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Study on the effect of the thermal regime differences in roadbed slopes on their thawing features in permafrost regions of Qinghai–Tibetan plateau
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Cold Regions Science and Technology 53 (2008) 334 – 345 www.elsevier.com/locate/coldregions
Study on the effect of the thermal regime differences in roadbed slopes on their thawing features in permafrost regions of Qinghai–Tibetan plateau Chou Ya-ling ⁎, Yu Sheng, Wei Ma State Key Laboratory of Frozen Soils Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou 730000, China Received 8 December 2006; accepted 28 April 2007
Abstract For the permafrost regions, numerical models are established for analyzing the possible changing tendency of the permafrost thawing features under various surface materials, embankment heights and strikes for a period of 50 years. Surface materials are gravelly and asphalt. Embankment heights range from 0 m to 5.0 m with a step of 0.5 m. For the embankment strike, east to west (EW), southwest to northeast (SW–NE), south to north (SN) and symmetrical route are taken into consideration. The thermal boundary condition is with the assumption that the air temperature will warm up by 1.1 °C during the next 50 years. The calculated results indicate that there is a great difference in thawing features between the asymmetrical and the symmetrical routes. Beneath both the gravelly and the asphalt surfaces, for embankments with south-facing and north-facing slopes, which are defined as the shadowy– sunny slope, calculations show: (1) The maximum thaw depth is closely related to time, the surface materials and the embankment heights. The maximum thaw depths of the low embankments have little to do with the roadbed strike. But the maximum thaw depths of the high embankments are very much influenced by the roadbed strike, and it sharply changes with the variation of the embankment heights and climatic warming. (2)The distance from the location where the maximum thaw depth occurs to the embankment centric line has nothing to do with time, but is closely related to the surface materials, the embankment heights and strikes. Moreover, it is linearly related to the embankment heights. (3) Under the same embankment height and roadbed strike, the distance from the point where the maximum thaw depth occurs to the centric line of the embankment beneath the gravelly surface is larger than that beneath the asphalt surface. However, the maximum thaw depth beneath the asphalt surface is much larger than that beneath the gravelly surface. To some extent, the asphalt surface partially offsets the shadowy–sunny slope effect, but it makes the maximum thaw depth become much larger. (4) When designing an embankment, besides considering the minimum and the maximum embankment height, the shadowy–sunny slope effect also should be taken into account. © 2007 Elsevier B.V. All rights reserved. Keywords: Permafrost; Roadbed strike; The shadowy–sunny slope; Thawing features; The maximum thaw depth
1. Introduction
⁎ Corresponding author. Tel.: +86 931 4967297; fax: +86 931 4967271. E-mail address: [email protected] (C. Ya-ling). 0165-232X/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2007.04.022
In permafrost regions, the construction of embankments changes the thermophysical features of the natural ground surface and atmosphere, and influences the thermodynamic and dynamic stability of the frozen
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soil layers. Establishing high roadbeds was considered a conventional measure to protect permafrost from thawing (Cheng et al., 2003). However, the higher the roadbed, the larger will be the area of the slope, and the thermal effect of the slope cannot be overlooked. Especially, when the two embankment slopes are south-facing and north-facing respectively, which is called the shadowy–sunny slope in Chinese, the difference of the thermal boundary conditions such as the solar radiation and surface turbulent flow will induce the transverse asymmetry of temperature field, and this will lead to a multitude of problems in permafrost roadbeds. After the roadbed is built, thermal effect problems associated with slope orientations also must be considered in the roadbed engineering protection measures in permafrost regions (Cheng, 2003). So far, many numerical computations on the embankment temperature fields in permafrost regions have failed to take the road strike into account and that the temperatures in the slopes are even lower than that in the surface (Zhang et al., 2006; Liu and Lai, 2004), which are still considered symmetrical thermal boundary conditions (Liu and Tian, 2002; Wen et al., 2005; Zhang et al., 2005). However, the fact is that there is no embankment with completely symmetrical thermal boundary conditions. The Fenghuoshan Section of the Qinghai–Tibet Highway extends from north to south. According to the field data for the years 1985 and 1986 in this section, there was an obvious thermal difference between the eastern slope and the western slope. The mean temperature of the eastern slope surface was 2.4 °C higher than that of the western slope(Wu et al., 1988). The asymmetrical thermal boundary conditions of the slopes indicated that the maximum thaw depth position had deviated in the transverse direction. The higher the roadbed, the greater is the transverse thermal
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deviation. Thus it is unreasonable to analyze permafrost thawing features only according to the symmetrical boundary conditions. From observational data on the Qinghai–Tibet Highway, if the thickness of the roadbed is greater than 3 m, the shadowy–sunny slope effect is quite obvious, and active cooling measures must be applied. It also is obvious there are shadowy–sunny slope phenomena in the embankment of the Qinghai– Tibet Railway (Chen et al., 2006). Field data were obtained from the section K369+000 to K369+100 along National Highway 214, whose strike is 246° and the surface is asphalt and concrete. Although the road was re-built in 2002, by the end of 2005 many longitudinal cracks had occurred on the south side of the roadbed (Fig. 1). Fig. 2 gives the profiles of permafrost table on 10 Nov. 2003 and geology of experimental cross-section K369+100. From Fig. 2, we can see the left artificial permafrost table is deeper than the right one and the maximum thaw depth position is not situated on the centric line of the roadbed. The cause was that the transverse thermal difference resulted in differential deformations and settlements, and this lead to the result that thaw settlement in the south-facing side is much larger and longitudinal cracks occurred on that side. On the Qinghai–Tibet Plateau, permafrost is quite sensitive to environmental changes and human activities. When roadbeds are built in permafrost regions, there will be different thermal regimes on the slopes because of different roadbed strikes. Various thawing features and engineering problems under embankments caused by the transverse thermal difference in slopes have already been discussed by researchers (Lai et al., 2004; Sheng et al., 2005; Dou et al., 2003; Sun, 2005). No work, however, has been found to quantitatively and systematically discuss the influence of the temperature
Fig. 1. Photo showing the longitudinal crack of section K369+100.
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Fig. 2. Profiles of permafrost table and geology of section K369+100.
differences of embankment slopes with various surface materials, roadbed heights and strikes on the embankment thawing features. To solve the abovementioned problems is very essential, and this work will provide a scientific basis for road construction and maintenance in permafrost regions of the plateau. Equations for heat conduction, coupled with phase transitions, will be obtained, so that a two-dimensional numerical model for the thawing features with different embankment geometrical parameters is established, with the assumption that the air temperature on the Qinghai–Tibet plateau will rise by 1.1 °C during the next 50 years (Li and Cheng, 1999). The finite element method will be applied for calculation with adjustable roadbed heights. The maximum thaw depths, changing with different embankments, will be analyzed for the next coming 50 years. 2. The computational model 2.1. Governing equations and finite-element formula Ignoring convection and mass transfer, and only considering the phase transitions and heat conduction, the 2-D equation for heat conduction in the soil layers can be described as follows: A AT A AT AT k k þ ¼ qc Ax Ax Ay Ay At
where, ρ — soil density, T — temperature, c — volumetric heat capacity of the soil, λ — coefficient of thermal conductivity, t — time. Tf ðsðtÞ; tÞ ¼ Tu ðsðT Þ; T Þ ¼ Tm
ð2Þ
ATf ATu dsðtÞ ku ¼ Lqw0 dt An An
ð3Þ
kf
where f and u denote frozen and unfrozen states, respectively. L — latent heat of water, w0 — the initial water content, Tm — temperature on the freeze–thaw interface, n — normal direction of the freeze–thaw interface. Latent heat of soil can be calculated by the following equation: Q ¼ Lqd ðw wu Þ
where Q — the latent heat of the soil, L — the latent heat of water, w — the water content, wu — the unfrozen water content. The unfrozen water content can be obtained by the following equations (Xu et al., 2001): wu ¼ aT b b¼
ð1Þ
ð4Þ
lnw0 lnwu lnT lnTf
a ¼ w0 Tfb
ð5Þ ð6Þ ð7Þ
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where T and Tf are the freezing temperatures of the soils at the initial water content w0 and wu, respectively. The finite element formula are: AT ½M þ ½KfT g ¼ fqg ð8Þ At Z qcNi Nj dX ð9Þ Mij ¼ R Xe
Z Kij ¼ R
Xe
k
ANi ANj ANi ANj þ dX Ax Ax Ay Ay
ð10Þ
Z qi ¼ R
Ce2
qNi dC
ð11Þ
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30 m depth from the natural ground surface. The road surface width is 7.5 m, and the slope gradient is 1:1.5. The computational dimensions are shown in Fig. 3, where part A is a sandy gravelly soil, part B is a silty clay, part C is a gravelly silty clay and part D is a weathered mudstone. The element structure is divided into 4-nodal elements and the element mesh diagram is shown in Fig. 4. Thermal parameters of the media were obtained from drilling data in Beiluhe, and are shown in Table 1. Beiluhe is at the South of the Beiluhe Basin, along the Qinghai– Tibet Railway, and is part of the diluvial alpine plain physiognomy. It is located at 34.85°N, 92.94°E, and the elevation is about 4635 m. The vegetation coverage is less than 20%, the air mean annual temperature is −3.82 °C. 2.3. Boundary conditions and initial conditions
where Ni and Nj are the shape functions. 2.2. Computational domain and physical parameters of soils Although the computational domain is symmetrical in terms of geometric shape with regard to the embankment centric line, the shadowy–sunny slope problems, namely asymmetrical thermal boundary conditions, have to be taken into account. The entire roadbed section has to be adopted in the calculations. Eleven embankment heights (h = 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0 m) are taken, and the physical domain for computation is extended to 20 m from the foot of the slopes and to the
The mean annual air temperature is taken as − 3.82 °C, and the mean annual temperatures and the temperature amplitudes of all the embankment surfaces with different strikes were obtained from the permafrost regions in Beiluhe (Cheng et al., 2003). The temperature varies by the following formula: 2pt p T ðx; y; tÞ ¼ T þ gðtÞ þ Asin þ 8760 2 ð12Þ P
P
P
P
P
ðx; yÞa AB; BC; CD; DE and EF where, T — the mean annual temperatures of all the embankment surfaces, A — temperature amplitudes of
Fig. 3. Computational domain.
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C. Ya-ling et al. / Cold Regions Science and Technology 53 (2008) 334–345 Table 2 Temperature boundary conditions
Fig. 4. Finite element mesh.
p all the boundaries, t — time, -initial phase, g(t) = R0t, 2 R0 — climatic warming velocity with R0 = 0.022 °C/ 8760 h, the value of T and PA are listed in Table 2. For the lower boundary KL, a temperature gradient of 0.038 °C/m was used (Zhang et al., 2005), accordingly the geothermal heat flux is calculated as q = 0.3079 kJ/(h m2): k
AT ¼ q An
ð13Þ P
P
The boundaries FK and AL are regarded as heat insulated: k
AT ¼0 An
ð14Þ
The initial condition is given as: T ðx; y; 0Þ ¼ T0
ð15Þ
where, the initial temperature distribution T0 was obtained using from the following method: taking the data under the natural ground surface of section DK1139+670 when the air temperature was the highest as the estimated value for the computational domain temperature field, it becomes steady by Eq. (12) after a long enough time without considering the climatic warming effect by making g(t) = 0. The temperature distributions at that moment are considered as the initial temperature filed. In the same way, the average temperature within 0.5 m under
Roadbed strike Boundary
The mean annual temperature (°C)
Amplitude (°C)
Air Natural ground surface Gravelly surface Asphalt surface East to west S-slope N-slope Southwest to SE-slope northeast NW-slope South to north W-slope E-slope Symmetrical Slopes route
− 3.82 − 1.32
11.5 12
0.38
14.5
2.88
15
1.96 − 2.26 1.43 − 1.23 0.54 0.1 0.32
12.6 15.5 13.2 15 13.8 14 13.9
Note: In the symmetrical route there is no difference in the temperatures on the two slopes.
the natural ground surface is estimated as the initial temperature of the roadbed fill. The position of the maximum thaw depth, without considering the climatic warming effect, is regarded as the original permafrost table. The original permafrost table in this case was −1.80 m, which is nearly consistent with the field data. 3. Computational results and analysis In order to confirm the calculations and to demonstrate that they are representative of real conditions, comparisons of the calculated results to actual data are discussed. The calculated temperature field of the embankment on 19 Oct in the 2nd year after construction is shown in Fig. 5, whose strike is 225°. Section DK1139+970 was built in 2001, whose strike is 230°, along the Qinghai–Tibet Railway. Fig. 6 gives the temperature field of experimental cross-section DK1139+970 on 19 Oct 2002 (Sheng et al., 2005). The two embankment heights are both 4.5 m and the surfaces are gravelly. From the two figures, we can see that the distributions of temperature fields in experimental and calculated embankments are very
Table 1 Thermal parameters of the materials in the computational domain Soil type
ρ (kg m− 3)
λf (J m− 1 °C− 1h− 1)
λu (J m− 1 °C− 1h− 1)
Cf kJ m− 3 °C− 1
Cu (kJ m− 3 °C− 1)
Water content
Sandy gravelly soil Silty clay Gravelly silty clay Weathered mudstone
2100 1920 1500 2200
5400 6480 7920 9005
5040 5400 3600 7200
1827 2188 2055 2640
2226 2438 2865 2970
0.08 0.20 0.50 0.32
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Fig. 5. Temperature field (°C) of the calculated embankment on 19 Oct in the 2nd year after construction.
similar. The tendency of 0 °C isotherms is both asymmetry, higher on the south than north. For embankments with symmetrical thermal boundary conditions, there is no thermal difference in the transverse direction, and the positions of the maximum thaw depths are always located along the centric line of the roadbed. But for embankments with the shadowy–sunny slope, the maximum thaw depths differ in the transverse direction as well as in the vertical direction. Thus, in order to check the thawing features, the maximum thaw depth is regarded as a criterion in the vertical direction. The distance from the location where the maximum thaw depth occurs to the embankment centric line is the criterion in the transverse direction. In order to easily narrate, the distance from the location where the maximum thaw depth occurs to the embankment centric line is called the transverse deviated
distance, which is explained in Fig. 2. Through the maximum thaw depth and the transverse deviated distance, the thawing features of the underlying permafrost for embankments along various strikes are weighted. 3.1. The changes in the maximum thaw depths 3.1.1. The maximum thaw depths change with time Figs. 7–9 indicate how the maximum thaw depths change with time for different roadbed strikes beneath both the gravelly and the asphalt surfaces. The embankment heights were 0.5 m, 3.0 m and 5.0 m, respectively. It can be seen from Fig. 7(a) and (b) that when the embankment is low (h = 0.5 m), the maximum thaw depths are increasing with time beneath both the gravelly and the asphalt surfaces. In the beginning of the
Fig. 6. Temperature field (°C)of section DK1139+970 on 19 Oct in the 2nd year after construction.
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Fig. 7. The maximum thaw depth beneath 0.5-m fill changing with time.
roadbed service, regardless of embankment strikes, the 0.5-m fill does not protect the underlying permafrost. Making a comparison between Fig. 7(a) and (b), it can be found that the maximum thaw depth beneath the asphalt surface is larger than that beneath the gravelly surface. The greater heat absorption characteristic of the asphalt surface makes the maximum thaw depth increase with time. Moreover, beneath both the gravelly and the asphalt surfaces, the maximum thaw depth is not related to the roadbed strike, and it can be concluded that the shadowy–sunny slope effect is not effective for low embankments.
Fig. 8(a) and (b) indicate that the maximum thaw depths beneath the gravelly surface are obviously different from those beneath the asphalt surface when the embankment height is 3.0 m. As is shown in Fig. 8 (a), the maximum thaw depth becomes larger and larger with time when the embankment has EW and SW–NE strikes. For the NS strike, at the very start, the maximum thaw depth basically remains at the original permafrost table (− 1.80 m), subsequently, it increases. In the symmetrical route, the maximum thaw depth gradually decreases, and then it starts increasing to − 1.64 m in the 35th year and to − 1.9 m in the 40th year after
Fig. 8. The maximum thaw depth beneath 3.0-m fill changing with time.
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Fig. 9. The maximum thaw depth beneath 5.0 m fill changing with time.
construction. For the 3.0 m high embankment beneath the gravelly surface, it is safe for 35 years of service after construction for the symmetrical route, but problems would happen on the sunny slope in embankments with the shadowy–sunny slope. Fig. 8(b) shows that beneath the asphalt surface, the maximum thaw depth linearly increases with time except for a little decrease during the first 3 years. Comparing Fig. 8(a) to (b), when the embankment height is 3.0 m, the maximum thaw depths are closely related to the roadbed strike beneath the gravelly surface, but unrelated to the roadbed strike beneath the asphalt surface. This may be because that the greater heat absorption characteristic of the asphalt surface partially offsets the transverse thermal deviation, but causes the maximum thaw depth becomes much larger. It can be seen from Fig. 9(a) and (b) that the shadowy–sunny slope effects are obvious beneath both the gravelly and the asphalt surfaces when the embankment height is 5.0 m. In Fig. 9(a), the maximum thaw depth linearly increases with time when the embankment is in the EW strike. In the SW–NE strike, the maximum thaw depth increased little during the first 8 years, and subsequently it increases more rapidly. In the SN strike, the maximum thaw depth decreases a little during the first 10 years, and then slowly increases more rapidly after the 30th year. The symmetrical embankment is generally safe during the entire running time. The maximum thaw depth remains in the fill from the 3rd to the 20th years. In Fig. 9(b), it can be seen that the maximum thaw depth linearly increases with time when
the embankment is in the EW and the SW–NE strikes. For the symmetrical embankment and the SN strike, the maximum thaw depth remains above the original permafrost table in the first 10 years, and then it increases linearly. 3.1.2. The maximum thaw depths change with embankment height Figs. 10 and 11 show how the maximum thaw depth changes with embankment height in the 20th and 50th years after construction, respectively. It can be seen there is much difference between the maximum thaw depth beneath the gravelly surface and that beneath the asphalt surface. In Fig. 10(a), beneath the gravelly surface, when the time is 20 years, the maximum thaw depths for the embankments for all roadbed strikes keep decreasing with the increase in the embankment height when the embankment is less than 1.0 m. Regarding the EW strike, when the embankment is higher than 1.0 m, the maximum thaw depth keeps increasing with the increase in the height. For the SW–NE strike, when the embankment is higher than 2.0 m, the maximum thaw depth keeps increasing with the increase in the height. For the SN strike, the maximum thaw depth keeps decreasing a little with the increase in the height. For the symmetrical embankment, the maximum thaw depth keeps markedly decreasing with the increase in the height, and when the embankment height is 5.0 m the maximum thaw depth is at the natural ground surface. In Fig. 10(b), it can be seen that beneath the asphalt surface, the maximum thaw depths for all roadbed
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Fig. 10. The maximum thaw depth in the 20th year changing with embankment height.
strikes keep generally decreasing with the increase in the height. When the embankment is less than 2.5 m, the maximum thaw depths for all roadbed strikes are approximately the same. But when the embankment is higher than 2.5 m, the more obvious the shadowy– sunny slope effect, the larger is the maximum thaw depth. When the embankment is higher than 4.0 m, the maximum thaw depth for the SN strike is larger than that for the symmetrical route. Beneath the gravelly surface, in Fig. 11(a), when time is 50 years, the maximum thaw depths for all roadbed strikes keep decreasing with the increase in the height when the embankment is less than 1.0 m. For the EW
strike, when the embankment is higher than 1.0 m, the maximum thaw depth keeps increasing with increase in the height. For the SW–NE strike, when the embankment is higher than 2.0 m, the maximum thaw depth keeps increasing with the increase in the embankment height. As for the SN strike, when the embankment is higher than 3.5 m, the maximum thaw depth slowly increases with the increase in the height. For the symmetrical embankment, the maximum thaw depth keeps decreasing with the increase in the height. From Fig. 11(b), beneath the asphalt surface, when the embankment is lower than 3.0 m, with the roadbed orientation turns from the EW strike to the SN strike, the
Fig. 11. The maximum thaw depth in the 50th year changing with embankment height.
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maximum thaw depth gradually increases. This may be due to that the thermal effect of low embankment slopes cannot completely offset the greater heat absorption characteristic of the asphalt surface. But when the embankment is higher than 3.0 m, with the roadbed orientation turns from the EW strike to SN strike, the maximum thaw depth gradually decreases. This may be due to the strong thermal effect of the high embankment slopes. The maximum thaw depths of various strikes, except for the EW strike, continue decreasing with the increase in the height. For the EW strike, when the embankment is higher than 4.0 m, the maximum thaw depth increases with the increase in the embankment height. The changing rule of the maximum thaw depth for the symmetrical embankment is similar to that for the SN strike. The higher the embankment, the larger is the slope area, and the stronger is the thermal effect of the slope. Especially to embankments with the remarkable shadowy–sunny slope effect, the positions of the maximum thaw depth are always situated under the south-facing slope. Therefore, the higher the embankment, the larger is the maximum thaw depth. By analyzing Figs. 10 and 11, it also is found that the shadowy–sunny slope problem becomes more serious with the increase in the embankment height. 3.2. Analysis on the transverse deviated distances 3.2.1. The transverse deviated distances change with time Fig. 12 demonstrate how the transverse deviated distance changes with time beneath both the gravelly and the asphalt surfaces, when the embankment height is 3.0 m. It can be found that the transverse deviated distance hardly changes with time, but it is different for different roadbed strikes and surfaces. Comparing
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Fig. 12(a) to (b), it can be found that in roadbeds with the shadowy–sunny slope, the transverse deviated distances beneath the gravelly surface are always larger than those beneath the asphalt surface. The same conclusion is reached by analyzing the other results. 3.2.2. The transverse deviated distance change with embankment height Fig. 13 illustrate how the transverse deviated distance changes with the embankment height beneath both the gravelly and the asphalt surfaces. It can be seen there is approximately a linear relationship between the transverse deviated distance and the height of embankments with the shadowy–sunny slope. As is shown in Fig. 13 (a), beneath the gravelly surface, when the embankment is low, the transverse deviated distances of the embankments for both the EW strike and the SW–NE strike are much larger than those for the SN strike. But with the increase in the embankment height, the transverse deviated distance of the embankment for the SN strike gradually becomes close to that for the EW strike. When the embankment is over 4.5 m high, the transverse deviated distances of the embankments for the EW, the SW–NE and the SN strikes are the same. Even though the mean annual temperature difference in the two slopes of the NS strike is 0.44 °C with the increase in the embankment height, the shadowy–sunny slope effect becomes stronger and stronger. As is shown in Fig. 13(b), beneath the asphalt surface, when the embankment is low, the transverse deviated distances of the embankments for the EW, the SW–NE and the SN strikes are close to each other. However, with the increase in the embankment height, the transverse deviated distances for the SN strike are more and more deviated from those for the EW and SW–NE strikes. This may be because the temperature difference
Fig. 12. The transverse deviated distance at 3.0 m changing with time.
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Fig. 13. The transverse deviated distance changing with embankment height.
in the two slopes of the SN strike is not too large, and the greater heat absorption characteristic of the asphalt surface partially offsets the shadowy–sunny slope effect and makes the maximum thaw depth position approximate the centric line of the roadbed. The regression equations between the transverse deviated distance and the embankment height are shown in Table 3. 4. Conclusions Based on the calculations and analyses, it can be concluded: (1) Beneath both the gravelly and the asphalt surfaces, the maximum thaw depth is dependent on time, surface materials, and the embankment heights. For low embankments, it is little influenced by the roadbed strike. For high embankments, it is greatly influenced by roadbed strike. Furthermore, it sharply changes with the variation of the embankment heights and with climatic warming. (2) Beneath both the gravelly and the asphalt surfaces, the distance from the location where
the maximum thaw depth occurs to the embankment centric line has nothing to do with time, but is closely related to the surface materials, embankment heights and strikes. Moreover, it is linearly related to the embankment height. (3) Under the same embankment height and roadbed strike, the distance from the location where the maximum thaw depth occurs to the embankment centric line beneath the gravelly surface is larger than that beneath the asphalt surface. However, the maximum thaw depth beneath the asphalt surface is much larger than that beneath the gravelly surface. To some extent, the greater heat absorption characteristic of the asphalt surface partially offsets the shadowy–sunny slope effect, but it also results in that the maximum thaw depth becomes much greater. (4) With the increase in the embankment height and the influence from climatic warming, the shadowy–sunny slope effect becomes quite serious. For embankments with the shadowy–sunny slope, increasing the embankment height only is not an ideal measure for protecting permafrost from thawing. When designing an embankment,
Table 3 The regression equations between the transverse deviated distance and the embankment height Surface
Embankment strike
Regression equation
Correlation coefficient/R2
Gravelly surface
Eastern to western Southwestern to northeastern South to north Eastern to western Southwestern to northeastern South to north
y = 1.203x + 2.0467 y = 1.3048x + 1.4767 y = 1.7807x − 0.76 y = 1.2598x + 0.1347 y = 1.1708x − 0.4007 y = 0.2012x + 0.0167
0.9869 0.9907 0.9929 0.9983 0.9873 0.9698
Asphalt surface
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besides considering the minimum and the maximum embankment height, the shadowy–sunny slope effect also should be taken into account. Acknowledgements This work was supported by the grant of the Knowledge Innovation Program of the Chinese Academy of Sciences, No.KZCX1-SW-04, and by the National Key Basic Research and Development Foundation of the Ministry of Sciences and Technology of China (Grant No. 2002CB412704) and by the National Natural Science Foundation of China (Grant No. 90102006). References Cheng, G.D., Jiang, H., et al., 2003. Thawing index and freezing index on the embankment surface in permafrost regions. Journal of Glaciology and Geocrylogy 25 (6), 603–607. Cheng, G.D., 2003. The impact of local factors on permafrost distribution and its inspiring for design Qinghai–Xizang railway. Science in China, Series D: Earth Sciences 33 (6), 602–607. Chen, J., Hu, Z.Y., Dou, S., et al., 2006. Shadowy–sunny slope problem along Qinghai–Tibet lines and its radiation mechanism. Cold Regions Science and Technology 44, 217–224. Dou, M.J., Hu, C.S., et al., 2003. Analysis on surface troubles of the Qinghai–Tibet Highway. Journal of Glaciology and Geocrylogy 24 (4), 439–444. Lai, Y.M., Zhang, S.J., Zhang, L.X., et al., 2004. Adjusting temperature distribution under the south and north slopes of
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embankment in permafrost regions by the ripped-rock revetment. Cold Regions Science and Technology 39, 67–79. Li, X., Cheng, G.D., 1999. A GIS-aided response model of high altitude permafrost to global change. Science in China, Series D: Earth Sciences 29 (2), 185–192. Liu, J.K., Tian, Y.H., 2002. Numerical studies for the thermal regime of a roadbed with insulation on permafrost. Cold Regions Science and Technology 35, 1–13. Liu, Z.Q., Lai, Y.M., 2004. Numerical analysis of temperature field in sections of ventilation subgrade on Qinghai–Tibetan railway line. Journal of Railway Engineering Society (1), 39–43. Sheng, Y., Ma, W., W.Z., et al., 2005. Analysis of difference in thermal state between south facing slope and north facing slope of railway embankment in permafrost region. Chinese Journal of Rock Mechanics and Engineering 24 (17), 3197–3201. Sun, Y.F., 2005. Permafrost engineering in the Qinghai–Tibet railway: research and practice. Journal of Glaciology and Geocrylogy 27 (2), 153–162. Wen, Z., Sheng, Y., Ma, W., et al., 2005. Evaluation of application of the insulation to embankment in Qinghai–Tibetan railway. Journal of Glaciology and Geocrylogy 27 (5), 603–607. Wu, Z.W., Cheng, G.D., Zhu, L.N., Liu, Y.Z., 1988. Roadbed Engineering in Permafrost Region. Publishing House of Lanzhou University, Lanzhou, pp. 43–45. Xu, X.Z., Wang, J.C., Zhang, L.X., 2001. Frozen Soil Physics. Science Press, Beijing. Zhang, M.Y., Zhang, J.M., Lai, Y.M., 2005. Numerical analysis for critical height of railway embankment in permafrost regions of the Qinghai–Tibetan Plateau. Cold Regions Science and Technology 41, 111–120. Zhang, M.Y., Zhang, J.M., Liu, Z.Q., et al., 2006. Temperature characteristic nonlinear analysis for new-type embankment structures for Qinghai–Tibetan railway under climatic warming. China Civil Engineering Journal 39 (2), 93–97.
Cold Regions Science and Technology 53 (2008) 334 – 345 www.elsevier.com/locate/coldregions
Study on the effect of the thermal regime differences in roadbed slopes on their thawing features in permafrost regions of Qinghai–Tibetan plateau Chou Ya-ling ⁎, Yu Sheng, Wei Ma State Key Laboratory of Frozen Soils Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou 730000, China Received 8 December 2006; accepted 28 April 2007
Abstract For the permafrost regions, numerical models are established for analyzing the possible changing tendency of the permafrost thawing features under various surface materials, embankment heights and strikes for a period of 50 years. Surface materials are gravelly and asphalt. Embankment heights range from 0 m to 5.0 m with a step of 0.5 m. For the embankment strike, east to west (EW), southwest to northeast (SW–NE), south to north (SN) and symmetrical route are taken into consideration. The thermal boundary condition is with the assumption that the air temperature will warm up by 1.1 °C during the next 50 years. The calculated results indicate that there is a great difference in thawing features between the asymmetrical and the symmetrical routes. Beneath both the gravelly and the asphalt surfaces, for embankments with south-facing and north-facing slopes, which are defined as the shadowy– sunny slope, calculations show: (1) The maximum thaw depth is closely related to time, the surface materials and the embankment heights. The maximum thaw depths of the low embankments have little to do with the roadbed strike. But the maximum thaw depths of the high embankments are very much influenced by the roadbed strike, and it sharply changes with the variation of the embankment heights and climatic warming. (2)The distance from the location where the maximum thaw depth occurs to the embankment centric line has nothing to do with time, but is closely related to the surface materials, the embankment heights and strikes. Moreover, it is linearly related to the embankment heights. (3) Under the same embankment height and roadbed strike, the distance from the point where the maximum thaw depth occurs to the centric line of the embankment beneath the gravelly surface is larger than that beneath the asphalt surface. However, the maximum thaw depth beneath the asphalt surface is much larger than that beneath the gravelly surface. To some extent, the asphalt surface partially offsets the shadowy–sunny slope effect, but it makes the maximum thaw depth become much larger. (4) When designing an embankment, besides considering the minimum and the maximum embankment height, the shadowy–sunny slope effect also should be taken into account. © 2007 Elsevier B.V. All rights reserved. Keywords: Permafrost; Roadbed strike; The shadowy–sunny slope; Thawing features; The maximum thaw depth
1. Introduction
⁎ Corresponding author. Tel.: +86 931 4967297; fax: +86 931 4967271. E-mail address: [email protected] (C. Ya-ling). 0165-232X/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2007.04.022
In permafrost regions, the construction of embankments changes the thermophysical features of the natural ground surface and atmosphere, and influences the thermodynamic and dynamic stability of the frozen
C. Ya-ling et al. / Cold Regions Science and Technology 53 (2008) 334–345
soil layers. Establishing high roadbeds was considered a conventional measure to protect permafrost from thawing (Cheng et al., 2003). However, the higher the roadbed, the larger will be the area of the slope, and the thermal effect of the slope cannot be overlooked. Especially, when the two embankment slopes are south-facing and north-facing respectively, which is called the shadowy–sunny slope in Chinese, the difference of the thermal boundary conditions such as the solar radiation and surface turbulent flow will induce the transverse asymmetry of temperature field, and this will lead to a multitude of problems in permafrost roadbeds. After the roadbed is built, thermal effect problems associated with slope orientations also must be considered in the roadbed engineering protection measures in permafrost regions (Cheng, 2003). So far, many numerical computations on the embankment temperature fields in permafrost regions have failed to take the road strike into account and that the temperatures in the slopes are even lower than that in the surface (Zhang et al., 2006; Liu and Lai, 2004), which are still considered symmetrical thermal boundary conditions (Liu and Tian, 2002; Wen et al., 2005; Zhang et al., 2005). However, the fact is that there is no embankment with completely symmetrical thermal boundary conditions. The Fenghuoshan Section of the Qinghai–Tibet Highway extends from north to south. According to the field data for the years 1985 and 1986 in this section, there was an obvious thermal difference between the eastern slope and the western slope. The mean temperature of the eastern slope surface was 2.4 °C higher than that of the western slope(Wu et al., 1988). The asymmetrical thermal boundary conditions of the slopes indicated that the maximum thaw depth position had deviated in the transverse direction. The higher the roadbed, the greater is the transverse thermal
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deviation. Thus it is unreasonable to analyze permafrost thawing features only according to the symmetrical boundary conditions. From observational data on the Qinghai–Tibet Highway, if the thickness of the roadbed is greater than 3 m, the shadowy–sunny slope effect is quite obvious, and active cooling measures must be applied. It also is obvious there are shadowy–sunny slope phenomena in the embankment of the Qinghai– Tibet Railway (Chen et al., 2006). Field data were obtained from the section K369+000 to K369+100 along National Highway 214, whose strike is 246° and the surface is asphalt and concrete. Although the road was re-built in 2002, by the end of 2005 many longitudinal cracks had occurred on the south side of the roadbed (Fig. 1). Fig. 2 gives the profiles of permafrost table on 10 Nov. 2003 and geology of experimental cross-section K369+100. From Fig. 2, we can see the left artificial permafrost table is deeper than the right one and the maximum thaw depth position is not situated on the centric line of the roadbed. The cause was that the transverse thermal difference resulted in differential deformations and settlements, and this lead to the result that thaw settlement in the south-facing side is much larger and longitudinal cracks occurred on that side. On the Qinghai–Tibet Plateau, permafrost is quite sensitive to environmental changes and human activities. When roadbeds are built in permafrost regions, there will be different thermal regimes on the slopes because of different roadbed strikes. Various thawing features and engineering problems under embankments caused by the transverse thermal difference in slopes have already been discussed by researchers (Lai et al., 2004; Sheng et al., 2005; Dou et al., 2003; Sun, 2005). No work, however, has been found to quantitatively and systematically discuss the influence of the temperature
Fig. 1. Photo showing the longitudinal crack of section K369+100.
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Fig. 2. Profiles of permafrost table and geology of section K369+100.
differences of embankment slopes with various surface materials, roadbed heights and strikes on the embankment thawing features. To solve the abovementioned problems is very essential, and this work will provide a scientific basis for road construction and maintenance in permafrost regions of the plateau. Equations for heat conduction, coupled with phase transitions, will be obtained, so that a two-dimensional numerical model for the thawing features with different embankment geometrical parameters is established, with the assumption that the air temperature on the Qinghai–Tibet plateau will rise by 1.1 °C during the next 50 years (Li and Cheng, 1999). The finite element method will be applied for calculation with adjustable roadbed heights. The maximum thaw depths, changing with different embankments, will be analyzed for the next coming 50 years. 2. The computational model 2.1. Governing equations and finite-element formula Ignoring convection and mass transfer, and only considering the phase transitions and heat conduction, the 2-D equation for heat conduction in the soil layers can be described as follows: A AT A AT AT k k þ ¼ qc Ax Ax Ay Ay At
where, ρ — soil density, T — temperature, c — volumetric heat capacity of the soil, λ — coefficient of thermal conductivity, t — time. Tf ðsðtÞ; tÞ ¼ Tu ðsðT Þ; T Þ ¼ Tm
ð2Þ
ATf ATu dsðtÞ ku ¼ Lqw0 dt An An
ð3Þ
kf
where f and u denote frozen and unfrozen states, respectively. L — latent heat of water, w0 — the initial water content, Tm — temperature on the freeze–thaw interface, n — normal direction of the freeze–thaw interface. Latent heat of soil can be calculated by the following equation: Q ¼ Lqd ðw wu Þ
where Q — the latent heat of the soil, L — the latent heat of water, w — the water content, wu — the unfrozen water content. The unfrozen water content can be obtained by the following equations (Xu et al., 2001): wu ¼ aT b b¼
ð1Þ
ð4Þ
lnw0 lnwu lnT lnTf
a ¼ w0 Tfb
ð5Þ ð6Þ ð7Þ
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where T and Tf are the freezing temperatures of the soils at the initial water content w0 and wu, respectively. The finite element formula are: AT ½M þ ½KfT g ¼ fqg ð8Þ At Z qcNi Nj dX ð9Þ Mij ¼ R Xe
Z Kij ¼ R
Xe
k
ANi ANj ANi ANj þ dX Ax Ax Ay Ay
ð10Þ
Z qi ¼ R
Ce2
qNi dC
ð11Þ
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30 m depth from the natural ground surface. The road surface width is 7.5 m, and the slope gradient is 1:1.5. The computational dimensions are shown in Fig. 3, where part A is a sandy gravelly soil, part B is a silty clay, part C is a gravelly silty clay and part D is a weathered mudstone. The element structure is divided into 4-nodal elements and the element mesh diagram is shown in Fig. 4. Thermal parameters of the media were obtained from drilling data in Beiluhe, and are shown in Table 1. Beiluhe is at the South of the Beiluhe Basin, along the Qinghai– Tibet Railway, and is part of the diluvial alpine plain physiognomy. It is located at 34.85°N, 92.94°E, and the elevation is about 4635 m. The vegetation coverage is less than 20%, the air mean annual temperature is −3.82 °C. 2.3. Boundary conditions and initial conditions
where Ni and Nj are the shape functions. 2.2. Computational domain and physical parameters of soils Although the computational domain is symmetrical in terms of geometric shape with regard to the embankment centric line, the shadowy–sunny slope problems, namely asymmetrical thermal boundary conditions, have to be taken into account. The entire roadbed section has to be adopted in the calculations. Eleven embankment heights (h = 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0 m) are taken, and the physical domain for computation is extended to 20 m from the foot of the slopes and to the
The mean annual air temperature is taken as − 3.82 °C, and the mean annual temperatures and the temperature amplitudes of all the embankment surfaces with different strikes were obtained from the permafrost regions in Beiluhe (Cheng et al., 2003). The temperature varies by the following formula: 2pt p T ðx; y; tÞ ¼ T þ gðtÞ þ Asin þ 8760 2 ð12Þ P
P
P
P
P
ðx; yÞa AB; BC; CD; DE and EF where, T — the mean annual temperatures of all the embankment surfaces, A — temperature amplitudes of
Fig. 3. Computational domain.
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C. Ya-ling et al. / Cold Regions Science and Technology 53 (2008) 334–345 Table 2 Temperature boundary conditions
Fig. 4. Finite element mesh.
p all the boundaries, t — time, -initial phase, g(t) = R0t, 2 R0 — climatic warming velocity with R0 = 0.022 °C/ 8760 h, the value of T and PA are listed in Table 2. For the lower boundary KL, a temperature gradient of 0.038 °C/m was used (Zhang et al., 2005), accordingly the geothermal heat flux is calculated as q = 0.3079 kJ/(h m2): k
AT ¼ q An
ð13Þ P
P
The boundaries FK and AL are regarded as heat insulated: k
AT ¼0 An
ð14Þ
The initial condition is given as: T ðx; y; 0Þ ¼ T0
ð15Þ
where, the initial temperature distribution T0 was obtained using from the following method: taking the data under the natural ground surface of section DK1139+670 when the air temperature was the highest as the estimated value for the computational domain temperature field, it becomes steady by Eq. (12) after a long enough time without considering the climatic warming effect by making g(t) = 0. The temperature distributions at that moment are considered as the initial temperature filed. In the same way, the average temperature within 0.5 m under
Roadbed strike Boundary
The mean annual temperature (°C)
Amplitude (°C)
Air Natural ground surface Gravelly surface Asphalt surface East to west S-slope N-slope Southwest to SE-slope northeast NW-slope South to north W-slope E-slope Symmetrical Slopes route
− 3.82 − 1.32
11.5 12
0.38
14.5
2.88
15
1.96 − 2.26 1.43 − 1.23 0.54 0.1 0.32
12.6 15.5 13.2 15 13.8 14 13.9
Note: In the symmetrical route there is no difference in the temperatures on the two slopes.
the natural ground surface is estimated as the initial temperature of the roadbed fill. The position of the maximum thaw depth, without considering the climatic warming effect, is regarded as the original permafrost table. The original permafrost table in this case was −1.80 m, which is nearly consistent with the field data. 3. Computational results and analysis In order to confirm the calculations and to demonstrate that they are representative of real conditions, comparisons of the calculated results to actual data are discussed. The calculated temperature field of the embankment on 19 Oct in the 2nd year after construction is shown in Fig. 5, whose strike is 225°. Section DK1139+970 was built in 2001, whose strike is 230°, along the Qinghai–Tibet Railway. Fig. 6 gives the temperature field of experimental cross-section DK1139+970 on 19 Oct 2002 (Sheng et al., 2005). The two embankment heights are both 4.5 m and the surfaces are gravelly. From the two figures, we can see that the distributions of temperature fields in experimental and calculated embankments are very
Table 1 Thermal parameters of the materials in the computational domain Soil type
ρ (kg m− 3)
λf (J m− 1 °C− 1h− 1)
λu (J m− 1 °C− 1h− 1)
Cf kJ m− 3 °C− 1
Cu (kJ m− 3 °C− 1)
Water content
Sandy gravelly soil Silty clay Gravelly silty clay Weathered mudstone
2100 1920 1500 2200
5400 6480 7920 9005
5040 5400 3600 7200
1827 2188 2055 2640
2226 2438 2865 2970
0.08 0.20 0.50 0.32
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Fig. 5. Temperature field (°C) of the calculated embankment on 19 Oct in the 2nd year after construction.
similar. The tendency of 0 °C isotherms is both asymmetry, higher on the south than north. For embankments with symmetrical thermal boundary conditions, there is no thermal difference in the transverse direction, and the positions of the maximum thaw depths are always located along the centric line of the roadbed. But for embankments with the shadowy–sunny slope, the maximum thaw depths differ in the transverse direction as well as in the vertical direction. Thus, in order to check the thawing features, the maximum thaw depth is regarded as a criterion in the vertical direction. The distance from the location where the maximum thaw depth occurs to the embankment centric line is the criterion in the transverse direction. In order to easily narrate, the distance from the location where the maximum thaw depth occurs to the embankment centric line is called the transverse deviated
distance, which is explained in Fig. 2. Through the maximum thaw depth and the transverse deviated distance, the thawing features of the underlying permafrost for embankments along various strikes are weighted. 3.1. The changes in the maximum thaw depths 3.1.1. The maximum thaw depths change with time Figs. 7–9 indicate how the maximum thaw depths change with time for different roadbed strikes beneath both the gravelly and the asphalt surfaces. The embankment heights were 0.5 m, 3.0 m and 5.0 m, respectively. It can be seen from Fig. 7(a) and (b) that when the embankment is low (h = 0.5 m), the maximum thaw depths are increasing with time beneath both the gravelly and the asphalt surfaces. In the beginning of the
Fig. 6. Temperature field (°C)of section DK1139+970 on 19 Oct in the 2nd year after construction.
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Fig. 7. The maximum thaw depth beneath 0.5-m fill changing with time.
roadbed service, regardless of embankment strikes, the 0.5-m fill does not protect the underlying permafrost. Making a comparison between Fig. 7(a) and (b), it can be found that the maximum thaw depth beneath the asphalt surface is larger than that beneath the gravelly surface. The greater heat absorption characteristic of the asphalt surface makes the maximum thaw depth increase with time. Moreover, beneath both the gravelly and the asphalt surfaces, the maximum thaw depth is not related to the roadbed strike, and it can be concluded that the shadowy–sunny slope effect is not effective for low embankments.
Fig. 8(a) and (b) indicate that the maximum thaw depths beneath the gravelly surface are obviously different from those beneath the asphalt surface when the embankment height is 3.0 m. As is shown in Fig. 8 (a), the maximum thaw depth becomes larger and larger with time when the embankment has EW and SW–NE strikes. For the NS strike, at the very start, the maximum thaw depth basically remains at the original permafrost table (− 1.80 m), subsequently, it increases. In the symmetrical route, the maximum thaw depth gradually decreases, and then it starts increasing to − 1.64 m in the 35th year and to − 1.9 m in the 40th year after
Fig. 8. The maximum thaw depth beneath 3.0-m fill changing with time.
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Fig. 9. The maximum thaw depth beneath 5.0 m fill changing with time.
construction. For the 3.0 m high embankment beneath the gravelly surface, it is safe for 35 years of service after construction for the symmetrical route, but problems would happen on the sunny slope in embankments with the shadowy–sunny slope. Fig. 8(b) shows that beneath the asphalt surface, the maximum thaw depth linearly increases with time except for a little decrease during the first 3 years. Comparing Fig. 8(a) to (b), when the embankment height is 3.0 m, the maximum thaw depths are closely related to the roadbed strike beneath the gravelly surface, but unrelated to the roadbed strike beneath the asphalt surface. This may be because that the greater heat absorption characteristic of the asphalt surface partially offsets the transverse thermal deviation, but causes the maximum thaw depth becomes much larger. It can be seen from Fig. 9(a) and (b) that the shadowy–sunny slope effects are obvious beneath both the gravelly and the asphalt surfaces when the embankment height is 5.0 m. In Fig. 9(a), the maximum thaw depth linearly increases with time when the embankment is in the EW strike. In the SW–NE strike, the maximum thaw depth increased little during the first 8 years, and subsequently it increases more rapidly. In the SN strike, the maximum thaw depth decreases a little during the first 10 years, and then slowly increases more rapidly after the 30th year. The symmetrical embankment is generally safe during the entire running time. The maximum thaw depth remains in the fill from the 3rd to the 20th years. In Fig. 9(b), it can be seen that the maximum thaw depth linearly increases with time when
the embankment is in the EW and the SW–NE strikes. For the symmetrical embankment and the SN strike, the maximum thaw depth remains above the original permafrost table in the first 10 years, and then it increases linearly. 3.1.2. The maximum thaw depths change with embankment height Figs. 10 and 11 show how the maximum thaw depth changes with embankment height in the 20th and 50th years after construction, respectively. It can be seen there is much difference between the maximum thaw depth beneath the gravelly surface and that beneath the asphalt surface. In Fig. 10(a), beneath the gravelly surface, when the time is 20 years, the maximum thaw depths for the embankments for all roadbed strikes keep decreasing with the increase in the embankment height when the embankment is less than 1.0 m. Regarding the EW strike, when the embankment is higher than 1.0 m, the maximum thaw depth keeps increasing with the increase in the height. For the SW–NE strike, when the embankment is higher than 2.0 m, the maximum thaw depth keeps increasing with the increase in the height. For the SN strike, the maximum thaw depth keeps decreasing a little with the increase in the height. For the symmetrical embankment, the maximum thaw depth keeps markedly decreasing with the increase in the height, and when the embankment height is 5.0 m the maximum thaw depth is at the natural ground surface. In Fig. 10(b), it can be seen that beneath the asphalt surface, the maximum thaw depths for all roadbed
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Fig. 10. The maximum thaw depth in the 20th year changing with embankment height.
strikes keep generally decreasing with the increase in the height. When the embankment is less than 2.5 m, the maximum thaw depths for all roadbed strikes are approximately the same. But when the embankment is higher than 2.5 m, the more obvious the shadowy– sunny slope effect, the larger is the maximum thaw depth. When the embankment is higher than 4.0 m, the maximum thaw depth for the SN strike is larger than that for the symmetrical route. Beneath the gravelly surface, in Fig. 11(a), when time is 50 years, the maximum thaw depths for all roadbed strikes keep decreasing with the increase in the height when the embankment is less than 1.0 m. For the EW
strike, when the embankment is higher than 1.0 m, the maximum thaw depth keeps increasing with increase in the height. For the SW–NE strike, when the embankment is higher than 2.0 m, the maximum thaw depth keeps increasing with the increase in the embankment height. As for the SN strike, when the embankment is higher than 3.5 m, the maximum thaw depth slowly increases with the increase in the height. For the symmetrical embankment, the maximum thaw depth keeps decreasing with the increase in the height. From Fig. 11(b), beneath the asphalt surface, when the embankment is lower than 3.0 m, with the roadbed orientation turns from the EW strike to the SN strike, the
Fig. 11. The maximum thaw depth in the 50th year changing with embankment height.
C. Ya-ling et al. / Cold Regions Science and Technology 53 (2008) 334–345
maximum thaw depth gradually increases. This may be due to that the thermal effect of low embankment slopes cannot completely offset the greater heat absorption characteristic of the asphalt surface. But when the embankment is higher than 3.0 m, with the roadbed orientation turns from the EW strike to SN strike, the maximum thaw depth gradually decreases. This may be due to the strong thermal effect of the high embankment slopes. The maximum thaw depths of various strikes, except for the EW strike, continue decreasing with the increase in the height. For the EW strike, when the embankment is higher than 4.0 m, the maximum thaw depth increases with the increase in the embankment height. The changing rule of the maximum thaw depth for the symmetrical embankment is similar to that for the SN strike. The higher the embankment, the larger is the slope area, and the stronger is the thermal effect of the slope. Especially to embankments with the remarkable shadowy–sunny slope effect, the positions of the maximum thaw depth are always situated under the south-facing slope. Therefore, the higher the embankment, the larger is the maximum thaw depth. By analyzing Figs. 10 and 11, it also is found that the shadowy–sunny slope problem becomes more serious with the increase in the embankment height. 3.2. Analysis on the transverse deviated distances 3.2.1. The transverse deviated distances change with time Fig. 12 demonstrate how the transverse deviated distance changes with time beneath both the gravelly and the asphalt surfaces, when the embankment height is 3.0 m. It can be found that the transverse deviated distance hardly changes with time, but it is different for different roadbed strikes and surfaces. Comparing
343
Fig. 12(a) to (b), it can be found that in roadbeds with the shadowy–sunny slope, the transverse deviated distances beneath the gravelly surface are always larger than those beneath the asphalt surface. The same conclusion is reached by analyzing the other results. 3.2.2. The transverse deviated distance change with embankment height Fig. 13 illustrate how the transverse deviated distance changes with the embankment height beneath both the gravelly and the asphalt surfaces. It can be seen there is approximately a linear relationship between the transverse deviated distance and the height of embankments with the shadowy–sunny slope. As is shown in Fig. 13 (a), beneath the gravelly surface, when the embankment is low, the transverse deviated distances of the embankments for both the EW strike and the SW–NE strike are much larger than those for the SN strike. But with the increase in the embankment height, the transverse deviated distance of the embankment for the SN strike gradually becomes close to that for the EW strike. When the embankment is over 4.5 m high, the transverse deviated distances of the embankments for the EW, the SW–NE and the SN strikes are the same. Even though the mean annual temperature difference in the two slopes of the NS strike is 0.44 °C with the increase in the embankment height, the shadowy–sunny slope effect becomes stronger and stronger. As is shown in Fig. 13(b), beneath the asphalt surface, when the embankment is low, the transverse deviated distances of the embankments for the EW, the SW–NE and the SN strikes are close to each other. However, with the increase in the embankment height, the transverse deviated distances for the SN strike are more and more deviated from those for the EW and SW–NE strikes. This may be because the temperature difference
Fig. 12. The transverse deviated distance at 3.0 m changing with time.
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Fig. 13. The transverse deviated distance changing with embankment height.
in the two slopes of the SN strike is not too large, and the greater heat absorption characteristic of the asphalt surface partially offsets the shadowy–sunny slope effect and makes the maximum thaw depth position approximate the centric line of the roadbed. The regression equations between the transverse deviated distance and the embankment height are shown in Table 3. 4. Conclusions Based on the calculations and analyses, it can be concluded: (1) Beneath both the gravelly and the asphalt surfaces, the maximum thaw depth is dependent on time, surface materials, and the embankment heights. For low embankments, it is little influenced by the roadbed strike. For high embankments, it is greatly influenced by roadbed strike. Furthermore, it sharply changes with the variation of the embankment heights and with climatic warming. (2) Beneath both the gravelly and the asphalt surfaces, the distance from the location where
the maximum thaw depth occurs to the embankment centric line has nothing to do with time, but is closely related to the surface materials, embankment heights and strikes. Moreover, it is linearly related to the embankment height. (3) Under the same embankment height and roadbed strike, the distance from the location where the maximum thaw depth occurs to the embankment centric line beneath the gravelly surface is larger than that beneath the asphalt surface. However, the maximum thaw depth beneath the asphalt surface is much larger than that beneath the gravelly surface. To some extent, the greater heat absorption characteristic of the asphalt surface partially offsets the shadowy–sunny slope effect, but it also results in that the maximum thaw depth becomes much greater. (4) With the increase in the embankment height and the influence from climatic warming, the shadowy–sunny slope effect becomes quite serious. For embankments with the shadowy–sunny slope, increasing the embankment height only is not an ideal measure for protecting permafrost from thawing. When designing an embankment,
Table 3 The regression equations between the transverse deviated distance and the embankment height Surface
Embankment strike
Regression equation
Correlation coefficient/R2
Gravelly surface
Eastern to western Southwestern to northeastern South to north Eastern to western Southwestern to northeastern South to north
y = 1.203x + 2.0467 y = 1.3048x + 1.4767 y = 1.7807x − 0.76 y = 1.2598x + 0.1347 y = 1.1708x − 0.4007 y = 0.2012x + 0.0167
0.9869 0.9907 0.9929 0.9983 0.9873 0.9698
Asphalt surface
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