*2.3. Boundary Conditions*

At seabed surface (*z* = 0), the vertical effective stress and shear stress is assumed to be zero and the water pressure is directly acting on it.

$$
\sigma\_z' = \tau\_{\mathbf{x}z} = \mathbf{0}, \text{ and } \ p\_\mathbf{s} = P\_\mathbf{b}. \tag{18}
$$

where *P<sup>b</sup>* is the dynamic wave pressure at the seabed surface, which is obtained by the wave model.

For the soil resting on the seabed bottom and lateral boundaries, zero displacements and impermeable are considered at the seabed bottom (*z* = −*h*), i.e.,

$$u\_s = w\_s = 0, \quad \text{and} \quad \frac{\partial p\_s}{\partial z} = 0,\tag{19}$$

In addition, the boundary condition of tunnel surface is assumed to be impermeable with zero displacements, i.e.,

$$
\mu\_s = w\_s = 0, \quad \text{and} \quad \frac{\partial p\_s}{\partial n\_v} = 0,\tag{20}
$$

where *n<sup>v</sup>* denotes normal vector of the tunnel surface.
