A probabilistic study on the geometrical design of gravity retaining walls

The purpose of this study is to introduce a relatively simple method of probabilistic analysis on the dimensions of gravity retaining walls which might lead to a more accurate understanding of failure. Considering the wall geometries in the case of allowable stress design, the probability of wall failure is not clearly defined. The available factor of safety may or may not be sufficient for the designed structure because of the inherent uncertainties in the geotechnical parameters. Moreover, two cases of correlated and uncorrelated geotechnical variables are considered to show how they affect the results.

This study is based on the failure and stability of gravity retaining walls which can be stated in three different modes of sliding, overturning and the foundation-bearing capacity failure. Each of these modes of failure might occur separately or simultaneously with a corresponding probability. Monte Carlo simulation and Taylor series method as two conventional methods of probability analysis are implemented, and the results of an assumed example are calculated and compared together.

The probability analysis of the failure in each mode is calculated separately and a global failure mode is introduced as the occurrence of three modes of sliding, overturning and foundation-bearing capacity failure. Results revealed that the global mode of failure can be used along with the allowable stress design to show the probability of the worst failure condition. Considering the performance and serviceability level of the retaining structure, the global failure mode can be used. Furthermore, the correlation of geotechnical variables seems to be relatively more dominant on the probability of global failure comparing to each mode of failure.

The introduced terminology of global mode of failure can be used to provide more information and confidence about the design of retaining structures. The resulted graphs maintain a thorough insight to choose the right dimensions based on the required level of safety.