Tunnel Face Pressure (EPB/Slurry)
Estimate the face support pressure needed to stabilize the excavation front of a mechanized tunnel, p = K·γ·H, from the earth pressure coefficient K (at rest K₀ ≈ 1−sinφ, or active), the soil unit weight γ (kN/m³) and the axis depth H (m). In closed-face TBMs (EPB or slurry), the pressurized chamber must balance the earth and water pressure at the front, avoiding both collapse (insufficient pressure) and blow-out (excessive pressure). Face pressure is the most critical operational parameter of a TBM, adjusted in real time per cover, water table and soil type. This gives the earth component; total pressure adds hydrostatic water pressure and a safety margin. Enter the earth pressure coefficient, unit weight and depth.
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Tunnel face pressure (EPB/Slurry)
In a closed-face tunnel boring machine — either EPB (Earth Pressure Balance, which uses the pressurised excavated soil itself as support) or slurry (which uses a bentonite suspension) — the pressurised chamber at the front of the machine has to balance the pressure that ground and water exert on the excavation face. The earth component of that support pressure is estimated as p = K·γ·H, from the earth pressure coefficient K (at rest, K₀ ≈ 1 − sin φ; in the active condition, smaller), the soil unit weight γ and the axis depth H. Face pressure is the most critical operational parameter of a TBM, since it steers between two cliffs: too little pressure and the face collapses — soil flows into the chamber, opening a cavity that propagates up to the surface as a sudden settlement (or even a hole swallowing the street); too much pressure and blow-out occurs — the ground heaves, slurry escapes to the surface or into neighbouring excavations, and the face loses confinement. The operator therefore trims the pressure in real time, ring by ring, as cover, water table and soil type vary along the alignment. This calculation yields only the earth share; the total design pressure adds the hydrostatic pressure of groundwater plus an operational safety margin. Getting face pressure right is what separates a successful urban tunnel from a collapse in the headlines. Enter the earth pressure coefficient, the unit weight and the depth.
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TBM Advance Rate
Calculate a tunnel boring machine's daily advance, advance = PR·U·h, from the instantaneous penetration rate PR (m/h, advance while actively boring), utilization U (0-1, the fraction of time actually boring) and operating hours per day h. The distinction between penetration and utilization is central: penetration depends on geology and cutterhead thrust/torque, but utilization — typically only 30-50% — is limited by ring building, cutter changes, maintenance, muck removal and downtime. Real advance is far below nominal penetration, and improving utilization often pays more than increasing penetration. Enter the penetration rate, utilization and hours per day.
Tunnel Support Pressure
Calculate the support pressure a tunnel lining must resist, pv = γ·Hp, from the rock mass unit weight γ (kN/m³) and the rock load height Hp (m) — typically from Terzaghi's method or geomechanical classifications (RMR, Q-system). Support pressure is the vertical stress the loosened rock zone exerts on the support (shotcrete, steel sets, final lining), and it drives the structural design of the lining. In shallow tunnels the load may be the full overburden; in deep tunnels, arching reduces it to a fraction. Estimating it correctly is decisive: underestimating leads to collapse, overestimating raises cost. Enter the unit weight and the rock load height.
Tunnel Volume Loss
Calculate the volume loss of a tunnel excavation, VL = Vs ÷ (π·D²/4)·100, the percentage ratio between the settlement trough volume per metre Vs (m³/m) and the excavated cross-section area (from diameter D). Volume loss quantifies how much soil 'disappeared' relative to the theoretical tunnel volume — caused by face relaxation, overexcavation, tail-gap closure behind the TBM shield and consolidation. It is the key control parameter for urban excavation: well-run EPB/slurry TBMs achieve 0.5-1.5% in soils; values above 2-3% indicate problems and excessive settlement. Enter the trough volume and the tunnel diameter.
Terzaghi Rock Load Height
Estimate the rock load height over a tunnel crown by Terzaghi's classic method, Hp = Cf·(B + Ht), from the rock load factor Cf (depending on mass quality — ~0 for intact rock to >2 for heavily fractured or swelling rock), the width B and the height Ht of the excavation. Hp represents the loosened rock zone above the tunnel that effectively loads the support — Terzaghi proposed that, due to arching in the mass, only a fraction of the total overburden acts on the lining. This loosening-load model is the historic basis for rock tunnel support design. Multiplying Hp by the unit weight gives the support pressure. Enter the load factor, width and height.
Peck Settlement Trough Width
Calculate the trough-width parameter of the surface settlement induced by tunnelling, i = K·z₀, by Peck's method, from the trough-width parameter K (~0.5 for clays, ~0.25-0.35 for sands) and the tunnel axis depth z₀. The surface settlement from ground loss follows a Gaussian (inverted bell) curve, and i is its standard deviation — the horizontal distance from the tunnel axis to the inflection point, defining the trough width. Larger i means a wider, gentler trough (clays); smaller means narrower and deeper (sands). This parameter is essential to predict damage to nearby buildings in urban tunnels. Enter the K parameter and the tunnel depth.
Tunnel Convergence
Calculate a tunnel's convergence — the relative radial deformation of the excavation, ε = (u ÷ r)·100 — from the radial displacement u (the inward movement of the walls toward the center, measured by extensometers or total station) and the excavation radius r, in the same unit. Convergence is the primary monitoring indicator in NATM (New Austrian Tunnelling Method): it measures how much the rock mass deforms after excavation, reflecting stress mobilization and support effectiveness. Low, stabilized convergence indicates a stable mass; high, growing or accelerating convergence signals squeezing, instability or insufficient support, requiring immediate reinforcement. Enter the radial displacement and the tunnel radius.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.