ROCK MASS PROPERTIES FOR TUNNELLING Robert Bertuzzi 2 nd November 2017 1
Driver Estimating the strength and deformation characteristics of a rock mass for tunnel design is generally based on empiricism as it is simply not practical to test the rock mass at a scale large enough. However, the database from which empirical methods are derived and against which analytical methods are tested, is rather limited in terms of large rock masses.
Presentation Intact rock strength Defect strength Rock mass classification Rock mass strength Rock mass modulus
Depth (m) Intact rock strength Numerous criteria Mohr-Coulomb Barton Griffith Drucker-Prager Wiebols-Cook Hoek-Brown Extension strain Bieniawski Lade Christensen You Zhou (H-B in 3D) UCS (MPa) 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80 4
Major Principal Stress, s 1 [MPa] Major Principal Stress, s 1 [MPa] 300 300 300 Hawkesbury Sandstone Brisbane Tuff Brisbane Phyllite 280 280 280 260 260 260 240 240 240 220 220 220 200 200 200 180 180 s 1 [MPa] 180 160 160 160 140 140 140 120 120 120 100 100 100 80 80 80 60 60 60 40 40 40 20 20 20 0 0 0-20 0 20 40 60 80 100-20 0 20 40 60 80 100-20 0 20 40 60 80 100 Minor Principal Stress, s Minor Principal Stress, s 3 [MPa] 3 [MPa] s 3 [MPa] 5
s 1 [MPa] s 1 [MPa] Intact rock strength criteria 1000 Any of the assessed criteria can provide good fits to tight test data Outlier test data, particularly UTS or BTS values, can significantly affect each of the criteria s parameters. The variation in test data swamps the differences in criteria. Even when all the criteria provide very good fits to the data based on the r 2 and SEE values and on the overall shape of the envelopes, many of the criteria are poor estimators of strength in the low stress region where many civil structures, such as tunnels, operate. The Hoek-Brown criterion over-predicts the tensile strength Curve-fitting following the Mostyn-Douglas method which allows for a variable a SEE - standard error of estimate Darley Dale Sandstone 900 800 700 600 500 400 300 200 100 0-10 10 30 50 70 90 110 130 150 170 190 210 230 250 270 290 310 330 350 370 390 Data 50 H-B (Mostyn & Douglas): 45 sc=10.6mpa mi=11.82 a=0.5 r2=0.991 Hoek-Brown: sc=9.3mpa mi=13.57 40r2=0.991 3D Hoek-Brown: sc=10mpa mi=12.65 r2=0.991 Lade: 35 a =9.97 h1 = 1000 m = 0.551 r2 =0.989 Wiebols-Cook: 30 sc = 13.4MPa phi = 22.8 r2=0.975 Christensen: sc = 10 MPa; st = 0.9 25MPa; r2=0.989 20 15 10 5 6 s 3 [MPa] Data H-B (Mostyn & Douglas): sc=79.9mpa mi=22.73 a=0.444 r2=0.983 Hoek-Brown: sc=79.3mpa mi=15.13 r2=0.979 3D Hoek-Brown: sc=79.3mpa mi=15.1 r2=0.979 Wiebols-Cook: sc = 152.8MPa phi = 26.3 r2=0.926 Christensen: sc = 160 MPa; st = 3.5 MPa; r2=0.909 Lade: a =34.89 h1 = 92380 m = 0.866 r2 =0.907 0-4 -2 0 2 4 6 8 10 s 3 [MPa]
Defect strength Defect continuity dominates rock mass properties Less than 1% of intact area in the plane of a defect is equivalent to heavy support systems 7
Defect strength φ = JRC log 10 JCS σ n + φ r Description [50 to 300 mm scale] Slickenside or Polished i Addition to b Very smooth, reflects light 0 Smooth Roughness not detected with finger +2 Defined ridges (slightly rough) Fine to medium sandpaper feel +6 Small steps (rough) Medium to coarse sandpaper feel +10 Very rough Very well defined ridges, steps +14 8
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Defect stiffness 10
Rock mass classification Terzaghi rock load Rock Quality Designation (RQD) Rock Structure Rating Rock Mass Rating (RMR) Mining RMR Slope RMR Rock Mass Index, Q Sydney Classification System Geological Strength Index (GSI) Rock Mass Index (RMi) 11
GSI 12
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Hawkesbury sandstone Reefton greywacke Ashfield shale Otago schist 14
Quantified GSI 100 Quantified GSI = Chart GSI ± 10 80 r2=0.679 60 40 20 0 Greenland Group Greywacke / argillite Otago Schist Ashfield Shale Hawkesbury Sandstone 0 20 40 60 80 100 Chart GSI 15
Rock mass strength Numerous criteria Massive brittle rock - Damage initiation spalling limited (DISL) s 1 = (0.33 to 0.5)s c +(1.4 to 2.6)s 3 Plane of weakness Barton-Bandis Hoek-Brown Cohesion weakening Friction strengthening Synthetic Rock Mass 16
The Hoek-Brown rock mass criterion based on very limited test work from Panguna andesite (23), the largest samples of which had 22.5 (572mm) diameters Hoek-Brown σ 1 σ c = σ 3 σ c + m σ 3 σ c + s σ 1 = σ 3 + σ c m σ 3 σ c + s a a = 0.5 to 0.65 for rock mass 17
Hawkesbury Sandstone Tunnels Upper Canal Tunnels Cataract 1880s by drill & blast, 3.2 m wide x 2.6 m high, horseshoe shaped, maximum depth of 70 m Devines 1880s by drill & blast, 2.85 m wide x 2.5m high, horseshoe shaped, maximum depth of 17 m Malabar Outfall Tunnel Excavated between 1986-1990 by roadheader 644 m long 1:4 decline, 5.3 m wide x 5.0 m high, arched roof, up to 175m depth, although the roof failure occurred at 100 m depth Sydney LPG Storage Cavern Excavated between 1996 2000 by drill & blast Four parallel galleries each 230 m long, 11 m wide x 14 m high, arched roofs, 124 m depth Northside Storage Tunnel Three TBM drives excavated between 1998 2000 7 km of 3.8 m diameter, depth 80 m 9 km of 6.5 m diameter, depth 60 m Cross City Tunnel 4 km of 6.0 m diameter, depth 80 m Excavated between 2003 2005 by roadheader 2 km long ventilation tunnel, 5.1 m wide x 5.5 m high, very slightly curved roof, 58 m depth Lane Cove Tunnel Excavated between 2004 2006 by roadheader 2.1 km long road tunnel of 9 m and 12.5 m width x 6 m high, very slightly curved roof, 20-40 m depth 18
σ 1 (MPa) σ 1 (MPa) 18 18 16 16 14 14 12 12 10 10 8 8 1m3: sc=22.2mpa, mi=12 Rock mass: sc=22.2mpa, m=4.11, s=0.0357, a=0.501 Initial spalling: 6.66MPa + 2s3 6 1m3: sc=22.2mpa, mi=12 6 Damage initiation: sc=22.2mpa, m=0.0972, s=0.0081, a=0.25 Cataract - failed 4 2 Rock mass: sc=22.2mpa, m=4.11, s=0.0357, a=0.501 Initial spalling: 6.66MPa + 2s3 Damage initiation: sc=22.2mpa, m=0.0972, s=0.0081, a=0.25 Cataract - stable (close) Devines - stable (close) CCT - stable (close) 4 2 Devines - failed CCT - failed Elgas - failed LCT - failed Malabar - failed Elgas - stable (close) NST - failed 0-1 0 1 2 3 4 LCT - stable (close) Malabar - stable (close) 0-1 0 1 2 3 4 σ 3 (MPa) NST - stable (close) σ 3 (MPa) 19
Pillar Load [MPa] Tributary Area Coal pillars C p = K w0.46 h 0.66 C p = Constant 0.64 + 0.36 w h [MPa] s 1 = (0.33 to 0.5)s c +(1.4 to 2.6)s 3 Damage initiation 25 Collapsed Pillars 20 FoS = 1.85 15 Australia 10 South Africa South Africa - weak USA - squeeze USA - massive 5 USA - local bursting India Cp UNSW linear 0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 w/h = R 20
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Proposed strength criterion for coal pillars Damage initiation threshold m b = 0.1296, s = 0.0081, a = 0.25 Spalling limit m b = 5.33, s = 0, a = 0.75 Macro-scale shear failure m b = 1.47, s = 0.07, a = 0.5 Maximum confined strength σ 1 σ 3 σ c = 0.6 range 0.5 and 0.7 22
Hard rock mines Underground mines Limestone Iron ore Sandstone Laboratory samples Stripa granite Lac du Bonnet granite Artificially jointed granite Quartzite Phyllite Other Ok Tedi core testing 23
Hard rock mines Current Equations (Hoek et al. 2002) Proposed Equations m b = m i e GSI 100 28 14D m b = m i e GSI 100 38 24D s = e GSI 100 9 3D s = e GSI 100 12 6D Τ Τ a = 1 2 + 1 6 e GSI 15 e 20 3 a = min[1, 1 2 Τ 1.0 + e ( GSI 10) 15 ] 24
Proposed m b /m i v GSI 25
Proposed s v GSI 26
Proposed a v GSI 27
Rock mass modulus The in situ test methodology and in situ stress need to be considered when assessing the reliability of in situ rock mass modulus. A further conclusion is that the more reliable estimates of in situ rock modulus are those derived from tests that engage larger volumes of rock; stepping from flat jack and plate load testing to seismic refraction tests and back-analysis of convergence data. 28
Em [GPa] Em [GPa] 20 18 16 14 100 12 10 8 Palmstrom Nejati et a 6 4 80 2 0 0 20 40 60 80 100 GSI 60 D = 0.5 Palmstrom & Singh (2001) Nejati et al (2014) 40 20 0 0 20 40 60 80 100 GSI 29
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Back-analysing modulus u r = Kσ v E a I 1 + σ v E a I 2 u θ = Kσ v E a I 3 + σ v E a I 4 Anisotropy E a E = 1 + ν A + B cos 2θ A = 1 2 2ν E E 1 + ν + 1 ν 2 + E E E E 1 ν2 1 E E ν 2 2 1 ν G G ν E E + 2 E E 1 E ν 2 E 1 ν 2 2 E E E E 1 ν2 1 E E ν 2 B = 1 2 1 ν2 E E E E 1 ν2 1 E E ν 2 2 1 ν G G ν E E + 2 E E 1 E ν 2 E 1 ν 2 31
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M2 & Castle Hill crossover Hawkesbury Sandstone E h = E v = 4500 to 6750 MPa, say 5500 MPa K = 2.7 to 3.1, say 3.0 Ashfield Shale E h = 720 MPa, E v = 1000 MPa K = 1.7 33
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