Implementation of a 3D Multilaminated Hydromechanical Model for Analysis of an Unlined High Pressure Tunnel

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1 COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug , 2006, Sanya, Hainan, China 2006 Tinghua Univerity Pre & Springer Implementation of a 3D Multilaminated Hydromechanical Model for Analyi of an Unlined High Preure Tunnel N. Schclar Leitão, L. N. Lama * LNEC Laboratório Nacional de Engenharia Civil, Av. do Brail 101, Liboa, Portugal nchclar@lnec.pt, llama@lnec.pt Abtract: The purpoe of thi paper i to report the firt tage of the implementation within FLAC 3D of a hydromechanical model uing an iterative procedure between two independent hydraulic and mechanical ub-model. The fracture network of the rock ma i conidered uing the multilaminated medium concept. The implemented model i illutrated through it application to the hydraulic circuit of the Venda Nova II hydroelectric power cheme, in Portugal. Key word: hydromechanical, permeability, preure tunnel INTRODUCTION In fractured rock mae in the preence of water, the excavation of an underground opening correpond to a diturbance of the fracture medium, which introduce a change in the tre field, a change in the water flow boundary condition a well a a local damage in the rock ma tructure. The change in the water flow condition caue variation in the eepage force, which are mechanical loading that introduce change in the tre field, thu inducing deformation in the fractured rock ma. In turn, thee deformation are reponible for change in the rock ma permeability, which will again introduce change in the water flow condition. The exitence of thi interaction between the hydraulic and the mechanical problem make it important to tudy thi problem a an integrated proce. A review of hydromechanical coupling in fractured rock, with pecial emphai on hydromechanical interaction a a reult of human activitie uch a underground injection and underground contruction can be een in Rutqvit et al. [1]. The purpoe of thi paper i to report the firt tage of the implementation within FLAC 3D [2] of a hydromechanical model uing an iterative procedure between two independent hydraulic and mechanical ub-model. The implemented model wa applied to the high preure hydraulic circuit of the Venda Nova II hydroelectric power cheme, which ha an unlined, high preure tunnel at great depth. HYDROMECHANICAL MODEL The hydromechanical behaviour of fractured rock mae i trongly influenced by the preence of joint. In fact, the joint are reponible, to a large extent, for the eepage that occur through the rock ma and they are alo the mot enitive element of the rock ma with repect to deformation under tre change. In order to adequately imulate the behaviour of the joint, it i advantageou to conider them individually, in an explicit manner. However, thi i only conceptually poible when a limited number of major dicontinuitie, uch a fault or hear zone, are to be conidered. If the rock ma ha everal joint et and the critical dimenion of the 274

2 tructure under analyi i large compared to the pacing of the joint, then it i more appropriate to conider a contitutive model that account for the fabric of the joint. Thi can be done uing the multilaminated medium concept, which wa introduced by Zienkiewicz & Pande [3] for the mechanical behaviour, and extending it alo to the hydraulic behaviour. In thi way, the permeability tenor of the rock ma can be conidered a the um of two term: one relative to the contribution of the rock material (a trictly continuou medium), K, and the other relative to the contribution of the total number n of joint et, c ij ij K [4]: ec ij n =1 ij K = K + K c ij with 3 g I ( e ) K ij = (1) 12ν ω where g i the acceleration of gravity, I i the mean intenity (equal to the invere of the mean pacing of the et along the normal to the plane), e i the mean hydraulic aperture of the et, and ν ω i the kinematic vicoity of water. The law propoed by Wei [5] wa adopted for repreentation of the influence of the mechanical behaviour on the fluid flow in the trictly continuou medium. Thi law conider that the permeability in each of it principal direction, K i, i a function of it initial value along that direction, K oi, and of the um of the train increment in the orthogonal plane, Δε j and Δε k : K i = K βi ( Δε j + Δε k ) oie ( i = 1,2,3; j = 2,3,1; k = 3,1,2) (2) where β i (i = 1,2,3) are empirical parameter that, according to Wei, depend on the deformability and on the hape of the rock pore. For the equivalent continuum ued in thi model, the mechanical and hydraulic behaviour for the joint et have alo to be conidered. With the value of the normal tre acting on each of the joint et, the normal diplacement caued by the normal tre, δ n, i computed and added to the initial aperture of the joint of the et, E o, in order to determine the final mechanical aperture: E o = E + δ (3) n To relate the hydraulic aperture and the mechanical aperture the law propoed by Elliot et al. [6] i ued, but the term that refer to the reidual hydraulic aperture of the model of Witherpoon et al. [7] i alo conidered. Thu the law ued here can be written a: re e = f ( E + e ) (4) E where f E i Elliot hydromechanical coupling parameter, E i the mechanical aperture and e re i the reidual aperture. IMPLEMENTATION OF THE MODEL USING FLAC 3D CODE The equivalent continuou model decribed above allow the ue of a continuum-baed modelling package. For thi analyi the FLAC 3D code wa adopted. FLAC 3D i a widely ued commercial code that i deigned for rock and oil mechanic and can alo handle hydraulic and fully coupled hydromechanical procee. For the propoed hydromechanical model, baed on an iteratively coupled approach, the FLAC 3D code i executed equentially to model the mechanical and the hydraulic behaviour. Although the FISH programming language embedded within FLAC 3D enable the computation of the train-induced change in permeability, it wa decided to do it externally uing a FORTRAN program. The ue of a more robut programming language uch a FORTRAN will facilitate further development in the propoed model. 275

3 The information between the FLAC 3D and the FORTRAN code i paed uing ASCII file, which can be read or written by FISH ubroutine during FLAC 3D execution. The et of command which control the running of FLAC 3D i given through the FLAC3D.INI initialization program which i automatically acceed upon tarting FLAC 3D with a run-time FORTRAN function. The FLAC 3D grid i configured for aniotropic fluid flow and the computed permeability tenor, Eq. (1), i given in term of it principal value. According to FLAC 3D definition, the hydraulic propertie are given in term of the mobility coefficient, k, expreed in it principal direction, k 1, k 2, k 3. The mobility coefficient k (m 2 /(Pa ec)) i related to the hydraulic permeability K (m/), given by Eq. (1), by the following expreion, where ρ i the water denity: f k K = (5) gρ f APLICATION OF THE MODEL TO A HYDRAULIC CIRCUIT 1. Venda Nova II cheme Venda Nova II cheme i a new hydroelectric upgrading project recently built in the north-wetern region of Portugal. Venda Nova II that take advantage of the 420 m difference in level between two exiting reervoir etablihed at the beginning of the 1950 and eparated by a ditance of only 4,500 m. It wa built almot excluively underground inide the north face of the Cabreira Mountain granite rock ma. It contruction involved everal tunnel, covering a total length of about 7.5 km, everal vertical and inclined haft of about 700 m in total length and two cavern incorporating the power-houe complex (Fig. 1). Figure 1: Venda Nova II overview, where: A = water intake, B = preure tunnel, C = upper urge chamber, D = powerhoue cavern, E = tailrace tunnel, F = acce adit, G = ventilation tunnel, H = water outlet The main powerhoue cavern i located in an intermediate poition in the hydraulic circuit, at a depth of about 350 m. The unlined headrace preure tunnel i 2.8 km long and ha a lope of 15%; it ection i a modified circumference of 6.3 m in diameter [8]. The maximum internal water preure i 4.5 MPa. The purpoe of thi application i to imulate the behaviour of the rock ma for the ervice internal preure intalled in the preure tunnel and to compare it with the behaviour oberved during the firt infilling of the hydraulic circuit, which took place between November and December

4 2. Finite difference grid To tudy the hydromechanical behaviour of the Venda Nova II cheme, a egment of the preure tunnel, three acce tunnel and the main powerhoue cavern were repreented embedded into a m 3 rock block (Fig. 2). B A C Figure 2: Schematic of the preure tunnel (A); main powerhoue cavern (B); and acce tunnel (C) The meh wa built uing only brick primitive 1. At firt, the excavation wa created uing FISH function to move the location of the gridpoint for each primitive to fit the tunnel hape and the main cavern. Sixteen primitive were ued to fit the tunnel hape and 59 primitive were ued to fit the main cavern hape. Then, the rock ma urrounding the excavation wa repreented. Thi wa done firt with the brick at the ame level of the tunnel, and then with the brick below and above the tunnel level. The creation of the meh wa thought a a cut-and-fold proce in order to obtain a meh a mooth and regular a poible (Fig. 3). In total 641 brick primitive, 94,352 grid point and 82,254 zone were ued. A better explanation of the meh generation proce can be een in Leitão et al. [9], although ome modification had to be introduced in order to enure the tability of the hydraulic analyi. Figure 3: Grid at tunnel level and main powerhoue cavern 1 Primitive: grid hape of pecific connectivity available in FLAC 3D which can be connected and conformed to create complex three-dimenional geometrie. 277

5 3. Mechanical analyi For the mechanical problem, roller boundary condition were applied on all ide of the domain except the top one, where the weight of the overburden wa applied. The rock ma wa conidered a an elatic material, with elatic modulu E = 30 GPa, Poion ratio ν = 0.15 and unit weight γ = MN/m 3. Although it i alo poible to ue a multilaminated model for the mechanical imulation, it influence wa not conidered relevant for thi tage of the tudy and will be implemented in future work. The analyi wa divided into two tage. In the firt tage, the model wa brought to a pre-excavation tre tate with a vertical tre σ zz equal to the elf weigh, a horizontal tre parallel to the preure tunnel σ xx = 2σ zz and a horizontal tre normal to the preure tunnel σ yy = σ zz. In the econd tage, the tunnel and the cavern were excavated. The mechanical propertie conidered in thi model reulted from a comprehenive tet programme carried out in the zone of the powerhoue cavern during the deign tage. 4. Hydraulic analye Three different hydraulic analye were carried out. In cae 1 and 2 the rock ma wa modelled a a continuou medium, but cae 1 conider the hydromechanical coupling parameter β = 0, i.e. a train independent permeability, wherea cae 2 adopted β = 5,000. An initial permeability coefficient K = 10-8 m/ wa adopted and thi i equivalent to an initial mobility coefficient k o = m 2 /(MPa ec). Thi correpond to permeability value typical for ound granitic rock mae with nearly cloed joint. In cae 3, a joint et wa conidered in order to imulate the main dicontinuity urface found during contruction (Fig. 4). A dip direction and a dip angle of 75º meaured in the global x y z ytem ued in the FLAC 3D model wa adopted. The joint et parameter ued in the computation were the intenity I = 0.5 m -1, the initial aperture E = 200 μm, the normal tiffne k n = 100 MPa, the reidual aperture e re = 5μm and Elliot hydromechanical coupling parameter f E = 1. Additionally, a train independent (β = 0) permeability coefficient K = 10-9 m/ (10 time maller then in cae 1) wa aumed in order to account for the rock ma behaviour excluding thi particular joint et. 80º 80º 72º 70º 58º 75º 66º 80º 80º Figure 4: Main dicontinuity urface 278

6 To determine the boundary condition it wa conidered that eepage wa etablihed from the preure tunnel into the rock ma during the preurization of the tunnel, thu etablihing unconfined flow condition. A water preure of 4.5 MPa wa impoed in the preure tunnel and zero water preure were impoed in all other underground opening. Imperviou boundarie were adopted for all ide of the domain except at the bottom, where a pore preure correponding to an initial poition of the water table at an elevation of 1 m wa conidered. 5. Modelling reult In the hydraulic analye correponding to cae 2 and 3 the permeability tenor wa firt calculated from the reult obtained in the mechanical analye. Fig. 5(a) and 5(b) repreent contour of the global component of the permeability tenor K zz around the preure tunnel, obtained in cae 2 and 3. The purpoe of thee figure i to illutrate the permeability change in the domain in the everal ituation conidered. Contour colour are graded from blue to red (blue i the minimum value and red i the maximum value). In cae 2 the application of Eq. (2) make the vertical permeability value change from the original 10-8 m/ to value that are up to 3 time higher and lower. For cae 3, the conideration of the joint et increae the vertical permeability by everal order of magnitude and the effect of the joint orientation i evident. K zz min = 0.33 x 10-8 m/ec K zz max = 2.96 x 10-8 m/ec K zz min = 0.71 x 10-8 m/ec K zz max = 1.63 x 10-6 m/ec (a) (b) Figure 5: Global component of the permeability tenor K zz contour, (a) cae 2, (b) cae 3 Fig. 6(a), 6(b) and 6(c) illutrate the pore preure ditribution obtained in cae 1, 2 and 3 for the total domain. The free urface i repreented by the line indicated in the cale with a zero pore preure. Zone of the domain with an indicated negative pore preure are outide the hydraulic domain. In cae 1 the free urface ha a uual bell hape. In cae 2, owing to the variability of the permeability, the calculated free urface i not o mooth and the hydraulic domain i maller and ha nearly vertical lateral boundarie. There i a much fater decreae in pore preure around the preure tunnel, while in the ret of the domain the pore preure variation i very mall. In cae 3 all the equal-preure line (including the free urface) have a hape that i much influenced by the orientation of the joint. In thi cae it can be oberved that higher preure reach further downtream and further elevation then in cae

7 (a) (b) (c) Figure 6: Pore preure contour, (a) cae 1, (b) cae 2, (c) cae 3 The pore preure ditribution around the preure tunnel for the three cae are hown in detail in Fig. 7. In the train dependent permeability analyi, cae 2, the pore preure decreae in the radial direction i much fater then in cae 1. Thi reult from the decreaed radial permeabilitie conidered in cae 2, which are a conequence of the increae in the hoop compreive train caued by the tunnel excavation. For cae 3, the large difference between the permeabilitie along the direction of the joint (ubvertical) and normal to the joint i clearly oberved. Table 1 indicate, for the three cae that were tudied, the calculated flow rate into tunnel G4, tunnel G5 and the main acce tunnel. For cae 1 and 2, the value of flow rate into tunnel G5 and the main acce tunnel are negligible and therefore all the water that flow from the preure tunnel i infiltrated into tunnel G4. Thi i the cloet tunnel to the preure tunnel and, a could be expected, function a a large drain in the rock ma and collect nearly all the water. The light decreae in the flow rate from cae 1 to cae 2 i jutified by the effect of the maller radial permeability in the train dependent calculation. Table 1: Flow rate into the acce tunnel Cae Flow rate (litre/ec) G4 G5 Main acce tunnel 1 0,

8 (a) (b) (c) Figure 7: Pore preure contour, (a) cae 1, (b) cae 2, (c) cae 3 In cae 3 the flow rate into the tunnel G4 i approximately 50 time higher than in cae 1 and 2, a a reult of the dominant contribution of the dicontinuity et for the overall hydraulic behaviour of the rock ma. The flow rate into tunnel G5 and into the main acce tunnel are no longer negligible, but are everal order of magnitude maller. 6. Comparion of the calculation reult with the oberved behaviour The firt infilling of the hydraulic circuit of the Venda Nova II hydroelectric cheme wa done in everal tage. Firt, the water wa allowed into the hydraulic circuit from the tailrace tunnel until it reached the level of the downtream reervoir. Then, the infilling continued from uptream, in everal tep. A large number of meaurement wa taken during thi proce in order to control the afety of the underground tructure and the operating condition of the hydraulic circuit. Of relevance for the preent application of the numerical model are the total value of the water infiltration in the underground opening in the vicinity of the preure tunnel. Fig. 8 how the water level in the preure tunnel and the total meaured infiltration in tunnel G4 and G5 during the whole proce of the firt infilling, until they reached tability. 281

9 The meaured value of infiltration in other tunnel and in the powerhoue were negligible when compared with thee two tunnel. Flow rate (liter/ec) Infiltration tunnel G4 Infiltration tunnel G5 Water level Water Level in the preure tunnel (m) 0 01-Nov 16-Nov 01-Dez 16-Dez 31-Dez 15-Jan 30-Jan 200 Figure 8: Evolution of the flow rate into tunnel G4 and G5 during the firt infilling In the firt tage of the firt infilling the value of the water infiltration meaured in tunnel G4 were high and much larger then in tunnel G5. It wa oberved that the water flowed into the tunnel mainly through a number of large conducting dicontinuitie with the orientation repreented in Figure 4. In order to control the water inflow, it wa decided to grout ome or thee dicontinuitie around tunnel G4. Thi reulted in the expected decreae in the water inflow into G4, but in an increae in the water inflow into G5. Thi mean that the effect of main drain, which in the beginning wa being performed by G4, wa partially tranferred to G5 due to the barrier created to the inflow into G4 by the grouting. Having thi in mind, comparion between the value of the meaured infiltration and the flow rate calculated with the numerical model can only be done for the total water infiltration in G4 + G5, ince thi tranfer of flow from G4 to G5 wa not conidered in the model. The total infiltration meaured in tunnel G4 and G5 at the end of the firt infilling wa approximately equal, with a value of around 4 litre/ec, which make a total of 8 litre/ec in the two tunnel. The light flow rate decreae after completion of the firt infilling wa due to grouting work. In cae 3, the total calculated flow rate into thee tunnel wa 9.7 litre/ec, which i very cloe to the meaured flow rate, with a difference of around 20%. In cae 1 and 2, the calculated flow rate are 50 time lower that the meaured one. From the reult obtained it i clear that conideration of the main conductive joint et, in cae 3, wa eential for modelling the hydraulic behaviour of the rock ma. Conideration of thi joint et in the model, with the propertie (orientation, intenity, aperture, tiffne) that were aumed, allowed to calculate flow rate into tunnel G4 and G5, conidered together, which match well the meaured value. On the other hand, when the rock ma wa conidered a an iotropic equivalent continuum, in cae 1, with permeability value typical for ound granitic rock mae, the calculated flow rate were 50 time lower. In other word, in order to calculate flow rate imilar to the meaured one, an iotropic permeability coefficient K = m/ would have to be conidered for the rock ma, which i a clearly large value. In thi application cae, the influence of a train dependent permeability, conidered in cae 2, did not affect much the calculated flow rate. However, it clearly changed the pore preure ditribution and the flow pattern in the rock ma. In a coupled analyi, thi would reult in eepage force different from cae

10 CONCLUSIONS The evaluation of the hydraulic behaviour of an unlined high preure tunnel wa addreed by numerical modelling with FLAC 3D. The implemented formulation relate permeability with train for the continuum. It alo allow conidering the influence of joint et in the hydraulic behaviour by mean of the multilaminated medium concept. Relation between the cloure of the joint under normal tre and it hydraulic propertie were alo implemented. A large meh wa generated to imulate the granitic rock ma where the Venda Nova II hydraulic circuit wa contructed, including a preure tunnel, everal other acce tunnel and the powerhoue. The 3 different hydraulic calculation cae that were imulated correpond to three different way to conider the rock ma permeability: iotropic and train independent in cae 1; train dependent in cae 2; aniotropic uing the multilaminate concept to conider one joint et, with an aperture dependent on the normal tre, in cae 3. Different pore preure ditribution in the domain and flow rate into the opening were obtained in the three cae. The reult were compared with the meaurement obtained during the infilling of the hydraulic circuit. The formulation implemented in cae 3 allowed a reaonable imulation of the flow rate, ince it conidered the dominant role played by a hydraulically conductive joint et on the water infiltration into the tunnel. The work preented in thi paper correpond to the early tage of implementation, within FLAC 3D, of a more complex model of the hydromechanical behaviour of rock mae, uing an iterative procedure between two independent hydraulic and mechanical ub-model and conidering the fracture network of the rock ma uing the multilaminated medium concept. Acknowledgement The permiion by EDP Produção EM to ue the data relative to the Venda Nova II project i acknowledged. Thi reearch i partly funded by the Portuguee Foundation for Science and Technology, under the project POCI/ECM/57495/2004. REFERENCES 1. Rutqvit J., Stephanon O. The role of the hydromechanical coupling in fractured rock engineering. Hydrogeology Journal, 2003; 11: Itaca Conulting Group, Inc. FLAC 3D Fat Lagrangian Analyi of Continua in 3 Dimenion, Ver. 2.1 Uer Manual. Minneapoli, Itaca, Zienkiewicz O.C., Pande G.N. Time-dependent multilaminate model of rock a numerical tudy of deformation and failure of rock mae. Int. J. for Num. and Analyt. Meth. in Geom., 1977; 1: Lama L.N. Contribution to Undertanding the Hydromechanical Behaviour of Preure Tunnel. PhD thei, Univerity of London, U.K., Wei L. Numerical Studie of the Hydro-Mechanical Behaviour of Jointed Rock. PhD thei, Univerity of London, U.K., Elliot G.M., Brown E.T., Boodt P.I., Hudon J.A. Hydromechanical behaviour of joint in the Carnmenelli granite, S.W. England. Proc. Int. Symp. on Fundamental of Rock Joint, Björkliden, 1985; Witherpoon P.A., Wang J.S.Y., Iwai K., Gale J.E. Vality of cubic law for fluid flow in a deformable rock fracture. Water Reource Re., 1980; 16(6): Oliveira M.A., Ribeiro V., Apolinário V., Cota J.A. The Venda Nova II pumped torage cheme. Int. J. on Hydropower & Dam, 2004; 11(5): Leitão N.S., Lama N.L. Modeling of the high preure circuit of the Venda Nova II hydroelectric cheme. Proc. Fourth Int. FLAC Symp. on Numerical Modeling in Geomechanic, Madrid,