## 1 Introduction  
In general, the value of the reliability index of a geotechnical structure, calculated using identical input parameters and assumptions, can vary significantly as a function of the applied method. The main reasons for this are related to assumptions and simplifications, which are introduced in the methods to simplify the reliability analysis. In other words, it is necessary to evaluate the reliability methods accuracies, i.e., research their suitability for application in different types of problem. Because of the differences in the mathematical expressions of the limit state definition among various geotechnical tasks, i.e., different forms of the performance function, it is not possible to give a generalized assessment of the suitability of a particular method of reliability to all geotechnical problems. However, it can be done on a case-by-case basis. The other possibility could be that a single method is suitable for application to a group of mathematically similar problems. The main goal of this paper is to assess the suitability of common reliability methods in the case of the ultimate limit state (ULS) of shallow foundations. The suitability of the following methods was assessed: Analytical First Order Second Moment (FOSM) method, Taylor Series, Point Estimate Method (PEM), First Order Reliability (FORM) method, Simplified FORM, and the Monte Carlo method. For this purpose, the following sub-goals were set:test the hypothesis of whether the factor of safety (FS) follows normal or lognormal distribution;
* probability method error definition;
* defining the criteria for method suitability assessment. Analytical FOSM, Taylor Series and PEM reliability methods use FS as an objective function to calculate the reliability index, and their accuracy depends greatly on the assumed statistical distribution of FS. The paper analyses the statistic characteristics of the performance function, and shows that, contrary to a common assumption, the FS in the case of this study is not normally or lognormally distributed. In order to quantify the error which arises from the incorrect assumption of the FS statistical distribution, its actual probability density functions (PDF) were created using the Monte Carlo method. The results obtained were fitted with normal and lognormal PDFs, and error sizes were estimated based on the obtained results. A review of relevant literature in the field of reliability in geotechnical engineering revealed a lack of information on the reliability method's accuracy and the statistical distribution of the performance function in the case of the ultimate limit state (ULS) of a shallow foundation. Generally, a criterion to estimate the suitability of one or another reliability method for application in geotechnical engineering tasks was not defined. This paper defines such a criterion, based on the error size of the calculated reliability index (\(\beta\)). Using the proposed criterion, an assessment of the applicability of reliability methods was made, using a simple example of a centrally loaded foundation. The results obtained were compared to the results from other studies in the available literature: stability of the embankments from [1] and retaining wall reliability [2]. In general, Analytical FOSM, Taylor Series, PEM and FORM methods result in a reliability index, while the Monte Carlo and Direct Integration result in the probability of failure (P\({}_{\text{f}}\)). In order to enable mutual comparisons in error sizes, the results of all methods were reported using a reliability index. The connection between \(\beta\) i P\({}_{\text{f}}\) is defined by the following relation [3]:  
\[\beta=-\Phi^{-1}(\text{P}_{\text{f}}), \tag{1}\]  
where  
\(\Phi^{-1}(. )\)--the inverse Gaussian distribution  
A detailed description of determining the reliability index using FOSM, PEM, FORM and the Monte Carlo is given in [3]. What is generally emphasized, considering the accuracy aspect of each method, is that each method provides a different level of accuracy.