Document Type : Original Research Paper
Authors
1 Faculty of Mining, Petroleum and Geophysics Engineering, Shahrood University of Technology, Shahrood, Iran
2 Division of Mining and Geotechnical Engineering, Luleå University of Technology, Luleå, Sweden
Abstract
The purpose of this work is to present an approach for the probabilistic stability analysis of tunnels considering the heterogeneity of geo-mechanical properties. A stochastic procedure is followed to account for the variability in the rock mass property characterization. The finite difference method is coupled with the Monte Carlo simulation technique to incorporate the randomness of rock mass properties. Moreover, a particular performance function is defined to investigate the excavation serviceability based on the permissible deformations. In order to validate the analysis, the probabilistic and the deterministic results are compared with the in-situ measurements. It can be observed that in both the probabilistic and deterministic analyses the largest displacements occur in the invert. In contrast, the smallest displacements are recorded in the sidewalls. Utilizing the performance function, the probability of failure for the invert, crown, left, and right wall is estimated as 100%, 68.8%, 16.2%, and 20.9%, respectively. Comparing the measured and calculated convergences, it is conjectured that the deterministic analysis underestimates the displacements, while the measured values are very close to the mean values predicted by the probabilistic analysis. The results obtained indicate that the presented approach could be a reliable technique compared to the conventional deterministic method.
Keywords
[1]. Pelizza, S., Oreste, P., Peila, D., and Oggeri, C. (2000). Stability analysis of a large cavern in Italy for quarrying exploitation of a pink marble. Tunnelling and underground space technology. 15 (4): 421-435.
[2]. Zhu, W., Li, S., Li, S., Chen, W. and Lee, C. (2003). Systematic numerical simulation of rock tunnel stability considering different rock conditions and construction effects. Tunnelling and underground space technology. 18 (5): 531-536.
[3]. Chehade, F. H., and Shahrour, I. (2008). Numerical analysis of the interaction between twin-tunnels: Influence of the relative position and construction procedure. Tunnelling and underground space technology. 23 (2): 210-214.
[4]. Funatsu, T., Hoshino, T., Sawae, H., and Shimizu, N. (2008). Numerical analysis to better understand the mechanism of the effects of ground supports and reinforcements on the stability of tunnels using the distinct element method. Tunnelling and Underground Space Technology. 23 (5): 561-573.
[5]. Idris, M. A., and Nordlund, E. (2019). Probabilistic-Based Stope Design Methodology for Complex Ore Body with Rock Mass Property Variability. Journal of Mining Science. 55 (5): 743-750.
[6]. Jiale, H., and Xiaohong, L. (2021). Reliability analysis considering spatial variability by combining spectral representation method and support vector machine. European Journal of Environmental and Civil Engineering. 25 (6): 1136-1157.
[7]. Behnia, M., and Seifabad, M. C. (2018). Stability analysis and optimization of the support system of an underground powerhouse cavern considering rock mass variability. Environmental Earth Sciences. 77 (18): 1-16.
[8]. Cai, M. (2011). Rock mass characterization and rock property variability considerations for tunnel and cavern design. Rock mechanics and rock engineering. 44 (4): 379-399.
[9]. Idris, M. A., Saiang, D., and Nordlund, E. (2011). Numerical analyses of the effects of rock mass property variability on open stope stability. In 45th US Rock Mechanics/Geo-mechanics Symposium, OnePetro.
[10]. Idris, M. A., Saiang, D., and Nordlund, E. (2012). Consideration of the rock mass property variability in numerical modelling of open stope stability. In Bergmekanikdag 2012: 12/03/2012-12/03/2012 (pp. 111-123), Stiftelsen bergteknisk forskning-Befo.
[11]. Idris, M. A., Nordlund, E., and Saiang, D. (2016). Comparison of different probabilistic methods for analyzing stability of underground rock excavations. The Electronic journal of geotechnical engineering. 21 (21): 6555-6585.
[12]. Seguini, M., and Nedjar, D. (2017). Modelling of soil–structure interaction behavior: geometric non-linearity of buried structures combined to spatial variability of soil. European Journal of Environmental and Civil Engineering. 21 (10): 1217-1236.
[13]. Tiwari, G., Pandit, B., Latha, G.M., and Babu, G.S. (2017). Probabilistic analysis of tunnels considering uncertainty in peak and post-peak strength parameters. Tunnelling and Underground Space Technology. 70: 375-387.
[14]. Tiwari, G., Pandit, B., Gali, M.L., and Babu, G.S. (2018). Analysis of tunnel support requirements using deterministic and probabilistic approaches in average quality rock mass. International Journal of Geo-mechanics. 18 (4): 1-20.
[15]. Heidarzadeh, S., Saeidi, A. and Rouleau, A. (2020). Use of probabilistic numerical modeling to evaluate the effect of geo-mechanical parameter variability on the probability of open-stope failure: a case study of the Niobec Mine, Quebec (Canada). Rock Mechanics and Rock Engineering. 53(3): 1411-1431.
[16]. Oreste, P. (2005). A probabilistic design approach for tunnel supports. Computers and Geotechnics. 32 (7): 520-534.
[17]. Fortsakis, P., Litsas, D., Kavvadas, M., and Trezos, K. (2011). Reliability analysis of tunnel final lining. Geotechnical Safety and Risk, ISGSR 2011, 409-418.
[18]. Langford, J. C., and Diederichs, M. S. (2013). Reliability based approach to tunnel lining design using a modified point estimate method. International Journal of Rock Mechanics and Mining Sciences. 60: 263-276.
[19]. Napa-García, G. F., Beck, A. T., and Celestino, T. B. (2017). Reliability analyses of underground openings with the point estimate method. Tunnelling and Underground Space Technology. 64: 154-163.
[20]. Kroetz, H. M., Do, N. A., Dias, D., and Beck, A. T. (2018). Reliability of tunnel lining design using the hyper-static reaction method. Tunnelling and Underground Space Technology. 77: 59-67.
[21]. Phoon, K. K., and Kulhawy, F. H. (1999). Characterization of geotechnical variability. Canadian Geotechnical Journal. 36 (4): 612-624.
[22]. Hoek, E. (1998). Reliability of Hoek-Brown estimates of rock mass properties and their impact on design. International Journal of Rock Mechanics and Mining Sciences. 35 (1):63-68.
[23]. Riedmuller, G. and Schubert, W. (1999). June. Rock mass modeling in tunneling versus rock mass classification using rating methods. In Vail Rocks, The 37th US Symposium on Rock Mechanics (USRMS). OnePetro.
[24]. Yu, X., Cheng, J., Cao, C., Li, E., and Feng, J. (2019). Probabilistic analysis of tunnel liner performance using random field theory. Advances in Civil Engineering.
[25]. Binder, K., and Heermann, D.W. (2010). Theoretical foundations of the Monte Carlo method and its applications in statistical physics. In Monte Carlo Simulation in Statistical Physics (pp. 5-67), Berlin, Heidelberg, Springer.
[26]. Hsu, S. C., and Nelson, P. P. (2006). Material spatial variability and slope stability for weak rock masses. Journal of Geotechnical and Geo-environmental Engineering. 132 (2): 183-193.
[27]. Mazraehli, M., and Zare, S. (2020). An application of uncertainty analysis to rock mass properties characterization at porphyry copper mines. Bulletin of Engineering Geology and the Environment. 79 (7): 3721-3739.
[28]. Fenton, G. A. (1999). Estimation for Stochastic Soil Models. Journal of Geotechnical and Geo-environmental Engineering. 125 (6): 470-485
[29]. Kim, H., and Major, G. (1978). Application of Monte Carlo techniques to slope stability analysis. In the 19th US Rock Mechanics Symposium.
[30]. Haldar, S., and Babu, G.S. (2008). Effect of soil spatial variability on the response of laterally loaded pile in undrained clay. Computers and Geotechnics. 35 (4): 537-547.
[31]. Song, K.I., Cho, G.C., and Lee, S.W. (2011). Effects of spatially variable weathered rock properties on tunnel behavior. Probabilistic Engineering Mechanics. 26 (3): 413-26.
[32]. Lü, Q., Xiao, Z., Zheng, J., and Shang, Y. (2018). Probabilistic assessment of tunnel convergence considering spatial variability in rock mass properties using interpolated autocorrelation and response surface method. Geoscience Frontiers. 9 (6): 1619–1629.
[33]. Yu, X., Cheng, J., Cao, C., Li, E., and Feng, J. (2019). Probabilistic Analysis of Tunnel Liner Performance Using Random Field Theory. Advances in Civil Engineering.
[34]. Zhang, W., Han, L., Gu, X., Wang, L., Chen, F., and Liu, H. (2020). Tunneling and deep excavations in spatially variable soil and rock masses: A short review. Underground Space.
[35]. Cai, M., Kaiser, P.K., Tasaka, Y., Maejima, T., Morioka, H., and Minami, M. (2004). Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations. International Journal of Rock Mechanics and Mining Sciences. 41 (5): 833-847.
[36]. Chen, D., Xu, D., Ren, G., Jiang, Q., Liu, G., Wan, L., and Li, N. (2019). Simulation of cross-correlated non-Gaussian random fields for layered rock mass mechanical parameters. Computers and Geotechnics. 112: 104–119.
[37]. Ching, J., Hu, Y G., Yang, Z.Y., Shiau, J.Q., Chen, J.C., and Li, Y.S. (2011). Reliability-based design for allowable bearing capacity of footings on rock masses by considering angle of distortion. International Journal of Rock Mechanics and Mining Sciences. 48 (5): 728–740.
[38]. Itasca. (2015). FLAC - Fast Lagrangian Analysis of Continua. Version 7.0. Minneapolis, Minnesota.
[39]. Jia, P., and Tang, C. A. (2008). Numerical study on failure mechanism of tunnel in jointed rock mass. Tunnelling and Underground Space Technology. 23 (5): 500-507.
[40]. Taghizadeh, H., Zare, S. and Mazraehli, M. (2020). Analysis of Rock Load for Tunnel Lining Design. Geotechnical and Geological Engineering. 38 (3): 2989-3005.
[41]. Xing, Y., Kulatilake, P. H. S. W., and Sandbak, L. A. (2018). Effect of rock mass and discontinuity mechanical properties and delayed rock supporting on tunnel stability in an underground mine. Engineering Geology. 238: 62-75.
[42]. Geodata (2016). Detailed design of Alborz main tunnel. Retrieved from Tehran-Shomal freeway project, Turin.
[43]. Hoek, E., Carranza-Torres, C., and Corkum, B. (2002). Hoek-Brown failure criterion-2002 edition. Proceedings of NARMS-Tac. 1 (1): 267-273.
[44]. Hoek, E., and Brown, E.T. (2019). The Hoek–Brown failure criterion and GSI–2018 edition. Journal of Rock Mechanics and Geotechnical Engineering. 11 (3): 445-463.
[45]. Hoek, E. and Diederichs, M.S. (2006). Empirical estimation of rock mass modulus. International Journal of Rock Mechanics and Mining Sciences. 43 (2): 203-215.
[46]. Yeglalp, T.M. and Mahtab, M.A. (1983). A proposed model for statistical representation of mechanical properties of rock. In the 24th US Symposium on Rock Mechanics (USRMS). OnePetro.
[47]. Grasso, P., Xu, S. and Mahtab, A. (1992). June. Problems and promises of index testing of rocks. In the 33rd US Symposium on Rock Mechanics (USRMS). OnePetro.
[48]. Hsu, S.C. and Nelson, P.P. (2002). Characterization of eagle ford shale. Engineering Geology. 67(1-2):169-183.
[49]. Gill, D.E., Corthésy, R., and Leite, M.H. (2005). Determining the minimal number of specimens for laboratory testing of rock properties. Engineering Geology. 78 (1-2): 29-51.
[50]. Sari, M. and Karpuz, C. (2006). Rock variability and establishing confining pressure levels. International Journal of Rock Mechanics and Mining Sciences. 43: 328-335.
[51]. Sari, M. (2009). The stochastic assessment of strength and deformability characteristics for a pyroclastic rock mass. International Journal of Rock Mechanics and Mining Sciences. 46 (3): 613-626.
[52]. Jiang, Q., Zhong, S., Cui, J., Feng, X.T., and Song, L. (2016). Statistical characterization of the mechanical parameters of intact rock under tri-axial compression: an experimental proof of the Jinping marble. Rock Mechanics and Rock Engineering. 49 (12): 4631-4646.
[53]. Sakurai, S. (1981). Direct strain evaluation technique in construction of underground opening. In the 22nd US Symposium on Rock Mechanics (USRMS), OnePetro.
[54]. Li, J., and Villaescusa, E. (2005). Determination of rock mass compressive strength using critical strain theory. In Proc. 40th US Symposium on Rock Mechanics, Anchorage, Alaska.
[55]. Kwasniewski, M., and Takahashi, M. (2010). Strain-based failure criteria for rocks: state of the art and recent advances. In ISRM International Symposium-EUROCK 2010, OnePetro.
[56]. Kong, X., Liu, Q., Pan, Y., and Liu, J. (2021). Stress redistribution and formation of the pressure arch above underground excavation in rock mass. European Journal of Environmental and Civil Engineering, 25(4), 722-736.
[57]. Kavvadas, M. J. (2003). Monitoring and modelling ground deformations during tunneling. In Proceedings of the 11th FIG Symposium on Deformation Measurements.
[58]. Jiang, Q., Su, G., Feng, X. T., Chen, G., Zhang, M. Z., and Liu, C. (2019). Excavation optimization and stability analysis for large underground caverns under high geo-stress: a case study of the Chinese Laxiwa project. Rock Mechanics and Rock Engineering, 52(3), 895-915.
[59]. Russo, G. (2014). An update of the “multiple graph” approach for the preliminary assessment of the excavation behavior in rock tunneling. Tunnelling and underground space technology, 41, 74-81.
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