05_김학준(72-96).hwp

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1 TUNNEL & UNDERGROUND SPACE Vol.28, No.1, 2018, pp ISSN: (Print) ISSN: (Online) RESEARCH ARTICLE 점하중시험을이용한국내암석의일축압축강도산정연구 김학준 * 대전대학교건설안전방재공학과 Estimation for the Uniaxial Compressive Strength of Rocks in Korea using the Point Load Test Hak Joon Kim * Department of Construction Safety and Diaster Prevention, Daejeon University *Corresponding author: hakkim@dju.ac.kr Received: January 30, 2018 Revised: February 10, 2018 Accepted: February 13, 2018 ABSTRACT Accurate estimation of the uniaxial compressive strength of rock is very crucial for the safety of construction activities occurring in the rock mass. However, the uniaxial compressive strength test is expensive and time consuming. Moreover, the uniaxial compressive strength test cannot be performed in the field. In order to solve this kind of problem, many foreign researchers investigated the use of the point load strength test for the estimation of uniaxial compressive strength of rock. However, the result of research obtained for rocks from other countries may not be directly applicable for rocks in Korea. The correlation between the point load strength index and the uniaxial compressive strength for rocks in Korea is suggested in the form of table by using the results of the extensive literature reviews and laboratory tests. The suggested result is expected to be used for the simple and quick estimation of uniaxial compressive strength of rocks in Korea. Keywords: Uniaxial compressive strength, Point load strength test 초록 암반에서공사를수행하는경우에는공사의안정성확보를위하여대상암반의일축압축강도를정확히평가해야한다. 그러나일축압축강도를산정하기위해서는많은비용과시간이필요하다. 또한현장에서는암석의일축압축강도시험을수행할수없다는문제점이있다. 이러한문제를해결하기위해점하중강도시험을이용하여암석의일축압축강도를산정하는방법이외국의많은연구자들에의하여조사되었다. 그러나외국의암석에서얻어진연구결과를그대로국내에서적용하는것은신뢰성에문제가있을수있다. 본연구에서는국내암석에대한점하중강도지수와일축압축강도의상관관계를광범위한국내외문헌조사와실내시험결과를통하여도표로제시하였다. 본연구결과는국내암석의일축압축강도를간편하고신속하게추정하는데활용될수있을것으로기대된다. 핵심어 : 일축압축강도, 점하중강도시험 서론 암석의일축압축강도는 RMR 이나 Q 와같은암반분류법에필수적으로사용되는인자이며공사현장의지반공학적설계에서가 C The Korean Society for Rock Mechanics This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

2 Estimation for the Uniaxial Compressive Strength of Rocks in Korea using the Point Load Test 73 장중요한인자로간주된다. 암석의일축압축강도시험에는일반적으로원주형시료가사용되며일축압축시험기가필요하므로시료제작을포함한시간과노력이필요하다. 점하중시험기는현장에휴대가가능하며불규칙한시료에적용이가능하다는장점이있으므로암석의일축압축강도를산정하기위하여널리사용되고있다. 따라서국내외적으로현장에서간편하게간접적인방법을사용하여암석의일축압축강도를산정하려는많은연구가수행되었다. 국내현장에서점하중강도를이용하여일축압축강도를결정하는경우, 외국에서연구된결과를그대로국내암석에적용하여사용하는경우가일반적이다. 또한국내에발표된연구결과는대부분어떤특정지역의암석을대상으로상관관계식이제시되었다. 본연구에서는점하중강도를이용하여국내암석의일축압축강도를산정하는관계식과이러한상관관계식의한계점등을국내외의광범위한문헌조사와실내시험결과등을종합하여제시하고자한다. 점하중강도지수와일축압축강도상관관계연구현황 점하중강도지수암석의점하중강도시험은점하중시험기에암석시료를장착한후수행되는데, 직경방향시험의경우파괴하중을시료직경의제곱, 타형태의시료는등가직경의제곱으로나누어암석의점하중강도지수 (Point Load Strength Index, Is) 를구한다. 점하중강도시험은코어시료뿐만아니라불규칙암괴등을시험편으로사용할수있으며현장에서도시험이가능하다는장점이있다. 일반적으로점하중강도지수와일축압축강도는선형관계를보이는것으로알려져있다. 따라서점하중강도지수를이용하여암반분류나지반설계등에서널리사용되고있는일축압축강도를결정하려는연구가국내외에서활발히수행되었다. 암석의점하중강도지수는원통형시료의직경방향시험 (diametral test) 과축방향시험 (axial test), 육면체시료의블록시험 (block test), 불규칙한시료시험 (irregular lump test) 등다양한형태의시료시험을이용하여산정이가능하다. ISRM(1985), KSRM(2007), ASTM (2016) 은암석의점하중강도표준시험법을제시하였다. 국외연구현황 D Andrea et al.(1964) 을포함하여 60 70년대부터많은연구자들은점하중강도시험을이용하여일축압축강도를추정하는방법을제시하였다. Broch and Franklin(1972), Bieniawski(1975), Singh and Singh(1993) 등은직경 50 mm의시료에서얻어진점하중강도지수에 24의환산계수 (conversion factor) 를곱하면암석의일축압축강도를얻을수있음을제안하였으며이환산계수는국내외에서널리사용되고있다. Broch and Franklin (1972), Brook(1980, 1985), Hassani et al.(1980), Forster(1983), Turk and Dearman(1985), Chau and Wong(1996) 등은코어시료의직경이 50 mm가아닌경우의점하중강도지수의보정방법을제시하였다. ISRM(1985) 에의하면환산계수는평균적으로 20 25의범위를보이지만이방성암석의경우에는 15 50까지의범위를보인다. Smith(1997) 는환산계수를가능한특정지역별혹은암종별로결정하여사용하고, 기존의문헌에제안된환산계수는단지개략적인강도추정이나상대적인강도값추정에만활용할것을제안하였다. 이것은특히강도가약하거나포화된암석의경우, 환산계수가많은오차를유발할수있기때문이다. Hawkins(1998) 는문헌조사결과를토대로암상이나상태에따라환산계수가 7 68까지의범위를보이므로지역별로적당한값을사용할것을제안하였다. Kahraman(2001) 도임의의환산계수를이방성암석에적용하는경우에는일축압축강도의오차가 100 % 까지발생할수있음을지적하였다. Fener et al.(2005) 의문헌조사결과에서도환산계수는 사이의넓은범위를보였다. Yilmaz(2009) 는점하중시험의단점으로 (i) 시험암석이일반적으로이방성이고불균질하지만시험이매우국부적으로수행됨,

3 74 Hak Joon Kim (ii) 유효하지않은불규칙적인파괴가자주발생하여너무많은시험편이요구됨, (iii) 하중을가하는동안에시험편을고정시키기어려운점등을제시하였다. 점하중강도지수 (x) 와일축압축강도 (y) 의상관관계식은 y=ax, y=ax+b, y=ax b, y=ax 2 +bx, y=aln(x)+b, y=ae bx 등의다양한형태가있다. 이러한상관관계식중에서 y=ax (a는환산계수 ) 형태가가장널리사용되고있으며 y=ax 형태의식을제외한다양한유형의상관관계식도 Table 1과같이많은연구자들에의하여제시되었다. y=ax 형태의식은 2.5 절에서상세히논의하였다. Table 1. Equations correlating the UCS to the point load strength index expressed in various types Rock types Conversion equations UCS Range (MPa) References Dolostone, sandstone, limestone 1 (r 2 =NG*) (USA) Gunsallus and Kulhawy (1984) Sandstone 1 (r 2 =0.81) (Turkey) Ulusay et al. (1994) Limestone, marlstone, sandstone 1 (r 2 =0.82) (Greece) Tsiambaos and Sabatakakis (2004) Sedimentary (various) 1 (r 2 =0.78) (Turkey) Kahraman and Gunaydin (2009) Sedimentary rock 1 (r 2 =0.61) Sandstone 1 (r 2 =0.79) (Various) Tziallas et al. (2009) Gypsum (air-dried) 1 (r 2 =0.94) (Iran) Gypsum (sat.) 1 (r 2 =0.94) (Iran) Heidari et al. (2012a) (r 2 =0.91) marly rock 1 ln (r 2 =0.929) (r 2 =0.90) (r 2 =0.82) (Iran) Azimian and Ajalloeian (2014) Sandstone 1 (r =0.65) (Calcareous) (United Arab Emirates) Elhakim (2015) Sedimentary (various) 1 (r 2 =0.85) (Turkey) Kaya and Karaman (2016) Igneous (various) 2 (r 2 =0.68) (Turkey) Kahraman and Gunaydin (2009) Igneous rock 2 (r 2 =0.91) (Various) Tziallas et al. (2009) Igneous (various) 2 (r 2 =0.79) (Turkey) Kaya and Karaman (2016) Metamorphic (various) 3 (r 2 =0.77) (Turkey) Kahraman and Gunaydin (2009) Metamorphic rock 3 (r 2 =0.75) (Various) Tziallas et al. (2009) Schist 3 (r 2 =0.74) (India) Basu and Kamran (2010) Phyllite 3 Ln (r 2 =0.884) (r (Portugal) =0.843) Andrade and Saraiva (2010) Metagreywacke 3 (r 2 =NG*) (Portugal) Hornfels 3 (r 2 =0.99) (Iran) Fereidooni (2016) Metamorphic (various) 3 (r 2 =0.74) (Turkey) Kaya and Karaman (2016) Sandstone, limestone, dolomite, marble, gneiss 4 (r 2 =0.884) (USA) Cargill and Shakoor (1990) Coal measure rocks 4 (r 2 =0.86) (Turkey) Other rocks 4 (r 2 =0.72) (Turkey) Kahraman (2001) Chalk, pumice, tuff 4 (r 2 =NG*) 3-13 (Canada) Quane and Russel (2003) Various (All rock) 4 (r 2 =0.61) (Turkey) Various (n<1%) 4 (r 2 =0.72) (Turkey) Kahraman et al. (2005) Various (n>1%) 4 (r 2 =0.75) (Turkey) Various 4 (r 2 =0.72) (Turkey) Fener et al. (2005) Andesite/basalt, sandstone, gypsum, marble 4 (r 2 =0.639) (Turkey) Yilmaz (2009) All types 4 (r 2 =0.56) (Turkey) Kahraman and Gunaydin (2009) All rock types 4 (r 2 =0.66) (Various) Tziallas et al. (2009) All types 4 (r 2 =0.81) (Turkey) Kaya and Karaman (2016) *NG: Not given in the references, *UN: Unknown, 1: Sedimentary rock, 2: Igneous rock, 3: Metamorphic rock, 4: Various rocks

4 Estimation for the Uniaxial Compressive Strength of Rocks in Korea using the Point Load Test 75 국내연구현황 Bae et al.(1991) 은편마암에대한일축압축강도와점하중강도지수의상관관계를연구하였는데약한면의방향을고려하여구한결정계수 (r 2 =0.81) 가방향을고려하지않고얻어진결정계수 (r 2 =0.36) 보다더높았다. Lee et al.(2003) 에의하면층리를가진셰일의경우층리에평행한방향과수직방향으로구한점하중강도지수의비율은약 2.2로서평행한방향의점하중강도지수는수직방향의약 50% 로나타났다. Lee and Youn(2009) 은대구셰일의이방성을고려한상관관계를연구하였는데층리각을 90 로고정시킨상태에서의환산계수는 14.4로서 ISRM(1985) 의층리가없는무결암시료에대한일반적인환산계수인 22와는많은차이가있었다. Baek et al.(2006) 은안동지역의흑운모화강암에대하여상관관계식을제시하였는데선형관계식이가장높은결정계수 (r 2 ) 를나타내었다. Kim et al.(2008) 은호상흑운모편마암의경우일축압축강도시험이일반적으로엽리방향과수직으로수행되므로점하중강도지수는직경방향보다축방향으로얻어진시험결과를활용하는것이타당한것으로판단하였다. 또한엽리와수직으로재하되는조건인축방향으로얻어진점하중강도지수가직경방향으로얻어진점하중강도지수보다더크게측정되었으며풍화암과연암보다는보통암과경암의경우엽리가암석의강도에더큰영향을주고있음을확인하였다. 이외에도국내의많은연구자들이특정지역의암석에대한상관관계를제안하였으며 y=ax 형태의식을제외한다양한유형의상관관계식은 Table 2와같다. 국내암석에서얻어진결정계수 (r 2 ) 의평균은 0.85로국외암석의평균 0.79보다모든암종에서더상관성이높았는데이는국내연구결과가특정지역암석에서집중적으로수행되었기때문으로판단된다. 상관관계에영향을주는인자 국내외의많은연구자들이점하중강도지수를이용하여암석의일축압축강도를결정하려는연구를진행하였다. 국내외의광범 위한문헌조사를통하여상관관계에영향을주는인자를조사한결과를요약하면다음과같다. 암석시료의크기와모양일축압축강도와점하중강도사이의상관관계는암석시료의크기, 암석시료의길이와직경의비율, 시료의모양등과연관이있다는것은많은실험결과를통하여입증되었다 (Broch and Franklin, 1972; Bieniawski, 1975; Brook, 1980; Hassani et al., 1980; Broch, 1983; Forster, 1983; Turk and Dearman, 1985; Chau and Wong, 1996 등 ). Hawkins(1998) 의실험에의하면시료의직경이증가할수록그리고원통형시료가육면체시료보다환산계수가더컸다. Lee et al.(2011) 은선형회귀분석 (Linear regression analysis) 을적용하여강원도지역화강암의점하중강도와일축압축강도를산정하는관계식을제안하였는데관계식에는시료의폭과두께를고려하였다. 일축압축강도와인장강도비율점하중강도시험에서암석은인장을받아파괴가발생하므로점하중강도지수에의한암석의일축압축강도추정의정확성은일축압축강도와인장강도의비율에따라달라진다 (Hoek, 1977; Chau and Wong, 1996; Singh et al., 2012). Sheorey(1997) 에의하면일축압축강도와인장강도의비율 (R=σ c /σ t ) 은 2.7부터 39까지다양한값을보이며문헌상평균값은 14.7이다. R값은암종과암석의생성기원에따라달라지며일반적인경암의경우이비율은약 10, 이암 (mudstone) 이나점토암 (claystone) 은 5정도이다 (Cai, 2010). Karaman et al. (2015) 에의하여제시된 R값은화산암 6.27, 변성암 5.97, 퇴적암 7.02이었다.

5 76 Hak Joon Kim Table 2. Correlating equations expressed in various types for rocks in Korea Rock Types UCS-Point Load Strength (MPa) References Shale 1 (r 2 =0.88) Volcanic breccia 1 (r 2 =0.94) Chung and You (1997) Black shale (Daegu) 1 (r 2 =0.87): coring bedding plane (r 2 =0.89): coring bedding plane Red shale (Daegu) 1 (r 2 =0.91): coring bedding plane (r 2 =0.84): coring bedding plane Kim et al. (2001) Tuff (Goheung) 1 (r 2 =0.903) Kim et al. (2004) Limestone 1 (r 2 =0.786) Woo (2005) Sandstone 1 (r 2 =0.839) (r 2 =0.962) Shale 1 (r 2 =0.626) (r 2 =0.852) Mudstone 1 (r 2 =0.750) (r 2 =0.857) Min and Moon (2006) Sedimentary rocks 1 (r 2 =0.808) (r 2 =0.931) Sandstone 1 (r 2 =0.738) Shale 1 (r 2 =0.745) Min et al. (2008) Limestone 1 (r 2 =0.78) Kim et al. (2012) Black shale (Daegu) 1 (r 2 =0.84): coring bedding plane Red shale (Daegu) 1 (r 2 =0.89): coring bedding plane Kwag et al. (2013) Granite (J*) 2 (r 2 =0.867) Granite (C*) 2 (r 2 =0.839) Lee and Lee (1995) Granite porphyry 2 (r 2 =0.96) Chung and You (1997) Granite (Chunyang)-J* 2 (r 2 =0.882) Woo (2005) Biotite granite (J*) 2 (r 2 =0.821) Baek et al. (2006) Biotite granite (C*) 2 (r 2 =0.860) Eom et al. (2008) Granite (Geochang)-J* 2 (r 2 =0.75) Kim (2015) Schistose granite (J*) 3 (r 2 =0.94) Biotite gneiss 3 (r 2 =0.91) Chung and You (1997) Granitic gneiss 3 (r 2 =0.94) Biotite gneiss 3 (r 2 =0.84) Cha et al. (2007) Gneiss 3 (r 2 =0.870) Min et al. (2008) Gneiss 3 (r 2 =0.870) (r 2 =0.93) Kwon (2012) Granite (C*), Biotite granite (C*), Granitic gneiss (J*), Porphyric granite (J*), Alkali granite (J*) 4 (r 2 =0.80) Woo (2014) *C: Cretaceous, J: Jurassic, 1: Sedimentary rock, 2: Igneous rock, 3: Metamorphic rock, 4: Various rocks 암석의종류 Pells(1975) 에의하면 24의환산계수가조립현무암 (dolerite), 노라이트 (norite), 휘석암 (pyroxenite) 과같은암석의일축압축강도추정에는약 20 % 의오차를보일수있었다. Vallejo et al.(1989) 은암종의차이로인하여사암보다셰일의환산계수가더작은것으로결론지었다. 그러나 Rusnak and Mark(1999) 는암종보다는셰일의강도가작아서환산계수가더작은것으로해석하였다. Fener et al.(2005) 은암석의종류, 암석의미세조직, 그리고실험상태의차이가환산계수에영향을미칠수있음을실험을통하여제시하였다. Kahraman and Gunaydin(2009) 의실험과 Tziallas et al.(2009) 의문헌조사결과에의하면화성암, 변성암, 퇴적암으

6 Estimation for the Uniaxial Compressive Strength of Rocks in Korea using the Point Load Test 77 로구분하여얻어진환산계수의상관계수가전체암석의환산계수보다일반적으로더높았다. Singh et al.(2012) 은 10개의서로다른암종으로구성된 318개의 NX규격코어를이용하여인도지역의암석에대한점하중강도지수와일축압축강도사이의상관관계를제시하였다. 실험에의하면암종에따라환산계수의차이가있었으며, 암종별로시료가하중을받을때응력- 변형률관계가다르며, 암종별이방성으로인하여이러한차이가발생하는것으로추정하였다. 그러나전반적으로강한암석이약한암석에비하여환산계수가더컸으므로암종보다는암석강도를환산계수차이의가장중요한요인으로간주하였다. Chung and You(1997) 는국내암석의풍화정도에따른일축압축강도, 점하중강도의범위와 6개암종에대한일축압축강도와점하중강도의상관관계를제시하였다. 일축압축강도와점하중강도의상관관계식은선형의관계식 (y=kx+c) 을갖는것으로분석되었으며 K는 13 23의넓은분포를갖고있으며각암종의결정계수 (r 2 ) 는 까지로높은신뢰성을보였다. 그러나 6개암종을종합하면 K는 15, 결정계수 (r 2 ) 는 0.64로신뢰성이더낮았다. 따라서점하중강도를이용하여암석의일축압축강도를추정할경우에는암종별로다른상관관계식을사용할것을제안하였다. Min and Moon(2006) 과 Kim et al.(2012) 도연구사례마다환산계수의차이가보이는이유를암석의생성원인과조성차이에기인하는것으로해석하였다. Kaya and Karaman(2016) 은성인에따라화성암은화산쇄설암 (pyroclastic rock), 화산암, 심성암으로, 퇴적암은화학적 (chemical) 과쇄설성 (clastic), 그리고변성암은엽리상 (foliated) 과비엽상 (nonfoliated) 으로더욱세분하여환산계수를산정하였다. 이들은암석의지질학적기원이환산계수에큰영향을미치며따라서암석의성인에따라서다른환산계수를이용할것을제안하였다. 그러나 y절편이 0인환산계수로나타낸그들의실험결과를분석해보면화성암의결정계수는 0.77, 화산쇄설암 0.85, 화산암 0.59, 심성암 0.49, 퇴적암의결정계수는 0.85, 화학적퇴적암 0.15, 쇄설성퇴적암 0.59, 변성암의결정계수는 0.72, 엽리상암석 0.56, 비엽상암석 0.55로대체로성인에따라더욱세분한환산계수의결정계수가더낮았다. 암석의산출지역 Lee and Lee(1995) 에의하면모든종류의국내화강암에서측정한점하중강도지수와일축압축강도사이의상관계수 (r=0.902) 보다불국사화강암 (r=0.916) 과대보화강암 (r=0.931) 으로구별하여측정한상관계수가약간더높았다. Kim et al.(2012) 은임계지역에분포하는석회암을대상으로일축압축강도와점하중강도지수사이의상관관계를연구하였으며국내타지역의석회암을대상으로수행된연구와비교하였다. 연구결과, 동일한석회암이라도국내분포지역에따라상관관계가다를수있다는결론을얻었다. Heidari et al.(2012a) 은이란의 Gachsaran 층에서나타나는석고암 (gypsum rock) 의점하중강도지수와일축압축강도의상관관계식을제시하였는데다른지역의석고암에는사용하지말것을제안하였다. Cha et al.(2007) 은경기도편마암복합체내경기동부지역에분포하고있는호상흑운모편마암에대하여상관관계를분석한결과지역별로상관관계의차이가있었다. 상관관계가가장큰차이를보이는곤지암지역의상관관계를광주지역에적용할경우암석의일축압축강도가약 65 MPa 작게산정이되었다. Min and Moon(2006) 은같은퇴적암이라도산출지역별로환산계수가차이가보이는이유를퇴적이력, 입자구조및광물조성의차이때문일것으로추정하였다. 암석의강도 Abbs(1985) 의연구에의하면약하고기공이있는탄산염암석의경우환산계수가 4에불과하였다. Goodman (1989) 은강도가약한암석일경우 24의환산계수사용이매우큰오차를보일수있음으로주의해야함을강조하였다. Bieniawski(1989) 는 RMR 을이용한암반분류에서, 일축압축강도가 25 MPa 이하의암석에서는점하중강도지수를이용한무결암강도산정을권장하지않

7 78 Hak Joon Kim 았다. Vallejo et al.(1989), Smith(1997), Sabatakakis et al.(2008), Nuri et al.(2012) 의실험에서도약한암석의환산계수가더작은경향을보였다. Rusnak and Mark(1999) 의실험결과에서는연암의환산계수가경암보다작은것은일부확인하였으나이러한경향이명확하지는않았다. Koncagül and Santi(1999) 에의하면점하중강도지수는강도가큰암석의경우값이더크게증가하는경향이있으며시료의모양에따라다양한값을보였다. 따라서점하중강도지수는암석의강도를일정하게측정하지못한다고결론지었다. Quane and Russell(2003) 은점하중강도가 5 MPa 이상의강한암석에서는선형관계식, 4 MPa 이하의약한암석에서는비선형관계식을사용할것을권장하였다. Tsiambaos and Sabatakakis(2004) 는퇴적암인석회암, 이회암, 사암등의환산계수가강도에따라차이가있음을제시하였다. 이들의실험결과에의하면점하중강도지수가 2 MPa 이하는 13, 2 5 MPa 사이는 20, 5 MPa 보다더큰경우는 28의환산계수를보였다. Singh et al.(2012) 에의하면점하중강도지수를일축압축강도로변환하는환산계수는 14와 24 사이의범위를보였는데편마암계통의콘달라이트 (Khondalite) 암석에서의예외가있지만일반적으로경암일수록환산계수값이증가하는경향이있었다. 따라서점하중강도시험의결과는연암과경암이다르게해석되어야한다고결론지었으며연암 ( 일축압축강도 25 MPa이하 ) 의환산계수는 14 16, 경암은 21 24를제안하였다. 연암의경우에는환산계수의상관계수도낮았는데이것은연암의화학조성, 이방성, 파괴양상등의차이에의한것으로추정하였다. 그러나 Cargill and Shakoor(1990) 의실험결과에서는경암이연암보다환산계수의상관계수가더낮았다. 시료의포화도 Vallejo et al.(1989) 에의하면시료가포화되어있을경우에환산계수가증가하는경향이있었다. Nuri et al. (2012) 도이라크지역의석회암, 석고암, 사암의습윤시료환산계수가건조시료환산계수보다더크다고보고하였다. 특히석회암과석고암보다사암의습윤시료환산계수 (22.7) 가건조시료환산계수 (11.8) 와큰차이를보였는데사암이공극이많고압축강도가낮은것에기인하는것으로해석하였다. 그러나 Bell(1995) 의보통암과경암에대한연구결과에의하면, 습윤한시료의환산계수는 7 26( 평균 14), 건조시료의환산계수는 15 30( 평균 20) 이었다. Smith(1997) 의연구결과에서도습윤한석회암의환산계수 (23) 가건조시료 (27.2) 보다더작은값을보였다. Hawkins(1998) 와 Kahraman et al. (2005) 은일축압축강도와점하중강도지수가함수비에영향을받으므로현장에서는함수비를고려하여환산계수를사용할것을권장하였다. 그러나일축압축강도가 25 MPa 이하인열수변질 (hydrothermally altered) 된연암의경우, 함수비가환산계수에미치는영향은거의없었다 (Kohno and Maeda, 2012). 결론적으로, 일반암석의경우포화도가환산계수에영향을주고있으나암종에따라습윤한시료와건조시료의환산계수크기에차이가있었다. 암석의이방성및불균질성일축압축강도는축방향으로시험이수행되지만점하중강도지수는직경방향으로도시험이수행되므로특히암석이이방성인경우에는축방향시험과환산계수가달라질수있다. 따라서 Greminger(1982) 는점하중강도지수를이용하여이방성암석의일축압축강도를추정할경우상당한오차가발생할수있음을강조하였다. Broch(1983) 는축방향과직경방향으로측정한점하중강도지수를이용하여암석강도의이방성을측정하는방법을제시하였다. Vallejo et al.(1989) 과 Kim et al. (2004) 의실험에서는직경방향으로측정한점하중강도지수는축방향으로측정한값보다훨씬작았다. Rusnak and Mark(1999) 는일축압축강도산정을위해서는직경방향보다축방향으로수행한점하중강도지수를활용할것을권장하였다. Kwon(2012) 은 18개지역에서총 260개의편마암시료를채취하여점하중강도지수와일축압축강도의상관관계를연구하였다. 연구를위하여불연속면과수직된방향으로 NX

8 Estimation for the Uniaxial Compressive Strength of Rocks in Korea using the Point Load Test 79 규격의공시체를제작하여일축압축시험과점하중강도시험을수행하였다. 일축압축강도와점하중강도지수의상관관계는직경방향보다축방향으로수행한점하중강도지수가일축압축강도와더높은상관성을보였다. Min and Moon(2006) 에의하면층리혹은불연속면을포함한울산지역퇴적암의경우에서도축방향에서얻어진점하중강도지수가일축압축강도와더높은상관성을보였는데일축압축강도의측정값과예측값의결정계수 (r 2 ) 가축방향은 0.93, 직경방향은 0.79이었다. 암석이뚜렷한불연속면을보이지않더라도암석자체의불균질성으로인하여암석의강도가달라질수있으며이것이환산계수에영향을미칠수있다 (Idris et al., 2011; Elhakim, 2015). 특히석회질암석의경우에는불균질성이심해서일축압축강도와점하중강도지수의변동계수 (coefficient of variation) 가각각 39% 와 59% 이었다 (Kulhawy and Prakoso, 2001). Diamantis et al.(2009) 도그리스지역사문암의환산계수가다소분산되는이유를암석학적인다양성, 사문암화작용 (serpentinization) 의차이등으로해석하였다. 암석의풍화도현장에서암석의풍화는균일하게발생되지않으므로풍화가진행된암석에서점하중강도시험이나일축압축시험을수행할경우에는실험값이다소분산될것을예상할수있다. Pells(1975) 와 Read et al.(1980) 에의하면일축압축강도와점하중강도지수의상관관계가암석의종류와풍화도에따라달랐다. 특히일축압축강도와점하중강도지수의시험이서로직각방향으로수행되므로암석이이방성인경우에는이러한차이가더컸다. Kim et al.(2008) 의연구에서도, 이방성암석의경우암석강도에미치는엽리방향의영향이풍화도에따라달랐다. Elhakim(2015) 도암석풍화도의차이가실험값분산원인중의하나로지적하였다. 암석의공극률 Palchik and Hatzor(2004) 는다공질백악 (porous chalk) 에서의실험결과를토대로공극률이 18% 에서 40% 로증가하면환산계수가 18에서 8로감소한다고보고하였다. Kahraman et al.(2005) 은공극률이일축압축강도와점하중강도지수의상관관계에미치는영향을조사하기위하여 38종 ( 화성암 11종, 변성암 9종, 퇴적암 18종 ) 의암석에대한실험을수행하였다. Palchik and Hatzor(2004) 의결과와달리공극률과환산계수는직접적인상관관계를보이지않았는데이것은이들이다양한암석에대한실험을수행한반면에 Palchik과 Hatzor는 1가지암종만을대상으로실험을수행하였기때문으로해석되었다. 그러나공극률이 1 % 보다큰그룹과작은그룹으로암석을나누어각그룹별로결정한상관관계가모든암종에대한상관관계보다더높았으며, 공극률이더작은강한암석이공극률이큰암석보다환산계수가더큰경향을보였다. Fereidooni(2016) 의혼펠스에대한실험결과에의하면점하중강도지수와공극률은반비례지수 (Inverse exponential) 관계를보인다. 그러나 Kahraman et al.(2005) 의실험결과를분석해보면공극률이큰암종이공극률이작은암종보다더강한경우도있었다. 따라서공극률과환산계수의직접적인상관관계는일부암석의동일한암종에만적용되는것으로판단된다. 점하중시험시의콘의침투심도 Broch and Franklin(1972) 은강한암석의경우에만파괴시콘이암석내부로침투하지않아서점하중시험기의시험전콘간격을직경 (D) 로간주할수있다고하였다. ISRM(1985) 도암석이크거나강한경우에는시험전콘사이간격을암석시료직경 (D) 로간주해도오차가작다고규정하였다. 그러나 Basu and Aydin(2006) 의레이저거리측정기를이용한연구에의하면풍화된화강암

9 80 Hak Joon Kim 보다신선한화강암의콘침투 (cone penetration) 심도가더컸다. 따라서신선한암석의파괴시의콘사이간격을고려하여점하중강도지수값을보정해주는경우에환산계수의결정계수가상당히높아졌고환산계수도더작았다. 이들은문헌조사에서제시된강한암석의환산계수의결정계수 (r 2 ) 가콘침투심도때문에더낮은것으로해석하였다. 콘침투심도가거의영향을미치지않는압축강도의상한값은주로암종이나암석의미세구조에의하여결정된다. 취성암석에서침투심도는인장강도가감소할수록감소하지만세립질암석이더작을수있다. 그러므로성분이유사한암석이라도입도가다른경우에는환산계수를별도로산정할것을권장하였다. 기타 Chau and Wong(1996) 에의하면일축압축강도와점하중강도사이의상관관계는암석의압축강도와인장강도의비율, 시료의길이와직경과함께암석의포아송비가영향을미친다. Rusnak and Mark(1999) 는점하중강도지수와일축압축강도사이의관계가다양하게나오는이유를암석의일축압축강도산정의부정확성, 점하중강도지수산정의부정확성, 그리고두시험사이의실제값차이등의 3가지로제시하였는데특히일축압축강도시험자체의부정확성을가장큰요인으로추정하였다. 즉같은지역의동일한암석이라도일축압축강도가다양할수있다는것이다. Kaya and Karaman(2016) 의경우에도, 터키동부흑해지역암석에대한환산계수 (17.92) 를실험을통하여산출하였는데같은지역의기존문헌조사에서얻은실험결과를포함한환산계수 (14.81) 와약간의차이를보였다. Woo(2014) 에의하면, 흡수율이유사한암석시료들끼리시료군을나누어강도평균을구한후상관관계를분석한경우더높은결정계수를보였다. 결론적으로점하중강도지수를이용하여일축압축강도를산정할경우에사용하는환산계수는암석고유의불균질성과이방성이외에도암석시료의직경, 암석시료의길이와직경의비율, 시료의모양, 일축압축강도와인장강도의비율, 암석의종류, 암석의종류가동일하더라도분포지역의차이, 암석강도, 시료의포화도, 풍화도, 공극률, 점하중강도시험시콘의침투심도, 포아송비, 일축압축강도와점하중강도시험자체의정확성, 미세균열등의다양한요인에영향을받는다. 특히암석은일반적으로같은지역의동일한암석이라도풍화도나광물조성의차이등에의하여균질하지않는데일축압축시험과점하중시험에는동일한시료가사용되지않으므로환산계수가영향을받을것으로판단된다. 점하중강도지수와일축압축강도상관관계 Fener et al.(2005) 은 21개의논문에제시된일축압축강도 (y) 와점하중강도지수 (x) 의상관관계를요약하여제시하였는데, 상관관계식에는 y=ax, y=ax+b, y=ax b, y=ax 2 +bx 등의다양한형태가있었으며 y=aln(x)+b, y=ae bx 등의관계식도 Azimian and Ajalloeian(2014) 등에의하여제시되었다. 상관관계식중에서 y=ax 형태가가장널리사용되고있으며이식에서 a를환산계수라고한다. Sabatakakis et al.(2008) 의실험결과에의하면지수함수 (exponential function) 로표현한상관관계식의결정계수 (0.81) 가 y절편이 0인경우의결정계수 (0.71) 보다약간더높았다. Tziallas et al.(2009) 도문헌조사결과를이용하여모든종류의암석, 퇴적암, 화성암, 변성암, 사암에대한상관관계식을별도로제시하였는데지수함수가원점회귀식보다약간더높은결정계수를보였으나퇴적암을제외하고큰차이는없었다. Heidari et al.(2012b) 에의하면점하중강도지수를이용하여암석의일축압축강도를추정할때 y절편이 0인환산계수를사용하는것보다 y절편을갖는관계식이더정확한결과를보였다.

10 Estimation for the Uniaxial Compressive Strength of Rocks in Korea using the Point Load Test 81 Forster(1983) 는일반적으로점하중강도지수를이용하여암반분류에사용되는암석의일축압축강도를산정할경우, 일축압축시험자체의오차를고려했을때 ±20% 의오차는충분히정확한것으로간주될수있다고판단하였다. 또한 Ulusay et al.(1994), Min and Moon (2006), Diamantis et al.(2009), Sheraz et al.(2014), Elhakim(2015) 등은선형회귀분석을사용하여상관관계를구하는경우점하중강도지수가 0이어도일축압축강도가 y축의절편만큼존재하는모순이있으며강도가클수록 y축의절편이증가하여참값과의편차가더크다는문제점을지적하였다. 따라서일축압축강도와점하중강도지수의상관관계는환산계수로나타낼것을권장하였다. 점하중강도지수와일축압축강도의상관관계를제시한국내외의논문들로부터얻어진결정계수 (r 2 ) 는 Table 3과같다. Table 1에제시된외국사례의경우, 다양한식으로부터얻어진암종별평균결정계수는퇴적암 0.83, 화성암 0.79, 변성암 0.82이었으며예상대로다양한암석에서얻어진결정계수는 0.72로가장낮았다. Table 2에제시된국내사례의경우에는, 다양한식에서산출된결정계수 (r 2 ) 의암종별평균은퇴적암 0.84, 화성암 0.85, 변성암 0.90이었으며예상대로다양한암석에서얻어진결정계수는 0.80으로가장낮았다. Table 3에의하면국내외모든암석에서, y절편이 0인환산계수를사용한경우의결정계수는다양한식에서얻어진결정계수보다는다소낮았으나그차이가크지않았다. Vallejo et al.(1989) 과 Rusnak and Mark(1999), Cha et al.(2007), Elhakim(2015), Kaya and Karaman(2016) 의연구결과에서도 y절편이 0인환산계수가표준회귀식과비교하여정확도가떨어지지않았다. Kim et al.(2012) 도원점회귀분석을이용하더라도결정계수가일반회귀식과큰차이가없었으며, 원점회귀분석에서얻어진값 (26.43) 이 Min and Moon(2006) 이제안한환산계수 ( 강도비 ) 를이용하여얻어진값 (26.30) 과유사한결과를보였으므로원점회귀분석에서얻어진값을사용할것을권장하였다. 일축압축강도의산정을위하여 24의환산계수가국내외에서널리사용되고있으며 RMR 암반분류의일축압축강도산정에도 25의환산계수가사용되고있다. 따라서일축압축강도와점하중강도지수시험의정확성, 기존의사례연구, 사용의편리성등을종합했을때다양한형태의식보다는단순한환산계수를사용하여암석의일축압축강도를산정하는것이가장합리적인것으로판단된다. Table 3. Coefficients of determination (r 2 ) for equations correlating the UCS to the point load strength index Rocks in foreign countries Rocks in Korea Various type equations Conversion factors Various type equations Conversion factors Sedimentary rocks Igneous rocks Metamorphic rocks Various rock types Total rock averages 점하중강도지수와일축압축강도환산계수 국외사례연구 국외에서많은연구자들이환산계수를발표하였으며퇴적암은 Table 4, 화성암, 변성암, 다양한암석은 Table 5 와같다. Table 3

11 82 Hak Joon Kim Table 4. Conversion factors correlating the UCS to the point load strength index for sedimentary rocks from foreign countries Rock types Conversion factor UCS Range (MPa) References Sandstone, limestone, mudstone (r 2 =UN*) UN* Carter and Sneddon (1977) Sedimentary rocks 29 (r 2 =0.884) Hassani et al. (1980) Sandstone, siltstone 16 (r 2 =UN*) Read et al. (1980) Sandstone (r 2 =NG*) Forster (1983) Limestone 26.5 (r 2 =UN*) Sandstone 24.8 (r 2 =UN*) UN* Hawkins and Olver (1986) Siltstone 9 (r 2 =UN*) Limestone, sandstone, anhydrite, halite 21.8 (r 2 =UN*) O Rourke (1989) Sandstone 17.4 (r 2 =NG*) NG* Shale 12.5 (r 2 =NG*) NG* Vallejo et al. (1989) Siltstone 14.7 (r 2 =UN*) Sandstone 18 (r 2 =UN*) UN* Das (1985) Shale 12.6 (r 2 =UN*) Mudstone 16 (r 2 =UN*) UN* Wilson (1976) Sandstone/limestone 24 (r 2 =NG*) Shale 12.6 (r 2 =NG*) NG* Smith (1997) Shale 21.8 (r 2 =NG*) Siltstone 20.2 (r 2 =NG*) Sandstone 20.6 (r 2 =NG*) Rusnak and Mark (1999) Limestone 21.9 (r 2 =NG*) Sandstone 14.1 (r 2 =UN*) UN* Jermy and Bell (1991) Limestone, marlstone, sandstone PLS (Total)-25.3 (r 2 =0.71) PLS<2 13 (r 2 =0.49) 2<PLS<5 24 (r 2 =0.36) Sabatakakis et al. (2008) PLS>5-28 (r 2 =0.53) Limestone, marlstone, sandstone 23 (r 2 =0.75) Tsiambaos and Sabatakakis (2004) Sandstone (Calcareous) 2.86 (r 2 =0.64) Elhakim (2015) Sedimentary (various) (r 2 =0.85) Kaya and Karaman (2016) Sandstone 19 (author s suggestion) Ulusay et al. (1994) Mudrock 21.4 (r 2 =0.856) Lashkaripour (2002) Chalk ( 백악, 퇴적암 ) 8-18 (r 2 =NG*) Palchik and Hatzor (2004) sandstone, siltstone, 13.4 (r 2 =0.89) 1-11 Agustawijaya (2007) Sedimentary rock (r 2 =0.48) Sandstone (r 2 =0.62) Tziallas et al. (2009) Wet Sedimentary rocks 10 (PLS<2), 16 (PLS 2-5), 24 (PLS>5) (r 2 =NG*) NG* Hawkins (1998) Limestone (dry) 14.7 (r 2 =NG*) 29 Limestone (wet) 15.8 (r 2 =NG*) 18 Sandstone (dry) 11.8 (r 2 =NG*) 12 Sandstone (wet) 22.7 (r 2 =NG*) 3 Nuri et al. (2012) Gypsum (dry) 14.4 (r 2 =NG*) 33 Gypsum (wet) 16.0 (r 2 =NG*) 20 Dolostone, sandstone, limestone 23.8 (r 2 =NG*) Gunsallus and Kulhawy (1984) *NG: Not given in the references, *UN: Unknown

12 Estimation for the Uniaxial Compressive Strength of Rocks in Korea using the Point Load Test 83 Table 5. Conversion factors correlating the UCS to the point load strength index for igneous, metamorphic, and various rocks from foreign countries Rock types Conversion factor UCS Range (MPa) References Basalts 1 20 (r 2 =UN*) Read et al. (1980) Dolerite (r 2 =NG*) Forster (1983) Granite 1 16 (r 2 =0.563) Ghosh and Srivastava (1991) Granitic rocks (r 2 =0.960) Tugrul and Zarif (1999) Igneous (various) (r 2 =0.77) Kaya and Karaman (2016) Granite (considering cone penetration) 1 18 (r 2 =0.97) Granite (no correction) 1 21 (r 2 =0.93) Basu and Aydin (2006) Granite (Dry) 1 30 (r 2 =0.96) Granite (Saturated) 1 24 (r 2 =0.98) Irfan and Dearman (1978) Igneous rock (r 2 =0.88) Tziallas et al. (2009) Greenstone (r 2 =NG*) 12 Forster (1983) Quartzite (r 2 =0.960) Singh and Singh (1993) Metamorphic (various) (r 2 =0.72) Kaya and Karaman (2016) Serpentinite (r 2 =0.74) Diamantis et al. (2009) Metamorphic rock (r 2 =0.78) Tziallas et al. (2009) Various (r 2 =0.774) Broch and Franklin (1972) Sandstone, quartzite, norite (r 2 =NG*) Bieniawski (1975) Hard rock (r 2 =0.884) Soft rock (r 2 =0.813) Singh et al. (2012) Granite/tuff (r 2 =0.533) (Avg.=100) Chau and Wong (1996) Various 3 22 (r 2 =NG*) Brook (1985) Sandstone, limestone, dolomite, marble, gneiss 3 24 (r 2 =NG*) Cargill and Shakoor (1990) (r 2 =0.533) 2-22 Various (r 2 =0.624) Karaman et al. (2015) All types (r 2 =0.79) Kaya and Karaman (2016) Basalt, granite, hornfels (r 2 =NG*) Quane and Russel (2003) Hydrothermally altered rock (dacite, tuff, sandstone, conglomerate) (r 2 =0.85) 1-25 Kohno and Maeda (2012) All rock types (r 2 =0.62) Tziallas et al. (2009) Dry Sedimentary & Igneous rocks 3 15 (PLS<2), 20 (PLS 2-5), 25 (PLS>5) (r 2 =NG*) NG* Hawkins (1998) *NG: Not given in the references, *UN: Unknown, 1: Igneous rock, 2: Metamorphic rock, 3: Various rocks 에의하면화성암의결정계수는 0.88로가장높았으며다양한암석은 0.71로가장낮았다. 퇴적암의환산계수는 ( 평균 17.7), 화성암 ( 평균 19.0), 변성암 ( 평균 17.1), 다양한암석은 ( 평균 19.0) 의범위를보였다. 국외의모든사례연구에서얻어진환산계수의평균은 18.1이었다. 모든암종의환산계수평균값은기존에국내외에서널리사용되고있는 24보다는작았으며암종별로유의미한결과를보이지않았다. 본연구에서제시한사례연구에의하면약한암석의환산계수가더작은경향을보였으므로 Table 4와 5 중에서암석의압축강도를알수있는데이터에대해서만추가적으로암석의강도별환산계수를분석하였다 (Table 6). ISRM(1981) 의일축압축강도

13 84 Hak Joon Kim Table 6. Average conversion factors for different rock types from foreign countries Rock types Conversion factor UCS Range (MPa) Sedimentary rock Igneous rock Metamorphic rock Various rock types Average for all conversion factors 에의한무결암분류에의하면 25 MPa 이하는연암 (low strength) 혹은극연암 (very low strength), MPa은보통암, MPa은중경암, 100 MPa 이상은경암혹은극경암에해당된다. Table 6에의하면일축압축강도가 50 MPa 이하인모든암석의평균환산계수가 15보다작았다. 특히일축압축강도가 25 MPa 이하인암석에서는상대적으로더낮은환산계수를보였으며, 10 이하의매우낮은환산계수를보이는경우도있었다 MPa의암석은환산계수가 19.5, MPa의암석은환산계수 19.6으로유사하였다. 또한 100 MPa이상암석의평균환산계수는 20.4, 150 MPa이상암석의평균환산계수는 22.6이었다. 외국의사례조사를통해서얻은결론은, 환산계수는 Bieniawski(1989) 의제안과같이일축압축강도가 25 MPa 이상의암석에서만사용하는것이권장되며 MPa 암석은환산계수 15, MPa의암석은환산계수 20, 150 MPa 이상의암석은 23 의환산계수를사용하는것이적절한것으로판단된다. 국내사례연구 국내에서도많은연구자들이환산계수에대한연구를수행하였으며이를종합하면 Table 7 과같다. Table 3 에의하면화성암의

14 Estimation for the Uniaxial Compressive Strength of Rocks in Korea using the Point Load Test 85 결정계수는 0.92로가장높았으며퇴적암은 0.76으로가장낮았다. 점하중강도시험의축방향실험을제외하면, 퇴적암의환산계수는 ( 평균 20.6), 화성암 ( 평균 20.4), 변성암 ( 평균 18.8), 다양한암석은 17.7의범위를보였다. 국내의모든사례연구에서얻어진환산계수의평균은 19.7이었다. 축방향실험결과를포함할경우의환산계수평균은퇴적암 19.7, 변성암 17.3, 전체암석 18.8로서약 1정도작은값을보였다. 국내암석의환산계수의평균값은외국사례연구와마찬가지로모든암종에서기존에국내외에서널리사용되고있는 24보다는작았으며암종별로유의미한결과를보이지않았다. 국내암석의강도별환산계수는 Table 8과같다. 본연구에서수집된국내사례에서는일축압축강도의평균값이 50MPa이하인경우는없었으며, MPa 암석은환산계수가 19.6, MPa 암석의환산계수는 20.0이었다. 국외사례의경우 MPa의암석은환산계수가 19.5, MPa의암석은환산계수 19.6이었으므로국내와국외암석의환산계수는일축압축강도에따라거의유사하였다. 국내사례연구의경우일축압축강도가 150 MPa 이상인암석에대한실험결과도상당수포함되었으나평균값이 150 MPa이상인암석을대상으로제시된환산계수사례는얻을수없었다. Table 7. Conversion factors correlating the UCS to the point load strength index for rocks in Korea Rock Types Conversion factor UCS Range (MPa) References Sedimentary rocks (r 2 =0.82) (middle 94) Lee et al. (2000) Limestone (Janggun) (r 2 =0.570) (avg. 70) Woo (2005) Sedimentary rocks (axi.) (avg. 89) Sandstone (axi.) (avg. 106) Shale (axi.) (avg. 93) Min and Moon (2006) Mudstone (axi.) (avg. 54) Shale (r 2 =0.86) (middle 85) Lee and Youn (2009) Limestone (r 2 =0.78) (avg. 88) Kim et al. (2012) Granite (Chunyang)-J* (r 2 =0.97) (middle 93) Baek et al. (1997) Glassy volcanic rock (r 2 =not given) 66 Kang et al. (2005) Granite (Chunyang)-J* (r 2 =0.869) (avg. 101) Woo (2005) Biotite gneiss (Total) (r 2 =0.82) (avg. 92) Biotite gneiss (Gonjiam) (r 2 =0.81) (avg. 76) Biotite gneiss (Bundang) (r 2 =0.82) (avg. 81) Biotite gneiss (Gwangju) (r 2 =0.69) (avg. 126) Cha et al. (2007) Biotite gneiss (Dukso) (r 2 =0.72) (avg. 99) Biotite gneiss (Yangpyung) (r 2 =0.85) (avg. 76) 22.2 (r 2 =0.79) (middle 88) Biotite gneiss (axi.) (r 2 =0.72) (middle 82) Kim et al. (2008) Gneiss (r 2 =not given) (axi.) (r 2 =not given) (avg. 95) Kwon (2012) Granite (C*), Biotite granite (C*), Granitic gneiss (J*), Porphyric granite (J*), Alkali granite (J*) (r 2 =0.77) (avg. 117) Woo (2014) * 1: Sedimentary rock, 2: Igneous rock, 3: Metamorphic rock, 4: Various rocks, axi.: axial test, J*:Jurassic, C*:Cretaceous

15 86 Hak Joon Kim Table 8. Average conversion factors for different rock types in Korea Rock types Conversion factor UCS Range (MPa) 20.6 (19.7)* Sedimentary rock 20.2 (19.5)* (20.5)* Igneous rock (17.3)* Metamorphic rock 18.4 (16.8)* Various rock types (18.8)* Average for all conversion factors 19.6 (18.6)* (19.6)* ( )* : Including test data from axial direction 국내외사례연구에의한환산계수제안 환산계수는다양한인자들에의하여영향을받을수있으나이러한인자들을모두고려하여환산계수를결정하는것은실무적으로적용하기어렵다. 국내외사례연구결과에의하면환산계수는암종이나산출지역보다는일축압축강도와밀접한상관성이있는것으로판단된다. 일축압축강도가 25 MPa 이하의암석은환산계수가매우다양하므로환산계수는일축압축강도가 25 MPa 이상의암석에서만사용하는것이권장되며 MPa 암석은환산계수 15, MPa 이상의암석은환산계수 20, 150 MPa 이상의암석은 23의환산계수를사용하는것이적절한것으로판단된다. 그러나현장에서는암석의점하중강도지수를먼저측정한후환산계수를이용하여일축압축강도로환산하게되므로점하중강도지수에따른환산계수값을제시하는것이필요하다. 또한일축압축강도의범위에따라하나의환산계수를제시하는것은약간의일축압축강도의차이에따라환산계수의차이가크게발생할수있는데, 예를들면어떤암석의일축압축강도가 149 MPa인경우에는 20, 151 MPa인경우 23의환산계수를사용해야하는문제점이있다. 일축압축강도를구간별환산계수를이용하여점하중강도지수로환산한후, 각구간별비례관계를가정하여점하중강도지수에대한환산계수를구하면 Table 9와같다. 환산계수는점하중강도지수가 1.5 MPa이상일경우에만사용하고, 환산계수식을이용할경우소수점으로환산계수가계산될수있는데소수첫번째자리에서반올림하여정수로이용하는것이권장된다. Hawkins(1998) 가건조한퇴적암과화성암에서얻은환산계수는 15(PLS<2 MPa), 20(PLS 2 5 MPa), 25 (PLS>5 MPa) 인데, Table 9를이용하여이범위의환산계수를계산하면 PLS 1.5 MPa은 15, PLS 2 5 MPa은 17 22( 평균 19.5), PLS>5 MPa은 22 23이므로비교적유사한결과를보인다. 그러나 Sabatakakis et al. (2008) 이석회암, 이회암, 사암으로부터구한환산계수 13(PLS<2 MPa), 24(PLS 2 5 MPa), 28(PLS>5 MPa) 과는다소차이가있다. 결론적으로, 국내외암석에대한사례연구결과점하중강도지수가 1.5 MPa( 혹은일축압축강도 25 MPa) 미만인암석의경우환산계수의신뢰성이매우떨어져서사용하지않는것이권장된다. 또한환산계수가암석의강도와밀접한상관성이있어서강도가증가할수록환산계수가증가하는경향이뚜렷하므로국내외에서널리사용되는 24와같은하나의환산계수를사용하여암석의일

16 Estimation for the Uniaxial Compressive Strength of Rocks in Korea using the Point Load Test 87 축압축강도를추정하는것은많은오차를유발할수있다. 점하중강도지수 6.5 MPa( 혹은일축압축강도 150 MPa) 이상의경암이나 극경암에서는환산계수가더이상증가하지않으므로 23 의환산계수를적용하는것이적절할것으로판단된다. Table 9. Suggested conversion factors for rocks in Korea obtained using literature reviews Point load strength index (PLS, MPa) Conversion factor* < 1.5 Do not use < PLS PLS < PLS PLS > * Natural number 환산계수의국내현장적용 본연구결과의신뢰성을검증하기위하여, 점하중강도시험을수행하였다. 일축압축시험과점하중강도시험의시료규격과절차는한국암반공학회에서제안한 KSRM(2005, 2007) 의표준시험법을적용하였다. 시험은모두 NX 크기의직경을가진시추코어를사용하였으며, 점하중시험의경우직경방향시험은직경과길이의비율이 1:2, 축방향시험은 1:1의시료가주로사용되었다. 국내암석에서수행된일축압축강도와점하중강도지수를요약하면 Table 10과같다. 일축압축시험은무결암 (intact rock) 에서수행되는데국내암석의무결암강도가일반적으로양호하므로, MPa의일축압축강도를가진보통암에해당되는암석시료에대한자료취득에는어려움이있었다. 본연구에사용된국내암석의일축압축강도평균은최소 59 MPa에서최대 197 MPa로중경암 경암에해당된다. 일축압축강도시험은표준시험법에따라모든사례에서 3개이상의시험결과를이용하였으나점하중시험은균질한시료채취의어려움으로인하여 10개이하의시료에서얻어진결과도 Table 10에포함하였다. 그러나최대값과최소값을제외한나머지값을평균하여점하중강도지수를결정하였으며취득한점하중시험결과의분산이크지않았으므로시료수의부족으로인한오차는크지않을것으로판단된다. 세종시의쥐라기흑운모화강암은직경과축방향으로점하중시험이수행되었다. 세종시화강암의경우이방성을보이지않아서직경방향과축방향의점하중강도지수가거의동일하였으며환산계수는 10이었다. 충북옥천군대흥교에서시추된역암시료의일축압축강도는 6개시료의평균으로부터 87 MPa로결정되었으며환산계수는 15이었다. 대전시동구대전대학교캠퍼스내에서채취된화강편마암의일축압축강도평균은 97 MPa, 환산계수는 16이었다. 대전하소일반산업단지에서시추된암석은화강암질이많은편암이며석영, 감람석, 운모등의광물을포함하고있다. 5개시료의평균으로부터얻어진암석의일축압축강도는 102 MPa이었다. 직경과축방향으로점하중시험이수행되었으며직경방향은직경과길이의비율이 1:2.5, 축방향은 1:0.9 1 의시료가사용되었다. 이방성을보이는편암의특성상환산계수는직경방향 12, 축방향 25로상당히큰차이를보였다. 경기도화성시갈천리지역호상편마암의평균일축압축강도는 112 MPa이며환산계수는 24로국내외에서널리사용되고있는환산계수와동일하였다. 강원도홍천군굴업리지역의편마암은선캄브리아기의자류석편마암으로직경과축방향으로점하중시험이수행되었다. 이지역편마암의평균일축압축강도는 125 MPa이었으며환산계수는직경방향 22, 축방향 17로이방성을보였다. 세종시새롬동에서

17 88 Hak Joon Kim Table 10. Comparison of conversion factors obtained from this study Rock type Location σ c (MPa) Granite (Jr.) Sejong 44.4, 46.3, Conglomerate Granitic gneiss Schist Banded gneiss Gneiss Granitic gneiss Granite (Cre.) Granite (Jr.) Granite (Cre.) *axial test Okcheon Daejeon Daejeon Hwaseong Hongcheon Sejong Iksan Icheon Daejeon PLS (MPa) Test results Avg. Test results Avg. 75.2, 80.2, 88.3, 89.4, 90.3, , 90.0, 90.8, 97.8, 105.1, , 101, 107, 110, , 97.7, 107.2, 108.0, 120.7, , 108.5, 118.3, 140.6, , 114.3, 131.3, 140.6, , 170.4, 176.0, , 184.4, 185.6, 194.9, 214.8, , 191.7, 195.1, 200.0, 200.4, , 3.9, 4.7, 6.2, 6.6, 7.0, , 4.8, 5.7, 6.4, 6.4, 8.7 σ c /PLS Conversion factors from this study , 5.7, 5.8, 6.0, , 5.7, 5.9, 6.2, , 8.0, 8.3, 8.5, 8.6, 8.9, 9.0, 9.2, 9.6, , 2.8, 3.4, 3.5, 3.6, 3.6, 3.8, 4.7, 5.7, * , 4.6, 4.7, 4.9, , 4.8, 4.8, 5.0, 5.4, 7.0, 7.6, , 5.7, 6.3, 6.6, 8.4, 10.2, , 4.8, 5.0, 6.2, 6.3, 6.5, , 7.1, 7.2, 8.3, 10.6, 11.1, , 6.5, 6.5, 6.6, 6.6, 6.6, 6.8, 6.8, 7.5, , 5.8, 6.0, 6.1, 6.1, 6.1, 6.3, 6.3, 6.3, * * * , 7.0, 7.0, 7.1, , 6.8, 7.4, 7.4, 시추된선캠브리아기편마암질화강암의평균일축압축강도는 130 MPa이었으며직경과축방향으로점하중시험이수행되었다. 편마암질화강암의환산계수는직경방향 22, 축방향 15로이방성을보였다. 익산시의황등화강암은백악기흑운모화강암이며직경과축방향으로점하중시험이수행되었다. 화강암의평균일축압축강도는 171 MPa이었고, 환산계수는직경방향 26, 축방향 28로비교적유사하였다. 경기도이천시이천소방서인근에서채취된쥐라기화강암의평균일축압축강도는 196 MPa로경암에해당되며환산계수는 28이었다. 대전동구대전대학교건설부지에서채취된백악기화강암의평균일축압축강도는 197 MPa, 환산계수는 27이었다. Table 10의 10개사례연구에의하면환산계수는시료채취지역이나암종보다일축압축강도에가장큰영향을받는다. 일축압축강도와환산계수의관계는 Fig. 1과같은데일축압축강도가증가할수록환산계수가증가하는경향이뚜렷하였다. 약 MPa의범위의일축압축강도를가진암석의경우, 일축압축강도 (x) 와환산계수 (y) 는 y=0.108x (R 2 =0.72) 의관계식을보

18 Estimation for the Uniaxial Compressive Strength of Rocks in Korea using the Point Load Test 89 였다. 본연구에서문헌조사결과를통하여도출한환산계수와비교하면, 일축압축강도가 100 MPa이하암석의경우에는측정된환산계수가예상치보다작았고, MPa에서는예상치와측정치가유사하였으며 170 MPa이상의암석은예상환산계수보다더크게측정되었다. 세종과익산시지역의화강암은점하중강도시험의방향이환산계수에큰영향을미치지않았다. 그러나편암, 편마암, 화강편마암과같은변성암은직경방향과축방향의환산계수가상당히큰이방성을보였다. 따라서이방성을보이는암석의경우에는어느한방향의점하중시험결과를가지고암석의일축압축강도를추정하는것은매우큰오차를유발할수있다. Rusnak and Mark (1999) 는직경방향보다축방향으로수행한점하중강도지수를활용하여일축압축강도를산정할것을권장하였다. 이방성이뚜렷한편암의경우에는축방향점하중강도지수를활용하여일축압축강도를산정하는것이기존연구결과와유사하였으나이방성이육안으로뚜렷하지않은편마암의경우에는직경방향의결과가기존연구와일치하였다. 결론적으로, 변성암의경우에는강도가이방성일가능성이있으므로환산계수적용에주의해야하며특히육안으로약한면이관찰되는경우에는이를고려하여점하중시험의방향을결정해야한다. 즉약한면과수직방향의일축압축강도를추정할경우에는점하중시험도일축압축시험과동일한방향으로시험이수행되어야한다. 고찰및토의 본연구에서문헌조사결과를통하여도출한 Table 9 의환산계수를 10 개의사례연구에적용한결과, 24 의동일한환산계수를적 용하는경우보다는정확성이높았다. 그러나일축압축강도가 MPa 인암석의경우에는측정된환산계수가예상치보다작 았고, MPa 에서는예상치와측정치가유사하였으며 MPa 인암석은예상환산계수보다더크게측정되었다. Fig. 1. Relationship between uniaxial compressive strength and conversion factors 본연구와기존연구결과에서도출된공통된결론은암석의일축압축강도가증가할수록환산계수가증가하며따라서특정지역 이나혹은암종에따라특정한환산계수를제시할수는없다는것이다. 특정지역의특정암석에대하여동일한장비를가지고시험 을수행하여얻어진환산계수의결정계수 (r 2 ) 평균은국내암석 0.80, 국외암석 0.78 로비교적높은상관성을보였으나 24 와같은특

19 90 Hak Joon Kim Table 11. Suggested conversion factors for rocks in Korea Point load strength index (PLS, MPa) Conversion factor σc (MPa) < 1.5 Do not use < < PLS < (or 6 PLS + 5) 25 < σc < < PLS < (or 0.75 PLS ) 50 < σc < 정한환산계수를모든암석에일률적으로적용하는것은큰오차를야기할수있다. 이것은상관관계에영향을주는인자들이매우다양하기때문으로판단된다. 실제로 10개사례연구에서, 일축압축강도와환산계수는결정계수 (R 2 ) 0.72의비교적높은상관관계를보였다 (Fig. 1). 따라서암석의강도를고려하여환산계수가적용되는것이타당하다. Fig. 1의경우환산계수 24에해당하는암석의일축압축강도는약 150 MPa이다. 현장에서는암석의점하중강도지수를이용하여일축압축강도를산정하게되므로점하중강도지수의범위별로환산계수가제시되어야한다. 암석의점하중강도지수에따라환산계수를제시하더라도특정암석의일축압축강도의추정에는오차가필연적으로수반될수있으나하나의환산계수를사용하는것보다는더신뢰성있게일축압축강도를추정할수있을것으로판단된다. 국내외암석에대한사례연구결과점하중강도지수가 1.5 MPa( 혹은일축압축강도 25 MPa) 미만인암석의경우환산계수의신뢰성이매우떨어져서사용하지않는것이권장된다. 점하중강도지수가 6.5 MPa이하인암석은국내외사례연구를통하여도출한 Table 9의환산계수를사용하고점하중강도지수가 6.5 MPa( 일축압축강도약 150 MPa) 이상인경우에는기존에널리사용되고있는 24의환산계수를사용할것이권장된다. 이것은비록 150 MPa이상의국내암석에서는 24보다약간더큰환산계수가예상되지만기존에 24가널리사용되었고보수적인가정이며더큰환산계수를사용하여일축압축강도가다소증가되더라도이미암석의강도가양호하므로설계에큰영향을주지않을것이기때문이다. 국내외문헌조사결과와본연구를통하여최종적으로제시된환산계수는 Table 11과같다. Table 9에서는점하중강도지수가 MPa과 MPa 사이의환산계수는수식으로주어졌으나환산계수의정확도를고려했을때각각 17과 22를사용해도무방할것으로판단된다. 향후국내암석에대한점하중강도지수와일축압축강도자료가더축적될경우 Table 11에서제안된환산계수의신뢰성검증과보완이기대된다. 결론 본연구에서는광범위한국내외문헌조사와실내시험결과를통하여국내암석에대한점하중강도지수와일축압축강도의상관 관계를제시하였다. 본연구로부터얻어진결과는다음과같다. 1. 광범위한사례연구를통하여, 암석시료의크기와모양, 일축압축강도와인장강도비율, 암석의종류, 암석의산출지역, 암석의강도등점하중강도지수와일축압축강도의상관관계에영향을주는인자들을제시하였다. 2. 국내외암석에대한점하중강도지수와일축압축강도의다양한상관관계식을결정계수와함께제시하였다. 3. 국내외암석의환산계수분석을통하여암석의점하중강도지수의범위에따른환산계수를제시하였으며점하중강도지수가 1.5 MPa이하일경우에는환산계수를사용하지말것을제안하였다.

20 Estimation for the Uniaxial Compressive Strength of Rocks in Korea using the Point Load Test 문헌조사를통해도출한환산계수를국내 10개현장사례에적용하여환산계수의신뢰성을검증하였으며최종적으로환산계수를제안하였다. 5. 편암, 편마암과같이육안으로이방성이관찰되거나이방성을보일가능성이있는암석의경우에는얻고자하는방향의일축압축강도와동일한방향으로점하중강도시험을수행한후환산계수를적용해야한다. 향후국내암석에대한점하중강도지수와일축압축강도자료가더축적될경우본논문에서제안된환산계수의신뢰성검증과보 완이기대된다. 사사 이논문은 2016 학년도대전대학교교내학술연구비지원에의해연구되었음. References Abbs, F.A., 1985, Use of the point load strength index in weak carbonate rocks, In: strength testing of marine sediments: Laboratory and in-situ measurements, American Society for Testing and Materials, Special Technical Publication 833, R. C. Chaney and K. R. Demars, Editors, Agustawijaya, D.S., 2007, The uniaxial compressive strength of soft rock, Civil Engineering Dimension, Vol. 9, Andrade, P.S. and Saraiva, A.A., 2010, Physical and mechanical characterization of phyllites and metagreywackes in central Portugal, Bulletin of Engineering Geology and the Environment, Vol. 69, ASTM, 2016, Standard test method for determination of the point load strength index of rock and application to rock strength classifications, ASTM D , American Society for Testing Materials, West Conshohocken, Philadelphia. Azimian, A. and Ajalloeian, R., 2014, An empirical correlation of uniaxial compressive strength with P-wave velocity and point load strength index on marly rocks using statistical method, Geotechnical and Geological Engineering, Vol. 32, Bae, D.S., Song, M.Y., and Kim, K.S., 1991, The anisotropic mechanical characteristics of the metamorphic rocks distributed in the Samkwang-Mine area, Cheongyang, Chungnam, The Journal of Engineering Geology, Vol. 1, Baek, S.C., Kim, K.B., Lee, K.D., 1997, Evaluation of rock uniaxial compressive strength using point load strength index and shore scleroscope hardness, Proceedings of Korean Society of Engineering Geology, Spring conference, Baek, S.C., Kim, Y.T., Kim, H.T., Yoon, J.S., Lee, Y.G., 2006, Evaluation of rock uniaxial compressive strength using ultrasonic velocity, Journal of Korean Geo-Environmental Society, Vol. 7, Basu, A. and Aydin, 2006, Predicting uniaxial compressive strength by point load test: significance of cone penetration, Rock Mechanics and Rock Engineering, Vol. 39, Basu, A. and Kamran, M., 2010, Point load test on schistose rocks and its applicability in predicting uniaxial compressive strength,

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