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.
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TBM advance rate
The daily advance of a tunnel boring machine (TBM) is advance = PR·U·h, and the formula hides the most important lesson in mechanised tunnelling: the difference between penetration and utilisation. The penetration rate PR (m/h) is the speed at which the machine moves forward while it is actually cutting — it depends on the geology (rock strength) and on the machine (cutterhead thrust and torque, condition of the discs). It is the number that looks impressive in brochures. But utilisation U — the fraction of time the machine really excavates — typically runs at only 30% to 50%, and it governs the real schedule. The rest of the time the TBM sits idle: erecting lining rings (in shielded machines, every stroke requires stopping to build a ring of segments), replacing worn cutter discs (an intervention inside the chamber, under pressure, slow and hazardous), under maintenance, waiting on muck removal logistics, or facing geological surprises (fault zones, water inflow, boulders). Real advance therefore falls far below what nominal penetration would suggest — a machine penetrating at 3 m/h does not achieve 72 m per day, but perhaps 20 to 30. The practical consequence is counter-intuitive and valuable: improving utilisation (faster ring building, predictive maintenance, better logistics) usually buys more advance per day than raising raw penetration. Managing downtime is the true productivity game in TBM tunnelling. Enter the penetration rate, the utilisation and the operating hours per day.
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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.
Annular Grout Volume (Backfill)
Calculate the theoretical annular backfill grout volume per lining ring of a mechanized tunnel, V = (π/4)·(De² − Di²)·L, from the excavation diameter De (the TBM cutterhead cutting diameter), the segment ring outer diameter Di and the ring length L. Behind the TBM shield an annular gap forms (between excavated ground and lining, from overcut and shield taper) that must be filled immediately with grout injected through the tail. This filling is essential: it prevents ground relaxation (reducing volume loss and surface settlement), locks the ring in place and ensures uniform ground-lining contact. Actual injected volume exceeds theoretical (factor 1.1-1.5). Enter the excavation and ring diameters and the ring length.
Advance per Blast (Pull)
Calculate the effective advance per blast (pull) in drill-and-blast tunnelling, advance = L·η, from the drilled hole length L (m) and the blast efficiency η (0-1). Not all drilled depth converts to advance: part is lost because the hole bottoms do not always break fully, leaving a 'socket'. Typical efficiency is 85-95% — depending on the blast pattern, rock type and execution. Advance per blast, times the cycles per day, sets the rock face productivity. Maximizing it reduces cycles and schedule, but very long holes lose drilling accuracy and efficiency. Enter the drilled length and the blast efficiency.
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.
Welding Travel Speed
Compute the welding travel speed (arc advance) by dividing the bead length by the time taken, in mm/min. It is a fundamental parameter that, together with voltage and current, defines the heat input: welding too fast produces narrow beads with little penetration; too slow overheats and deposits excess material. Enter the bead length and the welding time.
Falling-Rate Drying Period Time
Computes the duration of the falling-rate drying period under the model where the rate drops linearly with free moisture starting at the critical moisture: t = m_s × X_c ÷ (A × N_c) × ln(X_c ÷ X₂). Moisture contents go in as free moisture on a dry basis, that is, with the equilibrium moisture already subtracted, which is why X₂ can never be zero — drying down to equilibrium would take infinite time, exactly what the logarithm says. Compared with the constant-rate period this is the expensive stretch: every kilogram of water removed costs far more time than in the previous stretch, because internal transport now sets the pace. Enter the dry solid mass, the critical moisture, the final free moisture, the exposed area and the constant rate at the critical moisture.
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.