## 2 Materials and Methods
### Testing Procedure  
Remolded or reconstructed samples can be used to determine residual strength with DS and RS devices [2]. [PERSON] et al., 1971 [11] pointed out that the residual shear strength is not affected by the deformation of the samples (previous stress history). Remolded samples for testing were prepared first by air drying and then by grinding the soil in an avan. The samples were then sieved through a 1.0 mm sieve, mixed with distilled water to the desired moisture content for compaction, and allowed to hydrate for at least 24 h.  
The remolded samples for testing were compacted directly into an oedometer apparatus with an outer diameter of 100 mm and incrementally loaded vertically up to a maximum vertical stress of 400 kPa. After 24 h, the sample was extruded from the oedometer mold and placed into the RS apparatus. For the DS apparatus, the samples were prepared in the same way as for the RS apparatus. Afterward, the sample was first compacted into a square mold with dimensions of 6 \(\times\) 6 cm and then extruded into the shear box.  
According to the recommendations of the ASTM D6467-13 standard [35], sample preparation at the liquid limit is advised for these tests. However, samples prepared at the liquid limit were not suitable for testing due to the extrusion of the sample around the porous stone during consolidation. Similar observations were noted by [PERSON] et al. (2018) and [PERSON] et al., 2022 [36; 37]. For this study, the samples were prepared with the moisture content close to the plastic limit. Figure 5 shows the appearance of the samples after testing in the ring shear and direct shear apparatuses.  
Figure 4: (**a**) Matesi direct shear apparatus. (**b**) Two-dimensional model of the direct shear apparatus [34] (Reprinted/adapted with permission from Ref. [[PERSON] et al., 2015]) Legend: 1—frame of the apparatus, 2—system for transmitting horizontal load, 3—digital control unit, 4—device for measuring horizontal linear displacements, 5—device for measuring horizontal load, 6—device for measuring vertical linear displacements, 7—system for transmitting vertical load, 8—plate for transmitting uniform vertical load, 9, 10—shear box.  
The samples were consolidated and sheared under vertical loads of 50, 100, 200, and 400 kPa. During shearing, a constant vertical pressure was maintained. In selecting the shear rate, the criterion was set to ensure the rate was slow enough to eliminate the occurrence of excess pore pressure on the failure plane at a predefined failure criterion. [PERSON] et al., 1970 [38] found that the measured residual shear strength was not affected by an increase in displacement rate from 0.02 to 60 mm/min. [PERSON], 1985 [12] concluded that there is less than 5% variation in the value of the angle of internal friction for shear rates ranging from 0.05 to 0.35 mm/min. The Japanese Geotechnical Society, 2010 [39] suggests a shear rate of 0.02 mm/min for direct shear apparatuses. To arrive at an acceptable shear rate for this study, remolded samples were tested at a shear rate of 0.02 mm/min in both apparatuses  
In an ideal scenario, the residual shear strength of soil can be defined as the shear strength at which shear stresses and the sample's volume remain constant with further increases in horizontal displacements (deformation) [40]. For the ring shear test, [PERSON]. 1992) [41] concluded that, if the shear torque remains constant for more than 1 h, it indicates residual shear strength. In this study, the test samples were sheared to a displacement of about 360 mm, resulting in a constant torque value for at least the last 150 h of shearing.