Simulation of Heat Transfer during Artificial Ground Freezing Combined with Groundwater Flow

Transcription

1 Smulaton of Heat Transfer durng Artfcal Ground Freezng Combned th Groundater Flo Ru Hu *1, Quan Lu 1 1 School of Earth Scence and Engneerng, Hoha Unversty, Nanjng, Chna *Correspondng author: No.8 Fochengx Road, Nanjng, Chna, rhu@hhu.edu.cn Abstract: Based on the heat transfer and seepage theory n porous meda th fnte element method, a 2D numercal model as establshed to smulate the changes of temperature feld and the process of freezng all formaton durng a strengthenng project of a metro tunnel th artfcal ground freezng method (AGF). The smulaton results sho that the freezng all appears n an asymmetrcal shape as the horzontal groundater flo s normal to the axal of the tunnel. Along the groundater flo drecton, freezng all forms sloly and on the upstream sde the thckness of the freezng all s thnner than that on the donstream sde. The closure tme of the freezng all ncreases at the mddle of the both up and donstream sdes. The average thckness of the freezng all on the upstream sde s mostly affected by the groundater flo velocty. Artfcal ground freezng method (AGF), patented by Poetch n Germany n 1883, s a constructon technology hch freezes the ater n the ground by artfcal refrgerant to create a hgh-strength freezng all. In ths study, the AGF method s appled to smulate a sol body strengthenng project at the portal of a metro tunnel n Guangzhou, Chna. The locaton of the project s shon n Fgure 1. Wth ths method, the crculaton of refrgerant (-30 C brne) n the pre-bured ppes can reduce the subsurface temperature tll the pore ater freezes and the freezng all forms. Hence, the temperature dstrbuton n the underground s the key controllng factor durng the artfcal freezng actvtes. Keyords: Artfcal ground freezng method, groundater flo, temperature feld, freezng all, effectve hydraulc conductvty. 1. Introducton The artfcal ground freezng (AGF) method has been dely used n cvl and mnng engneerng. Its prncple s to crculate a flud refrgerant (ca. -30 C) through a pre-bured ppe netork n the subsurface n order to form a freezng all for constructon strengthenng. The knoledge of the n-stu temperature dstrbuton s the key factor th respect to the development of the freezng all. The man physcal process s a transent heat conducton phenomenon th phase change. In common cases, the temperature change s only consdered as a heat conducton process. Hoever, th groundater of hgh flo veloctes, the nfluence of the ater-ce phase change on the flo propertes should not be neglected. In ths ork, e performed a case study of a strengthenng project of a metro tunnel th AGF method, consderng the nfluence of groundater flo. Fgure 1. The locaton of the project n Guangzhou, Chna. (Note that the pont A ndcates the overve poston on the ground. The real project poston s belo ths pont n the subay underground) 2. Model Defnton In ths project, thn the freezng area, the formaton s muddy sand. The groundater flo drecton s manly horzontal and normal to the axal of tunnel. Thus, e used a 2D model to smplfy the smulaton of heat transport n a saturated aqufer. The model geometry s shon n Fgure 2a. Both of the length and heght of ths model are 20m. Fve montorng ponts are set to verfy the accuracy of ths numercal model by the comparson of transent temperature value beteen the n-stu measurements and the calculated results. Fgure 2b s the model grd meshed by COMSOL Multphyscs.

2 In a saturated aqufer, the heat transport process manly ncludes the release of latent heat, heat conducton and heat convecton. The temperature feld T s governed by the heat transport equaton: T S [ + QG (1) t T C eq λeq T ] C f u T ρ L = here λeq s bulk thermal conductvty (calculated by volumetrc average approxmaton); u s seepage velocty, calculated by the Darcy s la; S s the saturaton of ater n the pores; S / T s sold fracton, hch s equal to the dervatve of S th respect to T. Fgure 2a. Model geometry Fgure 2b. Model grd (meshng by COMSOL) 2.1 Model Assumptons Ths model s smplfed to an deal case th the follong assumptons: (1) The ce s mmoble, the medum s nondeformable; (2) The aqufer s fully saturated and ts total porosty remans constant; (3) The freezng pont depresson due to solute concentratons s neglgble. 2.2 Governng Equatons The dstrbuton of temperature n the aqufer has a great nfluence on seepage feld n ths case. On the one hand, because of ce formaton durng the phase change, the orgnal pore channel s blocked hch may temporarly change the groundater flo systems. On the other hand, although ce formaton s accompaned by the expanson of volume, the pore ater, at that moment, has much loer flo ablty n frozen area. Therefore, the ater flo n the frozen zone can be gnored th respect to the effect of pore expanson. The total ground ater flo feld s governed by the Darcy s la as folloed: p k r Kρ ( 1 ε S ) SOP + [ ( p + ρ g D)] t µ S = QS + ε ( ρ ρ ) (2) t, here S OP s the specfed pressure storatvty and kr s the relatve permeablty (used to represent the decrease of permeablty n the ater-ce phase transformaton zone), descrbed by Heavsde functon. 2.3 Intal & Boundary Condtons Temperature: accordng to the pror n-stu temperature montorng data at destnaton freezng depth, the ntal ground temperature s about 15 C. The box chart of ntal temperatures n dfferent thermo-observaton holes s shon n Fgure 3a.

3 Temperature boundary condton: the lateral all of freezng ppe s the coolng source of freezng system and the change of lateral all temperature has a great effect on temperature dstrbuton n the hole system. The temperature montorng values of man-ppe, through hch the refrgerant can flo to the freezng all, can be approxmately used to estmate the lateral all temperature. Accordng to the temperature montorng data of loop manppe (T out ) durng montorng perod (40 days), the lateral all temperature fttng functon and curve are shon n Fgure 3b. Wth the smulaton softare COMSOL Multphyscs, a 2D cross secton of a horzontal AGF project (Fgure 2a) s selected and a numercal model s set up, hch s based on full couplng of temperature and flo felds by combnng physcal nterfaces of Darcy's La and Heat Transfer n Porous Meda. Frstly, the Darcy s velocty u s selected as a couplng varable and lnked to the temperature feld. Subsequently, as the pore ater gradually turns nto ce, the permeablty n freezng zone s decreased. At ths phase, e ntroduce a varable of effectve hydraulc conductvty k r hch can be descrbed by a functon of temperature change. At ths pont, k r s assgned by a step functon (Fgure 4a): k ( T ) = (1 k ) flc2hs( T T, δ T ) + k (1.3) r r P r here flc2 hs s a Heavsde functon and k r s an arbtrary small mnmum value for frozen area permeablty (cannot be equal to zero, or the flo equaton cannot be solved. Here t s lmted at 10-6.) Fgure 3a. Box chart of ntal ground temperature Smlarly, the saturaton of ater S and ts dervatve curves are shon n Fgure 4b. Fgure 4a. The curve of relatve permeablty Fgure 3b. Fttng curve of ppe all temperature (T out ) Groundater flo: the flo velocty obtaned through feld test s 0.2m/d. Based on the Darcy s la, the head dfference beteen up and donstream s calculated as 0.8m. 3. Use of COMSOL Multphyscs Softare Fgure 4b. Sold fracton and volume fracton of unfrozen ater

4 The energy conservaton problem durng freezng phase change s solved by apparent heat capacty method and the related parameter change s descrbed by a step functon (References 2). The correspondng mesh s generated through automatc remeshng (Fgure 2b). Ths model s valdated th n-stu temperature observatons. 4. Results and Dscusson Table 1 n the Appendx shos the parameters used for the calculaton n ths model. The smulaton results of temperature and permeablty coeffcent at varous tmes (7d, 14d, 21d, 28d, and 35d) are shon n Fgure 5. (a) (b) 28 Days 21 Days 14 Days 7 Days

5 35 Days Fgure 5. (a)temperature dstrbuton and (b) permeablty coeffcent (temperature belo 0 C) results & Darcy s velocty feld (black arros) for project example at varous tmes The temperature dstrbuton maps (Fgure 5a) sho that as the freezng tme ncreases, the cold temperature from freezng ppes s manly conducted to donstream and has less mpact on upstream. The permeablty coeffcent chart (Fgure 5b) mples the formaton process of freezng all. The freezng alls at the top and bottom form faster than that at the updonstream. On the 35th day (closure tme), the freezng all as completely closed. Fgure 6. Relatonshp beteen freezng all crcle closure tme and flo velocty Fgure 6 shos the varaton curve beteen freezng all crcle closure tme and flo velocty. By ncreasng flo velocty, the crcle closure tme of freezng all ncreases nonlnearly. Wth velocty greater than 1.5m/d, the closure tme ncreases dramatcally. Fgure 7 shos the varaton curve beteen average all thckness n each drecton and correspondng flo velocty. The nfluence of flo velocty on the average thckness of the upstream all s the most obvous. 5. Conclusons Concluded th the results at dfferent tmes, the temperature contour maps combned th permeablty coeffcent and groundater flo velocty feld (Fgure 5) ndcate that the freezng all appears n an asymmetrcal shape as the horzontal groundater flo s normal to the axal of the tunnel. Along the groundater flo drecton, freezng all forms sloly and on the upstream sde the thckness of the freezng all s thnner than that on the donstream sde. The closure tme of the freezng all ncreases at the mddle of the both up and donstream sdes. The average thckness of the freezng all on the upstream sde s mostly affected by the groundater flo velocty. Wth the successful valdaton of ths model, ths numercal smulaton could provde further gudance n ths AGF project n the future. 6. References Fgure 7. Relatonshp beteen average all thckness n each drecton and correspondng flo velocty 1. Harlan RL. Analyss of coupled heat-flud transport n partally frozen sol. Water Resources Research (1973). 2. Jeffrey M. McKenze, et. al. Groundater flo th energy transport and ater ce phase change: Numercal smulatons, benchmarks, and applcaton to freezng n peat bogs. Advances n Water Resources (2007).

6 3. Vtel M, Rouabh A, Tjan M, et al. Modelng heat transfer beteen a freeze ppe and the surroundng ground durng artfcal ground freezng actvtes. Computers and Geotechncs (2015). 4. Vtel M, Rouabh A, Tjan M, et al. Modelng heat and mass transfer durng ground freezng subjected to hgh seepage veloctes. Computers and Geotechncs (2016). 5. S. Papakonstantnou, G. Anagnostou, E. Pmentel. Evaluaton of ground freezng data from the Naples subay. Ice (Geotechncal Engneerng) (2013). 6. Pmentel E, Papakonstantnou S, Anagnostou G. Numercal nterpretaton of temperature dstrbutons from three ground freezng applcatons n urban tunnellng. Tunnellng and Underground Space Technology (2012). 7. Appendx Table 1: Base case model parameters Parameter Value Densty of sol ρ s (kg/m 3 ) 1800 Densty of ater ρ (kg/m 3 ) 1000 Densty of ce ρ (kg/m 3 ) 920 Thermal conductvty of sol λ (W/(m. K)) s 0.85 Thermal conductvty of ater λ (W/(m. K)) 0.6 Thermal conductvty of ce λ (W/(m. K)) 2.14 Heat capacty of sol c s (J/(kg. K)) 1220 Heat capacty of ater c (J/(kg. K)) 4200 Heat capacty of ce c (J/(kg. K)) 2100 Porosty n 0.4 Permeablty coeffcent k (m/d) 5 Latent heart of formaton L (J/kg)