Probabilistic Model for Tunneling Project Using Markov Chain

Actual tunnel advance rates from the Outfall Tunnel of the Boston Harbor Cleanup Project are analyzed. It is shown that states of work and nonwork for the tunnel boring machine can be modeled with a Markov chain. A general probabilistic approach is proposed for developing the cumulative distribution function (CDF) of the total length that can be tunneled in a given time frame. Simulation models are developed to verify the results of the analytical model and also to simulate the distribution for the time necessary to tunnel a certain length (in this case the remainder of the tunnel). The validity of the predictive model is verified using the data from the completed project. The proposed approach may be used for relatively long tunnels with durations extending over several months where the tunneling has already begun and sufficient progress data have been collected. The data from progress up to a certain date may be used for forecasting the length of tunnel that can be constructed in a specified duration.