Abstract
Concrete-lined pressure tunnels have been widely used for water conveyance in pumped storage hydropower. With increasing internal water pressure, the tunnels are at higher risk of leakage, and the flow regime in the surrounding rocks is likely to transition from laminar to non-Darcian. Grouting has been considered as a cost-effective technique for controlling leakage in pressure tunnels, and an optimization design is usually needed to save the cost. This study proposes to use the Forchheimer’s law-based model for design optimization of grouting for a concrete-lined tunnel in hard rocks subjected to 8 MPa internal water pressure. The hydraulic conductivity K of the surrounding rocks is determined from packer tests, and the excavation-induced K variation is characterized by an equivalent elasto-plastic model. The non-Darcian coefficient β is estimated from K with a calibrated power-law scaling. It is proposed that a proper design of grouting should be able to limit the region with significant non-Darcian effect within the grouted zone, in addition to other commonly-used criteria for leakage, seepage erosion and fracturing failure in the surrounding rocks. It is found that when the quality of grouting is controlled to a standard of K = 6 × 10−8 m/s, the optimal depth of grouting is 6 m in fractured rocks and 12 m in fault zones. Hydraulic tests and seepage measurements confirm that this design scheme has been well implemented at the site, and is effective in controlling pore pressure and leakage to the level predicted by the Forchheimer’s law-based simulation.
Highlights
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The quality control criterion and depth of grouting are optimized with Forcheimer’s law-based flow simulation for a pressure tunnel.
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It is proposed that significant non-Darcian flow effect should be limited within the grouted zone for optimization design of grouting.
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The optimized design scheme of grouting was implemented, and its effectiveness in leakage control is validated by seepage measurements.
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Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
References
Bian K, Liu J, Xiao M, Liu ZP (2016) Cause investigation and verification of lining cracking of bifurcation tunnel at Huizhou pumped storage power station. Tunn Undergr Space Technol 54:123–134. https://doi.org/10.1016/j.tust.2015.10.030
Bobet A, Fakhimi A, Johnson S, Morris J, Tonon F, Yeung MR (2009) Numerical models in discontinuous media: review of advances for rock mechanics applications. J Geotech Geoenviron Eng 135(11):1547–1561. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000133
Butrón C, Gustafson G, Fransson Å, Funehag J (2010) Drip sealing of tunnels in hard rock: A new concept for the design and evaluation of permeation grouting. Tunn Undergr Space Technol 25(2):114–121. https://doi.org/10.1016/j.tust.2009.09.008
Cappa F, Guglielmi Y, Rutqvist J, Tsang CF, Thoraval A (2006) Hydromechanical modelling of pulse tests that measure fluid pressure and fracture normal displacement at the Coaraze laboratory site, France. Int J Rock Mech Min Sci 43(7):1062–1082. https://doi.org/10.1016/j.ijrmms.2006.03.006
Cardenas MB, Slottke DT, Ketcham RA, Sharp JM (2009) Effects of inertia and directionality on flow and transport in a rough asymmetric fracture. J Geophys Res 114:B06204. https://doi.org/10.1029/2009JB006336
Chen YF, Hu SH, Wei K, Hu R, Zhou CB, Jing LR (2014) Experimental characterization and micromechanical modeling of damage-induced permeability variation in Beishan granite. Int J Rock Mech Min Sci 71:64–76. https://doi.org/10.1016/j.ijrmms.2014.07.002
Chen YF, Hu SH, Hu R, Zhou CB (2015) Estimating hydraulic conductivity of fractured rocks from high-pressure packer tests with an Izbash’s law-based empirical model. Water Resour Res 51(4):2096–2118. https://doi.org/10.1002/2014WR016458
Chen YF, Liao Z, Zhou JQ, Hu R, Yang ZB, Zhao XJ, Wu XL, Yang XL (2020) Non-Darcian flow effect on discharge into a tunnel in karst aquifers. Int J Rock Mech Min Sci 130:104319. https://doi.org/10.1016/j.ijrmms.2020.104319
Chen YF, Zhou CB, Sheng YQ (2007) Formulation of strain-dependent hydraulic conductivity for a fractured rock mass. Int J Rock Mech Min Sci 44(7):981–996. https://doi.org/10.1016/j.ijrmms.2006.12.004
Chen YF, Zhou CB, Jing LR (2009) Modeling coupled THM processes of geological porous media with multiphase flow: theory and validation against laboratory and field scale experiments. Comput Geotech 36(8):1308–1329. https://doi.org/10.1016/j.compgeo.2009.06.001
Chen YF, Zhou CB, Zheng H (2008) A numerical solution to seepage problems with complex drainage systems. Comput Geotech 35(3):383–393. https://doi.org/10.1016/j.compgeo.2007.08.005
Cooke CE Jr (1973) Conductivity of fracture proppants in multiple layers. J Pet Technol 25(09):1101–1107. https://doi.org/10.2118/4117-PA
Dausse A, Guihéneuf N, Parker BL (2021) Impact of flow geometry on parameter uncertainties for underdamped slug tests in fractured rocks. J Hydrol 592:125567. https://doi.org/10.1016/j.jhydrol.2020.125567
Ding XL, Weng YH, Zhang YT, Xu TJ, Wang TL, Rao ZW, Qi ZF (2017) Stability of large parallel tunnels excavated in weak rocks: A case study. Rock Mech Rock Eng 50(9):2443–2464. https://doi.org/10.1007/s00603-017-1247-6
Forchheimer P (1901) Wasserbewegung durch boden. Z Ver Dtsch Ing 45:1782–1788
Gao CL, Zhou ZQ, Li ZH, Li LP, Cheng S (2020) Peridynamics simulation of surrounding rock damage characteristics during tunnel excavation. Tunn Undergr Space Technol 97:103289–103307. https://doi.org/10.1016/j.tust.2020.103289
Gao M, Zhang CG, Oh J (2023) Assessments of the effects of various fracture surface morphology on single fracture flow: A review. Int J Min Sci Technol 33(1):1–29. https://doi.org/10.1016/j.ijmst.2022.07.005
Garcia LA, Shigidi A (2006) Using neural networks for parameter estimation in ground water. J Hydrol 318:215–231. https://doi.org/10.1016/j.jhydrol.2005.05.028
Hoien AH, Nilsen B (2014) Rock mass grouting in the Loren tunnel: case study with the main focus on the Groutability and feasibility of drill parameter interpretation. Rock Mech Rock Eng 47:967–983. https://doi.org/10.1007/s00603-013-0386-7
Huang JX, Fu PC, Settgast RR, Morris JP, Ryerson FJ (2019) Evaluating a simple fracturing criterion for a hydraulic fracture crossing stress and stiffness contrasts. Rock Mech Rock Eng 52:1657–1670. https://doi.org/10.1007/s00603-018-1679-7
Illman WA, Hughson DL (2005) Stochastic simulations of steady state unsaturated flow in a three-layer, heterogeneous, dual continuum model of fractured rock. J Hydrol 307(1–4):17–37. https://doi.org/10.1016/j.jhydrol.2004.09.015
Javadi M, Sharifzadeh M, Shahriar K, Mitani Y (2014) Critical Reynolds number for nonlinear flow through rough-walled fractures: the role of shear processes. Water Resour Res 50(2):1789–1804. https://doi.org/10.1002/2013WR014610
Jeannin PY (2001) Modeling flow in phreatic and epiphreatic karst conduits in the Hölloch cave (Muotatal, Switzerland). Water Resour Res 37(2):191–200. https://doi.org/10.1029/2000WR900257
Jorne F, Henriques FMA (2016) Evaluation of the grout injectability and types of resistance to grout flow. Constr Build Mater 122:171–183. https://doi.org/10.1016/j.conbuildmat.2016.06.032
Karami M, Kabiri-Samani A, Nazari-Sharabian M, Karakouzian M (2019) Investigating the effects of transient flow in concrete-lined pressure tunnels, and developing a new analytical formula for pressure wave velocity. Tunn Undergr Space Technol 91:102992. https://doi.org/10.1016/j.tust.2019.102992
Kikuchi K, Igari T, Mito Y, Utsuki S (1997) In situ experimental studies on improvement of rock masses by grouting treatment. Int J Rock Mech Min Sci 34(3–4):1380–2147. https://doi.org/10.1016/S1365-1609(97)00183-4
Ku CY, Hsu SM, Chiou LB, Lin GF (2009) An empirical model for estimating hydraulic conductivity of highly disturbed clastic sedimentary rocks in Taiwan. Eng Geol 109(3–4):213–223. https://doi.org/10.1016/j.enggeo.2009.08.008
Li HY, Zhang YC, Wu J, Zhang XY, Zhang LW, Li ZW (2020a) Grouting sealing mechanism of water gushing in karst pipelines and engineering application. Constr Build Mater 254:119250. https://doi.org/10.1016/j.conbuildmat.2020.119250
Li X, Chen YF, Hu R, Yang ZB (2017) Towards an optimization design of seepage control: A case study in dam engineering. Sci China-Technol Sci 60(12):137–150. https://doi.org/10.1007/s11431-016-9160-y
Li Z, Liu HX, Dun ZL, Ren LW, Fang JJ (2020b) Grouting effect on rock fracture using shear and seepage assessment. Constr Build Mater 242:118–131. https://doi.org/10.1016/j.conbuildmat.2020.118131
Liu HH, Lin BQ, Jiang CL (2019) A new method for determining coal seam permeability redistribution induced by roadway excavation and its applications. Process Saf Environ Protect 131:1–8. https://doi.org/10.1016/j.psep.2019.08.019
Liu C, Zhang DL, Zhang SL (2021) Characteristics and treatment measures of lining damage: A case study on a mountain tunnel. Eng Fail Anal 128:105595. https://doi.org/10.1016/j.engfailanal.2021.105595
Liu MM, Chen YF, Zhan HB, Hu R, Zhou CB (2017a) A generalized Forchheimer radial flow model for constant-rate test. Adv Water Resour 107:317–325. https://doi.org/10.1016/j.advwatres.2017.07.004
Liu QS, Lei GF, Peng XX, Lu CB, Wei L (2018) Rheological characteristics of cement grout and its effect on mechanical properties of a rock fracture. Rock Mech Rock Eng 51(2):613–625. https://doi.org/10.1007/s00603-017-1340-x
Liu RC, Yu LY, Jiang YJ (2017b) Quantitative estimates of normalized transmissivity and the onset of nonlinear fluid flow through rough rock fractures. Rock Mech Rock Eng 50(4):1063–1071. https://doi.org/10.1007/s00603-016-1147-1
Liu W, Chen YF, Hu R, Zhou W, Zhou CB (2016) A two-step homogenization-based permeability model for deformable fractured rocks with consideration of coupled damage and friction effects. Int J Rock Mech Min Sci 89:212–226. https://doi.org/10.1016/j.ijrmms.2016.09.009
Lu ZK, Wrobel LC (1997) Analysis of the high pressure tunnel of the Guangzhou pumped storage power station. Proc Inst Civil Eng-Munic Eng 124(1):25–31. https://doi.org/10.1680/iwtme.1997.29287
Marwa EM (2004) Geotechnical considerations in an unlined high pressure tunnel at Lower Kihansi in Tanzania. Bull Eng Geol Environ 63(1):51–55. https://doi.org/10.1007/s10064-003-0225-2
Mathias SA, Butler AP, Zhan H (2008) Approximate solutions for Forchheimer flow to a well. J Hydraul Eng 134(9):1318–1325. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:9(1318)
Oda M (1985) Permeability tensor for discontinuous rock masses. Geotechnique 35(4):483–495. https://doi.org/10.1680/geot.1985.35.4.483
Pachoud AJ, Manso PA, Schleiss AJ (2017) Stress intensity factors for axial semi-elliptical surface cracks and embedded elliptical cracks at longitudinal butt welded joints of steel-lined pressure tunnels and shafts considering weld shape. Eng Fract Mech 179:93–119. https://doi.org/10.1016/j.engfracmech.2017.04.024
Panthi KK, Nilsen B (2010) Uncertainty analysis for assessing leakage through water tunnels: A case from nepal himalaya. Rock Mech Rock Eng 43:629–639. https://doi.org/10.1007/s00603-009-0075-8
Pardoen B, Talandier J, Collin F (2016) Permeability evolution and water transfer in the excavation damaged zone of a ventilated gallery. Int J Rock Mech Min Sci 85:192–208. https://doi.org/10.1016/j.ijrmms.2016.03.007
Peters RR, Klavetter EA (1988) A continuum model for water movement in an unsaturated fractured rock mass. Water Resour Res 24(3):416–430. https://doi.org/10.1029/WR024i003p00416
Qian X, Xia CC, Gui Y (2018) Quantitative estimates of non-Darcy groundwater flow properties and normalized hydraulic aperture through discrete open rough-walled joints. Int J Geomech 18(9):04018099. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001228
Quinn PM, Cherry JA, Parker BL (2011) Quantification of non-Darcian flow observed during packer testing in fractured sedimentary rock. Water Resour Res 47(9):178–187. https://doi.org/10.1029/2010WR009681
Quinn PM, Parker BL, Cherry JA (2013) Validation of non-Darcian flow effects in slug tests conducted in fractured rock boreholes. J Hydrol 486:505–518. https://doi.org/10.1016/j.jhydrol.2013.02.024
Rutqvist J, Noorishad J, Tsang CF, Stephansson O (1998) Determination of fracture storativity in hard rocks using high-pressure injection testing. Water Resour Res 34(10):2551–2560. https://doi.org/10.1029/98WR01863
Sen Z (1989) Nonlinear flow toward wells. J Hydraul Eng 115(2):193–209. https://doi.org/10.1061/(ASCE)0733-9429(1989)115:2(193)
Singh KK, Singh DN, Ranjith PG (2015) Laboratory simulation of flow through single fractured granite. Rock Mech Rock Eng 48(3):987–1000. https://doi.org/10.1007/s00603-014-0630-9
Singh KK, Singh DN, Ranjith PG (2016) Effect of sample size on the fluid flow through a single fractured granitoid. J Rock Mech Geotech Eng 8(3):329–340. https://doi.org/10.1016/j.jrmge.2015.12.004
Snow DT (1969) Anisotropic permeability of fractured media. Water Resour Res 5(6):1273–1289. https://doi.org/10.1029/wr005i006p01273
Su XP, Li HL, Liu JL, Shen ZH, Ren XY, Zhou L (2022) Experimental study on nonlinear flow in granite tensile and shear fractures. Int J Geomech 22(12):04022241. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002606
Tani ME (2003) Circular tunnel in a semi-infinite aquifer. Tunn Undergr Space Technol 18(1):49–55. https://doi.org/10.1016/S0886-7798(02)00102-5
Tsang YW, Tsang CF (1987) Channel model of flow through fractured media. Water Resour Res 23(3):467–479. https://doi.org/10.1029/WR023i003p00467
Varol A, Dalgic S (2006) Grouting applications in the Istanbul metro Turkey. Tunn Undergr Space Technol 21(6):602–612. https://doi.org/10.1016/j.tust.2005.11.002
Wang Q, Gao HK, Yu HC, Jiang B, Liu BH (2019) Method for measuring rock mass characteristics and evaluating the grouting-reinforced effect based on digital drilling. Rock Mech Rock Eng 52(3):841–851. https://doi.org/10.1007/s00603-018-1624-9
Wen Z, Huang GH, Zhan HB (2011) Non-Darcian flow to a well in a leaky aquifer using the Forchheimer equation. Hydrogeol J 19(3):563–572. https://doi.org/10.1007/s10040-011-0709-2
Widmann R (1996) International society for rock mechanics on grouting. Int J Rock Mech Min Sci Geomech Abstr 33:803–847. https://doi.org/10.1016/S0148-9062(96)00015-0
Wu AQ, Zhao W, Zhang YH, Fu X (2023) A detailed study of the CHN-BQ rock mass classification method and its correlations with RMR and Q system and Hoek-Brown criterion. Int J Rock Mech Min Sci 162:105290. https://doi.org/10.1016/j.ijrmms.2022.105290
Xiao F, Liu Q, Zhao ZY (2021) Information and knowledge behind data from underground rock grouting. J Rock Mech Geotech Eng 13(6):1326–1339. https://doi.org/10.1016/j.jrmge.2021.06.013
Yang MJ, Yue ZQ, Lee PKK, Su B, Tham LG (2002) Prediction of grout penetration in fractured rocks by numerical simulation. Can Geotech J 39(6):1384–1394. https://doi.org/10.1139/T02-063
Zeng Z, Grigg R (2006) A criterion for non-Darcy flow in porous media. Transp Porous Media 63(1):57–69. https://doi.org/10.1007/s11242-005-2720-3
Zimmerman R, Alyaarubi A, Pain C, Grattoni C (2004) Non-linear regimes of fluid flow in rock fractures. Int J Rock Mech Min Sci 41(3):163–169. https://doi.org/10.1016/j.ijrmms.2004.03.036
Zhang DL, Fang Q, Lou HC (2014) Grouting techniques for the unfavorable geological conditions of Xiang’an subsea tunnel in China. J Rock Mech Geotech Eng 6(5):438–446. https://doi.org/10.1016/j.jrmge.2014.07.005
Zhang L, Feng K, Gou C, He C, Liang K, Zhang HH (2019a) Failure tests and bearing performance of prototype segmental linings of shield tunnel under high water pressure. Tunn Undergr Space Technol 92:103053. https://doi.org/10.1016/j.tust.2019.103053
Zhang W, Dai BB, Liu Z, Zhou CY (2019b) On the non-Darcian seepage flow field around a deeply buried tunnel after excavation. Bull Eng Geol Environ 78(1):311–323. https://doi.org/10.1007/s10064-017-1041-4
Zhang W, Liu M, Bian K, Cong PT, Yuan WH (2021) Modelling the hydro-mechanical behaviour of high-pressure tunnel with emphasis on the interaction between lining and rock mass. Comput Geotech 139:104382. https://doi.org/10.1016/j.compgeo.2021.104382
Zhang Y, Zhang DL, Fang Q, Xiong LJ, Yu L, Zhou MZ (2020) Analytical solutions of non-Darcy seepage of grouted subsea tunnels. Tunn Undergr Space Technol 96:103–182. https://doi.org/10.1016/j.tust.2019.103182
Zhang ZY, Nemcik J (2013) Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures. J Hydrol 477:139–151. https://doi.org/10.1016/j.jhydrol.2012.11.024
Zhou CB, Zhao XJ, Chen YF, Liao Z, Liu MM (2018) Interpretation of high pressure pack tests for design of impervious barriers under high-head conditions. Eng Geol 234:112–121. https://doi.org/10.1016/j.enggeo.2015.01.008
Zhou JQ, Hu SH, Fang S, Chen YF, Zhou CB (2015) Nonlinear flow behavior at low Reynolds numbers through rough-walled fractures subjected to normal compressive loading. Int J Rock Mech Min Sci 80:202–218. https://doi.org/10.1016/j.ijrmms.2015.09.027
Zhou JQ, Chen YF, Wang LC, Cardenas M (2019) Universal relationship between viscous and inertial permeability of geologic porous media. Geophys Res Lett 46(3):1441–1448. https://doi.org/10.1029/2018GL081413
Zhou YF, Su K, Wu HG (2017) Hydro-mechanical interaction analysis of high pressure hydraulic tunnel. Tunn Undergr Space Technol 47:28–34. https://doi.org/10.1016/j.tust.2017.06.006
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Financial support from the National Natural Science Foundation of China (Grant Nos. 51925906 and U2340228) and the Natural Science Foundation of Hubei Province (Grant No. 2022CFA028) is gratefully acknowledged.
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Chen, YF., He, JG., Lei, WJ. et al. Optimization Design of Consolidation Grouting Around High-Pressure Tunnel Considering Non-Darcian Flow Effect. Rock Mech Rock Eng (2024). https://doi.org/10.1007/s00603-024-03906-6
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DOI: https://doi.org/10.1007/s00603-024-03906-6