Document Type : Review Paper
Authors
Faculty of Mining, Petroleum & Geophysics Engineering, Shahrood University of Technology, Shahrood, Iran
Abstract
The deformation modulus of rock mass is necessary for stability analysis of rock structures, which is generally estimated by empirical models with one to five input parameters/indexes. However, appropriate input parameter participation to establish a sound basis for a reliable prediction has been a challenging task. In this study, the concept of the principal input parameters was developed based on an analytical method with an emphasis on in situ stress. Based on analytical methods, Young’s modulus of intact rock, the joint’s shear and normal stiffness, joint set spacing, and in situ stress are introduced as the main principal input parameters. A review of seventy empirical models revealed that most of them suffered from a lack of analytical parameters. Due to considering practical issues, the geological strength index (GSI) is replaced with joint set spacing; moreover, the in situ stress effect is perceived by combining Young’s modulus and joint stiffness with specific confining pressure and normal stress, respectively. The integration of the analytical base input parameters and practical issues enhanced the reliability of empirical models due to the reasonable prediction of the deformation modulus to numerical or analytical deformability analysis.
Keywords
Main Subjects
[1]. Chun, B.S., Ryu, W.R., Sagong, M., and Do, J.N. (2009). Indirect estimation of the rock deformation modulus based on polynomial and multiple regression analyses of the RMR system. International Journal of Rock Mechanics and Mining Sciences, 46, 649–658.
[2]. Hoek, E., & Brown, E.T. (1997). Practical estimates of rock mass strength. International Journal of Rock Mechanics and Mining Sciences, 34(8), 1165-1186.
[3]. Menard, L. (1975). The Menard pressuremeter: Interpretation and application of the pressuremeter test results to foundations design. Sols Soils, 26, 5–43.
[4]. Wittke, W. (2014). Rock mechanics based on an anisotropic jointed rock model (AJRM), John Wiley & Sons, Part C, Chp. 15, 57 P.
[5]. Goodman, R.E., Van, T.K., and Heuze, F.E. (1968). Measurement of rock deformability in boreholes. The 10th United States Symposium on Rock Mechanics (USRMS). OnePetro, Austin, May, 20–22.
[6]. Aksoy, C.O., Geniş, M., Aldaş, G.U., Özacar, V., Özer, S.C., and Yılmaz, Ö. (2012). A comparative study of the determination of rock mass deformation modulus by using different empirical approaches. Engineering Geology, 131, 19–28.
[7]. Hashemi, M., Moghaddas, S., and Ajalloeian, R. (2010). Application of rock mass characterization for determining the mechanical properties of rock mass: a comparative study. Rock Mechanics and Rock Engineering, 43, 305–320.
[8]. Hua, D., Jiang, Q., Liu, R., Gao, Y., and Yu, M. (2021). Rock mass deformation modulus estimation models based on in-situ tests. Rock Mechanics and Rock Engineering, 54, 5683–5702.
[9] Bieniawski, Z.T. (1974). Engineering classification of jointed rock masses. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Pergamon, 11, 244.
[10]. Gokceoglua, C., Sonmeza, H., and Kayabasib, A. (2003). Predicting the deformation moduli of rock masses. International Journal of Rock Mechanics and Mining Sciences, 40, 701–710.
[11]. Hoek, E., Carranza-Torres, C., & Corkum, B. (2002). Hoek-Brown failure criterion-2002 edition. Proceedings of NARMS-Tac, 1(1), 267-273.
[12]. Hoek, E. and Diederichs, M.S. (2006). Empirical estimation of rock mass modulus. International Journal of Rock Mechanics and Mining Sciences, 43, 203–215.
[13]. Shahverdiloo, M.R. and Zare, S. (2021b). A new correlation to predict rock mass deformability modulus considering loading level of dilatometer tests, Geotechnical and Geological Engineering, 39, 5517–5528.
[14]. Shahverdiloo, M.R. and Zare, S. (2023). Experimental study of normalized confining pressure effect on Young’s modulus in different rock types. Arabian Journal of Geosciences, 16, 1–12.
[15]. Shen, X., Chen, M., Lu, W., and Li, L. (2017). Using P wave modulus to estimate the mechanical parameters of rock mass,. Bulletin of Engineering Geology and Environment, 76, 1461–1470.
[16]. Zhang, L. (2010). Method for estimating the deformability of heavily jointed rock masses. Journal of Geotechnical and Geoenvironmental Engineering, 136, 1242-1250.
[17]. Duncan, J.M. and Goodman, R.E. (1968). Finite element analysis of slopes in jointed rocks. U.S. Army Corps of Engineers Rep. TR No. 1-68, Washington, D.C.
[18]. Kulhawy, F.H. (1978). Geomechanical model for rock foundation settlement. Journal of the Geotechnical Engineering Division, 104, 211-227.
[19]. Chen, E.P. (1989). A constitutive model for jointed rock mass with orthogonal sets of joints, ASME Trans. J. Appl. Mech, 56, 25–32.
[20]. Amadei, B. (1983). Rock anisotropy and the theory of stress measurements, Lecture notes in engineering, C.A. Brebbia and S.A. Orszag, eds., Springer, Berlin, 478 P.
[21]. Amadei, B. and Savage, W.Z. (1993). Effect of joints on rock mass strength and deformability. Chapter 17 in Comprehensive Rock Engineering, 1, 331-365.
[22]. Huang, T.H., Chang, C.S., and Yang, Z.Y. (1995). Elastic moduli for fractured rock mass. Rock Mechanics and Rock Engineering, 28, 135-144.
[23]. Fossum, A.F. (1985). Effective elastic properties for a randomly jointed rock mass. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 22, 467-470.
[24]. Gerrard, C.M. (1982). Elastic models of rock masses having one, two, and three sets of joints. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts.
[25]. Oda, M (1988). An experimental study of the elasticity of mylonite rock with random cracks. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstract. 25, 59–69.
[26]. Kulatilake, P. H., Wang, S., & Stephansson, O. (1993, October). Effect of finite size joints on the deformability of jointed rock in three dimensions. In International journal of rock mechanics and mining sciences & geomechanics abstracts (Vol. 30, No. 5, pp. 479-501). Pergamon.
[27] Cai, M., & Wang, X. (2015, May). A non-uniform velocity model and flac/specfem2d coupled numerical simulation of wave propagation in underground mines. In ISRM Congress (pp. ISRM-13CONGRESS). ISRM.
[28]. Cui, L., Sheng, Q., Zheng, J., Xie, M., and Liu, Y. (2022). A unified deterioration model for elastic modulus of rocks with coupling influence of plastic shear strain and confining stress. Rock Mechanics and Rock Engineering, 55, 7409–7420.
[29]. Hsieh, A., Dyskin, A.V., and Dight, P. (2014). The increase in Young's modulus of rocks under uniaxial compression. International Journal of Rock Mechanics and Mining Sciences, 70, 425–434.
[30]. Marinos, P. and Hoek, E. (2001), Estimating the geotechnical properties of heterogeneous rock masses such as flysch. Bulletin of Engineering Geology and Environment, 60, 85–92.
[31]. Yang, S.Q., Jing, H.W., Li, Y.S., and Han, L.J. (2011). Experimental investigation on mechanical behavior of coarse marble under six different loading paths. Experimental Mechanics, 51, 315–334.
[32]. Labrie, D., Conlon, B., Anderson, T., & Boyle, R. F. (2004). Measurement of in-situ deformability in hard rock. Proceedings ISC-2 on Geotechnical and Geophysical Site Characterization, Porto, Portugal. Ed. Milpress, 963-970.
[33]. Song, Y.H., Ju, G.H., and Sun, M. (2011). Relationship between wave velocity and deformation modulus of rock masses. Rock and Soil Mechanics, 32, 1507–1567.
[34]. Shahverdiloo, M.R. and Zare, S. (2021a). Studying the normal stress influential factor on rock joint stiffness using CNL direct shear test. Arabian Journal of Geosciences, 14, 1–11.
[35]. Van, P., & Vásárhelyi, B. (2014). Sensitivity Analysis of GSI based Mechanical Characterization of Rock Mass. Periodica Polytechnica, Civil Engineering, 58(4), 1-8.
[36]. Goodman, R.E. (1989). Introduction to Rock Mechanics ( edition). New York, Wiley, 562 P.
[37]. Coon, R.F. and Merritt, A.T. (1970). Predicting in-situ modulus of deformation using rock quality indexes, Special Technical Publication No. 477. American Society for Testing Materials, Philadelphia.
[38]. Bieniawski, Z.T. (1978). Determining rock mass deformability: experience from case histories. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 15, 237–247.
[39]. Serafim, J.L. and Pereira J.P. (1983). Consideration of the geomechanical classification of Bieniawski. In Proc. Int. Symposium on Engineering Geology and Underground Construction, Lisbon, Sep. 12–15, 1, 12.
[40]. Gardner, W.S. (1987). Design of drilled piers in Atlantic Piedmont. Foundations and excavations in decomposed rock of the Piedmont province, ASCE, Reston, 9, 62–86. https://cedb.asce.org/CEDBsearch/record.jsp?dockey=0051472.
[41]. Nicholson, G.A. and Bieniawski, Z.T. (1990). A nonlinear deformation modulus based on rock mass classification. International Journal of Mining and Geological Engineering, 8, 181–202.
[42]. Grimstad, E.D. and Barton, N. (1993). 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, Oct. 22–26, 46–66. https://www.scirp.org/(S(i43dyn45teexjx- 455qlt3d2q))/reference/referencespapers.aspx?referenceid=2013391
[43]. Mitri, H.S., Edrissi, R., and Henning J.G. (1995). Finite–element modeling of cable–bolted stopes in hard–rock underground mines. Transactions–Society for Mining Metallurgy and Exploration Incorporated, 298: 1897–1902.
[44]. Palmström, A. (1996). Characterizing rock masses by the RMi for use in practical rock engineering, part 2: some practical applications of the rock mass index (RMi). Tunnelling and. Underground Space Technology, 11, 287–303.
[45]. Verman, M., Singh, B., Viladkar, M.N., and Jethwa, J.L. (1997). Effect of tunnel depth on the modulus of deformation of rock mass. Rock Mechanics and Rock Engineering, 30, 121–127.
[46]. Palmström, A. and Singh, R. (2001). The deformation modulus of rock masses—comparisons between in-situ tests and indirect estimates. Tunnelling and Underground. Space Technology, 16, 115–131.
[47]. Barton, N. (2002). Some new Q-value correlations to assist in site characterisation and tunnel design. International Journal of Rock Mechanics and Mining Sciences, 39, 185-216. doi.org/10.1016/S1365-1609(02)00011-4
[48]. Kayabasi, A., Gokceoglu, C.A.N.D.A.N., and Ercanoglu, M.U.R.A.T. (2003). Estimating the deformation modulus of rock masses: a comparative study. International Journal of Rock Mechanics and Mining Sciences, 40, 55–63. doi.org/10.1016/S1365-1609(02)00112-0.
[49]. Zhang, L. and Einstein, H.H. (2004). Using RQD to estimate the deformation modulus of rock masses. International Journal of Rock Mechanics and Mining Sciences, 41, 337–341. doi.org/10.1016/S1365–1609(03)00100–X.
[50]. Ramamurthy, T. (2004). A geo–engineering classification for rocks and rock masses. International Journal of Rock Mechanics and Mining Sciences. 41, 89–101.
[51]. Sonmez, H., Gokceoglu, C., and Ulusay, R. (2004). Indirect determination of the modulus of deformation of rock masses based on the GSI system. International Journal of Rock Mechanics and Mining Sciences, 41, 849–857.
[52]. Galera, J.M., Alvarez, M., and Bienawski Z.T. (2005). Evaluation of the deformation modulus of rock masses: Comparison by pressuremeter and dilatometer tests with RMR prediction. In: ISP5–PRESSIO 2005 International Symposium, 2, 239–256. https://subterra–ing.com/wp–
[53]. Chun, B.S., Lee, Y.J., and Jung S.H. (2006). The evaluation for estimation method of deformation modulus of rock mass using RMR system. Journal of the Korean GEO–environmental Society, 7, 25–32.
[54]. Sonmez, H., Gokceoglu, C., Nefeslioglu, H.A., and Kayabasi, A. (2006). Estimation of rock modulus: for intact rocks with an artificial neural network and for rock masses with a new empirical equation, International Journal of Rock Mechanics and Mining Sciences, 43, 224–235.
[55]. Givshad, A.D., Memarian, H., and Rezaei, F. (2008). Investigation on deformability modulus of asmary formation rock mass, by dilatometer tests. The International Society for Rock Mechanics– International Symposium–5th Asian Rock Mechanics Symposium, OnePetro, Tehran, Nov. 24–26,. 239–246.
[56]. Beiki, M., Bashari, A., and Majdi, A. (2010). Genetic programming approach for estimating the deformation modulus of rock mass using sensitivity analysis by neural network. International Journal of Rock Mechanics and Mining Sciences, 47, 1091–1103.
[57]. Mohammadi, H. and Rahmannejad, R. (2010). The estimation of rock mass deformation modulus using regression and artificial neural networks analysis. Arabian Journal of Sciences and Engineering, 35, 205.
[58]. Shen, J., Karakus, M., and Xu, C.(2012). A comparative study for empirical equations in estimating deformation modulus of rock masses. Tunnelling and Underground Space Technology, 32, 245–250.
[59]. Ajalloeian, R. and Mohammadi, M. (2014). Estimation of limestone rock mass deformation modulus using empirical equations. Bulletin of Engineering Geology and Environment.
[60]. Nejati, H.R., Ghazvinian, A., Moosavi, S.A., and Sarfarazi, V. (2014). On the use of the RMR system for estimation of rock mass deformation modulus. Bulletin of Engineering Geology and Environment, 73, 531–540.
[61]. Karaman, K., Cihangir, F., and Kesimal, A. (2015). A comparative assessment of rock mass deformation modulus. International Journal of Mining Sciences Technology, 25, 735–740.
[62]. Alemdag, S., Gurocak, Z., Cevik, A., Cabalar, A.F., and Gokceoglu, C. (2016). Modeling deformation modulus of a stratified sedimentary rock mass using neural network, fuzzy inference, and genetic programming. Engineering Geology, 203, 70–82. doi.org/10.1016/j.enggeo.2015.12.-002.
[63]. Rezaei, M., Ghafoori, M., and Ajalloeian, R. (2016). Comparison between the in-situ tests’ data and empirical equations for estimation of deformation modulus of rock mass. Geosciences Research, 1, 47–59.
[64]. Ramamurthy, T., Madhavi Latha, G., and Sitharam, T.G. (2016). Modulus ratio and joint factor concepts to predict rock mass response. Rock Mechanics and Rock Engineering, 50, 353–366.
[65]. Radovanović, S., Ranković, V., Anđelković, V., Divac, D., and Milivojević, N. (2018). Development of new models for the estimation of deformation moduli in rock masses based 3on in-situ measurements. Bulletin of Engineering Geology and Environment, 77, 1191–1202.
[66]. Slavko, T. and Veljko, L. (2019). A model for estimation of stress–dependent deformation modulus of rock mass. International Journal of Mining and Geo–Engineering, 53, 63–67.
[67]. Cai, M., Kaiser, P.K., Uno, H., Tasaka, Y., and Minami, M. (2004). Estimation of rock mass deformation modulus and strength of jointed hard rock masses using the GSI system. International Journal of Rock Mechanics and Mining Sciences, 41, 3–19.
[68]. Daraei, A., Sharifi, F., Qader, D. N., Hama Ali, H. F., and Kolivand, F. (2023). Prediction of the static elastic modulus of limestone using downhole seismic test in Asmari formation. Acta Geophys, 72, 247–255.
)