Confined Flow into a Tunnel during Progressive Drilling: An Analytical Solution

A convolution integral is developed to evaluate transient, drilling speed-dependent discharge rates into a tunnel gradually excavated in a homogeneous infinite aquifer. Comparison with the classical instantaneous-drilling evaluation commonly used in practice reveals drastically reduced early-time discharge rates, higher maximum rates, and similar long-term rates. Dimensionless-type curves are provided to help assess total discharge sensitivity to drilling time and predict safer maximum flow rates.