Theoretical investigation of the effect of stress on the performance of support systems based on Rock Mass Rating (RMR) support recommendations

Ground Support 2016 — E. Nordlund, T.H. Jones and A. Eitzenberger (eds) Theoretical investigation of the effect of stress on the performance of support systems based on Rock Mass Rating (RMR) support recommendations Ertugrul Karakaplan, Pamukkale university, Turkey Hakan Başarir, The university of western Australia, Australia Johan Wesseloo, Australian centre for geomechanics, The university of western Australia, Australia Abstract The Rock Mass Rating (RMR) classification system is widely used to design support systems for underground openings. For underground openings, excavated in the same quality rock mass, the system proposes the same support system independent from the depth of the opening. This study theoretically analyses the performance of RMR proposed support for openings excavated in the same quality rock masses at different depths. A very comprehensive numerical modelling programme was conducted. Different case studies were collected from current literature, presenting the results of the underground support design projects conducted by different researchers. The quality of the rock masses range from poor to fair. Using the collected information, numerical models of selected cases were constructed and internal support pressure equivalent to RMR proposed support systems was applied. Next, the in situ stress conditions were changed by assigning different depths and corresponding displacements were calculated. A critical strain criterion was used to evaluate the relative performance of the RMR proposed support systems. The support pressure necessary for keeping the strain below critical strain values was found iteratively for each case study, under changing stress conditions. Finally, an empirical equation and graph were produced showing the relationship between RMR, depth and the support pressure ratio, obtained by dividing necessary support pressure by RMR proposed support pressure. It was concluded that the pressure supplied by the RMR system is adequate for the openings excavated in good quality rock masses and rock masses at shallow depth. However, as the rock quality decreases and the depth increases, the support pressure provided by the proposed support system may not be adequate for maintaining the opening’s stability. KEYWORDS: Rock Mass Rating (RMR) system, rock mass classification, empirical design, numerical modelling, critical strain, support system performance evaluation. 1 Introduction Due to the complex geological and geotechnical environment, the design of underground mining openings such as drifts and shafts is always considered as a difficult problem. For many years empirical methods have provided a practical solution to these problems and they have been used widely for the assessment of the support requirements to ensure stability. One widely used design method is the RMR system proposed by Bieniawski (1974). The system was developed using a database mainly composed of tunnels excavated in sedimentary rocks at relatively shallow depths and, therefore, relatively low stress conditions. In 1989, the system was updated and the database was expanded (Bieniawski, 1989) by adding 351 different case studies. Ground Support 2016, Luleå, Sweden | 1 Theoretical investigation of the effect of stress on the performance of support systems… E. Karakaplan, H. Basarir, J. Wesseloo The input parameters of the system are: uniaxial compressive strength of the rock material (UCS), rock quality designation (RQD), joint spacing, joint conditions and groundwater conditions. Different values for each of the parameters are assigned and the overall basic rating is obtained by summing up the individual components weightings. Corrections are applied to basic RMR values to take into account the effect of joint set orientation relative to excavation direction. Based on this final value, the support system is proposed for the underground opening (Bieniawski, 1989). Although the system is widely used, some researchers proposed different corrections such as stress correction, blasting adjustment, and weakness plane consideration as mentioned by Ulusay and Sonmez (2007). Apart from rock mass properties, which are accounted for in the RMR system, the opening stability is also governed by the opening geometry and stress conditions that are not accounted for in the RMR system and, therefore, not incorporated in the support recommendations. Since the support recommendations proposed by the RMR system are based on a database dominated by relatively shallow excavations, the question arises as to how different stress conditions would affect the performance of the suggested support. This study theoretically investigates this question and it is limited to a comparison of support performance for a circular opening under uniform loading conditions; a simplification that needs to be addressed in further studies. 2 Methodology The methodology used in this study is briefly described as follows:  Rock mass strength and deformability properties were calculated, as suggested by Hoek et al. (2002), based on the geological strength index (GSI) values (Hoek et al. 1995), Hoek-Brown constant (mi) and unconfined compressive strength (UCS).  Calculation of equivalent support pressure, provided by RMR proposed support systems (PRMR), using equations suggested by Carranza-Torres and Fairhurst (2000).  Numerical evaluation of tunnel strain, with varying support pressure and depth. ○ For depths ranging from 50 to 1,000 m the calculated support pressure was applied as an active internal pressure in the model and resulting displacement and tunnel strain were calculated for different stress conditions. ○ The necessary support pressure (Pg), to limit the total tunnel strain to 2%, was determined iteratively for different depths. Analyses were performed for a range of rock mass conditions. The specific rock mass conditions used in the study were those corresponding to that encountered at three tunnels, for which the ground support was based on the suggested support from the RMR system (Appendix A). 3 Case studies and rock properties The collected case studies are composed of three roadway tunnels (Ghafoori et al. 2006; Sari et al. 2008; Satı ı, 2007). The stre gth a d defor a ilit properties al ulated usi g the i for atio prese ted i these studies were used as input for a two-dimensional finite element method based software. For most cases, GSI values were supplied. For the cases where GSI values were not available, they were estimated using the suggested equation GSI=RMR89-5 (Hoek and Brown, 1997), where RMR89 was 1989 version of Bieniawski`s RMR classification (Bieniawski, 1989) calculated by setting the groundwater rating to 15 and the adjustment for joint orientation to zero. A comprehensive review of the relationship between RMR and GSI was presented by Osgoui and Ünal (2005). The first case, Osmangazi tunnel, is located in the Bilecik province of Turkey. The width, height and length of the tunnel are 12.5, 9.6 and 2500 m, respectively. Seven different rock masses were observed through 2 |Ground Support 2016, Luleå, Sweden Ground Support - Theory and Advancement the route of the Osmangazi tunnel (Sari et al. 2008). Kallat highway tunnel is the second case, located in the Masshad province of Iran. The width, height and length of the Kallat tunnel are 8, 8.4 and 725 m, respectively. Three different rock masses were encountered through the Kallat tunnel. The last case study is the Sehzadeler highway tunnel, located in the Amasya province of Turkey. Its width, height and length are 12, 9, 345 m, respectively. There were four different rock masses observed in the Sehzadeler tunnel. Rock mass and material properties such as GSI, RMR, intact rock strength (UCS), intact rock deformation modulus (Ei), Hoek Brown constant (mi), Poisson`s ratio (), and unit weight () of the rock units observed through the tunnels are given in Table 1. The depth of the Osmangazi, Kallat and Sehzadeler tunnels ranges from 30 to 280, 40 to 160 and 30 to 100 m, respectively. Table 1 Rock mass and material properties of rock units observed along tunnel route Case Osmangazi tunnel (Sari et al. 2008) Kallat tunnel (Ghaforri et al. 2006) Sehzadeler tunnel (Satici, 2007) 4 , MN/m3 Rock unit RMR GSI UCS, MPa Ei, MPa mi ν 1 37 27 3 3976 4 0,25 0,25 2 50 45 72 6905 13 0,28 0,28 3 55 50 90 8715 18 0,31 0,31 4 63 58 63 6698 23 0,30 0,30 5 66 61 81 7873 23 0,29 0,29 6 63 58 75 7675 21 0,32 0,32 7 65 60 85 7703 18 0,31 0,31 1 53 48 55 18000 29 0,30 0,30 2 46 41 45 19000 19 0,31 0,31 3 40 35 35 12000 10 0,32 0,32 1 58 53 65 19000 17 0,30 0,30 2 43 38 45 10000 11 0,30 0,30 3 51 46 55 13000 9 0,30 0,30 4 34 29 10 10000 12 0,30 0,30 Numerical modelling In this study, a two-dimensional finite element method based software, Phase2, was used. By means of a prepared patch, rock properties and opening geometries can easily be changed. Moreover, the corresponding tunnel displacement readings can be recorded automatically. For each rock unit, unsupported and supported cases were analysed by applying different stress conditions in terms of depths. In total, 462 runs were conducted. The calculation of rock properties, prediction of internal support pressure, model geometries, stress conditions and the assessment of necessary support pressure for retaining opening stability are the main components of numerical modelling, as explained below. 4.1 Rock properties The mechanical properties of the rock masses were calculated using the equations suggested by Hoek et al. (2002), as they would be used as input parameters for numerical analysis. The rock units observed through the routes of the tunnels and their strength and deformability properties such as rock mass deformation modulus (Em), Hoek Brown constants (mb, sm), are presented in Table 2. Ground Support 2016, Luleå, Sweden | 3 Theoretical investigation of the effect of stress on the performance of support systems… Table 2 E. Karakaplan, H. Basarir, J. Wesseloo Calculated rock mass properties to be used in numerical analysis Case Rock unit Em, MPa mb sm 1 121 0.15 0.0002 2 878 0.89 0.0011 3 1648 1.51 0.0019 4 2389 2.53 0.0047 5 3564 2.90 0.0065 6 2738 2.32 0.0047 7 3221 2.19 0.0058 1 3965 0.0002 2 2397 0.15 0.00006 3 1496 0.05 0.00005 1 4280 1.28 0.0019 2 1212 0.32 0.0002 3 2210 0.38 0.0005 4 790 Osmangazi tunnel (Sari et al. 2008) Kallat tunnel (Ghaforri et al. 2006) Sehzadeler tunnel (Satici, 2007) 4.2 0.4 0.14 0.00002 Model geometry and calculation of internal support pressure and critical strain As the opening geometries are different, the equivalent radius approach allowing the use of circular shape for the openings with different shapes (Curran et al. 2003) was used. The calculated equivalent diameters for the Osmangazi, Kallat and Sehzadeler tunnels are 11.24 m, 9.03 m and 10.20 m, respectively. The equivalent support pressures of the RMR proposed support systems were calculated using the method proposed by Carranza-Torres and Fairhurst (2000). The calculated support pressures were applied to the opening as internal support pressure. The used equations are listed below. For each depth, the calculated support pressure of the RMR proposed support system was applied and corresponding displacements were calculated. Ph where: = σ − [1 − Ph maximum support pressure of shotcrete, MPa. t shotcrete thickness, m. σ R τ 2 ] (1) uniaxial compressive strength of shotcrete, MPa. outer radius of support, m. �� where: P 2 � � =� maximum support pressure of rockbolt, MPa. f maximum carrying capacity of rockbolt, MPa. 4 |Ground Support 2016, Luleå, Sweden �� (2) Ground Support - Theory and Advancement s s peripheral distance between rockbolts, m. the out of plane distance between bolts, m. P where: σys θ Is + As [ − P maximum support pressure of steel set, MPa. D the depth of cross-section, m. A cross-sectional area, m2. I 4.3 = As Is + .5 ] − o θ (3) section moment of inertia, m4. σ S distance between steel sets, m. R equivalent radius, m. θ angle between blocks, radian. strength of steel, MPa. Stress conditions The calculation of the horizontal stresses is a difficult task, especially for shallow tunnels. Hoek and Brown (1980) analysed in situ measurements around the world and concluded that horizontal stresses vary at shallow depth, whereas they tend to be closer to equal to the vertical stresses in deep environments. For si pli it s sake, similar to the previous studies (Asef et al. 2000; Sari, 2007; Basarir, 2008; Basarir et al. 2010), in this study hydrostatic stress conditions were applied. The vertical stress is calculated as the overburden stress. This simplifying approach may not be appropriate for support design in general. In this study, however, we are performing a comparative study. Future extension of this analysis should take the stress ratio into account. 4.4 The prediction of support performance and the pressure necessary for keeping opening stability In order to quantify the effect of different stress conditions on the performance of the proposed support systems, a robust and dimensionless measure of support performance is necessary. Sakurai (1983) suggested the use of tunnel strain, defined as the ratio between opening width and observed displacement, as a stability indicator. Hoek (2000) suggested that when the strain value of 2% is exceeded, the stability of the opening cannot be maintained. The 2% criterion is a questionable design criterion, but for the purpose of comparison it provides a robust and simple measure to compare the support performance under different stress conditions. In this study, the total opening was strain defined as the maximum elasto-plastic displacement normalised to equivalent tunnel diameter. For the considered highway tunnels, the 2% critical strains were calculated and corresponding limiting displacements were determined as 0.23, 0.18 and 0.20 m for the Osmangazi, Kallat and Sehzadeler tunnels, respectively. The support pressure necessary for keeping the opening strain or limiting deformation less than calculated was found iteratively and recorded as required support pressure (Pg). The flowchart showing the steps followed to obtain Pg is shown in Figure 1. Ground Support 2016, Luleå, Sweden | 5 Theoretical investigation of the effect of stress on the performance of support systems… Figure 1 E. Karakaplan, H. Basarir, J. Wesseloo The flowchart followed for the determination of required support pressure (Pg) The graph showing the relationship between depth and critical strain for the case studies is given in Figure 2. Figure 2 5 The relationship between depth and strain for RMR suggested support systems for the case studies Analysis of numerical modelling results The graph showing the relationship between depth and required support pressure for keeping the strain less than 2% for the rock masses with different qualities is shown in Figure 3. As the quality of rock mass increases, the required support pressure decreases. For the same rock mass quality as the depth increases the required support pressure also increases. The rate of the increment changes depending on the quality of the rock mass. 6 |Ground Support 2016, Luleå, Sweden Ground Support - Theory and Advancement Figure 3 Necessary support pressure to keep the stability of the opening excavated in different quality rock masses and depths To embrace the rock masses not included in the numerical analysis, a multiple regression modelling technique was employed. In regression modelling, the dependent variable is the ratio of required support pressure to RMR proposed support pressure (Pg/PRMR). Independent variables are specified as RMR and depth. As it can be understood from the high multiple coefficient of determination (R2) 88.27 % obtained, the model established a valid relationship between dependent and independent variables. In Equation 4, a, b and c are constants and the values of these constants are 0.065928, 0.889308 and 1.524772, respectively. The multiple regression model also implies that the depth has a strong effect on the support ratio as the largest constant is related to the depth (H). � ���� = ��� � (4) The contour map drawn by using the derived regression equation is shown in Figure 4. The case studies are also shown in Figure 4. As it can be seen from Figure 4, Pg/PRMR values for the case studies are lower than or around 1 (indicated using dashed line). This shows that for the case studies the support pressure provided by the RMR proposed support system are equal to or higher than the necessary support pressure required for keeping the strain less than 2%. Ground Support 2016, Luleå, Sweden | 7 Theoretical investigation of the effect of stress on the performance of support systems… Figure 4 6 E. Karakaplan, H. Basarir, J. Wesseloo Contour map showing the relationship between RMR and depth for different support ratios (Pg/PRMR) Conclusions and recommendations In this study the performance of the support systems proposed by the RMR classification system is evaluated theoretically by numerical modelling. The opening or tunnelling strain concept proposed by Sakurai (1983) and Hoek (2000) was used as a performance indicator for RMR proposed support systems. For the analysis of the performance of RMR proposed support systems, a two-dimensional finite element method based software was used (Rocscience, 2009). The results obtained from finite element modelling were used for the construction of multiple regression models to cover the rock masses not included in the case studies. When the contour map drawn by using developed regression model was considered the following conclusions were derived. The pressure provided by the RMR proposed support system seems to be adequate for the openings excavated at shallow depth and in good quality rock masses. As the quality of rock mass decreases and the depth increases, the proposed support system may not be adequate to ensure excavation stability. Considering the case studies used, it can be concluded that depth or stress conditions should be considered together with the rock properties. Therefore, for major projects, in addition to the use of empirical methods such as the RMR system, the use of numerical modelling to check the performance of the proposed support system is strongly recommended. In this study, in order to make a systematic approach, hydrostatic stress conditions were assumed; similar to other studies presented in the current literature. This approach can be considered as adequate for preliminary analysis, whereas for detailed and major projects the stresses should be measured in field and used in the analysis. An equivalent diameter approach is used in this study and it was assumed that in circular openings excavated under hydrostatic stress conditions, support elements were loaded symmetrically and there was not any bending moment acting on them. Whereas in reality, support elements like shotcrete and steel sets can be loaded asymmetrically and may be affected by bending moment due to surface roughness. Therefore, in practice the support pressure can be higher than those presented in this study. Due to the selected failure criterion, it was assumed that the rock mass does not contain any dominant discontinuity that can lead to anisotropic behaviour or structural instability. 8 |Ground Support 2016, Luleå, Sweden Ground Support - Theory and Advancement For the considered case studies presented in the current literature, it was seen that the support pressure ratio (Pg/PRMR) value was around or lower than 1. In other words, for the considered case studies the support pressure produced by RMR suggested support systems are close to or higher than the required support pressure. To the author s knowledge for the case studies used in this study, there was not any stability problem. This is compatible with the results obtained from this simplified methodology for these cases, and the results of this methodology, although simplified, appear reasonable. References Asef, MR, Reddish, DJ & Lloyd, PW 2000, Rock-Support interaction analysis based on numerical methods , Geotechnical and Geological Engineering, 18, pp. 23-27. Basarir, H 2008, Analysis of rock-support interaction using numerical and multiple regression modelling , Canadian Geotechnical Journal, vol. 45, pp. 1-13. Basarir, H, Genis, M & Ozarslan, A 2010, The analysis of radial displacements occurring near the face of a circular opening in weak rock mass , International Journal of rock Mechanics and Mining Sciences, 47 (5), pp. 771-83. Bieniawski, ZT 1989, Engineering rock mass classifications, New York, Wiley & Sons. Bieniawski, ZT 1974, Geomechanics classification of rock masses and its application in tunnelling , Proceedings of the Third International Congress on Rock Mechanics (s. 27-32), Denver, International Society of Rock Mechanics. Carranza-Torres, C & Fairhurst, C 2000, Application of the convergence confinement method of tunnel design to rock masses that satisfy the Hoek-Brown failure criterion , Tunnelling and Underground Space Technology, 15(2), pp. 187-213. Curran, J, Hammah, R & Yacoub, T 2003, A Two-Dimensional Approach for Designing Tunnel Support in Weak Rock , November 2013, Rocscience research papers: http://www.rocscience.com/assets/files/uploads/7689.pdf Ghafoori, M, Lashkaripour, GR, Sadeghi, H & Tarigh Azali, S 2006, Comparison of predicted and actual behaviour and engineering geological characterization of Kallat tunnel , in Proceedings of the IAEG Symposium (s. 1-8), The Geological Society of London. Hoek, E, Carranza-Torres, C & Corkum, B 2002, Hoek-Brown Failure Criterion - 2002 Edition , in Proceedings of the 5th North American Rock Mechanics Symposium, Toronto, Canada, vol. 1, pp. 267-273. Hoek, E 2000, Big tunnels in bad rock , ASCE Journal of Geotechnical and Geoenvironmental Engineering, pp. 726-740. Hoek, E & Brown, E 1997, Practical esti ates of ro k ass stre gth , Int. J. Rock Mech. Min. Sci., pp. 1165-1186. Hoek, E, Kaiser, P & WF, B 1995, Support of underground excavations in hard rock, Rotterdam, AA Balkema. Hoek, E & Brown, E. 1980, Underground excavations in rock, London, Instn Min. Metall. Osgoui, R & Ünal, R 2005, Rock reinforcement design for unstable tunnels originally excavated in very poor rock mass , Underground space use: Analysis of the past and lessons for the future (s. 291-296). Rocscience 2009, Rocscience-Phase2, Finite element anal sis of e avatio s a d slopes , Toro to, Rocscience Inc. Sakurai, S 1983, Displacement measurements associated with the design of underground openings , pp. 1163-1178, s. Field Measurements in Geomechanics, Zürich. Sari, D 2007, Rock mass respo se odel for ir ular ope i gs , Canadian Geotechnical Journal, 44, pp. 891-904. Sari, YD, Paşa eh etoğlu, AG, Çetiner, E & Dönmez, S 2008, Numerical analysis of a tunnel support design in conjunction with empirical methods , International Journal of Geomechanics, pp. 74-81. Satici, O 2007, The stability analysis of T4 (Kucukbelvar) tunnel on Kavak Merzifon highway , Hacettepe University, MSc Thesis, Ankara, Turkey. Ulusay, R & Sonmez, H 2007, Engineering Properties of Rock Masses, The Chamber of Turkish Geological Engineers, Ankara, Turkey. Ground Support 2016, Luleå, Sweden | 9 Theoretical investigation of the effect of stress on the performance of support systems… E. Karakaplan, H. Basarir, J. Wesseloo Appendix A Support system proposed by the RMR system for a 10m wide horseshoe opening (see notes) (after Bieniawski, 1989) Rock mass class Excavation Support Rock bolts (20 mm dia., fully grouted) Very good rock I Full face RMR: 81-100 3 m advance Good rock II Full face RMR: 61-80 1-1.5 m advance. Complete support 20 m from face. Fair rock III Top heading and bench. RMR: 41-60 1.5-3 m advance in top heading. Commence support after each blast. Complete support 10 m from the face. Poor rock IV Top heading and bench. RMR: 21-40 1.0-1.5 m advance in top heading. Install support concurrently with excavation, 10 m from face. Very poor rock V Multiple drifts. RMR: <20 0.5-1.5 m advance in top heading. Install support concurrently with excavation. Shotcrete as soon as possible after blasting. Shotcrete Generally no support required except spot bolting Locally bolts in crown 3 m long, spaced 2.5 m with occasional wire mesh. 50 mm in crown where required. None Systematic bolts 4 m long, spaced 1.5-2 m in crown and walls with wire mesh in crown 50-100 mm in crown and 30 mmm in sides. None Systematic bolts 4-5 m long, spaced 1-1.5 m in crown and walls with wire mesh. 100-150 mm in crown and 100 mm in sides. Light to medium ribs spaced 1.5 m where required Systematic bolts 5-6 m long, spaced 1-1.5 m in crown and walls with wire mesh. Bolt invert. 150-200 mm in crown, 150 mm in sides, and 50 mm on the face. Medium to heavy ribs spaced 0.75 m with steel lagging and forepoling if required. Close invert. Shape: Horseshoe; Width: 10; Vertical stress <25 MPa; drilling and blasting. 10 |Ground Support 2016, Luleå, Sweden Steel sets