3-2. Earth pressure (Ps) acting on the sides of the model ice
The earth pressure acting on the sides of the ice can be active, at rest or passive, depending on the situation. In the experiments, a little great passive earth pressure was adopted.
here κ meets Z'(κ) = 0.
Kps = tan2（π/4 + φ/2)
The gouging depth (Z) is expressed as follows:
Z = X tan i - ζ(X) (3)
Here, ζ(X) is the gouging-curve, which is the locus of point B in Fig-2.
3-3. Accumulation height of sand (Z') during the movement of the ice
On the assumption that with no compression of sand and no decrease in the spaces between the sand grains, the quantity of the sand pushed aside by the model ice is equal to the sum of the quantity accumulated at the front and the quantity that flows out to the sides of the ice, and that the underwater angle of repose is constant at any place, its relationship can be expressed as follows:
Fig-3. The model to calculate the accumulation height of sand
3-4. Equation of motion in the horizontal direction
The equation of motion of the ice is expressed as follows:
3-5. Equation of motion in the vertical direction
Since the velocity of the ice is constant in the horizontal direction, the acceleration is zero. However, the acceleration occurs in the vertical direction because we assumed that the ice moves along a function ζ(X). Consequently,
h' is the draft, and when ho serves as the intial draft in X =0, the following formula is obtained:
h' = ho - ζ(X) (8)
3-6. Frictional force (FV) acting on the back of the ice between the ice and the connector FREE
