rethccouredmeon-owtedstinin a

e anaonsisted rockperlygeologates ouced p

drawdown on the groundwater inow rate and the porewater in 2

Engineering Geology 110 (2010) 3342

Contents lists available at ScienceDirect

Engineering

e lspressure distribution around the tunnel, and this study presents anapproach to take into account these effects.

2. Current Practice

Current engineering practice to estimate groundwater inow rateinto unlined rock tunnels relies on analytical solutions which assumea homogeneous, isotropic porous medium around the tunnel. Themain controlling variables are the location of the groundwater level

ln H a

where, Qin = groundwater inow rate into a unit length of tunnel;a = radius of tunnel; keq = equivalent hydraulic conductivity of asurrounding jointed rock mass; and H = initial hydraulic head fromthe center of tunnel.

It should be noted that Eq. (1) assumes that the groundwater tableremains at the initial level throughout the tunnel excavation, and thegroundwater inow type is relatively vertical into a shallow tunneland radial into a deep tunnel. However, the groundwater rechargeand the rock-mass permeability. Generally, rtests are used to estimate the representaticonductivity of the jointed rock mass for thevariance in the measured packer hydraulic

Corresponding author. Tel.: +1 614 464 4500; fax:E-mail address: orangedreamer@hotmail.com (J. Mo

1 Former Adjunct Faculty, University of Illinois, Urban

0013-7952/$ see front matter 2009 Elsevier B.V. Aldoi:10.1016/j.enggeo.2009.09.002ermeability reduction iney variables discussed inuced groundwater level

proposed by Harr (1962) can be approximately estimated as

Q 2Hkeq 1the vicinity of tunnel (lining-like zone). The kthis paper, are the effect of excavation-ind1. Introduction

Field observations indicate that thcurrent engineering practice are not cing ground water ow into an unlinefactors that these solutions do not profactors include presence of signicantter level drawdown, inadequate estimfrom packer tests, and excavation-indlytical solutions used inntly accurate in estimat-tunnels due to various

take into account. Theseical features, groundwa-f hydraulic conductivity

assumed to reect the hydraulic conductivity distribution along thetunnel alignment (Heuer, 1995, 2005).

The water ow rate into a tunnel as well as the pore-waterpressure distribution in the surrounding homogeneous isotropic rockmass can be approximated using the mirror image tunnel methodproposed by Harr (1962), Goodman et al. (1965), Fernandez (1994).The ow net that develops under steady-state seepage is shown inFig. 1. The inow rate per unit length of tunnel using the approachesults from eld packerve equivalent hydraulicanalytical solutions. Theconductivity values is

above shallow tuexcavation-induthe groundwateroof of tunnel andevelops into thdrawdown is remay be large enoinow rate. Thus

+1 614 464 0588.on).a, Illinois, USA.

l rights reserved.jointsDistinct element methodEffect of Excavation-Induced GroundwateJointed Rock Mass

J. Moon a,, G. Fernandez b,1

a URS Corporation, 277 W. Nationwide Blvd., Columbus, OH, USAb Geotechnical Consultant, 4 College Park Ct., Savoy, IL, USA

a b s t r a c ta r t i c l e i n f o

Article history:Received 7 April 2009Received in revised form 18 September 2009Accepted 23 September 2009Available online 1 October 2009

Keywords:Groundwater level drawdownGroundwater inowHydro-mechanically coupled behavior of

Analytical and empirical mtunnel do not adequately athe ow pattern as well aswater near the tunnel alignavoid a signicant excavatiestimating groundwater inanalytical solutions presennumerical analysis using dicoupled behavior of joints

j ourna l homepage: www.Level Drawdown on Tunnel Inow in a

ods used in current engineering practice for estimating inow rate into ant for the effect of groundwater level drawdown which triggers changes ofuctions of the hydraulic head. When there is no reservoir or a large body ofnt, the groundwater recharge above the tunnel might not be fast enough toinduced water level drawdown. This paper provides analytical methods forrate taking into account the groundwater table drawdown. The proposedhere compare well with eld observations as well as with results fromct element method which can adequately simulate the hydro-mechanicallyrock mass.

2009 Elsevier B.V. All rights reserved.

Geology

evie r.com/ locate /enggeonnels may not be fast enough to avoid a signicantced water level drawdown. Above shallow tunnels,r level drawdown can be large enough to reach thed a lateral steady-state ow instead of vertical owe tunnel. Above deep tunnels, the groundwater levellatively small compared with the tunnel depth butugh to induce a signicant reduction of groundwater, Eq. (1) is not appropriate to estimate groundwater

Fig. 1. Mirror Image Tunnel Method.

34 J. Moon, G. Fernandez / Engineering Geology 110 (2010) 3342inow rate when a large groundwater level drawdown takes place,and the groundwater inow rate should be estimated using modiedmethods that take into account the magnitude and shape ofgroundwater level drawdown trough.

3. Effect of Groundwater Level Drawdown

3.1. Numerical Modeling

The distinct element method (UDEC 3.0) was used in this study toevaluate the effect of the groundwater level drawdown which is notexplicitly taken into consideration in analytical solutions used incurrent engineering practice. A 2-dimensional numerical model usedin this study consists of an assembly of intact rock blocks and a 3 mdiameter tunnel excavated at 30 m to 150 m below the groundsurface. An intact rock block interact with adjacent blocks throughcontacts that are located along two conjugate persistent and equallyspaced joint sets, and the tunnel is intersected by 4 joints as shown inFig. 2. The initial groundwater table is located at 6 meters belowground surface.Fig. 2. NumeriIn the UDEC 3.0 program, blocks are assumed to be impermeableand the groundwater ows only through fractures between imper-meable blocks. The groundwater ow in a joint depends on theaperture of the joint, which is, in turn, affected by the pore waterpressure within the joint (hydro-mechanically coupled). The solutionfor estimating uid ow rate through a joint is based on the classicCubic Law, with corrections for non-parallel wedge-shaped fractures.In the numerical model presented in this study, the joints have aninitial hydraulic aperture of 300 mand initial joint normal stiffness of1.5710-3MPa/m (1.0107psf/ft) which correspond to a relativelyopen, soft joint representative of the range obtained from laboratorytests carried out with various rock types (Alvarez, 1997; Bandis et al.,1983).

Parametric studies with various size models were performed inorder to determine the optimum distance from the tunnel to thevertical and bottom boundaries ensuring that the hydraulic gradientsnear boundaries remain almost nominal. This step is of criticalimportance in the numerical analyses because the size of a model hasa large impact on water inow rates into a tunnel and pore waterpressure distribution around the opening. The water inow ratecal Model.

decreases with the distance of the boundary from the center of tunneland gradually converges to a constant value at the optimum distance.The optimum size of the numerical model was also comparedwith thesize at which the area of the contour of 10% or larger pore waterpressure change remains almost constant. The optimum distance ofboundary from the center of tunnel was nally determined on thebasis of these two criteria.

A free hydraulic boundary condition was applied at the upperboundary of the numerical model simulating dry weather conditions.Wet weather condition that may occur during tunnel excavation andmust impact the groundwater level drawdown and groundwaterinow rate, was not considered in this study. A hydrostatic porewaterpressure was applied below the initial groundwater level on bothvertical boundaries, assuming that the distance of vertical boundaryfrom the center of tunnel was far enough not to interfere with thegroundwater inow rate.

3.2. Reduction of Groundwater Flow into a Tunnel due to GroundwaterLevel Drawdown

The results from the numerical analyses described above arepresented in Fig. 3 that shows the estimated inow rate for severaltunnels excavatedat variousdepthsbelowthewater level. Thenumericalmodel results shown in Fig. 3 are compared with these obtained fromanalytical solutions, Eq. (1), assuming a homogeneous, isotropicmediumwith no hydro-mechanical coupling along the joints andwith a constantgroundwater elevation throughout tunnel excavation.

As indicated in Fig. 3, the inow rate estimated from the numericalmodels remains almost constant at a value of 50 lpm/100 m of tunnelfor all tunnel depths. This behavior reects the considerable effect ofthe groundwater level drawdown as excavation takes place.

On the other hand the results from the analytical solutions using

obtained with the numerical model, for shallow tunnels with 50meters below the ground surface. As the depth of the tunnel increasesthe inow rates obtained from the analytical solutions, Eq. (1),gradually decreases but still remain signicantly larger, 2 to 3 timesthe values obtained from the numerical model. The lower inow ratesestimated with the analytical solution result from the lower rockpermeability measured by the packer tests carried out at tunneldepth, which reect the joint closure as the in-situ stress increases.

The large difference in the tunnel inow rates estimated from thenumerical and analytical solutions using Eq. (1) derives from twomain effects; the groundwater level drawdown during excavation andthe reduction of rock mass permeability in the vicinity of the tunnelinduced by the increase in effective stress (i.e. stress concentrationand pore pressure reduction) around the opening. As indicated inFig. 3, in shallow tunnels the drop in groundwater level has apredominant effect in the inow rate reduction. However, the effect ofthe groundwater level drawdown ameliorates with depth and fordeep tunnels, the impact of the rock mass permeability reductionaround the opening in the inow rates becomes predominant.

3.3. Hydro-Mechanical Behavior of Joints around a Tunnel

An initial high rate of groundwater inow develops withinrelatively short time period after tunnel excavation due to the releaseof water stored in the joints within the vicinity of the tunnel. In thistime period, a signicant drop of porewater pressure with aconcurrent increase of effective normal stress takes place in thevicinity of the tunnel (lining-like zone). The initial high drop ofporewater pressure eventually decreases as the area of inuence isexpanded and groundwater level drawdown increases.

Figs. 4 and 5 show the pore water pressure change with time aftertunnel excavation for openings located at 30 m and 90 m below the

35J. Moon, G. Fernandez / Engineering Geology 110 (2010) 3342Eq. (1) show very large inow rates, about 8 times larger than theseFig. 3. Water Inow Reduction due to Efground surface, respectively. It should be noted that the time, t infect of Drawdown and Lining Effect.

36 J. Moon, G. Fernandez / Engineering Geology 110 (2010) 3342Figs. 4 and 5 is indicative of the hydraulic time step within whichhydraulic conditions are assumed to remain constant. In eachhydraulic time step, a series of mechanical relaxation steps areperformed in order to achieve continuity of ow at each domain andsome adjustments are made to account for changes in ow velocityand direction.

During the short ush ow period, the tunnel excavation affectsthe pore water pressure only in joints in the immediate vicinity of thetunnel excavation as shown in Figs. 4 and 5. Flush ow is mainlygenerated from the stored water in fractures in the vicinity of thetunnel as previously stated. During the bleed-off period (betweenush ow and steady-state ow condition), the groundwater level isinitially lowered within a relatively short horizontal range, and thenthe area of groundwater level drawdown gradually expands bothvertically but mainly horizontally with time until the ow into thetunnel becomes steady-state condition.

The groundwater level drawdown results in a signicant porewater pressure drop as shown in Fig. 6(a), which in turn reduces thehydraulic gradient around the tunnel and consequently decreases theinow rate into the opening. Fig. 6(a) shows the normalizedporewater pressure (steady state condition divided by initial pore-water pressure) distribution along a joint intersecting the tunnel at a

Fig. 4. Normalized Pore Water Distribution (D=30 m) with Respect to Initial Pore Wasteady-state inow condition. Fig. 6(b) shows the effective normalstress on the same joint which increases to about 2.5 to 3.5 times theinitial value in the area immediately around the opening due to theexcavation-induced stress concentration and the reduction of porewater pressure. The increase of joint effective normal stress triggers asignicant joint closure (Fig. 6(c)) within the lining-like zone and awater inow rate reduction.

Fig. 7 shows the relationship between the tunnel inow rate andthe time (hydraulic time steps) elapsed after excavation. In bothtunnel cases, 30 m and 90 m deep, about a 25% reduction of initialinow rate takes place instantly due to the development of the lining-like zone effect. Afterwards, the inow rates gradually decrease due togroundwater level drawdown. Fig. 7 also shows that larger ush owrate, but shorter bleed-off period (time required for inow ratereduction to the steady-state condition), are expected for a shallowtunnel (30 m deep tunnel) compared with the deeper tunnel (90 mdeep tunnel). A relatively fast inow rate reduction is expected in ashallow tunnel as shown in Fig. 7, because the ground above a shallowtunnel is more permeable than a deep tunnel and the groundwaterlevel drawdown propagates fast above the shallow tunnel.

Fig. 8 shows contours of rock joint aperture change induced bytunnel excavation at 30, 90 or 150 m below ground surface. The

ter Pressure Prior to Tunnel Excavation (Kni=1.5710-3MPa/m, aho=300 m).

37J. Moon, G. Fernandez / Engineering Geology 110 (2010) 3342gures show a series of circular contours of relatively large jointclosure within a tunnel-radius distance from the tunnel walls (lining-like zone). Joint closures ranging from 35% (30 m deep tunnel) to 70%(150 m deep tunnel) of the initial joint aperture were estimatedwithin around one tunnel-radius thick annulus zone around thetunnel (lining-like zone). The groundwater level drawdown aftertunnel excavation causes joint closure of 10 20 % of initial aperturein a large area around the tunnel.

4. Estimate of Groundwater Inow Rate into a Tunnel TakingAccount of Groundwater Level Drawdown

4.1. Method 1 (for s/H=1.0)

During a shallow tunnel excavation, the groundwater leveldrawdown reaches the tunnel crown, and the groundwater owpattern into the tunnel is similar to that into a trench (Cording, 2004;

Fig. 5. Normalized Pore Water Distribution (D=90 m) with Respect to Initial Pore WaRaymer, 2005). The groundwater inow rate into a tunnel can beestimated using the trench inow equation shown below

QD Method1 =keq2RzHH2

Rxa2

where, keq = equivalent hydraulic conductivity of the jointed rockmass around a tunnel; Rz=vertical inuence distance of groundwaterlevel drawdown from the initial groundwater level; Rx = horizontalinuence distance of groundwater level drawdown from the center oftunnel; a = tunnel radius; and H = initial hydraulic head above thetunnel springline.

The analytical solution (Eq. (2)) shown above is applicable onlywhen the groundwater level drawdown reaches the tunnel depth(s= H, see Fig. 9). As shown in Figs. 4 and 5 the vertical extend of theinow below the tunnel reaches the distance of about H~2H belowthe invert, where H is the initial hydraulic head above the tunnel

ter Pressure Prior to Tunnel Excavation (Kni=1.5710-3MPa/m, aho=300 m).

38 J. Moon, G. Fernandez / Engineering Geology 110 (2010) 3342springline. On these basis, the authors recommend using a value of2H~3H for the vertical inuence distance, Rz in Eq. (2) to estimate thesteady-state inow rate. If an impermeable barrier is located within a2H~3H distance from the initial groundwater level, the Rz value

Fig. 6. Joint Hydro-Mechanical Condition

Fig. 7. Inow Rates Chshould bemade equal to the distance between the initial groundwaterlevel and the top of impermeable barrier.

As discussed in previous sections, the tunnel in a jointed rock massexperiences groundwater inow reduction due to joint closure in the

s prior and after Tunnel Excavation.

ange with Time.

39J. Moon, G. Fernandez / Engineering Geology 110 (2010) 3342vicinity of tunnel due to porewater pressure drop and stressconcentration (lining-like zone). Therefore, the estimated inowrate using Eq. (2) also needs to be adjusted for considering the lining-like zone effect (Moon, 2007).

4.2. Method 2 (for s/H0.5)

Based on the results obtained from the numerical modelsdescribed above and the review of existing eld observations andmeasurements (Cook and Warren, 1999), the authors proposed the

Fig. 8. Normalized Joint Aperture Contours (Method 2 to estimate inow rates in moderately to deep tunnels, inexcess of 100 m below the groundwater level, where the groundwaterlevel drawdown, s, is moderate and under steady-state ow thedepressed groundwater level is still above the tunnel roof.

Key parameters obtained from numerical models carried out withtunnels excavated at various depths, ranging from 85 m to 150 m, inrocks with soft, open joints are summarized in Table 1. The values inthis table indicate typical values of the ratio of the drawdown, s overthe initial height, H of the water level above spring line ranging from0.4 to 0.16. Field measurements in a tunnel in L.A. with an initial head,

Kni=1.5710-3MPa/m, aho=300 m).

r In

40 J. Moon, G. Fernandez / Engineering Geology 110 (2010) 3342H above the tunnel of about 250 m reported (Cook andWarren, 1999)an excavation induced drawdown, s of about 0.2 of the initial head.Thus, in authors' opinion the results in Table 1 can also be extended torocks with stiffer close joints where the groundwater level draw-downs tend to be smaller.

During the excavation of moderately deep tunnels, H>100 m, thelateral recharge may prevent a signicant groundwater leveldrawdown. Above moderately deep tunnels the slope of the lowered,steady-state groundwater table is relatively at and the ratio of thedrawdown, s over initial hydraulic head, H can be assumed to belower than 0.5. Under these considerations an adjusted mirror imagetunnel method can be applied to estimate groundwater inow rateusing the lowered groundwater level (

H = H s) as shown in Eq. (3)

below. It should be noted that the analytical solution in Eq. (3) alsoneeds to be adjusted to include the permeability reduction effect dueto joint closure in the vicinity of tunnel (lining-like zone effect).

2k H

Fig. 9. Trench WateQD Method2 =eq

ln 2H=a 3

where, keq = equivalent hydraulic conductivity of the jointed rockmass around the tunnel; a = tunnel radius;

H = lowered hydraulic

Table 1Inow Rate Estimate Using Analytical Solutions.

H(m)

s(m)

s/H(m)

Rx(m)

Lining-like ZoneEffect Factor

Inow Rate Estimate

Numerically Measured Mirror Im

FL (Fig. 11) QD Qo

(lpm/100 m) (lpm/100

24 24 1.0 305 0.70 58.8 38485 36 0.42 457 0.58 59.0 183116 35 0.30 549 0.56 47.2 130146 24 0.16 686 0.55 40.5 98head from the tunnel springline; and H= initial hydraulic head fromthe tunnel springline.

A relationship between the drawdown, s over initial hydraulichead ratio, H estimated from the numerical analyses, versus the initialhydraulic head, H above tunnel is shown in Fig. 10. As indicated in thisgure, the magnitude of this ratio gradually decreases with tunneldepth from a value of about 0.5 for 100 m deep tunnels to about aconstant value of about 0.2 for deep tunnels in excess of 200 m. Themagnitude of

H = Hs in Eq. (3) can be estimated from Fig. 10 to

assess the inow rate, QD, for moderate to deep tunnels.As described above the lining-like zone effect should also be

considered in addition to the groundwater level drawdown effect toobtain a reliable estimate of the tunnel inow rate. For this purpose,the relationship between the ratio of tunnel inow, Q L taking intoaccount the lining-like zone effect over the inow rate, QO assuminga homogeneous, isotropic medium and initial hydraulic head, H wasplotted in a function of tunnel depth in Fig. 11. The values of theinow rates Q and Q for various tunnel depths were obtained

ow for Method 1.L O

from Fig. 3. Thus, for any tunnel depth the value of QD estimatedfrom Eq. (3) can be multiplied by the ratio of Q L/QO in Fig. 11 toaccount for the lining-like zone effect and obtained an approximatetunnel inow rate value.

age Tunnel Method Method 1 Method 2

keq FLQD-Method-1 keq FLQD-Method-2

m) (cm/sec) (lpm/100 m) (cm/sec) (lpm/100 m)

2.29E-4 74.5 N/AN/A 2.68E-5 61.8N/A 1.49E-5 51.2N/A 9.29E-6 44.8

Fig. 10. Effect of Groundwater Level Drawdown.

Fig. 11. Effect of Lining-Like Zone.

41J. Moon, G. Fernandez / Engineering Geology 110 (2010) 3342

5. Conclusion

Analytical solutions to estimate tunnel inow rates used in currentengineering practice generally assume a constant groundwater levelthroughout tunnel excavation that overestimates the groundwaterinow rate into the tunnel. Analytical methods need to be modied toincorporate the level of drawdown as well as the correspondingequivalent rock permeability resulting from the drop in pressure aswellas the excavation induced stress concentration around the opening. Thisstudy presents a simple analytical method for estimating groundwaterinow rate into a tunnel considering both groundwater level drawdownand rock mass permeability reductions. This study also presents theeffects of groundwater level drawdown on the hydro-mechanicalbehavior of joints and on the water inow rate into tunnel.

References

Alvarez, T.A., 1997. A Study of the Coupled Hydromechnical Behavior of Jointed RockMasses Around Pressure Tunnels, Ph.D. Thesis, University of Illinois at Urbana-Champaign.

Bandis, S.C., Lumsden, A.C., Barton, N., 1983. Fundamentals of rock joint deformation.Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 20 (6), 249268.

Cook, R.F., Warren, S., 1999. Groundwater control for the Los Angeles Metro Systembeneath the Santa Monica Mountains. Geo-Engineering for Underground Facilities:Geotechnical Special Publication, vol. 90, pp. 8292.

Cording, E.J. (2004) Personal Communication.Fernandez, G., 1994. Behavior of pressure tunnels and guidelines for liner design.

J. Geotech. Eng. ASCE 120 (10), 17681791.Goodman, R., Moye, D., Schalkwyk, A., Javendel, I., 1965. Ground-water inow during

tunnel driving. Eng. Geol. 2 (2), 3956.Harr, M.E., 1962. . Chap. 10 Groundwater and Seepage, pp. 249264.Heuer, R.E., 1995. Estimating rock tunnel water inow. Rapid Excavation and Tunneling

Conference, pp. 4160. Chap. 3.Heuer, R.E., 2005. Estimating rock tunnel water inow-II. Rapid Excavation and

Tunneling Conference, pp. 394407. Chap. 30.Moon, J.-S. (2007) Evaluation and Assessment of Inow Rates in Tunnels Excavated in

Jointed Rock Mass, The University of Illinois at Urbana-Champaign, Doctoral Thesis.Raymer, J.H., 2005. Groundwater inow into hard rock tunnels: A new look at inow

equations. Rapid Excavation and Tunneling Conference, pp. 457468.

42 J. Moon, G. Fernandez / Engineering Geology 110 (2010) 3342

Effect of Excavation-Induced Groundwater Level Drawdown on Tunnel Inflow in a Jointed Rock MassIntroductionCurrent PracticeEffect of Groundwater Level DrawdownNumerical ModelingReduction of Groundwater Flow into a Tunnel due to Groundwater Level DrawdownHydro-Mechanical Behavior of Joints around a Tunnel

Estimate of Groundwater Inflow Rate into a Tunnel Taking Account of Groundwater Level DrawdownMethod 1 (for s/H=1.0)Method 2 (for s/H0.5)

ConclusionReferences