TBM Calculations

How to Calculate TBM Cutter Wear, Hydraulic Power, and Plate Yield: Core Tunnel Boring Formulas

Work the five core tunnel boring equipment formulas in real units, from disc cutter wear rate and hydraulic power load to plate yield and spare cutter buffers, each with a fully worked example.

Five calculations carry most of the engineering weight in tunnel boring and heavy civil equipment work: disc cutter wear rate, hydraulic power load, steel plate yield, segment handling capacity, and the spare cutter buffer that ties consumption to procurement. Every input comes from documents you already hold, shift reports, PLC trend logs, mill test certificates, and nesting plans, so the real failure modes are unit errors and bad averaging. This guide works each formula in SI units against one consistent example: a 6.6 m diameter EPB machine advancing 18 m per day, with a cutterhead fabricated from 80 mm S690 quenched and tempered plate. Pricing and benchmark targets are covered in separate guides; this one is strictly about running the math.

Disc cutter wear rate is usually reported as excavated volume per cutter. Face area A = (π/4) × D², so a 6.6 m machine cuts 34.2 square meters per meter of advance. A 1,000 m drive excavates 34,200 cubic meters; if logs show 190 cutters consumed, wear rate = 34,200 / 190 = 180 cubic meters per cutter. Rolling distance is more diagnostic: track life in km = 2 × π × track radius × RPM × boring minutes / 1,000. A 17 inch (432 mm) disc survives 300 to 600 km in abrasive granite with CAI above 4, and 800 km or more in soft limestone. The Disc Cutter Wear Rate calculator runs both conventions and treats gauge positions, which wear 1.5 to 2 times faster, separately.

Hydraulic power load uses P (kW) = Q (L/min) × p (bar) / 600, applied circuit by circuit. A screw conveyor motor drawing 220 L/min at 280 bar absorbs 220 × 280 / 600 = 102.7 kW. Six thrust and drive pumps at 250 L/min and 350 bar deliver 6 × 145.8 = 875 kW of hydraulic power; divide by 0.85 pump efficiency and 0.95 motor efficiency and electrical demand becomes 1,083 kW, which is what your substation or genset must actually supply. US spec sheets in gpm and psi use P (hp) = gpm × psi / 1,714, and mixing the two constants is the most common sizing error in this category. The Hydraulic Power Load calculator accepts either unit system.

Steel plate yield is net part mass divided by gross purchased mass, times 100. A cutterhead spoke and rib package needs 21.4 t of finished parts. Plasma cutting 80 mm plate leaves a 7 to 8 mm kerf, and you lose 10 to 15 mm of edge margin plus web spacing between parts, so a realistic nest lands near 74 percent: gross buy = 21.4 / 0.74 = 28.9 t. On standard 2,500 × 6,000 × 80 mm plates at 9.42 t each, that is four plates with one usable remnant. The Steel Plate Yield calculator computes nest efficiency from the part list and plate size, and each point of yield recovered cuts buy weight by roughly 0.4 t on a job this size.

Segment handling capacity is a cycle time calculation: segments per shift = (shift minutes × availability) / cycle time per segment. With a 7 minute erector cycle, a 5 plus 1 ring takes 42 minutes to build plus 8 minutes of regrip, so 50 minutes per 1.5 m ring. Hitting 18 m per day means 12 rings and 72 segments moving through the whole chain, gantry crane, segment car, feeder, and erector, each sustaining 3 segments per hour. Check every lift: an 8.5 t segment plus a 1.2 t vacuum lifter with a 25 percent dynamic allowance needs 12.1 t of hook capacity. The Segment Handling Capacity calculator identifies which link in the chain is the bottleneck.

The spare cutter buffer converts wear rate into an order policy. Daily consumption = (advance rate × face area) / wear rate = (18 × 34.2) / 180 = 3.4 cutters per day. With a 28 day replenishment lead time, cycle stock is 3.4 × 28 = 96 cutters. Add safety stock = z × sigma × the square root of lead time; with a daily demand standard deviation of 1.2 cutters and a 95 percent service level (z = 1.65), that is 1.65 × 1.2 × 5.29 = 10.5, so hold 107 on site at reorder. The Spare Cutter Buffer calculator runs the same logic per cutter position, since gauge discs turn over roughly three times faster than center discs.

Two habits keep these numbers honest. First, recalibrate inputs on a schedule: wear rates measured over the first 200 m of a drive routinely miss the long run average by 30 to 50 percent as ground conditions shift, so rerun the Disc Cutter Wear Rate and Spare Cutter Buffer calculations every 250 m. Second, cross check independent methods: volume per cutter and rolling distance should agree within 15 percent, and hydraulic power summed by circuit should match installed pump nameplate data within 10 percent. The same discipline extends to weld and site estimates, which the Weld Inspection Load and Field Commissioning Hours calculators handle with identical input and check logic.

Published 2026-07-02.