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Thermal stability analysis of crushed-rock embankments on a slope in permafrost regions
Cold Regions Science and Technology 106–107 (2014) 175–182
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Thermal stability analysis of crushed-rock embankments on a slope in permafrost regions Wansheng Pei a, Mingyi Zhang a,⁎, Yuanming Lai a, Long Jin b, Jon Harbor c a b c
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 Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, West Lafayette, IN 47907, USA
a r t i c l e
i n f o
Article history: Received 1 November 2013 Accepted 11 July 2014 Available online 18 July 2014 Keywords: Thermal stability Crushed-rock embankment Effect of slope Permafrost region
a b s t r a c t Highways/railways often pass across slope areas and their embankments are often built on the slopes in permafrost regions. It is difficult to ensure the thermal stability of the embankments at the slopes due to the effect of slopes. To protect the underlying permafrost, the crushed-rock embankments are often used in the slope areas. Therefore, it is very necessary to explore the thermal state of crushed-rock embankments located on the slopes. In this study, we studied numerically the temperature characteristics of three kinds of crushed-rock embankments located on a slope under global warming, i.e. crushed-rock interlay embankment, crushed-rock interlayer-revetment embankment and crushed-rock base embankment. Numerical results indicate that the crushed-rock interlayer embankment and the crushed-rock interlayer-revetment embankment, located on a slope with a ratio of 1:3.73 (about 15° from the horizontal), cannot effectively eliminate the negative effect of climate warming and construction-induced warming, and the effect of slope is still obvious on the thermal stability of permafrost under the crushed-rock interlayer embankment. However, the crushed-rock base embankment can significantly reduce the temperature of underlying permafrost and keep the underlying permafrost table stable for a long term; furthermore, the ground temperatures under the long side slope are far lower than those under the short side slope, and this will be more advantageous to control the slide of the embankment located on a slope and increase its stability. We also find that the three kinds of embankments cannot all remove the thermal effects of construction from themselves in a short term. Generally speaking, the crushed-rock base embankment structure can be very advantageous to the thermal stability of the embankment on a slope. © 2014 Elsevier B.V. All rights reserved.
1. Introduction A crushed-rock layer, as a highly porous medium (Lai et al., 2003), has been widely used to protect the underlying permafrost in the embankment engineering in cold regions. Examples include many important highway and railway engineering projects, such as the Qinghai–Tibet Highway and Qinghai–Tibet Railway in China, the Alaska Highway in the USA and the Baikal–Amur Railway in Russia (Cheng, 2005; Cheng and He, 2001). Typical construction methods include crushed-rock embankments, crushed-rock base (interlayer) embankments, crushed-rock revetment embankments and U-shaped (interlayer and revetment) crushed-rock embankments (Cheng et al., 2009; Lai et al., 2009; Zhang et al., 2005). The cooling mechanism results from the fact that the high permeability of such material would allow air convection to occur within it when unstable air pressure/temperature
⁎ Corresponding author. E-mail address: [email protected] (M. Zhang).
http://dx.doi.org/10.1016/j.coldregions.2014.07.005 0165-232X/© 2014 Elsevier B.V. All rights reserved.
gradients exist. At present, the heat and mass transfer theories have been developed in cold region engineering. The convective heat transfer effect in crushed-rock layer has been applied to control thaw settlement of permafrost embankment. The cooling effects of highly porous media embankments made from crushed rocks have been evaluated previously using numerical simulation, laboratory tests and in-situ observation. In detail, Goering (2003) numerically researched the convective heat transfer of crushed-rock embankment with an unsteady two dimensional finite-element model that is capable of solving the coupled governing equations of pore air flow and energy transport. Lai et al. (2006) analyzed numerically the velocity and temperature characteristics of open-boundary crushed-rock embankment under wind action based on the climatic and geological conditions of the Qinghai–Tibet Plateau. Zhang et al. (2009a, 2009b) found that the geometrical parameters including sloped angle, aspect ratio and so on have significant influence on the natural convection cooling effect of crushed-rock revetment by numerical calculations. Yu et al. (2005) researched the temperature properties of a traditional embankment and a ripped-rock revetment embankment by laboratory experiments and found that the
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30.0 m
3.0 m
O N
.5 1:1 C B A
3.1 m
ripped-rock revetment could cool embankment and adjust the temperature difference between the north-facing slope and the south-facing slope. Zhang et al. (2006) studied experimentally heat transfer mechanisms of a trapezoidal crushed-rock layer under two boundary conditions, i.e. cyclic temperature, air-flow, air-permeable/impermeable at the two side slopes and closed at both top and bottom, and found that the former is forced convective heat transfer and the latter is nature convective heat transfer. Sun et al. (2005) concluded that the cooling capacity of the coarse rock revetment excelled that of the fine rock revetment by analyzing the temperature fields of the experimental embankments with crushed rock slope protection in field. Wu et al. (2008) performed lots of in-situ observations and found that crushed rock-based embankment could effectively cool the roadbed, resulting in the decrease of permafrost temperatures and the rise of permafrost table, however the cooling effects were significantly different in warm and relatively cold permafrost areas. From these studies, we can conclude that crushed-rock layer can have a good cooling effect on the underlying soil layers. However, the previous researches usually focus on the crushedrock embankments located on the flat open areas. In fact, the highway/railway often passes across slope areas, e.g. valley and hillside, and thus their embankments are often built on the slopes. Because of the asymmetry thermal boundary conditions and the effect of gravity, it will be difficult to ensure the thermal stability of the embankments located on the slopes. Especially for the side slope of the embankment on the downward slope, the longer slope absorbs more heat energy than that on the upward slope, and this will not benefit the thermal stability of the embankment. To protect the underlying permafrost, the crushed-rock embankments are also often used on the slope areas. Therefore, it is very important to explore the thermal state of crushed-rock embankments at the slopes. In this paper, we focused on the influence of slope for crushed-rock embankments and proposed a model for crushed-rock embankments on a slope. In order to quickly research the effect of crushed-rock embankments on the underlying permafrost on a slope, we have used a numerical method. A large number of numerical simulations were carried out during the course of this study. However, only three kinds of embankment structures are presented in this paper. Namely, the temperature characteristics of crushed-rock interlay embankment, crushed-rock interlayer-revetment embankment and crushed-rock base embankment, located on a slope with a ratio of 1:3.73 (about 15° from the horizontal), have been analyzed for 20 years based on the assumption that the warming rate of air temperature on the Qinghai– Tibet Plateau will be 0.052 °C (Qin, 2002).
10.0 m I
D
II III V
y
The computational domain of crushed-rock embankment model on the slope is shown in Fig. 1. The ratio of slope OJ is 1:3.73 (about 15° from the horizontal). The embankment height is 3.1 m from the left slope toe. The computational domain is extended 30 m horizontally from the side slope toe (A and I) of the embankment, and 30 m downward from the natural ground surface at the left and right lateral boundaries, respectively. Three crushed-rock embankment structures are designed in the model. Case 1 Crushed-rock interlayer embankment. Namely, Parts I and III are the embankment fill, Part II is the crushed-rock interlayer with a thickness of 1.5 m, and Parts V and VI are the natural soil layers and they are subclay and weathered mudstone, respectively. Case 2 Crushed-rock interlayer-revetment embankment. Based on case 1, a crushed-rock revetment (Part IV) is added at the right side of the embankment with a horizontal width of 1.6 m. Case 3 Crushed-rock base embankment. Similarly, based on case 1, Part III is filled with crushed rocks. In the calculational domains, shown in Fig. 1, the specific heat of air at an elevation of more than 4500 m is Ca = 1.004 × 103 J/(kg ·°C), the thermal conductivity is λ = 2.0 × 10 − 2 W/(m · °C), the air density is ρa = 0.641 kg/m3, and the dynamic viscosity is μ = 1.75 × 10−5 kg/(m · s). The mean particle size of crushed rock is about 20.0 cm and the permeability and inertial resistance factor (Beta factor of non-Darcy flow) are k = 1.66 × 10− 5 m2 and B = 41.20 m− 1, respectively (Zhang et al., 2013). The thermal parameters of all media are listed in Table. 1 (Lai et al., 2009). 3. Governing equations According to the Design Specifications for Highway Alignment (2006) and actual embankment geometries in permafrost regions, the crushed-rock embankment structures on a slope at an elevation of 4500 m are taken as computational models (Fig. 1) in this paper. Considering the direction of geothermal heat flux and rationality of boundaries, the bottom boundary (ML) is set parallel to the natural ground surface (OJ) and the lateral boundaries (ONM and JKL) are perpendicular to the natural ground surface (OJ) and the bottom boundary (ML). According to the different heat transfer characteristics of different media, the embankment model is divided into two zones, i.e. crushed-
E H
1:1 F .5 1:3.7 3
IV
G x
I
30.0 m J
VI
K
30.0 m
M
2. Description of the models
L Fig. 1. Computational domain of crushed-rock embankment.
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Table 1 Thermal parameters of media in embankments. Physical variable
λf W/(m·°C)
Cf J/(m3·°C)
Crushed rock Fill soil Subclay Weathered mudstone
0.387 1.980 1.351 1.824
1.015 1.913 1.879 1.846
× × × ×
106 106 106 106
rock zone (porous media zone) and soil layer zone (solid zone). Therefore, the governing equations of different zones are described as follows. 3.1. Crushed-rock zone The thermal convection of fluid inside crushed-rock layer, which can be considered as porous media, is the process of heat and mass transfer. The natural convection is unsteady. The change of air density caused by air humidity change is far less than that caused by air temperature (Dou, 1996). Thus, the air convection effect caused by air temperature gradient is far larger than that caused by air humidity gradient in the crushed-rock layer. Therefore, only the convection caused by the air temperature gradient is considered in our model. In the analysis, only the motion of interstitial air is considered. Additionally, the porous media zones are modeled by the addition of a momentum term to the standard fluid flow equations. This term is composed of two parts: a viscous loss term and an inertial loss term. Under those conditions, governing equations for mass, momentum, and energy can be written as follows (Kong and Wu, 2002; Nield and Bejan, 1992): Continuity: ∂vx ∂vy þ ¼0 ∂x ∂y
∂p μ ¼ − vx −ρa Bjvjvx k ∂x
ð2aÞ
∂p μ ¼ − vy −ρa Bjvjvy −ρα g k ∂y
ð2bÞ
where jvj ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v2x þ v2y , B is the Beta factor of non-Darcy flow, k is the
permeability of the porous medium, μ is the dynamic viscosity of air, p* is the air pressure, ρa is the air density, and ρaB|v|vx is called the inertia-turbulent term. It is assumed that air is incompressible, and its density ρα is the function of temperature. In order to simplify the analysis, the Boussinesq approximation is employed (Kong and Wu, 2002; Nield and Bejan, 1992).
ρα ¼ ρa0 ½1−βðT−T 0 Þ
ð3Þ
where ρa0 and T0 are the reference values for density and temperature, and β is the coefficient of thermal expansion for air. Energy:
∂T
Ce
∂t
¼
∂ ∂ ∂T ∂T ∂T ∂T þ −C a ρa vx λe λe þ vy ∂x ∂x ∂y ∂y ∂x ∂y
ð4Þ
where Ca is the air specific heat at constant pressure; and Ce⁎ and λe⁎ are the effective volumetric heat capacity and effective thermal conductivity in porous medium.
Cu J/(m3·°C)
0.387 1.919 1.125 1.474
1.015 2.227 2.357 2.099
× × × ×
106 106 106 106
L (J/m3) 0.0 2.04 × 107 6.03 × 107 3.77 × 107
3.2. Soil layer zone The ratio of thermal conduction is far larger than that of convection in soil layers (An et al., 1990), so that the convection can be neglected. Thus, when only the conduction and phase change problem are considered, the heat transfer process in soil layers can be described as follows (Kong and Wu, 2002; Nield and Bejan, 1992; Zhao, 2002):
Ce
∂T ∂ ∂ ∂T ∂T þ : ¼ λe λe ∂t ∂x ∂x ∂y ∂y
ð5Þ
It is assumed that the phase change occurs in a range of temperature (Tm ± ΔT). When the effective heat capacity is determined, the effect of the temperature interval 2ΔT should be included. Assuming that Cf, Cu, λf and λu do not depend on temperature T. Then, the following definitions of Ce⁎ and λe⁎ may be obtained (Guo et al., 1988; Lai et al., 2009):
Ce ¼
ð1Þ
where vx and vy are the x and y components of air velocities, respectively Momentum:
λu W/(m·°C)
λe
¼
8 > <
Cf L C þ Cu þ f > 2 : 2ΔT Cu 8 > <
TbT m −ΔT T m −ΔT ≤T ≤T m þ ΔT T NT m þ ΔT
λf λu −λ f λ þ ½T−ðT m −ΔT Þ > f 2ΔT : λu
TbT m −ΔT T m −ΔT ≤T ≤T m þ ΔT T NT m þ ΔT
ð6aÞ
ð6bÞ
where subscripts f and u represent the frozen and unfrozen states, respectively; Cf and λf are the volumetric heat capacity and thermal conductivity of media in the frozen area, respectively; Cu and λu are the volumetric heat capacity and thermal conductivity of media in the unfrozen area, respectively; and L is the latent heat per unit volume. According to Qin (2002), the mean annual air temperature will be warmed up by 0.052 °C/a on the Qinghai–Tibetan Plateau in the future 50 years due to climatic change. Based on the related data (Cheng et al., 2003; Lai et al., 2009; Zhang et al., 2009a, 2009b), the variation equations of annual temperatures at different surfaces on the Qinghai–Tibetan Plateau are obtained. The mean annual air temperature is taken as − 4.0 °C. The air temperature varies according to Eq. (7): 2π π 0:052 th þ þ α0 þ t : T n ¼ −4:0 þ 11:5 sin 8760 2 8760 h
ð7Þ
The temperatures at the natural surfaces (OA and GJ for cases 1 and 3; OA and IJ for case 2; see Fig. 1) are changed according to Eq. (8): 2π π 0:052 T n ¼ −1:5 þ 12 sin th þ þ α0 þ t : 8760 2 8760 h
ð8Þ
The temperatures at the side slopes (CBA and DEFG for cases 1 and 3; CBA and DEHI for case 2; see Fig. 1) are varied according to Eq. (9): 2π π 0:052 T s ¼ 0:7 þ 13 sin th þ þ α0 þ t : 8760 2 8760 h
ð9Þ
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(a) July 15
The temperatures at the pavement surface CD (Fig. 1) are changed as Eq. (10): 2π π 0:052 th þ þ α0 þ t : T p ¼ 2:5 þ 15 sin 8760 2 8760 h
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In Eqs. (7)–(10), th refers to the computing time (hour), and α0 is the initial phase which is used to adjust the original computing time. The geothermal heat flux at the bottom boundary ML is q = 0.06 W/m2 and its direction is perpendicular to the boundary ML. The lateral boundaries (ONM and JKL) (Fig. 1) are assumed to be adiabatic (Lai et al., 2009). Usually, for a closed crushed-rock embankment structure, a geotextile is covered on the crushed rock layer, and then a thin layer of fine sand is paved (Ma et al., 2006). Therefore, the exchange of air does not occur between the crushed rock material of the embankment and the surface air. Here, we assumed no air flow across any boundary of the computational domain, that is, each boundary is considered impermeable and the normal velocity of air at each boundary is zero.
y/m
ð10Þ
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4. Solution method -15 -20 -20
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5. Results and analysis
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Because this problem, described in the embankment model mentioned above, is heavily nonlinear, its analytical solutions cannot be obtained and the governing equations must be solved numerically in this study. Therefore, the spatial and temporal discretization of the above governing equations is carried out by using finite volume method (Li, 2005; Tao, 2004). The discrete coupled equations can be solved in an iterative manner using a Successive Under-Relaxation Method for every time interval ΔT (Guo et al., 1988), and the iteration sequence is continued until the maximum normalized changes of all variables are less than 10−3. Using these methods, the temperature fields of the whole model can be obtained. Additional details and rationality concerning the numerical method used in this work can be found in the references (Lai et al., 2009; Li, 2005; Tao, 2004).
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x/m The initial temperature distributions of Parts V and VI in the three cases on July 15 are obtained through a long-term transient solution with the upper boundary condition (Eq. (7)) without considering the effect of climate warming, and the temperatures of Parts I, II, III and VI are determined by the temperature of natural ground surface in that date. The initial thermal conditions of the permafrost embankment are different for different construction dates. The worst temperature distributions occur on July 15, so we take July 15 as the initial time. In the 2nd year after the construction of the embankment, the air temperature is about −3.95 °C on October 15. In the 20th year after the construction of the embankment, the air temperatures are about 8.54 °C on July 15, −3.01 °C on October 15 and −14.48 °C on July 15, respectively.
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x/m Fig. 2. Temperature distributions of the crushed-rock interlayer embankment on October 15 in the 2nd year after its construction (unit: °C).
Fig. 3. Temperature distributions of the crushed-rock interlayer embankment in the 20th year after its construction ((a) July 15, (b) October 15, and (c) January 15) (unit: °C).
5.1. Case 1: crushed-rock interlayer embankment Fig. 2 shows the temperature distributions of crushed-rock interlayer embankment on October 15 in the 2nd year after its construction. This figure shows that although the 0 °C isotherm (permafrost table) almost keeps parallel with the original natural ground surface under the embankment, the ground temperature is obviously higher than that under the natural ground surface. It is further confirmed by the disappearance of the − 1.5 °C isotherms under the embankment. The temperatures at the natural surfaces are −1.38 °C. Fig. 3 shows the temperature distributions of crushed-rock interlayer embankment on July 15, October 15, and January 15 in the 20th year after its construction. From these figures, it can be seen that the ground temperatures are still higher under the embankment than those under the natural ground surface although the crushedrock interlayer has a nature convective cooling effect in cold seasons. The nature convective cooling effect can be confirmed by the curved isotherms in Fig. 3c. Furthermore, on October 15, the 0 °C isotherm rises under the left side slope of the embankment, however, decreases under the right side slope because of the long warmer right side slope of the embankment, induced by the effect of slope. On January 15, a residual thawed layer still exists in the embankment and its lower boundary is under the bottom of the embankment, and it will be
W. Pei et al. / Cold Regions Science and Technology 106–107 (2014) 175–182
(a) July 15 5 0
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disadvantageous to the thermal stability of the embankment. Therefore, adoption of crushed-rock interlayer embankment is insufficient to offset the underlying permafrost warming caused by both climate warming and construction-induced warming, and to eliminate the effect of slope in permafrost regions. The temperatures at the natural surfaces on July 15, October 15 and January 15 are 11.54 °C, − 0.44 °C and − 12.48, respectively.
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5.2. Case 2: crushed-rock interlayer-revetment embankment
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Fig. 4. Temperature distributions of crushed-rock interlayer-revetment embankment on October 15 in the 2nd year after its construction (unit: °C).
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5.3. Case 3: crushed-rock base embankment From case 2, it can be found that a revetment, which is paved at the right side slope of the embankment, can increase the cooling capacity of the embankment and eliminate the effect of slope, however it cannot completely remove the influence of climate warming and embankment construction, and the ground temperature under the embankment is
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Based on the fact that the 0 °C isotherms (permafrost table) under the right side slope are slightly downward; furthermore, the ground temperatures are far higher than those under natural ground surface because of the influence of climate warming and warmer long side slope due to the effect of slope. In order to increase the cooling capacity of the crushed-rock interlayer embankment and eliminate the effect of slope, a 1.6-m crushed-rock revetment (Part IV) is paved on the long right side slope of the crushed-rock interlayer embankment (case 1). This embankment structure is defined as crushed-rock interlayerrevetment embankment. Fig. 4 shows the temperature distributions of crushed-rock interlayer-revetment embankment on October 15 in the 2nd year after its construction. In this figure, a slight rise of 0 °C isotherm (permafrost table) at the right slope toe of the embankment shows that the crushed-rock revetment has a certain cooling effect on the underlying soil layers after it is finished for 1 year. However, the distributions of the − 1.5 °C isotherms still indicate that the embankment structure cannot remove the thermal influence from itself in a short term. The temperatures at the natural surfaces on October 15 are − 1.38 °C. Fig. 5(a–c) shows the temperature distributions of crushed-rock interlayer-revetment embankment on July 15, October 15, and January 15 in the 20th year after its construction. Compared with the crushedrock interlayer embankment (Fig. 3(a–c)), the temperature distributions are symmetrical under the embankment. Especially on October 15, the 0 °C isotherm (permafrost table) increases to the bottom of the embankment at the left and right side slopes of the embankment; furthermore, the −0.5 °C isotherms extend more to the middle part of the embankment. However, the ground temperatures are still relatively higher under the embankment, and a residual thawed layer on January 15 still exists in the embankment. These will be disadvantageous to the thermal stability of the embankment. Therefore, the crushed-rock interlayer-revetment embankment can eliminate the effect of slope and improve the thermal stability of the embankment, but the problem of ground temperature warming, which is induced by both climate warming and construction-induced warming, cannot be solved by this type of embankment in permafrost regions. The temperatures at the natural surfaces on July 15, October 15 and January 15 are 11.54 °C, −0.44 °C and −12.48, respectively.
-20 -20
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x/m Fig. 6. Temperature distributions of crushed-rock base embankment on October 15 in the 2nd year after its construction (unit: °C).
W. Pei et al. / Cold Regions Science and Technology 106–107 (2014) 175–182
rising. In order to ensure the thermal stability of the embankment and fully utilize the cooling characteristics of crushed-rock layer, a crushed-rock base embankment is presented. Namely, based on case 1, Part III is filled with crushed rocks (Fig. 1). Fig. 6 shows the temperature distributions of crushed-rock base embankment on October 15 in the 2nd year after its construction. This figure shows that the 0 °C isotherm (permafrost table) rises obviously under the embankment; however, the − 1.5 °C isotherms disappear under the embankment. These indicate that the crushed-rock base embankment structure cannot also remove the thermal influence from itself in a short term. The temperatures at the natural surfaces on October 15 are −1.38 °C. Fig. 7(a–c) shows the temperature distributions of crushed-rock base embankment on July 15, October 15, and January 15 in the 20th year after its construction. Fig. 7 shows that a −2.0 °C zone is formed under the right side slope on July 15 in the 20th year after its construction. On October 15, the 0 °C isotherm (permafrost table) significantly increases to the bottom of the embankment, and the ground temperatures under the right side slope are significantly lower than those under the left side slope and natural ground surface. On January 15 next year, the embankment is fully frozen under the strong air convection in the crushed-rock base layer, which is confirmed by the curved isotherms. Therefore, the crushed-rock base embankment can not
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x/m Fig. 8. Temperature distributions of the embankment without crushed rock on October 15 in the 2nd year after its construction (unit: °C).
only effectively reduce the ground temperature under it, but also ensure the thermal stability of the embankment located on a slope in permafrost regions. Furthermore, it will be advantageous to control the slide of the embankment at the slope in permafrost regions because of the fact that the ground temperatures under the right (long) side slope of the embankment are far lower than those under the left (short) side slope. The temperatures at the natural surfaces on July 15, October 15 and January 15 are 11.54 °C, −0.44 °C and −12.48, respectively. In order to perfectly illustrate the good cooling effect of the crushedrock base embankment, the temperature characteristics of the embankment without crushed rock are given in Figs. 8 and 9. Fig. 8 shows the temperature distributions of the embankment without crushed rock on October 15 in the 2nd year after its construction. The distributions of − 0.5 °C, − 1.0 °C, and − 1.5 °C isotherms move down obviously. The temperatures at the natural surfaces on October 15 are −1.38 °C. Fig. 9(a–c) shows the temperature distributions of the embankment without crushed rock on July 15, October 15, and January 15 in the 20th year after its construction. The thermal effect under embankment is significant (compared with that in Figs. 3, 5, and 7). −0.3 °C, and −0.5 °C isotherms are obviously low. On July 15, the −1.0 °C isotherms under the left of the embankment disappear. Large residual thawed layer exists under the embankment on January 15, which is disadvantageous to the thermal stability of the embankment. Compared with the embankments without crushed rock, it could be found that crushed-rock embankments have significant cooling effect. The temperatures at the natural surfaces on July 15, October 15 and January 15 are 11.54 °C, −0.44 °C and −12.48, respectively. In addition, we analyze the variation of temperatures with depth at the centerlines of the embankments in the four cases on October 15 in the 20th year after their construction, shown in Fig. 10. From Fig. 10, it can be also found that the temperature distributions are similar at the centerlines of the crushed-rock interlayer embankment and crushedrock interlayer-revetment embankment. The 0 °C isotherm (permafrost table) under embankment without crushed rock is lower than the other three crushed-rock embankments on October 15 in the 20th year after construction. However, the temperature of the crushed-rock base embankment is obviously higher than those of the two embankments above the original natural ground surface, but becomes lower under the depth of − 4.0 m. Those differences are caused by the strong air convective cooling effect of crushed-rock base layer in cold seasons (see Figs. 3c, 5c and 7c). Fig. 11 shows the distributions of 0 °C isotherms under the crushedrock base embankment on October 15 in different years after its construction. In the figure, the numbers 1, 2, 5, 10 and 20 are the different years after the crushed-rock base embankment is finished. From the figure, it can be seen that the 0 °C isotherm (permafrost table) is hardly changed under the crushed-rock base embankment in the 1st year after it is constructed. This is from the fact that the crushed-rock base embankment is constructed on July 15 and the natural convection of air in cold seasons did not suffer until the following October 15. From the 2nd year, the permafrost table rises to the bottom of the embankment
W. Pei et al. / Cold Regions Science and Technology 106–107 (2014) 175–182
(a) July15
5
5 10
0
y/m
181
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20
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2
5 -15
-20
-15
-10
-5
0
5
10
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40
x/m
-5 -10 -15
(b) October 15
5
y/m
-20
-20 -20 -15 -10 -5
y/m
5
10 15 20 25 30 35 40
Fig. 11. Distributions of 0 °C isotherms under the crushed-rock base embankment on October 15 in different years after its construction.
-5 -10
6. Conclusions
-15 -20 -20
-15
-10
-5
0
5
10
15
20
25
30
35
40
x/m
(c) January 15
5 0
y/m
0
x/m
0
-5 -10 -15 -20 -20
-15
-10
-5
0
5
10
15
20
25
30
35
40
x/m Fig. 9. Temperature distributions of the embankment without crushed rock in the 20th year after its construction ((a) July 15, (b) October 15, and (c) January 15) (unit: °C).
at the right side, and then keeps stable; at the left side, the 0 °C isotherm has a little variation, but is still kept above the natural permafrost table. These indicate that the crushed-rock base embankment can increase the 0 °C isotherm under it, and keep the 0 °C isotherm stable from the 2nd to 20th years.
5 0
Depth(m)
1
0
(1) Crushed-rock interlayer embankment, crushed-rock interlayerrevetment embankment and crushed-rock base embankment all have active cooling effects on the underlying permafrost, however the crushed-rock interlayer embankment and the crushed-rock interlayer-revetment embankment cannot effectively eliminate the negative effect of climate warming and construction-induced warming, and the effect of slope is still obvious under the crushed-rock interlayer embankment; however, the crushed-rock base embankment can significantly reduce the temperature of underlying permafrost and ensure the thermal stability of the embankment on a slope. (2) For the crushed-rock base embankment, the ground temperatures under the long (right) side slope are far lower than those under the short (left) side slope, and this will be more advantageous to increase the stability of the embankment located on a slope. (3) We also find that the three kinds of embankments cannot all remove the thermal effects of construction from themselves in a short term, therefore, it is very important to select the appropriate construction date for embankment to determine the thermal effect in permafrost regions. Acknowledgments
-5
Original nature ground surface
-10
Crushed-rock interlayer embankment Crushed-rock interlayer-revetment embankment Crushed-rock base embankment Embankment without crushed rock
-15 -20 -2
Based on the thermal effects of the natural slope, the temperature characteristics of three kinds of crushed-rock embankments, i.e., crushed-rock interlayer embankment, crushed-rock interlayerrevetment embankment and crushed-rock base embankment, located on a slope with a ratio of 1:3.73 (about 15° from the horizontal), are numerically analyzed considering global warming. Some conclusions are drawn:
0
2
4
6
8
10
Temperature(oC) Fig. 10. Variations of temperatures with depth at the centerlines of the embankments on October 15 in the 20th year after construction.
This research was supported by the CAS Action-Plan for West Development (grant no. KZCX2-XB3-19), the 100-Talent Program of the Chinese Academy of Sciences (granted to Dr. Mingyi Zhang), the Knowledge Innovation Program of the Chinese Academy of Sciences (grant no. KZCX2-EW-QN301), the National Natural Science Foundation of China (grant nos. 41101068, 41230630), the National Key Basic Research Program of China (973 program grant no. 2012CB026102), and the Youth Innovation Promotion Association, CAS. References An, W.D., Wu, Z.W., Ma, W., et al., 1990. Interaction among Temperature, Moisture and Stress Fields in Frozen Soil. Lanzhou Univ. Press, Lanzhou.
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Cheng, G.D., 2005. A roadbed cooling approach for the construction of Qinghai–Tibet railway. Cold Reg. Sci. Technol. 42 (2), 169–176. Cheng, G.D.,He, P., 2001. Linearity engineering in permafrost areas (in Chinese). J. Glaciol. Geocryol. 23 (3), 213–217. Cheng, G.D., Jiang, H., Wang, K., et al., 2003. Thawing index and freezing index on the embankment surface in permafrost regions. J. Glaciol. Geocryol. 25 (6), 603–607. Cheng, G.D., Wu, Q.B., Ma, W., 2009. Innovative designs of permafrost roadbed for the Qinghai–Tibet Railway. Sci. China Ser. E Technol. Sci. 52 (2), 530–538. Dou, Z., 1996. Studies on the relationships between the elevation, air pressure, air temperature, relative humidity and air density and their influences on the classification of electrician product. Environ. Technol. 4, 001. Goering, D.J., 2003. Passively cooled railway embankments for use in permafrost areas. J. Cold Reg. Eng. 17 (3), 119–133. Guo, K.L., Kong, X.Q., Chen, S.N., 1988. Computational Heat Transfer. University of Science and Technology of China Press, Hefei. Kong, X.Y., Wu, J.B., 2002. A bifurcation study of non-Darcy free convection in porous media. Acta Mech. Sinica 34 (2), 177–185. Lai, Y.M., Zhang, L.X., Zhang, S.J., et al., 2003. Cooling effect of ripped-stone embankments on Qing–Tibet railway under climatic warming. Chin. Sci. Bull. 48 (6), 598–604. Lai, Y.M., Zhang, M.Y., Liu, Z.Q., et al., 2006. Numerical analysis for cooling effect of open boundary ripped-rock embankment on Qinghai–Tibetan railway. Sci. China Ser. D 49 (7), 764–772. Lai, Y.M., Zhang, M.Y., Li, S.Y., 2009. Theory and Application of Cold Regions Engineering. Science Press, Beijing. Li, R.X., 2005. Basis of Finite Volume Method. National Defense Industry Press, Beijing. Ma, W., Yu, S.S., Wu, Q.B., et al., 2006. Study on in-situ monitoring technology of cooling roadbed in permafrost regions of Qinghai–Tibet plateau. Chin. J. Rock Mech. Eng. 25 (3), 563–571. Nield, D.A., Bejan, A., 1992. Convection in Porous Media. Springer-Verlag, New York.
Qin, D.H., 2002. The Comprehensive Evaluating Report on the Environment Evolvement in West China. Science Press, Beijing. Sun, Z.Z., Ma, W., Li, D.Q., 2005. In situ test on cooling effectiveness of air convection embankment with crushed rock slope protection in permafrost regions. J. Cold Reg. Eng. 19 (2), 38–51. Tao, W.Q., 2004. Numerical Heat Transfer, second edition. Xi'an Jiaotong University Press, Xi'an. The Ministry of Transport of the People's Republic of China, 2006. Design Specification for Highway Alignment. China Communications Press, Beijing. Wu, Q.B., Lu, Z.J., Zhang, T.J., et al., 2008. Analysis of cooling effect of crushed rock-based embankment of the Qinghai–Xizang Railway. Cold Reg. Sci. Technol. 53, 271–282. Yu, W.B., Lai, Y.M., Zhang, X.F., et al., 2005. Experimental study on ripped-rock revetment embankment in permafrost regions. Chin. J. Geotech. Eng. 27 (10), 1233–1236. Zhang, M.Y., Lai, Y.M., Liu, Z.Q., et al., 2005. Nonlinear analysis for the cooling effect of Qinghai–Tibetan railway embankment with different structures in permafrost regions. Cold Reg. Sci. Technol. 42 (3), 237–249. Zhang, M.Y., Lai, Y.M., Yu, W.B., et al., 2006. Laboratory investigation of the heat transfer characteristics of a trapezoidal crushed-rock layer under impermeable and permeable boundaries. Exp. Heat Transf. 19 (4), 251–264. Zhang, M.Y., Cheng, G.D., Li, S.Y., 2009a. Numerical study on the influence of geometrical parameters on natural convection cooling effect of the crushed-rock revetment. Sci. China Ser. E Technol. Sci. 52 (2), 539–545. Zhang, M.Y., Lai, Y.M., Dong, Y.H., 2009b. Numerical study on temperature characteristics of expressway embankment with crushed-rock revetment and ventilated ducts in warm permafrost regions. Cold Reg. Sci. Technol. 59 (1), 19–24. Zhang, M.Y., Lai, Y.M., Li, D.Q., et al., 2013. Experimental study on ventilation characteristics of a concrete-sphere layer and a crushed-rock layer. Int. J. Heat Mass Transf. 59, 407–413. Zhao, Z.N., 2002. Heat Transfer. Higher Education Press, Beijing.
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Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions
Thermal stability analysis of crushed-rock embankments on a slope in permafrost regions Wansheng Pei a, Mingyi Zhang a,⁎, Yuanming Lai a, Long Jin b, Jon Harbor c a b c
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 Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, West Lafayette, IN 47907, USA
a r t i c l e
i n f o
Article history: Received 1 November 2013 Accepted 11 July 2014 Available online 18 July 2014 Keywords: Thermal stability Crushed-rock embankment Effect of slope Permafrost region
a b s t r a c t Highways/railways often pass across slope areas and their embankments are often built on the slopes in permafrost regions. It is difficult to ensure the thermal stability of the embankments at the slopes due to the effect of slopes. To protect the underlying permafrost, the crushed-rock embankments are often used in the slope areas. Therefore, it is very necessary to explore the thermal state of crushed-rock embankments located on the slopes. In this study, we studied numerically the temperature characteristics of three kinds of crushed-rock embankments located on a slope under global warming, i.e. crushed-rock interlay embankment, crushed-rock interlayer-revetment embankment and crushed-rock base embankment. Numerical results indicate that the crushed-rock interlayer embankment and the crushed-rock interlayer-revetment embankment, located on a slope with a ratio of 1:3.73 (about 15° from the horizontal), cannot effectively eliminate the negative effect of climate warming and construction-induced warming, and the effect of slope is still obvious on the thermal stability of permafrost under the crushed-rock interlayer embankment. However, the crushed-rock base embankment can significantly reduce the temperature of underlying permafrost and keep the underlying permafrost table stable for a long term; furthermore, the ground temperatures under the long side slope are far lower than those under the short side slope, and this will be more advantageous to control the slide of the embankment located on a slope and increase its stability. We also find that the three kinds of embankments cannot all remove the thermal effects of construction from themselves in a short term. Generally speaking, the crushed-rock base embankment structure can be very advantageous to the thermal stability of the embankment on a slope. © 2014 Elsevier B.V. All rights reserved.
1. Introduction A crushed-rock layer, as a highly porous medium (Lai et al., 2003), has been widely used to protect the underlying permafrost in the embankment engineering in cold regions. Examples include many important highway and railway engineering projects, such as the Qinghai–Tibet Highway and Qinghai–Tibet Railway in China, the Alaska Highway in the USA and the Baikal–Amur Railway in Russia (Cheng, 2005; Cheng and He, 2001). Typical construction methods include crushed-rock embankments, crushed-rock base (interlayer) embankments, crushed-rock revetment embankments and U-shaped (interlayer and revetment) crushed-rock embankments (Cheng et al., 2009; Lai et al., 2009; Zhang et al., 2005). The cooling mechanism results from the fact that the high permeability of such material would allow air convection to occur within it when unstable air pressure/temperature
⁎ Corresponding author. E-mail address: [email protected] (M. Zhang).
http://dx.doi.org/10.1016/j.coldregions.2014.07.005 0165-232X/© 2014 Elsevier B.V. All rights reserved.
gradients exist. At present, the heat and mass transfer theories have been developed in cold region engineering. The convective heat transfer effect in crushed-rock layer has been applied to control thaw settlement of permafrost embankment. The cooling effects of highly porous media embankments made from crushed rocks have been evaluated previously using numerical simulation, laboratory tests and in-situ observation. In detail, Goering (2003) numerically researched the convective heat transfer of crushed-rock embankment with an unsteady two dimensional finite-element model that is capable of solving the coupled governing equations of pore air flow and energy transport. Lai et al. (2006) analyzed numerically the velocity and temperature characteristics of open-boundary crushed-rock embankment under wind action based on the climatic and geological conditions of the Qinghai–Tibet Plateau. Zhang et al. (2009a, 2009b) found that the geometrical parameters including sloped angle, aspect ratio and so on have significant influence on the natural convection cooling effect of crushed-rock revetment by numerical calculations. Yu et al. (2005) researched the temperature properties of a traditional embankment and a ripped-rock revetment embankment by laboratory experiments and found that the
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30.0 m
3.0 m
O N
.5 1:1 C B A
3.1 m
ripped-rock revetment could cool embankment and adjust the temperature difference between the north-facing slope and the south-facing slope. Zhang et al. (2006) studied experimentally heat transfer mechanisms of a trapezoidal crushed-rock layer under two boundary conditions, i.e. cyclic temperature, air-flow, air-permeable/impermeable at the two side slopes and closed at both top and bottom, and found that the former is forced convective heat transfer and the latter is nature convective heat transfer. Sun et al. (2005) concluded that the cooling capacity of the coarse rock revetment excelled that of the fine rock revetment by analyzing the temperature fields of the experimental embankments with crushed rock slope protection in field. Wu et al. (2008) performed lots of in-situ observations and found that crushed rock-based embankment could effectively cool the roadbed, resulting in the decrease of permafrost temperatures and the rise of permafrost table, however the cooling effects were significantly different in warm and relatively cold permafrost areas. From these studies, we can conclude that crushed-rock layer can have a good cooling effect on the underlying soil layers. However, the previous researches usually focus on the crushedrock embankments located on the flat open areas. In fact, the highway/railway often passes across slope areas, e.g. valley and hillside, and thus their embankments are often built on the slopes. Because of the asymmetry thermal boundary conditions and the effect of gravity, it will be difficult to ensure the thermal stability of the embankments located on the slopes. Especially for the side slope of the embankment on the downward slope, the longer slope absorbs more heat energy than that on the upward slope, and this will not benefit the thermal stability of the embankment. To protect the underlying permafrost, the crushed-rock embankments are also often used on the slope areas. Therefore, it is very important to explore the thermal state of crushed-rock embankments at the slopes. In this paper, we focused on the influence of slope for crushed-rock embankments and proposed a model for crushed-rock embankments on a slope. In order to quickly research the effect of crushed-rock embankments on the underlying permafrost on a slope, we have used a numerical method. A large number of numerical simulations were carried out during the course of this study. However, only three kinds of embankment structures are presented in this paper. Namely, the temperature characteristics of crushed-rock interlay embankment, crushed-rock interlayer-revetment embankment and crushed-rock base embankment, located on a slope with a ratio of 1:3.73 (about 15° from the horizontal), have been analyzed for 20 years based on the assumption that the warming rate of air temperature on the Qinghai– Tibet Plateau will be 0.052 °C (Qin, 2002).
10.0 m I
D
II III V
y
The computational domain of crushed-rock embankment model on the slope is shown in Fig. 1. The ratio of slope OJ is 1:3.73 (about 15° from the horizontal). The embankment height is 3.1 m from the left slope toe. The computational domain is extended 30 m horizontally from the side slope toe (A and I) of the embankment, and 30 m downward from the natural ground surface at the left and right lateral boundaries, respectively. Three crushed-rock embankment structures are designed in the model. Case 1 Crushed-rock interlayer embankment. Namely, Parts I and III are the embankment fill, Part II is the crushed-rock interlayer with a thickness of 1.5 m, and Parts V and VI are the natural soil layers and they are subclay and weathered mudstone, respectively. Case 2 Crushed-rock interlayer-revetment embankment. Based on case 1, a crushed-rock revetment (Part IV) is added at the right side of the embankment with a horizontal width of 1.6 m. Case 3 Crushed-rock base embankment. Similarly, based on case 1, Part III is filled with crushed rocks. In the calculational domains, shown in Fig. 1, the specific heat of air at an elevation of more than 4500 m is Ca = 1.004 × 103 J/(kg ·°C), the thermal conductivity is λ = 2.0 × 10 − 2 W/(m · °C), the air density is ρa = 0.641 kg/m3, and the dynamic viscosity is μ = 1.75 × 10−5 kg/(m · s). The mean particle size of crushed rock is about 20.0 cm and the permeability and inertial resistance factor (Beta factor of non-Darcy flow) are k = 1.66 × 10− 5 m2 and B = 41.20 m− 1, respectively (Zhang et al., 2013). The thermal parameters of all media are listed in Table. 1 (Lai et al., 2009). 3. Governing equations According to the Design Specifications for Highway Alignment (2006) and actual embankment geometries in permafrost regions, the crushed-rock embankment structures on a slope at an elevation of 4500 m are taken as computational models (Fig. 1) in this paper. Considering the direction of geothermal heat flux and rationality of boundaries, the bottom boundary (ML) is set parallel to the natural ground surface (OJ) and the lateral boundaries (ONM and JKL) are perpendicular to the natural ground surface (OJ) and the bottom boundary (ML). According to the different heat transfer characteristics of different media, the embankment model is divided into two zones, i.e. crushed-
E H
1:1 F .5 1:3.7 3
IV
G x
I
30.0 m J
VI
K
30.0 m
M
2. Description of the models
L Fig. 1. Computational domain of crushed-rock embankment.
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177
Table 1 Thermal parameters of media in embankments. Physical variable
λf W/(m·°C)
Cf J/(m3·°C)
Crushed rock Fill soil Subclay Weathered mudstone
0.387 1.980 1.351 1.824
1.015 1.913 1.879 1.846
× × × ×
106 106 106 106
rock zone (porous media zone) and soil layer zone (solid zone). Therefore, the governing equations of different zones are described as follows. 3.1. Crushed-rock zone The thermal convection of fluid inside crushed-rock layer, which can be considered as porous media, is the process of heat and mass transfer. The natural convection is unsteady. The change of air density caused by air humidity change is far less than that caused by air temperature (Dou, 1996). Thus, the air convection effect caused by air temperature gradient is far larger than that caused by air humidity gradient in the crushed-rock layer. Therefore, only the convection caused by the air temperature gradient is considered in our model. In the analysis, only the motion of interstitial air is considered. Additionally, the porous media zones are modeled by the addition of a momentum term to the standard fluid flow equations. This term is composed of two parts: a viscous loss term and an inertial loss term. Under those conditions, governing equations for mass, momentum, and energy can be written as follows (Kong and Wu, 2002; Nield and Bejan, 1992): Continuity: ∂vx ∂vy þ ¼0 ∂x ∂y
∂p μ ¼ − vx −ρa Bjvjvx k ∂x
ð2aÞ
∂p μ ¼ − vy −ρa Bjvjvy −ρα g k ∂y
ð2bÞ
where jvj ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v2x þ v2y , B is the Beta factor of non-Darcy flow, k is the
permeability of the porous medium, μ is the dynamic viscosity of air, p* is the air pressure, ρa is the air density, and ρaB|v|vx is called the inertia-turbulent term. It is assumed that air is incompressible, and its density ρα is the function of temperature. In order to simplify the analysis, the Boussinesq approximation is employed (Kong and Wu, 2002; Nield and Bejan, 1992).
ρα ¼ ρa0 ½1−βðT−T 0 Þ
ð3Þ
where ρa0 and T0 are the reference values for density and temperature, and β is the coefficient of thermal expansion for air. Energy:
∂T
Ce
∂t
¼
∂ ∂ ∂T ∂T ∂T ∂T þ −C a ρa vx λe λe þ vy ∂x ∂x ∂y ∂y ∂x ∂y
ð4Þ
where Ca is the air specific heat at constant pressure; and Ce⁎ and λe⁎ are the effective volumetric heat capacity and effective thermal conductivity in porous medium.
Cu J/(m3·°C)
0.387 1.919 1.125 1.474
1.015 2.227 2.357 2.099
× × × ×
106 106 106 106
L (J/m3) 0.0 2.04 × 107 6.03 × 107 3.77 × 107
3.2. Soil layer zone The ratio of thermal conduction is far larger than that of convection in soil layers (An et al., 1990), so that the convection can be neglected. Thus, when only the conduction and phase change problem are considered, the heat transfer process in soil layers can be described as follows (Kong and Wu, 2002; Nield and Bejan, 1992; Zhao, 2002):
Ce
∂T ∂ ∂ ∂T ∂T þ : ¼ λe λe ∂t ∂x ∂x ∂y ∂y
ð5Þ
It is assumed that the phase change occurs in a range of temperature (Tm ± ΔT). When the effective heat capacity is determined, the effect of the temperature interval 2ΔT should be included. Assuming that Cf, Cu, λf and λu do not depend on temperature T. Then, the following definitions of Ce⁎ and λe⁎ may be obtained (Guo et al., 1988; Lai et al., 2009):
Ce ¼
ð1Þ
where vx and vy are the x and y components of air velocities, respectively Momentum:
λu W/(m·°C)
λe
¼
8 > <
Cf L C þ Cu þ f > 2 : 2ΔT Cu 8 > <
TbT m −ΔT T m −ΔT ≤T ≤T m þ ΔT T NT m þ ΔT
λf λu −λ f λ þ ½T−ðT m −ΔT Þ > f 2ΔT : λu
TbT m −ΔT T m −ΔT ≤T ≤T m þ ΔT T NT m þ ΔT
ð6aÞ
ð6bÞ
where subscripts f and u represent the frozen and unfrozen states, respectively; Cf and λf are the volumetric heat capacity and thermal conductivity of media in the frozen area, respectively; Cu and λu are the volumetric heat capacity and thermal conductivity of media in the unfrozen area, respectively; and L is the latent heat per unit volume. According to Qin (2002), the mean annual air temperature will be warmed up by 0.052 °C/a on the Qinghai–Tibetan Plateau in the future 50 years due to climatic change. Based on the related data (Cheng et al., 2003; Lai et al., 2009; Zhang et al., 2009a, 2009b), the variation equations of annual temperatures at different surfaces on the Qinghai–Tibetan Plateau are obtained. The mean annual air temperature is taken as − 4.0 °C. The air temperature varies according to Eq. (7): 2π π 0:052 th þ þ α0 þ t : T n ¼ −4:0 þ 11:5 sin 8760 2 8760 h
ð7Þ
The temperatures at the natural surfaces (OA and GJ for cases 1 and 3; OA and IJ for case 2; see Fig. 1) are changed according to Eq. (8): 2π π 0:052 T n ¼ −1:5 þ 12 sin th þ þ α0 þ t : 8760 2 8760 h
ð8Þ
The temperatures at the side slopes (CBA and DEFG for cases 1 and 3; CBA and DEHI for case 2; see Fig. 1) are varied according to Eq. (9): 2π π 0:052 T s ¼ 0:7 þ 13 sin th þ þ α0 þ t : 8760 2 8760 h
ð9Þ
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(a) July 15
The temperatures at the pavement surface CD (Fig. 1) are changed as Eq. (10): 2π π 0:052 th þ þ α0 þ t : T p ¼ 2:5 þ 15 sin 8760 2 8760 h
5 0 -5 -10 -15 -20 -20
-15
-10
-5
0
5
10
15
20
25
30
35
40
15
20
25
30
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40
15
20
25
30
35
40
x/m
(b) October 15 5 0
y/m
In Eqs. (7)–(10), th refers to the computing time (hour), and α0 is the initial phase which is used to adjust the original computing time. The geothermal heat flux at the bottom boundary ML is q = 0.06 W/m2 and its direction is perpendicular to the boundary ML. The lateral boundaries (ONM and JKL) (Fig. 1) are assumed to be adiabatic (Lai et al., 2009). Usually, for a closed crushed-rock embankment structure, a geotextile is covered on the crushed rock layer, and then a thin layer of fine sand is paved (Ma et al., 2006). Therefore, the exchange of air does not occur between the crushed rock material of the embankment and the surface air. Here, we assumed no air flow across any boundary of the computational domain, that is, each boundary is considered impermeable and the normal velocity of air at each boundary is zero.
y/m
ð10Þ
-5 -10
4. Solution method -15 -20 -20
-10
-5
0
5
10
(c) January 15 5 0 -5 -10 -15 -20 -20
5. Results and analysis
-15
x/m
y/m
Because this problem, described in the embankment model mentioned above, is heavily nonlinear, its analytical solutions cannot be obtained and the governing equations must be solved numerically in this study. Therefore, the spatial and temporal discretization of the above governing equations is carried out by using finite volume method (Li, 2005; Tao, 2004). The discrete coupled equations can be solved in an iterative manner using a Successive Under-Relaxation Method for every time interval ΔT (Guo et al., 1988), and the iteration sequence is continued until the maximum normalized changes of all variables are less than 10−3. Using these methods, the temperature fields of the whole model can be obtained. Additional details and rationality concerning the numerical method used in this work can be found in the references (Lai et al., 2009; Li, 2005; Tao, 2004).
-15
-10
-5
0
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Fig. 3. Temperature distributions of the crushed-rock interlayer embankment in the 20th year after its construction ((a) July 15, (b) October 15, and (c) January 15) (unit: °C).
5.1. Case 1: crushed-rock interlayer embankment Fig. 2 shows the temperature distributions of crushed-rock interlayer embankment on October 15 in the 2nd year after its construction. This figure shows that although the 0 °C isotherm (permafrost table) almost keeps parallel with the original natural ground surface under the embankment, the ground temperature is obviously higher than that under the natural ground surface. It is further confirmed by the disappearance of the − 1.5 °C isotherms under the embankment. The temperatures at the natural surfaces are −1.38 °C. Fig. 3 shows the temperature distributions of crushed-rock interlayer embankment on July 15, October 15, and January 15 in the 20th year after its construction. From these figures, it can be seen that the ground temperatures are still higher under the embankment than those under the natural ground surface although the crushedrock interlayer has a nature convective cooling effect in cold seasons. The nature convective cooling effect can be confirmed by the curved isotherms in Fig. 3c. Furthermore, on October 15, the 0 °C isotherm rises under the left side slope of the embankment, however, decreases under the right side slope because of the long warmer right side slope of the embankment, induced by the effect of slope. On January 15, a residual thawed layer still exists in the embankment and its lower boundary is under the bottom of the embankment, and it will be
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disadvantageous to the thermal stability of the embankment. Therefore, adoption of crushed-rock interlayer embankment is insufficient to offset the underlying permafrost warming caused by both climate warming and construction-induced warming, and to eliminate the effect of slope in permafrost regions. The temperatures at the natural surfaces on July 15, October 15 and January 15 are 11.54 °C, − 0.44 °C and − 12.48, respectively.
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5.3. Case 3: crushed-rock base embankment From case 2, it can be found that a revetment, which is paved at the right side slope of the embankment, can increase the cooling capacity of the embankment and eliminate the effect of slope, however it cannot completely remove the influence of climate warming and embankment construction, and the ground temperature under the embankment is
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Based on the fact that the 0 °C isotherms (permafrost table) under the right side slope are slightly downward; furthermore, the ground temperatures are far higher than those under natural ground surface because of the influence of climate warming and warmer long side slope due to the effect of slope. In order to increase the cooling capacity of the crushed-rock interlayer embankment and eliminate the effect of slope, a 1.6-m crushed-rock revetment (Part IV) is paved on the long right side slope of the crushed-rock interlayer embankment (case 1). This embankment structure is defined as crushed-rock interlayerrevetment embankment. Fig. 4 shows the temperature distributions of crushed-rock interlayer-revetment embankment on October 15 in the 2nd year after its construction. In this figure, a slight rise of 0 °C isotherm (permafrost table) at the right slope toe of the embankment shows that the crushed-rock revetment has a certain cooling effect on the underlying soil layers after it is finished for 1 year. However, the distributions of the − 1.5 °C isotherms still indicate that the embankment structure cannot remove the thermal influence from itself in a short term. The temperatures at the natural surfaces on October 15 are − 1.38 °C. Fig. 5(a–c) shows the temperature distributions of crushed-rock interlayer-revetment embankment on July 15, October 15, and January 15 in the 20th year after its construction. Compared with the crushedrock interlayer embankment (Fig. 3(a–c)), the temperature distributions are symmetrical under the embankment. Especially on October 15, the 0 °C isotherm (permafrost table) increases to the bottom of the embankment at the left and right side slopes of the embankment; furthermore, the −0.5 °C isotherms extend more to the middle part of the embankment. However, the ground temperatures are still relatively higher under the embankment, and a residual thawed layer on January 15 still exists in the embankment. These will be disadvantageous to the thermal stability of the embankment. Therefore, the crushed-rock interlayer-revetment embankment can eliminate the effect of slope and improve the thermal stability of the embankment, but the problem of ground temperature warming, which is induced by both climate warming and construction-induced warming, cannot be solved by this type of embankment in permafrost regions. The temperatures at the natural surfaces on July 15, October 15 and January 15 are 11.54 °C, −0.44 °C and −12.48, respectively.
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rising. In order to ensure the thermal stability of the embankment and fully utilize the cooling characteristics of crushed-rock layer, a crushed-rock base embankment is presented. Namely, based on case 1, Part III is filled with crushed rocks (Fig. 1). Fig. 6 shows the temperature distributions of crushed-rock base embankment on October 15 in the 2nd year after its construction. This figure shows that the 0 °C isotherm (permafrost table) rises obviously under the embankment; however, the − 1.5 °C isotherms disappear under the embankment. These indicate that the crushed-rock base embankment structure cannot also remove the thermal influence from itself in a short term. The temperatures at the natural surfaces on October 15 are −1.38 °C. Fig. 7(a–c) shows the temperature distributions of crushed-rock base embankment on July 15, October 15, and January 15 in the 20th year after its construction. Fig. 7 shows that a −2.0 °C zone is formed under the right side slope on July 15 in the 20th year after its construction. On October 15, the 0 °C isotherm (permafrost table) significantly increases to the bottom of the embankment, and the ground temperatures under the right side slope are significantly lower than those under the left side slope and natural ground surface. On January 15 next year, the embankment is fully frozen under the strong air convection in the crushed-rock base layer, which is confirmed by the curved isotherms. Therefore, the crushed-rock base embankment can not
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only effectively reduce the ground temperature under it, but also ensure the thermal stability of the embankment located on a slope in permafrost regions. Furthermore, it will be advantageous to control the slide of the embankment at the slope in permafrost regions because of the fact that the ground temperatures under the right (long) side slope of the embankment are far lower than those under the left (short) side slope. The temperatures at the natural surfaces on July 15, October 15 and January 15 are 11.54 °C, −0.44 °C and −12.48, respectively. In order to perfectly illustrate the good cooling effect of the crushedrock base embankment, the temperature characteristics of the embankment without crushed rock are given in Figs. 8 and 9. Fig. 8 shows the temperature distributions of the embankment without crushed rock on October 15 in the 2nd year after its construction. The distributions of − 0.5 °C, − 1.0 °C, and − 1.5 °C isotherms move down obviously. The temperatures at the natural surfaces on October 15 are −1.38 °C. Fig. 9(a–c) shows the temperature distributions of the embankment without crushed rock on July 15, October 15, and January 15 in the 20th year after its construction. The thermal effect under embankment is significant (compared with that in Figs. 3, 5, and 7). −0.3 °C, and −0.5 °C isotherms are obviously low. On July 15, the −1.0 °C isotherms under the left of the embankment disappear. Large residual thawed layer exists under the embankment on January 15, which is disadvantageous to the thermal stability of the embankment. Compared with the embankments without crushed rock, it could be found that crushed-rock embankments have significant cooling effect. The temperatures at the natural surfaces on July 15, October 15 and January 15 are 11.54 °C, −0.44 °C and −12.48, respectively. In addition, we analyze the variation of temperatures with depth at the centerlines of the embankments in the four cases on October 15 in the 20th year after their construction, shown in Fig. 10. From Fig. 10, it can be also found that the temperature distributions are similar at the centerlines of the crushed-rock interlayer embankment and crushedrock interlayer-revetment embankment. The 0 °C isotherm (permafrost table) under embankment without crushed rock is lower than the other three crushed-rock embankments on October 15 in the 20th year after construction. However, the temperature of the crushed-rock base embankment is obviously higher than those of the two embankments above the original natural ground surface, but becomes lower under the depth of − 4.0 m. Those differences are caused by the strong air convective cooling effect of crushed-rock base layer in cold seasons (see Figs. 3c, 5c and 7c). Fig. 11 shows the distributions of 0 °C isotherms under the crushedrock base embankment on October 15 in different years after its construction. In the figure, the numbers 1, 2, 5, 10 and 20 are the different years after the crushed-rock base embankment is finished. From the figure, it can be seen that the 0 °C isotherm (permafrost table) is hardly changed under the crushed-rock base embankment in the 1st year after it is constructed. This is from the fact that the crushed-rock base embankment is constructed on July 15 and the natural convection of air in cold seasons did not suffer until the following October 15. From the 2nd year, the permafrost table rises to the bottom of the embankment
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at the right side, and then keeps stable; at the left side, the 0 °C isotherm has a little variation, but is still kept above the natural permafrost table. These indicate that the crushed-rock base embankment can increase the 0 °C isotherm under it, and keep the 0 °C isotherm stable from the 2nd to 20th years.
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(1) Crushed-rock interlayer embankment, crushed-rock interlayerrevetment embankment and crushed-rock base embankment all have active cooling effects on the underlying permafrost, however the crushed-rock interlayer embankment and the crushed-rock interlayer-revetment embankment cannot effectively eliminate the negative effect of climate warming and construction-induced warming, and the effect of slope is still obvious under the crushed-rock interlayer embankment; however, the crushed-rock base embankment can significantly reduce the temperature of underlying permafrost and ensure the thermal stability of the embankment on a slope. (2) For the crushed-rock base embankment, the ground temperatures under the long (right) side slope are far lower than those under the short (left) side slope, and this will be more advantageous to increase the stability of the embankment located on a slope. (3) We also find that the three kinds of embankments cannot all remove the thermal effects of construction from themselves in a short term, therefore, it is very important to select the appropriate construction date for embankment to determine the thermal effect in permafrost regions. Acknowledgments
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Based on the thermal effects of the natural slope, the temperature characteristics of three kinds of crushed-rock embankments, i.e., crushed-rock interlayer embankment, crushed-rock interlayerrevetment embankment and crushed-rock base embankment, located on a slope with a ratio of 1:3.73 (about 15° from the horizontal), are numerically analyzed considering global warming. Some conclusions are drawn:
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This research was supported by the CAS Action-Plan for West Development (grant no. KZCX2-XB3-19), the 100-Talent Program of the Chinese Academy of Sciences (granted to Dr. Mingyi Zhang), the Knowledge Innovation Program of the Chinese Academy of Sciences (grant no. KZCX2-EW-QN301), the National Natural Science Foundation of China (grant nos. 41101068, 41230630), the National Key Basic Research Program of China (973 program grant no. 2012CB026102), and the Youth Innovation Promotion Association, CAS. References An, W.D., Wu, Z.W., Ma, W., et al., 1990. Interaction among Temperature, Moisture and Stress Fields in Frozen Soil. Lanzhou Univ. Press, Lanzhou.
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