Probability distribution for the shear strength of seafloor sediment in the KR5 area for the development of manganese nodule miner

Abstract

Probability distribution for shear strengths of seafloor sediment is investigated in order to apply one of the probability distributions to a reliability based design for the development of a tracked vehicle of deepsea manganese nodule miner. Shear strengths of seafloor sediment were measured using a shear vane meter at 2 cm steps until reaching the total sampled depth. The seafloor sediments were collected by multiple corer in the KR5 (Korea Reserved 5) area in the Clarion-Clipperton fracture zone of the northeastern equatorial Pacific depth between 1997-2006. A representative value of TSS (Transition Shear Strength) at VCS (Vehicle Contact Surface) is proposed as 1.0 kPa. It is assumed that the upper sediment of VCS would be removed together with the nodules due to the hydraulic momentum of the water-jet of the miner while deep-sea mining. The shear strength of seafloor sediment is calculated by using a linear interpolation of 2 cm intervals down to 22 cm in depth under the VCS from the original data. Descriptive statistics are provided in a box plot and in a table for the calculated shear strength at each depth. Distribution fitting is performed with respect to 65 probability models using one of the four distribution fitting methods: Maximum Likelihood Estimation, Method of Moments, Least Square Estimation, and Methods of L-Moments. The K-S (Kolmogorov-Smirnov) test is applied to decide whether the shear strength data comes from a hypothesized probability distribution. Test statistics, the maximum distance between the empirical CDF (Cumulative Distribution Function) of the shear strength data, and the theoretical CDF of a probability distribution are used as the decision criterion based on significant fit and best fit. The probability distributions regarded as significant fits and best fits are decided for each depth. The minimum average and minimum standard deviation of test statistics are selected for the criteria choosing the best fit at all depths. It is concluded that the Wakeby distribution is the best fit with respect to the smallest average. The log-logistic distribution is also the best fit with respect to the smallest standard deviation. This distribution also has the 3rd rank in the average criterion.