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Mechanized Tunneling & Underground Civil Engineering, CSM / NTNU Hard-Rock TBM Performance

Hard-Rock TBM Cutterhead Thrust, Torque & Daily Advance

Calculate Total Cutterhead Normal Thrust (MN), Cutterhead Drive Torque (MN·m), Net Boring Rate of Penetration ROP (m/h), and Daily Utilization-Adjusted Tunnel Advance (m/d).

Entering 260 MPa quartzite cuts TBM disc penetration from 7.2 to 2.4 mm/rev while abrasive cutter changes slash shift utilization to 28%—collapsing advance from 32.7 to 7.3 m/day!

Under the **Colorado School of Mines (`CSM`) and NTNU Mechanized Tunneling Models**, a **Hard-Rock Tunnel Boring Machine (`TBM`)** (`Bore Diameter D` m dressed with `N_c` `17`-inch or `19`-inch constant-cross-section disc cutters at Normal Force `F_n` kN/cutter and Rolling-to-Normal Drag Coefficient `RC = F_r / F_n`) requires **Total Propel Cylinder Thrust `T_{head} = (N_c * F_n) / 1,000`** (`MN`, plus shield/gripper friction) and **Cutterhead Torque `M_{head} = (N_c * (F_n * RC) * (0.30 * D)) / 1,000`** (`MN·m`, where **`r_{eff} ~= 0.30 * D`** is the cutter-array weighted moment arm)! Yet tunnel schedules hinge on separating **Instantaneous Net Boring ROP `I_{ROP} = (p * RPM * 60) / 1,000`** (`m/h` at Penetration `p` mm/rev) from **Daily Advance Rate `AR = I_{ROP} * 24 * (U / 100)`** (`m/day`), where **Machine Utilization `U` (`30%–50%`)** deducts ring-build/regrip strokes, muck train swaps, probe drilling, and worn cutter-ring changes!

Verify on a `6.8` m Metro Rail Hard-Rock TBM in Gneiss—Excavation_Diameter `D` = 6.80 m (B2), `17`-inch_Disc_Cutters `N_c` = 44 (B3), Normal_Thrust_per_Cutter `F_n` = 245 kN (B4), Rolling_Coefficient `RC` = 0.085 (B5), Penetration `p` = 7.20 mm/rev (B6), Cutterhead_Speed = 7.50 RPM (B7), and Daily_Utilization `U` = 42.0% (B8): Total Cutterhead Thrust equals `10.78` MN (E2), Cutterhead Torque equals `1.87` MN·m (E3), Net Boring `ROP` equals `3.24` m/h (E4), and Daily Tunnel Advance equals **`32.7` m/day** (E5)!

CSM / NTNU Hard-Rock TBM KPI (D=6.8 m, 44 Cutters, 7.5 RPM)FormulaVerified Output
Total Cutterhead Thrust (MN)(Cutter_Count_N * Normal_Fn_kN) / 100010.78 MN (12.54 MN @ 285 kN max ring load)
Cutterhead Drive Torque (MN·m)(N * (Fn * RC) * (0.30 * Diam_D)) / 10001.87 MN·m (1.41 MN·m shallow glazed cut)
Instantaneous Net ROP (m/h)(Penetration_mm_rev * RPM * 60) / 10003.24 m/h (1.08 m/h in 260 MPa quartzite)
Daily Tunnel Advance (m/day)Net_ROP_m_hr * 24 * (Utilization_Pct / 100)32.7 m/d (7.3 m/d schedule stall!)

CSM / NTNU Hard-Rock TBM Disc Thrust, Moment Arm & Utilization Advance Formula

Validate `Bore_Diameter D` in `[2.5, 16.0]` m, `Cutter_Count N_c` in `[15, 110]`, `Cutter_Normal_Load F_n` in `[80, 350]` kN, `Rolling_Drag RC` in `[0.03, 0.20]`, `Penetration p` in `[0.5, 20.0]` mm/rev, `Cutterhead_RPM` in `[1.5, 15.0]`, and `Utilization U` in `[5, 75]`%!

=LET(db_m, B2, nc_i, B3, fn_k, B4, rc_f, B5, pn_m, B6, nr_p, B7, ut_p, B8, rp_h, (pn_m * nr_p * 60) / 1000, IF(OR(db_m < 2.5, db_m > 16, nc_i < 15, nc_i > 110, fn_k < 80, fn_k > 350, rc_f < 0.03, rc_f > 0.2, pn_m < 0.5, pn_m > 20, nr_p < 1.5, nr_p > 15, ut_p < 5, ut_p > 75), "Invalid TBM Input", ROUND(rp_h * 24 * (ut_p / 100), 1)))

Massive Quartzite Dyke (`F_n = 285` kN, `p = 2.4` mm/rev, `U = 28%`) Schedule Double-Hit Check

Bore into `260` MPa high-quartz dyke rock: even jacking `19`-inch cutter thrust up to `B4 = 285` kN (`12.54` MN head thrust in E2), shallow `B6 = 2.40` mm/rev indentation (`RC` drops to `B5 = 0.055`, Torque E3 = `1.41` MN·m) plus abrasive ring replacements (`B8 = 28%` utilization) slashes Net ROP E4 to `1.08` m/h and **collapses Daily Advance E5 `4.5x` to `7.3` m/day**!

=IF(ISTEXT(E5), E5, ROUND((B3 * (B4 * B5) * (0.3 * B2)) / 1000, 2))

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