Wet-bored pile construction is a commonly used technique by contractors for building bored piles. This method involves the use of a special drilling fluid, known as bentonite slurry, to support the borehole walls and prevent their collapse during the drilling process. Given the importance of such a soil stability problem, the present paper aims to study borehole stability and its associated failure mechanisms of all relevant design parameters. In particular, we focus on the investigation of the depth and diameter of the cylindrical borehole for anisotropic and non-homogeneous clays. To achieve this goal, the advanced finite element limit analysis (FELA) method alongside the upper and lower bounds limit analysis is used as a numerical tool to perform a series of the parametric study. The dimensionless variables utilized in this study consist of a practical range of depth ratio (H/D), dimensionless strength gradient (rH/Suc0), and anisotropic strength ratio (re). The newly obtained numerical results are in good agreement with previous studies, and therefore several design charts are confidently produced for the design of cylindrical borehole stability using a dimensionless stability number. The study continues to explore the associated failure mechanisms using the graphical output of velocity fields. The artificial neural network (ANN), which is one of soft-computing techniques, is utilized to establish a surrogate model for predicting the borehole stability and also developing a correlation equation based on FELA results. This correlation equation is useful to practical engineers as it can be used to predict the stability number N and factor of safety (FS) in their daily design practices.