Estimating the modulus of elasticity of the rock material from compressive strength and unit weight

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1 Sept_47-52:Templte Joul 11/10/08 11:26 AM Pge 621 Syopsis Estimtig the modulus of elsticity of the ock mteil fom compessive stegth d uit weight by I. Ock* The modulus of elsticity of ock mteil (E i ) is impott ock popety tht is used s iput pmete i the desig stge of egieeig pojects such s dm d tuel costuctios, miig excvtios, d so foth. Howeve, detemitio of the modulus of elsticity is sometimes difficult to obti by lbotoy tests becuse high-qulity coes e equied. Fo this eso, empiicl methods fo pedictig the modulus of elsticity of ock mteil hve bee popul esech topics i ecetly published litetue. I this study, the eltioships betwee the uixil compessive stegth (UCS), uit weight (γ) d modulus of elsticity fo diffeet types of ocks wee lysed by usig 177 dt obtied fom lbotoy tests cied out o coes obtied fom dill holes withi the e of the Kdıköy-Ktl Meto lie (Istbul, Tukey). Keywods: Kdikoy Ktl Meto, uixil compessive stegth, uit weight, estimtig the modulus of elsticity. Itoductio The modulus of elsticity of ock mteil is oe of the most impott ock popeties used i desigig civil d miig pojects such s dm d tuel costuctios o mie lyout desig. High-qulity coe smples e eeded to obti this pmete usig lbotoy tests. Sometimes it is vey difficult to obti highqulity coes fom pticully thily bedded d hevy ock msses. Becuse of this, the plig egiee my estimte the modulus of elsticity fom the othe ock popeties by usig pedicto equtios published i the litetue. Aufmuth (1973), Schpzis (1990), d Xu et l. (1990) used Schmidt hmme to estimte the modulus of elsticity. Some of the othe eseches, icludig Schpzis (1990), Rohde d Feg (1990), Tuğul d Zif (1999), Plchik (1999), d Lshkipou d Nkhei (2001) pefeed usig uixil compessive stegth to estimte the modulus of elsticity. Aothe tem of eseches (Somez et l d Somez et l. 2004b) costucted ecet empiicl ppoches by usig multiple iput pmetes such s uit weight d UCS fo the estimtio. Somez et l. (2006) poposed tificil eul-etwok-bsed pedictio cht tht cosideed uit weight d UCS s iput pmetes. I this study, 177 dt sets icludig UCS, E i d γ hve bee used. These dt hve bee obtied fom 177 dillig holes log the 21.6 km oute betwee the Kdikoy d Ktl Meto tuels. The ogoig costuctio wok is beig coducted by the Istbul Metopolit Muiciplity. The tests of UCS (Figue 1), uit weight d modulus of elsticity wee pefomed o the coe smples i ccodce with the pocedue suggested by ISRM (1981). Avege coe legth is 13.8 cm, vege dimete is Legth/dimete tio is bout 2.2. The vege UCS vlue is 43.8 MP. The vege modulus of elsticity vlue is 10.0 GP. The vege uit weight vlue is 26.6 kn/m3. The me vlues of some geotechicl pmetes of the ock smples collected fom the tuel oute e give i Tble I. The geologicl sectio of the egio is give i Figue 2. Geel ifomtio bout the poject of the Kdikoy-Ktl il tspot system d meto tuels The Kdikoy-Ktl il tspot system poject stts t Kdikoy d psses though the disticts of Uskud, Mltepe d Ktl. The legth of the il tspot system is 21.6 km d costuctio of 16 sttios is pled. The elevtio of the ilwy t the Kdikoy sttio is 36.0 metes below the se level. The Kdikoy-Ktl il tspot system is itegted with the Mmy udese il * Istbul Metopolit Muiciplity d Istbul Uivesity, Miig Egieeig Deptmet, Istbul, Tukey The Southe Afic Istitute of Miig d Metllugy, SA ISSN X/ Ppe eceived Oct. 2007; evised ppe eceived July T s c t i o P p e The Joul of The Southe Afic Istitute of Miig d Metllugy VOLUME 108 REFEREED PAPER OCTOBER

2 Sept_47-52:Templte Joul 11/10/08 11:26 AM Pge 622 Estimtig the modulus of elsticity of the ock mteil Figue 1 () Test specime befoe UCS test (b) test specime fte UCS test (c) typicl stegth peiod of test cuve obtied fom the UCS tests Tble I The me vlues of geotechicl popeties of the ock smples (IBB, 2005) Fomtio Lithology Uit weight Poisso tio Itel fictio Cohesio (MP) Uixil comp. Modulus of (kn/m³) gle (º) stegth (MP) elsticity (GP) Tky Sdst.-siltst.-clyst Tuzl Shle Ktl Shle-limestoe Kutkoy Sdstoe-coglom Dolyob Limestoe Figue 2 Kdikoy-Ktl meto system geel geology (IBB, 2005b) tuel poject, which will joi the Euope d Asi hlves of Istbul t the Ibhimg Sttio with tuel ude the se. Both pssege tspottio d the coectio to the Euope side of Istbul with the Mmy Poject will be povided with the itegtio with the Mmy Poject (Figue 3). The meto system is composed of double tuels hvig dimete of 6.10 metes. The depth of the tuels fom the sufce is ppoximtely 30 metes d the distce betwee two tuels is 32 metes. The pssege cpcity fo oe wy is pled t bout pesos/hou. The tuels will be excvted by two tuel boig mchies (TBM) d two eth pessue blce mchies (EPBM). The sttio pltfom tuels, ccess tuels, shfts, switch tuels d coectio tuels e excvted cosideig the ew Austi tuelig method (NATM), usig impct hmmes d od hedes. Dtbse used fo sttisticl lysis The dt sets, composed of uixil compessive stegth, uit weight d modulus of elsticity, wee obtied fom lbotoy expeimets cied out o the dillig coes obtied by the Diectote Geel of IETT, Istbul Metopolit Muiciplity fo Kdıköy Ktl Ril Tspot System. While the vlues of uixil compessive stegth 622 OCTOBER 2008 VOLUME 108 REFEREED PAPER The Joul of The Southe Afic Istitute of Miig d Metllugy

3 Sept_47-52:Templte Joul 11/10/08 11:26 AM Pge 623 Estimtig the modulus of elsticity of the ock mteil compessive stegth d uit weight vlues except fo those of the Dolyob fomtios. The pedictio pefomces of suggested eltios e give i Tble III. Pedictio pefomces of these equtios wee evluted by usig both coeltio coefficiet () d the oot me sque eo (RMSE), give i Equtios [8] d [8b] espectively. T s c t i o Figue 3 Mi oute of Kdikoy-Ktl meto system vy betwee 1.9 MP d MP, the modulus of elsticity chges fom 0.7 GP to 38.4 GP. The uit weights vy betwee 22.5 kn/m3 d 28.9 kn/m3. The vitio histogms of the dt e give i Figue 4. The distibutio of the dt o the modulus tio gph suggested by Deee d Mille (1966) is show i Figue 5. P p e The eltioships betwee the modulus of elsticity, compessive stegth d uit weight The eltioships betwee the uixil compessive stegth d the modulus of elsticity of the ock mteil collected fom ech fomtio log the Kdikoy Ktl Meto System oute hve bee ivestigted septely usig dt sets obtied fom ech geologic fomtio (Tble II). The eltios e lso lysed by usig the whole dtbse without septig the dt ito geologicl fomtios (Tble II d Figue 6). While the coeltio coefficiet of the eltio betwee E i d UCS ws obtied s 0.809, the eltioship betwee E i d γ ws lso sought (Figue 7) d coeltio coefficiet of 0.50 ws obtied. To icese the pedictio cpcity, the eltio betwee E i d multiple iput pmetes such s UCS d γ ws lso ivestigted by usig combied pmete (CP) s used i the litetue (Somez et l. 2004). Whe the whole dtbse ws cosideed, the eltio betwee E i, UCS d γ hvig coeltio coefficiet of ws obtied (Figue 8 d Tble II). Pedictio pefomce of suggested equtio The mesued d pedicted vlues of the modulus of elsticity usig equtios fom 1 to 5 e give i Figue 9. The pedicted d mesued vlues fo ll the fomtios give vey sigifict coeltio coefficiets log 1:1 lie except fo the Dolyob fomtio, with coeltio coefficiet of The othe vlues e s follows: fo the Tky, Tuzl, Ktl d Kutköy fomtios, the coeltio coefficiets e 0.92, 0.90, 0.75, d 0.91, espectively; fo ll the fomtios, the coeltio coefficiets e 0.81 (fom Equtio [6]) d 0.83 (fom Equtio [7]). I shot, the equtios obtied fom the sttisticl lysis show tht the elsticity modulus of ock smples epesetig diffeet geologicl fomtios c be pedicted sufficietly fom Figue 4 The histogms d sttisticl evlutios of the dt used i to pedict Ei The Joul of The Southe Afic Istitute of Miig d Metllugy VOLUME 108 REFEREED PAPER OCTOBER

4 Sept_47-52:Templte Joul 11/10/08 11:26 AM Pge 624 Estimtig the modulus of elsticity of the ock mteil Modulus of elsticity Ei (GP) Modulus of elsticity Ei (GP) Umxil compessive stegth, UCS (MP) Figue 5 The distibutio of the dt bse o the modulus te gphic by Deee d Mille (1966) Modulus of elsticity Ei (GP) Modulus of elsticity Ei (GP) Uit weight, γ (kn/m3) Figue 7 Coeltio betwee uit weight d modulus of elsticity fo ll fomtios Figue 6 Coeltio betwee UCS d modulus of elsticity fo ll fomtios Figue 8 Coeltio betwee UCS, γ d modulus of elsticity fo ll fomtios Tble II Sttisticl eltioships fo estimtio of modulus of elsticity fo diffeet geologic fomtios d ll fomtios togethe Equtios Numbe of dt Fomtio Lithology E i = UCS (1) 73 Tky Sdst.-siltst.-clyst E i = UCS (2) 8 Tuzl Shle E i = UCS (3) 38 Ktl Shle-limestoe E i = UCS + 1.1γ (4) 20 Kutköy Sdstoe-coglemet E i = UCS (5) 34 Dolyob limestoe E i = UCS (6) 177 All fom. All lithology bove E i = CP CP = L UCS0.689Lγ4.95 (7) 177 All fom. All lithology bove OCTOBER 2008 VOLUME 108 REFEREED PAPER The Joul of The Southe Afic Istitute of Miig d Metllugy

5 Sept_47-52:Templte Joul 11/10/08 11:26 AM Pge 625 Estimtig the modulus of elsticity of the ock mteil Tble III List of suggested equtios fo estimtig the modulus of elsticity, equied pmetes d pedictio cpcity of these Equtio(s) Lithology Requied pmete(s) RMSE E i = UCS (1) Sdst.-siltst.-clyst. E i = UCS (2) Shle UCS o UCS d γ E i = UCS (3) Shle-limestoe E i = UCS + 1.1γ (4) Sdstoe-coglemet. E i = UCS (5) Limestoe E i = UCS (6) All lithology bove UCS E i = CP CP = L UCS0.689Lγ4.95 (7) All lithology bove UCS d γ T s c t i o P p e Modulus of elsticity Eim (GP) Cummultive fequecy Pecetge eo, PE (%) Figue 9 Coss-coeltio betwee pedicted d mesued vlues of Ei fom Equtios [1 5] Figue 10 The eltio betwee pecetge eo d cumultive fequecy Coclusios [8] [8b] whee x d y e stdd devitios, x d x' e the mesued d pedicted vlues, espectively, d is the umbe of dt. If the model hs excellet pedictio cpcity, the d RMSE will be 1 (o -1) d zeo, espectively. I dditio, by usig 177 dtsets collected fom vious lithologic types of ock, pecetge eos e dw (Figue 10). Pecetge eos fo ppoximtely 75% of the dt e less th 50%. Theefoe, the poposed empiicl equtios hve stog pedictio cpcity d c be used to estimte the modulus of elsticity of itct ock fo pcticl puposes. Detemitio of the modulus of elsticity of ocks equies high qulity coe smples; theefoe, it is sometimes difficult to detemie the modulus of elsticity usig diect methods pplied to coe smples obtied fom difficult goud coditios such s sttified (thily bedded), highly fctued d block-i-mtix ock. I this study, to ovecome these poblems, sevel bsic equtios wee poposed by usig extesive dtbse icludig modulus of elsticity, uit weight d uixil compessive stegth of itct ock. The sigifict eltioships i the sttisticl lysis wee evluted by usig wide ge of dt fom diffeet ocks of diffeet geologic fomtios. The dtbse used is of get impotce fo cuet egieeig pplictios i Istbul sice it is obtied fom dt of 177 dilligs cied out log 21.6 km tuel oute o the Asi side of Istbul. The empiicl equtio peseted hs stog pedictio cpcity d c be used to estimte the modulus of elsticity of itct ock fo pcticl puposes. It is cocluded tht the modulus of elsticity c be estimted sigifictly fom the uixil compessive The Joul of The Southe Afic Istitute of Miig d Metllugy VOLUME 108 REFEREED PAPER OCTOBER

6 Sept_47-52:Templte Joul 11/10/08 11:26 AM Pge 626 Estimtig the modulus of elsticity of the ock mteil stegth d uit weight of the ock usig pesetly poposed pedictio equtios. It is suggested tht the give pedictio equtios my lso be used i the ie ogoig meto pojects ude costuctio i Istbul tht pss though the geologic fomtios fom which the dt used i this study ws gtheed. The utho is vey ppecitive of Pofesso Nuh Bilgi fo his get cotibutios to the muscipt d his kid help. Refeeces AUFMUTH, R.E. A systemtic detemitio of egieeig 20 citei fo ock. Bull. of Assoc. of Egieeig Geology, vol. 11, pp DEERE, D.V. d MILLER, R.L. Egieeig Clssifictio d Idex Popeties of Itct Rock, Deptmet of Civil Egieeig, Uivesity of Illiois, pp ISRM. Itetiol Society fo Rock Mechics Suggested Methods: Rock Chcteiztio., Testig d moitoig, E.T. Bow (ed.), Pemgo Pesss, Lodo IBB. Istbul Metopolit Muiciplity, IETT Geel Diectote, KdikoyKtl Meto Poject Geotechicl Repot IBB. Istbul Metopolit Muiciplity, IETT Geel Diectote, Egieeig Geology Repot,. The Poject of the Istbul Kdikoy Ktl Ril Tspot System. 2005b. LASHKARIPOUR, G.R. d NAKHAEI, M. A Sttisticl Ivestigtio o Mudocks Chcteistics. Rock Mechics, pp OCTOBER 2008 ROHDE, J. d FENG, H. A1ysis of the Vibility of Ucofied Compessio Tests of Rock, Rock Mechic d Rock Egieeig, vol. 23, pp SACHPAZIS, C.I. Coeltig Schmidt Hdess with Compessive Stegth d Youg s Modulus of Cbote Rocks, Bull. It. Assoc. Eg. Geol. vol. 42, pp Ackowledgemets 626 PALCHIK V. Ifluece of Poosity d Elstic Modulus o Uixil Compessive Stegth i Soft Bittle Poous Sdstoes, Rock Mechic d Rock Egieeig, vol. 32, o. 4, pp VOLUME 108 REFEREED PAPER SÖNMEZ, H., GÖKÇEOĞLU, C., KASAPOĞLU, K.E., TUNCAY, E., d ZORLU, K. A empiicl equtio fo estimtig elsticity modulus of itck ock. Rockmec VIIth, Regiol Rock Mechics Symposium, Sivs-Tukey SÖNMEZ, H., TUNCAY, E., d GÖKÇEOĞLU, C. Models to pedict the uixil compessive stegth d the modulus of elsticity fo Ak gglomete, Itetiol Joul of Rock Mechics & Miig Scieces, vol. 41, 2004b. pp SONMEZ, H., GOKCEOGLU, C., KAYABAS, A., d NEFESLIOGLU, H.A. Estimtio of ock modulus: fo itct ocks with tificil eul etwok d fo ock msses with ew empiicl equtio, Itetiol Joul of Rock Mechics & Miig Scieces, vol. 43, o. 2, pp TUĞRUL, A. d ZARIF, I.H. Coeltio of mielogicl d textul chcteistics with egieeig popeties o selected gitic ock fom Tukey, Egieeig Geology, vol. 51, pp XU S., GRASSO, P., d MAHTAB A. Use of schmidt hmme fo estimtig mechicl popeties of wek ock. 6th Itetiol IAEG Cogess, pp The Joul of The Southe Afic Istitute of Miig d Metllugy