## 1 Introduction  
Due to the formation history of rocks, they are usually associated with an anisotropic mechanical behavior. Pure isotropy is only encountered to a limited extent in natural rock formations [1], which is why the consideration of direction-dependent physical properties is all the more important in order to make realistic engineering predictions for the given task. Anisotropy is encountered at various scales in rock engineering, from the scale of the entire rock mass down to the scale of the intact rock [2]. Intact rock anisotropy, also referred to as inherent anisotropy [3], is associated with the formation history of most sedimentary and metamorphic rocks resulting in preferential planes of cleavage, lamination, bedding, foliation or schistity [4, 5]. Paying attention to inherently anisotropic rock behavior is particularly relevant in petroleum and geothermal engineering for the assessment of the material's fracability and the prediction of wellbore stability along with deformations and stresses around boreholes [6]. Inherent elastic anisotropy is also an important factor to be considered for the interpretation of stress measurements, e.g., overcoming experiments [7, 8], and other in situ tests in underground engineering, such as pressuremeter tests [9]. Consequently, a thorough determination of the intact rock's anisotropic character with respect to its physical properties is vital. This especially holds for the evaluation of the material's orientation-dependent deformability. Commonly, a transversely isotropic material model is adopted for the description of the elastic deformability of laminated or foliated rocks with clear visibility of the plane orientations (class B rocks) [10]. Thereby, a plane of isotropy is assumed to be present in the direction of the rocks' planar fabrics with an axis of symmetry normal to them. Five independent parameters are required to fully describe a transversely isotropic solid [11]: \(E\) and \(E^{\prime}\), describing the Young's moduli parallel and normal to the plane of isotropy; the Poisson's ratios \(\
u\) and \(\
u^{\prime}\), characterizing lateral strain in the plane of isotropy resulting from a normal strain applied within this plane and normal to it; and the transverse shear modulus \(G^{\prime}\) associated with the shear modulus normal to the plane of isotropy. The shear modulus \(G\) within the isotropy plane is not an independent parameter, for which the relationship of \(G=E/[2(1+\
u)]\) is given. The determination of the elastic constants is based on the conduction of various static and dynamic laboratory tests. For most applications in geomechanics, however, the static constants, resulting from the corresponding testing methods, are more suitable [12]. The standard procedure for the determination of the static constants represents the conduction of at least three uniaxial compressive strength (UCS) tests in directions normal, parallel and inclined to the planes of isotropy combined with oriented lateral strain measurements [10]. [PERSON] et al. [13] suggested the use of a least-squares approximation scheme in case more than the required minimum number of strain measurements are included in the assessment of the five elastic constants. [PERSON] et al. [14] established a procedure for the consideration of a large number of tests for the evaluation of the elastic constants of a transversely isotropic slate relying on the solution of a non-linear optimization problem. Lately, [PERSON] et al. [15] developed an evaluation technique for the five elastic constants based on averaged circumferential strain measurements on cylindrical specimens in UCS tests. This was performed to increase test practicality and to reduce the influence of errors due to deviations in otherwise required oriented strain measurements from the ideal measuring directions.