7.3.4 Results of regression analyses
The equations and correlation coefficients obtained from the plots are given in Table 3. An exponential function is adopted to fit the variation in mass results:
m=1-aex/t (1)
where m is the mass variation in different cycles; a and t are constants; x is the experimental period.
Meanwhile, a power function is adopted to fit the variations in surface hardness and P-wave velocity results:
H (Vp) =1-axc (2)
where H (Vp) is the variation in surface hardness (P-wave velocity) in different cycles; a and c are constants; x is the experimental period.
The correlation coefficients for mass, surface hardness and P-wave velocity versus the cycles of three experiments range between 0.95 and 0.98, suggesting that they can capture the changes of these parameters. All these results are basically consistent with Fang et al. (2015) and Ă–zbek (2014).
The variation in mass is only applicable to the sandstone weathering rate with cracks or flaking. The surface hardness and P-wave velocity of each sample gradually decrease with increasing cycles, which can be considered as the acceleration of sandstone weathering rate. It is thus limited to evaluate the weathering rate by calculating the variation in mass of sandstone, and the variation in surface hardness and P-wave velocity can be properly established to test the approximate value of the weathering rate (Li, Wang, & Chikaosa, 2008). The approximate value of sandstone weathering rate can be established using the following formula:
V = 1-A XC (C>0) (3)
where V is the approximate value of the weathering rate; A is the coefficient of weathering decline, i.e., the higher the coefficient of weathering decline is, the faster the weathering rate is; X is the weathering period; and C is a constant.