Applkation of the Finite Element lUethod to a microzonation study of the Salonica Region A. A. I{.Ol'i';SOI'OUL()~ ("') - C .. A. SYl{}L\I\EZ1S (U) Rcccived on .Inne l,ith, 1!li3 SU)DIARY. - 'l'he main ohjcrt. of the present lJaper is an iltt('mlIJ to lJl"eHent u mo(ld for t.h(· estilllation o[ the g"l"Onnll mow'ments Ilnring an t'urth- I]nalw, nsinl; thc }'initc .Element )let.hod. SOllle lJr('liminar.l' re8ults for t.hc suhsoi! o[ the Halonica l'q~ion ilH' sullScqu('ntly culeulat('d, nsing- this Iliodel, accol"lling to thc cxisting geological anll SCiSlllOlogkill Ilata of thc rcgion. }'inally, Home generill conclusions are Ilerived. RIASSUNTO. -- SCOllO lJrincipale Ili qllcsto lann'o 1.' IIn t('ntajjvo Ili llrcscntilrc nn lllollello per la valutazione Ilei movill)('nti 11('1 suolo dllrante un tcrremoto wmfrm'IHlo Ilei ,\[dollo Ildl'ElClllcnto Finii.o. CSi1lulo 1]111)· st ' uitilllo eli in hasc ili Ilati gcologiei C sismici giù esistenti, si Hono ]lrimil 1'illcolati alcnni 1"Ìsllltati 1)('1' il sott.osllolo della regillne Ili "alonirl'O traen. Ilone, infinc, alcune conehlHioni di camtterl' generale. 1. - TNTRODl:CTION Among the varioU8 exi8ting denuitiol18, r-.licrozoning can be (Ielined as the stndy of small Iam] areas ulldcr Ioral gcoIogy eonditions and earthqnakc rharartcristirs, scrving- a·f\ a guide for safcr land use amI safcI' ronstruction, areonling to the s])ecilied ]oca] difTereuces iu enrt.h- quake attack on stl'Uct.nres. Ju November 1971 dnrillg thc fil'st mceting of thc "\I"orking g-I'OUp on )Iirrozoning in Belgmde, S~~lonica was chosell as a site for the Piloto )Iicrozoning study according to t.he ]lIall of o}lcratiou or thc usnp- UNBSCO Projert for the seismicity of 1.he Ballmn RegiOlI. (.) Civil Eng.t:"NESCO Pmject on the HeiHmieit.y of the Balkan Reg-ion . :-rational 'l'echnicul Fnivc1"sit.y o[ Atlwns. (**) Dr. Civ. Eng, Lednrer, Institllte o[ Strllctural Analysis allll AseiSlllic Research. National 'l'cchniral Vnivel'sit.y of Athens. ;'14 A. A. lWUSSOPOULOS - C. A. SYlnrAKEzrs The }l1ll'}IOSe of the l'l'eSent ]la]lC'l' on 3Iipl'ozonation is an attem}lt by the authol's to present a moael [01' the estinmtion of the ground movements during an earthquake, using the Finite Element J\Iethod. U~ing t,his model, some earthquake eharaet,el'isties of t,he sllbsoil o[ Saloni('a al'l~ sllbsequently {'alclllated aC'(,ol'ding to tlw I~xisting gl~olo­ gical allll seislllologi('al Ilata for the l'egion allll some generai conclusions are derived, as a contl'iblltion to the UNDP-UNESCO Pl'ogramme. The mai n idea of the model pl'Oposed in this l)al)er was dis{'msed dUl'ing tlw "Seminar on ::\IiCl'OzonM,ion" held by Ui'lESCO in 'l'hess(l·- loniki, on A]ll'il 9-13, 1973. '. - .MOD:EL CIL\iL\CTERISTICS For the aevcIopment of the modcl, an clastic layel' o[ unifol'm thickness H and width equal to unity is considerea, based on the bed- l'Opk (snblayer) which is assumed to be l)la.ne {Fig. 1 l. I " ~~ .... • -- Fig. 1 The l'l'esent, st,udy is coneent,rated un the eHects alln to sheal' waves "\vhieh arn of Vl'imary im]lortan{'e in tlw micl'Omning ]ll'oblem. ::\Iol'l~oyel' it is assumell that the llil'ection of wave ])J'o]Jagation in the l'ock is il'l'elevant amI so the bedl'ock is tramIatel1 bOI1ily. Though, the motion of tlw bndroek snrfa{'e between points B a,nll C is assnmed as a l'igid body lllotion allll the aceeleration is t,(lkml {'onstant along the surfa{'e Be of t,he bedl'O{,k, This is possible as the wavn length AB in the beal'ock is eX]leetnll t~) bn mu{'h grea,tel' than the wave length AA in alluvium (Fig. 1). Al'l'LICATIO~ or l' In }'I~JTE };I.E"E~T "METllOn, l,l'C, 515 It is al.~o assumed t.hat. thc main contribution for the exeitation of soil at. a ]Ioint -4' (FiK. 1) of t.lte sUl'facc is trom thc l'egion H-C of hmgth L. Points out of the rCKion B-C, surh as ]lOint D, hll"VP not signiiieant. clIeet on ]lOint A' since the enerKY at D will be refl'aete(l at t.hc rock-soil interface ana ]ll'o]mgated vertieally. For the lml'posc of detel'mining the displacements of lIte grouml surfacB dUl'ing the earth- quakc thc lenght L is tnken as a varying ]Iat'amet.er. During t.hc present st.1Hly t.he distribuhon of accclcrat.ion along t.hc hcight. of t.he alluv ium fO!' thc regi011 B-C COnSiaBl'e!l is assumcd varabolic with a law of tlistribution: é(X, JI) = 10 0 + c(x)· y: whcre cix) is a funetion of x. In the abovc eXl)ression thc fIrst. t.crm 10 0 is t.he C'onstnnt aecclcra.- hon or t.hc alluvium lnyel' due t.o tllc betlroek movcment.. 'l'he 8N'011(1 t.crm BA '-= c(x)!I~ desC'ribcs thc acceleration at cacl! voint. of Ihc allu- ·vium laYBl', auc t.o l'elative 1ll0"vpment of t.he layer 1.0 the betll'ock. A eosinmoi(la.l distribution of nC'celernt.ions along t.he hmgth of thc layer: is assum('.(l with K(y) vary ing from zero at. thc be(lrork surfnce 1.0 it~ mnximum value at tlw groumI smface. 'lihis maxim\1m val\1c is the aiffel'encc lwtwecn thc maximum aC'celerations llt thc ground surface alHl thc bctlroek surfaec, On fig. :2 th is cosinusoitlnl d istl'ibut.ion of SECTIONS, B-B' I · OO1g +OD12 g , , ,l e +0.000; -. F L 9 2 A. A. llOGS~OPOrLOS - ~. A. SY101AKEZIH acC'elemtions is shown for tile subsoil of Salonica eomi(lerell in tlle }lresellt }laver, for whieh the groulld fHufaee aeeelemtioll all(l tile bell- l"OC"k surfaee aeeeleration are foulld equal to O.lìg and O.lOg reS}leC- tively, aH sho\\"l1 ili the lIext }laragravh~. IJl1ring the }lre~ellt stud~- a ~eetioll I1CC'l1' of the layer is eOIl- sielered at a llloment where the eosillllsoiclal aeeeleration wave haH the shave of lig. 2. Tile ~e}laration of tlli~ fwf't.ion i~ }lermitted heeause the axes C'C', HH' are axef\ oi antimetl'y oI loalling and ~o 110 horizolltal for('e~ lwt along them after se}laration. Por tile Ilet,ermination of the eharaC'teristies oI tlle gl"Ol1ncl mo\'e- lllentf\, tlle Finite Blemellt 3Iethod is a}lvlied (a). A suitable computer }ll"Ogramme waH uHed for the eaHe cOIIHidered. 1'he ~urfaee of the layer exalllilled of length L and height H i~ divieled by horizolltal and YI'l"tipallilles into 1'I]ualredangI11ar l'lements "" " " -~,_o._",_~. " , " ~ ~: ( • .• J ' . 0-----'-' : " r of lenght c:Lc anll heigilt 1111, orelerecl in llines and II! polllmm. Tllese reetangular elements are subf\equently ~ubdi"il1ecl into tTiangular elemelltf\ (Fig. 3) for l'IJllveniellee of vrogramllling alli! eomVllting. Tlle lllaSH of t11e examinell layer is 1'0mic1ered 1'01H'entratell on tile joints of the finite elelllent system. Namely all joints are comillerell a~ llH1Sf\ }lOintf\ witb lllass ilI (,OiTe~WJlle1ing to the maSH of one redangular element Lb:-Lly (Fig. 3) exce}lt for tbc jointf\ of the bOlll1llaries wllere the ma~s i~ ilI (2 alleI the eOl"ller~ ,dwl'e the lllass is .Jl (J. The wl'ight H oI the mass .Jl if\ H =- !1x·!1y·y wilere y i~ the mean ~jleeitic ,,-eight of the layer at the regimI of the joint C'omillerel!. The Ilorizontal Seif\lllil' force af'tillg statienlly on eaeh joint is Ir .= 6('1', li) 11 ,dlCTe 6('1', li) is the funl'tion Ilef\eribing the di~triblltion of tlle f\eiSlllic ael'cleration over the HllI"faee of the la;rer. APPLI('AT10X 01<' T lll F1XITE IlLE~IEXT ~1}:T110j), }:T(', ,i17 3, - SBJP.)TICTTY OF TUE RE(TTOX 'rhe m'ban area, of Saloniea is not aseiilmif'. }Ially Htl'Ollg (,:\l'th- qllakes have shaken the regiOlI ,dth (le8hudive results in the pagt, 'l'hl' mOHt deHt l'Ildive emt,hquake IOI' tlw ('ity of Sa]ollica 8eems io have hecn the ~l\()('k of ,July 5, 190~ with nmximlllll illtmlHity "III-IX of the l\1ercalli-Sieberg H(':l1e. 'rhe lllaoximum int,enHil,y OhHcI've11 in t.he area of Salollka OV('I' the }lel'iod 1800-1!)72 is, according t{) the cxiHting map of isolines of maximllm int,ensit,ieH of t.he l'egion, IX (legreeil oI the Mercalli scale. AN'Oi'l1ing t,o t,he elllpil'ieal fOl'nlUla fol' t.he gl'oumI sei8mie a('f'de- l'ation ag for t,he re/(ion of Greef'e: a. = O.~W-O.1·[ +0.01 . I2 ,\'\wre 1 i~ the }laximUlll eX}lect,e<1 int,ensity of the Mel'calli scale, t.he maximum aceelel'at,ion eX}lederI at the gl'OlllH] sUl'hwe fol' tlw rcgion of Salonica is O.17q. 'l'lw pl'0dominant j}criod T aI an cXj}ecterI ea.rthquake is given by t.he fOl'mllla: log '}' = O,2HM-1.:)2 givcn by mummut,su (1 ()HO) and fOillld equal aj}j}roximat.ely io O.·H) Hee, for a magllibH]P .ilI = ii.5. Salonica is ncar in t.l10 cent.el' of the arca bOllndc<1 by tlle }lamllels .j(H'Ì-4-1°N an(l t,hl' lnt'l'il1i:lllS ~2,GoB-23.5oK 'rhe lW~U'{\St, fMi around Salonica ,\'!lich getWmtcl] lar/(e cal't.hquakp8 al'P at (listances J5km- 30km, 1mt. t,hc str011/(er neal' l1estl'uC'l,iyp eart,hquakeg al'0 frum !iO km epiC'ent,ml di~tances, 1'he l'ctmn j}crio(]s far slmllrn\' Hl!MkH whif'h 01'- C'mcd in t.]1C' regi 011 of Salonica, are 18-2:) ~' ('al's for .:11 = 5.5, -l5 ·i)5 yml-l's for il! = H, 110-1:)f) ycarH Ior.:ll = H,5, awI ~75-335 yeal's fOl'.ilI =7 C'), 4-. - GBOl.OGlCAL .H'V TRC'TOXlC CHAHACTRRTRTTC~ OF 'l'HE lmmox 'l'hp sllhsoil oi t.lw l'egion of SalolliNl is not homogen('()1Is an<1 val'ips Irom j}lace to pIace. Alluvium C'omolida,t.ed sand l1uncs, gra,nit.ic metamol'j}hies ek, are t.h(' 1IS1ial tyj}es of soil whi(,h com}l08P the sl1b- soil of t.hc re/(ion. ,:; ) R .A • • \. ROUi'li'lOPOU I.OS - C. A . i'l l"IO IAKEZH! T IIC surfaee layer may be assumed to have a mean thicklless of 20m nbove the 1Ied1'o('1, . I II l'ig. J are Sh OWll SOllW t.ypi ca l hOI'(;hole8 of the regimi of SalOlli ca. l'rom thcse cham.cte1'istie boreholes an d .... ,~ ." .. eOR EH O L ES , , ... , ... " . _., • • _"-"C.".. ... .,'" .... 0' ... . "00 • 00 . "" , .... . "" • ... , .. <..,.,.. ..... , .... .. ~ .. , . ........ " « .. , • ••• • ot·he1'8 exist illg we emi a]f;u :l,CC',c]lt an avel'age water leve l a.t 1\ depth of Brn. Alth ough t,he m l.-'(: hallical char:\Ct.e I·istics or th e !Huface l aycr ma y va!')' from pIa ce to l liace, t hc smaii ~lua.ll t i tics of the cxist.ing sand, pe1'mi t U~ to consiùer t hc layer ùuring thc pl'esent l)1'elim in l\ ry stwly as allllvi lll11. ' l'h (' ('hlll':Wt(>1'i81i(.1) o r 111i ); allu\" inm an' ('s lima1 (',J ai! ftlllowing: Bl' lnw t lll' walCl ' ICrI' l t lll' alhlYiulll is l'om}l ll'h.I.\' ~:ll\l l 'att'd allil l he fI ]!cdJjt wI·iglit. i,~ gi v I'n h,I' the COl'mula: y = r ,-lI(Y.,.-) wl1l'1'I' -Ji ifl t.hl· ]!uroilil~', y. il; th(' S!le>e>if Ì<' wI' ighl of 111(' ~olid par ti('h'il, nlld y", is the spe eilie \H'iglit ui tllC' lI'a!pr. 1·'01' tlip Yahw~ or ì" :!.7:1, Ji -= tUO alld y", = l, th(' Ynhw (Ii tlie ~ahmllpd ~]le<'iti(' \\'(' i~ht or lh(' I;lyel' i.~ found y = :!.O ii t / m J , .. \bon' t!te wat{'!' 1('''1' ] 1]1(' :d lll"inl1l i .~ l' :l l'i ly iSl.1 t u n ll ('I I R lld lit e ex iiJ lilig Illl'lI l) lIrl'llwlII s s ho l\' il Ilwa n ":llu(' o( r = 1 .80tjm 3 • Thl' labora I OJ'~' t 1'S11) f rom eXa lllill l'l l SII(>('i m(' 11 1$ ,<; 1111Wt'l l a IllI ih' t>al isla cttu 'y s 1rl'Ilg1h llt'J'lllif.t i ng n .~ t u an'{' llt a Illlli ll lli 1i\ IIr {'Iil st i"ily H - 300kgj('m~. Thc P(li~~oJl '~ l~l t io ii' lakl'll l'qual t o Ihl' l'alUl' 1'-- OA5. Vimdlr, thl' vplueily (lf S·wn\'('s ili lhp aIlu\'inm is as~t1m('d l'qllal tu v, = O.2i'i km/Hl'(·. The afOl'C llwlltiollPl1 nlhl\'itllll Ih']losit i ~ ('UIlSil]l'\'l'd to be i'tl'Oll g ('nu tlgh cnablill/.t thc npplk:l t,iol1 of tht' l'la .~tit tli('OI'~· HIlII mkl'oli'('mOi' tec hu iqul' s. At'I'Ol'd i ll g" lo thl' ('x i!;1 in$! j.('('ultlj.('icalil a ta , 111 (' bl' llnwk of I hl' l'l'g iOII u( S a lonka ('u ll s ifitS Ilmill ly 01 li 1I 1('S1Ot1('1) a lll i 111:II'hl('I$. 'l'Il{' nwd lallic' al Ch ;U";lC1<'I'is l il'" of lilìlC:'ltO)1I' aI'<.' ,!t' l1 foii ty f! = :? ,:111, IIlUl11l 11l i; uf (' Iasl il'i t.y ... 1E~ entl !!C1) i1l'(' CHli llmtt'l l fili' l11 c bt', l l'(wk u f thl' 1"('j.(' iOll u r ~alo11iell l'q\la l to t'" = :!.5 k m fs c(', l'. - 1.0 k m f iil'(' , '[, I IP~ {' 1'$1II1i';; al'(' HllJJ I'Oxi- A. A. ROUSSOPOlJLOS - C. A. SYIDfAI,EZIS mate estimations, since there are no yet accurate measuremenh, oI the wave veloeities of the region. As mentiolled before the maximum aeeeleration 011 the ground sul'faee is ea,kulated aeeording to thc (,xiflt,illg data, for an inttlll~ity I = IX allll fOllnd ('qual to 0.17 g. 'rhe corre~})olllling intemity lo at thc sllrIacc nf the hedrock i~ caleulatcd from thc )INlvedcv Iormula ("l: I o =l-LlI whcl'tl I is i,lw ~ul'face int.cnsity and LlI is givcn by the eXlll'cssion: (Y"'") . Lll = LJT~ -+- ,1 I", = 1.67 log + J' · e - U'OU-y!1>l whcrc yovo and Y11'1 are the values oI seismic impedance or l'igidit.y Ior UIC bedroek and the alluvium respedively, 71 is the depth of Lhe '''ater level in met(m; amI v is a, eonstani, eoeffieient taken pqual Lo 0.8 for the regi 011 eonsi!1cred. li'nr thc value~ y l = 2.0 L!m~ VI = 0.25 km!ser l'o = 2.30 tjm3 , v o = l.0 kmjsee and li = 8.0 m, ,,'e have i,ha,t LlI = I and hcnce lo = VTTT, corresponding to a bedrock sul'faee accelemtion equal to 8 0 = 0.10g. 'l'his avproximat,e vn.lllc fnl' the bedl'ock a,ccel(, - ratioll is uf\ed in the present l)apcr bccausc, thcre are no oLhcr, more a.ccumtc data , available Ior the regimI. From the s(,ismnLpdonie ma,p of the l'tlgion of Salolliel\ we cali O!)fWI'V(, thc following zones having common bOl'ders: a) pnf\i,-teetonie del)Osit.; bl eOml)lex geosynclìne of Yan111r; c) Serbomaccdonian ma,',,~if (Ridge). 5. - J{,ESUT,Té\ - COl'\(:T,l;SI01'\S Four eases 01 Iree zones 01 a del)i,h 20m are cnnsidered with values 01 the paramei,er L equal to 25m, 50m, 75m, 100m, respeet.ivcly. The st.el)f\ Llx, .i1y along the aXCf\ o,,~, oy arc taken equal to 5m aneI ·1m rCf\pectivdy for all ca,'!Cf\. In Figs. 6(1. , Ob, 6e, 6d t.he horizontalrelativc to thc hedl'Ock displace- ments ò~ along Uw depi,h ti of the Hlluvium layer considercd are shown. Namely, Ior ea,eh case of Iength L, tlw horizolltal displaeements along vertieal sedions nf the alluvium layer, taken cvery 5m, are presented. The ordina,tes x oI each scctinn arc written on the corresponding curvp. ,\l'1'J.1 CAT 1QX O ~' TUt: "l Xln: ~:u:.\n:XT MET ll 0 1>. t:T('. 52 1 L·2!im L . ~Om " . . ~. F io 6 . ~ , ~ .. L dOOm '" 1;22 ln Fig. T tllc Yltriation of thc Ilol"izontal dis}llacemcnts (5~ witll tlle lpngtlt L is sllown for tlle grollnd slufaee. ..\s s(,L'n from tlle 1'ig-\11'e T tlle nmximum displa('('mL'nls do not nu·.v significantly f01' rl'lativdy Ilig-Il values or tlle lt'ng-th [., ~.(cm) " • • '-----",_----.oo,-----~, .,_----.,,_----L (m ) Flg. 7 H is to be notcd finally that lite ealcnlal.ion of the dispiacelllents of tllc alluvium layel" aCe()1'i1ing 1.0 I.he Finite Blement. :illethod 11111Ht tnke int.o eonsidemtion the elaBI.ic Ol" anelastie }H'opm"ties of tlle alln- Vi11111 i~o1lHidered and Illainly its anisot.ropie st.renghl., witlt \.he best possible accun\ey. On fig-ml',~ H, in the shaded regioni'! j.}\C CUl"Yes whieh are not inll11em'ei1 ,~ignifi(,:l1lllr by I.lte boulHlary ('owlitions of thc cdgcs BE', GU' (Iig. ~) are shown. lt is suggeste,'mlhquakc HI'Rj!OlIge oj Foulldaliol. '//Hi/criaIH. "l'l"ol'eediIlI!:H of the 3n\ Elll"Opeall :-iylll- ]loHilllll OIl Earthqllake Eug-iIl('('l"iug-", :-iotia, pp. 3()!J·31i. (2) BUB"OY, :-i. ('i. Hl., IHiV. - Seismic :;oll;'nlj (lf Zagrcb. "l'l"Oe(>(~jlilll-,'1ò of the :1\\ ElIropean SYllIposilllll on Earthqllake Eugineel"iug-", :'\ofia, pp. !J5·jU2. AJ'I'LICATIO~ 01' TUE FIXIT}; ELE~IEXT _\IE1'llOIl, ETC. (~) llll ,\hOl'OUI.OS, .1., IOil. - (fellNal ('ollsilleralion8 al"'lll a .lJiero::OI;ill[J SIIlII!1 (11111 'J'lIrsHrdolliki IIH a sile fo)" such a slnll!}. B,'lgl":ul. (-l) GALA~OPc)ULO~, A. G., IOil. - , ... ·rismu!0!J.I!. Ath('II~. (~) GAUS, :\T. l'., KIIEIlIF, :IL A., IOi2. - Zil/wlioll (Imi .1firro:rJ//alion. "l'n)(,l'eIiÌllg-~ of litI' lni,01"nntionnl Confel"('!l('l' Oli :I[il'l'm:onation", \YaHlting-ton, S('atUp, I. (") llJHI~~, l. :\1., :-iEJ':J), Il. B., IfHii. h'I'S}JOII.W of Hurlh !fO///,"H dllriJlIj 8(rJ"lh,/,w/," ~ . "l'ro('('c,linl-(s of tltc ,\.:-:;.C.E.", 93, R:\13. l'I KAX,U, h" 1%(;, - l"'l,m",,1 li"'p;,';",,1 F""",[" l''' "" C'1"",,,"",';,II,, of H/roll[J /<,'arlllljllll!;C .1l"lionH. ''l'1"o{'{'eIiÌllgs of .11l]HlI1 ElIl'thqnnke ]~lll-(inccring Rylll]JOi'-inlll", (8) }\OIl ,\YASIII, Il., }\AfI ,\)II, Il., lf)i2. - A mdlwll for loeal8ri8mic inll'Jlsi/y :::onill[JIlIrlf!S Oli- Ih{' Imsis of Nub80il condi/iolls. "l'wl·cl',lin.!:!;s of 1"he IntcmntÌollnl ('ollferclIrc on :\JÌen,7.onntion", \VnHhillg-ton, Rl'attlc, Il, l'l'. 513-528. (") :llEJJ\-EJJEV, K_, 1f)0:;. - 8n.rJilll'erin!J 8ei8111oI0[J!I. "Al'. of :-kÌe!l('c C'KSR". ('O) l'AP.L~TA~L\TTOU, D .. 1., ]flil. - (;l'''unrl lIIolion 01111 rI'HIIOIIS{' of Barlh 81)"lIdllrf R subire/nl /0 s/roJlIj 8rulhljuukl's. l'h. ll. TlteHÌ~ ]lIl\}(>l'inl l'o\\f'I-(c, T.'lll,l'lll. (Il) SEEll, Il. B., IOlii. _ H/opI' s/abilil!} lIurin.rJ Eartllljllllke. "l'l"ol'el'liillgs of tllc A.S.C,E.", 93, S'14. (lO) STEFA~OU, G., IDiO. _ Ali upaimelllalulHl/hrorrlicrd inres/i!Jalirl/l illl" /111' perfora/ed :::O!leN fil)" IlItderl)" )"l'lIclor pre~s!!re UNSe/S. l'h. D. 'l'hesiH, lml,erial {'olleg-l', Lowlon. (l") :-:;'l'El'lm~SO~, \Y. R" ]Uil. - 8dsmic Jliero:::ollilllj iII S~ II' Zealu/ld. "Bnllptin of 1"he Ne\\" t.l'nlllIH1, So{'id.,Y for Earth(lllllkc Enl-(ilwpr- Ìllg",4, l, :\Ian'h. ('-') \YlI, T, H., IDlii. - Soil JII'clwllic8, Allyn alll\ Ba{'oll, Im', B,,~ton.