## 3 Test Data Statistics Analysis  
### Determination of PLS Is(50) of Irregular Lump Samples  
For irregular rock samples for PLS testing, the uncorrected PLS index \(I_{\mathrm{s}}\) is calculated using Equation (1), as suggested by the ISRM. The equivalent core diameter \(D_{\mathrm{e}}\) should be calculated according to Equation (2):  
\[I_{\mathrm{s}}=P/D_{\mathrm{e}}^{2} \tag{1}\]  
\[D_{\mathrm{e}}^{2}=4 WD^{\prime}/\pi \tag{2}\]  
where \(P\) is the failure load, \(W\) is the sample average width, \(D^{\prime}\) is the instantaneous distance between two loading points of rock sample failure. The measurement error for \(W\) and \(D^{\prime}\) should be within \(\pm 5\%\) and \(\pm 2\%\), respectively.  
The PLS index should be established as the strength value of the sample with a 50 mm \(D_{\mathrm{e}}\) size (\(I_{\mathrm{s(50)}}\)). The size correction factor \(F\) can be used to convert \(I_{\mathrm{s}}\) to \(I_{\mathrm{s(50)}}\), and the revised calculation equation of \(I_{\mathrm{s(50)}}\) is proposed as follows:  
\[I_{\mathrm{s(50)}}=FI_{\mathrm{s}}=\left(\frac{D_{\mathrm{e}}}{50}\right)^{m}I _{\mathrm{s}} \tag{3}\]  
where \(m\) is the correction power index, which is related to rock properties.  
Figure 5 shows the typical location of carbonaceous slate's relationship between \(P\) and \(D_{\mathrm{e}}^{2}\), and a straight line is used to fit the data of \(P\) and \(D_{\mathrm{e}}^{2}\). From the fitting line, the failure load \(P\) of the 50 mm \(D_{\mathrm{e}}\) can be obtained. Then, the \(I_{\mathrm{s(50)}}\) can be calculated.  
Table 2 shows the results of the PLS test. The determination coefficient \(R^{2}\) of \(P\)- \(D_{\mathrm{e}}^{2}\) ranges from 0.69 to 0.85, showing a good correlation. The average determination coefficient of lump-structure carbonaceous slate is about 0.81, and the average determination coefficient of layer-structure carbonaceous slate, in which the loading direction is perpendicular to the lamina plane, is about 0.83. In contrast, the determination coefficient of layer-structure carbonaceous slate, in which the loading direction is parallel to the lamina plane, is slightly lower, with an average value of 0.76. The main reason is the difference in lamina plane bonding degree.  
Figure 5: \(P\)-\(D_{\mathrm{e}}^{2}\) fitting curve of carbonaceous slate in the Luang Prabang Suture Zone: (**a**) Lump structure; (**b**) layer structure loaded perpendicular to lamina plane; (**c**) layer structure loaded parallel to lamina plane.  
The corrected PLS changes notably with carbonaceous slate structure and loading direction. For the lump-structure carbonaceous slate, the cracks extended gradually until the fracture plane was formed and rock failure occurred. The \(I_{\mathrm{s(50)}}\) range is from 0.06 MPa to 0.31 MPa, and the average is 0.16 MPa. For the layer-structure carbonaceous slate loaded perpendicular to the lamina plane, the surface of the sample was first crushed, and the brittle rock failure occurred directly. The \(I_{\mathrm{s(50)}}\) range is from 0.64 MPa to 1.25 MPa, and the average is 0.97 MPa. For the layer-structure carbonaceous slate loaded parallel to the lamina plane, tensile failure occurred along the weak lamina plane. The \(I_{\mathrm{s(50)}}\) is substantially affected by the lamina plane bonding force, the range is between 0.49 MPa and 0.71 MPa, and the average is 0.58 MPa.