In practical geotechnical engineering the factor of safety is still determined by means of simple limit equilibrium analysis in many cases. However, because displacement finite-element analysis is routinely applied for assessing displacements and stresses for working load conditions, this technique is increasingly being used to calculate ultimate limit states and, consequently, factors of safety, usually by means of the so-called strength reduction technique, and results which are comparable to those obtained with limit equilibrium methods have been reported in the literature. However, owing to the inherent assumptions of limit equilibrium analyses, they do not always provide unique factors of safety. The purpose of this paper is on the one hand to compare the strength reduction method with rigorous limit analyses which are based on collapse theorems of plasticity, and on the other hand to investigate if a shortcoming of the strength reduction method, namely possible numerical instabilities for non-associated plasticity, can be overcome. Two examples are considered, namely slope stability and tunnel face stability. Finally an important note on the definition of the factor of safety for effective and total stress analysis under undrained conditions is provided.

The classification of soils into categories with a similar range of properties is a fundamental geotechnical engineering procedure. At present, this classification is based on various types of cost- and time-intensive laboratory and/or in situ tests. These soil investigations are essential for each individual construction site and have to be performed prior to the design of a project. Since Machine Learning could play a key role in reducing the costs and time needed for a suitable site investigation program, the basic ability of Machine Learning models to classify soils from Cone Penetration Tests (CPT) is evaluated. To find an appropriate classification model, 24 different Machine Learning models, based on three different algorithms, are built and trained on a dataset consisting of 1339 CPT. The applied algorithms are a Support Vector Machine, an Artificial Neural Network and a Random Forest. As input features, different combinations of direct cone penetration test data (tip resistance q_c, sleeve friction f_s, friction ratio R_f, depth d), combined with “defined”, thus, not directly measured data (total vertical stresses σ_v, effective vertical stresses σ’_v and hydrostatic pore pressure u₀), are used. Standard soil classes based on grain size distributions and soil classes based on soil behavior types according to Robertson are applied as targets. The different models are compared with respect to their prediction performance and the required learning time. The best results for all targets were obtained with models using a Random Forest classifier. For the soil classes based on grain size distribution, an accuracy of about 75%, and for soil classes according to Robertson, an accuracy of about 97–99%, was reached.