cm and 76 cm collided with boards attached to bridge piers at an angle of 67° from the horizontal plane, the average maximum ice pressure was 7.3 kgt/ccm2, 8.7 kgf/ccm2 and 9.6 kgf/ccm2, respectively. Given a vertically attached board, these values will be converted into 15.5 kgf/ccm2, 18.5 kgf/ccm2 and 20.4 kgf/ccm2, because from a study by Saeki et aI.6)the ice pressure on the board fixed at an angle of 67° from the horizontal plane is 0.47 times as large as the ice pressure on the board vertically fixed. The temperature at that time was about 0 ℃. Butkovich7 reported that the unconfined compressive strength of fresh water ice is between 16.2 kgf/ccm2 and 20.4 kgf/ccm2 at 0℃. Consequently, the dimensionless maximum impact force in the experiment by Neill was between 0.86 and 1.13 when the unconfined compressive strength of ice was 18 kgf/ccm2. Neill gave no information on the size of the ice used for his experiment, but we consider the size to be quite large because of the river width of 300 m and the ice thickness of 38 cm to 76 cm. Therefore, the momentum also appears to be considerably larger than the momentum of our experiment, while its dimensionless maximum impact force was about I. This shows that although the impact ice force increases with an increase in the momentum, the impact ice force is constant above a certain value of the momentum.
4. Example of the Calculation of the Impact Ice Force on the Gate of Sea Embankments
Saeki et al.1) and Takahashi et al.2)studied the impact velocities between ice floes and upright structures when the ice floes run up onto the shore by tsunamis, using data of installation sites of such structures and differences in the topography. According to their studies, the impact velocity is greater as the breaking wave height increases and as the size of an ice floe decreases. Kunimatsu et al.3) clarified the relationship between the size and thickness of ice floes along the Okhotsk Sea coast. From their results, the ice floes are considered to be almost square, and the thickness (h) increases with an increase in the length of one side (b), but the rate of the increase gradually reduces
In this study, we considered waves with a breaker height (Hb) of 3.6 m as a tsunami model and also a model in which an upright structure is placed at a site five times as far as a breaker height from the shoreline and where both land and water areas have an equal gradient (1/30). As waves break and run up onto the shore, the wave height in front of the structure will be about 0.9 m (Saeki et al.1). Therefore, collisions with the structure are difficult given this model, because sea ice with a thickness of over 0.9 m will make contact with the bottom of sea. Since the ice is a square with sides 3.0 m when its thickness is about 0.9 m (Kunimatsu et al.3), many of the ice floes running up will be those with sides below 3.0 m. In this experiment, ice plates with sides corresponding to 0.9 m, 2.1 m and 3.0 m in actual length were used. The ice thickness for each of the sizes of these ice plates was 40 cm, 76 cm and 90 cm, respectively. When the proportion of ice cover is 20%, which is the proportion where the impact velocity (Cic) of these floes with structures reaches the maximum, the impact velocities of the ice floes with sides of 0.9 m, 2.1 m and 3.0 m are 5.6 m/s, 3.9 m/s and 4.0 m/s (Takahashi et al.2), respectively. And the momentum (M) of the ice floes immediately before the collision is also 167 kg m/s, 1200 kg m/s and 2976 kg m/s, respectively, from the calculation. We found that the momentum of the ice with sides of 3 m is the largest, which is far larger than the momentum in our experiment. The dimensionless impact ice force from the experiment by Neill 5) is not so large, being about 1, in spite of a large momentum; this is applied to determine the maximum impact ice force as Fmax = bh σ c That is, the maximum impact ice force is determined by the area of contact (bh) between the ice and structure and the unconfined compressive strength (σ c) of ice, without depending on the momentum.
The ice floes we discuss here are the drift ice that begins to freeze in the northern region of the Okhotsk Sea around November, and floats through the Nemuro Strait as far as the Pacific coast of Hokkaido. Cold air masses from Siberia contribute to the growth of the drift ice moving south. With the growth, the salinity concentration of the ice decreases, resulting in a decrease in the density. When the drift ice reaches the coast of Hokkaido, its strength has been reduced. The strength of the ice that reaches the Pacific coast of Hokkaido is about 10 kgf/ccm2 after 90 days from the beginning of freezing and when the ice temperature is -2℃.
When σ c = 10 kgf/ccm2 and the ice floe has sides of 3.0 m and a thickness of 90 cm, the maximum impact ice force is calculated to be 270 tf. In reality the cross-sections of ice floes are not homogeneous; their shape is polygonal and the contact length is less than 3.0 m. Furthermore, since not all angles formed when the ice floe collides with a structure are vertical, the impact ice forces in reality are smaller than that from this calculation (270 tf).
In the future, further investigation is needed to find the lateral shape of the drift ice along the Okhotsk coast of Hokkaido and the effect of the shape on the ice forces exerted when the ice collides with structures.
