Axial Force-Balance Modeling and Field Validation of an EPB Shield During Air-Assisted Excavation in Hard Rock

When an earth pressure balance (EPB) shield operates in hard rock under air-assisted excavation, the conventional face-pressure term for full-chamber EPB operation is no longer directly applicable, while chamber air pressure and cutterhead–rock interaction become important components of the axial load. This study proposes an axial force-balance model for partially filled air-assisted excavation in hard rock. An effective air-pressure action-area coefficient is introduced to account for uncertainty in the air-pressure reaction, while unit-penetration torque, together with cutterhead rotational speed and advance rate, is used to represent the equivalent hard-rock excavation resistance. Field data from a hard-rock section of the Qingdao Metro are used for parameter identification, air-pressure-term ablation, sensitivity analysis, continuous-block validation, and cross-line validation. At the representative condition of χa = 0.75, the left-line model achieves R2 = 0.771, an RMSE of 1158.6 kN, and a correlation coefficient of 0.878 between measured and calculated total thrusts. Removing the air-pressure reaction reduces model accuracy and markedly increases the correlation between the residuals and air pressure, confirming that this term cannot be neglected. Refitting the same model structure to the right line yields R2 = 0.647, whereas direct transfer of the left-line parameters performs poorly. This indicates cross-line applicability of the model structure but condition dependence of its parameters. The proposed model provides a physically constrained framework for interpreting ring-averaged shield thrust and evaluating deviations between measured and calculated thrusts during air-assisted excavation in hard rock.