A probabilistic design approach to the reinforced fill over a void problem

¹ Civil Engineering Department, Royal Military College of Canada, Kingston, Ontario, Canada
² Civil Engineering Department, Queen’s University, Kingston, Ontario, Canada

^* Corresponding author: bathurst-r@rmc.ca

Abstract

Current design methods for the problem of a thin reinforced fill over a void are based on analytical solutions which are most often solved using an allowable (working) stress deterministic (factor of safety) approach. However, in practice there are uncertainties in the estimate of the input parameter values that appear in the analytical equations. The paper shows how margins of safety for the limit states that appear in the wellknown BS8006 method can be computed using Monte Carlo simulation or an equivalent closed-form solution for reliability index. Reinforcement strain, strength and stiffness limit states are formulated to include input parameter uncertainty and model accuracy. The probabilistic limit state solutions are expressed by simple equations that are easily implemented in an Excel spreadsheet. The paper shows that using a probabilistic approach provides a more nuanced appreciation of the margins of safety for these limit states than deterministic factor of safety approaches. The probabilistic approach demonstrated in this paper is also in alignment with the movement toward reliability theory performance-based design of reinforced soil structures.