Table 4.

The calculations of total compaction work using the integral equation.

Total Work Calculated Under Specified Conditions W(τ, φ)	Determination Coefficient R2 (SD)	Displacement l (SD), mm	Total Compaction Work, J (SD)
$W_{(f_1,ABS25\%)}={\int }_0^{0.001\cdot l}-2\times {10}^{-5}{x}^6+0.0004x^5-0.0028x^4+0.0088x^3-0.01x^2+0.0035x$	0.9690 (0.0335)	6.93 (0.001)	8.296 × 10−8 (7.043 × 10−8) a
$W_{(f_1,ABS50\%)}={\int }_0^{0.001\cdot l}0.0139x^2-0.0123x$	0.9717 (0.0051)	3.50 (0.033)	7.514 × 10−8 (2.572 × 10−7) a
$W_{(f_2,ABS25\%)}={\int }_0^{0.001\cdot l}7\times {10}^{-5}{x}^2+0.0011x$	0.9595 (0.0028)	5.34 (0.009)	1.571 × 10−8 (4.735 × 10−7) a
$W_{(f_2,ABS50\%)}={\int }_0^{0.001\cdot l}6\times {{10}^{-4}x}^2+0.0002x$	0.9846 (0.0461)	8.65 (1.299)	1.234 × 10−8 (6.399 × 10−5) a

SD—standard deviation, ^a—homogeneous groups.