Rubble Macro-porosity of Level Ice Accumulation on Wide Sloping Offshore Structures

Abstract

1. Ice block size distribution have significant effect on rubble porosity. The length and thickness of the ice blocks in the ice rubbles is measured with image processing approach. Correlation analysis shows that the ice block length has strong relation with ice thickness and E modulus (COV ~ 0.96). The term ∜Eh is a precise indicator the ice block length. The correlation is best when the power of h and E are between 0 and 1. Experimental data also shows that block thickness has no obvious relation with the flexural strength. At the low velocity v = 0.045m/s, the formula fits the experimental data is given as: (l_block ) ̅=0.096*∜(Eh_i )+0.001. At the high velocity v = 0.2m/s, the experimental data shows no clear relation with ice properties. The experimental data also shows that the ice block length decreases with increasing ice velocity. 2. Ice block thickness affects the length-to-thickness ratio and the fractional volume of fine ice. The experimental data shows between 0.008 to 0.013 m of thickness reduction appears at low velocity interaction (0.045m/s). These reduced thickness takes 17% to 24% of total thickness. At higher velocity (0.2m/s), between 0.011 to 0.016 m of thickness is reduced, taking between 26% to 32% of total ice thickness. The thickness reduction is the result of shaving a soft layer off the ice surface during the rubble accumulation process. Field observations may explain the soft layer as a skeleton layer (typically has a thickness of 2.5 cm) which is dependent on ice grow rate and independent of ice thickness. The experimental data shows the thickness reduction increases as increasing ice velocity, and also linearly related to ice thickness. Simple formulas to estimate block size is proposed: at low velocity (v = 0.045m/s), h_rd=0.189h_i+0.001; at high velocity (v = 0.2 m/s), h_rd=0.224h_i+0.003. 3. A ice block in rubble is the result of several breaks, while ice breaking in bending is simpler and well understood. The ice breaking lengths is estimated by two different approaches: processing images taken by surface cameras and analyzing ice load pattern. The results have good fit with each other. This proves the reliability of the data. A correlation analysis shows the breaking length is closely related to the ice block length. Two formulas are proposed to estimated block length with ice breaking length: (l_block ) ̅=0.356(l_image ) ̅+0.035 (COV = 0.79); (l_block ) ̅=0.529(l_force ) ̅+0.015 (COV = 0.97) 4. Two approaches are used to analyze experimental data to obtain rubble porosity: buoyance force method and analyzing the mount of the collected ice. Former researchers have found formulas to estimate ice rubble which consists of uniform particle. A new formula is proposed based on the old formula. The basic idea is that the space between uniform ice blocks is filled with fine ice. The assumptions behind formula are: 1.ice rubble consists fine ice and ice blocks; 2. Ice blocks has uniform size; 3. Ice blocks builds up the rubble structure and fine ice does not affect the rubble volume. The calculated values fit better with the experiential data. Another new approach is proposed by taking wide particle size distribution into account. The basic assumption behind this approach is that the void space between two particles is only determined by the void space around the smaller particle. 5. The two new approaches have several variations by replacing the block size terms in the formulas with terms containing h_i,E,l_force and l_image. These terms may be relatively easier to obtain especially when the ice rubble is accumulated underwater.