# An Empirical Approach for Tunnel Support Design through Q and RMi Systems in Fractured Rock Mass

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

_{c}), respectively. The system was initially developed for tunneling cases in hard and jointed rock mass [19], and thus, this system is more often applied in jointed rock mass [20]. However, its application in tunnel support design is limited to an equivalent dimension (D

_{e}) ranging from 2.5 to 30, and a Q value ranging from 0.1 to 40 [21].

_{b}) and volumetric joint count (J

_{v}). This leads to easier and quicker calculations of the tunnel support parameters; i.e., the ground condition factor G

_{c}and size ratio factor S

_{r}, especially cases where limited field investigations have been performed.

## 2. Materials and Methods

#### 2.1. Project Descriptions

**Project 1**

**Project 2**

**Project 3**

**Project 4**

**Project 5**

**Project 6**

#### 2.2. Characterization of Rock Mass Based on the Q System

_{n}denotes the rating of the number of joint sets, J

_{r}is the rating for the joint surface roughness, J

_{a}denotes the rating for the degree of alteration or clay-filling joint set, J

_{w}denotes the ratings for groundwater inflow and pressure effects, and SRF is the stress reduction factor. The ratio RQD/J

_{n}is the relative block size in a selected domain, J

_{r}/J

_{a}is a measure of the inter-block frictional strength in that domain, and J

_{w}/SRF is the effect of water, the strength–stress ratio, faulting, swelling or squeezing, and defined active stress.

_{c}is substantial in the properties of rock mass. Therefore, a normalization factor was applied to Equation (1) and modified to Q

_{c}(Equation (2)) [18]:

_{n}, J

_{r}, J

_{a}, J

_{w}, and σ

_{c}.

_{n}[17]. In jointed rock mass, the extreme value of the old SRF (1974 version) is proposed [42]. Equation (3) [43] and Equation (4) [42] are based on mining cases in South Africa and Australia, respectively, for the characterization of SRF (1974 version) for competent rock having rock stress problems.

^{3}. Equation (3) can be rewritten as Equation (5):

^{3}as the unit weight of the rock, as Equation (7):

_{n}ratio, and revealed that a massive rock can have a ratio from 25 to 200, while a jointed rock mass has a typical ratio of 10. According to the rock mass fabric index approach, the maximum limit of the RQD/J

_{n}ratio for a jointed rock mass is 16.5 [45]. The relationship between the RQD/J

_{n}ratio and SRF in hard rock under high stress directs that, for jointed rock mass, the SRF value that was suggested for massive rock in Table 2 is too high [17]. The Q-system parameters were characterized for those selected sections where the RQD/J

_{n}ratio <16.5, and the intact rock strength to the major principal stress ratio (σ

_{c}/σ

_{1}) is in the range of two to five.

_{n}and σ

_{c}/σ

_{1}are displayed in Figure 2. In Figure 2a, the strength–stress ratio is in the range of two to five for Project 1 and 2. The data statistics show that all of the sections of Project 3 experienced a strength–stress ratio higher than 3.5. In the case of Project 4, this ratio is less than 3.5. In Figure 2b, the relative block sizes in the majority of the sections are in the range of six to eight.

#### 2.3. SRF Calculation Through Back Analysis

_{e}, in addition to the rock quality (Q or Qc); however, rock bolt spacing (S

_{b}) is a function of rock quality only. This spacing of rock bolts was used for the back-calculation of the tunneling quality index (Q

_{1}). The thickness of the fiber-reinforced shotcrete is a function of the tunnel span and the tunneling quality index. The thickness of the fiber-reinforced shotcrete, along with the tunnel span, was also used for the back-calculation of the tunneling quality index (Q

_{2}). The D

_{e}is the ratio of tunnel width/span and the excavation support ratio (ESR). The ESR value depends on the country safety standards [20] as well as on the quality of the rock mass [19]. The relation of rock bolt length (L

_{b}) to D

_{e}for hydropower tunnels, i.e., Project 2 and Project 4, reveals that a value of one for ESR is an appropriate rating for headrace tunnels, and was also used in this study.

**Example 1**

- Tunnel span or D
_{e}(m) = 11.17 - Rock bolt spacing (m) = 1.6
- Shotcrete thickness (cm) = 9
- Q
_{1}= 0.7 - Q
_{2}= 1.7 - Q or Q
_{c}= 1.03

_{c}) was due to the additional normalized factor in Equation (1), the support chart remained unchanged. The resultant tunneling quality index from back analysis was defined as Q or Q

_{c}. Equations (1) and (2) were rearranged to Equations (8) and (9), respectively, and two different SRFs (SRF

_{Q}or SRF

_{QC}) were calculated, taking the back-calculated rock quality value of either Q or Q

_{c}, respectively.

#### 2.4. RMi System and Tunnel Support Design

#### 2.4.1. Rock Mass Characterization by RMi System

_{c}due to the penetrated joints. The RMi system indicates the approximate uniaxial compressive strength of a rock mass by combining σ

_{c}and a jointing parameter (JP) using Equation (10):

- σ
_{c}= Intact rock uniaxial compressive strength - JP = Joint parameter (a parameter that combines the main joint features in the rock mass)
- jC = Joint condition factor (Equation (12))
- V
_{b}= Block volume (m^{3})

_{b}and jC. The jC can be estimated by joint roughness (jR), joint alteration (jA), and joint size/length (jL) using Equation (12):

#### 2.4.2. Tunnel Support Design by RMi System in Discontinuous Ground

_{c}) and the size ratio factor (S

_{r}), respectively, using Equations (13) and (14), as shown in Figure 4. The support parameters, which include all of these features, are used in the support chart.

- SL = Adjustment parameter for stress level
- C = Gravity adjustment parameter for support in the roof or wall
- CF = Continuity factor, which is the ratio of the tunnel diameter (D
_{t}) and the block diameter (D_{b}), differentiating between continuous and discontinuous ground and discontinuous ground having CF in the range from five to 100 - C
_{0}= Adjustment for joint orientation - N
_{j}= Adjustment for number of joint sets

_{r}/J

_{a}and jR/jA values, as shown in Table 4.

_{b}) and the volumetric joint count (J

_{v}) is given in Equation (15), where block shape influences the correlation [47]:

_{v}is the number of joints intersecting a volume of one m

^{3}.

_{v}, the degree of jointing is classified into six classes, from a very low degree of jointing (J

_{v}< 1) to crushed rock (J

_{v}> 60). Random joints may represent a significant part of the total number of discontinuities, and neglecting them would lead to the erroneous quantification of the discontinuity nature of the rock mass [48]. A rule of thumb for the calculation of J

_{v}is given in Equation (16) [49]:

_{1}, S

_{2}, and S

_{3}are the average spacings for the joint sets, N

_{r}is the number of random joints in the actual location, and A is the area in m

^{2}.

_{v}is from RQD or the joint frequency, as given in Equations (17) and (18) [22,47]:

_{1}= 2 for the average condition, and N

_{1}is the number of joints per unit length (joint frequency).

_{f}is the fracture frequency rating. The joint frequency can be calculated from N

_{f}using a graph of rating for the discontinuity density [52].

## 3. Results

#### 3.1. Back-Calculated SRF Comparison with Previous Work

_{Q}values are compared with them. For the given values, Equation (4) gives a higher value of SRF than Equation (5). This exponential Equation (4) agreed with Barton for the calculation of SRF in highly stressed jointed rock mass [53]. The second part of Equation (5) has a negligible effect on the SRF value for σ

_{c}/σ

_{1}< 5. SRF was calculated from Equation (4) for different field stress ratios, and the details of the differences compared with back-calculated SRF (SRF

_{Q}) values are shown in Figure 5.

_{c}/σ

_{1}.

#### 3.2. Suggested SRF for Highly Stressed Jointed Rock Mass

_{Q}for all of the sections. The SRF

_{Q}values are plotted against RQD/J

_{n}for different σ

_{c}/σ

_{1}values, as shown in Figure 6a. These values are also plotted against σ

_{c}/σ

_{1}for different RQD/J

_{n}values, as shown in Figure 6b. A strong relationship was found between SRF

_{Q}and RQD/J

_{n}and σ

_{c}/σ

_{1}. The relations between SRF

_{Q}, RQD/J

_{n}, and σ

_{c}/σ

_{1}were used, and Equation (22), a new empirical equation, was developed:

_{QC}. This SRF

_{QC}value can also be obtained from Equation (23), using the normalized factor:

_{QC}values calculated from Equation (9) or Equation (23) were plotted against RQD/J

_{n}for different σ

_{c}values and ranges of σ

_{c}/σ

_{1}. The variation in SRF

_{QC}with RQD/J

_{n}is shown in Figure 7.

#### 3.3. Comparison of the Actual Installed Supports against the RMi-Suggested Supports

_{v}classification are given in Figure 8.

#### 3.4. Tunnel Support Design by RMi System on Discontinuous Ground Using the Q-System Support Chart

_{r}/J

_{a}. Similarly, the ground condition factors in Equation (13) can be rewritten as Equation (25) by introducing N

_{j}and C

_{0}into it from Equation (14), and replacing V

_{b}in terms of RQD using Equation (17). The constants a and b depend on jR/jA:

_{c}, σ

_{c}/σ

_{1}and RQD/J

_{n}), and the constants a, b, and c are given in Table 7, depending on the case number as in Table 4.

_{w}and C

_{0}are not properly included in the RMi and Q

_{c}systems, respectively [15,18], taking J

_{w}= one (dry condition) and C

_{0}= one (favorable joint orientation), the above two equations are based on the same parameters as the relation of N

_{j}, and the number of joint sets is given in Equation (26) [23]:

_{j}is the number of joint sets.

_{c}can be developed from the available data using Equations (24) and (25), keeping the limitations of the data of the four projects in this study.

_{c}. This Q

_{c}value is then adjusted for J

_{w}and used for the recommended support from the Q-system support chart. Ultimately, the groundwater factor is included in the RMi system and C

_{0}is included in the Q system.

## 4. Numerical Modeling

_{n}values were less than 16.5, and only 7.6% of the RQD/J

_{n}values were greater than 25. Similarly, for Project 6, of 13 boreholes (BH-01, 02, 03, 04, 05, 08, 09, 10, 11, 12, 13, 15, 26), in most of them, the degree of jointing was high to very high, resulting in RQD < 50%. Only BH-09 and BH-26 in Project 6 had predominantly moderate jointing, which corresponds to a range of RQD from 50% to 75% [37]. For simplicity and to reduce the number of cases that were numerically evaluated, J

_{r}= 3, J

_{a}= 1, and J

_{w}= 1 were used for empirical support design.

_{c}/σ

_{1}, within the limitations of this study (5 > σ

_{c}/σ

_{1}> 2). For different RQD/J

_{n}and σ

_{c}/σ

_{1}values, SRF values were determined using Equations (22) and (23). Based on the calculated tunneling quality index (Q or Qc) from Equations (1) and (2), preliminary supports were determined from the support chart of the Q system; the details are shown in Table 10.

_{n}and J

_{r}/J

_{a}values [45].

_{1}and σ

_{3}, and the criterion is used for plastic yielding when σ

_{3}is compressive. The fine mesh was simulated around the tunnel boundary for better results. The model was fixed at the sides and bottom, and vertical stresses (σ

_{yy}) were applied at the top of the model. The in situ stress environment was created using gravity, σ

_{yy}, and the FISH (a programming language embedded within FLAC that enables the user to define new variables and functions) function. During the three construction steps for each excavation stage, 40% 30%, and 30% relaxation were used.

## 5. Discussion

_{n}or σ

_{c}/σ

_{1}. In this study, the empirical equation that was developed for the characterization of SRF is a function of both RQD/J

_{n}and σ

_{c}/σ

_{1}, along with σ

_{c}. Figure 6a shows that SRF

_{Q}(the SRF value that was developed for the original Q-system equation, Equation (1)) significantly increases with relative block size. A maximum change in RQD/J

_{n}of less than seven results in a variation of 5.4 for SRF

_{Q}, while for a maximum change in RQD/J

_{n}greater than seven, SRF

_{Q}varies by approximately 15.05, which is larger by a factor of about 2.75. A total SRF

_{Q}change of 20.82 can be observed with RQD/J

_{n}for a given value of σ

_{c}/σ

_{1}. With an increase in RDQ/J

_{n}, the difference of SRF

_{Q}for different values of σ

_{c}/σ

_{1}is comparatively low for a given value of RQD/J

_{n}.

_{n}, the rate of decrease of SRF

_{Q}with respect to low values of σ

_{c}/σ

_{1}is large compared to high values of σ

_{c}/σ

_{1}. For a σ

_{c}/σ

_{1}value below 3.5, the maximum fluctuation in σ

_{c}/σ

_{1}for a given value of RQD/J

_{n}results in a variation of the SRF

_{Q}value of about 2.49. Fluctuation in σ

_{c}/σ

_{1}by an equal amount in its upper limit (above 3.5) can change SRF

_{Q}by 1.35 approximately, which is about 1.84 times smaller. The maximum change in SRF

_{Q}is 4.09 with σ

_{c}/σ

_{1}for any given value of RQD/J

_{n}. The available data indicate that the maximum value of the relative block size is 12.

_{QC}with RQD/J

_{n}also depends on σ

_{c}as well as σ

_{c}/σ

_{1}. For the same value of σ

_{c}/σ

_{1}, high principal stress (σ

_{1}) requires rock with a high σ

_{c}value. The high level of stress means that more support is required, and hence, a high value of SRF

_{QC}. The maximum variation of SRF

_{QC}with RQD/J

_{n}is 18.5 for σ

_{c}= 100 MPa, with σ

_{c}/σ

_{1}ranging from three to four (Figure 7b), and the minimum variation is 7.38 for σ

_{c}= 37.5 MPa (Figure 7c). During the design stage of a tunnel, when inadequate information exists, then, with knowledge of σ

_{c}(which is the most basic parameter to be determined) and the location of the tunnel, Figure 7 can be used to approximate values of SRF

_{QC}for different values of RQD/J

_{n}. In the construction phase of a tunnel, when most of the information is in hand at the excavation face, Equations (22) and (23) can be used to calculate SRF

_{QC}. The maximum rating of σ

_{c}is 100, as shown in Table 3; therefore, the calculated SRF

_{Q}and SRF

_{QC}have the same value for tunnel sections where σ

_{c}= 100 MPa. In the remaining sections, SRF

_{QC}< SRF

_{Q}, and the difference depends on σ

_{c}.

_{c}/σ

_{1}> 5. Equation (13) shows that a high value of SL is favorable, but it is not applicable when σ

_{c}/σ

_{1}< 5, as shown in Table 2. The comparison of actual installed supports with those supports that are suggested by RMi showed that the suggested support was heavier than the actual. The equations for the calculation of Q

_{c}and G

_{c}are rewritten in such a way that each equation is the function of the same parameter, and a relation is developed between the two, keeping in view the limitation of data.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Feng, X.-T.; Hudson, J.A. Rock Engineering Design; CRC Press: Boca Raton, FL, USA, 2011. [Google Scholar]
- Stille, H.; Palmström, A. Classification as a tool in rock engineering. Tunn. Undergr. Space Technol.
**2003**, 18, 331–345. [Google Scholar] [CrossRef] - Rehman, H.; Ali, W.; Naji, A.; Kim, J.-J.; Abdullah, R.; Yoo, H.-K. Review of rock-mass rating and tunneling quality index systems for tunnel design: Development, refinement, application and limitation. Appl. Sci.
**2018**, 8, 1250. [Google Scholar] [CrossRef] - Laubscher, D. Geomechanics classification of jointed rock masses-mining applications. Trans. Instn. Min. Met.
**1977**, 86, A1–A8. [Google Scholar] - Laubscher, D. Design aspects and effectiveness of support systems in different mining conditions. Inst. Min. Met. Trans.
**1984**, 93, A70–A81. [Google Scholar] - Liu, Z.-X.; Dang, W.-G. Rock quality classification and stability evaluation of undersea deposit based on m-irmr. Tunn. Undergr. Space Technol.
**2014**, 40, 95–101. [Google Scholar] [CrossRef] - Unal, E. Modified rock mass classification: M-rmr system. In Milestones in Rock Engineering; A. A. Balkema: Rotterdamn, The Netherland, 1996. [Google Scholar]
- Tomás, R.; Delgado, J.; Serón, J. Modification of slope mass rating (smr) by continuous functions. Int. J. Rock Mech. Min. Sci.
**2007**, 44, 1062–1069. [Google Scholar] [CrossRef] - Tomas, R.; Cuenca, A.; Cano, M.; García-Barba, J. A graphical approach for slope mass rating (smr). Eng. Geol.
**2012**, 124, 67–76. [Google Scholar] [CrossRef] - Taheri, A.; Taheri, A.; Tani, K. Modified rock mass classification system for preliminary design of rock slopes. In Rock Mechanics in Underground Construction, Proceedings of the 4th Asian and International Rock Mechanics Symposium 2006 (with Cd-rom); World Scientific Publishing Co. Pte Ltd.: Singapore, 2006. [Google Scholar]
- Francioni, M.; Stead, D.; Sciarra, N.; Calamita, F. A new approach for defining slope mass rating in heterogeneous sedimentary rocks using a combined remote sensing gis approach. Bull. Eng. Geol. Environ.
**2018**, 1–22. [Google Scholar] [CrossRef] - Pasculli, A.; Calista, M.; Sciarra, N. Variability of local stress states resulting from the application of monte carlo and finite difference methods to the stability study of a selected slope. Eng. Geol.
**2018**, 245, 370–389. [Google Scholar] [CrossRef] - Barton, N. TBM perfomance estimation in rock using Q
_{TBM}. Tunn. Tunn. Int.**1999**, 31, 30–34. [Google Scholar] - Von Preinl, Z.B.; Tamames, B.C.; Fernández, J.G.; Hernández, M.Á. Rock mass excavability indicator: New way to selecting the optimum tunnel construction method. Tunn. Undergr. Space Technol. Inc. Trenchless Technol. Res.
**2006**, 3, 237. [Google Scholar] [CrossRef] - Palmstrom, A.; Stille, H. Ground behaviour and rock engineering tools for underground excavations. Tunn. Undergr. Space Technol.
**2007**, 22, 363–376. [Google Scholar] [CrossRef] - Barton, N.; Lien, R.; Lunde, J. Engineering classification of rock masses for the design of tunnel support. Rock Mech.
**1974**, 6, 189–236. [Google Scholar] [CrossRef] - Grimstad, E.; Barton, 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, Fagemes, Norway, 18–21 October 1993. [Google Scholar]
- Barton, N. Some new q-value correlations to assist in site characterisation and tunnel design. Int. J. Rock Mech. Min. Sci.
**2002**, 39, 185–216. [Google Scholar] [CrossRef] - NGI. Using the Q-System, Rock Mass Classification and Support Design. Available online: Https://www.ngi.no/eng/Services/Technical-expertise-A-Z/Engineering-geology-and-rock-mechanics/Q-system (accessed on 17 December 2018).
- Palmstrom, A.; Broch, E. Use and misuse of rock mass classification systems with particular reference to the q-system. Tunn. Undergr. Space Technol.
**2006**, 21, 575–593. [Google Scholar] [CrossRef] - Palmstrom, A.; Blindheim, O.; Broch, E. The q-system-possibilities and limitations. In Proceedings of the Norwegian Annual Tunnelling Conference on Fjellsprengningsteknikk/Bergmekanikk/Geoteknikk, Oslo, Norway, 6–7 July 2002; pp. 41.1–41.43. [Google Scholar]
- Palmstrom, A. Rmi—A Rock Mass Characterization System for Rock Engineering Purposes. Ph.D. Thesis, University of Oslo, Oslo, Norway, 1995. [Google Scholar]
- Palmström, A. Recent developments in rock support estimates by the rmi. J. Rock Mech. Tunn. Technol.
**2000**, 6, 1–19. [Google Scholar] - Stille, H.; Palmström, A. Ground behaviour and rock mass composition in underground excavations. Tunn. Undergr. Space Technol.
**2008**, 23, 46–64. [Google Scholar] [CrossRef] - Naji, A.; Rehman, H.; Emad, M.; Yoo, H. Impact of shear zone on rockburst in the deep neelum-jehlum hydropower tunnel: A numerical modeling approach. Energies
**2018**, 11, 1935. [Google Scholar] [CrossRef] - Barton, N. Deformation phenomena in jointed rock. Geotechnique
**1986**, 36, 147–167. [Google Scholar] [CrossRef] - Konicek, P.; Soucek, K.; Stas, L.; Singh, R. Long-hole destress blasting for rockburst control during deep underground coal mining. Int. J. Rock Mech. Min. Sci.
**2013**, 61, 141–153. [Google Scholar] [CrossRef] - Mazaira, A.; Konicek, P. Intense rockburst impacts in deep underground construction and their prevention. Can. Geotech. J.
**2015**, 52, 1426–1439. [Google Scholar] [CrossRef] - Carter, T. Himalayan Ground Conditions Challenge Innovation for Successful TBM Tunnelling; Invited Paper in Proc. Hydrovision India 2011 Conf, Delhi. SESSION 5c: (Risk Management in Tunnelling); Golder Associates: Toronto, ON, Canada, 2011; 20p. [Google Scholar]
- Naji, A.M.; Emad, M.Z.; Rehman, H.; Yoo, H. Geological and geomechanical heterogeneity in deep hydropower tunnels: A rock burst failure case study. Tunn. Undergr. Space Technol.
**2019**, 84, 507–521. [Google Scholar] [CrossRef] - Geoconsult-Typsa. Geotechnical Interpretative Report, Lowari Tunnel; National Highway Authority: Islamabad, Pakistan, 2004.
- Neelum-Jhelum-Consultants. Rock Parameters—Neelum Jhelum Project; Water and Power Development Authority (WAPDA): Lahore, Pakistan, 2011.
- Khan, M.S.; Tahir, S.; Gillani, A.; Khan, M.W. Evaluation of tunnel excavation methods for neelum jhelum hydro power project, pakistan. J. Am. Sci.
**2011**, 7, 1232–1236. [Google Scholar] - Yang, J.; Chen, W.; Zhao, W.; Tan, X.; Tian, H.; Yang, D.; Ma, C. Geohazards of tunnel excavation in interbedded layers under high in situ stress. Eng. Geol.
**2017**, 230, 11–22. [Google Scholar] [CrossRef] - Tahir, M. Determination of Strength Parameters for Kohat Tunnel-ii. Master’s Thesis, University of Engineering and Technology Peshawar, Peshawar, Pakistan, 2010. [Google Scholar]
- Hussain, S.; Ur Rehman, Z.; Mohammad, N.; Tahir, M.; Shahzada, K.; Wali Khan, S.; Salman, M.; Khan, M.; Gul, A. Numerical modeling for engineering analysis and designing of optimum support systems for headrace tunnel. Adv. Civ. Eng.
**2018**, 2018. [Google Scholar] [CrossRef] - Khawar, M. Development of Correlation between Rock Classification System and Modulus of Deformation. Ph.D. Thesis, University of Engineering and Technology, Lahore, Pakistan, 2013. [Google Scholar]
- Ali, W.; Mohammad, N.; Tahir, M. Rock mass characterization for diversion tunnels at diamer basha dam, Pakistan—A design perspective. Int. J. Sci. Eng. Technol.
**2014**, 3, 1292–1296. [Google Scholar] - Diamer-Basha-Consultants. Geology and Engineering Geology, Tender Design Report, Diamer Basha Dam Project; Water and Power Development Authority: Lahore, Pakistan, 2008.
- Wang, C.; Bao, L. Predictive analysis of stress regime and possible squeezing deformation for super-long water conveyance tunnels in Pakistan. Int. J. Min. Sci. Technol.
**2014**, 24, 825–831. [Google Scholar] [CrossRef] - Schubert, W.; Goricki, A.; Riedmuller, G. The guideline for the geomechanical design of underground structures with conventional excavation. Felsbau
**2003**, 21, 13–18. [Google Scholar] - Peck, W. Determining the stress reduction factor in highly stressed jointed rock. Aust. Geomech.
**2000**, 35, 57–60. [Google Scholar] - Kirsten, H. Case histories of groundmass characterization for excavatability. In Rock Classification Systems for Engineering Purposes; ASTM International: West Conshohocken, PA, USA, 1988. [Google Scholar]
- Kumar, N.; Samadhiya, N.K.; Anbalagan, R. Application of rock mass classification systems for tunneling in Himalaya, India. Int. J. Rock Mech. Min. Sci.
**2004**, 41 (Suppl. S1), 852–857. [Google Scholar] [CrossRef] - Tzamos, S.; Sofianos, A. A correlation of four rock mass classification systems through their fabric indices. Int. J. Rock Mech. Min. Sci.
**2007**, 44, 477–495. [Google Scholar] [CrossRef] - Rehman, H.; Naji, A.; Kim, J.-J.; Yoo, H.-K. Empirical evaluation of rock mass rating and tunneling quality index system for tunnel support design. Appl. Sci.
**2018**, 8, 782. [Google Scholar] [CrossRef] - Palmstrom, A. Measurements of and correlations between block size and rock quality designation (rqd). Tunn. Undergr. Space Technol.
**2005**, 20, 362–377. [Google Scholar] [CrossRef] - Grenon, M.; Hadjigeorgiou, J. Evaluating discontinuity network characterization tools through mining case studies. Soil Rock Am.
**2003**, 1, 137–142. [Google Scholar] - Palmström, A. The volumetric joint count-a useful and simple measure of the degree of rock jointing. Proc. 4th Int. Cong. Int. Assoc. Eng. Geol.
**1982**, 5, 221–228. [Google Scholar] - Hudson, J.; Priest, S. Discontinuities and rock mass geometry. Int. J. Rock Mech. Min. Sci. Géoméch. Abstr.
**1979**, 16, 339–362. [Google Scholar] [CrossRef] - Gibson, W. Rock mass strength derived from rock mass characterization. In Proceedings of the Alaska Rocks 2005, The 40th US Symposium on Rock Mechanics (USRMS), Anchorage, AK, USA, 25–29 June 2005. [Google Scholar]
- Lowson, A.; Bieniawski, Z. Critical Assessment of rmr Based Tunnel Design Practices: A Practical Engineer’s Approach. In Proceedings of the SME, Rapid Excavation and Tunnelling Conference, Washington, DC, USA, 23–26 June 2013; pp. 180–198. [Google Scholar]
- Barton, N. Rock mass characterization for excavations in mining and civil engineering. In Proceedings of the International Workshop on Rock Mass Classification in Underground Mining, Pittsburgh, PA, USA, 31 May 2007; pp. 3–13. [Google Scholar]
- Hoek, E.; Carranza-Torres, C.; Corkum, B. Hoek-brown failure criterion—2002 edition. Proc. NARMS-TAC Conf.
**2002**, 1, 267–273. [Google Scholar] - Carranza-Torres, C.; Diederichs, M. Mechanical analysis of circular liners with particular reference to composite supports. For example, liners consisting of shotcrete and steel sets. Tunn. Undergr. Space Technol.
**2009**, 24, 506–532. [Google Scholar] [CrossRef]

**Figure 2.**Percentage frequency of (

**a**) intact rock strength (σ

_{c}) to major principal stress (σ

_{1)}ratio (σ

_{c}/σ

_{1}); (

**b**) relative block size (RQD/J

_{n}) for the first four tunnel projects.

**Figure 3.**Procedure for the back-calculation of the tunnel quality index (Q or Qc) from actual tunnel spans and installed supports [46].

**Figure 5.**Difference in back-calculated stress reduction factor (SRF

_{Q}) with calculated SRF through Equation (4).

**Figure 6.**Relation of SRF

_{Q}with RQD/J

_{n}and σ

_{c}/σ

_{1}. (

**a**) SRF

_{Q}vs. RQD/J

_{n}for different σ

_{c}/σ

_{1}values; (

**b**) SRF

_{Q}vs. σ

_{c}/σ

_{1}for different RQD/J

_{n}values.

**Figure 7.**Variation of SRF

_{QC}with relative block size for different values and ranges of σ

_{c}and σ

_{c}/σ

_{1}, respectively.

**Figure 9.**Actual and RMi-suggested support differences in term of (

**a**) rock bolt spacing (

**b**) shotcrete thickness (positive value on the x-axis indicates that the recommended support is heavier than the actual).

**Table 1.**The fitness of empirical rock mass classification systems for different ground behaviors during tunnel excavation. Q: tunneling quality index, RMi: rock mass index, RMR: Rock Mass Rating.

Ground Behavior | Empirical Rock Mass Classification System | ||
---|---|---|---|

RMR | Q | RMi | |

Stable | 2 | 2 | 1–2 |

Fragment(s) or block(s) fall | 1–2 | 1–2 | 1–2 |

Cave-in | 3 | 2–3 | 2 |

Running ground | 4 | 4 | 4 |

Buckling | 4 | 3 | 3 |

Rupturing from stress | 4 | 3 | 3 |

Slabbing, spalling | 4 | 2 | 2 |

Rock burst | 4 | 3–4 | 2 |

Plastic behavior (initial) | 4 | 3–4 | 3 |

Squeezing ground | 4 | 3 | 3 |

Raveling from slaking or friability | 4 | 4 | 4 |

Swelling ground | 4 | 3 | 3 |

Flowing ground | 4 | 4 | 4 |

Water ingress | 4 | 4 | 4 |

**Table 2.**The stress reduction factor (SRF) rating is the function of stress–strength ratios in the case of competent rock having rock-stress problems.

Stress Level | σ_{θ}/σ_{c} | σ_{c}/σ_{1} | SRF ** | SRF * | |
---|---|---|---|---|---|

1 | Open joints, low stress at shallow depth | <0.01 | >200 | 2.5 | 2.5 |

2 | Favorable stress condition at medium stress level | 0.01–0.3 | 200–10 | 1 | 1 |

3 | Very tight structure due to high in situ stresses | 0.3–0.4 | 10–5 | 0.5–2 | 0.5–2 |

4 | Moderate slabbing after one hour in massive rock | 05–0.65 | 5–3 | 5–50 | 5–9 |

5 | Slabbing and rockburst after a few minutes in massive rock | 0.65–1.0 | 3–2 | 50–200 | 9–15 |

6 | Heavy rockburst (strain burst) and immediate dynamic deformation in massive rock | >1.0 | <2 | 200–400 | 15–20 |

_{c}= Intact rock uniaxial compressive strength; σ

_{1}= Major principal stress; σ

_{θ}= tangential stress; ** Grimstad (1993) [17] * Barton (1974).

Project | No. of Sections | σ_{c} (MPa) | J_{r} | J_{a} | J_{w} | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Project 1 | 258 | 37.5 | 56.25 | 60 | 65 | 75 | 3 | 1 | 1 | |||

Project 2 | 204 | 40 | 45 | 50 | 60 | 75 | 80 | 90 | 100 | 1.5 | 1 | 1 |

2 | ||||||||||||

1 | ||||||||||||

3 | ||||||||||||

Project 3 | 50 | 82 | 86 | 3 | 1 | 0.66 | ||||||

0.66 | ||||||||||||

Project 4 | 30 | 54 | 75 | 3 | 1 | 1 |

**Table 4.**Ratio of joint roughness and joint alteration rating based on Q and RMi systems for the four projects.

Case No. | J_{r}/J_{a} | jR/jA | Project |
---|---|---|---|

1 | 3 | 5 | LT, KT, GGHPP |

2 | 1.5 | 1.5 | NJHEP |

3 | 0.75 | 0.5 | NJHEP |

4 | 0.5 | 0.375 | NJHEP |

**Table 5.**Ground conditions (G

_{c}) and size ratios (S

_{r}) for all of the tunnel sections of the four tunnels.

Parameter | Project | |||
---|---|---|---|---|

1 | 2 | 3 | 4 | |

UCS (MPa) | 37.5–75 | 40–100 | 82 and 86 | 54 and 75 |

jR/jA | 5 | 0.375–1.5 | 5 | 5 |

jL | 1 | 1 | 1 | 1 |

J_{v} | 5.0769–42.769 | 6.7–49.77 | 6.8–87.0 | 7–37.05 |

V_{b} (m^{3}) | 0.00046–0.275 | 0.00029–0.1194 | 0.000055–0.1142 | 0.00071–0.105 |

D_{b} | 0.0772–0.65038 | 0.066–0.492 | 0.038–0.485 | 0.0891–0.4717 |

JP | 0.05697–0.31638 | 0.00314–0.099 | 0.032–0.25 | 0.0639–0.244 |

CF | 17.175–159.009 | 19.659–145.9 | 19.375–247.67 | 7.84–41.52 |

C_{0} | 1–3 | 1–3 | 1–3 | 2 and 3 |

N_{j} | 0.75–1.2 | 0.75–1.2 | 0.5–1 | 0.8–1.5 |

SL | 1.5 | 1.5 | 1.5 | 1.5 |

C | 1 | 1 | 1 | 1 |

G_{c} | 4.8–35.59 | 0.26–9.81 | 3.21–25.33 | 7.193–27.49 |

S_{r} | 45.37–636.036 | 40.85–583.62 | 29.54–371.51 | 15.69–110.72 |

Stress Level (SL) | Approximate Overburden | Rating |
---|---|---|

Very low | <10 m | 0.1 |

Low | 10–35 m | 0.5 |

Moderate | 35–350 m | 1 |

High | >350 m | 1.5 |

Case No. | a | b | c |
---|---|---|---|

1 | 2.44 | 0.804 | 3 |

2 | 2.123 | 1.023 | 1.5 |

3 | 2.058 | 1.173 | 0.75 |

4 | 2.08 | 1.275 | 0.5 |

Joint Orientation | Rating of C_{0} |
---|---|

Favorable | 1 |

Fair | 1.5 |

Unfavorable | 2 |

Very unfavorable | 3 |

Project | Rock Type | Case Number | Unit Weight (KN/m^{3}) | UCS (MPa) | Young’s Modulus E (GPa) | Poisson’s Ratio | mi |
---|---|---|---|---|---|---|---|

5 | GN | 1 | 28.6 | 100 | 42 | 0.2 | 23 |

UMA | 2 | 31.7 | 80 | 24 | 0.152 | 25 | |

6 | SS-1 | 3 | 27 | 80 | 40 | 0.2 | 17 |

SS-2 | 4 | 27 | 50 | 30 | 0.15 | 17 |

Case No. | Tunnel Span (m) | RQD/J_{n} | J_{r}/J_{a} | σ_{c}/σ_{1} | Q or Q_{c} | Rock Bolt Length (m) | Rock Bolt Spacing (m) | Shotcrete Thickness (cm) |
---|---|---|---|---|---|---|---|---|

1 | 15.4 | 11 | 3 | 5 | 1.5 | 4 | 1.7–1.8 | 9–12 |

2 | 8.5 | 3 | 4 | 1.7 | 4 | 1.7–1.8 | 9–12 | |

3 | 8.5 | 6 | 3 | 3 | 1.6 | 2.9 | 1.7–1.8 | 6–9 |

4 | 3 | 3 | 2.2 | 0.9 | 2.9 | 1.7 | 9 |

Case No. | GSI | m_{b} | s | a | c (MPa) | ɸ ° | E (GPa) | σ_{t} (MPa) |
---|---|---|---|---|---|---|---|---|

1 | 75 | 9.418 | 0.0622 | 0.501 | 5.374 | 52.29 | 34.29 | 0.66 |

2 | 72 | 9.197 | 0.0446 | 0.501 | 4.565 | 50.69 | 18.445 | 0.388 |

3 | 68 | 5.421 | 0.0286 | 0.502 | 4.6 | 44.31 | 26.545 | 0.422 |

4 | 58 | 3.793 | 0.0094 | 0.503 | 2.899 | 39.09 | 14.24 | 0.124 |

_{b}= reduced value of m

_{i}; s and a are rock mass constants in Hoek–Brown failure criterion; c and ф are equivalent strength parameters in Mohr–Coulomb failure criterion and σ

_{t}tensile strength of rock mass [54].

**Table 12.**Total displacement (mm) at different points along the tunnel perimeter with and without support.

Case No. | a | a’ | b | b’ | c | c’ | d | d’ | e | e’ |
---|---|---|---|---|---|---|---|---|---|---|

1 | 9.9 | 9.6 | 6.8 | 6.4 | 2.8 | 2.6 | 7.5 | 7.5 | 2.9 | 2.8 |

2 | 18.5 | 17.4 | 13.3 | 12.6 | 4.6 | 4.3 | 14.5 | 14.5 | 5.9 | 5.7 |

3 | 9.0 | 8.6 | 7.3 | 7.1 | 2.5 | 2.3 | 6.6 | 6.6 | 4.0 | 3.9 |

4 | 16.4 | 15.1 | 13.3 | 12.7 | 5.2 | 4.46 | 13.2 | 13.2 | 8.6 | 8.2 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lee, J.; Rehman, H.; Naji, A.M.; Kim, J.-J.; Yoo, H.-K. An Empirical Approach for Tunnel Support Design through *Q* and *RMi* Systems in Fractured Rock Mass. *Appl. Sci.* **2018**, *8*, 2659.
https://doi.org/10.3390/app8122659

**AMA Style**

Lee J, Rehman H, Naji AM, Kim J-J, Yoo H-K. An Empirical Approach for Tunnel Support Design through *Q* and *RMi* Systems in Fractured Rock Mass. *Applied Sciences*. 2018; 8(12):2659.
https://doi.org/10.3390/app8122659

**Chicago/Turabian Style**

Lee, Jaekook, Hafeezur Rehman, Abdul Muntaqim Naji, Jung-Joo Kim, and Han-Kyu Yoo. 2018. "An Empirical Approach for Tunnel Support Design through *Q* and *RMi* Systems in Fractured Rock Mass" *Applied Sciences* 8, no. 12: 2659.
https://doi.org/10.3390/app8122659