Stability of Low Crested and Submerged Breakwaters: A Reanalysis and Model Development

Low-crested and submerged structures (LCS) play an integral part in the stabilization of shorelines for recreational purposes, yet there are a plethora of empirical models and gaps in the understanding of their stability and damage progression. The objectives were: i) to evaluate the present formulae, ii) explore variable importance, iii) formulate a stability model, iv) extend the current datasets and v) explore a new model for LCS. The literature points to an increasing understanding of the initiation of damage of LCS and recent exploration of the shear stress-induced erosion (van Rijn, 2019). Assessment of two existing models (Kramer, 2006 and Van der Meer and Daemen, 1994) points to reliability in predicting initiation of damage but limitations in skill in modelling progression of damage, for Re \u3e40,000. Two analytical models (and two variations) developed herein point to difficulty (skill) in predicting damage initiation (progression) and the benefit of removing transmitted wave energy. A scale model testing programme added 124 new data points and confirms the importance of relative crest height, increased relative vulnerability of the seaward slope and crest and damage progression. Exploration of several improvements in the model was useful in deriving an LCS model that predicted damage similar to the pooled data and offered insights into the importance of i) seaward slope erosion, ii) drag and lift forces, and iii) Shield\u27s stress relation to relative depth and stone size, Re and gradation. Importantly, damage progression is likely to be non-linear. The model is likely to be conservative and best applied for

Non-equilibrium Thermodynamics of Spacetime

It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS = dQ/T hold for all local acceleration horizons through each spacetime point, where dS is one quarter the horizon area change in Planck units, and dQ and T are the energy flux across the horizon and Unruh temperature seen by an accelerating observer just inside the horizon. Here we show that a curvature correction to the entropy that is polynomial in the Ricci scalar requires a non-equilibrium treatment. The corresponding field equation is derived from the entropy balance relation dS =dQ/T+dS_i, where dS_i is a bulk viscosity entropy production term that we determine by imposing energy-momentum conservation. Entropy production can also be included in pure Einstein theory by allowing for shear viscosity of the horizon.Comment: 4 pages. Dedicated to Rafael Sorkin on the occasion of his 60th birthda