Barton Q-System Rock Support Calculator
Underground rock engineering & tunneling: Determine the NGI Rock Mass Quality Index ($Q$), equivalent excavation dimension ($D_e$), maximum unsupported span, and permanent support category.
NGI Q-System Classification Parameters
Q-Index Classification & Support Class
Barton Q-Index Value
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Logarithmic index scale
Rock Mass Quality Class
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Descriptive rating
Equivalent Dimension $D_e$
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meters ($Span / ESR$)
Max Unsupported Span
--
meters ($2 \cdot ESR \cdot Q^{0.4}$)
Support Category (1 to 9)
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Grimstad & Barton (2002)
Est. Permanent Roof Load
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MPa (support pressure)
Barton Support Chart ($D_e$ vs $Q$)
The Norwegian Geotechnical Institute (NGI) support chart links $Q$ and $D_e$ to 9 standardized permanent tunnel reinforcement categories.
The Barton NGI Q-System Mechanics
The Barton Q-index is the product of three distinct geotechnical quotients representing block size, inter-block shear strength, and active stress state:
$$Q = \left( \frac{RQD}{J_n} \right) \times \left( \frac{J_r}{J_a} \right) \times \left( \frac{J_w}{SRF} \right)$$
$$D_e = \frac{\text{Span or Height}}{ESR}, \quad S_{\text{max}} = 2 \times ESR \times Q^{0.4}$$
Values of $Q$ span six orders of magnitude (from $0.001$ for exceptionally poor crushed ground up to $1000$ for exceptionally good massive granite). The permanent roof support pressure is estimated via $p_{\text{roof}} = \frac{2 \sqrt{J_n}}{3 J_r} Q^{-1/3}$.
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