## 1 Introduction  
Hydraulic fracturing has been widely applied in coal mining recently with various purposes, such as permeability enhancement of highly gassy coal seams and caveability control of hard roofs [1]. Theoretically, hydraulic fractures (HFs) are classified into two types based on their shapes and propagation planes relative to borehole axes, namely axial HFs (or termed longitudinal HFs, which are parallel to borehole axes) [2] and radial HFs (also called transverse HFs or penny-shaped HFs, which are perpendicular to borehole axes) [3]. The former HF type is common in the oil industry, and perforations must be generated around the cased borehole as artificial weaknesses (i.e., flow channels) for hydraulic fracturing and oil extraction [4]. Occasionally, the perforation direction is unparallel to the HF favorite propagation plane (that is, perpendicular to the minimum in situ stress direction) due to the local change of the in situ stress direction. Thus, axial HFs tend to re-orientate after their initiation, which usually leads to undesirable screen-out that blocks proppant transport [5]. On the contrary, open boreholes are popular with mining HFs. A specific cutting machine is used to produce a radial initial notch around the borehole wall as an artificial weakness for the initiation of a radial HF in the mining industry [6]. This technique is termed directional hydraulic fracturing (DHF) by many researchers [7; 8; 9; 10]. The radial initial notch is expected to guide initiation and propagation of the HF in order to achieve orientation-controllable HFs in the rock mass (e.g., Figure 3 in [PERSON] and [PERSON] [7] and Figure 2 in [PERSON] et al. [11]), since the HF orientation is the priority when HFs aim at inducing caring of hard roofs in coal mining [12]. Nevertheless, evidence from numerical modelling [13] and laboratory experiments [14] shows that the HF could undergo re-orientation after its directional initiation from the initial notch. Therefore, the HF re-orientation mechanism needs further comprehension for effective application of DHF at mine sites. This paper focuses its scope on identifying factors affecting DHF and revealing irregular three-dimensional HF geometries through laboratory experiments in totally transparent gelatin samples. Re-orientation of axial HFs from oriented perforations has been well studied [15; 16; 17]. However, investigating the re-orientation of radial HFs becomes much more complicated because neither the plane strain assumption (which is commonly used to study the re-orientation of axial HFs [18; 19]) nor the plane stress assumption are applicable to a radial-shaped HF. Hence, immature and time-consuming three-dimensional fluid-solid coupled numerical modelling must be performed to simulate DHF [13; 20]. Most laboratory experiments on hydraulic fracturing are conducted in untransparent materials (e.g., rocks), and the existing experimental results of DHF provided by [PERSON] et al. [14] only presented the final HF path from a two-dimensional section plane (see Figure 13 in [PERSON] et al. [14]). The complete HF development process (i.e., HF initiation and propagation) and the tortuous three-dimensional HF geometry remain invisible. In addition, the simulation of the initial notch (which is the key part of DHF) in [PERSON] et al. [14] is questionable. First, metal molds were used by [PERSON] et al. [14] to simulate initial notches, which are much stiffer than their cement samples (having a Young's modulus of 8.4 GPa) and can hardly apply hydraulic pressure to mold-sample interfaces to induce the required stress concentration. Second, borehole axes in all the experiments in [PERSON] et al. [14] were vertical, and notches (i.e., metal molds) were inclined to specific angles in different test scenarios. This differs from the fact that deviated boreholes are used at mine sites and initial notches are perpendicular to borehole axes. In this study, we first use transparent gelatin samples to study DHF performed with deviated boreholes.