## 1 Introduction  
Wellbores drilled in sedimentary basins encounter different rocks with different mechanical responses. Shale makes up approximately 50 percent of all sedimentary rocks in the stratigraphic record [1], and the majority of deep drilling operations come across this rock [2]. In the oil and gas industry, more than 75% of the world drilling is carried out in shales, which are responsible for the major source (90%) of instability [3]. Currently, the mitigation of the effects of anthropogenic greenhouse gas emissions should lead to oil and gas output being in gradual decline. However, depleted oil and gas fields are good targets for CO\({}_{2}\) and H\({}_{2}\) storage [4; 5; 6; 7]. In these depleted fields, new wellbores must be drilled for gas injection operations. Consequently, drilling operation in shale is still a matter of concern [8; 9; 10; 11; 12; 13; 14; 15; 16; 17]. The prediction of the mud pressure to avoid wellbore instability requires the knowledge of the mechanical properties of the rock. The determination of the shale mechanical properties at large depth is still a problem. An accurate assessment of rock mechanical properties is through laboratory tests; however, core retrieval at large depths can be a difficult task [18]. In fact, shale cores can be subject to alteration as they are retrieved from the subsurface due to changes in pressure, temperature and oxidation state [19]. Furthermore,the processes of specimen preparation can induce damage [20]. All these problems can make the results of tests uncertain. As the process of rock coring can damage the material, the mechanical properties can be obtained from laboratory tests carried out on outcropping formations with structures close to the rock at a large depth [21]. The laboratory tests for the geomechanical characterization of shales with anisotropic strength consists of uniaxial and triaxial tests carried out at five or more inclinations of the weakness planes. The tests should be repeated at least twice for each inclination of the weakness planes, to verify their reliability. Therefore, the extensive process of coring and testing can result in being expensive and time consuming. More often, the mechanical properties of the rock at large depths are obtained from indirect measurements by using correlations with log data and microscopic models [22; 23]. These empirical correlations are used to obtain a continuous profile with the depth of the elastic and strength properties [24] and, for a given wellbore, log-derived data, are correlated with the rock properties measured in laboratory. In general, the empirical relationships with log data are valid in the basin from where they were set up. A thorough review of published empirical relations is given in [25; 26]. Furthermore, [27] presented new correlations for deep-water reservoirs and shale oil and shale gas formations. Recently, the Machine Learning Approach and hybrid neural net based models were proposed for the indirect determination of the uniaxial compressive strength and internal friction angle of shale [28; 29]. According to [22; 23; 24; 30], the mechanical properties obtained by log and microscopic models are affected by relevant uncertainty and cannot provide a thoroughgoing characterization of the rock. Shale often exhibits variation in strength properties along and across the lamination planes. This variation must be taken into consideration when carrying out stability analyses of wellbores [17]. However, the transverse isotropy of shale is not specifically addressed in the indirect approaches. The effect of water weakening in a variety of sedimentary rocks has been widely investigated (i.e., [17; 31; 32; 33; 34; 35]). On the other hand, the low permeability of shale rock can induce undrained conditions, immediately after drilling (short term). The undrained pore fluid pressure evolution can enhance plasticity [36; 37; 38; 39].