Unified Mechanical Erosion Model for Multi-phase Mass Flows

Erosion poses a great challenge in multi-phase mass flows as it drastically changes flow behavior and deposition pattern by dramatically increasing their masses, adversely affecting population and civil structures. There exists no mechanically-explained, unified multi-phase erosion model. We constitute a novel, unified and comprehensive mechanical erosion rates for solid and fluid phases and demonstrate their richness and urgency. This is achieved by seminally introducing interacting stresses across erosion-interface. Shear resistances from the bed against shear stresses from the landslide are based on consistent physical principles. Proposed multi-phase interactive shear structures are mechanically superior and dynamically flexible. Total erosion rate is the sum of solid and fluid erosion rates which are mechanically extensive and compact. Erosion rates consistently take solid and fluid fractions from the bed and customarily supply to solid and fluid components in the flow. This overcomes severe limitations inherited by existing models. For the first time, we physically correctly construct composite, intricate erosion velocities of particle and fluid from the bed and architect the complete net momentum productions that include all interactions between solids and fluids in the landslide and bed. We invent stress correction, erosive-shear-velocity, super-erosion-drift and erosion-matrix characterizing complex erosion processes. By embedding well constrained extensive erosion velocities, unified erosion rates and net momentum productions including erosion-induced inertia into mass and momentum balances, we develop a novel, mechanically-explained, comprehensive multi-phase model for erosive mass flows. As new model covers a broad spectrum of natural processes it offers great opportunities for practitioners in solving technical, engineering problems related to erosive multi-phase mass flows

Extended landslide velocity and analytical drag

The landslide velocity plays a dominant role in estimating impact force and devastated area. Here, based on Pudasaini and Krautblatter (2022), I develop a novel extended landslide velocity model that includes the force induced by the hydraulic pressure gradient which was neglected by all the existing analytical landslide velocity models. By a rigorous conversion between this force and inertia, I develop two peer systems expecting to produce the same results. However, this contradicts with our conventional wisdom. This raises a question of whether we should develop some new balance equations. I compare the two velocity models that neglects and includes the force induced by the hydraulic pressure gradient. Analytical solutions produced by the two systems are different. The new model is comprehensive, elegant, and yet an extraordinary development as it reveals serendipitous circumstances resulting in a pressure-inertia-paradox. Surprisingly, the mass first moves upstream, then it winds back and accelerates downslope. The difference between the extended and simple solution widens strongly as the force associated with the hydraulic pressure gradient increases, demonstrating its importance. Viscous drag plays an important role in controlling the landslide dynamics. However, no explicit mechanical and analytical model exists for this. The careful sagacity of the graceful form of new velocity equation results in a mechanically extensive, dynamically evolving analytical model for viscous drag, the first of this kind. A dimensionless drag number is constructed. Contrary to the prevailing practices, I have proven that drags are essentially different for the expanding and contracting motions, an entirely novel perception. Drag coefficients are close to the often used empirical or numerical values. But, now, I offer an innovative, physically-founded analytical model for drag in mass flow simulation

The Trouble with Trebles: What Violates G.S. 75-1.1?

At first glance the North Carolina Unfair and Deceptive Trade Practices Act appears to be a broad, almost unconstitutionally vague statute. Its federal counterpart, the Federal Trade Commission Act, evoked similar responses when it was first enforced. Like the FTC Act, North Carolina General Statute § 75-1.1 has taken shape through judicial interpretation and legislative modification. (North Carolina General Statutes hereinafter referred to as G.S.). As this process has proceeded over the last decade or so, many aspects of the scope and application of the statute have been determined. No general answer, however, has been given to the question of just what does violate the statute. The boundary between a simple breach of contract, rendering one liable for at most simple damages, and an unfair trade practice, rendering one liable for treble damages and attorney\u27s fees, remains ill-defined. The significance of the question is clear, both to the used car dealer and his customer arguing over an $800 automobile, and to the businessman whose$8,000,000 deal falls through. This problem is highlighted, but not illuminated, by the conflict of analytical processes between the Supreme Court of North Carolina and the U.S. Court of Appeals for the Fourth Circuit. This conflict is evidence of uncertainty in the objectives of the statute and uncertainty among the judiciary as to the basic desirability of the statutory remedy

Reconstruction of the 1941 GLOF process chain at Lake Palcacocha (Cordillera Blanca, Peru)

The Cordillera Blanca in Peru has been the scene of rapid deglaciation for many decades. One of numerous lakes formed in the front of the retreating glaciers is the moraine-dammed Lake Palcacocha, which drained suddenly due to an unknown cause in 1941. The resulting Glacial Lake Outburst Flood (GLOF) led to dam failure and complete drainage of Lake Jircacocha downstream, and to major destruction and thousands of fatalities in the city of Huaráz at a distance of 23 km. We chose an integrated approach to revisit the 1941 event in terms of topographic reconstruction and numerical back-calculation with the GIS-based open-source mass flow/process chain simulation framework r.avaflow, which builds on an enhanced version of the Pudasaini (2012) two-phase flow model. Thereby we consider four scenarios: (A) and (AX) breach of the moraine dam of Lake Palcacocha due to retrogressive erosion, assuming two different fluid characteristics; (B) failure of the moraine dam caused by the impact of a landslide on the lake; and (C) geomechanical failure and collapse of the moraine dam. The simulations largely yield empirically adequate results with physically plausible parameters, taking the documentation of the 1941 event and previous calculations of future scenarios as reference. Most simulation scenarios indicate travel times between 36 and 70 min to reach Huaráz, accompanied with peak discharges above 10 000 m3 s−1. The results of the scenarios indicate that the most likely initiation mechanism would be retrogressive erosion, possibly triggered by a minor impact wave and/or facilitated by a weak stability condition of the moraine dam. However, the involvement of Lake Jircacocha disguises part of the signal of process initiation farther downstream. Predictive simulations of possible future events have to be based on a larger set of back-calculated GLOF process chains, taking into account the expected parameter uncertainties and appropriate strategies to deal with critical threshold effects