Reliability Analysis Using Finite Elements for Geotechnical Slope Stability Evaluations
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This thesis contributes to the application of reliability analysis in geotechnical slope stability analysis, particularly for clay slopes. Case studies demonstrate the applicability of the presented theoretical framework where the Finite Element Method (FEM) is applied for stability assessment. A main focus of the study is to adapt existing reliability methodologies to evaluation of reliability of clay slope stability using finite elements. Methodologies to perform reliability analysis in geotechnical engineering have long existed, but in design slope stability analyses are still carried out in a deterministic framework. The lack of data sets suited for statistical analyses, misconceptions that reliability analyses are too complex to perform and that reliability analyses are currently not anchored in design guidelines are frequent arguments against the use of reliability analyses in (onshore) geotechnical design. As a response to these misconceptions, this study presents reliability analyses performed based on data sets which are representative for data sets available to geotechnical engineers as to extent and quality, and with software tools well-known to practicing engineers. The stability analyses are performed with the FE-code PLAXIS, which is widely used in geotechnical engineering in Norway and as it is beneficial to be able to use FE-models together with reliability methods. This makes engineers able to quantify uncertainty while at the same time being able to evaluate slope stability using tools automatically searching for the most critical shear surface and to incorporate advanced soil models. Several reliability methods, both optimization and sampling methods, have been applied, and coupled with stability analysis in PLAXIS either through a predefined toolbox running the reliability analysis and the coupling to the stability analysis or through a Response Surface technique approach. Reliability methods have been coupled with PLAXIS through the probabilistic toolbox Prob2B from TNO. Reliability analysis performed with Prob2B and PLAXIS using c − φ reduction for stability evaluations has proved possible, but here some care must be taken. In addition to some limitations as for stochastic modelling of the pore pressure in this coupling, the reliability analysis becomes sort of a ’black box’ for the engineer in this way, requiring limited knowledge of how a reliability analysis really work. Sampling methods in combination with c − φ reduction can become very time-consuming in cases of small failure probabilities and requires large computer capacity (although this is a general challenge, and not at all limited to the use of Prob2B for the reliability analysis). FORM-analysis, however, is quite effective, but can be time-consuming when the number of random variables is high. It is fair to note that Prob2B has been successfully applied for reliability analysis coupled with PLAXIS before, where other limit state definitions (LSFs) than based on the Multiplier Safety Factor (MSF) from c − φ reduction have been used. In Chapter 5 and throughout the thesis the First-Order Reliability Method with Response Surface techniques (FORM-RS) is found to be a suitable reliability approach for slope stability evaluations based on finite elements. A FORM-approach based on Low (2007a) is coupled with a Response Surface approach, with deterministic FE analysis in PLAXIS as a stand-alone analysis tool. The method proves to be robust and reliable, and approachable for practicing engineers already familiar with PLAXIS and Excel. FORM-RS provides a good balance between computational cost and accuracy. Although the FE tool PLAXIS was used to calculate the factor of safety F in this study, the methodology is independent of the stability analysis. Thus any available analysis method can be applied to the proposed methodology. The presented FORM-RS framework is used successfully to provide additional information on the safety margin of both a standing clay slope (Bakklandet, Norway, in Chapter 6) and to predict the likelihood of the Leistad landslide, Norway, in Chapter 7. For Bakklandet, an annual pf including both the spatial variation of the effective strength parameters and the temporal variation of the pore pressure is found. The Leistad site is a relatively flat clay area consisting of a clay layer over a firmer layer (with varying magnitude) over a soft, partly sensitive clay layer, down to a depth of up to 30 m. Material parameters are presented in detail for the marine clay sediments at Leistad, increasing the generic knowledge of the likely range of engineering parameters for marine clays. The calculated probability of failure of the Leistad landslide is found to be as high as 40%. The failure probability is estimated for scenarios based on an increasing amount of data. The increased amount of data available do not change the reliability level of the site significantly, indicating that data sets engineers trust to be representative is more important than collecting huge amounts of data. What is needed is enough data to identify layers and important features of the sediments, and data sets which describes the soil behaviour well and addresses the engineering problem in question.