*3.1. Estimation of Non-Linear Constitution Equation*

The dredged-reclaimed clay with a high void ratio should be estimated using finite strain consolidation theory due to huge deformations. The finite strain consolidation is suitable to analyze large deformations, considering the variation in the compressibility and permeability of clay as per effective stress. The variation in compressibility and permeability depend on the relationship void ratio (e)–effective stress (σ')–permeability coefficient (k) during analysis, and this relationship is called the constitutive relationship of finite strain consolidation theory [13,14]. The constitutive relationship between void ratio–effective stress and void ratio–permeability is examined in this section to choose a suitable constitutive relationship equation in Korea.

The constitutive relation equations were mostly the proposed exponential function and power function. Somogyi [8,9] proposed Equations (1) and (2) of the power function using the empirical data of void ratio–effective stress and void ratio–permeability:

$$\mathbf{e} = \mathbf{A} \sigma^{\prime B} \tag{1}$$

$$\mathbf{k} = \mathbf{C}e^{D} \tag{2}$$

where A, B, C, and D are the decided coefficients including the material properties observed during the test or empirical study. These equations were used in this study due to the following three considerations. First, there should be an equation that was proposed from research on Korean clay. Second, there should be an equation that represents a reasonable relationship between the void ratio–effective stress and void ratio–permeability coefficient in the high void ratio range. Finally, there should be a simple equation to propose a design chart.
