Abstract
The shear strength parameters of the discontinuity surfaces should be acquired for the investigation of discontinuity-controlled instabilities in rock masses. Particularly in weak rocks, it is highly challenging to collect samples from the field and prepare laboratory test samples without affecting the features of the discontinuities. Therefore, empirical methods are gaining importance for determining the strength of discontinuities in such rocks. The purpose of this study is to assess how well the Barton-Bandis criterion performed on samples with low strength under low normal stresses. Artificial samples using various plaster-water mixtures having low compressive strengths with standard roughness profiles were prepared for conducting direct shear tests. The input parameters of Barton-Bandis criterion were determined by laboratory experiments; empirical failure envelopes were drawn, and the results were compared. Based on detailed evaluations, it was seen the criterion has some limitations for low normal stresses. Besides, to determine the joint compressive strength parameter, needle penetration test may be more effective than the Schmidt hammer test especially for low strength materials with the unweathered discontinuity surfaces. According to the results of comparison among digitized data from profilometer, photogrammetric approach (SfM), and optical scanner (SLS) methods, conclusion demonstrates that all of them can be preferred to determine the joint roughness coefficient (JRC) in an acceptable range for the Barton-Bandis criterion. Among them, profilometer and SfM are both easily accessible to all users. However, it should be emphasized that profilometer is still more practical method to estimate the JRC.
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References
Abellan A, Oppikofer T, Jaboyedoff M, Rosser NJ, Lim M, Lato MJ (2014) Terrestrial laser scanning of rock slope instabilities. Earth Surf Proc Land 39:80–97. https://doi.org/10.1002/esp.3493
Agisoft Metashape (2019) https://www.agisoft.com/
Alejano LR, Muralha J, Ulusay R, Li CC, Perez-Rey I, Karakul H, Chryssanthakis P, Aydan Ö (2018) ISRM suggested method for determining the basic friction angle of planar rock surfaces by means of tilt tests. Rock Mech Rock Eng 51:3853–3859. https://doi.org/10.1007/s00603-018-1627-6
An P, Fang K, Jiang Q, Zhang H, Zhang Y (2021) Measurement of rock joint surfaces by using smartphone structure from motion (SfM) photogrammetry. Sensors 21(3):922–944. https://doi.org/10.3390/s21030922
Artec, Artec Eva Portable 3D Scanner. https://www.artec3d.com/
Asadi MS, Rasouli V, Barla G (2013) A laboratory shear cell used for simulation of shear strength and asperity degradation of rough rock fractures. Rock Mech Rock Eng 46:683–699. https://doi.org/10.1007/s00603-012-0322-2
Asadizadeh M, Moosavi M, Hossaini MF, Masoumi H (2018) Shear strength and cracking process of non-persistent jointed rocks: an extensive experimental investigation. Rock Mech Rock Eng 51:415–428. https://doi.org/10.1007/s00603-017-1328-6
Atapour H, Moosavi M (2013) Some effects of shearing velocity on the shear stress deformation behaviour of hard–soft artificial material interfaces. Geotech Geol Eng 31:1603–1615. https://doi.org/10.1007/s10706-013-9687-6
Avşar EÖ, Bozkurtoğlu E, Aydar U, Şeker DZ, Kaya Ş, Gazioğlu C (2016) Determining roughness angle of limestone using optical laser scanner. Int J Environ Geoinformatics 3(3):57–75. https://doi.org/10.30897/ijegeo.306482
Aydan Ö, Shimizu Y, Kawamoto T (1996) The anisotropy of surface morphology and shear strength characteristics of rock discontinuities and its evaluation, Rock Mechanics, Rock Mechanics: tools and techniques, Proceedings of the 2nd North American Rock Mechanics Symposium 19–21June, Montreal, Quebec, Canada, (eds: M. Aubertin, F. Hassani, H. Mitri) Balkema AA 1391–1398. https://doi.org/10.1007/BF01019939
Aydan Ö, Ulusay R (2013) Geomechanical evaluation of Derinkuyu antique underground city and its implications in geoengineering. Rock Mech Rock Eng 46:731–754. https://doi.org/10.1007/s00603-012-0301-7
Aydan Ö (2012) The inference of physico-mechanical properties of soft rocks and the evaluation of the effect of water content and weathering on their mechanical properties from needle penetration tests. Symposium of ARMA, Chicago, Paper No. ARMA12–639
Ban L, Qi C, Chen H, Yan F, Ji C (2020) A new criterion for peak shear strength of rock joints with a 3D roughness parameter. Rock Mech Rock Eng 53:1755–1775. https://doi.org/10.1007/s00603-019-02007-z
Barton N (1973) Review of a new shear-strength criterion for rock joints. Eng Geol 7:287–332. https://doi.org/10.1016/0013-7952(73)90013-6
Barton N, Bandis S (1980) Some effects of scale on the shear strength of joints. Int J Rock Mech Min Sci Geomech Abstr 17:69–73. https://doi.org/10.1016/0148-9062(80)90009-1
Barton N, Choubey V (1977) The shear strength of rock joints in theory and practice. Rock Mech 10:1–54. https://doi.org/10.1007/BF01261801
Barton N, Bandis S (2017) Characterization and modeling of the shear strength, stiffness and hydraulic behavior of rock joints for engineering purposes, Rock Mechanics and Engineering Volume 1: Principles, Xia-Ting Feng (Eds.), CRC Press/Balkema, London 3–40. https://doi.org/10.1201/9781315364261
Belem T, Homand-Etienne F, Souley M (2000) Quantitative parameters for rock joint surface roughness. Rock Mech Rock Eng 33(4):217–242. https://doi.org/10.1007/s006030070001
Berisavljević D, Berisavljević Z, Melentijević S (2022) The shear strength evaluation of rough and infilled joints and its indications for stability of rock cutting in schist rock mass. Bull Eng Geol Environ 81:113. https://doi.org/10.1007/s10064-022-02580-8
Bistacchi A, Griffith WA, Smith SAF, Di Toro G, Jones R, Nielsen S (2011) Fault roughness at seismogenic depths from LIDAR and photogrammetric analysis. Pure Appl Geophys 168:2345–2363. https://doi.org/10.1007/s00024-011-0301-7
Bolla A, Paronuzzi P (2020) Geomechanical field survey to identify an unstable rock slope: the Passo della Morte case history (NE Italy). Rock Mech Rock Eng 53:1521–1544. https://doi.org/10.1007/s00603-019-01963-w
Cacciari PP, Futai MM (2021) The Influence of Fresh and Weathered Rock Foliation on the Stability of the Monte Seco Tunnel 54:537–558. https://doi.org/10.1007/s00603-020-02292-z
Cao P, Deng H, Chen Y, Fu N (2019) The shear characteristic and failure mechanism study of infilled rock joints with constant normal load. J Vibroengineering 21(4):940–951. https://doi.org/10.21595/jve.2018.20055
Chiliza SG, Hingston EDC (2018) Back analysis of an ancient rockslide at Lake Fundudzi. Limpopo Province, South Africa, Bull Eng Geol Environ 77:29–47. https://doi.org/10.1007/s10064-016-1001-4
Choi SO, Chung S (2004) Stability analysis of jointed rock slopes with the Barton-Bandis constitutive model in UDEC. Int J Rock Mech Min Sci 41(1):581–586. https://doi.org/10.1016/j.ijrmms.2004.03.103
Cotecchia V, De Bellis P, Lollino P, Monterisi L, Tria C (2009) Geostructural survey and stability analysis of the calcareous cliff of Vieste (Gargano-Southern Italy). Bull Eng Geol Environ 68:35–45. https://doi.org/10.1007/s10064-008-0169-7
Develi K, Babadağlı T, Çömlekçi C (2001) A new computer-controlled surface-scanning device for measurement of fracture surface roughness. Comput Geosci 27(3):265–277. https://doi.org/10.1016/S0098-3004(00)00083-2
Dotta G, Gigli G, Ferrigno F, Gabbani G, Nocentini M, Lombardi L, Agostini A, Nolesini T, Casagli N (2017) Geomechanical characterization and stability analysis of the bedrock underlying the Costa Concordia cruise ship. Rock Mech Rock Eng 50:2397–2412. https://doi.org/10.1007/s00603-017-1219-x
Du S, Hu Y, Hu X (2009) Measurement of joint roughness coefficient by using profilograph and roughness ruler. J Earth Sci 20(5):890–896. https://doi.org/10.1007/s12583-009-0075-3
Duzgun HSB, Bhasin RK (2009) Probabilistic stability evaluation of Oppstadhornet Rock Slope. Norway, Rock Mech Rock Eng 42:729–749. https://doi.org/10.1007/s00603-008-0011-3
Fan W, Cao P (2020) A new 3D JRC calculation method of rock joint based on laboratory-scale morphology testing and its application in shear strength analysis. Bull Eng Geol Environ 79:345–354. https://doi.org/10.1007/s10064-019-01569-0
Fardin N (2008) Influence of structural non-stationarity of surface roughness on morphological characterization and mechanical deformation of rock joints. Rock Mech Rock Eng 41(2):267–297. https://doi.org/10.1007/s00603-007-0144-9
Fardin N, Feng Q, Stephansson O (2004) Application of a new in situ 3D laser scanner to study the scale effect on the rock joint surface roughness. Int J Rock Mech Min Sci 41:329–335. https://doi.org/10.1016/S1365-1609(03)00111-4
Fathi A, Moradian Z, Rivard P, Ballivy G, Boyd AJ (2016) Geometric effect of asperities on shear mechanism of rock joints. Rock Mech Rock Eng 49:801–820. https://doi.org/10.1007/s00603-015-0799-6
Garcia-Luna R, Senent S, Jimenez R (2021) Using telephoto lens to characterize rock surface roughness in SfM models. Rock Mech Rock Eng 54:2369–2382. https://doi.org/10.1007/s00603-021-02373-7
Ge Y, Lin Z, Tang H, Zhao B (2021) Estimation of the appropriate sampling interval for rock joints roughness using laser scanning. Bull Eng Geol Environ 80:3569–3588. https://doi.org/10.1007/s10064-021-02162-0
Grasselli G, Wirht J, Egger P (2002) Quantitative three-dimensional description of a rough surface and parameter evolution with shearing. Int J Rock Mech Min Sci 39:789–800. https://doi.org/10.1016/S1365-1609(02)00070-9
Gui Y, Xia C, Ding W, Qian X, Du S (2017) A new method for 3D modeling of joint surface degradation and void space evolution under normal and shear loads. Rock Mech Rock Eng 50:2827–2836. https://doi.org/10.1007/s00603-017-1242-y
Haque A (1999) Shear behaviour of soft rock joints under constant normal stiffness, Dissertation, University of Wollongong
He L, Zhao Z, Chen J, Liu D (2020) Empirical shear strength criterion for rock joints based on joint surface degradation characteristics during shearing. Rock Mech Rock Eng 53:3609–3624. https://doi.org/10.1007/s00603-020-02120-4
Hong E, Kwon T, Song K, Cho G (2016) Observation of the degradation characteristics and scale of unevenness on three-dimensional artificial rock joint surfaces subjected to shear. Rock Mech Rock Eng 49:3–17. https://doi.org/10.1007/s00603-015-0725-y
Huang J, Sun C, Wu X, Ling S, Wang S, Deng R (2020) Stability assessment of tunnel slopes along the Dujiangyan City to Siguniang Mountain Railway. China, Bull Eng Geol Environ 79:5309–5327. https://doi.org/10.1007/s10064-020-01913-9
Indraratna B, Thirukumaran S, Brown ET, Zhu S (2015) Modelling the shear behaviour of rock joints with asperity damage under constant normal stiffness. Rock Mech Rock Eng 48:179–195. https://doi.org/10.1007/s00603-014-0556-2
ISRM (2007) The complete ISRM suggested methods for characterization, testing and monitoring: 1974–2006, R. Ulusay, J.A. Hudson (Eds.), Suggested methods prepared by the ISRM commission on testing methods, compilation arranged by th ISRM Turkish National Group, Ankara
Jahanian H, Sadaghiani MH (2015) Experimental study on the shear strength of sandy clay infilled regular rough rock joints. Rock Mech Rock Eng 48:907–922. https://doi.org/10.1007/s00603-014-0643-4
Jang HS, Jang BA (2015) New method for shear strength determination of unfilled, unweathered rock joint. Rock Mech Rock Eng 48:1515–1534. https://doi.org/10.1007/s00603-014-0660-3
Jang HS, Kang SS, Jang BA (2014) Determination of joint roughness coefficients using roughness parameters. Rock Mech Rock Eng 47:2061–2073. https://doi.org/10.1007/s00603-013-0535-z
Jiang Y, Li B, Tanabashi Y (2006) Estimating the relation between surface roughness and mechanical properties of rock joints. Int J Rock Mech Min Sci 43:837–846. https://doi.org/10.1016/j.ijrmms.2005.11.013
Jiang Q, Feng X, Song L, Gong Y, Zheng H, Cui J (2016) Modeling rock specimens through 3D printing: tentative experiments and prospects. Acta Mech Sin 32(1):101–111. https://doi.org/10.1007/s10409-015-0524-4
Jorda-Bordehore L, Herrera R (2018) Rapid field test for shear strength characterization of dacite at Cerro Rico de Potosi (Bolivia): tilt test with a Schmidt hammer and compass-clinometer. Bull Eng Geol Environ 77:867–875. https://doi.org/10.1007/s10064-018-1232-7
Kahraman S, Aloglu AS, Aydin B, Saygin E (2017) The needle penetration test for predicting coal strength. J South Afr Inst Min Metall 117(6):587–591
Kaya A, Akgün A, Karaman K, Bulut F (2016) Understanding the mechanism of slope failure on a nearby highway tunnel route by different slope stability analysis methods: a case from NE Turkey. Bull Eng Geol Environ 75:945–958. https://doi.org/10.1007/s10064-015-0770-5
Kaya A, Karaman K, Bulut F (2017) Geotechnical investigations and remediation design for failure of tunnel portal section: a case study in northern Turkey. J Mt Sci 14(6):1140–1160. https://doi.org/10.1007/s11629-016-4267-x
Kim T, Jeon S (2019) Experimental study on shear behavior of a rock discontinuity under various thermal, hydraulic and mechanical conditions. Rock Mech Rock Eng 52:2207–2226. https://doi.org/10.1007/s00603-018-1723-7
Kwon S, Xie L, Park S, Kim K, Min K, Kim KY, Zhuang L, Choi J, Kim H, Lee TJ (2019) Characterization of 4.2-km-deep fractured granodiorite cores from Pohang Geothermal Reservoir. Korea, Rock Mech Rock Eng 52:771–782. https://doi.org/10.1007/s00603-018-1639-2
Le H, Huang W, Chien C (2021) Exploring micromechanical behaviors of soft rock joints through physical and DEM modeling. Bull Eng Geol Environ 80:2433–2446. https://doi.org/10.1007/s10064-020-02087-0
Lee YH, Carr JR, Barr DJ, Hass CJ (1990) The fractal dimension as a measure of the roughness of rock discontinuity profiles. Int J Rock Mech Min Sci Geomech Abstr 23(6):453–464. https://doi.org/10.1016/0148-9062(90)90998-H
Li Y, Zhang Y (2015) Quantitative estimation of joint roughness coefficient using statistical parameters. Int J Rock Mech Min Sci 77:27–35. https://doi.org/10.1016/j.ijrmms.2015.03.016
Li Y (2016) A constitutive model of opened rock joints in the field, Dissertation, The University of New South Wales
Liu Q, Tian Y, Ji P, Ma H (2018) Experimental investigation of the peak shear strength criterion based on three-dimensional surface description. Rock Mech Rock Eng 51:1005–1025. https://doi.org/10.1007/s00603-017-1390-0
Ma H, Tian Y, Liu Q, Pan Y (2021) Experimental study on the influence of height and dip angle of asperity on the mechanical properties of rock joints. Bull Eng Geol Environ 80:443–471. https://doi.org/10.1007/s10064-020-01904-w
Maerz NH, Franklin JA, Bennett CP (1990) Joint roughness measurement using shadow profilometry. Int J Rock Mech Min Sci Geomech Abstr 27(5):329–343. https://doi.org/10.1016/0148-9062(90)92708-M
Magsipoc E, Zhao Q, Grasselli G (2020) 2D and 3D roughness characterization. Rock Mech Rock Eng 53:1495–1519. https://doi.org/10.1007/s00603-019-01977-4
Marsch K, Wujanz D, Fernandez-Steeger TM (2020) On the usability of different optical measuring techniques for joint roughness evaluation. Bull Eng Geol Environ 79:811–830. https://doi.org/10.1007/s10064-019-01606-y
Miller RP (1965) Engineering classification and index properties for intact rock, Dissertation, University of Illinois
Milne D, Hawkes C, Hamilton C (2009) A new tool for the field characterization of joint surfaces, ROCKENG09: Proceedings of the 3rd CANUS Rock Mechanics Symposium, Diederichs M and Grasselli G (Eds.), Toronto, Paper 4169
Mirzaghorbanali A (2013) Shear behavior of rock joints under cyclic loading and constant normal stiffness conditions, Dissertation, University of Wollongong
Mo P, Li Y (2017) Estimating the three-dimensional joint roughness coefficient value of rock fractures. Bull Eng Geol Environ 78:857–866. https://doi.org/10.1007/s10064-017-1150-0
Nguyen HT, Fernandez-Steeger TM, Wiatr T, Rodrigues D, Azzam R (2011) Use of terrestrial laser scanning for engineering geological applications on volcanic rock slopes – an example from Madeira island (Portugal). Nat Hazard 11:807–817. https://doi.org/10.5194/nhess-11-807-2011
Oh J, Li Y, Mitra R, Canbulat I (2017) A numerical study on dilation of a saw-toothed rock joint under direct shear. Rock Mech Rock Eng 50:913–925. https://doi.org/10.1007/s00603-016-1142-6
Okada S, Izumiya Y, Iizuka Y, Horiuchi S (1985) The estimation of soft rock strength around a tunnel by needle penetration test. J Jap Soc Soil Mech Found Eng 33(2):35–38
Özvan A, Dinçer İ, Acar A, Özvan B (2014) The effects of discontinuity surface roughness on the shear strength of weathered granite joints. Bull Eng Geol Environ 73:801–813. https://doi.org/10.1007/s10064-013-0560-x
Park JW, Lee YK, Song JJ, Choi BY (2013) A constitutive model for shear behavior of rock joints based on three-dimensional quantification of joint roughness. Rock Mech Rock Eng 46:1513–1537. https://doi.org/10.1007/s00603-012-0365-4
Rahimi MR, Mohammadi SD, Heidari M, Jalali SH (2020) Evaluation of the needle penetration test to estimate the uniaxial compressive strength of gypsum rocks. Arab J Geosci 13:14. https://doi.org/10.1007/s12517-019-4989-5
Ram BK, Basu A (2019) A modified JRC-JCS model and its applicability to weathered joints of granite and quartzite. Bull Eng Geol Environ 78:6089–6099. https://doi.org/10.1007/s10064-019-01531-0
Richards RL (1975) The shear strength of joints in weathered rock, Dissertation, University of London
Singh HK, Basu A (2018) A comparison between the shear behavior of ‘real’ natural rock discontinuities and their replicas. Rock Mech Rock Eng 51:329–340. https://doi.org/10.1007/s00603-017-1334-8
Solak KC, Tuncay E, Ulusay R (2017) An investigation on the mechanisms of instabilities and safe design of the south slope at a lignite pit (SW Turkey) based on a sensitivity approach. Bull Eng Geol Environ 76:1321–2134. https://doi.org/10.1007/s10064-017-1025-4
Sow D, Rivard P, Peyras L, Breul P, Moradian ZA, Baconnet C, Ballivy G (2016) Comparison of joint shearing resistance obtained with the Barton and Choubey Criterion and with direct shear tests. Rock Mech Rock Eng 49:3357–3361. https://doi.org/10.1007/s00603-015-0898-4
Spreafico CM, Francioni M, Cervi F, Stead D, Bitelli G, Ghirotti M, Girelli VA, Lucente CC, Tini MA, Borgatti L (2016) Back analysis of the 2014 San Leo landslide using combined terrestrial laser scanning and 3D distinct element modelling. Rock Mech Rock Eng 49:2235–2251. https://doi.org/10.1007/s00603-015-0763-5
Sturzenegger M, Stead D (2009) Close-range terrestrial digital photogrammetry and terrestrial laser scanning for discontinuity characterization on rock cuts. Eng Geol 106:163–182. https://doi.org/10.1016/j.enggeo.2009.03.004
Tang ZC, Wong LNY (2016) Influences of normal loading rate and shear velocity on the shear behaviour of artificial rock joints. Rock Mech Rock Eng 49:2165–2172. https://doi.org/10.1007/s00603-015-0822-y
Tang H, Ge Y, Wang L, Yuan Y, Huang L, Sun M (2012) Study on estimation method of rock mass discontinuity shear strength based on three-dimensional laser scanning and image technique. J Earth Sci 23(6):908–913. https://doi.org/10.1007/s12583-012-0301-2
Tatone BSA, Grasselli G (2010) A new 2D discontinuity roughness parameter and its correlation with JRC. Int J Rock Mech Min Sci 47:1391–1400. https://doi.org/10.1016/j.ijrmms.2010.06.006
Tatone BSA, Grasselli G (2013) An investigation of discontinuity roughness scale dependency using high-resolution surface measurements. Rock Mech Rock Eng 46:657–681. https://doi.org/10.1007/s00603-012-0294-2
Tatone BSA (2009) Quantitative characterization of natural rock discontinuity roughness in-situ and in the laboratory, Dissertation, University of Toronto
Tse R, Cruden DM (1979) Estimating joint roughness coefficients. Int J Rock Mech Min Sci Geomech Abst 16:303–307. https://doi.org/10.1016/0148-9062(79)90241-9
Tuncay E (2009) Rock rupture phenomenon and pillar failure in tuffs in the Cappadocia region (Turkey). Int J Rock Mech Min Sci 46:1253–1266. https://doi.org/10.1016/j.ijrmms.2009.01.011
Tuncay E, Ulusay R (2001) Deterministic and probabilistic treatments of multiplanar pitwall failures at Himmetoglu (Turkey) coal mine. Can Geotech J 38:828–849. https://doi.org/10.1139/t01-015
Ulusay R, Ergüler ZA (2012) Needle Penetration Test: Evaluation of Its Performance and Possible Uses in Predicting Strength of Weak and Soft Rocks 149–150:47–56. https://doi.org/10.1016/j.enggeo.2012.08.007
Ulusay R, Aydan Ö, Ergüler ZA, Ngan-Tillard DJM, Seiki T, Verwaal W, Sasaki Y, Sato A (2014) ISRM Suggested method for the needle penetration test. Rock Mech Rock Eng 47:1073–1085. https://doi.org/10.1007/s00603-013-0534-0
Yang ZY, Lo SC, Di CC (2001) Reassessing the joint roughness coefficient (JRC) estimation using Z2. Rock Mech Rock Eng 34(3):243–251. https://doi.org/10.1007/s006030170012
Yang J, Rong G, Hou D, Peng J, Zhou C (2016) Experimental study on peak shear strength criterion for rock joints. Rock Mech Rock Eng 49:821–835. https://doi.org/10.1007/s00603-015-0791-1
Yu X, Vayssade B (1991) Joint profiles and their roughness parameters. Int J Rock Mech Min Sci Geomech Abst 28(4):333–336. https://doi.org/10.1016/0148-9062(91)90598-G
Zhang X, Jiang Q, Chen N, Wei W, Feng X (2016) Laboratory investigation on shear behavior of rock joints and a new peak shear strength criterion. Rock Mech Rock Eng 49:3495–3512. https://doi.org/10.1007/s00603-016-1012-2
Zhang G, Karakus M, Tang H, Ge Y, Jiang Q (2017) Estimation of joint roughness coefficient from three-dimensional discontinuity surface. Rock Mech Rock Eng 50:2535–2546. https://doi.org/10.1007/s00603-017-1264-5
Zhou HW, Xie H (2004) Anisotropic characterization of rock fracture surfaces subjected to profile analysis. Phys Lett A 325:355–362. https://doi.org/10.1016/j.physleta.2004.04.006
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Solak, K.C., Tuncay, E. An evaluation on Barton-Bandis shear strength criterion for discontinuities in weak materials under low normal stresses. Bull Eng Geol Environ 82, 411 (2023). https://doi.org/10.1007/s10064-023-03434-7
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DOI: https://doi.org/10.1007/s10064-023-03434-7