The temperature features for different ventilated-duct embankments with adjustable shutters in the Qinghai–Tibet railway

The temperature features for different ventilated-duct embankments with adjustable shutters in the Qinghai–Tibet railway

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  The temperature features for different ventilated-duct embankmentswith adjustable shutters in the Qinghai–Tibet railway Li Guoyu  a  , Li Ning  a , b, *, Quan Xiaojuan  a  a  State Key Laboratory of Frozen Soil Engineering, CAREERI, Chinese Academy of Science, Lanzhou, Gansu 730000, China  b  Institute of Geotechnical Engineering, Xi’an University of Technology, Xi’an, Shanxi 710048, China Received 12 February 2005; accepted 26 August 2005 Abstract Considering the global warming and the temperature difference between the sunny slope and the shading slope of theembankment in the Qinghai–Tibet railway, the cooling effects for different ventilated-duct embankments with adjustable shutterson the permafrost are studied with 3-D numerical simulations. The numerical results indicated that their temperature fields havedistinct difference; the permafrost tables under the adjustable ventilated-duct embankments are raised and the thaw bulbs aredegenerated gradually; they are able to ensure the thermal stability of the permafrost under the scenario of climatic warming but theordinary embankment is not. D  2005 Elsevier B.V. All rights reserved.  Keywords:  Adjustable ventilated-duct embankment; Climatic warming; Temperature features; Qinghai–Tibet railway; Thermal stability 1. Introduction The Chinese Qinghai–Tibet Railway traverses over a 632 km permafrost zone, 550 km of which is con-tinuous per mafrost, and 82 km of which is patchy permafrost (Cheng, 2003a,b). When the embankment of the Railway is constructed in permafrost regions, it typically has a large influence on the thermal regime of the ground, due to the fact that the railway embank-ment modifies pre-existing surface condition and asso-ciated ground-surface energy balance. In the past,many projects have employed varying thickness of gravel fill, or in some cases foam type insulationwith gravel fill to thermally protect the underlyingfrozen ground. Recently several different engineeringmeasures are performed at Beiluhe Test Site in Qin-ghai–Tibet Plateau in China based on the principles of cooling the subsoil. These measures have played aneffectively cooling role on permafrost mainly by con-trolling radiation, conduction and convection such asthe sun-shaded embankment, crushed-stone embank-ment, crushed-stone-slope embankment, ventilated-duct embankment and thermosyphon embankment etc. (Ma et al., 2002). The ventilated embankment is an effective ap- proach to cool foundation soils of the roadway. Zar-ling et al. (1983) presented the results of both anexperimental and analytical research program under-taken to develop design criteria to determine the rela-tionship between air flow rates and temperaturedifference, heat transfer rates, and air duct length for an air duct system whose axes are parallel to thelongitudinal axis of the road. Some researchers present  0165-232X/$ - see front matter   D  2005 Elsevier B.V. All rights reserved.doi:10.1016/j.coldregions.2005.08.002* Corresponding author. State Key Laboratory of Frozen Soil En-gineering, CAREERI, Chinese Academy of Science, Lanzhou, Gansu730000, China. Tel.: +86 931 4967290; fax: +86 931 8271054.  E-mail address: (L. Ning).Cold Regions Science and Technology 44 (2006) 99–  the other kinds of air duct systems whose axes are perpendicular to the longitudinal axis of the road andgo through the embankment  above the srcinal ground surface (Lai et al., 2004). Li et al. (2004) used the finite element method to analyze the ordinary venti-lated-duct embankment, in which both ends of the buried ducts are fully open, and the adjustable venti-lated-duct embankment, in which the duct was buriedwith two automatic temperature-controlled shuttersat both ends. Su et al. (2004) systemically operatednumerical analysis of the temperature field of theventilated embankment in high-temperature frozensoil region under different layouts of ventilated duct system, such as duct span, duct diameter, buried depthof the ducts and the height of the embankment. Andthe optimized design of the ventilated duct system is proposed; an experimental ventilated embankment wasconstructed in Beiluhe Test Site of the Qinghai–Tibet  by Niu et al. (2003). Some thermal data were collectedover a two-year period. The results indicated that theventilated embankment was active and effective incooling the per mafrost underlying the embankment.Yu et al. (2003) performed a model test on the coolingeffect of the railway ventilated duct embankment inlaboratory. Their results showed that the ventilatedducts were able to supply  b cooling  Q   energy for theembankment soil and protect permafrost.But the above researchers considered neither thethermal difference between the sunny slope and theshading slope of the railway embankment and theclimatic warming, nor the adjustability of the shuttersequipped at ends. The Qinghai–Tibet Railway is a statekey project which is expected to run over 100 years. Sothe climate change should be taken into considerationunder the conditions of climatic warming (Cheng,2003a,b). Sheng et al. (2004) analyzed the difference of thermal state between sunny and shading slopes of the embankment of the railway based on the observa-tional data at Beiluhe Test Site. He found that the meanannual ground temperature at the depth of 0.5 m on (a) Ventilated duct with one adjustable shutter(c) Ventilated embankment with two adjustable shutters (d) The ordinary embankment (b) Ventilated embankment with one adjustable shutter Concret air ductAutomatic temperaturecontrolled shutterAIB EJFC D      4    m 7.1m30m      2    m     2     8    m GH 1  :  1  .5    EmbankmentActive layerPermafrost layerConcret air ductAutomatic temperaturecontrolled shutterAIB EJFC D      4    m 7.1m30m      2    m     2     8    m GH 1  :  1  .5    EmbankmentActive layerPermafrost layerAIB EJFC D      4    m 7.1m30m      2    m     2     8    m GH 1  :  1  .5    EmbankmentActive layerPermafrost layer Fig. 1. Various embankment models.  L. Guoyu et al. / Cold Regions Science and Technology 44 (2006) 99–110 100  sunny slope was 3  8 C higher than that on shading slope.According to the climatic prediction in China (Qin,2002), the mean annual air temperature of the Qin-ghai–Tibet Plateau will increase by 2.2–2.6  8 C until2050. On the other hand, the adjustability of shuttershas a positive impact on the temperature drop of per-mafrost. So it is necessary to study the above presentedwork considering the climate change and temperaturedifference between side slopes and the adjustability of the shutters.In this paper, 3-D embankment models of Qinghai– Tibet Railway located at Beiluhe Test Site in thePlateau with an elevation of about 4700 m is simulatedwith the consideration of different automatically tem- perature-controlled shutters. The shutters are openedautomatically when the air temperature outside theduct is lower than a certain temperature. Otherwisethey are closed automatically. The ventilated-duct em- bankment with one shutter is shown in Fig. 1(b). Theventilated-duct embankment with two shutters and theordinary embankment are shown in Fig. 1(c) and (d),respectively.Three-dimensional temperature characteristics of three types of embankment models presented are per-formed considering the temperature difference betweenthe sunny slope and the shading slope by 3  8 C and theclimatic warming by 2  8 C within 50 years. 2. Governing equations and numerical methods In cold regions, the foundation soils always experi-ence freezing–thawing cycles with phase change peri-odically. Thus, the problem discussed becomes anonlinear problem of heat transfer with phase change.Using the method of Sensible Heat Capacity, the heat conduction process in the embankment with phasechange and the differential equations of the problemof three dimensional temperature fields can be de-scribed as follows simply by assuming no convectionand no water infiltration into the embankment (Taylor and Luthin, 1978). C  *  B T  B t   ¼  BB  x  k *  B T  B  x  þ  BB  y  k *  B T  B  y  þ  BB  z   k *  B T  B  z   ð 1 Þ where  C  * and  k * are equivalent volumetric heat capac-ity and equivalent thermal conductivity, respectively.  T  is the temperature.Since this kind of problem is a heavily nonlinear one, its analytical solution cannot be obtained. Weobtained its solution by using a numerical analyticalmethod. Using Galerkin’s method, the following finiteelement formulae can be obtained.  M  ½   B T  B t   þ  K  ½   T  f g ¼  F  f g   ð 2 Þ where  M  ij   ¼ XZ  X C  *  N  i  N   j  d  X  ð 3 Þ  K  ij   ¼ XZ  X k *  B  N  i B  x  d   B  N   j  B  x  þ  B  N  i B  y  d   B  N   j  B  y  d  X þ XZ  C a T  a  N  i  N   j  d  C  ð 4 Þ  F  i  ¼ XZ  C a T  a  N  i d  C  ð 5 Þ where  N  i  and  N    j   are shape functions. 3. Boundary modeling and parameters All of the embankment models are 4 m high, whichare constructed of non-frost-susceptible material, name-ly sand gravel soil. The thickness of the active layer is 2m which is silty clay, the permafrost layer 15 m deepwhich is poorly weathered mudstone. The ducts are placed at 50 cm above the srcinal ground surface.The diameter and the thickness of them are 40 and 6cm, respectively, with a space of 1.2 m between cen-terlines of two ducts. Their thermal parameters of var-ious materials are given in Table 1. In this paper, a 20- node block element is used and each node has onedegree of freedom. The whole model is divided by7632 elements and 38,747 nodes. Fig. 2 shows thecomputational model and the mesh of elements. Thetime interval D t  , the time step used in the calculation, is6 h.In Table 1,  C   and  C  + represent the volumetric heat capacity of the materials at negative and positive tem- peratures, respectively. k  , k + show the thermal conduc-tivity at negative and positive temperature, respectively.  L  is latent heat. Table 1The thermal parameters of various materials q  C  C  + k  k +  L kg/m 3 10 3 J/(kg  8 C) J/(m  8 C s) J/m 3 Sand gravel fill 1800 0.94 1.21 1.58 1.13 20.4  10 6 Concrete duct 2400 1.00 1.00 1.77 1.70 0Active layer 1500 1.2 1.50 1.04 0.72 60.3  10 6 Permafrost layer 1300 1.50 1.90 1.22 0.87 37.7  10 6  L. Guoyu et al. / Cold Regions Science and Technology 44 (2006) 99–110  101  The air temperature and ground surface temperatureobserved in Wudaoliang Region in Qinghai–Tibet Pla-teau are employed to determine the boundary conditionof the computational domain (Su et al., 2004). The air  temperature will be used for the internal air temperatureinside the ducts. The ground surface temperature will be used for the ground surface temperatures of theshading slope and the driving surface. The yearly av-erage air temperature is   5.25  8 C and the yearly aver-age ground surface temperature is   0.89  8 C in thisregion. The annual variation of air temperature is22.28  8 C. Considering the climatic warming by 2  8 Cwithin 50 years, the air temperature and the groundsurface temperature is changed according to the follow-ing formulae (6) and (7). T  a  ¼   5 : 25  þ  11 : 14sin   2 p 8760  t   þ  2 : 59  þ  2 : 050    365    24  t   ð 6 Þ T  g  ¼   0 : 89  þ  14 : 34sin   2 p 8760  t   þ  2 : 71  þ  2 : 050    365    24  t  :  ð 7 Þ In the ventilated duct embankment with one shutter,it is assumed that the shutter opens automatically whenthe air temperature outside the duct is lower than 0  8 C.The convective heat transfer occurs between the wall of the duct and the air inside the duct. The coefficient of convective heat transfer between them is 15.0 w/m 2 (Zhang, 1989). The yearly average air temperatureinside the duct is 0.5  8 C higher than that outside theduct based on the fact from the measured data (Lai et al., 2004). So the air temperature inside the duct ischanged according to the following formula: T  ai  ¼   4 : 75  þ  11 : 14sin   2 p 8760  t   þ  2 : 59  þ  2 : 050    365    24  t  :  ð 8 Þ When air temperature outside the duct is above 0  8 Cin the ventilated duct embankment with one shutter, theshutter is closed automatically. The air temperatureinside the duct is changed linearly along the duct lengthaccording to Fig. 3 at a certain time (Zarling et al., 1983). Fig. 3 shows the temperature change along the duct length on August 1.According to the Adherent Layer Theory and thefact from the observational data in Plateau (Wu et al.,1998), the yearly average ground surface temperature of ordinary humid clay is 2.5  8 C higher than the yearlyaverage air temperature. So the temperature of nativeground surfaces AB and EF is changed according thefollowing formula: T  n  ¼   2 : 75  þ  11 : 14sin   2 p 8760  t   þ  2 : 59  þ  2 : 050    365    24  t  :  ð 9 Þ The ground surface temperatures of the shadingslope DE, namely the right-hand side slope of  Fig.1(b) and the driving surface CD are changed accordingto Eq. (7).The yearly average ground surface temperature of sunny slope, namely the left-hand side slope of  Fig.1(b) is 3  8 C higher than that of the shading slope due to Fig. 2. The mesh of element.  L. Guoyu et al. / Cold Regions Science and Technology 44 (2006) 99–110 102  the difference of solar radiation based on the observa-tional data (Sheng et al., 2004). So the surface temper-ature of the sunny side slope BC is changed accordingto the following formula: T  gy  ¼   2 : 11  þ  14 : 34sin   2 p 8760  t   þ  2 : 71  þ  2 : 050    365    24  t  :  ð 10 Þ The geothermal gradient on the permafrost base HGis 0.04  8 C/m (Zhou et al., 2000). The boundaries AH and FG are adiabatic.According to the air temperature data observed inventilated tunnels and culverts, the air temperatureinside the ducts is lower than air temperature (Su et al., 2004). So the air temperature inside the duct isassumed and changed according to Eq. (11) in theventilated duct embankment with two shutters, whenthe shutters are closed. When the shutter is open theconvective heat transfer occurs between the air insidethe duct and the wall of the duct. The air temperatureinside ducts is changed according to Eq. (8). T  c  ¼   0 : 44  þ  2 : 050    365    24  t  :  ð 11 Þ The initial temperature of the embankment fill is 2 8 C, which is the monthly average surface temperaturein September, because the embankment was accom- plished in September. The initial temperature of theactive layer and permafrost layer can be gained througha long-term transient solution of Eq. (1) with the upper  boundary condition Eq. (7) without considering theeffect of the climatic warming. 4. Numerical results The numerical simulation analysis for the 3D tem- perature field of the different embankment models isconducted and the results are shown in Figs. 4–9.Fig. 4(a),(b) and(c) showthe instantaneous isothermsonFebruary1,inthefirstyearafteritsconstructionfortheordinary embankment, the ventilated duct embankment with one shutter, the ventilated duct embankment withtwo shutters, respectively. It should be noted that resultsare shown for only the upper 5 m of permafrost soil eventhough the simulations extend to a depth of 20 m.Fig. 4(a)showsthatthereisabigthawingbulbbeneaththe ordinary embankment which still remains thawed onJanuary1,inthefirstyearafteritsconstruction.Thisisdueto the heat of the warmer fill thawing some permafrost.Theupperlimitofthe0 8 Cthawingbulbis  0.99matthecenterline and the lower limit is   2.58 m at this point inthe annual cycle. The temperature beneath the sunnyslope is about    9  8 C and the temperature under theshadingslopeisabout   12 8 CinFig.4(a).Thisindicates that the temperature distribution in the embankment isslightlyunsymmetrical due to the temperature difference between the sunny slope and the shading slope.Fig. 4(b) shows that there are some 0  8 C thaw bulbsonly under the sunny slope of the embankment. Theground temperature under this embankment is lower and the thawing bulb is smaller than that of  Fig. 4(a) due to the cooling effect of the buried duct duringwinter months. Note that the isotherms of  Fig. 4( b) above the buried duct have a distinct asymmetry but they remain frozen. The ground temperature beneaththe buried duct has significantly decreased comparedwith that of  Fig. 4(a). The isotherms beneath the original ground surface remain almost horizontal. Fig. 3. Air temperature change along the duct length inside it on August 1.  L. Guoyu et al. / Cold Regions Science and Technology 44 (2006) 99–110  103
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