*4.1. Representative Constitutive Relationship Equation for Each Region*

The constitutive relationship equations for a total of 23 dredged clay specimens from three regions and six groups were obtained through back analysis and the results of the centrifugal experiments. The equation of the power function is shown on a log–log scale and is the deduced representative equation for each of the six groups. The units of the constitutive equation are kPa of effective stress and m/day of permeability coefficient.

The Busan-L marine clay (Busan marine clays with low liquid limit) with a liquid limit in the 40–60% range in the Busan region dredged clay was analyzed using six specimens (bs-a, b, c, d, e, f). A constitutive relationship equation for the six specimens is shown in Figure 10 of the log–log scale. The representative constitutive relationship equation (bs-L-clay) of Busan-L marine clay can be expressed as e = 3.1σ 0−0.19 and <sup>k</sup> = <sup>9</sup> <sup>×</sup> <sup>10</sup>−<sup>6</sup> *e* 5.5 (A <sup>=</sup> 3.1, B <sup>=</sup> <sup>−</sup>0.19, C <sup>=</sup> <sup>9</sup> <sup>×</sup> <sup>10</sup>−<sup>6</sup> , D = 5.5) using the arithmetic mean on the log–log plot, as shown in Figure 10. The representative constitutive relationship equations of Busan-L marine clay had the coefficient of determination of 0.87 on void ratio–effective stress and 0.84 on void ratio–permeability. The Busan-H marine clay had a high liquid limit (LL = 60–80%) and was analyzed using four specimens (bs-g~k), as shown in Figure 11. The representative constitutive relationship equations of Busan-H clay (bs-H-clay) can be expressed as e = 4.3σ 0−0.20 and <sup>k</sup> = <sup>6</sup> <sup>×</sup> <sup>10</sup>−<sup>6</sup> *e* 4.5, and had the coefficient of determination of 0.97 on void ratio–effective stress and 0.88 on void ratio–permeability.

**Figure 10.** Constitutive relationship of Busan L marine clay (bs-L-clay): (**a**) void ratio vs. effective stress; (**b**) void ratio vs. permeability.

**Figure 11.** Constitutive relationship of Busan H marine clay (bs-H-clay): (**a**) void ratio vs. effective stress; (**b**) void ratio vs. permeability.

The Gwangyang-L marine clay with LL = 40–60% and the representative constitutive equation (gy-L-clay) of e = 2.9σ 0−0.18 and <sup>k</sup> = <sup>9</sup> <sup>×</sup> <sup>10</sup>−<sup>6</sup> *e* 6.0 was analyzed using five specimens (gy-a~e), as shown in Figure 12. The equations of gy-L-clay had the coefficient of determination of 0.95 on void ratio–effective stress and 0.86 on void ratio–permeability. The Gwangyang-H marine clay with a high liquid limit of 60–80% and the representative constitutive equation (gy-H-clay) of e = 3.9σ 0−0.20 and <sup>k</sup> = <sup>8</sup> <sup>×</sup> <sup>10</sup>−<sup>6</sup> *e* 4.5 was analyzed using four specimens (gy-f~j), as shown in Figure 13. The equations of gy-H-clay had the coefficient of determination of 0.88 on the e-σ 0 relationship and 0.77 on the e-k relationship.

**Figure 12.** Constitutive relationship of Gwangyang L marine clay (gy-L-clay): (**a**) void ratio vs. effective stress; (**b**) void ratio vs. permeability.

**Figure 13.** Constitutive relationship of Gwangyang H marine clay (gy-H-clay): (**a**) void ratio vs. effective stress; (**b**) void ratio vs. permeability.

The Incheon-L marine clay with LL = 20–30% and the representative constitutive equation (ic-L-clay) of e = 1.7σ 0−0.15 and <sup>k</sup> = <sup>1</sup> <sup>×</sup> <sup>10</sup>−<sup>4</sup> *e* 5.5 was analyzed using ic-b and ic-c specimens, as shown in Figure 14. The equations of ic-L-clay had the coefficient of determination of 0.98 on the e-σ 0 relationship and 0.92 on the e-k relationship. The representative constitutive equation (ic-H-clay) of the Incheon-H marine clay was e = 2.2σ 0−0.17 and k = <sup>5</sup> <sup>×</sup> <sup>10</sup>−<sup>5</sup> *e* 5.5, which was deduced from the ic-c and ic-d specimens, as shown in Figure 15. The equations of ic-H-clay had the coefficient of determination of 0.85 on the e-σ 0 relationship and 0.94 on the e-k relationship.

**Figure 14.** Constitutive relationship of Incheon L marine clay (ic-L-clay): (**a**) void ratio vs. effective stress; (**b**) void ratio vs. permeability.

**Figure 15.** Constitutive relationship of Incheon H marine clay (ic-H-clay): (**a**) void ratio vs. effective stress; (**b**) void ratio vs. permeability.

The representative constitutive relationship equations for each region are summarized in Table 3.


**Table 3.** Representative constitutive relationship equation.
