United void index for normalizing virgin compression of reconstituted clays

The intrinsic compression framework that uses the void index for normalizing the virgin compression of reconstituted clays has been widely applied for academic and practical purposes. Past studies have shown that the data of void index are scattered when the stress is out of the range from 100 to 1000 kPa. In this study, the key cause responsible for the scatter problem in the existing intrinsic compression framework is identified. A united void index is introduced for normalizing the compression curves of reconstituted clays over a wide stress range starting from the remoulded yield stress to 1000 kPa. The normalized unique line is termed the unified normalized compression line (UNCL). Its constitutive equation is established in terms of the united void index versus the effective vertical stress. The uniqueness of the UNCL is validated based on independent data from the literature and the data from the research team. It is suggested that the UNCL should be directly measured from the virgin compression. In the case without conducting consolidation tests, the correlations between the intrinsic parameters in the UNCL’s equation and two physical parameters are proposed for indirectly determining the UNCL. The accuracy of the empirical correlations is investigated via the comparisons between the calculated intrinsic parameters and the measurements.

SCATTER OF ROBOTS

In this paper, we investigate the scatter problem, which is defined as follows: Given a set of n robots, regardless of the initial position of the robots on the plane, eventually, no two robots are located at the same position forever. We show that this problem cannot be deterministically solved. Next, we propose a randomized algorithm. The proposed solution is trivially self-stabilizing. We then show how to design a self-stabilizing version of any deterministic solution for the Pattern Formation and the Gathering problems for any number n ≥ 2 of robots.