Numerical solutions for point masses sliding over analytical surfaces: Part 1

In this study, we introduce a system of differential equations describing the motion of a single point mass or of two interacting point masses on a surface, that is solved by a fourth-order explicit Runge\u2013Kutta (RK4) scheme. The forces acting on the masses are gravity, the reaction force of the surface, friction, and, in case of two masses, their mutual interaction force. This latter is introduced by imposing that the geometrical distance between the coupled masses is constant. The solution is computed under the assumption that the point masses strictly slide on the surface, without leaping or rolling. To avoid complications stemming from numerical errors related to real topographies that are only known over discrete grids, we restrict our attention to simulations on analytical continuous surfaces. This study sets the basis for a generalization to more complex systems of masses, such as chains or matrices of blocks that are often used to model complex processes such as landslides and rockfalls. The results shown in this paper provide a background for a companion paper in which the system of equations is generalized, and different geometries are presented

Numerical solutions for point masses sliding over analytical surfaces: Part 2

This paper is the second of two companion papers addressing the dynamics of two coupled masses sliding on analytical surfaces and interacting with one another. The motion occurs under the effect of gravity, the reaction force of the surface and basal friction. The interaction force maintains the masses at a fixed distance and lies on the line connecting them. The equations of motion form a system of ordinary differential equations that are solved through a fourth-order Runge\u2013Kutta numerical scheme. In the first paper we considered an approximate method holding when the line joining the masses is almost tangent to the surface at the instant mass positions. In this second paper we provide a general solution. Firstly, we present special cases in which the system has exact solutions. Second, we consider a series of numerical examples where the interest is focused on the trajectories of the masses and on the intensity and changes of the interaction force

Numerical Investigations on the Instability of Boulders Impacted by Experimental Coastal Flows

Coastal boulders transported inland by marine hazards, such as tsunamis and storms, are commonly found worldwide. Studies on the transport process of coastal boulders contribute to the understanding of a wide range of phenomena such as high-energy flow events, fluid-structure interaction, and coastal sediments. Consequently, it is crucial to understand how boulders move, but even more important to determine the instability condition for boulder transport. The hydrodynamic formulas including drag and lift coefficients are widely used to predict the incipient motion of boulders while few studies are conducted to evaluate the capability of these formulas. Recently, a series of laboratory experiments carried out at the Hydraulic Engineering Laboratory (Italian acronym LIDR) of the University of Bologna, Italy, revealed that boulders can start moving when the flow height and flow velocity are lower than the theoretical threshold computed by hydraulic formulas. In this paper, we use a numerical shallow water model to reproduce these freely available laboratory data with the aim of testing the capability of the model in capturing the main evolution of the process, and of casting new light on the instability condition of coastal boulders

Shallow landslides modeling using a particle finite element model with emphasis on landslide evolution

Abstract. Numerical modelling is a powerful tool to study the mechanism of landslides and constructs the foundation of many physically-based assessment methods applied to natural hazards. Usually, numerical analyses of landslides are carried out on the failure mechanism and on the propagation process separately. With the advantage of dealing with large deformation problems, the particle finite element method (PFEM), that is the particle extension of the traditional FEM, has the capability of simulating the entire evolution of the landslide from the generation to the deposition phase. To figure out the difference between a unified PFEM simulation and the usually adopted approaches that separate failure mechanism (static analysis) and run-out analysis (dynamic analysis), we implement a PFEM code that is applied first to a simple homogeneous slope model. Numerical results reveal that under the so-called critical condition the landslide comes to a stop with a slight modification of the original profile, while its profile is drastically changed if strength reduction is further applied. To test the capability of our model, we choose the 2013 Cà Mengoni landslide, northern Apennines, Italy, as a case study, since it behaved as if it were formed by homogeneous material. In virtue of the back-analysis of the run-out distance that we perform by using different material strength parameters, we show that the PFEM model is able to capture the variation of the observed landslide profile, and contributes to the understanding of the dynamics of the whole sliding process

On the evolution of elastic properties during laboratory stick-slip experiments spanning the transition from slow slip to dynamic rupture

The physical mechanisms governing slow earthquakes remain unknown, as does the relationship between slow and regular earthquakes. To investigate the mechanism(s) of slow earthquakes and related quasi-dynamic modes of fault slip we performed laboratory experiments on simulated fault gouge in the double direct shear configuration. We reproduced the full spectrum of slip behavior, from slow to fast stick slip, by altering the elastic stiffness of the loading apparatus (k) to match the critical rheologic stiffness of fault gouge (kc). Our experiments show an evolution from stable sliding, when k>kc, to quasi-dynamic transients when k ~ kc, to dynamic instabilities when k<kc. To evaluate the microphysical processes of fault weakening we monitored variations of elastic properties. We find systematic changes in P wave velocity (Vp) for laboratory seismic cycles. During the coseismic stress drop, seismic velocity drops abruptly, consistent with observations on natural faults. In the preparatory phase preceding failure, we find that accelerated fault creep causes a Vp reduction for the complete spectrum of slip behaviors. Our results suggest that the mechanics of slow and fast ruptures share key features and that they can occur on same faults, depending on frictional properties. In agreement with seismic surveys on tectonic faults our data show that their state of stress can be monitored by Vp changes during the seismic cycle. The observed reduction in Vp during the earthquake preparatory phase suggests that if similar mechanisms are confirmed in nature high-resolution monitoring of fault zone properties may be a promising avenue for reliable detection of earthquake precursors

Sequential coupled numerical simulations of an air/ground-source heat pump: Validation of the model and results of yearly simulations

Numerical simulations are important tools for the assessment of exploiting geothermal energy in heat pump applications. They can be used to evaluate the performance of the system, the long-term production scenarios and the sustainability of the geothermal reservoir. The present work introduces and describes a numerical model, in which a dedicated Matlab script has been realized to allow sequentially coupled simulations of a shallow geothermal reservoir and of a heat pump system. A mathematical model of a dual-source heat pump, working alternatively with the ground or the air as heat source/sink, has been developed in Matlab environment. The heat exchangers of the heat pump have been modelled considering the equations that govern the physical phenomena. The dynamic numerical simulator FEFLOW, based on the finite element method, has been used to simulate the behaviour of the geothermal reservoir, subjected to heat extraction/reinjection by a closed loop vertical heat exchangers field. This methodological approach is useful to evaluate the performance of the coupled system in the long term, and it is important for understanding the advantages and limits of the dual-source heat pump in assuring sustainability over time avoiding the depletion of geothermal resources. The models and their coupling have been calibrated and validated with experimental data from a shallow geothermal plant located in Tribano (Padova, IT). It consists of eight coaxial borehole heat exchangers 30 m deep, connected to a 16 kW dual-source heat pump prototype. The heat pump system provides heating and cooling to an office area. The coupled model has been used to compare the performance of the heat pump when working in air-mode only or in ground-mode only. This allowed the development of a switching control strategy between the two thermal sources. Yearly simulations with the switching strategy have shown that the seasonal performance factor of the dual-source heat pump during the heating mode can be 13.8 % higher compared to the one obtained with a conventional air source heat pump and 3.8 % higher with respect to a ground source heat pump

Mathematical Optimization Problems for Particle Finite Element Analysis Applied to 2D Landslide Modeling

n/

Earthquake-triggered landslides along the Hyblean-Malta Escarpment (off Augusta, eastern Sicily, Italy) – assessment of the related tsunamigenic potential

Abstract. Eastern Sicily is affected by earthquakes and tsunamis of local and remote origin, which is known through numerous historical chronicles. Recent studies have put emphasis on the role of submarine landslides as the direct cause of the main local tsunamis, envisaging that earthquakes (in 1693 and 1908) did produce a tsunami, but also that they triggered mass failures that were able to generate an even larger tsunami. The debate is still open, and though no general consensus has been found among scientists so far, this research had the merit to attract attention on possible generation of tsunamis by landslides off Sicily. In this paper we investigate the tsunami potential of mass failures along one sector of the Hyblean-Malta Escarpment (HME). facing Augusta. The HME is the main offshore geological structure of the region running almost parallel to the coast, off eastern Sicily. Here, bottom morphology and slope steepness favour soil failures. In our work we study slope stability under seismic load along a number of HME transects by using the Minimun Lithostatic Deviation (MLD) method, which is based on the limit-equilibrium theory. The main goal is to identify sectors of the HME that could be unstable under the effect of realistic earthquakes. We estimate the possible landslide volume and use it as input for numerical codes to simulate the landslide motion and the consequent tsunami. This is an important step for the assessment of the tsunami hazard in eastern Sicily and for local tsunami mitigation policies. It is also important in view of tsunami warning system since it can help to identify the minimum earthquake magnitude capable of triggering destructive tsunamis induced by landslides, and therefore to set up appropriate knowledge-based criteria to launch alert to the population

Landslide deposits

Eastern Sicily is affected by earthquakes and tsunamis of local and remote origin, which is known through numerous historical chronicles. Recent studies have put emphasis on the role of submarine landslides as the direct cause of the main local tsunamis, envisaging that earthquakes (in 1693 and 1908) did produce a tsunami, but also that they triggered mass failures that were able to generate an even larger tsunami. The debate is still open, and though no general consensus has been found among scientists so far, this research had the merit to attract attention on possible generation of tsunamis by landslides off Sicily. In this paper we investigate the tsunami potential of mass failures along one sector of the Hyblean-Malta Escarpment (HME). facing Augusta. The HME is the main offshore geological structure of the region running almost parallel to the coast, off eastern Sicily. Here, bottom morphology and slope steepness favour soil failures. In our work we study slope stability under seismic load along a number of HME transects by using the Minimun Lithostatic Deviation (MLD) method, which is based on the limit-equilibrium theory. The main goal is to identify sectors of the HME that could be unstable under the effect of realistic earthquakes. We estimate the possible landslide volume and use it as input for numerical codes to simulate the landslide motion and the consequent tsunami. This is an important step for the assessment of the tsunami hazard in eastern Sicily and for local tsunami mitigation policies. It is also important in view of tsunami warning system since it can help to identify the minimum earthquake magnitude capable of triggering destructive tsunamis induced by landslides, and therefore to set up appropriate knowledge-based criteria to launch alert to the population

A GIS interface to the new Euro-Mediterranean Tsunami Catalogue produced by the TRANSFER project

TRANSFER, acronym standing for “Tsunami Risk ANd Strategies For the European Region”, is a three-year EU-funded research project that tackled all the main fields of interest in tsunami research, ranging from the improvement of the existing tsunami catalogue and the inventory of seismic and non-seismic tsunami sources, to the assessment of tsunami hazard, vulnerability and risk through innovative deterministic and statistical methodologies, with the final goal of identifying the best strategies for the reduction of tsunami risk. One of the largest efforts produced by the TRANFER consortium has been to convey all the results obtained during the project life into a unique and standardised GIS platform. We present here in some detail the GIS implementation of the improved version of the Euro-Mediterranean Tsunami Catalogue, which is the result of a careful revision, re-analysis, correction and integration of the results produced in the nineties by the EU funded GITEC and GITEC-TWO projects. All the TRANSFER partners involved in this work made some relevant improvements of the quality of the database, in terms of inclusion of new events or updating (or even exclusion) of existing events. The major improvements introduced in the TRANSFER tsunami catalogue with respect to the previous ones are: 1) the enlargement of the geographical area containing historical events (now the catalogue integrates events belonging to the Levantine sea and to Iceland); 2) the inclusion of the tide-gauge data relative to specific historical events; 3) for few events, the position of the places for which tsunami run-up and inundation data are available; 4) the introduction of the 12- points tsunami intensity scale by Papadopoulos and Imamura (2001). The GIS environment and the power of the underlying Relational Database Management Systems (RDBMS) allows to query the database in several respects. The most obvious starts from the geographical map containing the position of the historical events plotted with symbol size and colours depending on their intensities. Two main ArcGIS tools are then used to access the other information on the event. The "Identify" tool opens up a mask from which the user can retrieve all the details on date, time, source region and sub-region, reliability, cause, source parameters (intensity, magnitude and focal depth for earthquakes), position of the source. In the same mask, different layers give access to the list of places hit by that specific tsunami, containing the position of the site and the maximum reported run-up and inundation distance, when available. Moreover, it contains the list of references to studies dealing with that particular event. On the other hand, the "Hyperlink" tool opens up a text file containing the full description of the event and, when available, diagrams of measured sea-level data and photographs or similar material. The whole catalogue can be accessed and queried also in table format, allowing the user to perform his/her specific searches