horizontal because the angle of rotation was negligible.
Fig-l. Diagram of the experimental devices
3. Formulae of calculations for ice forces using a simple mechanical model
Various external forces act on the model ice (Fig-2). These include the earth pressure acting on the front and sides of the model ice, the subgrade reaction and dynamic friction acting on the bottom of the model ice, and the buoyancy of the whole model. We disregarded the consecutive changes in the internal friction angle, nonuniformity of relative density of sand and the problems of permeability, because they are complicated here.
We assumed that the model ice moves along a function, Y = ζ(x) (called the gouging curve in this study), and we made this ζ the curve of the sixth order by using the method of least squares, from the observed values. When this gouging curve is settled definitely, the ice force (F) of the model ice can be obtained from (1) the equation of motion in the horizontal direction, (2) the equation of motion in the vertical direction and (3) the stability conditions of the ice. At this time, the ice force (F) corresponds to the pushing force with the oil jack in this experiment.
Fig-2. Mechanical model for ice gouging
3-1. Earth pressure (Pcp) acting on the front of the model ice
The earth pressure acting on the front of the ice is passive earth pressure. When using the Coulomb model, it is expressed as the formula (1). The sand in front of the ice has a two-angled slope.
where B is the width of the ice, and ζ is the friction angle
