Integrated method of tunnelling 441 The short-term support pressure in roof may be assessed by the following correlation (equation (4.6)) for arch opening given by Goel and Jethwa (1991). p roof = 7.5B 0.1 H 0.5 − RMR 20 RMR = 7.5 × 16 0.1 × 165 0.5 − 73 20 × 73 = 0.037 MPa The ultimate support pressure is read by the chart (Fig. 5.2) of Barton et al. (1974) as follows (the dotted line is observed to be more reliable than correlation). p roof = 0.9 × 1 × 1 kg/cm 2 or 0.09 MPa (The rock mass is in non-squeezing ground condition (H<350 Q 1/3 ) and so f ′ = 1.0. The overburden is less than 320 m and so f = 1.0.) It is proposed to provide the steel fiber reinforced shotcrete (SFRS) [and no rock bolts for fast rate of tunnelling]. The SFRS thickness (t fsc ) is given by the following correlation (equation (28.1)). t fsc = 0.6Bp roof 2q fsc = 0.6 × 1600 × 0.09 2 × 5.5 = 8cm = 16 cm (near portals) The tensile strength of SFRS is considerd to be about one-tenth of its UCS and so its shear strength (q sc ) will be about, 2 ×30/10 = 6.0 MPa, approximately 5.5MPa (UTS is generally lesser than its flexural strength). Past experience is also the same. The life of SFRS may be taken same as that of concrete in the polluted environment that is about 50 years. Life may be increased to 60 years by providing extra cover of SFRS of 5 cm. If SFRS is damaged latter, corroded part should be scrapped and new layer of shotcrete should be sprayed to last for 100 years. So recommended thickness of SFRS is t fsc = 13 cm = 21 cm (near portals) The width of pillar is more than the sum of half-widths of adjoining openings in the non-squeezing grounds. The width of pillar is also more than the total height of the larger of two caverns (18 m), hence proposed separation of 20 m is safe. The following precautions need to be taken: (i) The loose pieces of rocks should be scrapped thoroughly before shotcreting for better bonding between two surfaces. (ii) Unlined drains should be created on both the sides of each tunnel to drain out the ground water and then should be covered by RCC slabs for road safety. 442 Tunnelling in weak rocks (iii) The tunnel exits should be decorated by art and arrangement should be made for a bright lighting to illuminate well the tunnels to generate happy emotions among road users. REFERENCES Barton, N. (2002). Some new Q-valuecorrelations to assist in site characterisation and tunnel design. Int. J. Rock Mech. and Min. Sci., 39, 185-216. Barton, N., Lien, R. and Lunde, J. (1974). Engineering classification of rock masses for the design of tunnel support. Rock Mechanics, Springer-Verlag, 6, 189-236. Bischoff, J. A., Klein, S. J. and Lang, T. A. (1992). Designing reinforced rock. Civil Engineering, ASCE, 72, January. Bhasin, R., Singh, R. B., Dhawan, A. K. and Sharma, V. M. (1995). Geotechnical evaluation and a review of remedial measures in limiting deformations in distressed zones in a powerhouse cavern. Conf. Design and Construction of Underground Structures, New Delhi, India, 145-152. Duddeck, H. and Erdmann, J. (1985). On structural design models for tunnels in soft soil. Underground Space, 9, 246-259. Goel, R. K. and Jethwa, J. L. (1991). Prediction of support pressure using RMR classification. Proc. Indian Getech. Conf., Surat, India, 203-205. IS 15026:2002, Tunnelling Methods in Rock Masses-Guidelines. Bureau of Indian Standards, New Delhi, India, 1-24. Samadhiya, N. K. (1998). Influence of anisotropy and shear zones on stability of caverns. PhD thesis, Department of Civil Engineering, IIT Roorkee, India, 334. Singh, Bhawani,Viladkar, M. N., Samadhiya N. K. and Sandeep (1995). A Semi-empirical method for the design of support systems in underground openings. Tunnelling and Underground Space Technology, 10(3) 375-383. Zhidao, Z. (1988). Waterproofing and water drainage in NATM tunnel. Symp. Tunnels and Water, Ed: Serrano, Rotterdam, 707-711. 29 Critical state rock mechanics and its applications “All things by immortal power near or far, hiddenly to each other are linked.” Francis Thompson English Victorian Post 29.1 GENERAL Barton (1976) suggested that the critical state for initially intact rock is defined as the stress condition under which Mohr envelope of peak shear strength reaches a point of zero gradient or a saturation limit. Hoek (1983) suggested that the confining pressure must always be less than the unconfined compression strength of the material for the behavior to be considered brittle. An approximate value of the critical confining pressure may, therefore, be taken equal to the uniaxial compressive strength of the rock material. Yu et al. (2002) have presented a state-of-the-art on strength of rock materials and suggested a unified theory. The idea is that the strength criterion for jointed rock mass must account for the effect of critical state in the actual environmental conditions. The frictional resistance is due to the molecular attraction of the molecules in contact between smooth adjoining surfaces. It is more where molecules are closer to each other due to the normal stresses. However, the frictional resistance may not exceed the molecular bond strength under very high confining stresses. Hence, it is no wonder that there is a saturation or critical limit to the frictional resistance (Prasad, 2003). There should be limit to everything in the nature. Singh and Singh (2005) have proposed the following simple parabolic strength criterion for the unweathered dry isotropic rock materials as shown in Fig. 29.1. σ 1 − σ 3 = q c + Aσ 3 − Aσ 2 3 2q c for 0 < σ 3 ≤ q c (29.1) Tunnelling in Weak Rocks B. Singh and R. K. Goel © 2006. Elsevier Ltd 444 Tunnelling in weak rocks q c σ 1 − σ 3 σ 3 σ 3 =q c Fig. 29.1 Parabolic strength criterion. where A = 2 sin φ p 1−sin φ p φ p = the peak angle of internal friction of a rock material in nearly unconfined state (σ 3 = 0) and q c = average uniaxial compressive strength of rock material at σ 3 = 0. It may be proved easily that deviator strength (differential stress at failure) reaches a saturation limit at σ 3 = q c that is, ∂(σ 1 − σ 3 ) ∂σ 3 = 0atσ 3 = q c (29.2) Unfortunately, this critical state condition is not met by the other criteria of strength. It is heartening to note that this criterion is based on single parameter “A” which makes a physical sense. Sheorey (1997) has compiled the triaxial and polyaxial test data for different rocks which are available from the world literature. The regression analysis was performed on 132 sets of triaxial test data in the range of 0 ≤ σ 3 ≤ q c . The values of the parameter A, for all the data sets were obtained. These values were used to back-calculate the σ 1 values for the each set for the given confining pressure. The comparison of the experimental and the computed values of σ 1 is presented in Fig. 29.2. It is observed that the calculated values of σ 1 are quite close to the experimental values. An excellent coefficient of correlation, 0.98, is obtained for the best fitting line between the calculated and the experimental values. For comparing the predication of the parabolic criterion with those of the others, Hoek and Brown (1980) criterion was used to calculate the σ 1 values. The coefficient of correlation (0.98) forHoek–Brown predictions is observedto be slightly lowerand poor for weak rocks, when compared with that obtained for the criterion proposed in this chapter. Critical state rock mechanics and its applications 445 10 100 1000 10000 10 100 1000 10000 Experimental σ 1 (MPa) Calculated σ 1 (MPa) R 2 = 0.9848 Fig. 29.2 Comparison of experimental σ 1 values with those calculated through the proposed criterion (equation (29.1)) (Singh & Singh, 2005). In addition to the higher value of coefficient of correlation, the real advantage of proposed criterion, lies in the fact that only one parameter, A is used to predict the confined strength of the rock and A makes a physical sense. A rough estimate of the parameter A may be made without conducting even a single triaxial test. The variation of the parameter, A, with the uniaxial compressive strength (UCS), q c is presented in Fig. 29.4. A definite trend of A with UCS (q c ) is indicated by this figure and the best fitting value of the parameter A may be obtained as given below: A ∼ = 7.94 q 0.10 c for q c = 7 − 500 MPa (29.3) Fig. 29.3 compares experimental σ 1 values with those predicted by using equa- tion (29.3) without using the triaxial data. A high coefficient of correlation of 0.93 is obtained. Thus, the proposed criterion appears to be more faithful to the test data than Hoek and Brown (1980) criterion. This criterion is also better fit for weak rocks as the critical state is more important for rocks of lower UCS. The law of saturation appears to be the cause of non-linearity of the natural laws. 29.2 SUGGESTED MODEL FOR ROCK MASS The behavior of jointed rock mass may be similar to that of the rock material at criti- cal confining pressure, as joints then cease to dominate the behavior of the rock mass. 446 Tunnelling in weak rocks 10 100 1000 10000 10 100 1000 10000 Experimental σ 1 (MPa) Calculated σ 1 (MPa) R 2 = 0.9287 Fig. 29.3 Comparison of experimental σ 1 values with those predicted using present criterion without using triaxial test data (Singh & Singh, 2005). A/2q c q c (MPa) 0.8 0.6 0.4 0.2 100 200 3000 0.0 400 Fig. 29.4 Variation of parameter A/2q c with UCS of the intact rocks (q c ). Critical state rock mechanics and its applications 447 Therefore, one may assume that thedeviator strength will reach thecritical state at σ 3 = q c . As such, this critical confining pressure may be independent of the size of specimen. Perhaps the deviator strength may also achieve a critical state when intermediate princi- pal stress σ 2 ∼ = q c (equation (8.2)). Thus an approximate simple parabolic and polyaxial criterion is suggested for the underground openings as follows, σ 1 − σ 3 = q cmass + A(σ 2 + σ 3 ) 2 − A 4q c (σ 2 2 + σ 2 3 ) (29.4) for 0 < σ 3 ≤ q c and 0 < σ 2 ≤ q c where q cmass = uniaxial compressive strength of the rock mass, = 7γQ 1/3 MPa, (29.5) γ = unit weight of rock mass in gm/cc or t/m 3 , Q = post-construction Barton’s rock mass quality just before supporting a tunnel, A = 2 sin φ p 1−sin φ p , (29.6) φ p = the peak angle of internal friction of a rock mass and q c = average uniaxial compressive strength (UCS), upper bound of UCS for anisotropic rock material of jointed rock masses under actual environment. It may be verified by differentiating equation (29.4) that ∂(σ 1 − σ 3 ) ∂σ 3 = 0atσ 2 = σ 3 = q c ∂(σ 1 − σ 3 ) ∂σ 2 = 0atσ 2 = q c for any value of σ 3 The triaxial test data (σ 2 = σ 3 ) on models of jointed rocks was collected from Brown (1970), Brown and Trollope (1970), Ladanyi and Archambault (1972), Einstein and Hirshfeld (1973), Hoek (1980), Yazi (1984), Arora (1987) and Roy (1993). The parameter A was computed by the least square method as was done for the rock materials. An approximate correlation between A and q c was found as given below. A = 2.46 q 0.23 c (29.7) The polyaxial tests on cubes of jointed rocks at IIT Delhi suggest that the mode of failure at high σ 2 is brittle and not ductile as expected. This is seen in tunnels in medium to hard rocks. The angle ofinternal friction (φ p ) in equation(29.6) may be chosen from the correlation of Mehrotra (1993) (cited by Singh & Goel, 2002), according to RMR both for the nearly dry and saturated rock masses (Fig. 29.5). It is based on the extensive and carefully conducted block shear tests at various project sites in the Himalaya. It may be seen that φ p is significantly less for the saturated rock mass than that for the nearly dry rock mass for the same final RMR. So the parameter A will be governed by the degree of 448 Tunnelling in weak rocks Rock Mass at nmc Bieniawski (1982) 50 30 10 10 20 30 40 50 60 70 80 Angle of Internal Friction (φ), degree Rock Mass Rating (RMR) Saturated Rock Mass Bieniawski (1982) 50 30 10 10 20 30 40 50 60 70 80 Angle of Internal Friction (φ), degree Rock Mass Rating (RMR) Fig. 29.5 Relationship between rock mass rating (RMR) and angle of internal friction (φ p ) (Mehrotra, 1992) [nmc: natural moisture content]. saturation in equation (29.7). Hoek and Brown (1997) have developed a chart between friction angle φ p and geological strength index (GSI = RMR − 5 for RMR ≥ 23) for the various values of rock material parameter m r . It is seen that φ p increases significantly with increasing value of m r for any GSI. In the case of rock mass with clay-coated joints, equation (29.13) may be used to estimate φ p approximately. Equation (29.13) takes into account approximately the seepage erosion and piping conditions in the weak rock masses (Barton, 2002). Seepage erosion (flow of soil particles from joints due to the seepage, especially during rainy seasons) rapidly deteriorates the rock mass quality (Q) with time. Seepage may be encountered at great depths even in granite unexpectedly, due to the presence of a fault. “Uncertainty is the law of nature.” It should be mentioned that Murrell (1963) was the first researcher who predicted that major principal stress (σ 1 ) at failure increases with σ 2 significantly, but it reduces when σ 2 is beyond σ 1 /2 and σ 3 = 0. The three sets of polyaxial test data cited by Yu et al. (2002) shows a negligible or small trend of peaking in σ 1 when σ 2 ≫ q c . The attempt was made to fit in the proposed polyaxial strength criterion (equation (29.4)) in the above test data for rock materials (Dunham dolomite, trachite and coarse gained dense marble). The recent polyaxial test data on tuff (Wang and Kemeny, 1995) was also analyzed. The equation (29.4) was found to be fortunately rather a good fit into all the polyaxial test data at σ 2 <q c and σ 3 <q c . Critical state rock mechanics and its applications 449 Kumar (2002) has collected data of 29 km NJPC tunnel in gneiss in Himalaya as mentioned in Table 29.1. It may be noted that the rock mass strength (q cmass ) is too less than the expected tangential stress (σ θ ) along the tunnel periphery. The q cmass from linear criterion is some what less than σ θ . It is interesting to know that the parabolic polyaxial criterion predicts the rock mass strength (q ′′ cmass in equation (29.8)) in the range of 0.64 to 1.4 σ θ generally. In one situation, the rock mass was found to be in the critical state locally. It matches with the failure conditions in the tunnel beyond overburden of 1000 m where (mild rock burst or) spalling of rock slabs was observed. So the proposed simple polyaxial strength criterion (equation (29.4)) fits in the observations in the tunnels in the complex and fragile geological conditions in a better way than other criteria. Better fit also suggests that the peak angle of internal friction of rock mass may be nearly the same as that for its rock material in the case of unweathered rock mass. The equation (29.4) suggests the following criterion of failure of rock mass around tunnels and openings (σ 3 = 0 on excavated face and σ 2 = P o along tunnel axis), σ θ >q ′′ cmass = q cmass + A · P o 2 − A · P 2 o 4 · q c ≤ q cmass + A · q c 4 (29.8) where q ′′ cmass is the biaxial compressive strength of rock mass, corrected for greater depths. 29.3 RESIDUAL STRENGTH Mohr’s theory will be applicable to residual failure as a rock mass would be reduced to non-dilatant soil like condition. Thus, residual strength (σ 1 − σ 3 ) r of rock mass is likely to be independent of the intermediate principal stress. So, the following criterion is suggested. (σ 1 − σ 3 ) r = q cr + A r · σ 3 − A r · σ 2 3 2 · q c for 0 < σ 3 ≤ q c (29.9) where q cr = UCS of rock mass in the residual failure, = 2c r cos φ r 1−sin φ r (29.10) A r = 2 sin φ r 1−sin φ r , (29.11) c r = residual cohesion of rock mass, = 0.1 MPa = 0 if the deviator strain exceeds 10 percent, φ r = φ p − 10 ◦ ≥ 14 ◦ (29.12) tan φ p = (J r · J w /J a ) + 0.1 (based on Barton, 2002). (29.13) Singh and Goel (2002) have analyzed 10 tunnels in the squeezing ground condition considering linear criterion (J r /J a < 0.5, J w = 1.0 and γH ≪ q c ). There is a rather good Table 29.1 Comparison of tangential stress (σ θ ) and rock mass strength (q ′′ cmass ) considering intermediate principal stress. S. Overburden Q after UCS, q c φ p Aq cmass = q ′ cmass = q ′′ cmass = q cmass + AP o 2 − AP 2 o 4q c σ θ = 2γH No. H(m) Tunnelling (MPa) (deg) = 2 sin φ p 1−sin φ p 7γQ 1/3 (MPa) P o = γHq cmass + AP o 2 ≤ q cmass + Aq c 4 (MPa) (MPa) 1 1430 4.7 50 45 4.8 31.6 38.6 124.2 88.4 77.2 2 1420 4.0 32 37 3.0 30.0 38.3 87.5 53.1 76.6 3 1420 4.5 50 45 4.8 31.1 38.3 123.0 87.8 76.6 4 1320 1.8 32 37 3.0 23.1 35.6 ∗ 76.5 47.1 71.2 5 1300 3.5 50 45 4.8 28.7 35.1 112.9 83.4 70.2 6 1300 2.0 60 45 4.8 23.8 35.1 108.0 83.4 70.2 7 1300 1.8 55 45 4.8 23.1 35.1 107.3 80.5 70.2 8 1300 3.3 50 45 4.8 28.0 35.1 112.2 82.7 70.2 9 1230 2.2 50 45 4.8 24.7 33.2 104.4 77.9 66.4 10 1180 4.7 42 55 9.1 31.6 31.9 176.1 121.0 63.8 11 1180 2.0 34 30 2.0 23.8 31.9 55.7 40.7 63.8 12 1180 3.4 42 45 4.8 28.3 31.9 104.9 75.8 63.8 13 1100 7.5 42 45 4.8 37.0 29.7 108.3 83.1 59.4 14 1090 7.0 50 45 4.8 36.2 29.4 106.8 86.0 58.8 15 1060 3.8 50 45 4.8 29.4 28.6 98.0 78.4 57.2 Note: In NJPC tunnel, no rock burst was observed except slabbing and noises due to cracking at overburden (H ) above 1000 m. The angle of internal friction φ p for rock mass was assumed same as that for the rock material (gneiss) approximately. ∗ Rock mass is in the critical state locally as in situ stress along tunnel axis ( P o ) is more than UCS. [...]... Technology, 15, 187-213 Jaeger, J C and Cook, N.G.W ( 196 9) Fundamentals of Rock Mechanics Methuen and Co Ltd Art .5. 3, 51 3 Terzaghi, K and Richart, F E (1 95 2 ) Stresses in rock around cavities Geotechnique, 3, 57 -99 Jethwa, J L ( 198 1) Evaluation of rock pressures in tunnels through squeezing ground in lower Himalayas PhD thesis, Department of Civil Engineering, IIT Roorkee, India, 272 Daemen, J J K ( 19 75) Tunnel... Rock Mech Min Sci & Geomech Abstr., 13, 255 -2 79 Barton, N (2002) Some new Q-value correlations to assist in-situ characterisation and tunnel design Int J Rock Mechanics and Mining Sciences, 39( 2), 1 85- 216 Brown, E T ( 197 0) Strength of models of rock with intermittent joints J of Soil Mech & Found Div., Proc ASCE, 96 (SM6), 19 35- 194 9 Brown, E T and Trollope, D H ( 197 0) Strength of a model of jointed rock... Daemen and A Richard, Schultz, Proc 35th U.S Symposium on Rock Mechanics, A A Balkema, 95 0 Yaji, R K ( 198 4) Shear strength and deformation response of jointed rocks PhD thesis, IIT Delhi, India Yu, Mao-Hong, Zan, Yzee-Wen, Zhao, Jian and Yoshimine, Mitsutoshi (2002) A unified strength criterion for rock material Int Journal of Rock Mechanics and Mining Sciences, 39, 9 75- 98 9 Appendix I Tunnel mechanics “Experiments... Taipei, 111- 158 Hoek, E and Brown, E T ( 198 0) Empirical strength criterion for rock masses J Geotech Div., ASCE, 106 (GT9), 1013-10 35 Hoek, E and Brown, E T ( 199 7) Practical estimates of rock mass strength Int J Rock Mechanics and Mining Sciences, 34(8), 11 65- 1186 Kumar, Naresh (2002) Rock mass characterisation and evaluation of supports for tunnels in Himalayas PhD thesis, WRDTC, IIT Roorkee, 2 95 Ladanyi,... thesis, Water Resources Development Training Centre, IIT Roorkee, India, 2 95 Norwegian Geological Institute ( 199 3) Manual for mapping of rocks, prepared by rock engineering and reservoir mechanics section of NGI, for a Workshop on Norwegian Method of Tunnelling, Sept 199 3, New Delhi, 12 -54 Park, E S., Kim, H Y and Lee, H K ( 199 7) A study on the design of the shallow large cavern in the Gonjiam underground... ASCE, 96 (SM2), 6 85- 704 Einstein, H H and Hirschfeld, R C ( 197 3) Model studies on mechanics of jointed rock J of Soil Mech & Found Div Proc ASCE, 90 , 2 29- 248 Hoek, E ( 198 3) Strength of jointed rock masses Geotechnique, 33(3), 187-223 Hoek, E ( 198 0) An empirical strength criterion and its use in designing slopes and tunnels in heavily jointed weathered rock Proc 6th Southeast Asian Conf on Soil Engg, 19- 23,... >2 ( 29. 14) Jr · Jw > 0 .5 Ja ( 29. 15) ′′ qcmass and H > Hcr = 2.5qc γ ( 29. 16) Thus severe rock burst conditions may develop in hard rocks which has entered into the critical state (Po > qc ) and where the overburden (H ) exceeds the limit of equation ( 29. 16) It is assumed that the ratio of in situ minimum principal stress and overburden pressure (K) is about 0.4 ± 0.10 at great depths in equation ( 29. 16)... London, 1 59 , 273-280 Sheorey, P R ( 199 7) Empirical Rock Failure Criteria A A Balkema, The Netherlands, 176 Singh, Bhawani, Shankar, D., Singh, Mahendra, Samadhiya, N K and Anbalagan, R N (2004) Earthquake rick reduction by lakes along active faults 3rd Int Conf on Continental Earthquakes, III ICCE, APEC, Beijing, China, July, 11-14 454 Tunnelling in weak rocks Wang, R and Kemeny, J M ( 19 95 ) A new... Construction, Seoul, 3 45- 351 Samadhiya, N K ( 199 8) Influence of anisotropy and shear zones on stability of caverns PhD thesis, Civil Engineering Department, IIT Roorkee, India, 334 Singh, Bhawani and Goel, R K (2002) Software for Engineering Control of Landslide and Tunnelling Hazards A A Balkema, Swets & Zeitlinger, Chapter 26, 344 Singh, Bhawani, Viladkar, M N., Samadhiya N K and Sandeep ( 19 95 ) A semi-empirical... been deduced from extensive tables and charts of Norwegian Geological Institute (NGI) Thakur ( 19 95 ) evaluated critically this semi-empirical method on the basis of over 100 case histories and found it satisfactory Park et al ( 199 7) used this design method for four food storage caverns in Korea Samadhiya ( 199 8) has verified the semi-empirical theory for shotcrete support by threedimensional stress analysis . 45 4.8 28.7 35. 1 112 .9 83.4 70.2 6 1300 2.0 60 45 4.8 23.8 35. 1 108.0 83.4 70.2 7 1300 1.8 55 45 4.8 23.1 35. 1 107.3 80 .5 70.2 8 1300 3.3 50 45 4.8 28.0 35. 1 112.2 82.7 70.2 9 1230 2.2 50 45. 104.4 77 .9 66.4 10 1180 4.7 42 55 9. 1 31.6 31 .9 176.1 121.0 63.8 11 1180 2.0 34 30 2.0 23.8 31 .9 55 .7 40.7 63.8 12 1180 3.4 42 45 4.8 28.3 31 .9 104 .9 75. 8 63.8 13 1100 7 .5 42 45 4.8 37.0 29. 7 108.3. 63.8 13 1100 7 .5 42 45 4.8 37.0 29. 7 108.3 83.1 59 .4 14 1 090 7.0 50 45 4.8 36.2 29. 4 106.8 86.0 58 .8 15 1060 3.8 50 45 4.8 29. 4 28.6 98 .0 78.4 57 .2 Note: In NJPC tunnel, no rock burst was observed