Grout Spread and Leakage

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    Numerical modelling of grout spread and leakage into a tunnel in hard rock A case study

    Lisa Hernqvist & sa Fransson

    Division of GeoEngineering, Chalmers University of Technology, Gteborg, Sweden

    Patrik Vidstrand

    Bergab Consulting Geologists, Stampgatan, Gteborg, Sweden

    SYNOPSIS: During tunnel construction in fractured rock, a detailed hydrogeological description of therock is of importance for successful grouting design and estimating leakage thereof. A commonsimplification has been followed to assume the fractures as independent parallel plates; a 2D stackedmodel. However, analytical inflow predictions based on this model have not been found to be sufficientlyaccurate. The aim of this work is to study whether a more realistic 3D fracture model, viewing the fracture

    system as a network of connected fractures, could better explain the sealing effects of grout compared tothe 2D model.

    Inflow into a tunnel and grout penetration have been studied in a three dimensional fracture networkmodel, using the numerical groundwater flow code DarcyTools, version 3.1.

    Ideas developed from this study were then applied to a real case tunnel. Deviations from the analyticalprediction of inflow into the grouted tunnel can be understood, in part at least, by taking the connectivity ofthe rock volume into account.

    The results further enhance the importance of firm geological and hydrogeological characterization of therock mass that needs to be sealed with grout in order to reach at tolerable inflow rate of groundwater.

    1 INTRODUCTIONWhen planning the construction of a tunnel, there

    are limitations on how much water the tunnel isallowed to leak. These limits are related both to thefunction of the tunnel and protecting theenvironment from harmful draw-down conditions ofthe groundwater table. A common method forreducing tunnel leakage is grouting.

    When the local rock mass surrounding theenvisaged tunnel is grouted using the pre-groutingtechniques, as illustrated in Figure 1, the idea is forthe grout to fill the fractures the tunnel willintersect. The grout will spread differently into thefracture network depending on the fracturefrequency and anisotropy and the fracture apertures.

    Water pressure tests have commonly been usedto estimate the Lugeon value [1], where 1 Lugeon is

    a water take of 1 liter per minute per 1 m boreholeat a pressure of 1 MPa. The Lugeon value does not,however, provide information about the fracturestransmitting the water. Many fine fractures, each

    Figure 1. A tunnel under construction using the pre-grouting technique. A fan of boreholes is drilled at thetunnel face. These holes are injected with grout to producea grouted zone, the aim being that it will act as a shield toreduce water movement within the rock volumesurrounding the planned tunnel. The tunnel is thenexcavated into the grouted rock volume.

    World Tunnel Congress 2008 - Underground Facilities for Better Environment and Safety - India

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    leaking a small amount of water, may yield thesame Lugeon value as one single wide fracture [2].

    In attempting to reduce leakage it is very helpful todistinguish between such different situations, as thelarge number of fine fractures may be too small to

    be groutable, while one fracture of a larger aperturemay be easier to seal. A parameter that gives thisinformation is the individual fracture transmissivity,T, which is a measure of a fractures ability totransmit a fluid. It is the product of the hydraulicconductivity, K, and the fracture aperture, b so thatT = b K[3].

    When constructing a tunnel in fractured rock,one purpose of the pre-investigations is to get toknow the fracture system of the rock volume. Therock may have few or many fractures, indicated bythe fracture frequency. The fracture orientations

    may range from being isotropically, randomly,oriented, to being collected in a few dominatingsets. If there are dominating fracture sets, thefracture transmissivities/apertures may be related tothe orientation, so that fractures belonging to oneset are pervious, while other sets are comparativelydry. This is determined by the degree of anisotropy.An important cause is the stress conditions in therock.

    The inflow into the grouted tunnel can bepredicted using an inflow equation (Equation 1) [4,

    5] which is based on knowledge of the fractures onthe basis of the tunnel is expected to intersect. The

    input parameters are explained in Table 1. Thenecessary input is aperture and transmissivity foreach fracture along the tunnel length. The hydraulicaperture, calculated from the transmissivity T viathe cubic law ([6, 7]) is used as a measure of thefracture aperture. Even though it is not an accuratedescription of a real fracture, each fracture isassumed to have a constant aperture. The aperture isimportant not only because it limits how muchwater can flow through it, but also because it limitsthe groutability of a fracture. Firstly, because groutwill penetrate further in fractures with largeapertures than in small ones. Secondly, becausecement grouts, which are common in tunnelconstructions, contain grains that are unable to

    penetrate a fracture if it is too narrow. This isdetermined by evaluating grouts penetrability.

    Knowing which fracture apertures a certaingrout is assumed to be able to penetrate and seal,the transmissivities of the remaining, ungroutedfractures are summarized and an inflow is thencalculated. This can be a very useful tool in

    predicting whether a grout will seal the rock to alevel acceptable for the current tunnel project orwhether a grout with a better penetration/finer grainsize needs to be used.

    Figure 2. A tunnel surrounded by a grouted zone, showing some of the parameters of Equation1. The tunnel length L is not visible in the picture.

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    +

    +

    +

    =

    tgrt

    gr

    r

    t

    T

    T

    r

    H

    LHT

    q1ln1

    2ln

    /2

    0

    0(1)

    Table 1. The input parameters for Equation 1

    qgr The inflow into a grouted tunnel m3/s

    per mT0 T0 = Tn; the transmissivity of the

    ungrouted rock volume surrounding theenvisaged tunnel (n is the number ofintersecting fractures)

    m2/s

    Tgr The transmissivity of the grouted rockvolume surrounding the tunnel, aftersealing fractures larger than a certainaperture

    m2/s

    H The resting groundwater head thedistance to the ground surface m

    rt The tunnel radius mL The length of the tunnel mt The thickness of the injected zone

    surrounding the tunnelm

    The skin factor, describing local effectsof closing of fractures induced by theimmediate presence of the tunnel, suchas increased stresses, aeration andchemical precipitation.

    -

    However, the equation has sometimes beenfound to overestimate the inflow into the tunnel.One aim of this work is to try to understand some ofthe reasons for this, and how this overestimation

    may be related to the properties of the fracturenetwork. For this purpose, two scales of the

    problem are identified and analyzed in this work.Firstly, the situation in the grouted part of the rockvolume close to the tunnel, described by Tgr, isconsidered. Secondly, the situation further away inthe rock not reached by the grouting, described byT0, is considered. T0 and Tgr are shown in Figure 2and Table 1.

    1.1 The Grouted Rock Volume, Tgr

    Is it possible to show in a simple case that a 3Dapproach gives a better representation of the rockvolume than a stacked 2D approach? With the 2Dapproach it is assumed that all fractures are paralleland independent of each other and that the totaltransmissivity along a borehole is the sum of eachfracture transmissivity. This is analogous to theassumptions used for the inflow prediction

    equation, Equation 1. The 3D approach allowsfractures to have different orientations so that they

    intersect, allowing water as well as grout to spreadfrom one fracture to another. Consequently, theflow in such fractures is not independent.

    Two aspects were studied: 1) the inflow ofwater into a tunnel in ungrouted rock, and 2) thegrout penetration in the fractures.

    The analytical solution of the 2D approach hasbeen found to overestimate the inflow into manytunnels; the TASQ tunnel used as a case study inthis work being one such case [8]. One hypothesiswas that the tendency of the inflow predictionequation to overestimate the inflow may, at least insome rock volumes, have something to do with the3D properties of the fracture networks, which arenot considered in the equation. The idea is that the

    connectivity of the fracture network is ofimportance. Large fractures may supply smallerfractures with water. At depth, some of the narrowfractures may yield problematic amounts of water,although this can be difficult to handle using acement grout for which there is a lower limit onhow small the fractures to be grouted can be. Ahypothesis was that the flow into these finefractures can be reduced if a large (=groutable)intersecting fracture, which supplies the finefractures with water, is sealed by grouting.

    1.2 The Ungrouted Rock Volume Further Away, T0

    Surrounding the tunnel and the grouted rock is arock volume which is not reached by grout. This is

    put into the inflow prediction equation as theungrouted transmissivity T0 in the numerator. It isdebated how this value should be calculated.Sometimes the value of the ungrouted tunnel rockvolume has been used although it should perhapsdescribe the properties of the rock farther awayrather than the grouted zone. It should be differentdepending on the properties of the fracture network.If, for instance, there are fractures in many differentorientations and the transmissivity distribution isfairly even across the orientations, then the 3Dnetwork is relatively well connected and T0 should

    be accordingly high. If, on the other hand, there are

    only two or three dominating sets of fractureorientation, and if one of these is far moretransmissive than the other, then this may result in

    poor connectivity between different parts of therock volume, resulting in a low T0. Fracturefrequency is also of importance, since a high

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    fracture frequency generally means a betterconnected fracture network and hence a higher T0

    than with a low fracture frequency.

    2 MATERIALS AND METHOD

    2.1 The Numerical Model

    The numerical modeling was performed usingDarcyTools, version 3.1 [9]. This is a computercode for simulation of flow of groundwater in

    porous media such as soil and fractured media suchas fractured rock. DarcyTools uses an unstructuredCartesian grid. The water flow is based on theconcepts of conservation of mass and heat and onDarcian flow. Since April 2008 the code includes agrouting module to simulate grout injection in

    fracture networks [10]. The grouting model hasbeen validated on several cases in order todemonstrate its capacity to solve grout injectionunder the Darcy assumption. The grout can bemodeled as a Newtonian fluid or a Bingham fluid.In this work, the Bingham grouting model waschosen, since it applies to the cement grout used inthe tunnel used as a case study. DarcyTools models

    both the flow of grout and the groundwater.Grout penetration has been studied by many

    others. Jansson [11] describes grouting of 1Dchannels into pipes of different thickness,resembling flow in a fracture with pronouncedchannel flow. It can be seen from his results thatwhen grout reaches an intersection and continues to

    penetrate into channels of different sizes, the groutpenetrates most into the largest channels and least in

    the smallest ones. The pressure also has animportant effect as grout cannot penetrate far into a

    fracture which already has grout coming in from theother direction. Eriksson [12] has modeled groutflow in a fracture of varying aperture field using anorthogonal network of conductive elements(channels) of varying apertures. Shuttle et al [13]have simulated grouting into a fracture network,using an approach where grout penetration islimited by an available amount of grout and of amaximum depth of grout penetration. We do notknow about any previous numerical models elsethan DarcyTools using equations for both thegroundwater and the grout flow in fracturenetworks.

    2.2 The Conceptual Box Model

    To explore the effects originating from the 3Dfracture network, a conceptual box model with threefractures, one grouting borehole and one tunnel wasmodeled, as shown in Figure 3. The tunnel in themodel is not intended to resemble the case studytunnel; it is smaller, has a different tunnel contourand it only has one grouting borehole. The domainis 12 m long in the x-direction and 10 m long in they- and z-directions. The fractures are simplified intorectangles of constant aperture within each fracture,and they are perpendicular to the z-plane (the viewin Figure 3). For this box, fracture apertures andgroundwater pressure relevant in the TASQ tunnelrock volume were chosen. The pressure at the y-

    and z-planes (the planes parallel to the borehole)was kept constant at 10 bar (106 Pa). The fracture

    Figure 3. The conceptual model of the grout penetration and inflow study. The 2D-version with stacked

    parallel fractures to the left and the 3D network to the right. The fractures arenamed after the position of their intersection with the borehole.

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    apertures were chosen to resemble the largest, thesecond largest and the fifth largest fractures found

    along the TASQ tunnel: 130 m, 100 m and 70m.

    The modeling was performed in two steps:Step 1: Inflow into the ungrouted tunnel. Thetunnel, approximately cylindrical and with a radiusof 1.25 m, is removed from the rock volume. Theinflow of ground water into the tunnel, which waskept at atmospheric pressure, was modeled. Step 2:Grout penetration. Here, the tunnel was ignored.Grout was injected into the fractures through thegrouting borehole using a grouting pressure of 10

    bar (106 Pa) above the ground water pressure.The set-ups presented are shown in Table 2.

    Table 2: An overview of the four set-ups of the three

    fracture box model presented in this work. In each 2D-3D-pair of set-ups the same apertures are used; the differencebeing the orientation of the middle fracture, which isillustrated in Figure 3.

    Fracture apertures: 2Dmodels

    3Dmodels

    a x5: 70 mx6 / x6_rotated: 130 mx7: 100 m

    2Da 3Da

    b x5_short; The fracture wassmaller. It started at the

    border, reached the tunnelbut not the groutingborehole: 100 mx6 / x6_rotated: 130 m

    x7: 70 m

    2Db 3Db

    2.3 The Case Study

    The tunnel chosen for the case study is the TASQtunnel. It is part of the sp Hard Rock Laboratory,managed by SKB (Swedish Nuclear Fuel and WasteManagement Co), in Oskarshamn on the east coastof Sweden, Figure 4. The tunnel is also sometimescalled APSE as it was constructed for the spPillar Stability Experiment. The tunnel strikesapproximately NE-SW, is 70 m long, practicallyhorizontal and located at 450 m depth in fractured,granitic rock. The tunnel was constructed in 2003.

    There is an unusually good collection of

    hydrogeological data from the construction of theTASQ tunnel [16]. The data used for the study arepositions of and inflows into fractures as measuredin a number of boreholes. The inflows have beentransformed into transmissivities, using the currenthydraulic head 343 m water column. Grouting was

    done in two fans at the predicted wet part of thetunnel. A cement grout was used. Studies of the

    grouted section of the tunnel indicated that the groutsuccessfully sealed fractures with hydraulicapertures larger than 50 m, while smaller fractureswere not sealed [8].

    2.4 Analytical solutions

    The inflow into a grouted tunnel can be predictedusing Equation 1, based on which fractures are

    believed to be successfully sealed by the grout. Theequation assumes all fractures to be independent,which means that they are considered parallel andnot connected through a fracture network. These arethe same assumptions as for the 2D conceptual boxmodel in this work.

    3. RESULTS AND DISCUSSION

    3.1 The conceptual box model

    The results of Step 1, the inflow into the tunnelbefore grouting, are presented in Table 3. It is seenthat the inflow in the ungrouted models differ verylittle within each pair of 2D-3D models(approximately 2%).

    Table 3. The tunnel inflows before grouting Qpre ,for the presented models.

    Fracture apertures: 2D 3D

    a x5: 70 mx6 / x6_rotated: 130 mx7: 100 m

    Qpre =742l/min

    Qpre =728l/min

    b x5_short; The fracture wassmaller. It started at the

    border, reached the tunnel butnot the grouting borehole: 100mx6 / x6_rotated: 130 mx7: 70 m

    Qpre =607l/min

    Qpre =595l/min

    The grout penetration for the models isillustrated in Figure and 6. The tunnel is shown inthe figures to facilitate a discussion on inflow intothe grouted tunnel, even though it was not thereduring the grouting modeling. High groutconcentration is marked in white (in the grouting

    borehole as well as in the fractures), diluted grout ismarked in gray while the ungrouted parts of thefractures remain black. For the sake of simplicity it

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    may be assumed that in the white parts the fracturesare sealed, in the gray parts the inflow is reducedand in the black parts the inflow is unaffected by thegrout. For the sake of clarity, the apertures of thefractures are represented by different linethicknesses. This is, however, not true to the scaleof the figures. It can be clearly seen that the grouthas penetrated most into the widest fracture andleast into the finest fracture.

    It can be seen in Figure 5 that the 2Da tunnelmodel will leak at the fine fracture with least grout

    penetration. In the 3Da model, however, grout has

    spread from the thick fracture into the fine one,resulting in reduced inflow into the grouted tunnelfrom the fine fracture. If the fractures in the realrock resemble the 3D set-up, then this is oneexplanation for why Equation 1, using the 2Dassumptions, yields an overestimation of inflow intothe grouted tunnel.

    It is likely that some fractures which are notintersected by the grouting boreholes are stillintersected by the tunnel. Such a case is illustrated

    by the 2/3Db models illustrated in Figure 6. If therock looks like the 2Db model, this short fracturewill leak water into the tunnel. If, on the other hand,it is connected to grouted fractures as in the 3Dbmodel, then this fracture will be sealed to some extent.

    The models presented are examples of howgrouting a large fracture may also reduce the flowin smaller, connected fractures. There may befractures too fine to be groutable connected to a

    large fracture. These would not be expected to besealed, using Equation 1. If the large fracture isgrouted where it intersects such fine fractures, thefine ones may thereby be more or less cut off fromthe flow network and hence leak less water into thetunnel than predicted.

    Figure 4. The location of the sp Hard Rock Laboratory (sp HRL) in Sweden (left), and the position of theTASQ tunnel within SP HRL (right). (Pictures modified from [14] and from [15].)

    Figure 5. Grout penetration for 2Da and 3Da

    The TASQ

    tunnel

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    3.2 The Case Study

    The fracture network in the TASQ rock volume isquite anisotropic, as illustrated in the stereo plot inFigure 7. The data comes from a cored boreholedrilled before construction, parallel to and next tothe tunnel. The flow was measured in 3 m sections.Five of these sections had inflows. The fracturesfound in each of these sections are marked in thestereo plot with a separate symbol explained in thefigure. Fractures found in the dry sections aremarked by unfilled circles. Looking at the plot, itcan be seen that the fractures in the most flowingsection are all approximately vertical andapproximately perpendicular to the tunnelorientation. The fractures of the other flowingsections behave similarly. There are also a fair

    number of fractures with a more or less horizontalorientation and it can be seen that all of thesebelong to non-flowing sections of the borehole.Interpreting the facts seen in the stereo plot into adescription of the fracture network, it seems as ifthere is a dominant direction of wet fractures andthat other fracture directions which could connectthese conductive fractures do not do this. Thismeans that the anisotropy of the rock volume islarge.

    The fracture frequency at TASQ isapproximately two fractures per meter.

    For the TASQ inflow prediction usingEquation 1 fractures down to 50 m were assumedto be sealed based on the study of the grouted tunnel

    section [8]. Then the calculated predicted inflowwas Qgr= 20 l/min for the full length; with 2Dassumptions built into the equation. The measuredleakage, originating from the real 3D fracturenetwork, into the TASQ tunnel wasQmeasured= 5 l/min over the full tunnel length. The

    prediction was thus four times too large.There are a number of factors at TASQ which

    point towards the interpretation that there is a large,highly conductive backbone fracture just barelywithin reach of the grouting boreholes. It seemsreasonable that sealing this large fracture hasreduced inflow to the fractures it intersects, evenwhen these are too fine for cement grout to enter.Hence, this could be an explanation for theoverestimation of inflow of the 2D analytical

    prediction, since the flow would in reality bereduced in fine fractures not considered groutableusing the equation. And there are several other facts

    that can be interpreted as pointing towards thisexplanation [16].

    Firstly, several holes gave an unexpectedlylarge inflow compared to the interpretation ofnatural inflow tests of a long cored borehole parallelto the tunnel, drilled and investigated beforetunneling. Natural inflow tests give an estimation ofthe local hydraulic properties; the apertures offractures in the region where they are intersected bythe borehole. Two probe boreholes drilled andinvestigated during tunneling gave anapproximately 15-fold larger inflow than wasexpected for these sections. Evaluations of pressure

    build-up tests (PBT) of these two probe holes gaveapproximately 20-fold higher estimations of thetransmissivities. PBTs describe global hydraulic

    properties, which means parts of the fracture

    network out of the reach of natural inflow tests.Evaluation of a PBT of the first long cored boreholealso indicated a large structure of the same size. Afew of the grouting boreholes also gave a muchhigher inflow than predicted on the basis of theevaluation of natural inflow of the first long cored

    borehole; which could be a result of these groutingholes intersecting the large fracture captured by thePBTs. These facts indicate that the first long cored

    borehole intersected relatively narrow fractures, ornarrow parts of larger fractures, while there was atleast one much more conductive fracture at theoutskirts of the grouting boreholes, which was latersealed.

    Secondly, fracture mapping of the TASQtunnel shows traces of a conductive fracture in theroof of the tunnel at the location of theseunexpectedly high inflows. The grouting boreholesmay have intersected this fracture. The groutingseems to have sealed the rock volume successfully,which can be explained by the larger fracture beinggrouted directly or via connecting fractures.

    Thirdly, other boreholes within sp HRLwere monitored using a hydro-monitoring system(HMS) during the different steps of the constructionof the TASQ tunnel. There were pressure drops inthree of these holes, not very close to the TASQtunnel, directly related to the drilling of one probe

    borehole and also during the drilling of some of the

    grouting holes in one of the grouting fans. Ittherefore seems as if they are all connected via alarge fracture.

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    Figure 6. Grout penetration for 2Db and 3Db

    49.2 L/min, 48-51 m , 7 natural fractures

    11 L/min, 51-54 m , 4 natural fractures

    9 L/min, 57-60 m , 5 natural fractures

    5.8 L/min, 45-48 m , 5 natural fractures

    5 L/min, 63-66 m , 18 natural fractures

    0 L/min

    Figure 7. A stereo plot for the natural fractures along a cored borehole directly beside the TASQ tunnel. Different markers areused for fractures depending on the size of the inflow in the current section. From [17]. The tunnel

    strikes approximately NE-SW, marked by the dashed line

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    4 CONCLUSIONS

    The numerical modeling tool DarcyTools can beused to simulate both water flow and grout spreadin simple fracture networks.

    It has been shown that grout spread betweenconnected fractures in a 3D fracture network mayincrease the sealing effect of the grouting comparedto what would be predicted if the fractures wereassumed parallel and independent, 2D. A largefracture has the potential to spread grout further intothe network of connecting fractures than a finefracture.

    It is our interpretation that for the TASQ tunnelcase study larger fractures being grouted directly orvia connecting fractures is part of the explanationfor why the inflow into the grouted tunnel was

    lower than predicted. The grout penetrated a largebackbone fracture, which was the main channelfor water flow. This fracture was the core supplyingmany finer, connected fractures with water. Sealingit led to a reduction in or termination of the flow insome of these fractures, even when they hadapertures that were too small to be groutable.

    It seems clear that the connectivity of thefracture network is a critical factor and anisotropyand fracture frequency are two importantingredients. The degree to which this helps explainoverestimations of inflow into grouted tunnels usingEquation 1 should be explored further.

    ACKNOWLEDGEMENTS

    The grouting model, included in DarcyTools, wasdeveloped by Michel Ferry (MFRDC, Orvault,France). DarcyTools was developed by MichelFerry and Urban Svensson (CFA AB, Karlskrona,Sweden) and this work was financed by SKB AB(Swedish Nuclear Waste Management CompanyAB). The work described in this paper was alsofinanced by SKB AB.

    REFERENCES

    1. Kutzner, C., Grouting of Rock and Soil. 1996: A. A.Balkema, Rotterdam.

    2. Lombardi, G. Grouting of rock masses. inGeotechnical Special Publication. 2003. NewOrleans, LA.

    3. Fetter, C.W.,Applied Hydrogeology. Third ed. 1994,New Jersey: Prentice Hall.

    4. Hawkins, M. A Note on the Skin Effect. in AIME(1956) 207. 1956.

    5. Gustafson, G. and J. Claesson, Steering Parametersfor Rock Grouting. Rock Mechanics and MiningSciences. In preparation, 2004.

    6. Zimmerman, R.W. and G.S. Bodvarsson, Hydraulicconductivity of rock fractures. Transport in PorousMedia, 1996. 23(1): p. 1-30.

    7. Snow, D.T., Rock fracture spacings, openings, andporosities. Journal of the Soil Mechanics andFoundation Division, 1968. 94: p. 73-91.

    8. Hernqvist, L., et al.,Analyses of the grouting resultsfor a section of the APSE tunnel at sp Hard RockLaboratory. International Journal of RockMechanics and Mining Sciences, 2008.

    9. Svensson, U., H.-O. Kuylenstierna, and M. Ferry,DarcyTools version 3.1 - Concepts, Methods,Equations and Demo Simulations. Third Draft. 2008.

    10. Ferry, M., DarcyTools Grouting model. 2008, Inpreparation: Orvault, France.

    11. Jansson, T., Calculation Models for Estimation ofGrout Take in Hard Jointed Rock, in Civil and

    Environmental Engineering. 1998, Royal Institute ofTechnology: Stockholm.

    12. Eriksson, M., Prediction of Grout Spread andSealing Effect: A Probabilistic Approach. 2002,Royal Institute of Technology: Stockholm.

    13. Shuttle, D.A. and E. Glynn. Grout curtaineffectiveness in fractured rock by the discrete feature

    network approach. in Geotechnical SpecialPublication. 2003. New Orleans, LA.

    14. Rhn, I., et al.,sp HRL Geoscientific evaluation1997/2. Results from pre-investigations and detailedsite characterization. Summary report. 1997:Stockholm.

    15. SKB,Illustrator: Jan Rojmar.

    16. Emmelin, A., M. Eriksson, and . Fransson,Characterisation, design and execution of twogrouting fans at 450 m level, sp HRL. 2004,Swedish Nuclear Fuel and Waste Management Co.:Stockholm.

    17. Fransson, ., Development and verification of

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    BIOGRAPHICAL DETAILS OF THE AUTHORS

    Lisa Hernqvist graduated inEnvironmental Engineering fromChalmers University of Technology inGothenburg, Sweden, in 1994. She has

    been a PhD student at the sameuniversity since 2005 in theEngineering Geology Research Groupat the Division of GeoEngineering,

    Department of Civil and Environmental Engineering. Sheis conducting research on characterizing fracture networksin rock for grouting purposes.

    sa Fransson graduated in CivilEngineering from Chalmers Universityof Technology in Gothenburg,Sweden. In 2001, she obtained a Ph.D.in Engineering Geology at the same

    university. From 2001 to 2004 sheworked both at the university andfor VIAK Consulting Engineers. From

    2004 to present she has been an assistant professor at theDivision of GeoEngineering, Chalmers University of

    Technology.

    Patrik Vidstrand graduated in CivilEngineering from Chalmers Universityof Technology in 1995. He has been aresearch fellow at the same universitysince 1995 with a focus on conceptualand numerical modeling of

    palaeohydrogeology and long-termhydrogeology scenarios. In 1999,

    Patrik visited the University of Edinburgh as a guestresearcher. Since 2000 he has been a full-time consultantin engineering geology and hydrogeological research anddevelopment for agencies such as SKB and the Swedishroad- and rail administrations. Since 2006, Patrik has beenhead of the hydrogeology section at Bergab ConsultingGeologists in Gothenburg, Sweden.