Rock Mass Classification

VRGS classifies a rock mass in two parts, both kept in the Collections tree:

• A rock material is the intact rock: its UCS, the Hoek-Brown constant mi, its modulus and unit weight. Start from the typical values of a rock type and replace them with test values when you have them. See Rock Materials.
• A geotechnical domain is a rock mass made of one material. You give it the classification inputs, such as block size and RQD, the condition of the discontinuities, water and the Q parameters. It works out RMR89, Q, GSI, the generalised Hoek-Brown parameters, rock mass strength and modulus, and the equivalent Mohr-Coulomb strength, and for a tunnel the Q-system support guidance. See Geotechnical Domains.

Every result is shown as soon as an input changes, in the domain's Results group.

A domain is named, not drawn

A domain is a set of inputs with a name and notes. It is not yet a region on the mesh, so write in its Notes where it is and where its inputs came from.

Typical workflow

1. Add a rock material. Right-click Rock Materials in the Collections tree and choose New from Rock Type and a rock type, or New Custom Material for one of your own. Enter test values for UCS, mi and Ei where you have them, and set Source to say where they came from.
2. Map block size. Run Block Size on the outcrop and read the median Jv over the part of it that forms the domain.
3. Add a domain. Right-click Geotechnical Domains and choose New Geotechnical Domain. Choose its Rock Material.
4. Enter the inputs: Jv and RQD, the RMR89 condition of the discontinuities, the Q parameters, how GSI is to be found, the disturbance D, and whether it is a slope or a tunnel and how high or deep. For a tunnel, give its Span (m) and ESR under Tunnel Support (Q).
5. Read the results in the domain's Results group. Tick Show on Mohr Diagram to see its Hoek-Brown envelope on the Mohr diagram beside the planes and their joint strength.
6. Hand it on: Export Classification (CSV)..., or Add Data Sheet to Report for a data sheet in an open analysis report.

Many domains can be filled from a spreadsheet with Import Field Sheet (CSV)...; see Geotechnical Domains.

A classification is a range

The domain's GSI Spread (default 5) says how sure the GSI is. Every strength and stiffness result is worked out at the GSI and at GSI minus and plus the spread, and shown as value (low to high). Quote the range, not just the middle value.

RQD derived from Jv is labelled (derived from Jv) in the results, the CSV and the data sheet.

How each result is worked out

RQD

The logged RQD (%) when RQD Source is Field (logged), or derived from the domain's Jv when it is Derived from Jv: RQD = 110 − 2.5 Jv, kept between 0 and 100 (Palmström 2005).

RMR89

Basic RMR89 (Bieniawski 1989) is the sum of five ratings: strength + RQD + spacing + condition

• groundwater. It has no adjustment for the orientation of the discontinuities.

Rating	From	Values
Strength	The material's UCS (MPa)	≥250: 15; ≥100: 12; ≥50: 7; ≥25: 4; ≥5: 2; ≥1: 1; else 0
RQD	The RQD used	≥90: 20; ≥75: 17; ≥50: 13; ≥25: 8; else 3
Spacing	Spacing (m)	≥2: 20; ≥0.6: 15; ≥0.2: 10; ≥0.06: 8; else 5
Condition	Persistence, Aperture, Roughness, Infilling, Weathering	Persistence (m) under 1: 6, under 3: 4, under 10: 2, under 20: 1, else 0. Aperture (mm) 0: 6, under 0.1: 5, under 1: 4, under 5: 1, else 0. Roughness 6 / 5 / 3 / 1 / 0, Infilling 6 / 4 / 2 / 2 / 0 and Weathering 6 / 5 / 3 / 1 / 0, in the order of their lists.
Groundwater	Groundwater	Completely dry 15, Damp 10, Wet 7, Dripping 4, Flowing 0

Class: above 80 I Very good, above 60 II Good, above 40 III Fair, above 20 IV Poor, else V Very poor. The RMR89 Ratings row lists the five.

Q

Q = (RQD / Jn) · (Jr / Ja) · (Jw / SRF) (Barton, Lien & Lunde 1974), with RQD taken as no less than 10. The class runs from Exceptionally poor (below 0.01) through Extremely poor, Very poor, Poor (1–4), Fair (4–10), Good, Very good and Extremely good to Exceptionally good (400 and above).

GSI

From GSI Source:

• Chart (your pick) — the Chart GSI you read off the GSI chart.
• From Jv and joint condition — GSI = 1.5 JCond89 + RQD / 2 (Hoek, Carter & Diederichs 2013). JCond89 is the RMR89 condition rating of the domain's inputs, and RQD is the RQD used, logged or derived from Jv.
• From RMR89 — RMR89 with the groundwater rating set to dry (15), less 5 (Hoek 1995).

GSI and its range are kept between 10 and 100.

Hoek-Brown

The generalised Hoek-Brown criterion (Hoek, Carranza-Torres & Corkum 2002), at the GSI and the disturbance factor D:

$$m_b = m_i\,e^{(GSI-100)/(28-14D)},\qquad s = e^{(GSI-100)/(9-3D)},\qquad a = \tfrac12 + \tfrac16\left(e^{-GSI/15} - e^{-20/3}\right).$$

Result	Formula
Rock Mass UCS (MPa)	σci s^a
Global Strength (MPa)	σcm, Hoek et al. (2002), eq. 18
Tensile Strength (MPa)	−s σci / mb (negative: tension)
Erm (MPa)	Ei (0.02 + (1 − D/2) / (1 + e^((60 + 15D − GSI)/11))) (Hoek & Diederichs 2006), with Ei the material's Ei Used
Sigma 3 max (MPa)	The top of the stress range of the fit: for a slope 0.72 σcm (σcm / γH)^−0.91, for a tunnel 0.47 σcm (σcm / γH)^−0.94, with γ the material's unit weight and H the domain's Height or Depth (Hoek et al. 2002, eqs. 20–21)
Cohesion c' (MPa), Friction phi'	The equivalent Mohr-Coulomb strength over σ3 up to σ3max (Hoek et al. 2002, eqs. 13–14)

The Application (Slope or Tunnel) and Height or Depth (m) set only that stress range. The Hoek-Brown envelope on the Mohr diagram is drawn by Balmer's (1952) construction.

Tunnel support from Q

For a domain whose Application is Tunnel, the Q value gives support guidance from the opening's Span (m) and its excavation support ratio ESR, which reflects how safe the opening must be (Barton 2002: 0.8 for underground power stations up to 3–5 for temporary mine openings).

Result	Formula
Max Unsupported Span (m)	2 ESR Q^0.4 (Barton 2002). A span wider than this needs support, and the result says support needed; otherwise self-supporting.
Bolt Length (m)	2 + 0.15 span / ESR (Barton 2002).
Roof Support Pressure (MPa)	P = 2 √Jn Q^(−1/3) / (3 Jr) in kg/cm², converted to MPa (Barton, Lien & Lunde 1974).

These are the equations only. The support categories of the Q support chart — the bolt spacing and shotcrete thickness for each zone of span/ESR against Q — are not drawn; read the chart with the Q value and the equivalent dimension, span / ESR, for the support itself. A slope domain shows none of these.

When a domain cannot be evaluated

The Results group then shows Status: Not evaluated: and the reason. The reasons are that it names no rock material, its material is missing, the material needs a UCS, an mi or a unit weight above zero, the height or depth must be above zero, D must be 0–1, or no equivalent Mohr-Coulomb fit was found over the stress range.

Asking Athos

Athos can read the domains' classification and the sets' statistics through two read-only tools. Ask "What is the GSI of Domain A?" or "Classify the rock mass", and it quotes VRGS's figures with their basis and ranges. It does not make up figures for a domain that could not be evaluated.

References

1. Balmer, G. (1952). A general analytical solution for Mohr's envelope. Proceedings ASTM, 52, 1260–1271.
2. Barton, N., Lien, R., & Lunde, J. (1974). Engineering classification of rock masses for the design of tunnel support. Rock Mechanics, 6, 189–236.
3. Barton, N. (2002). Some new Q-value correlations to assist in site characterisation and tunnel design. International Journal of Rock Mechanics and Mining Sciences, 39, 185–216.
4. Bieniawski, Z. T. (1989). Engineering Rock Mass Classifications. Wiley, New York.
5. Hoek, E. (1995). Support of Underground Excavations in Hard Rock. Balkema, Rotterdam.
6. Hoek, E., Carranza-Torres, C., & Corkum, B. (2002). Hoek-Brown failure criterion — 2002 edition. Proceedings NARMS-TAC, Toronto, 267–273.
7. Hoek, E., Carter, T. G., & Diederichs, M. S. (2013). Quantification of the Geological Strength Index chart. 47th US Rock Mechanics / Geomechanics Symposium, ARMA 13-672.
8. Hoek, E., & Diederichs, M. S. (2006). Empirical estimation of rock mass modulus. International Journal of Rock Mechanics and Mining Sciences, 43, 203–215.
9. Marinos, P., & Hoek, E. (2000). GSI: a geologically friendly tool for rock mass strength estimation. Proceedings GeoEng 2000, Melbourne.
10. Palmström, A. (2005). Measurements of and correlations between block size and rock quality designation (RQD). Tunnelling and Underground Space Technology, 20, 362–377.

See also

• Rock Materials and Geotechnical Domains — every property, with its default.
• Block Size — Jv from the outcrop.
• Mohr Diagram — the Hoek-Brown envelope beside the planes.
• Geomechanics