelastic parameters transformed to the Prony series. Meanwhile, the application of the creep model to describe the creep properties of CA mortar under high-speed vehicle load needs to be further studied.
Competing Interests
The authors declare that they have no competing interests regarding the publication of this paper.
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