쉴드 TBM 굴진주요영향인자분석및굴진율예측모델제시 조선아 1* ㆍ김경열 2 ㆍ류희환 3 ㆍ조계춘 4 1 정회원, 한국전력공사전력연구원차세대송변전연구소구조내진연구실연구원 2 정회원, 한국전력공사전력연구원차세대송변전연구소구조내진연구실책임연구원 3 정회원, 한국전력공사전력연

쉴드 TBM 굴진주요영향인자분석및굴진율예측모델제시 조선아 1* ㆍ김경열 2 ㆍ류희환 3 ㆍ조계춘 4 1 정회원, 한국전력공사전력연구원차세대송변전연구소구조내진연구실연구원 2 정회원, 한국전력공사전력연구원차세대송변전연구소구조내진연구실책임연구원 3 정회원, 한국전력공사전력연구원차세대송변전연구소구조내진연구실선임연구원 4 정회원, 한국과학기술원건설및환경공학과교수 Study on the effective parameters and a prediction model of the shield TBM performance Seon-Ah Jo 1* ㆍKyoung-Yul Kim 2 ㆍHee-Hwan Ryu 3 ㆍGye-Chun Cho 4 1 Researcher, Structural & Seismic Tech. Group, Next Generation Transmission & Substation Laboratory, KEPCO Research Institute 2 Principal Researcher, Structural & Seismic Tech. Group, Next Generation Transmission & Substation Laboratory, KEPCO Research Institute 3 Senior Researcher, Structural & Seismic Tech. Group, Next Generation Transmission & Substation Laboratory, KEPCO Research Institute 4 Professor, Dept. of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology (KAIST) *Corresponding Author : Seon-Ah Jo, jsa816@kepco.co.kr OPEN ACCESS Journal of Korean Tunnelling and Underground Space Association 21(3)347-362(219) https://doi.org/1.9711/ktaj.219.21.3.347 eissn: 2287-4747 pissn: 2233-8292 Received March 8, 219 Revised April 13, 219 Accepted April 16, 219 This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/ licenses/by-nc/4./) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Copyright c219, Korean Tunnelling and Underground Space Association Abstract Underground excavation using TBM machines has been increasing to reduce complaints caused by noise, vibration, and traffic congestion resulted from the urban underground construction in Korea. However, TBM excavation design and construction still need improvement because those are based on standards of the technologically advanced countries (e.g., Japan, Germany) that do not consider geological environment in Korea at all. Above all, although TBM performance is a main factor determining the TBM machine type, duration and cost of the construction, it is estimated by only using UCS (uniaxial compressive strength) as the ground parameters and it often does not match the actual field conditions. This study was carried out as part of efforts to predict penetration rate suitable for Korean ground conditions. The effective parameters were defined through the correlation analysis between the penetration rate and the geotechnical parameters or TBM performance parameters. The effective parameters were then used as variables of the multiple regression analysis to derive a regression model for predicting TBM penetration rate. As a result, the regression model was estimated by UCS and joint spacing and showed a good agreement with field penetration rate measured during TBM excavation. However, when this model was applied to another site in Korea, the prediction accuracy 347

Seon-Ah Jo ㆍ Kyoung-Yul Kim ㆍ Hee-Hwan Ryu ㆍ Gye-Chun Cho was slightly reduced. Therefore, in order to overcome the limitation of the regression model, further studies are required to obtain a generalized prediction model which is not restricted by the field conditions. Keywords: TBM performance, Penetration rate, Uniaxial compressive strength, Rock mass properties, Regression analysis 초록도심지터널공사가많아지면서이에따른소음, 진동, 교통불편및민원저감을위해 TBM 굴착이증가하고있다. 그러나이러한추세에도불구하고국내 TBM 공동구설계및시공을위한기준들은대부분해외기술 ( 일본, 독일등 ) 을이용하고있어국내환경을고려하지못하고있다. 특히, 공동구 TBM 설계의주요기준이되는굴진율은대부분일축압축강도만으로산정되며이마저도실제현장특성과맞지않아개선이필요하다. 본연구에서는국내현장에적합한굴진율을예측하기위해수행되었다. 이를위해시공중인소단면쉴드 TBM 굴착현장의지반및굴진데이터를수집하고상관관계분석을통해굴진율에영향을미치는주요인자를파악하였다. 도출된영향인자들은통계적분석기법을기반으로한다중선형회귀분석에적용되어굴진율을예측하는회귀식의예측변수로이용되었다. 결과적으로회귀분석을통해도출된회귀식은일축압축강도와절리간격을예측변수로추정되었으며, 해외경험식과비교하여국내현장굴진율의예측정확도가높은것으로나타났다. 다만, 이회귀식을타국내현장에적용할경우예측오차가다소증가하였다. 회귀식이갖는이와같은적용한계를개선하기위해서는추가적인연구를통해현장조건에제약을받지않는굴진율예측모델도출이필요할것으로보인다. 주요어 : TBM 굴진성능, 굴진율, 일축압축강도, 암반특성, 회귀분석 1. 서론 전세계적으로도시화가진행되면서도심지지하공간활용에대한수요가증가하고있다. 과거도심지터널에주로적용된개착식공법이나발파공법등재래식공법은사고위험이높고소음 진동으로인한민원, 교통체증등여러문제를야기하였다. 기술적진보와더불어재래식공법이갖고있는문제를해결하기위해도심지지하공간, 특히터널시공에기계식굴착공법의적용사례가늘고있다. 기계식굴착장비의하나인쉴드 TBM (Shield tunnel boring machine) 은 198년후반처음국내에적용된이후적용사례가꾸준히증가하고있으며전력구나통신구, 하수관로등중 소구경의터널공사에서큰비중으로적용되고있다. 전세계적으로 TBM 활용이증가하면서굴착성능을높이기위한연구가국내외적으로활발하게이루어지고있다. 다양한연구를통해 TBM의굴진성능향상및예측을위한이론및경험적모델들이개발되었으며 Table 1 은대표적인굴진성능예측모델과각모델의주요변수를요약한것이다. 이러한연구들은 TBM 성능이몇가지주요지반특성및장비특성에의해예측될수있음을시사하고있다. 348

Study on the effective parameters and a prediction model of the shield TBM performance Table 1. Review of various performance prediction models Predicted parameter Researchers Ground factors Machine factors PR Graham (1976) UCS Cutter force PR Farmer and Glossop (198) Tensile strength Cutter force PR Tarkoy (1986) UCS - PR Hughes (1986) UCS PR CSM model (Rostami and Ozdemir, 1993) PR NTNU (Bruland, 1998) PR QTBM (Barton, 1999) PR or SE RME (Von Preinl et al., 26) UCS, Tensile strength UCS, Drilling rate index (DRI), Number of joint sets, Joint frequency and joint orientation, Porosity RQD, Jn, Jr, Ja, Jw, SRF, Rock mass strength, Cutter life index (CLI), Quartz content, Induced biaxial stress at the face, Porosity UCS, Abrasivity, Rock mass jointing at the face, Stand-up time, Water flows Cutter force, Fn, Cutter diameter Cutter spacing, Cutter tip width, Cutter radius, Cutter force, TBM diameter, RPM Cutter force, RPM, Cutter spacing, Cutter size and shape, Installed cutterhead power Cutter force TBM diameter, Cutter thrust, RPM and torque PR Yagiz (28) Peak slope index (PSI), α angle, UCS, - Distance between plane of weakness FPI Hassanpour et al. (211) UCS and RQD Cutter force, RPM FPI Hamidi et al. (21) UCS, RQD, Joint condition, α angle Cutter force, RPM FPI or Pe Delisio and Zhao (214) J v, UCS Friction force, Applied thrust force, Diameter of TBM Pe Benato and Oreste (215) UCS, GSI Fn FPI: field penetration index (kn/mm/rev) PR: penetration rate (m/hr) Pe: penetration depth (mm/rev) SE: specific energy (kj/m 3 ) J v : the volumetric joint count 초기굴진성능관련연구는암반의강도특성인일축압축강도를이용한굴진율산정방법에대한연구가주를이루었다 (Graham, 1976; Hughes, 1986; Tarkoy, 1986). 그러나이러한식들은암반의불연속면을고려하지못하며적용할수있는암반의강도도제한이있다. 349

Seon-Ah Jo ㆍ Kyoung-Yul Kim ㆍ Hee-Hwan Ryu ㆍ Gye-Chun Cho 이후암반의절리특성을고려한경험모델들이제안되었으며이중널리알려진경험모델은 CSM 모델과 NTNU 모델이다. CSM (Colorado School of Mines) 모델 (Rostami and Ozdemir, 1993) 은오랜기간축적한현장및실내실험자료를근거로개발되었으며암석학적분석, 일축압축강도, 인장강도, 밀도및세르샤마모시험등의결과를이용하였다. 그러나핵심기술을공개하지않아실무에활용하기에는어려움이있다. NTNU모델 (Bruland, 1998) 은노르웨이과학기술대학 (Norwegian University of Science and Technology, NTNU) 에서개발한경험적인 TBM 설계및시공기술로대부분의과정이공개되어있으나, 일반적이지않은암석학적실험들을필요로하고주로 open TBM 실적을바탕으로도출된경험식으로대부분쉴드 TBM을이용하는국내암반굴착과다소차이가있을수있다. 국내연구진도 NTNU 모델에이용되는암석특성지표들과 TBM 굴진성능이밀접한관련이있음을밝히고실내실험결과및현장데이터를이용하여굴진성능을예측하기위한모델을제안하는연구를수행하였다 (Chang et al., 27; Chang et al., 211; Chang et al., 212; Chang et al., 213). 그러나이들역시 NTNU 모델에사용되는암석특성지표를이용하므로이를위한실내실험수행이필요하며, 단일디스크커터에대한압입깊이산정모델이므로현장결과와는차이가있다. 기존의경험적예측모델의적용한계를극복하고대상현장에적합한모델을개발하기위해지반조사결과와굴진기록데이터를이용한경험식이다양하게제시되고있으며그중통계적분석기법을적용한연구가활발하게이루어지고있다. Yagiz (28) 는 TBM 굴진율과암반및암석특성인자의상관성분석을통해굴진율예측모델을제시하였고 Hassanpour et al. (211) 과 Delisio and Zhao (214) 는다중회귀분석을통해일축압축강도 (Uniaxial compressive strength, UCS) 와 RQD (rock quality designation) 로설명되는예측모델을개발하였다. Benato and Oreste (215) 는암반의절리특성과일축압축강도를이용한예측모델을제시하였다. 통계적회귀분석을통해제안된예측모델들은기존의 CSM 이나 NTNU모델보다대상현장에대한굴진성능예측정확도가높은것으로확인되었으나타현장적용시유사한지반환경및장비조건이아닐경우에는예측력이매우떨어져적용에한계가있다. 이와같이다양한굴진율예측모델들이연구를통해제안되고있으나아직까지국내현장에적용할수있는굴진율예측모델은극히제한적이다. 특히, 소구경 TBM의경우국내 TBM 실적의 8% 정도를차지하는데도불구하고굴진율예측과관련된많은연구가중구경이상 TBM을대상으로수행되고있는실정이다. 따라서본연구에서는국내소구경쉴드 TBM을대상으로한굴진성능평가및예측을위한연구를수행하였다. 이를위해국내 3.5 m급 TBM 터널현장으로부터지반및굴진데이터를수집하였다. 이를이용하여기존해외경험식들로부터국내현장굴진율을산정하고적용성을검토하였다. 또한굴진율에영향을미치는주요영향인자를파악하기위해지반특성인자와굴진특성인자인추력, 토크, 회전속도및굴진율과의상관성을분석하였다. 도출된영향인자를반영하여통계적분석기법을이용하여굴진율예측회귀식을제시하고예측굴진율의정확도개선을위한방안에대해고찰하였다. 35

Study on the effective parameters and a prediction model of the shield TBM performance 2. 대상현장조건 2.1 현장지질및지반조건대상현장은경기지역에공사중인연장 2,258 m의소단면쉴드 TBM 현장으로평면및단면상지질분포는 Fig. 1과같다. 시추조사결과에의하면대상현장의지층은최상부에매립층, 그하부는퇴적층또는풍화대, 기반암순으로구성되어있는것으로나타났다. 실제굴착이이루어지는지반은대부분경암으로지질은선캠브리아기의흑운모호상편마암과일부관입암류로구성되어있다. 지하수위는 G.L. -.1~-7.9 m로모든굴착구간이지하수위보다아래위치하나대부분구간이특별한이상대없이양호한암반이며투수계수가 3.95 1-5 ~1.26 1-4 cm/sec로높지않아지하수침투에의한영향은크지않을것으로예상된다. End point of the tunnel Alluvium & Marine deposit Open cut and cover L=2,374 m Biotite banded gneiss Biotite schist A Shield TBM drive A L=2,258 m Muscovite schist start point of the tunnel Inferred fault line. 4.km m 3 2 1-1 -2-3 A-A section Fig. 1. Geological strata of the TBM excavation site Table 2는현장지반에대한실내및현장실험결과를나타낸것이다. 일축압축강도는 2.1~97.3 MPa ( 평균 5. MPa) 범위로연 / 경암으로분류되었고평균탄성계수는 39.1 GPa로측정되었다. 터널구간에서평균 RQD 는 36.9% 였으며평균 RMR (rock mass rating) 은 49로 Ⅲ등급암반으로분류되어양호한암질을갖는것으로나타났다. 351

Seon-Ah Jo ㆍ Kyoung-Yul Kim ㆍ Hee-Hwan Ryu ㆍ Gye-Chun Cho Table 2. Properties of the rock located in the site passing through the tunnel Rock type Unit weight (kn/m 3 ) UCS (MPa) Elastic modulus (GPa) Soft rock 23 14.7~95.3 3.3 Hard rock 26 2.1~97.3 39.1 RQD (%) RMR 36.9 48.5 2.2 투입장비대상현장에투입된쉴드 TBM 장비는현장시방서에서요구하는기계적요건에맞춰개조한재사용장비이며굴착경 3.4 m의복합지반에적용가능한이토압식 (Earth pressure balance, EPB) 장비이다. 이토압식은굴착시커터헤드에의해절삭된토사가챔버를채우고쉴드잭에의해가압되어막장면토압과균형을이루면서막장안정을유지하는방식의장비이다. Table 3은투입된장비의제원을요약한표이다. 쉴드 TBM 장비는잭당 8 kn 의추력을가하는 12개의쉴드잭이최대 1,75 mm의스트로크 (stroke) 와 9,6 kn의총추력을가할수있다. 커터헤드의최대회전속도는 9. RPM이고, 최대토크는 1,25 kn m이다. 커터헤드에는암반절삭을위해직경 35 mm의싱글링타입 (face cutter 기준 ) 의디스크커터가 26본장착되어있다. 커터헤드의개율은 18% 이다. Table 3. Specification of EPB shield TBM Item Description TBM type EPB Excavation diameter (mm) 3,41 Length of the machine (mm) 8,6 Max. thrust force (kn) 9,6 Shield jack stroke (mm) 1,75 Max. cutterhead torque (kn m) 1,25 Max. RPM 9 Number of disc cutters (EA) 26 Disc cutter diameter (mm) 35 Opening ratio (%) 18 3. 데이터구축 회귀분석을위해현장지반자료와굴착중장비블랙박스 (blackbox) 에기록되는기계데이터를수집하였다. 지반인자는 Table 1에정리된선행예측모델의주요인자를바탕으로당현장에서수집가능한일축압축강도, 탄성계수, RQD, RMR 및절리간격 (J s ) 을이용하였다. 굴진데이터는총추력, 회전속도, 토크등이있으며굴진이진행되는동안장비에서연속적으로자동기록되는데이터를한세그먼트링길이 ( 약 1,2 mm) 간격으로편집하여 352

Study on the effective parameters and a prediction model of the shield TBM performance 이용하였다. 분석에이용한데이터항목을정리하면 Table 4와같다. 여기서굴진율 (penetration rate, PR) 은시간당굴진하는거리로식 (1) 과같이정의된다. 세그먼트한링의굴진거리 세그먼트한링의굴진시간 (1) Table 4. List of a database for statistical analysis Geological and ground properties Uniaxial compression strength, UCS (MPa) Elastic modulus, E (MPa) RQD (%) RMR Joint spacing, J s (cm) TBM operational parameter Penetration rate, PR (mm/rev) Thrust force, TF (kn) Rotation speed, RPM (rev/min) Averaged torque, Tq (kn m) 4. 데이터분석 4.1 지층및암반상태에따른굴진율특성분석암반상태에따른굴진율변화를분석하기위해종단지층도와세그먼트링별굴진율을 Fig. 2와같이중첩도시하였다. 현장굴진상황을고려할때굴진구간은 A, B, C 세구간으로구분할수있다. A구간은초기굴진을포함한 5 4 3 2 1-1 RMR -2-3 -4 A B C Ⅱ Ⅲ Ⅲ ⅣⅢ Ⅱ Ⅲ Ⅳ Ⅲ Ⅱ Ⅲ Ⅲ Ⅱ Ⅲ Ⅳ Ⅲ Ⅱ Ⅰ Ⅱ Ⅰ Ⅱ Ⅲ Fractured zone Weathered Soil Weathered rock Soft rock Hard rock -5-6 Designed tunnel line Actual tunnel line -7 2 4 6 8 1, 1,2 1,4 1,6 1,8 Ring No. Fig. 2. Variation of the penetration rate with the geological strata 353

Seon-Ah Jo ㆍ Kyoung-Yul Kim ㆍ Hee-Hwan Ryu ㆍ Gye-Chun Cho 구간으로현장지반상황에맞춰운전상태를조정하면서점진적으로굴진율상승시키는구간이다. B구간은지반상태에따라굴진인자가조정되는구간으로암반강도와암질변화가굴진율에영향을주고있는것으로보인다. 실제로 RMR 3, 4등급지반의굴진율이 RMR 1, 2등급지반의굴진율보다대체적으로크게나타나 RMR등급에따라굴진율이영향을받고있음을확인하였다. 마지막 C구간은종점부에도달하는곡선구간으로안전성확보를위해인위적으로굴진속도를낮춰운전하기때문에굴진율이감소한것으로판단된다. 4.2 일축압축강도에의한굴진율산정일축압축강도는굴진율예측모델을추정하는주요변수로가장많이사용되는지반특성인자이다 (Lee et al., 216). 따라서기존의일축압축강도로굴진율을추정한경험식을이용하여당현장의쉴드 TBM 굴진율을산정하고실제굴진율과비교하여적용성을검토하였다. 굴진율예측모델은별도의추가실험없이지반및굴진데이터로산정가능한 Graham (1976), Hughes (1986), Tarkoy (1986) 가제한한경험식을선정하였다 (Table 5). 당현장의일축압축강도값을이용하여굴진율예측경험식으로부터도출된굴진율은 Fig. 3과같다. 그림에서나타나듯이 Hughes 식으로산정된굴진율일부를제외하고대부분이굴진율을과다하게도출하여실제굴진율과상당한오차를보였다. 이는일축압축강도가실제굴착된암반의일축압축강도보다작거나운전자의인위적인조정 Table 5. Empirical models for predicting TBM performance based on UCS Proposer Correlation Note Graham (1976) 14 MPa < < 2 MPa Hughes (1986) - Tarkoy (1986) ln - 2 15 1 5 Field data Gramham(1976) Hughes(1986) Tarkoy(1986) 5 1, 1,5 2, Ring No. Fig. 3. Comparison between measured and calculated penetration rate 354

Study on the effective parameters and a prediction model of the shield TBM performance 에의해굴진율이지반상태와무관하게변경되면서나타난결과로보여진다. 당현장은굴진전구간에걸쳐특이한지반특성변화가없었고지질조건도편마암으로거의균일하게분포하는것으로나타나굴진율오차에일축압축강도의영향이크게작용한것으로예상된다. 따라서보다명확한원인을파악하고굴진율예측정확도를개선할수있는방안을모색하고자굴진특성과지반특성인자들을비교분석하였다. 4.3 지반인자와굴진율의상관관계분석국내쉴드 TBM 굴착현장으로부터수집된일축압축강도를포함한지반특성인자들과굴진율의상관성을분석하고굴진율에주로영향를미치는지반특성인자를파악하였다. 이때, 분석에이용된지반특성인자는암석특성인자와암반특성인자로구분하여분석하였다. Fig. 4는주요암석특성인자인일축압축강도및탄성계수와굴진율의상관관계를나타낸것이다. 당현장의일축압축강도와굴진율의상관성은매우미미 (R 2 <.15) 하였으며, 기존문헌 (Yagiz, 28; Shahriar et al., 212; Armetti et al., 218) 에서제시한상관계수 (R 2 =.26~.74) 와비교하여도상대적으로매우작게나타났다. 이는당현장의굴착심도가설계변경에의해변경되었음에도불구하고이를반영한지반특성값을고려하지못했기때문으로판단된다. 이와같은문제로설계굴착강도와실제굴착강도의차이에따른굴진율변화에대해서는 Kim et al. (213) 의연구에서도제기된바있다. 결과적으로일축압축강도와같이국지적인지반특성을대표하는인자는전구간의특성을반영하지못하기때문에지반조사시확인되지않은부분에서이상대조우나지반특성변화가나타날경우굴진율과의상관성이약화될수밖에없다. 6 6 5 4 3 2 1 R² =.149 5 4 3 2 1 R² =.7 2 4 6 8 1 12 UCS [MPa] (a) UCS 2 4 6 8 1 Elastic modulus [GPa] (b) Elastic modulus Fig. 4. Comparison between measured and calculated penetration rate correlation between the penetration depth and intact rock properties 암석특성인자와마찬가지로암반특성인자와굴진율과의상관성을분석하였다. Lee et al. (216) 에따르면주요영향인자중 TBM 굴진성능평가에주로이용되는암반특성인자는절리간격, 절리방향, 취성지수, RQD, RMR 등이있다. 그중당현장으로부터확보가능한데이터인절리간격, RQD, RMR에대해굴진율과상관관계 355

Seon-Ah Jo ㆍ Kyoung-Yul Kim ㆍ Hee-Hwan Ryu ㆍ Gye-Chun Cho 분석을수행하였으며, 이로부터 Fig. 5와같은결과를도출하였다. 암반특성인자중절리간격과굴진율의상관성은 R 2 값이.58로지반특성인자들중가장높게나타났고, RQD와 RMR도.36~.42의 R 2 값을보이며암석특성인자 ( 일축압축강도및변형계수 ) 와비교하여굴진율과상대적으로높은상관관계가있음을확인하였다. 모든암반특성인자들과굴진율은비선형적인반비례관계를보이며특히, RMR은선형관계보다포물선형태일경우 R 2 값이더높게나타나는데이러한경향은이미많은연구에서밝혀진결과이다 (Sapigni et al., 22; Hamidi et al., 21; Armetti et al., 218). 즉, 암질이불량해질경우오퍼레이터가막장면의안전을위해인위적으로굴진율을낮추기때문에 RMR이낮은영역 ( 일반적으로 RMR < 4) 에서는오히려굴진율이감소하고, 양호한암반상태 (4 < RMR < 7) 에서는커터압입이나암석파편 (chip) 형성이용이하여굴진율이높게나타난다. 6 6 5 4 3 2 1 R² =.581 5 4 3 2 1 R² =.3662 2 4 6 8 1 12 14 Joint spacing [cm] (a) Joint spacing 5 2 4 6 8 1 12 RQD [%] (b) RQD penetration rate [mm/min] 4 3 2 1 R² =.337 R² =.4218 2 4 6 8 1 RMR [-] (c) RMR Fig. 5. Correlation of the penetration depth with rock mass properties 당현장의암반특성인자와굴진율이비교적높은상관성을보이는것은암반특성인자와달리절리간격, RQD, RMR 등과같은암반특성인자는시추길이전반에대한암반평가를바탕으로결정되는지표로지역적변화에대한영향이암석특성인자에비해적기때문으로판단된다. 실제로굴착전구간에대해설계변경전 후 RMR등급을비교해본결과변화율이 7% 미만으로굴착심도변화에따른암질변화가크지않은것을확인하였다. 356

Study on the effective parameters and a prediction model of the shield TBM performance 4.4 굴진특성인자와굴진율의상관관계분석굴진특성인자들은굴착이진행되는동안쉴드 TBM 블랙박스에기록되는데이터들로본연구에서는추력, 토크, 회전속도를분석에이용하였다. 전구간에걸쳐총추력은대부분 1,~4, kn으로최대추력 (9,6 kn) 의 1~4% 에수준이었고토크는 2~4 kn m, 회전속도는약 7.2 RPM에서운전되었다. 약 1,72개의링별굴진데이터중시추위치에대응하는데이터를선정하여굴진율과상관관계를분석하고 Fig. 6과같은결과를도출하였다. 굴진특성인자들중총추력은굴진율과상당히유의한상관성 (R 2 =.62) 을보였으나 Fig. 6(b), 6(c) 의토크와회전속도는굴진율과뚜렷한상관관계가없는것으로나타났다. 실제굴착진행에있어운전방법은운전자의경험과노하우 (know-how) 에의해결정되나추력과 RPM을조정하여굴진율을제어하는게일반적이다. 데이터분석에서알수있듯이당현장에서는 RPM을일정하게유지하면서추력을조정하여굴진율을관리한것으로판단되며굴진율과추력의높은상관성도이로부터기인한것으로보여진다. 반면, 암반상태, 추력및회전속도에의해복합적인영향을받는출력변수인토크는굴진율과직접적인상관관계를유추하기어려웠다. 6 6 5 4 3 2 1 R² =.6211 5 4 3 2 1 R² =.14 1 2 3 4 Thrust force [kn] (a) Thrust force 6 1 2 3 4 5 Torque [kn m] (b) Torque 5 4 3 2 1 2 4 6 8 RPM (c) RPM Fig. 6. Correlation of the penetration rate with performance parameters 357

Seon-Ah Jo ㆍ Kyoung-Yul Kim ㆍ Hee-Hwan Ryu ㆍ Gye-Chun Cho 4.5 지반특성인자와굴진특성인자의상관관계분석앞서수행한상관관계분석으로부터당현장에서굴진율에영향을주는주요인자는절리간격, RQD, RMR 및총추력인것으로파악되었다. 이를이용하여주요인자들간의상관관계를분석하고굴진중지반특성이주요굴진인자와굴진율에미치는영향을파악하였다. Fig. 7은주요굴진인자인추력과지반특성인자들의상관관계를나타낸그림으로절리간격, RQD, RMR 모두추력과.3 이상의 R 2 값을보이며지반특성과추력간에비선형적상관관계가있음을확인하였다. 이러한경향은지반인자와굴진율의관계에서도확인한것으로추력이지반특성에따라조정되고있음을알수있다. 4, 4, Thrust force [kn] 3, 2, 1, R² =.3542 Thrust force [kn] 3, 2, 1, R² =.3639 2 4 6 8 1 12 14 2 4 6 8 1 Joint spacing [cm] RQD [%] (a) Joint spacing (b) RQD 4, Thrust force [kn] 3, 2, 1, R² =.433 R² =.3421 2 4 6 8 1 RMR [-] (c) RMR Fig. 7. Correlation of the thrust force with the geotechnical parameters such as joint spacing, RQD and RMR 5. 굴진율예측을위한회귀식제시 앞서수행한분석을통해현장데이터를활용하여다양한관점에서굴진율과의상관성을상호비교하고주요인자를검토하였다. 이를바탕으로당현장의굴진율을예측할수있는경험식을제시하고자회귀분석을수행하였다. 회귀분석절차는먼저최량부분집합분석을수행하여모든변수들로부터높은상관성을보이는변수들의조합을도출하고, 이변수조합에대해단계적회귀분석을수행하여최종적으로최대 R 2 값을갖는회귀식을도출 358

Study on the effective parameters and a prediction model of the shield TBM performance 하는과정으로이루어진다. 많은선행연구에서일축압축강도와굴진율과의상관성이밝혀졌으므로본연구에서는일축압축강도로추정되는예측굴진율의예측오차를줄이기위해지반특성인자중주요인자로확인된절리간격, RQD, RMR을포함하여단계적회귀분석을수행하였다. 그결과, 식 (2) 와같이일축압축강도와절리간격에자연로그를취한값을굴진율을추정하는주요변수로이용할경우설명력이 69% 로비교적양호한회귀식을도출하였다 (Table 6). ln log (2) 일축압축강도와절리간격으로추정된굴진율예측회귀식을해외경험식들과비교하기위해당현장과더불어다른국내현장 1곳 ( 현장) 에적용하여굴진율을예측하였다. 추가로고려된 현장은수도권서부지역에서공사가진행중인쉴드 TBM 굴진현장이다. Fig. 8은각각의경험식으로예측된굴진율과현장에서계측된실 Table 6. Prediction models estimated by regression analysis Parameter Model 1 Model 2 ln log -25.4-25.7 UCS -.8 Y-intercept 31.32 34.68 R 2 55.9 69. Adjusted R 2 54.1 66.1 Predicted R 2 5. 61.3 Residual error 27.1 18.9 1 1 8 8 Predicted PR [mm/min] 6 4 2 This paper Gramham(1976) Hughes(1986) Tarkoy(1986) 2 4 6 8 1 Predicted PR [mm/min] 6 4 2 This paper Gramham(1976) Hughes(1986) Tarkoy(1986) 2 4 6 8 1 Measured PR [mm/min] Measured PR [mm/min] (a) Target site (b) site Fig. 8. Comparison of the linear relation between predicted and measured penetration rate 359

Seon-Ah Jo ㆍ Kyoung-Yul Kim ㆍ Hee-Hwan Ryu ㆍ Gye-Chun Cho 제굴진율을비교한결과이다. 해외경험식으로산정된굴진율은실제굴진율과오차가 1% 를넘는데반해, 제안된회귀식을이용하여산정한굴진율은오차가 18% 로상대적으로작게나타났다. 현장의예측굴진율비교결과도당현장결과와유사하게나타났으나예측오차가당현장에비해다소크게산정되었다. 이는회귀식이갖는한계로많은연구에서언급된것이나, 그럼에도불구하고해외경험식과비교하여굴진율예측오차가현저히감소하는것을확인하였다 (Fig. 8(b)). 6. 결론 본연구에서는국내소단면쉴드TBM 현장의지반및굴진데이터를수집하고상호비교를통해굴진율과의상관관계를분석하여주요영향인자를파악하였다. 또한, 통계적분석기법을기반으로한회귀분석을수행하여당현장에적합한굴진율예측회귀식을도출하였다. 본연구를통해도출된결과는다음과같다. 1. 지반특성인자를암석및암반특성인자로구분하여굴진율과상호비교하였다. 암석특성인자인일축압축강도는범주적특성이적어시공중지역적변화에의해영향을많이받는반면, 암반특성인자들은상대적으로넓은범위를포괄하는특성으로지역적영향이적은것으로판단된다. 따라서본현장의데이터로판단시, 일축압축강도에비해암반특성인자인 RMR, 절리간격, RQD가굴진율과더높은상관성을보였다. 2. 본현장의굴진데이터로판단시, 굴진특성인자중추력은굴진율과상관성이가장높게 (R 2 =.62) 나타났으며회전속도가전구간에걸쳐거의일정하므로굴진율에영향을미치는주요굴진인자가추력임을확인하였다. 또한지반특성인자와추력의상관관계를분석한결과암반특성인자들과비교적유의한상관성을나타내면서추력이어느정도지반특성에영향을받고있음을확인하였다. 3. 쉴드 TBM 주요설계인자인굴진율을예측하기위한예측식을회귀분석을통해도출하였다. 회귀식은일축압축강도와절리간격을예측변수로할때가장높은설명력을나타냈으며, 도출된회귀식으로예측한굴진율과현장굴진율을비교한결과기존의해외경험식에비해오차율이크게감소하는것을확인하였다. 4. 도출된회귀식을타국내현장에적용하여현장굴진율및해외경험식과비교하였다. 예측굴진율은해외경험식에비해낮은오차율을보였으나예측오차가약 58% 로당현장에적용할때보다크게나타났다. 이처럼회귀식은다른현장에적용할경우예측력이떨어진다는한계가있다. 이를극복하기위해서는현장조건에제약없이적용가능한굴진율예측모델이도출되어야한다. 이를위해서향후다양한현장으로부터지반및굴진데이터를수집하여지반특성을일정한기준및조건에따라정량화하는연구를추후연구를통해수행하고자한다. 감사의글 본연구는국토교통부 ( 국토교통과학기술진흥원 ) 건설기술연구사업의 도심지소단면 (Ф3.5 m급 ) 터널식공동구설계및시공핵심기술개발 (19SCIP-B15148-5) 연구단을통해수행되었습니다. 연구지원에감사드립니다. 36

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