Rock Engineering CSE40411 Week Lecture (9:30-11:30) Room Y512 Tutorial (11:30-12:30) Room Y512 Laboratory (13:30-16:30) Room ZB216 Week Lecture (9:30-11:30) Room Y512 Tutorial (11:30-12:30) Room Y512 Laboratory (13:30-16:30) Room ZB216 1 (8/9) 2 (15/9) 3 (22/9) 4 (29/9) 5 (6/10) 6 (13/10) 7 (20/10) Topic 1 Topic 1/2 Topic 2 Topic 2 Topic 3 Topic 3 Topic 3 Topic 1/2 HW1 Topic 2/3 Lab 1 Group A Lab 1 Group B Lab 2 Group A HW2 8 (27/10) 9 (3/11) 10 (10/11) 11 (17/11) 12 (24/11) 13 (1/12) Mid-term test Topic 4 Topic 4 Topic 5 Topic 6 Topic 6 Show solutions Topic 4 Lab 2 Group B Lab 3 Group A HW3 Topic 5/6 Lab 3 Group B HW4 2 Lab 4 Group A Lab 4 Group B HW5 Index Properties of Rock and Rock Mass Classification Topic 1 3 4 Properties of Rock • • • • • • Density and specific gravity Porosity Point load strength Slaking and Durability Sonic velocity Permeability 5 Density Density (ρ) is defined as mass per unit volume, i.e., unit weight Mass ππ = Volume [kg/m3] or [g/cm3] Specific gravity G is the density of a material (ππ) at a reference temperature (usually 20°C) divided by the density of water (πππ€π€ ) at this temperature. ππ πΊπΊ = πππ€π€ 6 Determine specific gravity Quartz The Hong Kong granite, obtained from Po Lam road near Tseung Kwan O Biotite Plagioclase Determine the specific gravity based on the mineral contents Orthoclase 7 Determine the specific gravity based on the mineral contents i n πΊπΊ = οΏ½ πΊπΊππ ππππ i=1 Vi: Volume Percentage of each mineral phase ρdry=G ρw (1-φ) φ: porosity PbS (lead(II) sulfide) 8 Porosity Porosity (φ) is the ratio of the pore volume in a rock to the total bulk volume of that rock. Pore Volume × 100% ππ = Total Volume Total volume = Pore volume + Solid volume https://www.google.com/url?sa=i&url=http%3A%2F%2Fwww.deq.louisiana.gov%2Fassets%2Fdocs%2FWater%2FDWPP_forkidsandeducators%2FPorosityandPermeability.pdf&psig=AOvVaw0xiQxj21FI18oP8JY2J3NU&ust=1597831093220000&source=images&cd=vfe&ved=0CA0QtaYDahcKEwiApPWSv6TrAhUAAAAAHQAAAAAQCA Mineral grains Pores 9 Porosity – measurement Pore Volume × 100% , Total Volume We need usually unavailable. ππ = • • • • but pore volume is Density method – Measure solid volume and bulk volume to get pore volume: Mass Solid volume = Density Pore volume = Total volume − Solid volume Imbibition Method – Measure pore volume by measuring the volume of fluid the pore space can hold. Mercury Injection Method – measures the connected porosity and grain size and pore throat size distribution Gas Expansion Method – Pycnometer measures solid volume. Accurate and fast. 10 Volcanic tuff https://www.123rf.com/photo_121079580_tuff-also-known-as-volcanic-tuff-type-of-rock-made-of-volcanic-ash-stone-texture-.html Granite https://www.granitegold.com/porosity-of-granite/ 11 Saturation How much pore space is filled with fluid? water volume Water saturation: Sw = pore volume Oil saturation: So = oil volume pore volume Gas saturation: Sg = gas volume pore volume http://www.kgs.ku.edu/HighPlains/atlas/apst.htm 12 Index Test Properties • • • • Point load strength Slaking and Durability Sonic Velocity Permeability 13 Point load test • Subjecting a rock specimen to an increasingly concentrated load (through coaxial, truncated conical platens) until failure. • Calculate the point load strength index that can be used to classify the rocks. • A common method used is by estimating the uniaxial compressive strength. (ASTM D5731) Video demon online 14 Point load test L W L D D D Diametrical Test L>0.5D W W Axial Test 0.3W<D<W Block Test L>0.5D 0.3W<D<W 15 D Irregular Lump Test L>0.5D 0.3W<D<W Uncorrected point load strength index (Is) P Is = 2 De L P: load at failure [N] De: equivalent core diameter [mm2] W L D D D Diametrical Test De2 = D2 for diametral tests W W Axial Test Block Test D Irregular Lump Test De2 = 4A/π for axial, block, and lump tests, where A = WD (minimum cross-sectional area of a plane through the platen contact points). 16 (ASTM D5731) De2 = 4A/π for axial, block, and lump tests, where A = WD (minimum cross-sectional area of a plane through the platen contact points). 17 Typical Modes of Failure for Valid and Invalid Tests Valid diametrical tests Valid axial tests Valid block tests Invalid diametrical test Invalid axial test (ASTM D5731) 18 Point Load Strength Index 1. Uncorrected point load strength index P Is = 2 De P: load at failure [N] De: equivalent core diameter [mm2] 2. Calculate the size correction factor F = (De/50)0.45 3. Calculate corrected point load strength index (Is(50)) Is(50)=FIs 4. Calculate the mean Is(50) value from >10 tests, without the two highest and two lowest values 5. Further analysis • Rock classification • Estimation of uniaxial compressive strength 19 Shape Effect – sample length Is (MPa) L>0.5D, 0.3W < D < W 0 0.5 1 20 L/D Shape Effect – sample diameter I 50 = I s × F F= De 50 Is (MPa)  De ο£Ά F= ο£· ο£ 50 ο£Έ 0.45 Granite Sandstone For tests near the standard 50 mm size Claystone 10 50 21 De (mm) Correlation between point load strength index and uniaxial compression σc = 24 Is(50) σc = 20 Is(50) qu MPa (Franklin 1972) (Wong 2018) y = 20.404x r = 0.8361 24 I s(50) (Diametrical Test) I s(50) (Axial Test) Irregular lump test σc =20×Is(50), F=(De/50)0.56 (Wong, 2018) σc: Unconfined compressive strength Is(50): Point load strength index (50 mm diameter) 22 Slaking and Durability Sample: 10 lumps at ~50g each Apparatus : Drum is turned at 20 revolutions /min. 23 Slaking and Durability test https://www.youtube.com/watch?v=HbCgB-auLMs&feature=emb_logo 24 Slake Durability Index 1st cycle dry weight of rock retained inside drum × 100% Id : dry weight of rock before test 2nd cycle dry weight after the second cycle I2 : × 100% dry weight of rock before test 25 Gamble’s Slake Durability Classification % Retained After One 10-Minute Cycle (Dry Group Name Weight Basis) Very high durability >99 98-99 High durability Medium high durability 95-98 Medium durability 85-95 Low durability 90-85 Very Low durability <60 26 % Retained After Two 10Minute Cycles (Dry Weight Basis) >98 95-98 85-95 60-85 30-60 <30 If the rock has high durability, take three or more cycles for index If I2 value is from 0 to 10% determined by first cycle durability I1 = W first cycle W inital I1 × 100 % I2 Id 1 27 2 I3 I4 3 4 Cycle I5 5 I6 6 Shale and claystone immersed in water tends to absorb water and soften. For those soft rock with low slake-durability results should be subjected to soil classification tests. 28 Sonic velocity test • Ultrasonic pulse transmission technique. • Measurement of velocity of sound (elastic wave) to determine the degree of fissuring. Rock Fissures – small narrow fractures and cracks in rocks. https://jgs.lyellcollection.org/content/jgs/early/2020/01/20/jgs2019-142.full.pdf 29 P-wave and S-wave P-wave (primary / Longitudinal) S-wave (secondary/ shear wave) 30 How to measure the wave velocity The fissuring or pores inside the rock will affect the travel velocity of the waves: the more fissuring, the slower speed (the more travel time for the same distance) (primary / Longitudinal) S-wave (secondary/ shear wave) tp = travel time of P-wave L Vp = tp L Vs = ts t0 Rock sample P-wave Sonic Pulse Pore L Fissure t1 ts = travel time of S-wave tp=t1−t0 travel time of P-wave 31 Sonic Velocity test 32 How to represent the degree of Fissuring For same rock type: less fissures ο³ higher sonic velocity ο³ better quality How do we compare different rocks? Quality Index: IQ % = Vππ Vππ∗ × 100% VP : Measured P-wave velocity in the rock sample VP*: P-wave velocity in rock sample if it has no pores or fissures Vp 33 Vp* Typical Values of VP* for Rocks * Rock VP (m/s) Gabbro 7000 basalt 6500-7000 Limestone 6000-6500 Dolomite 6500-7000 Sandstone and quartzite 6000 Granitic rocks 5500-6000 Fourmaintraux (1976) 34 Typical Values of mineral contents * VP for Rocks by measuring the 1 Ci ∗ = οΏ½ VP VPi i P-wave Velocities of Minerals Mineral VP (m/s) Quartz 6050 Olivine 8400 Augite 7200 Amphibole 7200 Muscovite 5800 Orthcolase 5800 Plagioclase 6250 Calcite 6600 Dolomite 7500 magnetite 7400 Gypsum 5200 Epidote 7450 Pyrite 8000 From Fourmaintraux (1976) Ci : Volume proportion of mineral i in rock VPi: Longitudinal wave velocity in mineral i Amphibole Orthcolase Quartz 35 IQ % = 100 − 1.6 φp % φp : Porosity of non-fissured rock IQ% Extremely fissured 62.5 φp % 36 Fourmaintraux (1976) Permeability Hydraulic Permeability – the degree of interconnection between pores, fissures, and joints https://www.google.com/url?sa=i&url=http%3A%2F%2Fwww.deq.louisiana.gov%2Fassets%2Fdocs%2FWater%2FDWPP_forkidsandeducators%2FPorosityandPermeability.pdf&psig=AOvVaw0xiQxj21FI18oP8JY2J3NU&ust=1597831093220000&source=images&cd=vfe&ved=0CA0QtaYDahcKEwiApPWSv6TrAhUAAAAAHQAAAAAQCA 37 Darcy’s law In 1856, Darcy established an empirical relation for the flow of water (at ~20°C) through porous media, known as Darcy’s law: (β1 −β2 ) ππ = πΎπΎπΎπΎ πΏπΏ πππ πππ₯π₯ = πΎπΎπΎπΎ ππππ (flow in x direction) q: volumetric flow rate [m3/s] K: hydraulic conductivity [m/s] A: cross-section area [m2] h: hydraulic head [m] L: length of the sample [m] Q: volumetric flow = q·t [m3] Qin h1 Qout L A x direction 38 h2 Datum Darcy’s law πππ πππ₯π₯ = πΎπΎπΎπΎ (at ~20°C) ππππ ππ ππππ πππ₯π₯ = π΄π΄ µ ππππ q: volumetric flow rate [m3/s] k: hydraulic permeability [m2] A: cross-section area [m2] p: pressure [Pa] L: length of the sample [m] µ: fluid viscosity [m2/s] (µ of water: 1x10-6 m2/s at 20°C) Hydraulic conductivity is related to the hydraulic permeability as ππππππ πΎπΎ = µ ππ: gravitational acceleration [m/s2] ππ: density of water [kg/m3] 39 Darcy’s law ππ ππππ πππ₯π₯ = π΄π΄ µ ππππ • Permeability k is independent of the fluid properties (also called intrinsic permeability). • Darcy (D) (1 D ~ 1 × 10− 12 m2) and is the standard field unit for permeability. • Volumetric flow rate depends on the pressure difference (ππππ). 40 Measurement of hydraulic conductivity Falling Head Permeability Test πππ‘π‘2 πΏπΏ β0 K = 2 ln( ) β ππππ π‘π‘ dc2: sample diameter dt2: falling head tube diameter L: length of the sample h0: initial water level h: water level after t K: hydraulic conductivity ο k (Fetter 1980) 41 Measurement of hydraulic conductivity Constant Head Permeability Test K= ππππ Ath V: discharged water volume in time t L: length of the sample A: cross section area of the sample h: hydraulic head K: hydraulic conductivity ο k (Fetter 1980) 42 Lab permeability test ππππ = ππ1 − ππ2 ππππ = πΏπΏ P2 x direction L Rock sample A P1 ππ ππππ πππ₯π₯ = π΄π΄ µ ππππ ππ (ππ1 −ππ2 ) ππ = π΄π΄ ππ πΏπΏ πππππΏπΏ ππ = π΄π΄(ππ1 − ππ2 ) q: volumetric flow rate [m3/s] k: permeability [m2] A: cross-section area of the sample [m2] P: fluid pressure [m] L: length of the sample [m] µ: kinetic viscosity of water [m2/s] 43 Lab conductivity/permeability test http://www.kensains.com.my/controls_rock.html Permeability test in a testing cell (Hoek cell) 44 Table 2.4 Conductivities of Typical Rocks K (cm/s) for Rock with Water @ 20oC Rock Sandstone Lab Field 3 x 10-3 to 8 x 10 -8 1 x 10-3 to 3 x 10 -8 Navajo sandstone 2 x 10-3 Berea sandstone 4 x 10-5 Greywacke 3.2 x 10-8 10-9 to 5 x 10 -13 10-8 to 10 -11 5 x 10-12 2 x 10-9 to 5 x 10 -11 Limestone, dolomite 10-5 to 10 -13 10-3 to 10 -7 Salem limestone 2 x 10-6 Shale Pierre shale Basalt 10-12 10-2 to 10 -7 Granite 10-7 to 10 -11 10-4 to 10 -9 10-8 2 x 10-7 Schist Fissured schist 1 x 10-4 to 3 x 10 -4 Field test hydraulic conductivity >> Lab test values 45 Pumping test https://me.me/i/formation-of-a-cone-of-depression-infiltration-recharge-cone-of-804894 46 Pumping test - confined aquifer q Original groundwater table Observation well h2 h1 hw H (aquifer thickness) r1 confined aquifer r2 impermeable 2r0 ππ2 dr K 2ππ»π» β2 οΏ½ dh οΏ½ = ππ ππ1 ππ β1 In the radial (r) direction: dh dh q = KA = K 2πrH dr dr ππππ K 2πH dh = ππ ππ impermeable 47 ππ2 K 2ππ»π» (h2 − β1 ) ln = ππ ππ1 q ln(ππ2 /ππ1 ) K = 2ππH(β2 − β1 ) Pumping test - unconfined aquifer q Original groundwater table saturated aquifer thickness at radial distance r Observation well h h2 h1 hw r1 r unconfined aquifer r2 2r0 ππ2 dr K 2π β2 οΏ½ β dh οΏ½ = ππ β1 ππ1 ππ In the radial (r) direction: dh dh q = KA = K 2πrh dr dr ππππ K 2πh dh = ππ ππ 48 ππ2 Kπ 2 2 (β2 −β1 ) ln = ππ ππ1 q ln(ππ2 /ππ1 ) K = ππ(β22 −β12 ) Packer Test (Lugeon test) Maurice Lugeon, a Swiss geologist first formulated the test. https://www.geotech.hr/en/permeability-test-lugeon-test/ 49 Packer Test (Lugeon test) In situ test of formation conductivity/permeability performed by measuring the volume of water taken in a section of test hole when the interval is pressurized at given pressure. https://www.geotech.hr/en/permeability-test-lugeon-test/ Packers https://www.nve.no/Media/5313/lloydt-lugeon-test.pdf 50 Stage Pressure 1 0.50Pmax 2 0.75Pmax 3 Pmax 4 0.75Pmax 5 0.50Pmax Packer Test (Lugeon test) The average hydraulic conductivity of the rock mass is expressed in terms of Lugeon unit (1 Lu ≈ 1.3 × 10 −7 m/s). q ππ0 Lugeon value: Lu = × L ππ q - flow rate [liter/min] L - Length of the borehole test interval [m] P0 - Reference pressure of 1 MPa [MPa] P - Test pressure [MPa] 51 Packer Test (Lugeon test) Range of Lugeon values and the corresponding rock condition 52 Rock Mass Classification • Rock mass rating system (RMR) system • Q system (NGI system) 53 Rock Mass Rating (RMR) system Bieniawski (1975) proposed the geomechanics classification system: Rock Mass Rating (RMR) indicating rock quality from 1 to 100. Basic Parameters: 1.) Strength of intact rock 4.) Condition of Joints 2.) Rock Quality Designation (RQD) 5.) Groundwater Conditions 3.) Spacing of Joints 6.) Orientation of Joints 54 RMR Basic Parameters: 1.) Strength of intact rock 2.) Rock Quality Designation (RQD) 3.) Spacing of Joints 4.) Condition of Joints 5.) Groundwater Conditions 6.) Orientation of Joints 55 56 Rock-quality designation (RQD) Rock-quality designation (RQD) is a rough measure of the degree of jointing or fracture in a rock mass. 57 Rock Quality Designation (RQD) Σ length core pieces (length >2×diameter) ×100% RQD = Total length of core run Rock core 58 Rock Quality Designation (RQD) RQD = Σ > 10cm length Total length of core run ×100% 5 cm diameter core 0.61 + 0.21 = 55% RQD = 1.50 #1 – 9 natural fractures (joints) Spacing of Joints (most influential set) 59 10 cm https://dxi97tvbmhbca.cloudfront.net/upload/user/image/JJakubec_Roles_of_defects_in_rock_mass_classfication_201320191128184530242.pdf 60 5 cm Scale ππππππ = πππ ππππππ = πππ 10 cm ππππππ = πππππππ https://dxi97tvbmhbca.cloudfront.net/upload/user/image/JJakubec_Roles_of_defects_in_rock_mass_classfication_201320191128184530242.pdf 61 5 cm Scale 62 Joint spacing Spacing of Joints (most influential joint sets) 63 Joint spacing, condition, and water http://www.kgs.ku.edu/PRS/Ozark/well_1_32.html https://geologyengineering.com/2019/11/rqd-rock-quality-design/ 64 65 Basic Parameters: 1.) Strength of intact rock 2.) Rock Quality Designation (RQD) 3.) Spacing of Joints 4.) Condition of Joints 5.) Groundwater Conditions 6.) Orientation of Joints 66 Q system (NGI, Tunnel Quality Index) RQD Jr Jw × Q = × Ja Jn SRF (Barton et al., 1974) Environmental conditions influencing the behaviour of rock mass Jn : Joint set number Jr : Joint roughness number Ja : Joint alternation number Shear strength of the block surface Jw : Joint water reduction factor Size of joint block SRF : Stress reduction factor 67 68 69 Q system and the RMR system connection: RMR= 9 ln Q +44 (std 9.4) 70 End – Topic 1 Questions? Department of Civil and Environmental Engineering (CEE)
