Entropy-based reliability analysis and design in slope engineering

Abstract

Canada has a wide range of landslide types reflecting the diverse geomorphic and geologic environments in the nation’s landscape. Many civil engineering projects are located on or near sloping ground, and thus are potentially subject to various kinds of slope instability, which often produces extensive property damage and occasionally loss of life. A typical example is the massive landslide occurred on the Nipigon River, north of the town of Nipigon, Ontario in the 1990, which involved an estimated 300,000 cubic meters of soil and extended almost 350m inshore with a maximum width of approximately 290m. The traditional methods for slope stability investigation are reliant on deterministic approaches which involve an overall factor of safety to account for various uncertainties. It is found that critical geotechnical parameters such as shear strength parameters may be regarded as random variables respectively with a probability distribution rather than deterministic values or constants. In this research, an alternative approach of probabilistic reliability method is adopted in slope engineering, which allows for systematic analysis of uncertainties and for their inclusion in evaluating slope performance. The research focuses on entropy-based reliability analysis and design in slope engineering. The four sub topics are: 1. Introducing soil variables field testing by the vane shear test. 2. Proposing an entropy-based distribution free modelling for soil variables. 3. Developing a new reliability analysis method using entropy distributions. 4. Application of approach in the Nipigon slope’s analysis & design. Firstly, the research involves the application of the vane shear test on the Nipigon slope to obtain values of undrained shear strength (Su). Moreover, the research proposes an entropy-based distribution-free method for modeling of soil variables, using the combination of the maximum entropy formalism (MEF) and Akaike information criterion (AIC). The method is applied to generate the unbiased model for soil variables based on optimalorder moments from soil samples. The method can adjust the level of sophistication of the resulting probability as per the nature and quantity of data. Its application on soil data of the slope of the Nipigon River landslide area yields efficient results with the 3rd order being the optimal order representing the quantified information very precisely. Further, the research introduces a new reliability method to conduct a reliability analysis of the Nipigon slope. The approach involves the modification of the first-order reliability method to consider the non-normal variables of the entropy distributions adequately, supported by GEO-Slope software model analysis and response surface method to develop an explicit performance function. The approach developed can incorporate the uncertainties effectively and proficiently. The results imply that the Nipigon slope is hazardous with a probability of failure value touching 40%. The comparison of the proposed modified FORM with the GEO-Slope based Monte Carlo simulation indicated similarities in the results, consequently certifying the efficiency of the proposed algorithm. Ultimately, a reliability-based slope is designed for the Nipigon slope by implementing the proposed methodology. In the first case, pile reinforcement is applied to the failure slope to enhance the stability of the failure slope. However, the results display a spike in the reliability index, but the slope is found unstable. Therefore, the slope is redesigned by creating a homogeneous layer aided with pile reinforcement. The design reduces the probability of failure up to 10-6, thereby making it stable.