2.1.3. Mapping and Flow Rules

The classical radial mapping criterion developed by Dafalias [27] is used in the model, due to its effectiveness. The conventional radial mapping criterion was modified for soft clay in this research. The mapping rule is shown in Figure 3 and can be expressed as:

$$\begin{aligned} \overline{p} &= b(p - o\_p) + o\_p \\ \overline{s}\_{ij} &= b(s\_{ij} - o\_{i\bar{j}}) + o\_{i\bar{j}} \end{aligned} \tag{10}$$

2.1.3. Mapping and Flow Rules

where *b* is a scalar factor, that can be expressed as:

$$b = \frac{\delta\_0}{\delta\_0 - \delta'} \tag{11}$$

in which δ0−δ denotes the distance between the current stress point and the mapping center, and δ<sup>0</sup> indicates the distance from the current stress point to the image stress point. The loading index is calculated by imposing the consistency condition to its corresponding bounding surface equation: model parameter *β* controls the rate of damage accumulation. The decrease in *ω* represents the degradation in stiffness of the clay structure.

$$\Lambda = L = \frac{1}{\overline{\mathbb{K}}\_p} \left( \frac{\partial F}{\partial \overline{p}} d\overline{p} + \frac{\partial F}{\partial \overline{s}\_{ij}} d\overline{s}\_{ij} \right) \tag{12}$$

in which *K<sup>p</sup>* is the plastic modulus at image stress states. research. The mapping rule is shown in Figure 3 and can be expressed as:

**Figure 3.** Mapping rule in the bounding surface model. **Figure 3.** Mapping rule in the bounding surface model.
