Properties of Rock: Rock Mechanics Lecture Slides on Testing and Stress

Properties of Rock Determined from: Laboratory Testing Field Observation Numerical modeling 2 Laboratory testing Compressive strength Uniaxial Triaxial Point load test Tensile strength Brazilian 3 Basic theory F Axial Stress Axial Strain Lateral Strain Young’s Modulus l2 l1 Poisson’s Ratio Modulus of Rigidity x1 x2 4 Axial Stress F l2 l1 𝜎= 𝐹 𝐴 σ = Stress Pa (Pascal) F = Force N (Newton) A = Area m2 (Square meters) x1 x2 5 Axial Strain F Δ𝑙 l2 𝜀1 = 𝑙 = l1 x1 x2 6 𝑙2 −𝑙1 (𝑁𝑜 𝑢𝑛𝑖𝑡) 𝑙1 Lateral strain F Δ𝑙 𝜀1 = 𝑙 = l2 l1 x1 x2 7 𝑥2 −𝑥1 (𝑁𝑜 𝑢𝑛𝑖𝑡) 𝑥1 Young’s Modulus F 𝐸= l2 x1 x2 l1 8 𝑆𝑡𝑟𝑒𝑠𝑠 (𝑃𝑎) 𝐴𝑥𝑖𝑎𝑙 𝑆𝑡𝑟𝑎𝑖𝑛 Modulus of Rigidity G = FA / AΔx 9 Laboratory testing Uniaxial compression F End pieces of hardened steel to ensure good load distribution and to protect the laboratory equipment Specimen Cylindrically shaped rock sample Length:diameter = 2:1 – 3:1 Ends must be flat and parallel F 10 Laboratory testing Uniaxial compression 11 Laboratory testing Triaxial compression F “O” rings Lateral confinement with oil pressure Flexible jacket F 12 Laboratory testing Triaxial compression 13 Laboratory testing Point Load Test Is50 = P/d2 Qc =UCS = 24 Is50 14 Laboratory testing Point Load Index 15 Laboratory testing TENSILE TESTS Direct test Brazilian test 16 Laboratory testing Brazilian Test Length of Sample (l) = R > 25mm At Failure: p Strength P/ πR l = Qt = Tensile 17 Failure Along The Planes - Mohr- Coulomb Failure Criterion 18 Behavior of Rock • Homogenous: mechanical properties are the same everywhere within the solid body. • Isotropic: the mechanical behaviour is identical in every direction. In fact, in spite of its inhomogeneous structure, these assumptions hold for intact rock, which is free of major structural defects, such joints and bedding planes. • Continuum: mathematically identical mechanical behaviour at all points in a solid. 19 Behavior of Rock 20 Constitutive Behavior of Rock Perfectly Elastic 21 Constitutive Behavior- Idealized Substances 22 Stress • Pre- Mining - Virgin stress Tectonic stress Residual stress and Homeostasis • Induced Stress • Field Stress • Principal Stress 23 Stress Virgin Stress A (m2) 𝐹𝑜𝑟𝑐𝑒 𝑒𝑥𝑒𝑟𝑡𝑒𝑑 = 𝑚𝑔 𝑤𝑒𝑖𝑔ℎ𝑡 𝑊𝑒𝑖𝑔ℎ𝑡 = 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 × 𝑉𝑜𝑙𝑢𝑚𝑒 × 𝑔 𝑊𝑒𝑖𝑔ℎ𝑡 = 𝜌 × 𝐴 × ℎ × 𝑔 Depth = h (m) 𝐹𝑜𝑟𝑐𝑒 𝜌 × (𝐴 × ℎ) × 𝑔 𝑆𝑡𝑟𝑒𝑠𝑠 = = 𝐴𝑟𝑒𝑎 𝐴 ∴ 𝜎𝑣 = 𝜌𝑔ℎ 24 Stress Relationship between vertical and horizontal stress 𝜎ℎ = 𝑘𝜎𝑣 K1 0 —— —— —— — — — — — — — — — —— — — — —— — —— — — — — — — . . — — — — — — — 4 5 — 1000 D ep th(m ) — — 3 500 — . — — — —— — — 2 0 — — — — —— — — — — — — — — — — — 1 1500 2000 2500 — — — .. . . . — . — — . —— — — 3000 — — . . — — — — —— 3500 — — — — —— — — — — —— 25 All A,B a n d C d a ta Im p a la P la ts . C a rle to n v ille K le rk s d o rp R u s te n b u rg P la ts . 6 Stress Tectonic and Residual Stresses 26 Stress Induced and Field Stresses 27 Stress Induced Stress Around A circular Opening 28 Stress Induced Stress Around A circular Opening 29 Stress Principal stress Principal Stress is the largest stress component that exists at a specific point in the rock mass. It has a specific magnitude and direction that is determined by the tectonic forces acting on that rock mass as well as the geological structure that prevails. 30 ASSIGNMENT 31

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