High-Pressure Tunnel & Shaft Rule-of-Thumb Calculator

This calculator evaluates the two Norwegian preliminary screening checks from your reference: the earlier depth criterion h > c × H and the later rock-cover criterion L > (γw × H) / (γr × cosβ). Inputs stay on the left, the hosted reference image sits on the right, and the calculation breakdown updates automatically as you type. The constant c can be auto-derived from β or overridden manually in custom mode.

Criterion 1 · First Norwegian design criterion
h > c × H
Criterion 2 · Bergh-Christensen & Dannevig rule of thumb
L > (γw × H) / (γr × cosβ)

Input Parameters

Enter the geometric and material values used in the two rule-of-thumb checks.

1 Criterion 1 · Depth criterion

Formula: h > c × H
Water head at the point studied.
Vertical depth of the point studied.

2 Criterion 2 · Rock-cover criterion

Formula: L > (γw × H) / (γr × cosβ)
Shortest distance from the surface to the point studied.
Angle in degrees. The cosine uses degrees converted to radians.
Use any consistent basis. Only the γw/γr ratio matters.
Keep the same basis as γw.
These equations are rule-of-thumb checks for preliminary assessment. They should not replace detailed geological review, leakage assessment, or project-specific design verification.

Reference Geometry

The figure on the right is loaded from an image file in the same hosting folder as this page.

Reference geometry for the high-pressure tunnel and shaft screening checks.
Reference figure for visual context only. The checks below are calculated from the entered values, including automatic or custom selection of c.
H
Static water headHead at the point studied, measured vertically in metres.
h
Vertical depthDirect vertical depth from the surface to the studied point.
L
Shortest distanceShortest surface-to-point distance through rock cover.
β
Valley inclinationAverage valley-side inclination used in the cosine term and for auto c selection.
α
Shaft inclinationShown in the reference figure for geometry context; not used directly in these two checks.
c
Criterion 1 constantAuto mode uses β-based historic guidance; custom mode lets you override it manually.

Calculations & Interpretation

The section below shows the substituted equations, required minimum values, margins, and pass/fail outcome for each criterion.

Overall Screening Result
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Values update automatically as you type.
Criterion 1
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h compared with c × H
Criterion 2
—
L compared with required minimum

Criterion 1 · First Norwegian design criterion

Requirement: h > c × H
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Required minimum depth
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Margin
—
Check ratio
—
Entered depth
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    Criterion 2 · Valley-side inclination included

    Requirement: L > (γw × H) / (γr × cosβ)
    —
    Required minimum rock cover
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    Margin
    —
    Check ratio
    —
    Entered L
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      Notes: β is entered in degrees. The calculator internally uses cos(β × π / 180). For γw and γr, any consistent density or unit-weight basis may be used because the ratio controls the result. In auto mode, this tool applies c = 0.600 for β ≤ 35°, c = 1.000 for β ≥ 60°, and a linear interpolation between those two reference points for intermediate β values.