Rock Mechanics
Learning Objectives
- Describe the state of stress in rock masses.
- Differentiate between intact rock and rock mass properties.
- Apply Mohr-Coulomb and Hoek-Brown failure criteria to predict rock failure.
- Utilize empirical rock mass classification systems (RMR and Q-System).
- Understand common tunneling methods and their applications.
State of Stress in Rock Mass
In-situ stresses govern rock mass behavior during excavation.
Before excavation, rock is subjected to natural in-situ stresses:
Types of In-Situ Stresses
- Vertical Stress (): Primarily due to the weight of the overlying rock (overburden). , where is the unit weight and is depth.
- Horizontal Stress (): More complex, influenced by Poisson's ratio effect, tectonic history, and topography. Often quantified by the lateral earth pressure coefficient . In rock, can frequently exceed 1.0 (horizontal stress greater than vertical) due to locked-in tectonic stresses.
Rock Strength
The behavior of rock materials under engineering stress.
Rock Mechanics is the theoretical and applied science of the mechanical behavior of rock and rock masses. It is the branch of mechanics concerned with the response of rock to the force fields of its physical environment. A critical distinction in this field is between Intact Rock and the Rock Mass.
Intact Rock
The unfractured, continuous, and uniform blocks of rock material that exist between structural discontinuities. This is what is typically tested in the laboratory (e.g., Uniaxial Compressive Strength or UCS testing on core samples).
Rock Mass
The entire in-situ volume of rock, which includes both the intact rock blocks and all the geological discontinuities (fractures, joints, bedding planes, faults). These discontinuities significantly reduce the overall strength, stiffness, and stability of the mass compared to the intact rock.
Failure Criteria
Interactive Simulation
Interact with the Mohr's Circle simulation to see how major and minor principal stresses affect failure.
Mohr's Circle & Failure Envelope
Stresses (MPa)
Rock Properties
To predict when a rock mass will fail under complex stress states, engineers rely on mathematical failure criteria.
Mohr-Coulomb Criterion
The Mohr-Coulomb criterion is the most widely used linear empirical model for rock failure under shear stress. It is mathematically simple and widely implemented in basic geotechnical software. However, it often overestimates rock strength at high confining pressures because real rock failure envelopes are typically curved, not straight.
Mohr-Coulomb Criterion
A linear empirical model for rock failure under shear stress.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Shear Strength | MPa | |
| Cohesion - The inherent shear strength of the rock when there is zero normal stress clamping it together | MPa | |
| Normal Stress - The stress acting perpendicularly across the potential failure plane, pushing the surfaces together | MPa | |
| Angle of Internal Friction - A measure of the frictional resistance between the rock surfaces sliding past one another | degrees |
Hoek-Brown Criterion
The industry standard for modeling the non-linear failure of highly fractured rock masses.
Unlike Mohr-Coulomb, the Hoek-Brown failure criterion is an empirical, non-linear relationship developed specifically for rock masses. It explicitly accounts for the degree of fracturing (via the Geological Strength Index, GSI) and the quality of the intact rock pieces.
Hoek-Brown Criterion
An empirical, non-linear relationship developed specifically for rock masses.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Major effective principal stress at failure | MPa | |
| Minor effective principal stress at failure | MPa | |
| Uniaxial compressive strength (UCS) of the intact rock material | MPa | |
| Empirical constants derived from the rock type and the Geological Strength Index (GSI) of the rock mass. Intact, massive rock has s = 1 and a = 0.5. Highly crushed, poor-quality rock has s \approx 0. | dimensionless |
Rock Mass Classification
Empirical systems for quantifying the quality of complex geology.
Because it is nearly impossible to mathematically model every single joint in a large rock mass, engineers have developed several empirical classification systems. These systems convert qualitative geological observations into quantitative ratings used for design, particularly for estimating tunnel support requirements.
1. Rock Mass Rating (RMR)
Developed by Z.T. Bieniawski (1973), the Geomechanics Classification or RMR system assigns point ratings (summing from 0 to 100) based on six fundamental parameters:
RMR Parameters
- 1. Intact Rock Strength: Evaluated via UCS or point-load testing. (Max 15 points)
- 2. RQD (Rock Quality Designation): The percentage of intact core pieces longer than 10 cm recovered from a drill run. (Max 20 points)
- 3. Spacing of Discontinuities: How far apart the joints are. (Max 20 points)
- 4. Condition of Discontinuities: Accounts for joint roughness, separation, continuity, weathering, and infilling materials (like weak clay gouge). (Max 30 points)
- 5. Groundwater Conditions: Ranging from completely dry to flowing under high pressure. (Max 15 points)
- 6. Orientation of Discontinuities: A negative adjustment factor applied based on how favorable or unfavorable the strike and dip are relative to the tunnel axis or slope face.
2. Q-System (Barton)
Developed by N. Barton, R. Lien, and J. Lunde (1974) at the Norwegian Geotechnical Institute (NGI), the Q-system is specifically tailored for designing rock support (rockbolts and shotcrete) in tunnels and underground caverns. The values range logarithmically from 0.001 (exceptionally poor) to 1000 (exceptionally good).
Q-System
Rock mass classification system developed by Barton for designing rock support.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Block Size. Represents the relative block size. J_n is the Joint Set Number (e.g., massive rock = 0.5, two joint sets = 4, crushed rock = 20). | dimensionless | |
| Inter-Block Shear Strength. Represents friction. J_r is joint roughness (rough = 3, slickensided = 0.5). J_a is joint alteration or clay filling (tight and clean = 0.75, thick swelling clay = 15). | dimensionless | |
| Active Stress Environment. J_w is the joint water reduction factor (dry = 1.0, high pressure = 0.1). SRF is the Stress Reduction Factor, accounting for loosening loads in shallow tunnels or rock burst potential in deep, highly stressed tunnels. | dimensionless |
Tunneling in Rock
Excavation methods and stability in underground construction.
Stand-Up Time
Common excavation methods include:
Tunnel Excavation Methods
- Drill and Blast (D&B): The traditional, cyclical method used in hard rock. It is highly flexible for changing tunnel shapes and variable ground conditions but involves discontinuous progress (drill, load, blast, ventilate, muck, support).
- Tunnel Boring Machine (TBM): A massive machine providing continuous excavation, often installing pre-cast concrete support segments simultaneously. TBMs are exceptionally fast for long tunnels in relatively uniform, predictable ground but lack flexibility if unexpected fault zones are encountered.
- While Intact Rock is tested in the laboratory, the large-scale behavior of the Rock Mass in the field is governed almost entirely by geological discontinuities (joints, faults, bedding).
- The Mohr-Coulomb criterion is the fundamental linear model describing rock shear strength as a function of inherent cohesion, internal friction, and applied normal stress.
- The non-linear Hoek-Brown criterion is widely used to estimate the rock mass strength based on the intact rock strength and the Geological Strength Index (GSI).
- Empirical classification systems like RMR and the Q-System are essential engineering tools for quantifying complex geological conditions.
- The choice of tunneling method (e.g., Drill & Blast vs. TBM) heavily depends on the expected ground conditions, the required flexibility, and the tunnel's total length.