Company: Southwest Research Institute (SwRI)
Contracting Agent: Defense Special Weapons Agency (DSWA)

Purpose: To develop probabilistic structural analysis methods and computational tools to explore the effect of problem uncertainties on the survivability/vulnerability of underground tunnels subject to stress wave loading.

Background: Prior to this project, probabilistic analyses of tunnels were made using Monte Carlo simulation. Due to the inefficiency of the Monte Carlo method, only analytical or very simple numerical tunnel models could be employed. However, it has been well established by the DSWA geomechanics community that predicting tunnel response to highly dynamic loading requires accurate and sophisticated numerical models, which in turn require substantial computational resources. Thus, methods far more efficient than Monte Carlo are required.

Summary: A major advance in the state of the art was made by enabling probabilistic calculations to operate on sophisticated numerical tunnel deformation/damage models in an efficient manner. SwRI enhanced and integrated several advanced probabilistic analysis methods with a transient dynamic finite element program. Probabilistic analyses were performed and validated using simulation on several large-scale complex DSWA generic tunnel targets. The advanced probabilistic methods developed by SwRI were shown to be as accurate as Monte Carlo simulation, but orders of magnitude more efficient.

Several significant advances were made in the probabilistic algorithms to tailor their use for underground tunnel simulation: a capability for computing efficiently the confidence bounds on the calculated probability of failure due to random and systematic errors; a capability for handling non-normal correlated random variables; a new method for performing sensitivity analysis to assess the impact of changing the mean, standard deviation, or distribution type for any input random variable; and a methodology for treating the estimated coefficients in the finite element constitutive model as random variables.

Key Publications:

Thacker, B. H., and L.E. Schwer, P.E. Senseny, "Computational Model Comparisons with Static and Dynamic Experiments of Tunnels in Limestone," Proceedings of the 1993 ASME Winter Annual Meeting, 1995.

Thacker, B.H. and P.E. Senseny, "Probabilistic Structural Analysis of Deep Tunnels,", AMD-Vol. 134, Probabilistic Method in Geomechanics, A.F. Fossum (ed.), ASME, Scottsdale, Arizona, 1992.

Riha, D.S., and B.H. Thacker, J.D. Osnes, "Probabilistic Analysis of Deep Tunnels Involving Explicit Dynamic Finite Element Calculations, AMD-Vol. 134, Probabilistic Method in Geomechanics, A.F. Fossum (ed.), ASME, Scottsdale, Arizona, 1992.

Torng, T.Y. and B.H. Thacker, "Confidence Bounds Assessment for Probabilistic Structural Reliability Analysis, Proceedings of the 33rd SDM Conference, Paper No. AIAA-92-2409, Dallas, Texas, 1992.