π Lesson 17
D3
Understanding In-Situ Stress Regimes
In-situ stress is the natural pressure that rock underground feels from the weight of overlying rock, tectonic forces, and other geological processes β like how water pressure builds deeper in the ocean.
π― Learning Objectives
- β Explain the origin and components of in-situ stress using Mohrβs circle and principal stress notation
- β Analyze borehole breakout and core discing features to infer relative magnitudes of horizontal stresses
- β Apply the Andersonian stress regime classification to interpret regional tectonic setting and its implications for mine layout
- β Calculate vertical stress from overburden density and depth, and estimate horizontal stress magnitudes using empirical relationships (e.g., Terzaghi, Hoek & Brown)
- β Design stress measurement programs (e.g., hydraulic fracturing, overcoring) aligned with ISRM and ASTM standards
π Why This Matters
In-situ stress controls everything from pillar stability and tunnel convergence to the risk of violent rockbursts in deep mines β like at South Africaβs TauTona Mine (3.9 km deep), where unmanaged stress led to fatal seismic events. Misjudging stress magnitude or orientation can cause catastrophic failure, costly delays, or unsafe working conditions. Understanding it isnβt theoretical: itβs the foundation of every ground support decision, blast design, and excavation sequence.
π Core Principles
Stress in intact rock is described by a symmetric 3Γ3 tensor with three orthogonal principal stresses: Οβ (maximum), Οβ (intermediate), and Οβ (minimum). In most shallow to intermediate-depth mines, Οα΅₯ (vertical stress) dominates and approximates Οβ; however, in tectonically active or deep settings, horizontal stresses (Οββββ, Οββα΅’β) may exceed Οα΅₯. Stress regimes are classified using Andersonβs theory: normal (Οα΅₯ > Οββββ > Οββα΅’β), strike-slip (Οββββ > Οα΅₯ > Οββα΅’β), and reverse/thrust (Οββββ > Οββα΅’β > Οα΅₯). The stress ratio (K = Οβ/Οα΅₯) governs lateral confinement and influences failure mode β e.g., K > 1.5 often triggers shear-driven instability in stopes.
π Vertical Stress Estimation
Vertical (overburden) stress is the most reliably estimated component and serves as the baseline for inferring horizontal stresses. It assumes uniform rock density and neglects local topography or erosion β acceptable for preliminary design but refined via measurement in critical zones.
Overburden Vertical Stress
Οα΅₯ = Ξ³ Γ zEstimates vertical stress due to weight of overlying rock column.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| Οα΅₯ | Vertical stress | MPa | Compressive stress acting downward due to overburden |
| Ξ³ | Unit weight of rock | kN/mΒ³ | Average specific weight of overlying strata |
| z | Depth below surface | m | Vertical distance from ground surface to point of interest |
Typical Ranges:
Shallow open pit (<200 m): 3β5 MPa
Deep underground mine (1β3 km): 20β80 MPa
π‘ Worked Example
Problem: Given: average rock unit weight = 26.5 kN/mΒ³, depth below surface = 850 m. Calculate Οα΅₯.
1.
Step 1: Identify knowns β Ξ³ = 26.5 kN/mΒ³, z = 850 m
2.
Step 2: Apply Οα΅₯ = Ξ³ Γ z = 26.5 Γ 850 = 22,525 kPa = 22.5 MPa
3.
Step 3: Compare to typical range for 850 m depth (20β25 MPa); result falls within expected bounds.
Answer:
The vertical stress is 22.5 MPa, which falls within the safe and typical range of 20β25 MPa for this depth in competent crystalline rock.
ποΈ Real-World Application
At the Creighton Mine (Vale, Sudbury, Canada, 2.5 km depth), in-situ stress mapping revealed Οββββ β 2.1 Γ Οα΅₯ due to Paleoproterozoic compressional tectonics. This reversed stress regime (Οββββ > Οββα΅’β > Οα΅₯) explained pervasive shear fracturing along NW-striking faults and guided stope orientation β long-axis aligned NβS to minimize exposure to Οββββ. Hydraulic fracturing tests confirmed minimum horizontal stress (Οββα΅’β) at ~1.4 Γ Οα΅₯, enabling calibrated numerical models that reduced rockburst frequency by 40% post-implementation.
π§ Interactive Calculator
π§ Open Mine Ground Control & Rock Mechanics Calculatorπ Case Connection
π Underground Copper Mine Pillar Recovery Optimization
Post-extraction pillar instability threatening surface infrastructure