Abstract
The rock mass deformation modulus is an important parameter for analysis of the mechanical behaviour rock structures. Due to high cost, time consuming activity and difficulties in interpretation of in-situ measurements, a number of empirical methods have been developed to estimate the deformation modulus on the basis of classification systems. However, due to a large number of empirical equations, the practical rock engineers have encountered the question which empirical relationship provides the most reliable estimation of the deformation modulus. This paper combines a review of empirical equations and statistical analyses based on the case studies from Iranian geography. Results of ninety-nine plate jacking tests from three dams and hydropower projects were used to evaluate the predictive performance of these empirical methods. Statistical analyses show that the Hoek and Diederichs (Int J Rock Mech Min Sci 43:203–215, 2006) and Ajalloeian and Mohammadi (Bull Eng Geol Environ 73:541–550, 2014) relationships provide the most precise and accurate estimation of the deformation modulus based on the in-situ measurements.
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References
Ajalloeian R, Mohammadi M (2014) Estimation of limestone rock mass deformation modulus using empirical equations. Bull Eng Geol Environ 73:541–550. https://doi.org/10.1007/s10064-013-0530-3
Aksoy CO, Geniş M, Uyar Aldaş G, Özacar V, Özer SC, Yılmaz Ö (2012) A comparative study of the determination of rock mass deformation modulus by using different empirical approaches. Eng Geol 131-132:19–28. https://doi.org/10.1016/j.enggeo.2012.01.009
Alemdag S, Gurocak Z, Cevik A, Cabalar AF, Gokceoglu C (2016) Modeling deformation modulus of a stratified sedimentary rock mass using neural network, fuzzy inference and genetic programming. Eng Geol 203:70–82. https://doi.org/10.1016/j.enggeo.2015.12.002
Alemdag S, Gurocak Z, Gokceoglu C (2015) A simple regression based approach to estimate deformation modulus of rock masses. J Afr Earth Sci 110:75–80. https://doi.org/10.1016/j.jafrearsci.2015.06.011
Arora VK (1987) Strength and deformational behaviour of jointed rocks. Indian Institute of Technology, Delhi, India
Aydan O (1989) The stabilisation of rock engineering structures by rockbolts. In: Nagoya university. Nagoya, Japan
Aydan Ö, Ulusay R, Kawamoto T (1997) Assessment of rock mass strength for underground excavations. Int J Rock Mech Min Sci 34:18.e11–18.e17. https://doi.org/10.1016/S1365-1609(97)00273-6
Barton N Application of Q-system and index tests to estimate shear strength and deformability of rockmasses. In: International symposium on engineering geology and underground construction, Lisbon, Portugal, 1983. pp 51-70
Barton N The influence of joint properties in modelling jointed rock masses In: 8th ISRM Congress, Tokyo, Japan, 25-29 September, 1995. pp 1023-1032
Barton N Estimating rock mass deformation modulus for excavation disturbed zone studies. In: International Conference on Deep Geological Disposal of Radioactive Waste, Winnipeg, Minitoba Canada, 1996. pp 1-12
Beiki M, Bashari A, Majdi A (2010) Genetic programming approach for estimating the deformation modulus of rock mass using sensitivity analysis by neural network. Int J Rock Mech Min Sci 47:1091–1103. https://doi.org/10.1016/j.ijrmms.2010.07.007
Benson RP, Murphy DK, McCreath DR (1970) Modulus testing of rock at the Churchill falls underground powerhouse, Labrador. In: Determination of the in-situ modulus deformation of rock, ASTM STP 477. pp 89 - 116
Bertuzzi R (2017) Back-analysing rock mass modulus from monitoring data of two tunnels in Sydney, Australia. J Rock Mech Geotech Eng 9:877–891. https://doi.org/10.1016/j.jrmge.2017.05.005
Bieniawski ZT (1978a) Determining rock mass deformability: experience from case histories. Int J Rock Mech Min Sci Geomech Abstr 15:237–247. https://doi.org/10.1016/0148-9062(78)90956-7
Bieniawski ZT (1978b) Determining rock mass deformability: experience from case histories. Int J Rock Mech Min Sci Geomech Abstr 15:237–247
Bieniawski ZT A comparison of rock deformability measurements by Petite sismique, the Goodman jack and hlat jacks. In: Rapid Excavation and Tunneling Conference (RETC), Atlanta, 1979. SME
Brown ET (1970) Strength of models of rock with intermittent joints. J Soil Mech Found Div 96:1935–1949
Chun B-S, Lee Y-J, Seo D-D, Lim B-S (2006) Correlation deformation modulus by PMT with RMR and rock mass condition. Tunn Undergr Space Technol 21:231–232. https://doi.org/10.1016/j.tust.2005.12.011
Chun B-S, Ryu WR, Sagong M, Do J-N (2009) Indirect estimation of the rock deformation modulus based on polynomial and multiple regression analyses of the RMR system. Int J Rock Mech Min Sci 46:649–658. https://doi.org/10.1016/j.ijrmms.2008.10.001
Clerici A Indirect determination of rock masses - case histories. In: ISRM International Symposium - EUROCK 93, Lisbon, Portugal, 1993. pp 509-517
Coon RF, Merritt AH (1970) Predicting in situ modulus of deformation using rock quality indices. ASTM STP477
Diederichs MS, Kaiser PK (1999) Stability of large excavations in laminated hard rock masses: the voussoir analogue revisited. Int J Rock Mech Min Sci 36:97–117. https://doi.org/10.1016/S0148-9062(98)00180-6
Ebisu S, Aydan O, Komura S, Kawamoto T Comparative study on various rock mass characterization methods for surface structures. In: Rock characterization: ISRM symposium, Eurock 92, Chester, UK, 1992. pp 203-208
Einstein HH, Hirschfeld RC (1973) Model studies on mechanics of jointed rock. J Soil Mech Found Div 99:229–248
Fattahi H (2016) Application of improved support vector regression model for prediction of deformation modulus of a rock mass. Eng Comput 32:567–580. https://doi.org/10.1007/s00366-016-0433-6
Feng X, Jimenez R (2015) Estimation of deformation modulus of rock masses based on Bayesian model selection and Bayesian updating approach. Eng Geol 199:19–27. https://doi.org/10.1016/j.enggeo.2015.10.002
Galera JM, Álvarez M, Bieniawski ZT Evaluation of the deformation modulus of rock masses using RMR: comparison with dilatometer tests. In: ISRM 2007, Underground Works under Special Conditions, Lisbon, 2007. pp 71-77
Gardner WS Design of drilled piers in the Atlantic Piedmont. In: Smith RE (ed) Foundations and Excavations in Decomposed Rock of the Piedmont Province, New York, 1987. ASCE, pp 62-86
Gokceoglu C, Sonmez H, Kayabasi A (2003) Predicting the deformation moduli of rock masses. Int J Rock Mech Min Sci 40:701–710. https://doi.org/10.1016/S1365-1609(03)00062-5
Gokceoglu C, Yesilnacar E, Sonmez H, Kayabasi A (2004) A neuro-fuzzy model for modulus of deformation of jointed rock masses. Comput Geotech 31:375–383. https://doi.org/10.1016/j.compgeo.2004.05.001
Grimstad E, Barton (1993) N Updating the Q-system for NMT. In: Proceedings of the International Symposium on Sprayed Concrete-Modern use of wet mix sprayed concrete for underground support, Fagernes, Oslo. Norwegian Concrete Association, pp 46-66
Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci 34:1165–1186. https://doi.org/10.1016/S1365-1609(97)80069-X
Hoek E, Carranza-Torres C, Corkum B Hoek-Brown failure criterion - 2002 Edition. In: Proceedings of the 5th North American Rock Mechanics Symposium and 17th Tunnelling Association of Canada Conference (NARMS-TAC 2002), University of Toronto, 2002. pp 267-271
Hoek E, Diederichs MS (2006) Empirical estimation of rock mass modulus. Int J Rock Mech Min Sci 43:203–215
Isik NS, Doyuran V, Ulusay R (2008a) Assessment of deformation modulus of weak rock masses from pressuremeter tests and seismic surveys. Bull Eng Geol Environ 67:293–304. https://doi.org/10.1007/s10064-008-0163-0
Isik NS, Ulusay R, Doyuran V (2008b) Deformation modulus of heavily jointed–sheared and blocky greywackes by pressuremeter tests: numerical, experimental and empirical assessments. Eng Geol 101:269–282. https://doi.org/10.1016/j.enggeo.2008.06.004
Kallu RR, Keffeler ER, Watters RJ, Agharazi A (2015) Development of a multivariate empirical model for predicting weak rock mass modulus. Int J Min Sci Technol 25:545–552. https://doi.org/10.1016/j.ijmst.2015.05.005
Kang S-S, Kim H-Y, Jang B-A (2013) Correlation of in situ modulus of deformation with degree of weathering, RMR and Q-system. Environ Earth Sci 69:2671–2678. https://doi.org/10.1007/s12665-012-2088-y
Kavur B, Štambuk Cvitanović N, Hrženjak P (2015) Comparison between plate jacking and large flat jack test results of rock mass deformation modulus. Int J Rock Mech Min Sci 73:102–114. https://doi.org/10.1016/j.ijrmms.2014.09.022
Kayabasi A, Gokceoglu C, Ercanoglu M (2003) Estimating the deformation modulus of rock masses: a comparative study. Int J Rock Mech Min Sci 40:55–63. https://doi.org/10.1016/S1365-1609(02)00112-0
Khabbazi A, Ghafoori M, Lashkaripour GR, Cheshomi A (2013) Estimation of the rock mass deformation modulus using a rock classification system. Geomech Geoeng 8:46–52. https://doi.org/10.1080/17486025.2012.695089
Martins FF, Miranda TFS (2012) Estimation of the rock deformation Modulus and RMR based on data mining techniques. Geotech Geol Eng 30:787–801. https://doi.org/10.1007/s10706-012-9498-1
Mehrotra VK (1992) Estimation of engineering parameters of rock mass. University of Roorkee
Mitri H, Edrissi R, Henning J Finite element modeling of cable bolted stopes in hard rock ground mines. In: SME annual meeting, New Mexico, Albuquerque, 1994. pp 94-116
Mohammadi H, Rahmannejad R (2010) The estimation of rock mass deformation modulus using regression and artificial neural networks analysis. Arab J Sci Eng 35:205–217
Nejati HR, Ghazvinian A, Moosavi SA, Sarfarazi V (2014) On the use of the RMR system for estimation of rock mass deformation modulus. Bull Eng Geol Environ 73:531–540. https://doi.org/10.1007/s10064-013-0522-3
Nicholson GA, Bieniawski ZT (1990) A nonlinear deformation modulus based on rock mass classification. Int J Min Geol Eng 8:181–202. https://doi.org/10.1007/bf01554041
Palmström A (1995) RMi - a rock mass characterization system for rock engineering purposes. Oslo University
Palmström A (2001) Measurement and characterization of rock mass jointing. In: Sharma VM, Saxena KR (eds) In-situ characterization of rocks. A. A. Balkema
Palmström A, Singh R (2001) The deformation modulus of rock masses- comparisons between in situ tests and indirect estimates. Tunn Undergr Space Technol 16:115–131
Panthee S, Singh PK, Kainthola A, Das R, Singh TN (2016) Comparative study of the deformation modulus of rock mass. Bull Eng Geol Environ. https://doi.org/10.1007/s10064-016-0974-3
Radovanović S, Ranković V, Anđelković V, Divac D, Milivojević N (2017) Development of new models for the estimation of deformation moduli in rock masses based on in situ measurements. Bull Eng Geol Environ. https://doi.org/10.1007/s10064-017-1027-2
Ramamurthy T (2001) Shear strength response of some geological materials in triaxial compression. Int J Rock Mech Min Sci 38:683–697. https://doi.org/10.1016/S1365-1609(01)00035-1
Ramamurthy T (2004) A geo-engineering classification for rocks and rock masses. Int J Rock Mech Min Sci 41:89–101. https://doi.org/10.1016/S1365-1609(03)00078-9
Read SAL, Perrin ND, Richards LR Applicability of the Hoek-Brown failure criterion to New Zealand greywacke rocks. In: 9th ISRM Congress, 25-28 August, Paris, France, 1999. pp 655-660
Rezaei M, Asadizadeh M, Majdi A, Hossaini MF (2015) Prediction of representative deformation modulus of longwall panel roof rock strata using Mamdani fuzzy system. Int J Min Sci Technol 25:23–30. https://doi.org/10.1016/j.ijmst.2014.11.007
Ribacchi R (1988) Rock mass deformability; in situ tests, their interpretation and typical results in Italy. In: S S (ed) Second international symposium on field measurements in geomechanics, Kobe. Balkema, Rotterdam, pp 171–192
Rocha M Present possibilities of studying foundations of concrete dams. In: 3rd International Congress on Rock Mechanics, Denver, 1974. International Society for Rock Mechanics, pp 879-896
Roy N (1993) Engineering behaviour of rock masses through study of jointed models. Indian Institute of Technology, Delhi, India
Sanei M, Rahmati A, Faramarzi L, Goli S, Mehinrad A Estimation of rock mass deformation modulus in Bakhtiary dam project in Iran. In: 3rd ISRM SINOROCK Symposium, Rock Characterisation, Modelling and Engineering Design Methods, Shanghai, China, 2013. pp 161-164
Serafim JL, Pereira JP Consideration of the geomechanics classification of Bieniawski. In: International Symposium on Engineering Geology and Underground Constructions, 1983. pp 1133 - 1144
Sharma VM, Singh RB, Chaudhary RK Comparison of different techniques and interpretation of the deformation modulus of rock mass. In: Indian Geotechnical Conference (IGC), New Delhi1989. pp 439-443
Shen J, Karakus M, Xu C (2012) A comparative study for empirical equations in estimating deformation modulus of rock masses. Tunn Undergr Space Technol 32:245–250. https://doi.org/10.1016/j.tust.2012.07.004
Sonmez H, Gokceoglu C, Nefeslioglu HA, Kayabasi A (2006) Estimation of rock modulus: for intact rocks with an artificial neural network and for rock masses with a new empirical equation. Int J Rock Mech Min Sci 43:224–235. https://doi.org/10.1016/j.ijrmms.2005.06.007
Sonmez H, Gokceoglu C, Ulusay R (2004) Indirect determination of the modulus of deformation of rock masses based on the GSI system. Int J Rock Mech Min Sci 41:849–857. https://doi.org/10.1016/j.ijrmms.2003.01.006
Stephens RE, Banks DC Moduli for deformation studies of the foundation and abutments of the Portugues Dam - Puerto Rico. In: The 30th U.S. symposium on rock mechanics (USRMS), Morgantown, West Virginia, 1989. pp 31-38
Thorpe R, Watkins DJ, Ralph WE, Hsu R, Flexser S (1980) Strength and permeability tests on ultra-large Stripa granite core. University of California, Berkeley
Ulusay R, Hudson JA (2007) The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974-2006. International Society of Rock Mechanics. Compilation arranged by the ISRM Turkish National Group
Wittke W (1990) Rock mechanics (theory and applications with case histories). Springer-Verlag, Berlin
Yaji RK (1984) Shear strength and deformation response of jointed rocks. Indian Institute of Technology, Delhi, India
Zhang L, Einstein HH (2004) Using RQD to estimate the deformation modulus of rock masses. Int J Rock Mech Min Sci 41:337–341. https://doi.org/10.1016/S1365-1609(03)00100-X
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Bahaaddini, M., Hosseinpour Moghadam, E. Evaluation of empirical approaches in estimating the deformation modulus of rock masses. Bull Eng Geol Environ 78, 3493–3507 (2019). https://doi.org/10.1007/s10064-018-1347-x
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DOI: https://doi.org/10.1007/s10064-018-1347-x