A simple probabilistic approach for internal stability analysis and design of geosynthetic reinforced soil walls

Richard J. Bathurst

GeoEngineering Centre at Queen’s-RMC, Royal Military College of Canada, Kingston, Ontario, Canada

Geotechnical engineering is moving towards performance-based design which at its core uses reliability-based analysis and design concepts to quantify margins of safety for different limit states in probabilistic terms (or reliability index). This paper explains simple probabilistic analysis and design for internal stability limit states for geosynthetic reinforced soil walls. The general approach uses a closed-form solution for reliability index which is easily implemented in a spreadsheet and thus eliminates the need for Monte Carlo simulation. A novel feature of the formulation is that it includes uncertainty in the choice of nominal values [which is consistent with the notion of level of understanding that appears in the Canadian Highway Bridge Design Code] and the underlying accuracy of the load and resistance models that appear in each limit state equation using bias statistics. Here, bias is the ratio of observed value to predicted value using closed-form solutions for load and resistance found in the literature and design codes. The paper demonstrates how bias statistics for tensile load and pullout model accuracy can be gathered from load measurements recorded from instrumented walls and found in laboratory pullout box test databases. A design example for the case of a geogrid reinforced soil wall is used to demonstrate the general approach and to show how different combinations of load and resistance models with different accuracy expressed in probabilistic terms can have a large influence on design outcomes. The concepts are general and can be applied to any soil-structure interaction problem which can be expressed by a simple linear limit state performance function and for which bias statistics are available. The general approach explained in this paper is a complementary approach to traditional factor of safety methods for internal stability design of reinforced soil walls. The method provides the designer with another tool to make design decisions based on reliability index or equivalently, probability of failure.

References

Bathurst, R.J., Allen, T.M., Miyata, Y., Javankhoshdel, S. and Bozorgzadeh, N. 2019.  Performance-based analysis and design for internal stability of MSE walls. Georisk (on line) (https://doi.org/10.1080/17499518.2019.1602879).

Bathurst, R.J., Lin, P. and Allen, T.M. 2019. Reliability-based design of internal limit states for mechanically stabilized earth walls using geosynthetic reinforcement. Canadian Geotechnical Journal (on line) (https://doi.org/10.1139/cgj-2018-0074)

Bathurst, R.J. and Javankhoshdel, S. 2017. Influence of model type, bias and input parameter variability on reliability analysis for simple limit states in soil-structure interaction problems. Georisk 11(1): 42-54