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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 797953, 8 pages
Research Article

Planning Tunnel Construction Using Markov Chain Monte Carlo (MCMC)

1Departamento de Ingeniería en Minas, Universidad de Santiago de Chile, Santiago, Chile
2Departamento de Engenharia de Minas, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil

Received 10 April 2015; Revised 9 June 2015; Accepted 14 June 2015

Academic Editor: Zdeněk Kala

Copyright © 2015 Juan P. Vargas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Tunnels, drifts, drives, and other types of underground excavation are very common in mining as well as in the construction of roads, railways, dams, and other civil engineering projects. Planning is essential to the success of tunnel excavation, and construction time is one of the most important factors to be taken into account. This paper proposes a simulation algorithm based on a stochastic numerical method, the Markov chain Monte Carlo method, that can provide the best estimate of the opening excavation times for the classic method of drilling and blasting. Taking account of technical considerations that affect the tunnel excavation cycle, the simulation is developed through a computational algorithm. Using the Markov chain Monte Carlo method, the unit operations involved in the underground excavation cycle are identified and assigned probability distributions that, with random number input, make it possible to simulate the total excavation time. The results obtained with this method are compared with a real case of tunneling excavation. By incorporating variability in the planning, it is possible to determine with greater certainty the ranges over which the execution times of the unit operations fluctuate. In addition, the financial risks associated with planning errors can be reduced and the exploitation of resources maximized.