Study on the height effect of highway embankments in permafrost regions

Cold Regions Science and Technology 83–84 (2012) 122–130

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Study on the height effect of highway embankments in permafrost regions Long Jin a, b,⁎, Shuangjie Wang a, b, Jianbing Chen a, b, Yuanhong Dong b a b

State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou 730000, China Key Laboratory of Highway Construction & Maintenance Technology in Permafrost Regions, Ministry of Transport, CCCC First Highway Consultants Co., LTD, Xi'an 710065, China

a r t i c l e

i n f o

Article history: Received 1 April 2012 Accepted 23 July 2012 Keywords: Thaw settlement Height effect of embankment Mean annual ground temperature Rate of deformation

a b s t r a c t Thaw settlement is the main embankments distresses of highway in permafrost regions, according to survey data of the Qinghai–Tibet Highway (QTH). It can be effectively mitigated or even controlled by raising the embankment height. In view of this engineering problem, this study proposes the concept of the Height Effect of Embankment in Permafrost (HEEP). The concept represents the deformation and failure rules of embankment resulting from height variations. A thermal-elastic-plastic thaw settlement computational model is used to simulate the settlement processes of embankment, considering scenarios of different mean annual ground temperatures (MAGTs) and different heights. The model is validated by the field monitored data from a specific embankment section along the QTH. It is found that the total deformation of embankment is of considerable value and comes primarily from the thaw settlement of permafrost. Some special structures are recommended to supplement the built embankment, to ensure the stability of embankment in warm permafrost regions. The research results could provide essential theoretical and technological support for the transversal section design of highway embankments in permafrost regions. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Frozen soil consists of solid mineral particles, ice inclusions, liquid water (unfrozen water and tightly bound water) and gaseous inclusions (water vapour and air) (Tsytovich, 1985). It is a special type of soil that is highly sensitive to temperature changes. So its physical and mechanical features are intrinsically-unstable and are related to temperature. These characteristics are also influenced by the ice content, which is directly correlated to temperature and decreases with the rise of temperature. Permafrost covers an area of 35,760,000 km2 worldwide, which is approximately 24% of the world's land area (French, 1996). Many permafrost-related engineering problems have been settled during infrastructure constructions in permafrost regions over the past century; yet some of them remain unsolved (Ma et al., 2009). In Russia, the permafrost-related damage rate of Siberian Railway (No. 2, BAM Railway), built in the 1970s, was approximately 27.5% in 1994, and the damage rate of Siberian Railway (No. 1, The Trans-Siberian Railway), which has been operational for almost a century, was approximately 45% in 1996. In China, the permafrost-related damage rate of the Qinghai–Tibet Highway (QTH) was approximately 31.7% in 1990, while its damage rate in the northeastern region was approximately 40% (Cheng and He, 2001; Ma et al., 2009; Wu et al., 2002).

⁎ Corresponding author at: State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou 730000, China. E-mail address: [email protected] (L. Jin). 0165-232X/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.coldregions.2012.07.006

The thaw of underlying permafrost is mainly attributed to the damage of construction in permafrost regions, especially under the combined effect of global warming and engineering disturbance. Approximately 85% of the damage is found to be caused by thaw settlement according to the QTH survey data (Cheng et al., 2008). The annual maximal settlements can even reach 5–12 cm in severely affected sections (Fig. 1). This rapid deformation may result in a series of engineering problems, such as pavement cracking, differential settlements, pavement corrugating and road frothing. The stability of the embankment in permafrost regions thereby must be ensured that the embankment is not only thermally stable but also deformation stable. The deformation stability mainly embodies on the deformation magnitude and its influence on the pavement roughness. If the embankment settlement exceeds the tolerance of the design criteria in the design period or the subsequent service period, the practical traffic capacity of a highway in permafrost regions would be seriously degraded. A great deal of researches has widely focused on calculating and forecasting embankment deformation in permafrost regions. Wu et al. (1999) proposed an empirical formula that can describe the settlement of embankment based on an analysis of long-term monitoring data of the QTH. The monitored embankment settlement in permafrost regions is found to originate mainly from the thaw settlement and compression deformation (Qin et al., 2009; Zhang et al., 2007). Wang et al. (2005), based on elasto-plasticity theory and creep theory, simulated a variation of water content, temperature distribution and soil property. They established a two-dimensional model to calculate the stress and deformation of highway embankments in

L. Jin et al. / Cold Regions Science and Technology 83–84 (2012) 122–130

123

2. The mathematical model and equations 2.1. The thermal governing differential equations In frozen soil, both the effect of the convective heat transfer and the latent heat of vaporisation are negligible compared to the heat diffusion, the heat diffusion equation considering the ice-water phase change may be written as (Lai et al., 2009): Ce

Fig. 1. Thaw settlement of QTH at K2940 in the 1990s.

permafrost areas. Li et al. (2009) predicted the long-term stability of the Qinghai–Tibet Railway (QTR) embankment with a numerical formulation method. Li et al. (2012) studied the dynamic responses of the QTR embankment subjected to train loading in different seasons. Ma et al. (2011) discussed the mechanisms of the embankment deformations of the Qinghai–Tibet railway by considering detailed information on thermal and subsurface conditions based on monitoring data. Zheng et al. (2010) found that the thicker the embankment fill, the thicker the warm and ice-rich permafrost layer under the embankment and the greater the rise of the permafrost temperature. From the long-term maintenance experience of the QTH (Wang et al., 2008), it was found that raising the embankment height, a method now widely used in practical engineering, could effectively control the deformation and increase the stability of the embankment in permafrost regions (Fig. 2). So far, neither the field observations of nor numerical predictions of the embankment settlement in permafrost regions considers that the height of the built embankment exert a unique effect on the settlement processes. Based on this phenomenon, the Height Effect of Embankment in Permafrost (HEEP) concept is proposed in this paper, which represents the deformation and failure rules of the embankments in permafrost resulting from the change of height. A heat transfer model is used to predict the thermal evolution beneath the constructed embankment, whose settlement is modeled subsequently by a thermal-elastic-plastic thaw settlement model. The settlement prediction considers different scenarios of embankment heights and pays emphasis on the correlation between the height and deformation of the embankment. 45 40

39.86 37.39

disease rate /%

35 30.25

30

ð1Þ

where T is temperature, and λe and Ce are soil equivalent thermal conductivity and soil equivalent volumetric heat capacity of soil, respectively. The ice-water phase change takes place when soil temperature falls below the freezing temperature, Tp. There exists also the other temperature Tb below which the phase change is negligible (Qin and Tang, 2011). That is, phase change in frozen soil happens only when temperature falls in the range of [Tb, Tp]. A stepwise function can be used to compute the soil equivalent thermal conductivity and the soil equivalent volumetric heat capacity (Lai et al., 2009): 8 > C > > u < C L u þ Cf Ce ¼ þ > > T p −T b 2 > : Cf

λe ¼


 T > Tp
 T b ≤T≤T p


8 > λ > > u <

T > Tp

15 10.72

10 5 0~1

1~2

2~3

≥3

The height of embankment /m Fig. 2. The relationship between thaw settlement disease and embankment heights.




 λu −λf ðT−T b Þ T b ≤T≤T p λf þ > > T p −T b > : λf ðTbT b Þ

ð3Þ

where, subscripts f and u denote the frozen and unfrozen states, respectively; λ and C are the thermal conductivity and the volumetric heat capacity, respectively; and L is the latent heat, 340 kJ. 2.2. The thermal-elasto-plastic thaw settlement model of embankment The physical and mechanical features of frozen soil may vary considerably in the process of the ice-water phase change. At present, a real temperature-moisture-stress coupled model applicable to the permafrost regions has not been established because of the theory limitation and test-condition limitation. This paper thus turns to use the thaw-settlement coefficient method to calculate the thaw settlement deformation of frozen soil, avoiding the complicated thermal-mechanical coupling process. This method has several characteristics of specific physical meaning and can be widely applied by engineers. The mathematical description for the thaw-settlement coefficient method is as follows. The method states that the embankment deformation consists of elastic part, plastic part, and if existed, the volume deformation in the thaw settlement process. Thus, the deformation of the embankment can be expressed as: c

20

ð2Þ

ðTbT b Þ

t

e

p

t

dεij ¼ dεij þ dεij ¼ dε ij þ dε ij þ dεij

25

0

∂T ¼ ∇⋅ðλe ∇T Þ ∂t

ð4Þ

where dεijc is the compress strain increment generated in the embankment fill, seasonal thawed layer and permafrost layer; it contains an elastic part dεije and plastic part dεijp. Additionally, the former part can be expressed as: e

dεij ¼ C ijkl ðT Þdσ kl

ð5Þ

where Cijkl(T) is the elastic matrix related to temperature, and σkl is the stress tensor.

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L. Jin et al. / Cold Regions Science and Technology 83–84 (2012) 122–130

dεijp can be expressed as (the associated flow rule): p

dεij ¼ dλ

∂f ∂σ

2.4. The numerical model and the computational parameters ð6Þ

where dλ is the scale factor and f is the yield function. In this paper, the Mohr–Coulomb criterion was adapted. dεijt is the thaw settlement deformation increment. The ice in frozen soil thaws when the temperature exceeds the freezing temperature. Then dεijt happens and has to be computed. The phenomenon above is called the thaw settlement character of frozen soil. The computation can be done by use of a thaw-settlement coefficient: δ0 ¼

h1 −h2 h1

ð7Þ

where δ0 is the thaw-settlement coefficient; and h1 and h2 are the heights of frozen soil before and after the thawing state, respectively. With Eq. (7), the thaw settlement deformation increment of frozen soil can be obtained: t

dε ij ¼ δ0 ðT Þ

ð8Þ

where δ0(T) is the thaw-settlement coefficient related to temperature, which can be written as: 8 > > <

0 δf δ0 ðT Þ ¼ T −T ðT−T b Þ > p b > : δf

TbT b T b ≤T≤T p T > Tp

ð9Þ

ep

  2:6 2πt π ⋅t þ A sin tþ 365  24  50 8760 2

ð12Þ

T s ¼ T a þ ΔT

ð13Þ

where Ts, Ta and ΔT are the annual average temperature at upper boundaries, annual average air temperature and the adherent layer

B

A K J

I

C II

D E

III F

I

IV

ð10Þ

ep where Cijkl represents the thermal-elasto-plastic tensor, and hij is the stress tensor of thaw settlement. Consequently, we can obtain the thermal-elasto-plastic FEM equation with the increment theory of the virtual work principle:


 T ep T T T ∑ C e ∫Ω B C BdΩ C e ⋅Δu ¼∑ C e ∫Ω B hΔTdΩ þ Δp e

T ¼ Ts þ

(a) Physical model

The coefficient δ0(T) equals 0 when the temperature falls below the freezing temperature. It is a constant value of δf when the temperature exceeds the frozen temperature, being obtained in situ testing or can be easily looked up in specification (Wang et al., 2008). This paper adopts the value of δ0(T) by linear interpolation in the ice-water phase change range for the sake of the numerical convergence in this paper. From Eqs. (4) to (9), the constitutive equations for the thaw settlement are obtained with the increment theory of plasticity: dσ ij ¼ C ijkl dεkl −hij dT

In this section, the practical QTH embankment transversal section at the Chu Kumar River site was adopted as the computational model, shown in Fig. 3(a). The heights of the embankment models are assumed as 1.0 m, 2.0 m, 3.0 m and 4.0 m. The width of the pavement is 10 m, and the ratio of the slope is 1:1.5. According to the actual embankment geometries, the computational model can be divided into four parts. Part I consists of the embankment fill; part II, silty clay; part III, pebbly clay; part IV, strongly decayed mudstone. Half of the computational model was selected because geometric and boundary conditions are symmetry. The computational domain is extended for 30 m from the side-slope foot of the embankment and for 30 m under the natural ground surface. The air temperature in the Qinghai–Tibet Plateau is projected to warm by 2.6 °C in the next 50 years (Qin, 2002). Based on the adherent layer theory (Zang and Wu, 1999; Zhu, 1988) and the related data (Cheng et al., 2003; Lai et al., 2009; Zhang et al., 2006), the upper boundary temperature can be expressed as a sinusoidal wave: The temperature at surfaces AB, BC and CD:

e

G

H

(b) Numerical model

ð11Þ

where Δu and Δp are the vectors of displacement and load, respectively; B is the geometric matrix; and Ce is the transformation matrix. 2.3. The calculation steps The numerical solution of the thermal-elasto-plastic thaw settlement equation is obtained by use of following steps: (1) (2) (3) (4)

Predicting the temperature Ti and displacement ui at time ti; Determining the thermal parameters λe and Ce at time ti + 1; Computing the temperature Ti + 1 at time ti + 1 using Eq. (1); Calculating the mechanical parameters and thaw settlement coefficient δ0(T) at time ti + 1; (5) Estimating the displacement ui + 1 at time of ti + 1 using Eq. (11).

Fig. 3. Embankment model.

L. Jin et al. / Cold Regions Science and Technology 83–84 (2012) 122–130 Table 1 The values of Ts and ΔT. Ta/°C Ts/°C

Natural surface Embankment slope Asphalt pavement

−3.0

−3.5

−4.0

Adherent layer increment ΔT/°C

−0.5 1.0 3.5

−1.0 0.5 3.0

−1.5 0.0 2.5

2.5 4.0 6.5

ρ/kg.m−3

Embankment fill Silty clay Pebble clay Strong decayed mudstone

2183.6 2080 2070 2415

to the thaw settlement levels of the permafrost in specification, the thaw settlement coefficients of silty clay and pebbly clay are chosen as 0.15 and 0.10, respectively (Table 4). The embankment is assumed to be finished in July. In the computational model, the initial temperature field of Parts II, III and IV in July was obtained through a long-term transient solution with the upper boundary condition (Eq. (12)). At the same time, the initial temperature of Part I was assigned as the temperature of the natural ground surface. 3. Model verification

Table 2 Thermal parameters of media in embankment model. Physical variable

125

Thermal conductivity/ W ∙ (m ∙ °C)−1

Specific heat/ J∙(kg ∙ °C)−1

Frozen

Thaw

Frozen

Thaw

1.4 2.12 1.82 2.5

1.15 1.42 1.6 2

706.6 1222 977.2 981.8

861.7 1608 1266 1272

increment, respectively (Zhu, 1988); t is the service time of highway; A is the annual amplitude of ground surface temperature. The values of A are different at ground surfaces, with A is equal to 11.5 °C, 14.5 °C and 15.15 °C at the natural surface, embankment slope and asphalt pavement conditions, respectively (Lai et al., 2009). The values of Ts and ΔT are listed in Table 1. The lateral boundaries DG and AH are assumed to be adiabatic, and the geothermal gradient at boundary GH is 0.024 °C/m based on the measurement data (Wang et al., 2008; Zheng, 2007). For mechanical boundaries, the upper boundaries are free. The horizontal displacement at DG is 0. The horizontal and vertical displacements at GH are also equal to 0. Many studies have shown that some mechanical parameters of frozen soil are related to temperature (Li, 2008; Wu and Ma, 1994; Wu et al., 1988). Based on the experiment and some reference data (Zheng, 2007), the thermal and mechanical parameters are given in Tables 2 and 3. The thaw settlement coefficient can be obtained by in situ test or through specification databases (Wang et al., 2008). The thaw settlement coefficients in this paper were determined based on the “Code for engineering geological investigation of frozen ground” (Ministry of Construction of PRC, 2001). The borehole specimen at the Chu Kumar River site is shown in Fig. 4. The frozen soil types in these regions are usually ice-rich permafrost. They are generally called thaw settlement or strongly thaw settlement frozen soil (levels III–IV), on the basis of the engineering specification. According

To investigate the precision of the thermal-elasto-plastic thaw settlement model, the computational results and the monitoring data obtained from the Chu Kumar River sections of the QTH are described in Figs. 5 and 6. The test sections are located in the Chu Kumar River Plain, which has a flat topography. There is sparse vegetation in these regions, except for the developed thermokarst lakes. The heights of the embankment in these sections change within the range of 1.8 m to 3.8 m. The natural permafrost tables are from 2.7 m to 3.0 m; the artificial permafrost tables are from 5.7 m to 7.7 m. The frozen soil types in these regions are usually ice-rich permafrost; the mean annual ground temperature (MAGT) fluctuates from −0.8 °C to −1.0 °C. The level measurement was adopted to monitor the deformation in an interval of one month. Fig. 5 is the monitored data at the Chu Kumar River site. From this figure, it can be observed that the embankment settlement is approximately 8 cm over the course of 6 years' operation. And the annual deformation remains approximately constant. Briefly, the deformation process exhibits an undamped trend. As observed in Fig. 6, the calculated settlement is approximately 7 cm to 10 cm during the previous 6 years, which differs little from Fig. 5. The deformation trend is closely similar to the monitoring data. Hence, these consistencies substantiate that model proposed in this paper can credibly express the deformation process of highway embankment in permafrost regions. 4. Numerical results and analyses To analyse the deformation rules of different positions, characteristic points 1, 2 and 3, which denote the embankment surface, embankment bottom and the natural permafrost table before embankment construction, respectively, were marked in Fig. 3(b). 4.1. The long-term deformation rule of embankment in permafrost regions The settlement deformation at different positions tells that the thaw deformation of the sub-grade permafrost contributes mainly to the embankment settlement (Fig. 7). Overall, the deformation at

Table 3 Mechanical parameters of media in embankment model.

Embankment fill

Parameters

−20 °C

−5 °C

−2 °C

−1 °C

−0.05 °C

0 °C

20 °C

E (MPa)

31.2 0.13 0.8 40 700 0.15 1.3 25 72.6 0.13 0.6 34 880 0.25 38 28

25 0.13 0.5 40 176 0.18 1.3 25 50.8 0.13 0.6 34 731 0.25 38 28

23 0.14 0.3 40 74 0.2 1.3 22 45 0.14 0.6 34 666 0.25 38 28

22 0.19 0.1 40 13.17 0.22 1.3 14 40 0.19 0.6 34 572 0.25 38 28

21.2 0.22 0.03 38 3 0.24 0.1 12 36.9 0.35 0.15 31 500 0.25 38 28

21 0.24 0.001 28 2 0.4 0.007 12 34 0.45 0.003 30 500 0.25 32 14

21 0.24 0.001 28 2 0.4 0.007 12 34 0.45 0.003 30 500 0.25 32 14

μ

Silty clay

c (MPa) ϕ (°) E (MPa)

Pebbly clay

c (MPa) ϕ (°) E (MPa)

Strong decayed mudstone

c (MPa) ϕ (°) E (Mpa)

μ

μ

μ

c (MPa) ϕ (°)

Where, E, μ, c, ϕ are elastic modulus, Poisson's ratio, cohesion and internal friction angle respectively.

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0

settlement /cm

-5

heights

-10

1m 2m 3m 4m

-15 -20 -25

0

4

8

12

16

20

time /year Fig. 6. The calculated results of embankment settlement in permafrost regions at MAGT of −1.0 °C. Fig. 4. The borehole specimen at Chu Kumar River site.

Table 4 Thaw settlement coefficients of media in embankment model.

Thaw settlement coefficient

Embankment fill

Silty clay

Pebbly clay

Strong decayed mudstone

0.00

0.15

0.10

0.00

magnitude, especially for a low-height embankment at a high MAGT. Moreover, the deformation process does not display a damped trend, which must be given sufficient attention.

4.2. The analysis for the height effect of embankment in permafrost (HEEP) regions

the point of No. 1 is basically identical with the point of No. 2. It means that the compressive deformation of embankment fill (the difference of the deformation between the point of No. 1 and No. 2) and the seasonally thawed layer (the difference of deformation between the point of No. 2 and No. 3) are comparatively small, similar to other studies (Qin and Li, 2011; Qin et al., 2010). It further infers that in permafrost regions, the embankment settlement comes mainly from the thaw settlement deformation in the late service time. A low-height embankment at a high MAGT region would promote a greater thaw settlement deformation of permafrost (Fig. 7(b)). In contrary, a high-height embankment at a low MAGT region would suffer from a relatively small total deformation (Fig. 7(f)), because the permafrost is not thawed during the service time. This further validates that the embankment deformation originates mainly from the thaw settlement of permafrost. The reason is attributed to the disturbance of the initial thermal ground balance due to engineering construction. The settlement deformation would reach a considerable

Section 1

Fig. 8 indicates that the settlement process is related to the embankment height. In simple terms, the higher the embankment, the smaller the deformation will be. For the heights of 1.0 m and 4.0 m at an MAGT of − 0.5 °C, the settlements at the point of No. 1 are 27.47 cm and 24.86 cm, respectively, with a difference of 2.61 cm. However, when the MAGTs are − 2.0 °C and −3.0 °C, the differences are 7.20 cm and 6.07 cm, respectively, which indicate that they are obviously getting larger. This phenomenon is mainly caused by two aspects of the effect of embankment fill. First, the natural thermal-moisture process is disturbed when the embankment is built, which will lead to more heat absorption and thaw settlement. Second, the thermal resistance of the embankment fill can defend against the thermal invasion from the outside environment. The thicker the embankment fill, the more obvious the thermal resistance effect will be, so the smaller the settlement deformation will be. In warm permafrost regions, however, the effect of the resistance of embankment fills is lessened because of the

Section 2

Section 3

Section 4

4490.160

Altitude /m

4490.120

4490.080

4490.040

4490.000

4489.960 2004-02-27

2005-04-02

2006-05-07

2007-06-11

2008-07-15

Date Fig. 5. The settlement data of QTH obverted at K2939.

2009-08-19

2010-09-23

L. Jin et al. / Cold Regions Science and Technology 83–84 (2012) 122–130

(b) 5

0

0 No.1 No.2 No.3

-5 -10

settlement /cm

settlement /cm

(a) 5

-15 -20

No.1 No.2 No.3

-5 -10 -15 -20 -25

-25 -30

0

5

10

15

-30

20

0

5

time /year

20

-5

15

20

15

20

0

settlement /cm

settlement /cm

No.1 No.2 No.3

-10 -15

-5 -10

No.1 No.2 No.3

-15

-20 0

5

10

15

-20

20

0

5

time /year

10

time /year

(e) 0

(f) 3

-1

No.1 No.2 No.3

-2

2

settlement /cm

settlement /cm

15

(d) 5

0

-3 -4 -5

1 0 -1 No.1 No.2 No.3

-2

-6 -7

10

time /year

(c) 5

-25

127

0

5

10

15

20

-3

0

5

time /year

10

time /year

Fig. 7. The long-term settlement rules at different heights and MAGTs as (a) 1 m and −0.5 °C, (b) 4 m and −0.5 °C, (c) 1 m and −1.5 °C, (d) 4 m and −1.5 °C, (e) 1 m and − 3.0 °C, (f) 4 m and −3.0 °C.

higher external temperature air influence, meaning a weak effect of the HEEP. According to the survey data from the QTH (Ding and He, 2000), the permafrost tables beneath the embankment elevates to or maintains at the natural level in cold permafrost regions, such as the Kunlun Mountain and the Fenghuo Mountain. In warm permafrost regions, however, such as the Beiluhe Basin and the Qingshui River region, the permafrost tables beneath the embankment present an obvious downwards movement. This observed phenomenon is the same as the prediction in this paper. Hence, in warm permafrost regions, the thaw settlement is mainly influenced by air temperature, whereas the HEEP effect is not obvious. Thus, in these regions, the embankment height has less influence on the deformation, as indicated that the differences are less than 5.0 cm. This suggests that simply raising the height is insufficient to ensure the deformation stability of the embankments in warm permafrost regions. There is also an interesting phenomenon in Fig. 8(d) and (e). The deformation curves of the greater heights (4.0 m) descend first and then ascend. This phenomenon mainly appears in cold permafrost regions if the built embankment has a relatively greater height. On the one hand, the compressive deformation of the embankment fill and the seasonally thawed layer is relatively larger, compared to the settlement of a lower-height embankment. Furthermore, the artificial

permafrost table beneath the embankment has a downwards movement to a certain degree in the first year due to more thermal invasion, also resulting from the higher embankment construction, which will lead to certain thaw settlement. As the embankment is finished in summertime, the deformation curves are moving down first. On the other hand, the HEEP is obvious in these regions because of the lower air temperature. The foundation refreezes in a relatively short period (Fig. 9(a)) and the artificial permafrost table beneath the embankment has elevated in the second year, leading to some frost heave. Thus, the deformation curves are moving upwards. Otherwise, this phenomenon is not obvious with lower embankments. In these sections, the artificial permafrost table has a continuous downwards movement after the embankment construction (Fig. 9(b)), which results in the increasing deformation. 4.3. The deformation rate rule The deformation rate curves were used to further analyse the influence of MAGT and height on the deformation. In the warm permafrost regions (the MAGTs are − 0.5 °C and − 1.0 °C), the deformation rate increases very slowly with the increase of height (Fig. 10). But this rate slowly decreases with the increase of height in cold

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L. Jin et al. / Cold Regions Science and Technology 83–84 (2012) 122–130

(a) 0

(b)

-5

-10

heights 1m 2m 3m 4m

-15 -20

settlement /cm

settlement /cm

-5

heights

-10

1m 2m 3m 4m

-15 -20

-25 -30

0

0

4

8

12

16

-25

20

0

4

8

time / year

12

16

20

time / year

(c) 0

(d)

0

heights 1m 2m 3m 4m

-10

-15

-20

0

4

8

12

16

settlement /cm

settlement /cm

-5 -5

1m 2m 3m 4m

-10

-15

20

heights

0

4

8

time / year

12

16

20

time / year

(e) 5 settlement /cm

0 heights 1m 2m 3m 4m

-5

-10

-15

0

4

8

12

16

20

time / year Fig. 8. The settlement processes of various heights at different MAGTs as (a) −0.5 °C, (b) −1.0 °C, (c) −1.5 °C, (d) −2.0 °C, (e) −3.0 °C.

permafrost regions (MAGTs are − 2.0 °C and − 3.0 °C). Nevertheless, the embankment height has an unnoticed effect on the deformation. As illustrated in the calculated results, the increment of the deformation rate at MAGT of − 0.5 °C is only 0.24 cm/year when the height increases from 1.0 m to 4.0 m. The deformation rate is found to continue increasing with the rising of MAGT, regardless of the embankment heights. The increment of deformation rate reaches 1.17 cm/year when the MAGT increases from − 3.0 °C to − 0.5 °C at the height of 4.0 m. When MAGT increases from − 3.0 °C to − 1.5 °C (Fig. 11), the deformation rate increases slowly and then increases rapidly until the MAGT is above − 1.5 °C, which is a characteristic point with an obvious change of the deformation rate that is commonly used as a dividing point between the warm and cold permafrost regions in highway engineering (Wang et al., 2008). Therefore the deformation rate of the embankment is governed mainly by MAGT, but secondarily by the height. 4.4. Suggestion for engineering applications The computational results above may promise technical supports to the engineering design. In cold permafrost regions, increasing the

height of the built embankment can effectively ensure the deformation stability of embankments. This approach has many other advantages, such as convenient construction, low investment, etc and thus should be adopted firstly. In warm permafrost regions, however, the permafrost is at an obvious decaying trend; and thus, the influence of HEEP is gradually lessened. Some other special engineering measures are necessarily supplemented to stabilize the embankment in these regions. For example, an embankment can be armed with crushed rocks, ventilation ducts and thermosyphon, etc. The HEEP influences on the embankment deformation mainly due to the changes of thermal boundaries and thermal invasion from the outside environment, both of which are induced from the change of height. The changing rule can be conveniently reflected by the concept of HEEP, and it can be easily accepted by engineers and directly applied in practical design. It is noteworthy that the influence of the width effect is not considered in this paper because the QTH usually has a width of pavement of only 10.0 m. Therefore, the findings are only applicable to the highways of such grade. For the expressways, the width of the pavement is usually greater than 20.0 m. Thus, the geometric effects of the embankment, including the height and width effects, must be comprehensively considered, which requires further research.

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1.4

0

deformation rate /cm·year-1

Y/m

(a)

129

Operation time / year

-5

1 3 5

1.2 the heights

1 0.8 0.6 0.4 0.2 0

-10 0

5

10

1m 2m 3m 4m

0

-0.5

-1

-1.5

-2

-2.5

-3

-3.5

the mean annual ground temperature /oC

15

X/m Fig. 11. The change rules of deformation rates with MAGTs.

(b) condition. Additionally, it is difficult to ensure the long-term stability of the highway solely by raising the height. The MAGT is also found be considerably influenced the deformation rate of embankment. (d) Finally, some other special structures should be adopted to ensure the stability of the embankment in warm permafrost regions.

Y/m

0

Operation time / year

-5

1 3 5

Acknowledgments

-10 0

5

10

15

20

X/m Fig. 9. The artificial permafrost tables at MAGT of −2.0 °C with different heights as (a) 1.0 m, (b) 4.0 m.

5. Conclusion A thermal-elastic-plastic thaw settlement model is established to predict the settlement of the embankment in permafrost regions. It was validated by the monitoring data of the QTH. The settlement process of embankment was simulated to assess the influence of HEEP on the embankment deformation. Some valuable conclusions were obtained from this study: (a) The compressive deformation of embankment fill is usually small. The total deformation comes mainly from the thaw settlement of the permafrost layer, especially for the embankment of low height in warm permafrost regions. (b) The settlement deformation is affected by the HEEP in a large scale. The higher the embankment, the smaller the deformation will be. (c) The influence of HEEP on deformation wanes with the rising of MAGT. Notably, the deformation is considerable in warm permafrost regions, regardless of the height

deformation rate /cm•year-1

1.4 1.2 1 0.8

ο

-0.5 C ο

0.6

-1.0 C ο

-1.5 C

0.4

ο

-2.0 C ο

-2.5 C

0.2 0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

height /m Fig. 10. The change rules of deformation rates with embankment heights at different MAGTs.

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