## 3 Results and Discussion
Shear stress-horizontal displacement curves in reverse DS tests can sometimes be very difficult to interpret due to renewed peaks with changes in shear direction and the shape of the shear stress-horizontal displacement curve [43]. Shear strength parameters are defined by cohesion and the angle of internal friction [44,45]. However, the residual angle of internal friction varies depending on the soil properties and the magnitude of the normal stress, assuming that the residual cohesion of the soil is zero [2,29,40,46]. After reaching the residual state, all internal adhesive and cohesive effects within the specimen are depleted. At this stage, the particles in the specimen have lost their ability to maintain a mutual connection, meaning that there are no longer any additional cohesive forces to bind them together and it is considered that the value of cohesion is equal to zero. The values of cohesion obtained from testing ranged up to 0.4 kPa, and considering the previously mentioned points, it was adopted for further consideration that cohesion is equal to zero. The residual values of the angle of internal friction obtained in the DS apparatus for siltstone were in the range of \(\phi\)'R = 13.7-14.1\({}^{\circ}\), while for gray clay they were \(\phi\)'R = 12.2-12.6\({}^{\circ}\) (Figure 10). The residual values of the angle of internal friction obtained with the RS apparatus for siltstone were in the range of \(\phi\)'R = 11.8-12.9\({}^{\circ}\), while for gray clay, they were in the range of \(\phi\)'R = 9.9-10.8\({}^{\circ}\) (Figure 10). As previously mentioned, a cohesion value of \(c\)'R = 0 kPa was adopted for result interpretation. Figure 9: Shear stress versus horizontal displacement for (**a**) siltstone (**b**) gray clay. Generally speaking, based on the obtained results, it can be concluded that the residual angles of shear strength obtained from the RS for gray clay are 1.7-2.3\({}^{\circ}\) lower than the angle of internal friction obtained through the classical method for determining residual shear strength parameters in the DS apparatus. For siltstone samples, the difference in the residual angles of internal friction obtained from DS and RS was somewhat smaller, with values being 1.2-1.9\({}^{\circ}\) higher than those obtained from RS. According to [PERSON] et al., 2011 [47], the results of direct shear tests on bentonite and mudstone samples are nearly twice those from ring shear tests, and for loess, siltstone, and alluvial loess samples, they range from around 1.02 to 1.3. [PERSON] & [PERSON], 2013 [48], on the other hand, obtained similar \(\varphi\)'\({}_{\text{R}}\) values using both apparatuses. [PERSON] et al., 1988 [49] found that modified tests on Bromhead's ring shear apparatus yield lower values of residual friction angle compared to reverse direct shear tests. [PERSON] et al., 2011 [50] reported higher values in the DS apparatus compared to the RS apparatus for highly plastic carbonaceous clay and siltstone samples from the open-pit mine \"Tamnava-West Field,\" with higher values of 4-4.6\({}^{\circ}\) for clay and 1.3-2.0\({}^{\circ}\) for siltstone. Based on silt samples from a large landslide in Brazil, [PERSON], 2020 [51] reported internal friction angles of 12.0\({}^{\circ}\) in the DS apparatus and 7.7\({}^{\circ}\) in the RS apparatus. [PERSON], 2024 [52] reported \(\varphi\)'\({}_{\text{R}}\) values of 32.94-13.97\({}^{\circ}\) for 15 artificially prepared samples taken from the embankments of a dam reservoir with varying amounts of fine particles (d \(\leq\) 0.075 mm) and concluded that the residual shear strength of soil decreases with an increase in the percentage of fine particles. To determine the existence of a statistical difference between the values of the residual angle of internal friction obtained using the DS and RS apparatuses, as well as differences between the isolated geotechnical layers, the Tukey-Kramer test was conducted (Table 1).