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The stability properties of a freely rotating rigid body are governed by the intermediate axis theorem, i.e., rotation around the major and minor principal axes is stable whereas rotation around the intermediate axis is unstable. The stability of the principal axes is of importance for the prediction of rockfall. Current numerical schemes for 3D rockfall simulation, however, are not able to correctly represent these stability properties. In this paper an extended intermediate axis theorem is presented, which not only involves the angular momentum equations but also the orientation of the body, and we prove the theorem using Lyapunov’s direct method. Based on the stability proof, we present a novel scheme which respects the stability properties of a freely rotating body and which can be incorporated in numerical schemes for the simulation of rigid bodies with frictional unilateral constraints. In particular, we show how this scheme is incorporated in an existing 3D rockfall simulation code. Simulations results reveal that the stability properties of rotating rocks play an essential role in the run-out length and lateral spreading of rocks., Projekt DEAL

Does rock shape matter to the mitigation effects of trees on rockfall hazards? This question must be resolved in order to better quantify the protective role of mountain forests against rockfall. To probe this question, we investigate a single rock-tree interaction using non-smooth, hard-contact mechanics that allows us to consider rock shape at impact. The interaction of equant shaped rocks with cylinder-like tree stems is modeled. The equant shaped rocks are close to spherical but have a certain shape variability governed by the rock’s surface area ratio and aspect ratio. This work serves as an important follow-up study to the existing investigations from Toe et al. (Landslides 14: 1603-1614, 2017), where the effects of trees on block propagation are numerically investigated using spherical shaped rocks. The objective of our simulations is to understand how and to what extent, shape will influence energy dissipation and trajectory change. The primary results include: surface area ratio plays a more important role than aspect ratio in determining the rock’s post-impact dynamics. The primary parameters governing the rock kinematics after impact (i.e., block’s energy reduction, reflected rotational speed, and trajectory change) are impact velocity, impact eccentricity, and the tree stem diameter. The latter observation aligns well with previous findings and suggests that the shape factors, at least for nearly spherical rocks, can be integrated into the current block propagation models. However, from a statistical viewpoint, the anisotropic distribution of mass and hence the asymmetric moment of inertia of non-spherical rocks leads to stronger or weaker spin effects compared to mass- and volume-equivalent spheres. Apparently, the rotational motion of an irregular object serves as a kinetic energy reservoir leading to subsequent rock-tree impacts, and therefore significant differences in energy loss and trajectory in comparison to spherical shaped rocks. This effect must be further investigated using elongated and flattened blocks and underscores the importance of measuring rockfall rotation in experimental investigations.

An accurate modelling of rockfall runout continues to be a demanding challenge within the geotechnical and hazards engineering community. Most existing rockfall dynamic programs apply effective restitution coefficients to model the energy dissipation during the rock-ground interaction. Recent experimental measurements, however, reveal the limitations of effective restitution coefficients, especially to account for scarring with frictional rebound in soft compactable soils. This study proposes a three-dimensional, non-smooth computational mechanic approach to model dissipative rock-ground interactions in soft compactable soils. The ground is mathematically divided into a soft, compactable scarring layer and a hard rebound layer. The model considers the plastic deformation of the ground with rotating rocks of general, non-spherical shape. The simulated rockfall energy dissipation is validated at both the single impact and multi-impact levels using induced 780-kg rockfall experiments performed at Chant Sura, Switzerland, in 2018. Overall, the numerical results are in good quantitative agreement with the experimental measurements. Ongoing improvements of the scar drag model are to integrate rotational drag into the rock energy dissipation term, and to calibrate the drag parameters in depths using repetitive rockfall experiments spanning a greater range of rock shapes and masses.

This work focuses on the in-depth reconstruction of the full set of parameters of interest in single-block rockfall trajectories. A comprehensive understanding of rockfall trajectories holds the promise to enhance the application of numerical models for engineering hazard analysis. Such knowledge is equally important to investigate wider cascade problems in steep terrain. Here, we present a full four-dimensional trajectory reconstruction of the “Chant Sura” rockfall experiment performed with EOTA221 norm rocks. The data analysis allows a complete kinematic description of a rock's trajectory in real terrain and underscores the physical complexity of rock–ground interactions. In situ accelerometer and gyroscope data are combined with videogrammetric and unmanned aerial-systems mapping techniques to understand the role of rock rotations, ground penetration and translational scarring in rockfall motion. The exhaustive trajectory reconstruction provides information over the complete flight path such as translational velocity vectors, angular velocities, impact duration and forces, ballistic jump heights, and lengths. The experimental data provide insight into the basic physical processes detailing how rotating rocks of general shape penetrate, rebound and scar ground terrain. In future, the data will serve as a calibration basis to enhance numerical rockfall modelling.

Rockfall trajectories are primarily influenced by ground contacts, causing changes in acceleration and rock rotation. The duration of contacts and its influence on the rock kinematics are highly variable and generally unknown. The lack of knowledge hinders the development and calibration of physics-based rockfall trajectory models needed for hazard mitigation. To address this problem we placed three-axis gyroscopes and accelerometers in rocks of various sizes and shapes with the goal of quantifying rock deceleration in natural terrain. Short ground contacts range between 8 and 15 ms, longer contacts between 50 and 70 ms, totalling to only 6 % of the runtime. Our results underscore the highly nonlinear character of rock–ground interactions.

IEEE Transactions on Instrumentation and Measurement, 67 (4), ISSN:0018-9456, ISSN:1557-9662

We study how short duration powder avalanche blasts can break and overturn tall trees. Tree blow-down is often used to back-calculate avalanche pressure and therefore constrain avalanche flow velocity and motion. We find that tall trees are susceptible to avalanche air blasts because the duration of the air blast is near to the period of vibration of tall trees, both in bending and root-plate overturning. Dynamic magnification factors for bending and overturning failures should therefore be considered when back-calculating avalanche impact pressures.

We report on the ultrafast dynamics of charge order and structural response during the photoinduced suppression of charge and orbital order in a mixed-valence manganite. Employing femtosecond time-resolved resonant x-ray diffraction below and at the Mn $K$ absorption edge, we present a method to disentangle the transient charge order and structural dynamics in thin films of ${\mathrm{Pr}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_{3}$. Based on the static resonant scattering spectra, we extract the dispersion correction of charge-ordered ${\mathrm{Mn}}^{3+}$ and ${\mathrm{Mn}}^{4+}$ ions, allowing us to separate the transient contributions of purely charge order from structural contributions to the scattering amplitude after optical excitation. Our finding of a coherent structural mode at around $2.3\phantom{\rule{0.16em}{0ex}}\mathrm{THz}$, which primarily modulates the lattice but does not strongly affect the charge order, supports the picture of the charge order being the driving force of the combined charge, orbital, and structural transition.

Existing methods to calculate snow avalanche impact pressures on rigid obstacles are based on the assumption of no upslope pile-up of snow behind the structure at impact. Here we develop a method to predict avalanche impact pressures that accounts for the compaction and accumulation process. We show why this process leads to large impact pressures even at low avalanche approach velocities. The induced pressure depends on the incoming avalanche flow density relative to the ultimate compaction density because this determines the avalanche braking distance and therefore the flow deceleration in the upstream direction. The pile-up/accumulation process induces two additional pressures: (1) the static pressure of the pile-up zone and (2) the tractive stresses operating on the shear planes interfacing the accumulated and still moving avalanche snow. We demonstrate the use of the model on two theoretical examples and one real case study. Avalanche mitigation in maritime regions, or regions undergoing climate change with increasing wet snow avalanche activity, should consider the forces caused by the pile-up/accumulation process in engineering design.

2017 IEEE Sensors Applications Symposium (SAS), ISBN:978-1-5090-3202-0, ISBN:978-1-5090-3203-7

We apply grazing-incidence femtosecond x-ray diffraction to investigate the details of the atomic motion connected with a displacively excited coherent optical phonon. We concentrate on the low frequency phonon associated with the charge and orbital order in the mixed valence manganite La0.25Pr0.375Ca0.375MnO3 for T < 210 K. We measure the response of three superlattice reflections that feature different sensitivities to the motion of the unit cell constituents. The results support the assignment to a translational mode of the Mn4+ atoms together with the oxygen atoms connecting adjacent Mn4+ sites., 13 pages, 3 figures

We use time-resolved x-ray diffraction and magnetic optical Kerr effect to study the laser induced antiferromagnetic to ferromagnetic phase transition in FeRh. The structural response is given by the nucleation of independent ferromagnetic domains (\tau_1 ~ 30ps). This is significantly faster than the magnetic response (\tau_2 ~ 60ps) given by the subsequent domain realignment. X-ray diffraction shows that the two phases co-exist on short time-scales and that the phase transition is limited by the speed of sound. A nucleation model describing both the structural and magnetic dynamics is presented., Comment: 5 pages, 3 figures - changed to reflect version accepted for PRL

We review our recent activity in the field of photo-induced structural dynamics in crystalline solids studied using femtosecond X-ray diffraction techniques.

We directly measure by femtosecond time-resolved x-ray diffraction the E-g symmetry coherent phonon excited in bismuth by a strong optical pulse. The magnitude of the E-g mode observed is 0.2 pm peak-to-peak, compared against the 2.7-pm initial displacement of the fully symmetric A(1g) mode. The much smaller motion of the E-g mode is a consequence of the short lifetime of the electronic states that drive the atomic motion. The experimentally measured magnitude of the E-g motion allows us to rule out a previously suggested scenario for explaining the dynamics in bismuth that relies on strong coupling between these modes. DOI: 10.1103/PhysRevB.87.054301

We use time-resolved optical reflectivity to study the laser stimulated dynamics in the magnetic shape memory alloy Ni_2MnGa. We observe two coherent optical phonons, at 1.2 THz in the martensite phase and at 0.7 THz in the pre-martensite phase, which we interpret as a zone-folded acoustic phonon and a heavily damped amplitudon respectively. In the martensite phase the martensitic phase transition can be induced by a fs laser pulse on a timescale of a few ps., 3 figures

We investigate the structural response of charge and orbitally ordered (CO/OO) manganites to ultrafast optical excitation using optical reflectivity and x-ray diffraction as a probe. We study a La0.42Ca0.58MnO3 (LCMO) thin film and a La0.25Pr0.375Ca0.375MnO3 (LPCMO) single crystal. For both materials we observe oscillations in the optical responses that are assigned to a coherent optical phonon generated via displacive excitation. The coherent phonon disappears either when increasing the temperature above T-CO/OO or when raising the excitation fluence above a certain threshold. At low excitation fluences the amplitude and lifetime of this phonon behave similarly to the order parameter of the structural phase transition.