Correction of Point Load Strength on Irregular Carbonaceous Slate in the Luang Prabang Suture Zone and the Prediction of Uniaxial Compressive Strength

: Uniaxial compressive strength (UCS) testing requires high-quality core samples, which is a difﬁcult task for weak, highly fractured, thinly bedded, foliated, and weathered rocks. In addition, it is time-consuming and expensive. Because of the good relationship between rock point load strength (PLS) and UCS, the PLS could be used to estimate rock UCS quickly. The lump structure and layer structure of carbonaceous slate are revealed in the tunnels of the China–Laos Railway in the Laos Suture Zone as one of the important factors leading to tunnel squeezing deformation and support structures. To reveal the relationship between the PLS and UCS of carbonaceous slate in the Luang Prabang Suture Zone, PLS tests and UCS tests of lump-structure carbonaceous slate (lamina plane inconspicuous) and layer-structure carbonaceous slate (lamina plane conspicuous) were performed. Results show that the I s(50) of lump-structure carbonaceous slate ranged from 0.06 MPa to 0.30 Mpa, the I s(50) of layer-structure carbonaceous slates which were loaded perpendicular to the lamina plane ranged from 0.64 MPa to 1.25 MPa, the I s(50) of layer-structure carbonaceous slates which were loaded parallel to the lamina plane ranged from 0.49 MPa to 0.71 MPa, and the correction power index m ranged from 0.42 to 0.51 with an average value of 0.47. Four correlation expressions of carbonaceous slate relationships between PLS and UCS were ﬁtted by zero-intercept linear expression, nonzero intercept linear expression, power expression, and logarithmic expression, and the calculation results were compared with results calculated by the International Society of Rock Mechanics (ISRM) correlation equation. It is concluded that the correlation equation between UCS and PLS recommended by ISRM speciﬁcations easily causes soft rock strength overestimation, which affects the correct evaluation of the surrounding rock property and the structural design safety of tunnels and underground projects. The zero-intercept linear equation UCS = 18.45 I s(50) has better goodness of ﬁt and higher accuracy in predicting the UCS of the carbonaceous slate in the Luang Prabang Suture Zone.


Introduction
The Luang Prabang Suture Zone is located in the north-central part of Laos territory, which is the connection area of the Lanping-Simao terrane and the Indosinian terrane; it is named for the Luang Prabang Province of Laos [1][2][3], as shown in Figure 1. The China-Laos Railway crosses Laos Luang Prabang Suture Zone, and many tunnels have been built within the influence of the Luang Prabang Suture Zone. Affected by Luang Prabang Suture Zone, the tunnels' surrounding rock is an almost carbonaceous slate with low strength. Coupled with the serious influence of tectonic stress, the tunnels have caused the problem of squeezing deformation. The uniaxial compressive strength (UCS) of rock The PLS test method was first proposed by E. Broch and J. A Franklin [4]. Be the correlation between PLS and UCS, PLS was also considered the optimum me indirectly estimating the rock UCS. Based on related research, the International S Rock Mechanics (ISRM) proposed that the UCS of rock was equivalent to 20~25 t PLS (ISRM, 1985). Many relevant scholars had performed studies on the relation tween rock PLS and UCS based on different rocks in different countries and reg 18]. At present, the linear correlation was most widely used in two types of stren version, and some researchers had also presented various expressions, such a equations, exponential equations, logarithmic equations, and quadratic equation dition, relevant scholars had conducted relevant research on the failure mechan calculation method of PLS [19][20][21][22]. The failure mechanism of the point load test w on the tensile stress failure concept at the loading point position [23,24]. The cal method of the equivalent core diameter was widely adopted in the current PLS te ever, some relevant scholars still considered that the influence of the sample failu anism and the influence of the sample shape coefficient were much more sig [25,26].
According to recent research, the investigation of the correlation expressions PLS and UCS is largely based on several types of rocks limited to a specific are has obvious regional applicability and rock type applicability. In addition, the co expressions of soft rocks (UCS ≤ 30 MPa) are rarely presented. Carbonaceous sl common layered soft rock, and the relationship between PLS and UCS are ra searched, and the traditional correlation expressions are inapplicable. The main o of this study was to clarify the relationship between the PLS and UCS of carbo slate, which is a typical soft rock found in the Luang Prabang Suture Zone, Lao The PLS test method was first proposed by E. Broch and J. A Franklin [4]. Because of the correlation between PLS and UCS, PLS was also considered the optimum method for indirectly estimating the rock UCS. Based on related research, the International Society of Rock Mechanics (ISRM) proposed that the UCS of rock was equivalent to 20~25 times the PLS (ISRM, 1985). Many relevant scholars had performed studies on the relationship between rock PLS and UCS based on different rocks in different countries and regions [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. At present, the linear correlation was most widely used in two types of strength conversion, and some researchers had also presented various expressions, such as power equations, exponential equations, logarithmic equations, and quadratic equations. In addition, relevant scholars had conducted relevant research on the failure mechanism and calculation method of PLS [19][20][21][22]. The failure mechanism of the point load test was based on the tensile stress failure concept at the loading point position [23,24]. The calculation method of the equivalent core diameter was widely adopted in the current PLS test. However, some relevant scholars still considered that the influence of the sample failure mechanism and the influence of the sample shape coefficient were much more significant [25,26].
According to recent research, the investigation of the correlation expressions between PLS and UCS is largely based on several types of rocks limited to a specific area, which has obvious regional applicability and rock type applicability. In addition, the correlation expressions of soft rocks (UCS ≤ 30 MPa) are rarely presented. Carbonaceous slate, as a common layered soft rock, and the relationship between PLS and UCS are rarely researched, and the traditional correlation expressions are inapplicable. The main objective of this study was to clarify the relationship between the PLS and UCS of carbonaceous slate, which is a typical soft rock found in the Luang Prabang Suture Zone, Laos. Based on a series of PLS tests and UCS tests of carbonaceous slate with different structures and different loading directions, the relationship between PLS and UCS is established by considering irregular Appl. Sci. 2022, 12, 9147 3 of 11 samples and the size correction. The results could improve the accuracy of soft rock UCS estimating by PLS testing, and it will provide a design reference for soft rock engineering. It also will be beneficial to the prediction of the level of tunnel squeezing deformation.

Carbonaceous Slate Description
The part of the China-Laos Railway located in the Luang Prabang Suture Zone is approximately 42 km, as shown in Figure 1. All of the sampling sites are located in this area in different tunnels in which surrounding rock is dominated by carbonaceous slate. The revealed carbonaceous slate is a typical metamorphic rock, and it has two different structure types, such as lump structure and layer structure, as shown in Figure 2. The lump-structure carbonaceous slate's ( Figure 2a) compressive strength is very low, it can be crushed into pieces by hand, the lamina planes are inconspicuous, and it easily becomes soft in water. The layer-structure carbonaceous slate's ( Figure 2b) compressive strength is slightly higher than the lump-structure carbonaceous slate, and the lamina planes are conspicuous. The geological age of the two types of carbonaceous slate is from Palaeozoic to Mesozoic. The color is dark grey. Affected by the mineral composition, lamina plane bonding degree, water content, weathering degree, and other factors, the compression strength is variable. Because of more intense geological tectonic activities, such as tensile, fracture, collision, and extrusion in the Luang Prabang Suture Zone, the development degree of rock fissures and the rock mechanical properties are more complex. different loading directions, the relationship between PLS and UCS is established by considering irregular samples and the size correction. The results could improve the accuracy of soft rock UCS estimating by PLS testing, and it will provide a design reference for soft rock engineering. It also will be beneficial to the prediction of the level of tunnel squeezing deformation.

Carbonaceous Slate Description
The part of the China-Laos Railway located in the Luang Prabang Suture Zone is approximately 42 km, as shown in Figure 1. All of the sampling sites are located in this area in different tunnels in which surrounding rock is dominated by carbonaceous slate. The revealed carbonaceous slate is a typical metamorphic rock, and it has two different structure types, such as lump structure and layer structure, as shown in Figure 2. The lump-structure carbonaceous slate's ( Figure 2a) compressive strength is very low, it can be crushed into pieces by hand, the lamina planes are inconspicuous, and it easily becomes soft in water. The layer-structure carbonaceous slate's ( Figure 2b) compressive strength is slightly higher than the lump-structure carbonaceous slate, and the lamina planes are conspicuous. The geological age of the two types of carbonaceous slate is from Palaeozoic to Mesozoic. The color is dark grey. Affected by the mineral composition, lamina plane bonding degree, water content, weathering degree, and other factors, the compression strength is variable. Because of more intense geological tectonic activities, such as tensile, fracture, collision, and extrusion in the Luang Prabang Suture Zone, the development degree of rock fissures and the rock mechanical properties are more complex.

Sample Preparation
To obtain the correlation between UCS and PLS, A total of 16 different locations and 2 different structure types of carbonaceous slate were sampled for UCS testing and irregular rock PLS testing. The numbers of samples were a total of 700 rock samples for the PLS test and a total of 66 rock samples for the UCS test. Samples from the same location were used for the same UCS test and PLS test in order to minimize unexpected errors caused by the differential properties of samples from different spots, and the tests' invalid data were eliminated. The numbers of different locations' samples are shown in Table 1. The type of loading machine used in the PLS test is YSD-7. It consists of a load frame for applying loads up to 60 KN, on which a manual hydraulic jack is mounted. The specimens are loaded by two cone-shaped points. The applied load is measured by a pressure transducer.

Sample Preparation
To obtain the correlation between UCS and PLS, A total of 16 different locations and 2 different structure types of carbonaceous slate were sampled for UCS testing and irregular rock PLS testing. The numbers of samples were a total of 700 rock samples for the PLS test and a total of 66 rock samples for the UCS test. Samples from the same location were used for the same UCS test and PLS test in order to minimize unexpected errors caused by the differential properties of samples from different spots, and the tests' invalid data were eliminated. The numbers of different locations' samples are shown in Table 1. The type of loading machine used in the PLS test is YSD-7. It consists of a load frame for applying loads up to 60 KN, on which a manual hydraulic jack is mounted. The specimens are loaded by two cone-shaped points. The applied load is measured by a pressure transducer.
Rock sample preparation, test methods, and calculation procedures followed the ISRM standard [27]. The width and height of irregular samples used for the PLS test were controlled between 50 ± 30 mm, and the size of D satisfied the conditional expression of 0.3W < D < W and D < 2L, as shown in Figure 3. Because of the samples with low strength, the loading penetration depth would affect the accuracy of test results. Therefore, the instantaneous distance between the loading points of rock sample failure D was recorded as the basis of calculation. The numbers of each location are at least 30 samples. Rock sample preparation, test methods, and calculation procedures followed the ISRM standard [27]. The width and height of irregular samples used for the PLS test were controlled between 50 ± 30 mm, and the size of D satisfied the conditional expression of 0.3W < D < W and D < 2L, as shown in Figure 3. Because of the samples with low strength, the loading penetration depth would affect the accuracy of test results. Therefore, the instantaneous distance between the loading points of rock sample failure D' was recorded as the basis of calculation. The numbers of each location are at least 30 samples.  Rock samples used for the UCS test are cylindrical samples with 50 mm diameter and 100 mm height. However, as most carbonaceous slate's compression strength is low, cylindrical samples cannot be obtained by drilling the core, so a few cubic samples with a side length of 70 mm were used for the UCS test. The cylindrical samples were prepared by drilling the core in the surrounding rock, and the cubic samples were made by cutting and grinding. Each location has 2~3 groups for the UCS test, each group has 3 samples. Figure 4 shows the different samples for the UCS test. The type of loading machine used in the UCS test is a conventional machine that can only record the failure strength. Rock samples used for the UCS test are cylindrical samples with 50 mm diameter and 100 mm height. However, as most carbonaceous slate's compression strength is low, cylindrical samples cannot be obtained by drilling the core, so a few cubic samples with a side length of 70 mm were used for the UCS test. The cylindrical samples were prepared by drilling the core in the surrounding rock, and the cubic samples were made by cutting and grinding. Each location has 2~3 groups for the UCS test, each group has 3 samples. Figure 4 shows the different samples for the UCS test. The type of loading machine used in the UCS test is a conventional machine that can only record the failure strength.

Determination of PLS Is(50) of Irregular Lump Samples
For irregular rock samples for PLS testing, the uncorrected PLS index Is is calculated using Equation (1), as suggested by the ISRM. The equivalent core diameter De should be calculated according to Equation (2):

Determination of PLS I s(50) of Irregular Lump Samples
For irregular rock samples for PLS testing, the uncorrected PLS index I s is calculated using Equation (1), as suggested by the ISRM. The equivalent core diameter D e should be calculated according to Equation (2): where P is the failure load, W is the sample average width, D is the instantaneous distance between two loading points of rock sample failure. The measurement error for W and D should be within ±5% and ±2%, respectively. The PLS index should be established as the strength value of the sample with a 50 mm D e size (I s(50) ). The size correction factor F can be used to convert I s to I s(50) , and the revised calculation equation of I s(50) is proposed as follows: 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 e 2 , and a straight line is used to fit the data of P and D e 2 . From the fitting line, the failure load P of the 50 mm D e can be obtained. Then, the I s(50) can be calculated.

Determination of PLS Is(50) of Irregular Lump Samples
For irregular rock samples for PLS testing, the uncorrected PLS index Is is calculated using Equation (1) where P is the failure load, W is the sample average width, D is the instantaneous distance between two loading points of rock sample failure. The measurement error for W and D should be within ± 5% and ± 2%, respectively. The PLS index should be established as the strength value of the sample with a 50 mm De size (Is(50)). The size correction factor F can be used to convert Is to Is(50), and the revised calculation equation of Is(50) is proposed as follows: 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 De 2 , and a straight line is used to fit the data of P and De 2 . From the fitting line, the failure load P of the 50 mm De can be obtained. Then, the Is(50) can be calculated. 2.05kN

Fitting Result
No. (c)  Table 2 shows the results of the PLS test. The determination coefficient R 2 of P-De 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  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 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 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 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.

Determination of PLS Correction Power Index of Irregular Lump Samples
According to the I s(50) that was obtained (Table 2) The determination coefficient of ln(F)-ln(D e /50) is quite low, but these results are similar to the experimental results of various rocks that had been explored by relevant scholars [7,28,29]. Therefore, this study's fitting relationships are reliable.
The results show that the m range is from 0.42 to 0.51. Among these, the m average for lump-structure carbonaceous slate is 0.44, for the layer-structure carbonaceous slate loaded perpendicular to the lamina plane it is 0.46, and for the layer-structure carbonaceous slate loaded parallel to the lamina plane it is 0.49. It can be seen that the m of layer-structure carbonaceous slate is different because of the different rock structure and different loading direction, but it is close to 0.45, which is suggested by the standard of the ASTM. Based on this study, the equation I s(50) = (D e /50) 0.44 I s can be used for calculating the corrected PLS of lump-structure carbonaceous slate, and the equation I s(50) = (D e /50) 0.46 I s can be used for calculating the corrected PLS of layer-structure carbonaceous slate in which the loading direction is perpendicular to the lamina plane. The equation I s(50) = (D e /50) 0.49 I s can be used for calculating the corrected PLS of layer-structure carbonaceous slate in which the loading direction is parallel to the lamina plane.
ASTM. Based on this study, the equation Is(50) = (De/50) 0.44 Is can be used for calculating the corrected PLS of lump-structure carbonaceous slate, and the equation Is(50) = (De/50) 0.46 Is can be used for calculating the corrected PLS of layer-structure carbonaceous slate in which the loading direction is perpendicular to the lamina plane. The equation Is(50) = (De/50) 0.49 Is can be used for calculating the corrected PLS of layer-structure carbonaceous slate in which the loading direction is parallel to the lamina plane.  (c)

UCS Test Data Statistics Analysis
The calculation method of UCS is shown in Equation (5): where c  is the sample UCS, P is the failure load, and A is the cross-sectional area of the sample.
Different sizes of rock samples will lead to different structural compositions, such as internal microcracks, fissures, and structural planes. Rock samples with different aspect ratios will produce a friction effect at their end. For these two reasons, the failure mode and failure intensity during the UCS testing of rock samples will be different [30,31]. However, according to related scholars' studies, the cubic sample UCS could be transformed   5.18 MPa; this rock is extremely soft. Most carbonaceous slate with typical layer structures has thin-to medium-thickness layers, the rock mass is crushed, and the interlayer is argillaceous cementation. The UCS is substantially affected by layer thickness and lamina plane bonding force. Samples whose loading directions are perpendicular to the lamina plane range from

UCS Test Data Statistics Analysis
The calculation method of UCS is shown in Equation (5): where σ c is the sample UCS, P is the failure load, and A is the cross-sectional area of the sample. Different sizes of rock samples will lead to different structural compositions, such as internal microcracks, fissures, and structural planes. Rock samples with different aspect ratios will produce a friction effect at their end. For these two reasons, the failure mode and failure intensity during the UCS testing of rock samples will be different [30,31]. However, according to related scholars' studies, the cubic sample UCS could be transformed into a cylindrical sample by Equation (6) [32], where σ s is equivalent standard cylindrical sample UCS, is the cubic sample UCS, H is the equivalent cylindrical sample height, and W is the equivalent cylindrical sample diameter. this rock is extremely soft. Most carbonaceous slate with typical layer structures has thinto medium-thickness layers, the rock mass is crushed, and the interlayer is argillaceous cementation. The UCS is substantially affected by layer thickness and lamina plane bonding force. Samples whose loading directions are perpendicular to the lamina plane range from 15.34 MPa to 23.12 MPa, and samples whose loading directions are parallel to the lamina plane range from 6.13 MPa to 17.63 MPa. The anisotropy is significant.

Relationship between Corrected PLS and UCS
According to the proposed relationship equations by ISRM and the 'Code for Rock Test of Railway Engineering (China)', the UCS calculated results are generally larger than the UCS test results. Thus, these equations are not applicable for predicting the UCS of carbonaceous slate in the Luang Prabang Suture Zone. For this reason, and based on the PLS test and UCS test results of carbonaceous slate, four types of fitting correlations between PLS and UCS were established that are widely used in related research [32], and fitting equations were obtained as follows: Zero-intercept linear equation: Non-zero-intercept linear equation: Logarithmic equation: UCS = 6.63 ln I s(50) + 16.55 (10) According to the fitting equations, curves were drawn in Figure 7. Four fitting equations could reflect the relationship between the PLS and UCS of carbonaceous slate, and all determination coefficients are higher than 0.7. The logarithmic equation has the lowest fitting determination coefficient-the value is 0.76. The determination coefficients of the non-zero-intercept linear equation and the power equation are 0.83 and 0.84, respectively. The zero-intercept linear equation has the highest determination coefficient-the value is 0.96. Accordingly, the relationship between PLS and UCS is close to a linear dependence, and it can be expressed as UCS = 18.45I s(50) , which has higher accuracy in predicting the UCS of the carbonaceous slate in the Luang Prabang Suture Zone.
According to the fitting equations, curves were drawn in Figure 7. Four fitting equations could reflect the relationship between the PLS and UCS of carbonaceous slate, and all determination coefficients are higher than 0.7. The logarithmic equation has the lowest fitting determination coefficient-the value is 0.76. The determination coefficients of the non-zero-intercept linear equation and the power equation are 0.83 and 0.84, respectively. The zero-intercept linear equation has the highest determination coefficient-the value is 0.96. Accordingly, the relationship between PLS and UCS is close to a linear dependence, and it can be expressed as UCS = 18.45Is(50), which has higher accuracy in predicting the UCS of the carbonaceous slate in the Luang Prabang Suture Zone.

Discussion
Based on the PLS and UCS test results of the carbonaceous slate in the Luang Prabang Suture Zone, the correction power index m of standard rock samples with different structures and different loading directions was obtained, and the conversion equation between PLS and UCS was proposed. The results of the correction power index m are close to the conclusions of relevant researchers, such as the range from 0.443 to 0.600 proposed by Yin [8], and the 0.45 suggested by the ASTM. However, when the rock structure and loading direction are different, the correction power index m will be anisotropic. For a typical layered rock mass, it is recommended to select an applicable correction power index m for I s(50) estimation. The conversion equation between UCS and PLS proposed in this study is based on the strength test results of carbonaceous slate in the Luang Prabang Suture Zone, so the regional applicability is much stronger. For this reason, follow-up studies should further enhance the verification of carbonaceous slate in different regions.

1.
Carbonaceous slate is severely influenced by tectonic stress, and the UCS of rocks with different structures is significantly different. The average I s(50) of lump-structure carbonaceous slate is 0. 16  The relationship between the UCS and PLS of rocks is related to the rock type and geological environment. If the revealed surrounding rock of tunnel engineering is extremely soft, it will be extremely difficult to prepare the standard samples for UCS. For this situation, the PLS can estimate rock UCS effectively. Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.