pftlecture notes/Week 4-Part 2 MC.pdf Moon Hill, China RSE3010 MINE GEOTECHNICAL ENGINEERING WEEK 4...

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pftlecture notes/Week 4-Part 2 MC.pdf Moon Hill, China RSE3010  MINE GEOTECHNICAL ENGINEERING WEEK 4 THEORIES OF DEFORMATION AND FAILURE OF ROCKS: PART 2 • Uniaxial and Triaxial Compressive Behaviour • Mohr-Coulomb Criterion • Hoek-Brown Criterion • Griffith Theory • von Mises Criterion • Combined Failure Criteria 3 MONASH CIVIL ENGINEERING STRENGTH/FAILURE CRITERIA ▪ The behaviour law of a material  – defined as the relationship between the stress components that  indicate the state of strain that the material undergoes. It is a  broader concept than that of strength or failure criterion since it  refers to the relationship between the stresses throughout the  whole process of deformation of rock. ▪ Diagram of general failure criterion in 2D – Ki: other influencing factors  ▪ such as temperature, velocity – “Impossible” state of stress – Possible state of stress 4 MONASH CIVIL ENGINEERING MOHR-COULOMB CRITERION ▪ Mohr-Coulomb Criterion – The Mohr–Coulomb theory is  named in honour of Charles- Augustin de Coulomb and  Christian Otto Mohr.  – The criterion assumes that a shear  failure plane at  angle to the  minor principal stress is developed  in the brittle material – Coulomb’s shear strength () is  made up of two parts, a constant  cohesion (c), and the angle of  internal friction ()  = c + n tan n  c,  ‘Grandfather of Soil Mechanics’ Concepts of active and passive earth pressure  Concept of friction  Coined the term “Cohesion” 1 3 n   5 MONASH CIVIL ENGINEERING ▪ Stresses by Mohr’s Circle MOHR-COULOMB CRITERION 3 1  n 1. We start the Mohr’s diagram by constructing a 2D coordinate  system where the horizontal axis is the normal stress, σn, and the  vertical axis is the shear stress, . 2. Then we mark the magnitude of the minimum and the maximum  principal stresses σ3 and σ1, respectively, on the σn-axis.  6 MONASH CIVIL ENGINEERING ▪ Stresses by Mohr’s Circle MOHR-COULOMB CRITERION 3 1  n 3. Then we draw a circle (or,  more commonly, a semicircle)  through σ3 and σ1, so that the  circle/semicircle has a diameter  equal to σ1 – σ3. 7 MONASH CIVIL ENGINEERING ▪ Stresses by Mohr’s Circle MOHR-COULOMB CRITERION 4. We can use this diagram to  obtain the values of the normal  stress σn and the shear stress  on any crustal plane of interest.  Each plane is marked by a point  P on the circle/semicircle. 5. The point P is  connected to the centre  of the circle C through a  line that makes an angle  of 2θ with the positive  (right) part of the σn -axis. 3 1  n 2 ½ (1 + 3)  P C 8 MONASH CIVIL ENGINEERING ▪ Stresses by Mohr’s Circle MOHR-COULOMB CRITERION 3 1  n (n, ) 2 ½ (1 + 3)   n 180-2 6. The coordinates of P are then  σn and  . Thus, the circle consists  of an infinite number of points that  show the stresses on planes with  all possible values of θ. 7. The distance of the  centre C from the origin  equals (σ1 + σ3)/2. The  radius of the circle PC equals to (σ1 – σ3)/2,  which is also the  maximum shear stress  when the shear stress  reaches it maximum on  planes oriented at θ = 45◦. P C 9 MONASH CIVIL ENGINEERING ▪ Stresses by Mohr’s Circle MOHR-COULOMB CRITERION 3 1  n c  (n, ) ½ (1 + 3)   n  = ½ (1 – 3) sin(180–2) n = ½ (1 + 3) – ½ (1 – 3) cos(180–2)  = ½ (1 – 3) sin2 n = ½ (1 + 3) + ½ (1 – 3) cos2 180-2 2 P C The tangent point of the  Mohr circle with the straight  line represent:  (1) the stresses conditions  on the shear plane, and  (2) the inclination of the  shear plane, where the  shear failure occurs.  = c + n tan 0 1 3 n   10 MONASH CIVIL ENGINEERING MOHR-COULOMB CRITERION ▪ Failure Condition –  = c + n tan is a  straight line strength  envelope – In the diagram, when the  Mohr circle touches the  strength envelope, on the  touching point, the stress  condition on the shear  plane meets the criterion. – Failure occurs along the  shear plane when  stresses (n, ) meet  shear strength condition.   11 MONASH CIVIL ENGINEERING ▪ Failure Condition – Failure does not occur if the  Mohr circle (black) does not  touch the failure envelope. – Four ways to make Mohr  circle touching the failure  envelope: ▪ Increasing 1 (blue);   ▪ Decreasing 3 (red); ▪ Decreasing 1 and 3 at the  same time (green); ▪ Combination of the above  three. MOHR-COULOMB CRITERION 3 1  n 12 MONASH CIVIL ENGINEERING ▪ Orientation of Shear Failure Plane – From the Mohr circle, the strength envelope is perpendicular to  the line defined by 2, where    2 = /2 + , then,  = ¼  + ½  – which is the angle of failure plane to the minor principal stress 3.  MOHR-COULOMB CRITERION 1 3 n   13 MONASH CIVIL ENGINEERING ▪ Compressive and Tensile Strengths – Replacing  = ¼  + ½  in the equation of 1, it gives – when 3=0, 1 is uniaxial compressive strength c – when 1=0, 3 is tensile strength t MOHR-COULOMB CRITERION c  nt c0 13 c (1 – sin) t = (1 + sin) 2 2c cos c = 1 - sin 2c cos t = 1 + sin 14 MONASH CIVIL ENGINEERING ▪ Tensile Cut-Off – Tensile strengths given  by Mohr-Coulomb  Criterion is much higher  than the actual ones. – A tensile cut-off can be  applied at around  t’ = 1/10 c. – Mohr-Coulomb Criterion  used for rock mechanics  is a straight line at  compression with tensile  cut-off  MOHR-COULOMB CRITERION c   nt c 0 t′ Gives t = 1/3 c for  = 30° Actual t ≈ 1/8  1/15 c  2c cos t = 1 + sin 15 MONASH CIVIL ENGINEERING MOHR-COULOMB CRITERION ▪ RocData Software – Levenberg–Marquardt: non-linear least squares curve fitting – or Linear Regression  = c + n tan 3 (MPa) 1 (MPa) 0 75 3 99 10 120 14 139 21 146 46 206 70 265 100 330 16 MONASH CIVIL ENGINEERING MOHR-COULOMB CRITERION ▪ RocData Software – Wombeyan Marble – Update the Custom with Sigmax = 100 MPa ▪ Cohesion: 29.94 MPa ▪ Friction angle: 24.6° 3 (MPa) 1 (MPa) 0 75 3 99 10 120 14 139 21 146 46 206 100 330 17 MONASH CIVIL ENGINEERING MOHR-COULOMB CRITERION   = c + n tan c ▪ RocData Software – Linear Regression Wombeyan Marble Melbourne MudstoneBlackingstone Granite 18 MONASH CIVIL ENGINEERING MOHR-COULOMB CRITERION ▪ Mohr-Coulomb Criterion in 1 – 3 plots  ▪ The 1 – 3 plots for Mohr-Coulomb  Criterion are straight lines.  19 MONASH CIVIL ENGINEERING MOHR-COULOMB CRITERION ▪ Mohr-Coulomb Criterion in 1 – 3 plots  3 (MPa) 1 (MPa) 0 75 3 99 10 120 14 139 21 146 46 206 100 330 Wombeyan Marble c=93.3 MPa =67.6°  =  20 MONASH CIVIL ENGINEERING MOHR-COULOMB CRITERION 2. c=75 MPa 1. Hoek-Brown 4. t= -14 MPa ▪ Mohr-Coulomb Criterion in 1 – 3 plots  21 MONASH CIVIL ENGINEERING MOHR-COULOMB CRITERION ▪ Comments on the Mohr-Coulomb Criterion – It is suitable for estimating compressive strengths at low confining  stresses.  It much overestimates tensile strengths.  It also  overestimates compressive strengths at high confining stresses. – Most of the rock engineering activities are at shallow depths and  low confining stresses, so the criterion gives reasonable  estimations for rock material strengths c  nt c0 13 2 __MACOSX/lecture notes/._Week 4-Part 2 MC.pdf lecture notes/Week 2-Part 2 RQD.pdf Bryce Canyon National Park, Utah RSE3010  MINE GEOTECHNICAL ENGINEERING WEEK 2 ROCK MASS CLASSIFICATIONS: PART 2 • Intact Soil & Rock Classification • Rock Quality Designation (RQD) • Rock Tunnel Quality Q-System • Rock Mass Rating (RMR) • Geological Strength Index (GSI) • Rock Load Factor • Rock Structure Rating (RSR) • Rock Mass index (RMi) 3 MONASH CIVIL ENGINEERING MELBOURNE METRO ALIGNMENT MAP ▪ The Melbourne Metro Tunnel (MMT) presents many unique  challenges: construction of the 9km twin tunnels and 5 underground  stations involve TBMs, mined caverns and open cut excavations. 4 MONASH CIVIL ENGINEERING GEOLOGICAL PROFILE ALONG THE PROPOSED ALIGNMENT The Silurian bedrock in the area of the Melbourne Metro project is the Melbourne  Formation, which consists of mudstone, sandstone and siltstone that has been  folded, faulted and intruded with igneous rocks. These rocks have been  weathered to varying depths, with fresh (unweathered) rock sometimes existing  within the shallow profile. What is the geologic period of Silurian rock? 5 MONASH CIVIL ENGINEERING AHD (Australian Height Datum) GEOLOGICAL PROFILE ALONG THE PROPOSED ALIGNMENT Quaternary  Tertiary Silurian  Older Volcanic basalts  6 MONASH CIVIL ENGINEERING UNDERGROUND STATION: CBD NORTH, NOW STATE LIBRARY ▪ EES: Environmental Effects Statement (under the  Environment Effects Act 1978)  ▪ Plan View of selected station ▪ What does ‘GA15-BH169’ stand for? 7 MONASH CIVIL ENGINEERING UNDERGROUND STATION: CBD NORTH, NOW STATE LIBRARY ▪ Section Alignment ▪ Segment 11: TBM (Tunnel Boring Machine) Tunnel ▪ Segment 12: State Library Station, Underground Mine,  Tri-arch Cavern including central cavern and two platform  caverns https://metrotunnel.vic.gov.au/construction/cbd/building-cbd-stations https://metrotunnel.vic.gov.au/construction/cbd/building-cbd-stations 8 MONASH CIVIL ENGINEERING SOIL AND ROCK BOREHOLE LOGS ▪ Drilling Method, NMLC: Diamond Core - 52 mm 9 MONASH CIVIL ENGINEERING REPORT OF SOIL AND ROCK BOREHOLE 10 MONASH CIVIL ENGINEERING ABBREVIATIONS AND TERMS ▪ TCR = Total Core Recovery (%) – TRC(%)=(Length of core recovered)/(Length of core run)×100 ▪ SCR = Solid Core Recovery (%) – SCR(%)=( Length of cylindrical core recovered)/(Length of core run)×100 ▪ RQD = Rock Quality Designation (%) – RQD(%)=( Axial lengths of core >100 mm)/(Length of core run)×100 11 MONASH CIVIL ENGINEERING ROCK QUALITY DESIGNATION (RQD)  10 cm RQD = (L1 + L2 + … + Ln) / L  x 100% 12 MONASH CIVIL ENGINEERING ROCK QUALITY DESIGNATION (RQD) 1922-2018 ▪ Don U. Deere – 1955, PhD from University of  Illinois – 1962-1966, ISRM Board  Members with Charles Fairhurst – 1964, Rock Quality Designation  (RQD) – 1972, US National Committee  on Tunnelling Technology – Member of National Academy of

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