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Research on damage mechanics of modified soil sub-grade in cold regions under coupling effect of freeze-thaw cycle and load.

1. Introduction

Frost heave and thaw collapse of frozen soil sub-grade in cold regions have long been plaguing the stability and the normal operation of line projects. Frost heave, thaw collapse and frost soil are several phenomena arising when soil body of sub-grade is under load effect of trains during the freezing and thawing process, and they have close inner links. Soil frost heave and thaw collapse are complex processes, involving moisture migration, change of temperature field and effect of stress field. The sub-grade in Tibetan Plateau has long stayed in water-heat interaction in the system of atmosphere-active layer of soil body-permafrost (Li SQ., Gao LX., Chai SX., 2012). Due to the features of plateau, such as large temperature difference between day and night and prominent climate change, the sub-grade is easily to undergo relatively large frost heave and thaw collapse under the joint effect of water, heat and force; meanwhile, the intensity is prone to degrade, resulting in plastic failure. This is the fundamental reason why the sub-grade defects easily happen in the cold highland regions (Galvan, J. B., Recarte, L., & Perez- Ilzarbe, M. J., 2014).

With the great development of railway construction, currently the modified soil has been widely applied in paving sub-grade in cold regions due to its low price, relatively stable mechanical properties and relative high intensity. At present, the research on the basic properties and freeze-thaw damage characteristics of the modified soil is mainly conducted by test under the conditions of temperature change and frost-thaw cycle (Lai YM., Yang YG., Chang XX., 2010). Numerous studies have indicated that the frost- thaw effect can not only change the structure, intensity, volume, void ratio, permeability, density and modulus of the modified soil, but also speed up the damage.

There is lack of research on the freeze-thaw damage model of the modified soil now. Most studies of the rock body are conducted from the angle of material microstructure and literatures about researches of freeze-thaw mechanics with the method of damage mechanics are few. For instance, through the CT test, Ge Xiurun (Yang Gengshe, Zhang Quansheng, Pu Yibin., 2004) and other people have analyzed the extension law of rock microscopic damage and the damage characteristics. Through the CT scanning technology, Sun Xingliang (Lianbo, zhang guisheng., 2006) and other people have made a dynamic observation of the change of the permafrost's microstructure damage during the triaxial shear process, and analyzed the evolution mechanism of the permafrost's microstructure damage. Based on the distribution law of CT numbers of scanning rock, Yang Gengshe and other people (Jing GQ., Feng K., Gao L., Wang J., 2012) have established a mathematical model, and deduced the quantitative relationship between the rock damage density and CT numbers (Zhou FX., Lai YM. , 2010).

As an artificial remodeled soil, the modified soil has a high degree of compaction and a high intensity. In the aspect of mechanical damage, it has the elastic-brittle property similar to that of the concrete as well as the mechanical characteristic of the soil body. In the aspect of freeze-thaw damage, during the freezing process at low temperature, the moisture migration results in the increase in the moisture content on the frontal surface of the frozen soil body, thus intensifying the volume expansion and increasing the pore volume of the soil body. Meanwhile, the volume expansion from water to ice breaks the original structure, thus changing the property of the soil body. When the pore ice melts, some enlarged pores cannot return to their original states, so that the soil body becomes relatively loose and the binding strength between soil particles reduces, thus resulting in freeze-thaw damage (Xu XZ., Sun X., 2005).

Taking the sub-grade modified soil as the research object, using the constitutive theory of concrete damage, combining the actual mechanical properties of lime modified soil and cement modified soil, this paper makes a research on the its damage evolution law under the condition of freeze thawing and load coupling. We believe that: under the condition of freeze-thaw cycle, the damage of the modified soil can be equivalent to coupling of the two modes of freeze thawing and load. This paper considers the coupling of freeze thawing and load, explores the damage form and evolution process in the micro- level occurring inside the sub-grade modified soil, and establishes the freeze thawing-load damage model (Zhou FX., Lai YM., 2010).

Description of the problem.

2. Soil Damage Model Under the Freeze-Thaw Cycle and Load 2.1. Damage Model

Damage mechanics theory is a powerful tool to evaluate and predict materials and the macroscopic mechanical behaviors of its structure, and settle the issue concerning the failure of material or its structure in the practical engineering. When the material damage is analyzed through the damage mechanics theory, it is necessary to select the appropriate damage variables to define ad describe the damage degree of materials. According to the strain equivalence hypothesis created by Professor Lemaitre: the strain caused by the effect of total stress [sigma] on the damaged material is equivalent to the strain caused by the effect of the effective stress [sigma]' on the undamaged material, namely:

[epsilon] = [[igma].sup./]/[E.sub.0] = [sigma]/[E.sup./] (1)

The strain energy density of the damaged material is:

[rho][phi] = 1/2[E.sup./] [[sigma].sup.2] [rho][phi] = 1/2[E.sup./] [[epsilon].sup.2] (2)

According to the remained strain energy equivalent proposed by Sidoroff, namely:

[rho][phi] = 1/2[E.sup./] [[sigma].sup.2] = 1/2E [[sigma].sup./2] (3)

Wherein [[sigma].sup./] = [sigma]/1-D (4)

D is the damage factor.


[rho][phi] = 1/2E[(1-D).sup.2] [[sigma].sup.2] (5)

According to the orthogonal relationship, there is:

[epsilon] = [rho] [partial derivative][phi]/ [partial derivative][sigma] = 1/E[(1-D).sup.2][sigma] (6)

Namely, the stress-strain relationship is:

[sigma] = E[(1--D).sup.2][epsilon] (7)

The release rate of damage strain energy is:

y = [rho] [partial derivative][phi]/ [partial derivative]D = 1/E[(1- D).sup.3][[sigma].sup.2] = E(1-D)[[epsilon].sup.2] (8)

Assume the damage evolution equation is:

y = A([epsilon]) dD/dz (9)

Wherein, Z is the value indicating the transformation increase. It is the function of [epsilon] . So

dD/dz = 1/A9[epsilon]) E(1-D)[[epsilon].sup.2] (10)



Wherein, [z.sub.0] is the initial damage threshold (Bi GQ., Zhang X, Li GY., 2010), namely, when z > [z.sub.0], the material damage will happen. If taking A([epsilon]) = E/k [[epsilon].sup.2].

Then the damage evolution equation is:

D = 1-exp[-k(z-[z.sub.0])] (12)

We define: z = [[epsilon].sub.max], [[epsilon].sub.max] is the maximum strain that the material reached. For axial loading, z = [[epsilon].sub.max] = [epsilon].

2.2. Freeze-Thaw Damage Factor

Here we define a dependent variable [[epsilon].sub.n] that can indicate the freeze-thaw damage. It is a parameter reflecting the relation between the freeze-thaw frequency and the strain. To stabilize the ratio of the thaw deformation to the height of the soil body before freeze thawing, namely:

[[epsilon].sub.n] = [h.sub.0] -[h.sub.n]/[h.sub.0] (13)

Wherein, [h.sub.0] is the original height of the specimen; hn is the height of specimen after n-time freeze thawing, measured through test, n is the number of freeze-thaw cycles.

Consider the damage constitutive equation can be expressed as:

[sigma] = [(1--D).sup.2] E[epsilon] (14)


After discussion of the above equation, it can be seen that:

When there is no freeze-thaw damage, material only suffers the mechanical damage, then,


Equation (14) shows that the total freeze-thaw load bearing damage to the soil body changes along with 2 evolution approaches of freeze thawing and strain, reflecting the character that the freeze-thaw cycle index and strain are mutually coupled and affected with the material damage propagation, so that the damage mechanical behavior of frozen soil and damage propagation law can be relatively truly revealed.

Equations (14) and (15) show that, when [epsilon] = 1/2k, [sigma]-[epsilon] curve has the extreme point; when [epsilon] = 1/2k, [sigma]-[epsilon] curve has the inflection point, and therefore:

k = 1/2[[epsilon].sub.u] (17)

Wherein, [[epsilon].sub.u] is the strain at the stress-strain peak value of modified soil, therefore, equation (14) can be turned into.


If taking [[epsilon].sub.0 = 0, then equation (17) is changed as the damage factor under the condition of freeze-thaw cycle and load coupling:


3. Experimental Verification

3.1. Freeze-Thaw Cycle Test

The freeze-thaw process is the process of soil body from the unstable state to the stable state and the repeated freeze-thaw cycle changes its property and shape, so that the soil body develops towards a new dynamic stable state. In order to understand the impact of freeze-thaw cycle and load on the damage factor of specimen in an accurate way, it is required to measure its heights before and after freeze thawing, for subsequent calculations.

This paper respectively analyzes the 9% lime modified soil and 6% cement modified soil and studies the damage constitutive relation under the coupling effect of freezethaw cycle and load. The cement is 325 labeled Portland slag cement and the initial setting time is 4h; the lime is the calcium quicklime powder. Respectively mix the cement modified soil and lime modified soil, retain them for a day, process them into the cylindrical specimens of [phi]39.imm x 80mm, and then start the freeze-thaw cycle test. Put the prepared specimen into the freeze-thaw test chamber for freeze-thaw cycle test. It shall be maintained for i2 hours in the incubator at a negative temperature for freezing; and it shall be maintained for 12 hours in the incubator at 50 when thawing. This process is a freeze-thaw cycle period (Wang L., Zhang S., Peng SB., 2010).

The following figure is the temperature-time curve in the incubator in the freeze-thaw process.


The freeze-thaw cycle periods are selected as 0, 1, 3, 6, 8, 10 times. After the cycling times are reached, some specimens shall be taken for triaxial compression, and freeze- thaw cycle test shall be continued for the remaining specimens. Then observe the height change of the tested specimens, draw the relation chart A(sn)-n, which is shown in Figure 2.


3.2. Experimental Determination of the Thaw Coefficient

The relation between the height of specimen after the freeze-thaw stability and the cycle index is in exponential decrease, therefore, after regression, A-n can be fitted to the following equation.

A = 1- -a[e.sup.-n/l] + [h.sub.w]/[h.sub.0] (20)

hw is the specimen height after stability of repeated freeze-thaw cycles; ho is the original height of specimen; n is the freeze-thaw cycle index; a, l are the fitting test parameters. According to Figure 2, the fitting results are as follows:

It is difficult to obtain the thaw height of specimen in the final stable state, so it can be replaced by the basic thaw height after several freeze-thaw cycles. Figure 2 shows that, through the analysis of the results after 0, 1, 3, 6, 8, 10 freeze-thaw cycles, the specimen height and its moisture content basically remain constant. This indicates that its internal structure reaches a new dynamic balance though 8-time freeze-thaw cycles. The specimen volume is no longer affected by freeze-thaw effect. According to the above conclusion, this paper may select the specimen height at the 8-time cycle as the stable thaw height. In addition, it is suggested to select the specimen height at the 8-time cycle as the stable thaw height in the practical application.

3.3. Constitutive Model Verification Under the Freeze Thawing and load

After the sub-grade soil undergoes several freeze-thaw cycles, its defects continuously produce and expand, resulting in freeze-thaw damage inside the sub-grade. The load borne by the sub-grade soil under the condition of freeze-thaw cycle can be equivalent to the damage to the soil under the two kinds of loads. Thus, the damage factor should scientifically reflect the coupling effect of the freeze thawing and load.

Substitute equation (19) into the equation (18), and obtain the change law of the damage factor of the loaded soil through many freeze-thaw cycles. Therefore, the coupling damage factor can be expressed as equation (20):


The elastic modulus of the modified soil modulus in each freeze-thaw cycle can be calculated by the empirical formula (21):

The ratio of the increment of deviatoric stress corresponding to the axial strain of 1.0% to the increment of axial strain is used as the elastic modulus for the research on clay:

E = [DELTA][sigma]/[DELTA][epsilon] = [[sigma].sub.1.0%] - [[sigma].sub.0]/ [[epsilon].sub.1.0%] - [[epsilon].sub.0] (22)

Wherein, Act is the increment of deviatoric stress; [DELTA][epsilon] is the increment of axial strain, [[sigma].sub.1.0] is the deviatoric stress ([[epsilon].sub.1.0%]) corresponding to the axial strain of 1.0%; [[sigma].sub.0] and [[epsilon].sub.0] are respectively the initial stress and strain. Therefore, according to the measured data in the triaxial compression test and the formula (21), the elastic modulus of each modified soil in Table 1 can be concluded.

Combine the test data of modified soil in literature 8, and take the su of the damage factor as 2.0 % (Quan XJ., Li N., Li GY., 2004).

3.4. Constitutive Model Verification

Compare the test data and the results of equation (14), shown in the following figure:



Figure 3 and Figure 4 show the test data based on the triaxial compression test. Compared with the results curve obtained from the damage constitutive formula under the freeze thawing and load (14) proposed by this paper, it can be the calculation of damage can be better consistent with the observed results in terms of change trend especially at the rise of curve, and the test data is identical with the predicted data. However, in the strain softening stage, the fitting effect of the prediction curve is relatively poor. The reason, the author think, is that the constitutive model given by this paper is established based on the elastic-brittle damage of the concrete and considering freeze-thaw cycle and the plastic failure is also reflect after the invalidation of the modified soil, therefore, the constitutive model has limitations. Specimen stress curve takes the peak point as the demarcation point, namely, it is divided into ascent part and descent part. In test, we observe that the modified soil specimen has been damaged after the peak point. Therefore, the constitutive model of the damaged modified soil under the freezethaw cycle proposed in this paper has the features of utility in engineering utility and convenience in research.

4. Results

Figure 5 and Figure 6 show the change laws of the damage factor of the two kinds of modified soils under the effect of different freeze-thaw cycles and axial load, obtained from the Matlab programming calculation of equation (20).

Figure 5 and Figure 6 show that, the deterioration degree of the freeze-thaw damage of lime modified soil increases sharply with the increase in freeze-thaw cycles, especially compared with no freeze-thaw cycle, and there is significant difference of the damage degree, indicating that its freeze-thaw durability is poor. For the cement modified soil of 10 or less freeze-thaw cycles, the damage increases with the increase in freeze-thaw cycles and the intensity decreases slightly; in case of 10 -20 cycles, the damage variable changes little and the freeze-thaw damage tends to be constant, indicating that the mechanical properties of the cement modified will tend to be stable after a certain freezethaw cycles. The first freeze-thaw cycle affects the soil most largely. With the increase in the freeze-thaw cycle, the intensities tend to be constant values. Under the same freezethaw cycles, the damage respectively to the cement modified soil and lime modified soil increases with the increase in the strain. The initial stage of the load-bearing modified soil before freeze thawing is the damage attenuation stage. The micro-pores and microcracks in the soil gradually close and the density and intensity increase. Afterwards, the mechanical property of the modified soil is in the linear stage. When the deformation reaches a certain level, the damage to the modified soil begins to evolve and expand stably until the damage propagates at an accelerated speed. Accompanied are the micro- cracks initiation, propagation and convergence in the modified soil. The macroscopic damage occurs, then the intensity of the soil body is reached, and thus the damage occurs.



5. Conclusion

The freeze thawing and load induce the damage with the different mechanical mechanisms. They are mutually coupled and affected.The evolution law of the mechanical properties about the cement modified soil and lime modified soil obtained from the damage model under the freeze thawing and load, are consistent with test phenomena and analysis conclusion in literature 8.

1. The freeze thawing and load are bound to bring changes to the mechanical properties of the modified soil. The joint effect of the freeze thawing and load can intensify the total damage to the soil body. Based on the strain equivalence hypothesis, created by professor Lemaitre, this paper establishes the modified soil damage constitutive model under the coupling effect of the freeze-thaw cycle and load. Its calculated fitting results are relatively identical with the test data, indicating that the damaged modified soil constitutive formula is reasonable and feasible. This constitutive model is simple with clear concepts and with no need of assumptions. It has a good practical value.

2. Through damage calculation, under the same freeze-thaw cycles, the damage respectively to the cement modified soil and lime modified soil increases with the increase in the strain. On the same degree of damage, with the increase in the freeze-thaw cycles, the strains of two kinds of modified soils decrease. Under the different freeze-thaw cycles, when the damage variables of the cement modified soil tend to the maximum value, the strains are very close, indicating that the freeze-thaw cycle index has little impact on the intensity limit. Finally, the load damage results in the damage to the cement modified soil. The lime modified soil mainly suffers the freeze-thaw damage.

Recebido/Submission: 10/9/2015

Aceitacao/Acceptance: 27/11/2015


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Chen Hua (1)

Xi'an University of Science and Technology, 710054, Shaanxi, Xi'an, China

DOI: 10.17013/risti.18B.326-338

Zhang Li-qun (1),*, Cui Hong-huan (1)


(1) School of Civil Engineering, Hebei Institute of Architecture and Civil Engineering, 075000, Zhangjiakou, Hebei, China

DOI: 10.17013/risti.18B.339-350
Table 1--Fitting Results in Thaw Test

               A         L        R

Lime soil      0.15571   4.8653   0.884
Cement soil    0.14333   5.4216   0.892
Prime soil     0.13393   3.1842   0.931

Table 2--Elastic Modulus of Two Kinds of Modified Soils

                  [E.sub.0]           [E.sub.1]

6% Ceme-nt        1.92 * [10.sup.8]   1.53 * [10.sup.8]
Modi-fied Soil

9% Lime           2.43 * [10.sup.8]   1.95 * [10.sup.8]
Modified Soil

                  [E.sub.2]           [E.sub.3]

6% Ceme-nt        1.36 * [10.sup.8]   1.14 * [10.sup.8]
Modi-fied Soil

9% Lime           1.75 * [10.sup.8]   1.55 * [10.sup.8]
Modified Soil

                  [E.sub.4]           [E.sub.5]

6% Ceme-nt        9.3 * [10.sup.7]    9 * [10.sup.7]
Modi-fied Soil

9% Lime           1.3 * [10.sup.8]    1.21 * [10.sup.8]
Modified Soil
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Author:Li-qun, Zhang; Hong-huan, Cui
Publication:RISTI (Revista Iberica de Sistemas e Tecnologias de Informacao)
Article Type:Report
Date:Jun 30, 2016
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