Hydrogeology of the vicinity of Homestake mine, South ...Hydrogeology of the vicinity of Homestake...

Hydrogeology of the vicinity of Homestake mine, SouthDakota, USA

Larry C. Murdoch & Leonid N. Germanovich &

Herb Wang & T. C. Onstott & Derek Elsworth &

Larry Stetler & David Boutt

Abstract The former Homestake mine in South Dakota(USA) cuts fractured metamorphic rock over a regionseveral km2 in plan, and plunges to the SE to a depth of2.4 km. Numerical simulations of the development and

dewatering of the mine workings are based on idealizingthe mine-workings system as two overlapping continua,one representing the open drifts and the other representingthe host rock with hydrologic properties that vary witheffective stress. Equating macroscopic hydrologic proper-ties with characteristics of deformable fractures allows thenumber of parameters to be reduced, and it provides aphysically based justi!cation for changes in properties withdepth. The simulations explain important observations,including the co-existence of shallow and deep "owsystems, the total dewatering "ow rate, the spatialdistribution of in-"ow, and the magnitude of porosity inthe mine workings. The analysis indicates that a deep "owsystem induced by ~125 years of mining is contained withina surface-truncated ellipsoid roughly 8 km by 4 km in planview and 5.5 km deep with its long-axis aligned to the strikeof the workings. Groundwater "ow into the southern side ofthe workings is characterized by short travel times fromthe ground surface, whereas "ow into the northern side andat depth consists of old water removed from storage.

Keywords Groundwater "ow . Subsidence . Crystallinerocks . Fractured rocks . USA

Introduction

The Homestake mine in South Dakota (USA) was activefor 125 years and became one of the deepest and mostproductive gold mines in North America (Mitchell 2009).The last ore was hauled up the access shafts in 2002 andsince then the mine workings have been evaluated as a sitefor scienti!c experiments in physics, hydrogeology,microbiology, engineering and other disciplines. The siteevaluation was supported by the National Science Foun-dation as they developed plans for the Deep UndergroundScience and Engineering Laboratory (DUSEL). Planningof experiments for DUSEL has been on-going by thescienti!c community for the past decade.

An exploration program associated with mining oper-ations resulted in detailed understanding of the geology,particularly the geologic units containing gold (Caddey etal. 1991). However, compared to aspects of the rockstructure, stratigraphy, and petrology, the hydrogeology of

Received: 2 November 2010 /Accepted: 24 July 2011Published online: 11 October 2011

* Springer-Verlag 2011

L. C. Murdoch ())Environmental Engineering and Earth Science Department,Clemson University,340 Brackett Hall, Clemson, SC 29631, USAe-mail: [email protected].: +1-864-6562597

L. N. GermanovichSchool of Civil and Environmental Engineering,Georgia Institute of Technology,Mason 212 Building, Atlanta, GA 30332, USAe-mail: [email protected]

H. WangDepartment of Geosciences, A254 Weeks Hall,University of Wisconsin, Madison,1215 West Dayton Street, Madison, WI 53706-1692, USAe-mail: [email protected]

T. C. OnstottDepartment of Geosciences,Princeton University, Guyot Hall, Princeton, NJ 08544, USAe-mail: [email protected]

D. ElsworthDepartment of Geosciences,Penn State University,231 Hosler Building, University Park, PA 16802-5000, USAe-mail: [email protected]

L. StetlerGeology and Geological Engineering Department,South Dakota School of Mines,501 E. St. Joseph St, Rapid City, SD 57701, USAe-mail: [email protected]

D. BouttDepartment of Geosciences,University of Massachusetts-Amherst,248 Morrill IV-South, 611 North Pleasant Street, Amherst, MA01003-929, USAe-mail: [email protected]

Hydrogeology Journal (2012) 20: 27–43 DOI 10.1007/s10040-011-0773-7

the Homestake mine and encompassing region is rela-tively poorly known. The lack of hydrogeologic informa-tion has hampered the process of planning experiments forDUSEL and was a primary motivation for this inves-tigation. The future of DUSEL is unclear as of thiswriting, so the site will be referred to in the followingpages as the former Homestake mine.

The objective of this paper is to characterize thehydrogeologic parameters in the vicinity of the formerHomestake mine by modeling extant data derived fromthe effects of historical operations at the mine. Further-more, implications of this model are presented regardingthe interactions between the shallow local hydrologic "owsystems and the deeper "ow systems affected by themined-out cavities.

Setting

The former Homestake gold mine is near the center of theLead dome, a structural high roughly 20 km in diameter atthe northern end of the Black Hills in western SouthDakota. Both the Lead dome and the Black Hills to thesouth expose Proterozoic metamorphic rocks, which aredraped by Paleozoic sediments and cut by Laramide-ageigneous intrusions (Dewitt et al. 1986).

GeologyRocks encompassing and enveloping the former mine area compositionally diverse package of phyllite and schistthat was metamorphosed from greenschist to amphibolitefacies and highly deformed during the Proterozoic (Fig. 1;Caddey et al. 1990; 1991). The general structure consistsof the Lead anticlinorium and synclinorium, and thePoorman anticlinorium to the west. The longest wave-length of these folds is of the order of kilometers, and theiraxes plunge 35–50° to the southeast. Rock units withinthese folds are themselves highly folded at scales rangingfrom centimeters to 100s of meters. These secondary folds

are so tight that their amplitudes can be many timesgreater than their wavelengths and their limbs areessentially parallel (Fig. 1). For example, the amplitudeof the 15-Ledge fold is more than 1 km, but itswavelength is less than 100 m in the cross-section shownin Caddey et al. (1991, !g. J5).

Regional foliation is roughly parallel to the axial planesof the folds, with a strike approximately N20W and asteep dip to the NE (Rahn and Roggenthen 2002; Fig. 1).Ductile shear zones are also oriented roughly parallel tothe regional foliation (Caddey et al. 1991). Despite thecomplex folds in the vicinity of the Homestake mine, theorientation of the foliation is remarkably uniform acrossthe region.

Gold ore occurred in the hinges of secondary synforms,which plunge !40° to the SE approximately parallel to thestrike of foliation (Caddey et al. 1991). An open pit wasdug to recover shallow ores (Fig. 2) and the current townof Lead, SD inhabits its southern side. Miners followedthis ore trend to depth, so the underground mine workings

Fig. 1 Steeply dipping bedding and schistosity in metamorphicrocks near Lead, South Dakota, USA

Fig. 2 Cross-section and map of tunnels and shafts comprising theworkings at the former Homestake mine. Cross section based onDavis et al. (2009)

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at deeper levels are consistently offset to the southeastfrom the levels above (Fig. 2).

The mineThe mine consists of several hundreds of kilometers oftunnels and stopes contained within a volume of severalkm3. The plan view area of the workings ranges overseveral km2 at any given level and it extends to a depth of2.4 km as an irregular, inclined column plunging at !40°to the SE (Fig. 2). Individual levels of the mine are spaced30 m apart in the upper levels and 45 m apart below300 m. The regions between the horizontal workings arecut by myriad boreholes and stopes.

The mine evolved over approximately 125 years(Mitchell 2009; Fielder, 1970), and it is expected thatthe current hydrologic conditions are a product of thathistory. Mine workings grew in a complex pattern ofadvancing depth and lateral spreading as new ore wasdiscovered and removed. Nevertheless, the depth of themine increased at a remarkably uniform rate of 26 m/yruntil maximum depth was reached in 1975 (Fig. 3).Pumps were used to remove the in"owing water, so itfollows that the water level in the mine decreased roughly26 m/yr until 1975 and it was maintained at that level untilthe dewatering pumps were turned off in 2003. The waterlevel rose quickly over the next 5 years, and it was trackedby monitoring the times when electrical circuits at variouslevels shorted out. Dewatering was resumed in 2008, andthe resulting fall in water level was monitored with apressure transducer installed at depth (Davis et al. 2009;Zhan and Duex 2010).

Surface hydrologic budgetThe vicinity of the former Homestake mine is charac-terized by an active surface hydrologic system overlying alow permeability formation with slight ambient "ow(Driscoll and Carter 2001; Davis et al. 2003; Rahn andRoggenthen 2002). The average annual precipitation is0.7 m (2.22!10–8 m/s), the wettest in the Black Hills

(Driscoll and Carter 2001). Perennial streams are spacedon the order of 1 km (Fig. 4), and are characterized bybase"ow ranging from 0.4 to 0.7 of their total "ow(Driscoll and Carter 2001).

A hydrologic budget was estimated from a 10-year-long record of stream "ow from Whitetail Creek (station06436156), a 15-km2 drainage a few kilometers southwestof Lead, SD. The average total "ow (normalized towatershed area) in Whitetail Creek is 8.5 ! 10–9 m/s,which is roughly one third (0.37) of the averageprecipitation, and base "ow is 5.2 ! 10–9 m/s (Driscolland Carter 2001). These values were con!rmed using ahydrograph separation technique (Gustard et al. 1992;Institute of Hydrology 1980; Rutledge 1998).

The long-term average recharge "ux is assumed to be5.2 ! 10–9 m/s (0.16 m/yr), which is equal to the averagebase"ow. This requires that groundwater does not "ow toanother watershed. It is possible for recharge to differfrom base"ow in areas where the groundwater dividediffers from the surface water divide, and this certainlyoccurs in areas of the Black Hills underlain by karsti!edlimestone (Driscoll and Carter 2001). However, much ofthe Whitetail Creek watershed is underlain by metamor-phic rocks, so the potential confounding effect of karst onthe water budget is ignored here.

Hydrogeologic conceptual modelThe conceptual hydrogeologic model consists of a domeof low permeability rocks "anked and partly overlain bymore permeable rocks (Fig. 5). The surface hydrologyconsists of perennial streams at kilometer spacing (Carteret al. 2002), so it is assumed that sur!cial material is morepermeable and porous than underlying rocks. The sur!cialmaterial could be sedimentary rocks overlying themetamorphic basement, but it also could consist ofmetamorphic rocks that contain fractures with widerapertures or closer spacing than the metamorphic rock atdepth. Recharge to the shallow "ow system is assumed tobe consistent with the base"ow observed in the streams.

The mine is an intricate network of tunnels andborings, and even though the geometry of the network isfairly well known, it is too complex to represent explicitlyat the scale of many kilometers. Although extensive, the500-km of tunnels, mine workings, and back-!lled stopesare estimated to occupy less than 1% of the gross volume ofthe mine workings (Zhan 2002). Therefore, the mine-workings volume is idealized as two overlapping continua,one representing the open drifts and the other representingthe country rock left in place. This will enable a simpleassumption regarding the water "ux from/to the drifts andthe country rock (cf. Warren and Root 1963).

Lowering the water level at the mine is expected tohave captured groundwater "ow in a region that expandedoutward to affect the general vicinity of the mine.Continued mining and dewatering would have induceddownward "ow of water from the shallow "ow systemtoward the mine as well as "ow from greater depths wherewater has been removed from storage (Fig. 5).

Fig. 3 Depth-to-water in the Homestake mine as a function oftime (yellow squares) from Fielder 1970, Zhan 2002 Mitchell 2009.Connecting line segments were used in the analysis

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Numerical modeling

Field data needed to characterize the hydrogeologicconceptual model (Fig. 5) are sparse, so numerical modelsare developed to provide additional insights. One analysisrepresents the region as a two-dimensional cross section,whereas the other considers a three-dimensional domain.The general approach will be to represent the mineworkings and the rock as two separate, overlappingcontinua, which occupy the same volume and canexchange water. This allows the problem to be tractablecompared to discretizing the tunnels individually.

The two-dimensional (2-D) analysis and most of thethree-dimensional (3-D) analyses will be conducted usingmethods developed to study the pressure and "ow ofgroundwater in aquifers. These will be termed “hydrologic”analyses because they use methods typical of groundwaterhydrology. An additional 3-D poroelastic analysis will beconducted to estimate deformations resulting from changesin "uid pressure.

Fig. 4 Mine workings projected onto map of the vicinity of Lead, SD. Yellow circle with cross is projection of vertical reference line in thenumerical model

Fig. 5 Hydrogeologic conceptual model of the vicinity of theformer Homestake mine (green) looking ENE showing the shallowhydrologic system overlying the deep system. Solid arrows are "owlines originating as recharge and dashed lines are "ow released fromstorage

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Geometry and meshThe geometry of the mine is represented as an irregularpolygon that encompasses most of the mine workings(Fig. 6). The region representing the workings is a dual-porosity subdomain of crystalline rocks and an excavationnetwork. The whole problem domain extends 20 kmacross, which is the approximate diameter of the Leaddome (Fig. 6).

The 3-D model is shaped like a half cylinder with theregion representing the mine workings at the center. Theworkings are represented in 3-D by projecting the outlinein Fig. 6a as a horizontal prism. The mine workings areassumed to be contained in a region that is symmetricabout a vertical plane. Bedding and schistosity create afabric that is steeply dipping (dips of 60° or greater), andfor simplicity, it will be assumed that this fabric is vertical.These assumptions imply that the overall system issymmetric about a vertical plane, so only one half of itis simulated.

An unstructured mesh of approximately 104 triangular(2nd order) elements is used for the 2-D hydrologic modeland 105 tetrahedral elements in the 3-D model. Theminimum element span in the region representing themine is 50 m in the 2-D model and 120 m in the 3-Dmodel. The 2-D model includes small mesh elements nearthe ground surface to facilitate simulation of the shallow"ow system (Fig. 6b). Approximately 104 mesh elementswere used in the 3-D poroelastic analysis. The extradegrees of freedom in the poroelastic analysis required theuse of a mesh that was coarser than the hydrologicanalysis.

Governing physicsThe mine workings and the fractured rock are assumed tobe continuous domains occupying the same volume(Warren and Root 1963). The domain representing theworkings advances with time to simulate mining, andwater can "ow between the domains based on the relativemagnitudes of hydraulic head.

Rock domainIn the hydrologic analyses, the rock domain will besimulated combining mass and momentum balances used ingroundwater hydrogeology (Bear 1979;Wang and Anderson1982; Anderson and Woessner 1992):

r ! "Krh# $ Ss@h@t

% R "1#

where h=P/g+z is hydraulic head [basic units: L], K is thehydraulic conductivity tensor [L/T], Ss is the speci!cstorage coef!cient [1/L], R is a "uid source term [1/T],P is pore pressure [M/LT2], is unit weight of water[M/L2T2], and z is the vertical coordinate [L].

The poroelastic analysis also uses Eq. (1) withmodi!cations to Ss and R, and it is complemented by(Biot 1941; Detournay et al. 1993; Bai and Elsworth2000; Wang 2000) the coupling relation

E2"1& n#

r2ui &E

2"1& n#"1% 2n#@"

@xi$ ag

@P@xi

"2#

where ui is displacement of the solid in the ith direction[L], ! is volumetric strain, E is the drained Young’smodulus [M/LT2], " is the Biot-Willis coef!cient, and v isthe drained Poisson’s ratio. Hereafter, xi is the spatialcoordinates and the ‘i’ subscript is incremented from 1through 3 to indicate coordinate directions. The materialproperties in Eq. (2) consider effects of fractures andmatrix lumped together.

Mine workingsThe depth of the water in the mine, hw, can be inferredfrom historical records (Fig. 3). Hydraulic head in themine domain, hm, is determined by assuming the pressurehead in air-!lled workings is zero (atmospheric), so

hm $ z 0 > z > hw" # "3#

Fig. 6 Con!gurations of the numerical models. a Boundary conditions and geometry of 2-D model. b Mesh used in 2-D. c Geometry andboundary conditions used in 3-D. Symmetry is assumed, so only half the region is simulated. The coordinates are aligned with the plane ofsymmetry. The vertical line (z axis) through the workings is used for reference (e.g. Fig. 4). Surface encompassing the workings is used tocontrol the size of the mesh

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using coordinates de!ned in Fig. 6c. This is satis!ed ifthe walls of the workings are covered by a !lm of water.Drying from the ventilation system would lower thehead in the workings, but this is ignored in the currentmodel.

The lower reaches of the mine !lled with water after2003, and it will be assumed that the hydraulic head in the"ooded part of the workings is equal to the elevation ofthe free surface of the water

hm $ hw hwmin < z ' hw; t > 2003" # "4#

where hwmin is the minimum (deepest) water level(–2,400 m).

The approach outlined above makes use of the highpermeability of the mine workings by assuming that thehorizontal hydraulic head gradients in the large, karst-likeconduits are negligible. As such, the horizontal "ow withinthe mine workings is omitted from this formulation.

Coupling between the domainsCoupling between the rock and the mine domains isaccomplished using the source term in Eq. (1) with anapproach resembling that used for dual porosity mediawith two scales of permeability (Barenblatt et al. 1960;Warren and Root 1963; Elsworth and Bai 1992)

R $ Cg hm % h" # KL2

"5#

where L is a characteristic spacing between tunnels, andCg is a constant that depends on geometry, K is averagehydraulic conductivity (scalar). The workings occupy aregion of approximately Vw=5 km3, and they consist ofapproximately Ld=500 km of tunnels, so the averagespacing is assumed to be

L (!!!!!!!!!!!!!Vw=Ld

p$ 100m "6#

The geometric constant, Cg, depends on the shape andspacing of the tunnels. For example, if the tunnels areparallel and evenly spaced, then the characteristic timerequired for head affected by adjacent tunnels to interact is

t ) SsL2

K"7#

Each tunnel behaves like a line sink where the in"ow rateis assumed constant for a duration of !. Integrating theJacob (1940) log approximation to a transient linesource, the space-time average hydraulic head changein the formation at t=! is

Dh ) ln"2:25#4p

DQ0

K"8#

where "Q0 is the change in "ow rate per unit length of thetunnel. Solving Eq. (8) for "Q0 and normalizing by the

volume of the formation per unit length of each tunnel, L2,gives Cg=4"/ln(2.25)#15.6 in Eq. (5).

Coupling between the domains in the poroelasticanalysisThe poroelastic analysis includes full coupling betweendeformation and "uid pressure, which implies that thevolumetric strain rate of the solid contributes as anadditional "uid source to that given by Eq. (5) forhydrologic analysis. As a result, the poroelastic analysisuses

R $ Cg hm % h" # KL2

% a@"

@t"9#

as a source term in Eq. (1).An important consequence of the formulation outlined

above is that while water can "ow between the rock andmine-workings domains, the analysis does not explicitlyconsider "ow within workings. Rather, the mine-workingsare assumed in!nitely transmissive and equilibrate imme-diately to the prescribed head boundary conditions setwithin the mine. Although this does not allow "ow ratesto be explicitly evaluated within the mine workings, it isnevertheless a suitable representation of the differentresponse rates of the two media.

Boundary conditionsThe boundary conditions in the 2-D problem consist ofno-"ow conditions along the bottom and sides, andspeci!ed "ux equal to the recharge rate along the top ofthe simulated domain (recharge !ux=0.16 m/yr; Fig. 6a).The hydraulic head is speci!ed and set to 0 at pointsspaced 1 km apart along the upper boundary to representstreams (Fig. 6a).

Boundary conditions in the 3-D problem consist of auniform speci!ed-head condition (type I boundary con-dition) at the ground surface. This is justi!ed because thehydraulic head in the 2-D model varies only by 10s ofmeters at a depth of 100 m. This variation is small at thescale of the mine, so it seems reasonable to assume thehead is uniform as an initial evaluation. The disadvantageof this approach is that the 3-D model ignores details ofthe shallow "ow system, although it allows the exchangeof water between the shallow and deep "ow systems to beestimated. The advantage is that it reduces the executiontime by reducing the size of the mesh, and this was doneto facilitate solution of the problem. Boundary conditionsalong the sides and bottom of the 3-D model are zero "ux.

Fluid boundary conditions in the poroelastic analysisare the same as in the hydrologic analysis. The mechanicalboundary conditions assume !xed displacement along thebase, and roller boundary conditions along the verticalsides of the 3-D region (Fig. 6). The total stress is zero atthe upper surface.

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Rock propertiesRock properties are estimated from studies within themine, from regional evaluations, and from studies ofsimilar rocks elsewhere (Table 1). Rock properties varywithin the vicinity of Homestake, but it is assumedthat at the scale of the model, the hydrologic andmechanical properties of the rock are dominantlycontrolled by rock layering and stress. The orientationof the schistosity and layering appears to be fairlyconsistent across the region and some faults andfractures also follow this trend (Rahn and Roggenthen2002); therefore, it is assumed that properties at a givendepth are uniform, but vary with depth as a result of changesin effective stress.

The hydrologic analysis requires knowledge of thehydraulic conductivity, K, speci!c storage coef!cient,Ss, and effective porosity, ne. It is assumed that theseproperties are dominated by the effects of fractures.This allows macroscopic parameters to be estimatedusing basic characteristics of the fracture networkde!ned by a fracture density y (fracture area/volumeof enveloping rock), and an average hydraulic aperture#. The reciprocal of y is the average fracture spacing.The average hydraulic conductivity is (e.g., Bear 1979)

K $ yd3g12m "10#

assuming the fractures are parallel.Bedding and schistosity of rocks at Homestake

create a fabric that likely causes the hydraulicconductivity to be anisotropic. The strike of the rockfabric is approximately aligned with the N20W axis ofthe mine. The dip is steep (60° or greater) to the NE,so to simplify the analysis, the authors assume layeringde!ning the fabric is vertical. This allows the principalaxes of the anisotropy to be aligned with thecoordinate axes. Rahn and Johnson 2002 concludedthat Kmax/Kmin#5 at a nearby site underlain by foliatedmetamorphic rocks that are similar to the rocks in thevicinity of Homestake. There is no information aboutthe anisotropy in the vicinity of Homestake, so the

authors follow Rahn and Johnson 2002 and assumeKmax/Kmin#5. This was accomplished by calculatingKx=Kz=K using Eq. (10) and setting Ky=K/5,where the x-direction is along strike N20W (Fig. 6).

Effective porosity is assumed to be

ne $ yd "11#

The storage coef!cient for the hydrologic analysis isthe unconstrained speci!c storage, S#, which is given by,

S $ Ss $ g 1=Kb & ydb" # "12#

where $ is the compressibility of water, Kb is the bulkmodulus of the fractured rock, and it is implied thatchanges in the principal stresses due to changes in "uidpressure are independent of direction (d#xx#d#yy#d#zz)(Doe et al. 1982; Rutqvist 1995; Rutqvist et al. 1997;Svenson and Schweisinger 2007). The bulk modulus inEq. (12) is assumed to have components from deformablefractures and solid rock

1Kb

$ 1Ks

& Cny $ 3"1% 2n#Es

& Cny "13#

where Ks and Es are the bulk modulus and Young’smodulus of the solid, respectively. Cn is the fracturenormal compliance,

Cn $@d@se

"14#

where #e is effective stress. The approach in Eq. (13)uses the simplifying assumption that the fractures arerandomly oriented and interaction between fractures isignored (e.g., Germanovich and Dyskin 1994).

Changes in properties with depthHydrogeologic properties of fractured rock are expected tochange with depth because the increase in effective stress

Table 1 Available estimates of hydrogeologic properties in the vicinity of the former Homestake mine

Property Value Method Source

Hydraulic conductivity 10–9 m/s Pumping test in mine Zhan (2002)10–8 to 10–9 m/s Estimate Davis et al. (2009)

Porosity 0.01 Estimate Zhan and Duex (2010); Rahn and Roggenthen(2002); Driscoll and Carter 2001; Rahn (1985)

Speci!c storage 10–7 m–1 General value for fracturedcrystalline rock

Wang (2000); Domenico and Mif"in (1965)

Young’s modulus 90a, 58b, 77c GPa Average values from laboratory tests Pariseau (1985, table 21)Shear modulus !30 GPa Average values from laboratory tests Pariseau (1985)Poisson’s ratio 0.19a, 0.17b, 0.10c Laboratory studies on core from mine Pariseau (1985, table 21)

a Parallel to dip directionbNormal to schistosityc Parallel to strike

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closes the fractures and makes them stiffer. One approachto predicting this effect is to assume a relationshipbetween aperture and effective stress acting on thefractures. Several such relationships have been described(Jaeger et al. 2007; Bai and Elsworth 2000; Ruqvist andStephansson 2003), and according to Ruqvist andStephansson 2003, the most common one is

d $ do &do % dmin" #Cnise

do % dmin % Cnise"15#

where #o is the contact aperture, #min is the minimumaperture under in!nite stress, and Cni is the initial normalcompliance (i.e. the normal compliance at zero effectivestress) (Bandis and Barton 1983).

The compliance of the fracture can be obtained bysubstituting Eq. (15) into Eq. (14) as

Cn $Cni do % dmin" #2

do % dmin % Cnise" #2"16#

Effective stress is de!ned by

se $ sT & afP "17#

where %T is the total stress (tensile stresses are positive), Pis pore pressure, and $f for a single fracture is the ratio ofopen area to the total area of the fracture surface(Murdoch and Germanovich 2006). In general, $f of afractured medium will depend on the characteristics ofindividual fractures, as well as the fracture density andgeometry of the fracture network. For simplicity and toreduce the number of parameters, it is assumed that "f = ".

The initial vertical effective stress prior to mining isestimated as

sei $ % gr % gw" #d "18#

where gr and gw are the unit weights of rock and water,respectively, d is depth, and the vertical and horizontalstresses are assumed equal and as such lack a tectoniccomponent or horizontal displacement restraint. SubstitutingEq. (18) into Eqs. (10)–(16) gives the initial distribution ofmacroscopic hydrologic properties with depth. Changes ineffective stress are determined in the hydrologic analysis byassuming no change in total stress (%T) in Eq. (17), so onlychanges in pore "uid pressure (P) affect effective stress.

Poroelastic propertiesThe poroelastic analysis is conducted using the parameters:drained bulk Young’s modulus Eb; drained Poisson’s ratio, v;hydraulic conductivity, K; Biot-Willis coef!cient, $; and theBiot modulus, M. The drained bulk Young’s modulus isdetermined as

Eb $ Es1

1& q"19#

with

q $ EsCny3"1% 2n# "20#

which follows from Eq. (13). Neglecting the effects of thedifference between Poisson’s ratios of the fractured rockand the solid rock gives

a $ 1% Kb

Ks) 1% Eb

Es$ q

1& q"21#

The storage coef!cient in Eq. (1) for the poroelasticanalysis is (Wang 2000, equation 3.38)

S" $1M

$ Ss %3a2"1% 2n#

Eb"22#

where S# is given by Eqs. (12), (13) and (16), (17) with"f=$.

The effective stress, #e, in the poroelastic analysis isdetermined using Eq. (2) and elastic constitutive relations(e.g. Bai and Elsworth 2000; equation 2.6). The meanprincipal stress is added to the stress #ei in Eqs. (15) and(16) in the poroelastic analysis.

The advantage of taking the approach outlined above isthat it allows the eight macroscopic properties used in thehydrologic analysis (K, Ss, ne) and the poroelastic analysis(Kb, M, Eb, v, ") to be de!ned by six parametersdescribing the fracture system (%o, %min, Cni, y) and rockmatrix (v, Es) (Rutqvist 1995; Ruqvist and Stephansson2003; Baghbanan and Jing 2008). Five of these parame-ters (v, Es, %o, %min, Cni) are fairly well constrained orcalibrated (see below). This is similar to the concept ofeffective properties of heterogeneous (fractured) materials(Germanovich and Dyskin 1994) and provides a consis-tent basis for de!ning macroscopic properties that reducesthe degrees of freedom in the simulations. The aforemen-tioned mathematical problem was solved using theGalerkin !nite element method implemented in ComsolMultiphysics software.

Results

The analysis was conducted by running the 2-D and 3-Dsimulations in several steps. Initial results were obtainedusing the 2-D analyses (Fig. 7) with preliminary values ofparameters based on Table 1. These results showed thatthe variation in hydraulic head at shallow depths wassmall at the scale of the model (slopes less than 0.05), andthis !nding justi!ed the use of constant head conditionson the upper boundary of the 3-D model. The initial set ofparameters was then revised manually so the 3-D modelbest matched the available data. The new parameters wereused in the 2-D model to calculate the results shown in thefollowing. The parameters obtained by calibration wereremarkably similar to the original estimates, so theoriginal !ndings from the 2-D model were unaffected.

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Parameters obtained by calibrating the hydrologic modelwere used in the poroelastic model.

Calibration of 3-D modelValues of v=0.2 and Es=75 GPa were assumed based onvalues in Table 1 and a value of y=28 m–1 (fracturespacing#3.5 cm) was also assumed. The 3-D hydrologicmodel (Fig. 6c) was then calibrated by adjusting %o, %min,and Cni manually. The "ow rate into the mine wasestimated as a function of depth in increments of 200 mfrom the source term R in Eq. (1). Integrating R overvolume provided the total "ow rate.

The calibration exercise yielded estimates of %o=30 &m, %min=3.8 &m, and Cni=10

–10 m/Pa. These valuesgive a total "ow rate into the mine workings of 0.046 m3/sin the early 1990s. For comparison, the range of water"owing naturally into the mine given by Zhan 2002 andZhan and Duex 2010 for the same time period was 0.042–0.048 m3/s (Fig. 8). Water was also pumped into the mine,but this "ow was identi!ed by Zhan 2002 and omittedfrom the values given in the previous sentence.

The "ow into the mine increases with depth accordingto both the model results and !eld measurements given byZhan 2002. The modeled results overlap the observedin"ow rates, except at shallow depths (less than 1 km),where the observed cumulative in"ow is less than thatpredicted by the model (Fig. 9). The poroelastic analysisgives "ows that are similar to those of the hydrologicanalysis (Fig. 9).

The analysis of the in"ow during "ooding can be usedto provide an estimate of the void volume created by themining operation. During the 5 years when the water levelwas rising (2003–2008), the calculated (modeled) total

volume of water that "owed into the mine is 6.5 ! 106 m3.This volume of water !lls the voids created by miningoperations. The total volume of the region representing thelowest 1 km of the mine in the model is 1.78 ! 109 m3. Inthe absence of dewatering, this indicates that the normal-ized void volume (volume of voids created by mining/total volume of enveloping rock) of the lowest 1 km of themine is 0.0036.

For comparison, Zhan (2002; !gure 3.4) gives anestimate of the void volume remaining at the end ofmining to be 5 ! 106 m3 (4,000 acre ft) between 1,400 and2,400 m. This corresponds to a normalized void volume of0.0028. Rahn and Roggenthen (2002) estimated the totalvolume of voids created by overall mining operations tobe 2.1 ! 107 m3, and the total volume of the mine in themodel is 3.92 ! 109 m3, which gives a normalized voidvolume of 0.0053. Again, these magnitudes are reasonablysimilar.

The present simulations indicate a normalized voidvolume created by mining that is between values given byZhan (2002) and Rahn and Roggenthen (2002). Given theuncertainty in the estimates of the normalized volume, it is

Fig. 7 a Shallow and deep "ow systems predicted using the 2-Dmodel. Shallow "ow systems are shaded in the cross-section withpathlines shown in the inset. Dashed line is at a depth of 100 m.Blue dots are streams. Flow paths to the deep "ow system are inred. b Hydraulic head pro!le along dashed line in part a. Thickblack line plotted with scale on the left, thin purple line plotted with1:1 scale on the right. Thin black line is a horizontal reference

Fig. 8 Total simulated "owrate into mine workings using hydro-logic analysis (thick line) and poroelastic analysis (thin line) and thetotal "ow during dewatering according to Zhan 2002 (red circle)

Fig. 9 Cumulative "ow into the mine as a function of depth, fromhydrologic and poroelastic simulations (lines) and observations byZhan 2002 (blue squares and shaded band)

35


concluded that the value determined from the simulationsis consistent with the available data.

Distribution of propertiesThe macroscopic properties can be calculated fromparameters obtained through calibration, according toEqs. (16), (19) and (20). The analysis shows that becausethe properties are stress-dependent, they change by severalorders of magnitude in the upper few hundred meters. Theproperties are nearly uniform at depths below 1,000 m(Fig. 10) because the effective stress is high and thefracture apertures approach the minimum aperture, %min.Values of properties below 1,000 m are similar to valuesexpected from observations at the Homestake site or in thevicinity (Table 1).

The depth dependence of the hydraulic propertiesbefore and at the end of mining is also shown inFig. 10a. The effect of signi!cant changes (!10 MPa) ineffective stress on hydraulic parameters is remarkablymodest because according to Eq. (15) the stiffness of thefractures below a few hundred meters is such that theiraperture changes only slightly in response to changes instress.

Although the !eld data are sparse, K in Fig. 10 iswithin an order of magnitude of available estimates(Table 1). The marked increase in hydraulic conductivitywith decreasing depth is consistent with the developmentof a shallow hydraulic system where "ow is signi!cantlymore rapid than in the deeper system.

Shallow flow systemThe 2-D model shows the development of both shallowand deep "ow systems (Fig. 7a). The shallow "ow systemconsists of recharge that "ows laterally to nearby streams.Flow paths are limited to approximately the upper 100 mwhere K is several orders of magnitude larger than atgreater depths (Fig. 7a, inset). Shallow "ow systems arepresent across the entire model, including the area over-lying the shallow mine workings.

Flow pathlines in the shallow "ow system in the 2-Dmodel extend to depths of 100–140 m, which is consistentwith the regional estimate of 150 m for the depth of theshallow aquifer given by Rahn (1985). The maximumhydraulic head between streams is approximately 20 m inthe simulations. The topographic relief in the !eld area is100–150 m, which bounds the upper limit for themaximum hydraulic head between the streams. Thesimulations give maximum horizontal head gradients of0.04–0.05 (Fig. 7b). The hydraulic head drops by about70 m in the region overlying the shallow workings (0<x<3,000 m). This gives a horizontal hydraulic gradient ofapproximately 0.046.

The mine clearly has an effect on the elevation of thehydraulic head in the model, but it is remarkably smallcompared to the size of the mine. For comparison, Rahnand Johnson (2002) studied the groundwater near Nemo,SD, a town 30 km SE (along strike) of Homestake. Therocks beneath Nemo resemble those at Homestake, but therelief is more subdued, roughly 20 m. Rahn and Johnson(2002, !gure 3) show horizontal hydraulic head gradientsof 0.01–0.03 in their primary map area, and they infer ahead distribution with gradients of 0.06–0.08 in areas ofgreater relief on the periphery of their study area.

Pathlines roughly midway between the streams extendinto the deep subsurface where they curve towards andultimately discharge into the mine workings. These path-lines represent the interaction between the shallow anddeep "ow systems. Water that "ows from the groundsurface to the mine originates as recharge in the uplandsbetween streams. The number of pathlines entering thedeep system increases from the edge of the model to theregion overlying the shallow workings, indicating anincrease in "ux to the deep system. However, the "ux tothe deep system does not capture all of the recharge evendirectly over the shallow mine workings (Fig. 7a).

Deep flow systemThe deep "ow system is the region where "ow has beenaffected by operation of the mine. This region evolved asthe change in hydraulic head moved downward and the"ow system responded to dewatering throughout theoperation of the mine (Fig. 11). The deep "ow systemincludes a recharge capture zone where water originatingas recharge has "owed along a relatively short andgenerally downward path into the mine. Underlying thisis a storage capture zone where water has traveled along amuch longer path and is directed generally upward whencaptured by the deeper levels of the mine.

Fig. 10 a Hydraulic conductivity (K), speci!c storage (SS),hydraulic diffusivity (D), and effective porosity (ne) as functionsof depth along z axis, according to results of calibration. Black linesare initial values, red lines are values at the end of mining showingeffect of dewatering. b Young’s modulus (E) and Biot-Williscoef!cient (") as functions of depth

36


Recharge capture zoneFlow pathways from the ground surface to the mine andtravel times along these pathways were calculated usingvalues of ne determined from Eq. (11) and shown inFig. 10. The results show that pumping has captured wateroriginating as recharge from distances as far away asseveral kilometers from the surface expression of themine. The "ow paths are downward and curve toward themine where they are ultimately captured by the workingsat depths of several hundred meters (Fig. 13). The capturezone at the ground surface is roughly elliptical with amajor axis of 8,000 m and a minor axis of 4,000 m. Flowpaths beyond these distances have been affected by themine, but the travel time to the mine in this external regionis longer than 125 years, so those paths are outside of therecharge capture zone.

The vertical advective "ow velocity estimated fromDarcy’s Law is

vz $qzne

$ %d2g

12m@h@z

"23#

The vertical hydraulic head gradient, @h=@z, overlyingthe mine workings is approximately unity (Fig. 12a). Thisis a consequence of the pressure head being equal toatmospheric pressure at the top and bottom of thiszone. Using Eq. (23) with a fracture aperture %=4 &mnear %min gives a velocity of roughly 1 m/day. Using afracture aperture %=20 &m, which is roughly a median

between #min and #o, gives v=25 m/day. The mineworkings are 1,600–2,000 m deep along the south sideand it appears that the average travel time in thisregion is one to several years, but it could be on theorder of a month or less through localized fractureswith apertures of 10s of microns.

A zone of particularly fast travel from the surface to themine workings occurs in the vicinity of the shallowworkings. This zone extends to roughly 0.5 km southeastof the shallow workings with its southeastern edge in thevicinity of Whitewood Creek. The long axis of the 1-year-travel-time zone is 2,600 m and it trends N20W. A largerzone where travel times are less than 10 years has a longaxis of 6,000 m, and the 100-yr capture zone spans morethan 8,000 m (Fig 13b).

Storage capture zoneThe storage capture zone supplies the "ow into the lowermine workings. Water is released from storage due to thelarge decrease in pressure caused by dewatering the mine.The boundary of the storage capture zone is taken as theouter edge of the region from which water has beenreleased from storage and reached the mine. This zonewas delineated by tracing many particles paths andidentifying the most distant starting positions of pathsthat reached the mine. This zone is roughly elliptical inshape, with a major horizontal axis of 8,500 m and aminor axis of 4,000 m. The storage capture zone extends

Fig. 11 Hydraulic head (color !ood and grey tone) and particle paths (lines) as function of time (year indicated in each panel). The colorsindicating hydraulic head are scaled to the maximum change in each panel. Colors along pathlines indicate travel time, which is scaled tothe time since mining started. Grey "ll is hydraulic head outside of the mine. The grey scale for hydraulic head was used instead of the color"ood to highlight pathlines outside the workings

37


to approximately 5,500 m depth, according to the analysis(Fig. 13).

Flow velocity increases as the mine is approached. Theworkings are tightly enveloped by the 2 m/day isosurfaceof "ow velocity (Fig 13). The velocity isosurface of0.1 m/day is remarkably close to the current boundary ofthe storage capture zone. As a result, 0.1 to 2 m/dayappear to be the general range of "ow velocities in thestorage capture zone.

Interaction between the shallow and deep hydrologicsystemsWater "ows from the shallow to deep systems. The pre-mining "ow system has pathlines of a topographicallydriven system, originally calculated by Toth (1963). Inone of Toth’s examples, the depth of the basin is 300 m,the stream spacing is 1,600 m, and the amplitude of themaximum head between streams is 70 m. These param-

eters are within a factor of two to three to those in theBlack Hills.

The magnitude of the "ux from shallow to deep is ofinterest because it shows the impact that the deep systemhas on the shallow one. The vertical "ux in the 3-D modelwas calculated at a depth of 300 m and this was scaled tothe magnitude of recharge obtained from the hydrologicwater budget. The upper boundary condition in the 3-Dmodel assumes constant head, so the magnitude of thevertical "ux becomes whatever value is required to meetthe conditions imposed by the underlying mine workings.

The vertical "ux in the analysis is less than therecharge at a depth of 300 m, with the maximum ratioof the "uxes approximately 0.8. The maximum "ux occurswhere the workings are shallowest. This result indicatesthat some recharge "ux is available to discharge tostreams, even in the vicinity of the shallow workings.

Whitewood Creek crosses over the workings in aregion where the maximum "ux ratio is approximately0.6. The implication is that the rate at which WhitewoodCreek gains by groundwater discharge is diminished overthe workings, but the effect of the mine is insuf!cient forthe stream to lose water. This should be interpreted tomean that loss of water from Whitewood Creek to themine is unnecessary to explain the available data, but theresolution of the simulation is insuf!cient to rule out thisas a possibility.

DeformationDeformation resulting from pumping was evaluatedusing the poroelastic analysis outlined in section onnumerical modeling and the parameter distributions inFig. 10. Results show that the magnitude of deformation isparticularly sensitive to the magnitude of pressure changeand properties, E and ". Dewatering throughout the historyof mining results in subsidence over a region roughly the sizeof the recharge capture zone (Fig. 14), with a maximumdisplacement of 5 cm at the southern end of the shallowworkings (x=–1,000 m). The rise in water level from years2003–2008 causes doming that peaked in 2010 with amaximum amplitude of about 0.2 cm. The maximum

Fig. 12 a Hydraulic head and travel times in 2003. Hydraulic head in the region of the mine workings (colors) scaled to a maximum headchange of 2,400 m. Travel time along particle paths indicated by colors and given by scale. Grey tone shading is the region where verticalhydraulic gradient is between 0.5 and 2. b Perspective of mine workings and particle paths with the zones of surface capture. Travel timesfrom the ground surface to the mine range from less than 1 year (in region de!ned by orange dashed line), 10 years (within pink dashedline) and 120 years (within the purplish-blue dashed line)

Fig. 13 Perspective of isosurfaces of groundwater "ow velocity in1993 and particle paths since the start of mining (colored lines). Thelowest line of pathlines starts at a depth of 5.5 km. Colors onpathlines are scaled to travel time, where blue lines represent thelongest time. The isosurface of 0.1 m/day is the approximateenvelope of the region over which the mine has captured water fromstorage during its lifetime. The former mine workings is shown as ablue area. The grey area refers to the ground surface

38


displacement caused by the rise in water level occurs at x=2,000 m overlying the deepest part of the mine. Themaximum tilt magnitude along the N20W pro!le in 2010is approximately 0.4 &rad.

Discussion

The simulations con!rm the general expectations of theconceptual model (Fig. 5) and suggest additional detailsthat improve the resolution of the hydrogeology. It appearsthat in the vicinity of the former mine workings, fourmajor zones are distinguished by the source and the fate ofthe water "owing through them. These include the: (1)shallow "ow system; (2) recharge capture zone; (3)storage capture zone; and (4) former mine workings(Fig. 15).

The shallow "ow system is recharged by in!ltrationand discharges to local streams and controls activehydrologic processes in the region. By being a hydraulicsink, the mine has signi!cantly affected the deep "owsystem. Two capture zones—one zone where water isderived from recharge and another where it is removedfrom storage—have been identi!ed within the regionin"uenced by dewatering. The recharge capture zone ischaracterized by relatively short "ow paths from theshallow "ow system into the mine. The maximum vertical"ux supplied to the recharge capture zone is 0.8 of theambient recharge. This implies that water in the shallow

"ow system is diminished, but not depleted by dewateringat the mine (Fig. 7). The recharge capture zone extends todepths of approximately 1,800 m on the southeast sideand 800 m on the northwest side of the workings(Fig. 15). Water recovered from below those depths isderived from storage and is characterized by upward "owof older water. The deep "ow system receives a fraction ofthe ambient recharge to the shallow system.

The extent of the recharge capture zone on the surfaceis roughly elliptical with axes of 8 km ! 4 km. Average

Fig. 14 a Upward displacement from 2003 to 2010 along a cross-section through the N20W axis of the mine workings. Numbers aredisplacement in m. b Displacement pro!les at a depth of 500 m(dotted line in part a.) as a function of time (by year) caused by"ooding and dewatering using hydraulic heads in Fig. 3

Fig. 15 Hydrogeologic zones in the vicinity of the formerHomestake mine in a map and b section views. Mine workingswith levels separated by 200 m for scale (green). Yellow line in themine workings marks 1,500 m depth. Recharge capture zone wheretravel times are less than 1 yr is approximately within the orangedashed line, 10-yr travel time is within the pink dashed line and120–yr travel time is within the purplish-blue dashed line. Greyshaded region is where water has been removed from storage. Theshallow "ow system extends to depths of 100 m (blue)

39


travel times are less than 10 years over an inscribedelliptical region roughly 6 km ! 3 km with a zone of fastpaths where travel times are less than a year furtherinscribed within this and roughly 2.5 km ! 1.5 km(Fig. 15). Mine in"ow from water released from storageappears to have occurred over a region roughly8 km ! 4 km that extends to a depth of 5.5 km. The"ow of water beyond this region has been affected but hasnot been captured by the mine.

Boundaries between the capture zones are moving. Therecharge capture zone has been expanding downward andoutward and at the current rate of dewatering it willcontinue to do so, thereby moving the boundary betweenit and the storage capture zone. The storage capture zonewill also continue to expand as water mobilized manyyears ago reaches the mine. Eventually, the size of thestorage capture zone will diminish and the rechargecapture zone will expand to envelop the entire workings.Under steady conditions, the storage capture zone will beabsent altogether and the deep "ow system will includeonly recharge capture.

Cone of depressionPrevious investigations (Zhan and Duex 2010; Zhan 2002;Rahn and Roggenthen 2002) have assumed that a largecone of depression was created by the mine, but thisappears to be unnecessary to explain the available data.This is because the deep "ow system removes only afraction of the ambient recharge to the shallow system. Aconsequence of this is that even though the mine removeswater like a well, it need not create the classic cone ofdepression around a well where the water table drops,pores are drained and an extensive vadose zone is created.This is why the water table in Fig. 7 is only slightlydepressed. The authors suggest that the mine does indeedbehave like a large well, but instead of being analogous toa conventional well in an aquifer with a large depressedwater table, it instead resembles a well beneath a boundarycreated by the shallow "ow system that is roughly atconstant head. A reasonable analogy is a well beneath astream or lake (Kelly and Murdoch 2003). Interestingly,despite this difference in conceptual models, the radius ofin"uence of 2 km calculated by Zhan and Duex (2010)appears to be a reasonable estimate of the size of theregion where water is captured by the mine.

Open pitThe large open pit created as part of the shallow workingswas ignored when setting up the model, and simulationsare able to predict the observed in"ows reasonably well(Figs. 8 and 9). This suggests that the open pit has only aminor effect on the in"ow used to calibrate the model,which seems reasonable in light of the small area of the pit(!0.25 km2) compared to the area providing recharge tothe mine workings (!25 km2).

During heavy rainfall, the open pit may capturesigni!cant volumes of water that "ows into the under-ground workings. This in"ux of water is expected to resultin a short-lived pulse superimposed on the "ows causedby groundwater. The analyses considered here are limitedto in"ows resulting from steady-state, distributedrecharge, so effects of storm-related "ows are ignored.

Permeability, stress, and the shallow flow systemThe distribution of K used in the simulations (Fig. 10) wasbased solely on a relationship that K increases as theoverburden load decreases. Our results suggest a reductionin stress on cracks or pores can explain how the rockbecomes suf!ciently permeable to create a shallow "owsystem. Many other processes may further alter K once thepermeability has been increased enough to sustainsubstantial water "ow, but the results of this work showthat those other processes may be unnecessary—stressreduction alone is suf!cient to create conditions requiredfor a shallow "ow system. The importance of stress-dependent permeability on the development of shallow"ow systems was also recognized by Jiang et al. (2010).

Origin of mine waterThe results of the simulations suggest that water seepinginto the mine workings should span a broad range of agesand source areas. Water from locations near the peripheryof the workings has the best chance of representing "uidsnative to the formation and unaffected by interactions withthe workings themselves. The south side of the mine todepths of 1,600 m has the potential to be dominated bywater that originated as recharge within the last 10 years,and considerably younger water (<1 year since recharge)could be in!ltrating in the vicinity of the shallow work-ings, as well as up to 0.5 km south of the workings.Localized fractures with apertures larger than the averagecould be responsible for both larger than average "owrates and faster than average travel times.

Water that "ows from the shallow to the deep "owsystem is expected to be derived primarily from theuplands between streams (Fig. 7a). The upland areasinclude the town of Lead and the tailings pond (Fig. 15).The composition of the water entering the southeast sideof the mine could be affected by compounds from thesesource areas.

It is possible that water from Whitewood Creek, oranother local stream, enters the mine workings. This couldbe signi!cant because it could provide a mechanism formicrobes or dissolved compounds to "ow from surfacewater to the mine workings—other pathways involve thein"ow of groundwater. However, the streams are at lowhydraulic potential relative to the neighboring uplands, sohighly transmissive features such as fractures or boreholesin precisely the right location would be required to realizethis hypothetical pathway (Fig. 7). Fractures and bore-holes are common in the vicinity of the former Homestake

40


mine, so water "ow from streams to the workings cannotbe dismissed.

The northwestern and lower reaches of the mine areexpected to be dominated by water that was removed fromstorage. Flow velocities in the ambient "ow system (priorto mining) at depths below 1 km are expected to havebeen slow, so the water stored at those depths is likely tobe orders of magnitude older than the water in therecharge capture zone. The simulations suggest that waterarriving at the mine today may have been several km fromthe mine at the time mining started, and it seems likelythat the composition of the water would re"ect the longresidence times at depth.

Implications for deep EcoHydrologyThe "ow systems and hydrogeologic zones identi!ed bythis investigation (Fig. 15) are hypothesized to be a basicframework controlling the distribution and function ofmicrobial ecosystems in the vicinity of Homestake.Fracture apertures will constrain the size of microorgan-isms that can be transported to depth. For the valuesutilized in the model above, multi-cellular eukaryoticorganisms and larger protists will be restricted to theshallower zone above 100 m depth, whereas prokaryotesand smaller eukaryotes such as yeast cells like thosereported from 400-m deep fractures at Äspo (Ekendahl etal. 2003) and 200-m deep aquifers at Savannah River(Sinclair and Ghiorse 1989), could penetrate to the deepestlevels of the simulated region. Flow velocities and the insitu rates of aerobic microbial respiration will affect thedepth to which oxygenated water can penetrate, and thiswill in"uence the distribution of microbial communitiesand geochemical facies.

Those fractures that are part of the recharge capturezone would likely be aerobic or hypoxic depending uponthe location of their recharge zone and their microbialcommunity would be dominated by psychrotolerant tomesophilic aerobes and facultative anaerobes along withsome protists. If in situ aerobic rates are similar to thosereported for the Middendorf aquifer of South Carolina,then water with subsurface residence times up to7,000 years may still contain traces of O2 (Phelps et al.1994). Those fractures that are tapping into the storagecapture zone, however, may contain groundwater withresidence times of many thousands or more years, and becharacterized by microbial communities dominated byanaerobes with few, if any, protists. At depths shallowerthan the 4,850L level (1480m depth), the microbialcommunity would predominantly be mesophilic Proteo-bacteria, Crenarchaeota and Euryarchaeota (includingmethanogens), if the results reported from the Äspo HardRock Laboratory (Kotelnikova and Pedersen 1997; Ped-ersen 1997) and the South African Au mines (Gihring etal. 2006) where water ages are on the order of millions ofyears, are any guide. This hypothesis is consistent with thepredominance of Proteobacteria in the 16S rRNA genesequences from clone libraries of soil samples collected at

1.34 by Rastogi et al. (2009). Assuming a geothermalgradient of 20°C km–1, the boreholes from the 2-kmdepth or deeper tapping into the storage capture zonewould likely yield thermophilic anaerobes, perhaps lowdiversity communities dominated by members of theFirmicutes, since these have been found to dominate thedeep subsurface biosphere in South Africa at depthsgreater than 2.5 km (Moser et al. 2005) and have beenisolated from deep fractured rocks at other sites in thecontinental USA at depths greater than 2 km (Colwellet al. 1997; Liu et al. 1997a; b).

Conclusions

More than a century of dewatering has altered thehydrogeology in the vicinity of the Homestake mine inthe northern Black Hills of South Dakota. Two- andthree-dimensional simulations indicate that the shallowambient "ow system typical of the region is underlain bya deep "ow system created by mining activities. Thedeep "ow system includes a zone where the minecaptures water originating relatively recently as recharge,and another zone where water is much older and hasbeen released from storage in the enveloping rock. Thestorage capture zone has the shape of a surface-truncatedellipsoid, 8 km in maximum dimension, 4 km wide and5 km deep.

The calibrated simulations were able to explainimportant hydrologic observations available from the area,including the co-existence of shallow and deep "owsystems, the total "ow rate pumped from the workings,and the distribution of "ow and magnitude of porositywithin the former mine. The simulations assumed theregion was underlain by a uniform, anisotropic materialwhose hydrologic properties depend only on the effectivestress. Equating macroscopic properties with character-istics of deformable fractures allows the number ofparameters to be reduced, and it provides a physicallybased justi!cation for changes in properties with depth.Reduction in stress increases hydraulic conductivity byroughly 3 orders of magnitude as the ground surface isapproached, which appears to be an important feature inpromoting the development of a transmissive and complexshallow "ow system.

Acknowledgements We appreciate the support from the NationalScience Foundation under grants EAR- 0809820, EAR 0900163,CMMI 0919497, EAR 1036985, EAR 0969053 and EAR 0919357.

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http://pubs.usgs.gov/ha/ha747/

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Hydrogeology Journal (201 ) 20: 27–43 DOI 10.1007/s10040-011-0773-72

Hydrogeology of the vicinity of Homestake mine, South ...Hydrogeology of the vicinity of Homestake...

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