Rock Mechanics

A laboratory core can measure intact uniaxial compressive strength (UCS), deformation and failure behavior without sampling the joint that controls a tunnel wedge. Joint persistence, orientation, roughness, infill and water pressure can govern sliding or block release. Conversely, massive rock under high stress may fail through intact material. Neither a rock name nor high UCS establishes excavation stability.

Use a mapped discontinuity model for a persistent weak plane; use a suitable equivalent rock-mass model only when its scale and structure assumptions fit. Peak and residual strength, sample disturbance and the tested stress range must match the proposed analysis.

The estimate does not determine principal directions or horizontal stresses. Tectonic history, erosion, topography, anisotropy and excavation modify the stress field. The ratio $k=\sigma_h/\sigma_v$ can exceed one in rock; it is not a universal material constant. Measure or justify the stress field rather than infer it from depth alone. Excavation stresses differ from the pre-excavation field.

For an isotropic Mohr–Coulomb material in compression, the circle lies below the shear envelope when $R\lt C\sin\phi'+c'\cos\phi'$, touches it at equality, and extends beyond it when the inequality reverses. Equivalent triaxial compression at failure satisfies $\sigma_{1f}'=[\sigma_3'(1+\sin\phi')+2c'\cos\phi']/(1-\sin\phi')$.

Subtracting uniform pressure translates the circle left by $u$ and leaves its radius unchanged. Equal principal stresses give a visible point with zero shear. If $\sigma_3'\lt0$, opening and tensile strength need a separate model. Checking only the maximum-shear point is insufficient: the envelope is inclined. For an existing joint, check the stress at its actual orientation rather than assume the weakest theoretical plane exists.

At zero confinement the model gives $\sigma_{cm}=\sigma_{ci}s^a$. This need not equal intact UCS. The intact limit has $s=1$, $a=0.5$ and $m_b=m_i$. A dominant persistent weak plane needs explicit discontinuity analysis; do not hide directional sliding in a single isotropic strength. Equivalent Mohr–Coulomb parameters depend on the selected confinement interval. The square-root teaching curve below uses prescribed constants, not a mapped site.

The RMR89 basic rating sums five ratings: intact strength (maximum 15), RQD (20), discontinuity spacing (20), discontinuity condition (30) and groundwater (15). The discontinuity-orientation adjustment depends on the application and can reduce the basic rating. State the version, observations and adjustment; do not mix tables from different versions. UCS is a material input, while the final rating characterizes the investigated rock mass. A rating is not a computed factor of safety.

The three Q quotients represent jointing/block size, joint friction, and water/stress conditions. Support assessment needs both Q and equivalent dimension, with weakness-zone geometry and the handbook's limitations. Preserve parameter ranges rather than conceal spatial variability in one average. Q alone cannot specify bolt spacing or shotcrete thickness. Its stress rating can depend on intact strength even though UCS is absent from the displayed product.

Drill and blast is cyclic and permits changes in profile and excavation sequence. A TBM can achieve sustained mechanical excavation, but performance depends on abrasivity, strength, discontinuities, water, access, machine type and logistics. Not every TBM installs segments; an open hard-rock machine differs from a shielded system.

Deep massive rock warrants stress and brittle-failure investigation, not a guaranteed rockburst prediction. Weak ground warrants convergence and water assessment, not an assumption of inevitable crushing. Support selection considers load, displacement, energy demand, installation timing and system connections. Energy-absorbing support or yielding elements may be appropriate, but no generic bolt or method guarantees containment.

Observational tunneling uses a planned excavation/support sequence, monitoring, trigger criteria and predesigned responses. Control deformation within design limits; do not wait for all movement to cease before every final lining or prescribe NATM from a rock name. Reassess when mapping, pressure or convergence departs from the design assumptions.

• USACE, Rock Foundations, EM 1110-1-2908 (1994): discontinuities, testing and rock foundation mechanics.
• FHWA, Technical Manual for Design and Construction of Road Tunnels—Civil Elements, NHI-09-010 (2009), chapters 6 and 8: rock classification, excavation and difficult ground.
• Hoek, Carranza-Torres and Corkum, Hoek–Brown Failure Criterion—2002 Edition: equations, disturbance and equivalent parameters.
• NGI, Using the Q-system: Rock Mass Classification and Support Design (April 2025): logging conventions, ratings, equivalent dimension and limitations.