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. 2024 Apr 1;14:7685. doi: 10.1038/s41598-024-58235-z

Table 3.

The actual flow velocity of fissure water fitted using the equation limit method.

Type of groundwater Depth (m) Duration (m) Model Curve-fitting equation Va (μm/s) R2
Water in sand layer 13 2310 Logistic V(t) = 307.35 + 146.42/(1 + (t/11.25)0.81) 307.35 0.99
14 1970 Gauss V(t) = 434.49 + 16,264/(228.36 π2 e−2((t−313.52)/52155) 434.49 0.99
15 2900 Boltzmann V(t) = 497 + 22.44/(1 + e((t−843.51)/112.96)) 497.00 1
Fissure water in vesicular basalts 21 2320 ExpAssoc v(t) = 442.33(1 − e−x/17.45) + 69.85(1 − e−x/734.92) − 138.21 373.97 0.99
23 2260 ExpDec1 v(t) = 347.65–240.42e−t/25.06 347.65 0.93
25 1630 ExpDec1 v(t) = 340.04–72.77e−t/353.85 340.04 0.83
27 1980 ExpDec2 v(t) = 367.52 + 30.64e−t/1109–131.76e−t/45.05 367.52 0.96
29 2100 Logistic v(t) = 390.39–30.56/(1 + (t/506.89)3.23) 390.39 0.92
30 6260 Logistic v(t) = 453.35–65.46/(1 + (t/1328.82)1.91) 453.35 0.94
Fissure water in granites 120 560 ExpDec1 v(t) = 88.17 + 714.34e−t/13.18 88.17 0.83
131 680 Gauss v(t) = 230.52 + (33,980/(266(pi/2)0.5)e−2((t−225)/266)^2 230.52 0.98
141 770 ExpAssoc v(t) = 390.94–2544(1 − e−t/100.72) + 2410 (1 − e−t/105.5) 256.66 0.99
228 1810 ExpAssoc v(t) = 506.61–397.76(1 − e−t/38.81) + 122.25 (1 − e−t/2599.8) 285.10 0.89
236 810 ExpDec1 v(t) = 73.69 + 158.01e−t/89.88 73.69 0.80
Fissure water in limestone 134 6000 ExpDec1 v(t) = 364.50 + 122.04e−t/125.5 364.50 1
134 1700 ExpDec2 v(t) = 335.08–576.43e−t/28.8 + 87.56e−t/415.02 335.08 0.99
134 26,800 Logistic v(t) = 361.16 + 420.25/(1 + (t/39.34)6.98) 361.16 1
120 3430 Logistic v(t) = 220.21 + 217.20/(1 + (t/51.72)1.22) 220.21 1
Fissure water in schists 129 2750 ExpDec1 v(t) = 267.21 + 51.46e−t/181.21 267.18 1
129 920 ExpDec1 v(t) = 229.33 + 141.35e−t/69.91 229.33 1