Barton Q-System Rock Support Calculator

Geotechnical & tunneling mechanics: Calculate the NGI Q-index, equivalent dimension (De), maximum unsupported span, rock bolt spacing, and shotcrete lining.

NGI Q-System Parameters

Rock Quality Designation RQD (%): Core pieces >10 cm (min value 10)

Joint Set Number Jn:

Joint Roughness Jr:

Joint Alteration Ja:

Joint Water Reduction Jw:

Stress Reduction Factor SRF:

Excavation Span or Height (m): Tunnel width or cavern height

Excavation Support Ratio ESR:

Rock Mass Classification & Support Design

NGI Tunneling Quality Index Q

Equivalent Dimension (De)

Span / ESR

Max Unsupported Span

2 · ESR · Q^0.44

Roof Support Pressure

Empirical rock mass load

Recommended Bolt Spacing

Pattern rock bolting

Shotcrete Requirement

Fiber-reinforced concrete

Recommended Tools & Equipment

Tested hardware and components for high reliability

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Frequently Asked Questions

What is the physical meaning of the three quotients in Barton's Q-formula?

Barton's Q formula multiplies three distinct physical ratios: (RQD/Jn) measures relative block size; (Jr/Ja) represents inter-block shear strength and joint friction angle; and (Jw/SRF) represents the active stress quotient, accounting for pore water pressure and excavation induced overstressing.

How does the Excavation Support Ratio (ESR) affect tunnel support?

The ESR reflects the acceptable degree of risk and design working life. For temporary mining stopes where personnel access is minimal, ESR = 3 to 5 (requiring lighter support). For major civil road tunnels, railway systems, or nuclear underground installations, ESR = 0.8 to 1.0, mandating heavy permanent reinforcement.

Can the Q-system be used to estimate rock bolt length?

Yes. In empirical NGI guidelines, rock bolt length L in a tunnel roof of span B is approximated as L = 2 + 0.15 * (B / ESR). Wall bolt lengths typically scale as L = 2 + 0.15 * (H / ESR), where H is the excavation sidewall height.