19 Singleverticaldikes

19.1 Introduction

Dikeshavelongbeenregardedasimpermeablewallsin theearth'scrust,butrecentresearchhasshownthatdikescanbehighlypermeable.Theybecomesobyjointingasthemagmacools,byfracturingasaresultofshearing,orbyweathering.

If asingle,permeable,verticaldikebisectsacountry-rockaquiferwhosetransmissi-vityis severaltimeslessthanthatof thedike;a specificflowpatternwill becreatedwhenthedikeispumped.Insteadofaconeofdepressiondevelopingaroundthewell,asin anunconsolidatedaquifer,a troughof depressiondevelops(Figure19.1).Con-ventionalwell-flowequationsthereforecannotbeusedto analyzepumpingtestsincompositedike-aquifersystems.

Thehydraulicbehaviourofsuchsystemsisidenticaltothatofsingle-fractureaquifersystems.Nevertheless,theconceptsusedfor singleverticalfracturesin Chapter18(i.e.shortlengthandzerowidth)arenot realisticfor dikes,whoselengthcanvaryfromseveralkilometresto evenhundredsof kilometres,andwhosewidthcanvaryfromonemetreor lesstotensofmetres.

In thischapter,thedikeisassumedto beasshownin Figure19.IA.It is infinitelylong,hasa finitewidthanda finitehydraulicconductivity.Thedike'spermeabilitystemsfrom'a systemof uniformlydistributedfractures,extendingdownwardanddyingoutwithdepth.Belowthefracturedzone,thedikerockismassiveandimperme-able.Theupperpartof thedikeis alsoimpermeablebecauseof intensiveweatheringor a top claylayer.Thewaterin thefracturedpartof thedikeandin theaquiferin thecountryrockisthusconfined.

Thewellin thedikeis representedby a planesink.Whenthewellis pumpedataconstantrate,threecharacteristictimeperiodscanbedistinguished:earlytime,medi-umtime,andlatetime.

At earlytimes,all thewaterpumpedoriginatesfromstoragein thedikeandnoneiscontributedfromtheaquifer.A log-logplotofthetime-drawdownof thewellyields~straigh..0ineseg..1}1~ntwitbaslopeof0.5.Thegoverningequationsarethenidenticalwiththoseforearlytimesin Chapter18,butnowtheparallelflowoccursin thedikeinsteadofin theaquifer.

At mediumtimes,all thewaterpumpedis suppliedfromtheaquiferandnoneiscontributedfromstoragein thedike.Theflowin theaquifercanberegardedaspre-dominantlyparallel,butobliqueto thedike.A log-logplot of thetime-drawdownda~~JL2.!F_~i~~t~~~Qt witha~Iopeof 0.25 In inf'.retrole.um.li.t.er.a.tu~-,-tI\~me s~pe~~0~~j for fractureswiili-..iL!l~.!~Jnr.gIaulic...conductiYily._{Cinco

Ley etarl978} ~ ":JAt latetimes,thefl?w in the~quife.ri(~eudo-radial.A semi-19~P!ot

.?f thetime- //'

drawdowndataalsoyieldsastraIght-hnesegment. '-- kJ(. Jf~ if ~ l".arI{l~-Thechangein flowfromoneperiodto anotheris notabrupt;b~tgradual.Duringthesetransitionalperiods,atime-drawdownplot(whetheralog-logplotorasemi-logplot)yieldscurved-linesegments.

275

country rock dike country rock0

piezometrichead> 50S(WdTd)2/4T3

Procedure19.4- On semi-logpaper,plot thedrawdownSwversust (t on logarithmicscale);- Drawastraightlineofbestfit throughtheplottedpoints;- Determinetheslopeof thislineL1SandcalculateT =2.30Q/4TCL1s).

Remark

- For a pumpingtestof theusualduration,theabovemethodcanonlybeappliedto dikesnot widerthanafewcentimetresor to fractures. ('

(

Example19.1BoonstraandBoehmer(1986)andBoehmerandBoonstra(1987)describeapumpingtestthatwasconductedina IO-m-widefractureddoloritedikeatBrandwagTweeling,Republicof SouthAfrica.Thecountryrockconsistsofalternatinglayersofnon-pro-ductiveIow-permeablesandstones,siltstones,andmudstonesof theBeaufortseries,whichbelongtotheKarroosystem.

Thewellin thedikewaspumpedfor 2500minutesat a constantrateof 13.9lisor 1200m3/d.Drawdownsweremeasuredin thiswellandin twoobservationwells,onein thedikeat a distanceof 100m fromthepumpedwellandtheotherin theaquiferabreastof thepumpedwelland20mawayfromit. Table19.1givesthedraw-downdataof thethreewells.

283

284

ObservationwellinthedikeApplyingProcedure19.1to thedataof theobservationwellin thedike(x = 100m),weplotthesedrawdowndataon log-logpaperagainstthecorrespondingvaluesof time1.A comparisonwiththefamilyof typecurvesin Figure19.6showsthattheplottedpointsfall alongthetypecurvefor X = 1.0.Wechooseasmatchpoint,PointA, whereF(X,T)= 1andT = 100.On theobserveddatasheet,thispointhasthecoordinatess(lOO,t)= 2.29m andt = 23.5minutes.IntroducingtheappropriatenumericalvaluesintoEquations19.1,19.3,and19.4,weobtain

WdTd= 2.6x 1O4m3fdWdSd= 4.3X 10-4mST = 3.2x 10-4m2fd

Table19.1Drawdowndataofthepumpedwellandtwoobservationwells,PumpingTestBrandwagTweel-ing,SouthAfrica,afterBoonstraandBoehmer(1986)andBoehmerandBoonstra(1987)

Time x=O x = 100 Time x=O x = 100 Time x=O x = 100(min) (m) (m) (min) (m) (m) (min) (m) (m)

1 3.363 1.378 40 8.445 6.232 600 18.108 15.0312 4.118 2.068 50 8.864 6.606 750 18.948 15.9073 4.660 2.507 60 9.192 6.907 900 19.795 15.7044 5.025 2.818 75 9.724 7.349 1050 20.253 17.8136 5.582 3.360 100 10.366 8.031 1200 20.667 17.5658 6.081 3.846 125 11.120 8.885 1350 21.033 17.916

10 6.470 4.224 150 11.766 9.063 1500 21.076 17.94513 6.796 4.547 175 12.300 9.553 1700 21.389 18.28515 7.020 4.765 200 12.874 10.045 1900 21.486 18.40918 7.246 5.016 250 13.911 11.027 2100 18.48321 7.500 5.257 300 14.643 11.672 2300 18.85825 7.746 5.519 350 15.142 12.154 2500 19.10930 8.102 5.700 400 16.080 12.20735 8.324 6.044 500 17.252 14.324

.

Time y=O y = 20 Time y=O y = 20 Time y=O y = 20(min) (m) (m) (min) (m) (m) (min) (m) (m)

1 3.363 0.572 30 8.102 5.630 300 14.643 11.3232 4.118 1.249 35 8.324 3.006 350 15.142 11.7663 4.660 1.741 40 8.445 6.110 400 16.080 12.6224 5.025 2.540 50 8.864 6.500 500 17.252 14.8476 5.582 2.800 60 9.192 6.815 600 18.108 14.9178 6.081 3.422 75 9.724 7.320 750 18.948 15.421

10 6.470 3.905 100 10.366 7.858 900 19.795 16.33713 6.796 4.286 125 11.120 8.489 1050 20.253 16.69115 7.020 4.530 150 11.766 9.039 1200 20.667 17.12518 7.246 4.800 175 12.300 9.457 1350 21.033 17.56021 7.500 5.055 200 12.874 9.901 1500 21.076 17.58425 7.746 5.375 250 13.911 10.723 1700 21.389

s(100, t) in m

102

FIX.T)10'

10'

10-'

103 104t in minutes

100

10-3 10-2 10' 102 103 104

Figure19.6Thetime-drawdowndataof theobservationwellin thedike(x = 100m),matchedwithoneofthecurvesofthefamilyoftypecurvesdevelopedfromEquation19.2

ObservationwellintheaquiferApplyingProcedure19,2to thedataof theobservationwellin theaquifer,wematchthetime-drawdownratiodatawith thetypecurveF(ua),as shownin Figure19.7.Wechooseasmatchpoint,PointA, whereF(uJ = 1andl/u; = 10.On theobserveddatasheet,thispointhasthecoordinatess(20,t)/sw= 0.9andt = 5.3minutes.Intro-ducingtheappropriatenumericalvaluesintoEquation19.7,weobtain

T/S = 2.7x 105m2/d

CombiningtheresultsofProcedures19.1and19.2,wecanalsoobtainseparatevaluesforthetransmissivityandstorativityof theaquifer

T = 9.3m2/dS = 3.4X 10-5

PumpedwellFigure19.8showsthetime-drawdowndataof thepumpedwell,plottedon log-logpaper.Thisplotonlyexhibitsa straightlinewitha slopeof 0.25.Hence,wecannotapplyProcedure19.3.Instead,wechooseanarbitrarypointA onthisline,withcoordi-natesSw= 10.0mandt = 70.7minutes.IntroducingthesevaluesintoEquation19.15,we0btain

285

F(ua

10 I

S(y,t)

s;-101

10-1 4es

10-2

10-3101 10 101 102 103 104

l/u~

Figure19,7The time-drawdownratiodataof theobservationwell in theaquifer(y - 20m),matchedwith thetypecurveF(ua)

Swin metres

102DIKE

ool.o~-~

101

AI

0- 00_0

\0=0-0-0-0-0

0 -. o_o_o_o_o_o~'

0_0-'

10 101 t10270.7

103 104t in minutes

Figure19,8Time-drawdownrelationof thepumpedwell,showingthecharacteristicstraight-lineslopeof0,25formediumpumpingtimes

286

(WdTd)j(ST) = 425m4/d3/2

SUbstitjing the valuesof WdTdand ST obtainedwith Procedure19.1 into(WdTd) (ST),weget465,whichcorrespondsreasonablywellwiththevalueof 425obtainedwithProcedure19.3.

287

p.275 Single vertical dikes, Introductionp.276p.277 Curve fitting methods for observation wellsp.277 Boostra-Boehmer's curve fitting methodp.278p.279 Boehmer-Boostra's curve fitting methodp.280 Curve fitting methods for the pumped wellp.280 For early and medium pumping timesp.281p.282 For late pumping timesp.283p.284 Observation well in the dikep.285 Observation well in the aquiferp.285 Pumped wellp.286p.287