A basal slip model for Lagrangian finite element simulations of 3D landslides

A Lagrangian numerical approach for the simulation of rapid landslide runouts is presented and discussed. The simulation approach is based on the so‐called Particle Finite Element Method. The moving soil mass is assumed to obey a rigid‐viscoplastic, non‐dilatant Drucker–Prager constitutive law, which is cast in the form of a regularized, pressure‐sensitive Bingham model. Unlike in classical formulations of computational fluid mechanics, where no‐slip boundary conditions are assumed, basal slip boundary conditions are introduced to account for the specific nature of the landslide‐basal surface interface. The basal slip conditions are formulated in the form of modified Navier boundary conditions, with a pressure‐sensitive threshold. A special mixed Eulerian–Lagrangian formulation is used for the elements on the basal interface to accommodate the new slip conditions into the Particle Finite Element Method framework. To avoid inconsistencies in the presence of complex shapes of the basal surface, the no‐flux condition through the basal surface is relaxed using a penalty approach. The proposed model is validated by simulating both laboratory tests and a real large‐scale problem, and the critical role of the basal slip is elucidated. Copyright © 2016 John Wiley & Sons, Ltd.     

The flow dynamics of an extremely large volume pyroclastic flow,the 2.08-Ma Cerro Galán Ignimbrite,NW Argentina,and comparison with other flow types

The 2.08-Ma Cerro Galán Ignimbrite (CGI) represents a >630-km³ dense rock equivalent (VEI 8) eruption from the long-lived Cerro Galán magma system (∼6 Ma). It is a crystal-rich (35–60%), pumice (<10% generally) and lithic-poor (<5% generally) rhyodacitic ignimbrite, lacking a preceding plinian fallout deposit. The CGI is preserved up to 80 km from the structural margins of the caldera, but almost certainly was deposited up to 100 km from the caldera in some places. Only one emplacement unit is preserved in proximal to medial settings and in most distal settings, suggesting constant flow conditions, but where the pyroclastic flow moved into a palaeotopography of substantial valleys and ridges, it interacted with valley walls, resulting in flow instabilities that generated multiple depositional units, often separated by pyroclastic surge deposits. The CGI preserves a widespread sub-horizontal fabric, defined by aligned elongate pumice and lithic clasts, and minerals (e.g. biotite). A sub-horizontal anisotropy of magnetic susceptibility fabric is defined by minute magnetic minerals in all localities where it has been analysed. The CGI is poor in both vent-derived (‘accessory’) lithics and locally derived lithics from the ground surface (‘accidental’) lithics. Locally derived lithics are small (<20 cm) and were not transported far from source points. All data suggest that the pyroclastic flow system producing the CGI was characterised throughout by high sedimentation rates, resulting from high particle concentration and suppressed turbulence at the depositional boundary layer, despite being a low aspect ratio ignimbrite. Based on these features, we question whether high velocity and momentum are necessary to account for extensive flow mobility. It is proposed that the CGI was deposited by a pyroclastic flow system that developed a substantial, high particle concentration granular under-flow, which flowed with suppressed turbulence. High particle concentration and fine-ash content hindered gas loss and maintained flow mobility. In order to explain the contemporaneous maintenance of high particle concentration, high sedimentation rate at the depositional boundary layer and a high level of mobility, it is also proposed that the flow(s) was continuously supplied at a high mass feeding rate. It is also proposed that internal gas pressure within the flow, directed downwards onto the substrate over which the flow was passing, reduced the friction between the flow and the substrate and also enhanced its mobility. The pervasive sub-horizontal fabric of aligned pumice, lithic and even biotite crystals indicates a consistent horizontal shear force existed during transport and deposition in the basal granular flow, consistent with the existence of a laminar, shearing, granular flow regime during the final stages of transport and deposition.     

Development and Application of 2D and 3D GRASS Modules for Simulation of Thermally Driven Slope Winds

The ability to manage and process fully three‐dimensional information has only recently been made available for a few Geographical Information Systems (GIS). An example of integrated and complementary use of 2D and 3D GRASS modules for the evaluation and representation of thermally induced slope winds over complex terrain is presented. The analytic solution provided by Prandtl (1942) to evaluate wind velocity and (potential) temperature anomaly induced by either diurnal heating or nocturnal cooling on a constant angle slope is adopted to evaluate wind and temperature profiles at any point over both idealised and real complex terrain. As these quantities depend on the slope angle of the ground and on the distance from the slope surface suitable procedures are introduced to determine the coordinate n of a point in the 3D volume measured along the direction locally normal to the terrain surface. A new GRASS module has been developed to evaluate this quantity and to generate a 3D raster file where each cell is assigned the value of the cell on the surface belonging to the normal vector. The application of the algorithm implemented in GRASS to an ideal valley and to a real valley close to the city of Trento in the Alps provides results in accordance with data reported in the literature. An extension of Prandtl's (1942) model to take into account humidity and evaporation processes on the soil is also proposed and implemented.     

Constraining the dark matter annihilation cross-section with Cherenkov telescope observations of dwarf galaxies

The presence of dark matter in the halo of our Galaxy could be revealed through indirect detection of its annihilation products. Dark matter annihilation is one possible interpretation of the recently measured excesses in positron and electron fluxes, provided that boost factors of the order of 10³ or more are taken into account. Such boost factors are actually achievable through the velocity-dependent Sommerfeld enhancement of the annihilation cross-section. Here, we study the expected γ-ray flux from two local dwarf galaxies for which Cherenkov telescope measurements are available, namely Draco and Sagittarius. We use recent stellar kinematical measurements to model the dark matter haloes of the dwarfs and the results of numerical simulations to model the presence of an associated population of subhaloes. We incorporate the Sommerfeld enhancement of the annihilation cross-section. We compare our predictions with the observations of Draco and Sagittarius performed by MAGIC and HESS, respectively, and derive exclusion limits on the effective annihilation cross-section. We also study the sensitivities of Fermi and of the future Cherenkov telescope array to cross-section enhancements. We find that the boost factor due to the Sommerfeld enhancement is already constrained by the MAGIC and HESS data, with enhancements greater than ∼10⁴ being excluded.     

Surface flow boundary conditions in modeling land subsidence due to fluid withdrawal

Land subsidence due to subsurface fluid (water, gas, oil) withdrawal is often predicted by either finite element or finite difference numerical models based on coupled poroelastic theory, where the soil is represented as a semi-infinite medium bounded by the traction-free (ground) surface. One of the variables playing a most important role on the final outcome is the flow condition used on the traction-free boundary, which may be assumed as either permeable or impermeable. Although occasionally justified, the assumption of no-flow surface seems to be in general rather unrealistic. A permeable boundary where the fluid pressure is fixed to the external atmospheric pressure appears to be more appropriate. This paper addresses the response, in terms of land subsidence, obtained with a coupled poroelastic finite element model that simulates a distributed pumping from a horizontal aquifer confined between two relatively impervious layers, and takes either a permeable boundary surface, i.e., constant hydraulic potential, or an impermeable boundary, i.e., a zero Neumann flow condition. The analysis reveals that land subsidence is rather sensitive to the flow condition implemented on the traction-free boundary. In general, the no-flow condition leads to an overestimate of the predicted ground surface settlement, which could even be 1 order of magnitude larger than that obtained with the permeable boundary.     

Land uplift due to subsurface fluid injection

The subsurface injection of fluid (water, gas, vapour) occurs worldwide for a variety of purposes, e.g. to enhance oil production (EOR), store gas in depleted gas/oil fields, recharge overdrafted aquifer systems (ASR), and mitigate anthropogenic land subsidence. Irrespective of the injection target, some areas have experienced an observed land uplift ranging from a few millimetres to tens of centimetres over a time period of a few months to several years depending on the quantity and spatial distribution of the fluid used, pore pressure increase, geological setting (depth, thickness, and area extent), and hydro-geomechanical properties of the injected formation. The present paper reviews the fundamental geomechanical processes that govern land upheaval due to fluid injection in the subsurface and presents a survey of some interesting examples of anthropogenic uplift measured in the past by the traditional levelling technique and in recent times with the aid of satellite technology. The examples addressed include Long Beach, Santa Clara Valley, and Santa Ana basin, California; Las Vegas Valley, Nevada; Cold Lake and other similar sites, Canada; Tokyo and Osaka, Japan; Taipei, Taiwan; Krechba, Algeria; Upper Palatinate, Germany; Chioggia and Ravenna, Italy.     

Improved Leap—Frog Symplectic Integrators for Orbits of Small Eccentricity in the Perturbed Kepler Problem

I have improved the precision of the leap–frog symplectic integrators for perturbed Kepler problems at small eccentricities, without significant loss of CPU time. The integration scheme proposed is competitive, in some situations, with the so-called mixed variable integrators.     

Analysis of the Chaotic Behaviour of Orbits Diffusing along the Arnold Web

In a previous work [Guzzo et al. DCDS B 5, 687–698 (2005)] we have provided numerical evidence of global diffusion occurring in slightly perturbed integrable Hamiltonian systems and symplectic maps. We have shown that even if a system is sufficiently close to be integrable, global diffusion occurs on a set with peculiar topology, the so-called Arnold web, and is qualitatively different from Chirikov diffusion, occurring in more perturbed systems. In the present work we study in more detail the chaotic behaviour of a set of 90 orbits which diffuse on the Arnold web. We find that the largest Lyapunov exponent does not seem to converge for the individual orbits while the mean Lyapunov exponent on the set of 90 orbits does converge. In other words, a kind of average mixing characterizes the diffusion. Moreover, the Local Lyapunov Characteristic Numbers (LLCNs), on individual orbits appear to reflect the different zones of the Arnold web revealed by the Fast Lyapunov Indicator. Finally, using the LLCNs we study the ergodicity of the chaotic part of the Arnold web.     

Sun–Earth L_{1} and L_{2} to Moon transfers exploiting natural dynamics

This paper examines the design of transfers from the Sun–Earth libration orbits, at the \(L_{1}\) and \(L_{2}\) points, towards the Moon using natural dynamics in order to assess the feasibility of future disposal or lifetime extension operations. With an eye to the probably small quantity of propellant left when its operational life has ended, the spacecraft leaves the libration point orbit on an unstable invariant manifold to bring itself closer to the Earth and Moon. The total trajectory is modeled in the coupled circular restricted three-body problem, and some preliminary study of the use of solar radiation pressure is also provided. The concept of survivability and event maps is introduced to obtain suitable conditions that can be targeted such that the spacecraft impacts, or is weakly captured by, the Moon. Weak capture at the Moon is studied by method of these maps. Some results for planar Lyapunov orbits at \(L_{1}\) and \(L_{2}\) are given, as well as some results for the operational orbit of SOHO.     

The effects of differential subsidence and coastal topography on high-order transgressive-regressive cycles: Pliocene nearshore deposits of the Val d'Orcia Basin, Northern Apennines, Italy

This study focuses on the lowstand and early transgressive systems tracts of a basin-fill sequence of lower Pliocene nearshore deposits in the Val d'Orcia Basin of the Northern Apennines, Italy. The basin at that time was a semi-enclosed marine embayment, and, in the study area, its margin was subject to highly variable subsidence along the depositional strike, attributed to a decrease in tectonic displacement. The nearshore succession in the more rapidly-subsiding segment of the basin is around 20 m thick, comprising three storeys of laterally-stacked Gilbert-type delta lobes overlain by a shoal-water delta, whereas the nearshore succession in the adjacent, more slowly-subsiding segment, is up to 9 m thick. This succession is characterised by alternation of shoreface and offshore deposits, moderately wave-worked and covered by shoal-water deltaic facies.These coeval nearshore successions consist of several transgressive-regressive cyclothems. The development and lateral variation of the cyclothems was controlled by the local subsidence rate and coastal topographic gradient. Some of the cyclothems are considered to be higher-order sequences and others to be parasequences, with the former passing laterally into the latter in the area where the sea-level fall was countered by fast local subsidence. Some of the bounding surfaces are of limited lateral extent, with two parasequences passing laterally into a single one.Coastal topography controlled particularly the thickness of transgressive deposits. In the low-gradient setting of a delta plain, the relative sea-level rises caused major landward shifts of the shoreline and reduced fluvial sediment supply, with the formation of a transgressive lag in sediment-starved conditions. In the high-gradient coastal setting of the non-deltaic zone, the shoreline shift was minimal and had relatively little impact on local sediment supply, which promoted an accretionary transgression.At the end of the lowstand stage, the rate of sediment accumulation in the non-deltaic nearshore zone was lower, allowing the onset of subsequent transgression to be recorded considerably earlier than in the deltaic nearshore zone. This diachroneity suggests that facies criteria alone may not necessarily be a reliable basis for the recognition of systems tract boundaries.