The Mechanics of Landslide Mobility with Erosion

Abstract

<p>Erosion can dramatically change the dynamics and deposition morphology and escalate the destructive power of a landslide by rapidly amplifying its volume, turning it into a catastrophic event. Mobility is the direct measure of the thread posed by an erosive landslide as it plays a dominant role in controlling the enormous impact energy. However, no clear-cut mechanical condition has been presented so far for when and how the erosive landslide gains or loses energy resulting in enhanced or reduced mobility. We pioneer a mechanical model for the energy budget of an erosive landslide that delineates the enhanced or reduced mobility. A fundamentally new understanding is that the increased inertia due to the increased mass is not related to the landslide velocity, but it is associated with the distinctly different entrainment velocity emerging from the inertial frame of reference. The true inertia can be much less than incorrectly proposed previously. We eliminate the existing erroneous perception and make a breakthrough in correctly determining the mobility of the erosive landslide. We reveal that the erosion velocity plays an outstanding role in appropriately determining the energy budget of the erosive landslide. Crucially, whether the erosion related mass flow mobility will be enhanced, reduced or remains unaltered depends exclusively on whether the newly constructed energy generator is positive, negative or zero. This provides a first-ever explicit mechanical quantification of the state of energy, and thus, the precise description of mobility. This becomes a game-changer and fully addresses the long-standing scientific question of why and when some erosive landslides have higher mobility, while others have their mobility reduced. By introducing three important novel mechanical concepts: erosion-velocity, entrainment-velocity and energy-velocity, we demonstrate that the erosion and entrainment are essentially different processes. With this, we draw a central inference: that the landslide gains energy and enhances its mobility if the erosion velocity is greater than the entrainment velocity. The energy velocity delineates the three excess energy regimes: positive, negative and zero. We establish a mechanism of landslide-propulsion that emerges from the net momentum production, providing the erosion-thrust to the landslide. Analytically obtained velocity quantifies the effect of erosion in landslide mobility and indicates the fact that erosion can have the major control on the landslide dynamics. We have also presented a full set of dynamical equations in conservative form in which the momentum balance correctly includes the erosion induced change in inertia and the momentum production. This is a great advancement in legitimate simulation of landslide motion with erosion.</p>

Erosion Mechanisms of Debris Flow on the Sediment Bed

“…As physically modeled in Pudasaini and Krautblatter (2021), a comparison of detailed sensor data indicates that erosion mechanisms induced significant differences in the erosion pattern and mean erosion rate of CBS and WBS. As shown in Figures 10 and 11, the black traces depict flow surface level h ( t ), basal total normal stress σ ( t ) and basal pore‐fluid pressure p ( t ) measured as the released flows C1, C2, C4 and C6 interacted with the bed sediment at x = 5.8 m (Zheng, 2021).…”

“…g is gravitational acceleration. The shear stress τ d exerted on the debris flow is expressed as (Pudasaini & Fischer, 2020a; Pudasaini & Krautblatter, 2021) $$${\tau }_{d}=\mu (\rho gH\,\mathrm{cos}\alpha -{p}_{f})$$$ where, ρ is the flow‐front density and H is the flow depth. μ is the Coulomb friction coefficient and p f is the fluid stress in the debris flow.…”

“…Currently, the research of erosion mechanisms is focused on the invasive overlying flow (de Haas & van Woerkom, 2016). The feedback effect of the underlying bed sediment on the erosion process has rarely been studied (Pudasaini & Fischer, 2020a; Pudasaini & Krautblatter, 2021). In reality, debris‐flow erosion depends on the interaction between the flow and bed sediment.…”

“…We conducted a series of erosion experiments under closely controlled conditions to analyze the feedback effects of bed sediments on flow characteristics such as flow depth and velocity, investigate the difference in erosion rates, and discern the erosion patterns. Following the mechanical model by Pudasaini and Fischer (2020a) and Pudasaini and Krautblatter (2021), a hypothesis is proposed that the erosion of bed sediment strongly influences flow behavior, which in turn affects their erosion pattern and erosion rate. By observing how the type of bed sediment controls the erosion patterns, we were able to reveal the interaction between a debris flow and a sediment bed during erosion.…”

Helmoltz problem for the Riccati equation from an analogous Friedmann equation

“…where c 0,1 are constants, which describes many physical systems including, e.g., falling raindrops [21,22] or charges in constant electric field, avalanches [15], debris slides [16], geomagnetic fields [17], and box models of ocean basins [18]; the Riccati equation is also related to the Schrödinger, the Ermakov-Pinney, and other equations of fundamental physics [19,20]. A second order equation is naturally associated with Eq.…”