The IPLS test was conducted in accordance with ISRM Commission (1985) [8] . In the IPLS tests, the specimens were loaded to failure by application of a concentrated load through a pair of spherically truncated, conical platens. The testing machine consisted of conical loading platens, a loading frame, dial gauge, manual control handle, load cell, and load measuring system (Figure 2). The loading speed was set so that each specimen failed within 10 - 60 s. This was achieved using a manual control handle by loading each specimen continuously at a constant (as much as possible) loading speed up to approximately 100 N/s of load increase. The size-corrected IPLS index of a rock specimen was defined as the value of PLS that would have been measured by a diametral PLS test with diameter D = 50 mm ( D e 2 = 2500 mm², where D_e is the equivalent core diameter). The IPLS index can be represented by the formula:

I s ( 50 ) = F P D e 2 (1)

where F is the size correction factor, P is the peak load (failure load), and D_e is the equivalent core diameter. D_e is the diameter of a circle with an area equal to the minimum area of the cross sections containing the two loading points, and can be represented by the formula:

D e 2 = 4 W D ′ π (2)

where D_e is the equivalent core diameter, W is the specimen width, and D' is the distance between the two loading platens at the time of failure. The ISRM Commission (1985) [8] stipulated that if significant penetration of the conical platens occurs during the test, such as when testing soft rocks, the value of D' should be the final value of the distance between the two loading platens. Therefore, in this study, the PLS was calculated using the distance between the two loading platens at the time of failure:

D ′ = D − α (3)

where D' is the distance between the two loading platens at the time of failure, D is the distance between the two loading platens, and is the penetration distance of the conical platens. The distance between the two loading platens and the penetration distance of the conical platens were measured using slide calipers and a dial gauge (analog type), respectively. F can be represented by the formula:

F = ( D e 50 ) 0.45 (4)

where F is the size correction factor, and D_e is the equivalent core diameter.

In this study, irregular lump specimens were used for the IPLS tests (Figure 2). The IPLS test specimen sizes satisfied the conditional expression of 0.3W < D < W and 0.5 D < L (ISRM Commission (1985) [8] ; Figure 2).

The NP test was conducted in accordance to the methods proposed by Okada et al. (1985) [24] The needle penetrometer (Figure 3) consisted of the penetration needle, load indication ring, penetration and load scales, chuck, spindle, and penetration indication cap. The NP index can be represented by the formula:

NP   index = P a (5)

where P is the penetration load, and a is the penetration depth.

The IPLS, NP, and UCS tests in this study were performed using a laboratory testing machine with specimens in forced-dry, forced-wet, and natural-moist states. The forced-dry and forced-wet states included absolutely dry and fully water-saturated specimens, respectively. The specimens were dried in an electric oven at a temperature below 60˚C for 4 days or more to achieve a constant mass and were saturated with water for 15 days or more to achieve a constant mass, respectively (Kohno et al. (2010) [25] ).

A total of 9 different rock types were sampled, and the total number of rock specimens tested was 2413 for the IPLS test, 180 for the NP test, and 262 for the UCS test (Table 2). The number of specimens in Table 2 does not include invalid test specimens.

The relationships between the IPLS index and UCS in soft rocks with a UCS below 25 MPa are shown in Figure 4. Such samples that do not satisfy the number

fTf: Fine tuff, m Tf: Medium tuff, pm Tf: Pumice tuff, lap Tf: Lapilli tuff, weld Tf: Welded tuff, tfMs: Tuffaceous mudstone, tfSs: Tuffaceous sandstone, tf Cg: Tuffaceous conglomerate, Dac: Dacite.

( ): Numbers of sampling sites.

of specimens required for the coefficient of variation or those that have only one specimen were eliminated in IPLS and UCS tests, respectively; they were not included in the analysis. The correlations between the IPLS index and UCS in the forced-dry and forced-wet states were linear. The line drawn through the data points is the best fit, determined by the method of least squares regression. The equations and correlation coefficients for the forced-dry state were

UCS = 17.8 × (IPLS index), and R = 0.90 (Figure 4(a)), respectively.

And those for the forced-wet state were

UCS = 21.7 × (IPLS index), and R = 0.95 (Figure 4(b)), respectively.

Here, R is the correlation coefficient. The correlation coefficients for the forced-dry and forced-wet states were 0.90 and 0.95, respectively, indicating a strong correlation. We attempted to combine the forced-dry and forced-wet states. The equation and correlation coefficient for the line were

UCS = 18.9 × (PLS index), and R = 0.93 (Figure 4(c)), respectively.

Where R is the correlation coefficient. The scatter in the data points was lesser at low strengths, and slightly higher at higher strengths (Figure 4(c)). The relationship was established by combining those for the forced-dry and forced-wet states, and a strong correlation between them was observed as well. In soft rocks, the relationships between the IPLS index and UCS in the “forced-dry and forced-wet states (Figure 4(c))” and “natural-moist state (Figure 4(d))” were similar. Therefore, it can be concluded that it is also possible to apply the relationship to onsite tests of soft rocks in the natural-moist state, which is intermediate between the forced-dry and forced-wet states. The UCS under natural-moist state in this study was estimated based on water content of specimen.

The relationships between the NP index and UCS in soft rocks with a UCS below 25 MPa are shown in Figure 5. The equation and correlation coefficients for the natural-moist state are

UCS = 0.848 × (NP index)^0.619, and R = 0.74 (Figure 5), respectively,

Where R is the correlation coefficient. On comparing this equation to that proposed by Okada et al. (1985 [24] ; logUCS = 0.978 log (NP index) + 1.599) and Ulusay and Erguler (2012 [20] ; UCS = 0.4 (NP index)^0.929), there were differences observed in slope of the graph. One of the reasons why the equation in this study and that proposed by Okada et al. (1985) [24] and Ulusay and Erguler (2012) [20] differed was that the rock sample was a hydrothermally altered soft rock with a UCS below 25 MPa. Therefore, we need to choose either the equation proposed in this study (soft rocks) or that proposed by Okada et al. (1985) [24] and Ulusay and Erguler (2012) [20] (hard rocks). Thereby, we can obtain a more accurate value of UCS.

The discrepancies in the IPLS and UCS tests were calculated using a coefficient of variation:

C v = S x × 100 ( % ) (6)

where C_v is the coefficient of variation, S is the standard deviation, and x is the average of the IPLS (or UCS) test results. The coefficient of variation can be used to determine the number of specimens required for IPLS testing. The number of specimens required to obtain results within ϕ = 25% of the average value over a one-sided confidence interval at a 90% level of confidence was 5, 7, and 10 for a C_v of 20%, 30%, and 40%, respectively (dashed line in Figure 4(e)). The relationships between the number of IPLS test specimens and the coefficient of variation are shown in Figure 4(e). A sufficient number of specimens were used for most of the IPLS tests. The coefficient of variation for most UCS specimens was less than 25%, ensuring that precise measurements were obtained for these tests. Therefore, the IPLS and UCS testing methods established in this study were highly precise. On the other hand, the coefficient of variation for most NP specimens was less than 20%.