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Chapter 4 — Rock Mass Properties & The Geological Strength Index (GSI)

4.1 The Generalised Hoek-Brown Failure Criterion (2002 Edition)

For heavily fractured rock masses where individual structural blocks are small relative to the excavation footprint, the rock mass behaves as an isotropic equivalent pseudo-continuum. Hoek, Carranza-Torres, and Corkum (2002) formulated the generalised Hoek-Brown failure envelope:

\[\sigma_1' = \sigma_3' + \sigma_{ci} \left( m_b \frac{\sigma_3'}{\sigma_{ci}} + s \right)^a\]

Where: - \(\sigma_{ci}\) = intact rock uniaxial compressive strength - \(m_b\) = reduced value of the material constant \(m_i\) for the rock mass:

\[m_b = m_i \exp \left( \frac{\text{GSI} - 100}{28 - 14D} \right)\]
  • \(s\) and \(a\) are empirical constants describing rock mass fracturing and interlock:
\[s = \exp \left( \frac{\text{GSI} - 100}{9 - 3D} \right)\]
\[a = \frac{1}{2} + \frac{1}{6} \left( e^{-\text{GSI}/15} - e^{-20/3} \right)\]
  • \(D\) is the disturbance factor (\(0.0 \le D \le 1.0\)) accounting for blast-induced micro-fracturing and stress-relaxation during excavation.

4.2 The Geological Strength Index (GSI) System

The Geological Strength Index (GSI) replaces quantitative classification systems (RMR, Q) that were found to degrade in very poor, weak rock masses (\(RMR < 25\)). GSI relies on two visual geological observations:

  1. Rock Mass Structure (Macro-Scale Interlocking):
  2. Intact or massive: Few widely spaced discontinuities.
  3. Blocky: Well-interlocked cubical blocks formed by three intersecting orthogonal joint sets.
  4. Very blocky: Four or more joint sets creating multi-faceted angular blocks.
  5. Disturbed / folded: Folded, sheared, or faulted rock mass with angular blocks.
  6. Disintegrated: Poorly interlocked, heavily crushed gravel-sized fragments.
  7. Surface Quality of Discontinuities (Joint Wall Condition):
  8. Evaluated from Very Good (rough, unweathered, fresh walls) down to Very Poor (slickensided, soft clay gouge infill).
+-----------------------------------------------------------------------------------------+
|                               GEOLOGICAL STRENGTH INDEX (GSI)                           |
+---------------------+-------------------+---------------------+-------------------------+
| STRUCTURE           | Good Surface Cond | Fair Surface Cond   | Poor / Clayey Condition |
+---------------------+-------------------+---------------------+-------------------------+
| BLOCKY              |   GSI = 60 - 80   |    GSI = 50 - 65    |      GSI = 35 - 50      |
| VERY BLOCKY         |   GSI = 50 - 65   |    GSI = 40 - 55    |      GSI = 25 - 40      |
| DISTURBED / SEAMED  |   GSI = 35 - 50   |    GSI = 25 - 40    |      GSI = 15 - 30      |
| DISINTEGRATED       |   GSI = 20 - 35   |    GSI = 15 - 25    |      GSI < 15           |
+---------------------+-------------------+---------------------+-------------------------+

4.3 Equivalent Mohr-Coulomb Parameters (\(c', \phi'\))

Because most geotechnical numerical software (FLAC, PLAXIS, RS2) requires Mohr-Coulomb parameters, Hoek et al. derived equivalent cohesion (\(c'\)) and friction angle (\(\phi'\)) by fitting linear tangent lines to the non-linear Hoek-Brown curve over an upper stress range \(\sigma_{3,\max}'\):

\[\phi' = \arcsin \left[ \frac{6 a m_b (s + m_b \sigma_{3n}')^{a-1}}{2(1 + a)(2 + a) + 6 a m_b (s + m_b \sigma_{3n}')^{a-1}} \right]\]
\[c' = \frac{\sigma_{ci} \left[ (1 + 2a)s + (1 - a)m_b \sigma_{3n}' \right] (s + m_b \sigma_{3n}')^{a-1}}{(1 + a)(2 + a) \sqrt{1 + \left( 6 a m_b (s + m_b \sigma_{3n}')^{a-1} \right) / \left( (1 + a)(2 + a) \right)}}\]

4.4 Rock Mass Deformation Modulus (\(E_{rm}\))

Estimating the deformation modulus of the rock mass is crucial for calculating tunnel wall convergence and foundation settlement. The Hoek-Diederichs empirical equation (2006) provides:

\[E_{rm} = E_i \left( 0.02 + \frac{1 - D/2}{1 + e^{(60 + 15D - \text{GSI})/11}} \right)\]

Where \(E_i\) is intact rock Young's modulus (\(\text{MPa}\)). If laboratory \(E_i\) is unavailable, it can be approximated from the Modulus Ratio (\(MR\)): \(E_i = MR \cdot \sigma_{ci}\).

4.5 Canonical Terminology

English Term Canonical Vietnamese Translation Definition
Geological Strength Index (GSI) Chỉ số Cường độ Địa chất (GSI) Index (10–100) based on rock structure and joint condition
Disturbance factor \(D\) Hệ số tổn thương do nổ mìn \(D\) Factor (0–1) reducing rock mass strength due to blasting damage
Equivalent continuum Môi trường tựa liên tục tương đương Continuum model representing heavily jointed rock masses
Deformation modulus Mô đun biến dạng khối đá Elastic modulus representing total deformation of rock mass