The Savage-Hutter avalanche model: how far can it be pushed?

The Savage-Hutter (SH) avalanche model is a depth-averaged dynamical model of a fluid-like continuum implementing the following simplifying assumptions: (i) density preserving, (ii) shallowness of the avalanche piles and small topographic curvatures, (iii) Coulomb-type sliding with bed friction angle delta and (iv) Mohr-Coulomb behaviour in the interior with internal angle of friction phi> or =delta and an ad hoc assumption reducing the number of Mohr's circles in three-dimensional stress states to one. We scrutinize the available literature on information regarding these assumptions and thus delineate the ranges of validity of the proposed model equations. The discussion is limited to relatively large snow avalanches with negligible powder snow component and laboratory sand avalanches starting on steep slopes. The conclusion of the analysis is that the SH model is a valid model for sand avalanches, but its Mohr-Coulomb sliding law may have to be complemented for snow avalanches by a second velocity-dependent contribution. For very small snow avalanches and for laboratory avalanches starting on moderately steep and bumpy slopes it may not be adequate.     

Comparison of two contact models in the simulation of friction stir welding process

Two contact models are used to simulate the thermo-mechanical interaction process in friction stir welding. Comparison shows that the classical Coulomb friction model can be accurate enough for the simulation of friction stir welding in lower angular velocity. But in higher angular velocity, the classical Coulomb friction model fails to work due to the increase of the dynamic effect of the welding tool. Because the shear failure of material is considered in modified Coulomb friction model, the increase of the frictional stress on the tool–plate interface is limited by the shear failure. So, this model can keep valid even when the angular velocity of the welding tool is increased to a high level.     

Rapid motions of free-surface avalanches down curved and twisted channels and their numerical simulation

This paper presents a new model and discussions about the motion of avalanches from initiation to run-out over moderately curved and twisted channels of complicated topography and its numerical simulations. The model is a generalization of a well established and widely used depth-averaged avalanche model of Savage & Hutter and is published with all its details in Pudasaini & Hutter (Pudasaini & Hutter 2003 J. Fluid Mech. 495, 193-208). The intention was to be able to describe the flow of a finite mass of snow, gravel, debris or mud, down a curved and twisted corrie of nearly arbitrary cross-sectional profile. The governing equations for the distribution of the avalanche thickness and the topography-parallel depth-averaged velocity components are a set of hyperbolic partial differential equations. They are solved for different topographic configurations, from simple to complex, by applying a high-resolution non-oscillatory central differencing scheme with total variation diminishing limiter. Here we apply the model to a channel with circular cross-section and helical talweg that merges into a horizontal channel which may or may not become flat in cross-section. We show that run-out position and geometry depend strongly on the curvature and twist of the talweg and cross-sectional geometry of the channel, and how the topography is shaped close to run-out zones.     

Monte Carlo calibration of avalanches described as Coulomb fluid flows

The idea that snow avalanches might behave as granular flows, and thus be described as Coulomb fluid flows, came up very early in the scientific study of avalanches, but it is not until recently that field evidence has been provided that demonstrates the reliability of this idea. This paper aims to specify the bulk frictional behaviour of snow avalanches by seeking a universal friction law. Since the bulk friction coefficient cannot be measured directly in the field, the friction coefficient must be calibrated by adjusting the model outputs to closely match the recorded data. Field data are readily available but are of poor quality and accuracy. We used Bayesian inference techniques to specify the model uncertainty relative to data uncertainty and to robustly and efficiently solve the inverse problem. A sample of 173 events taken from seven paths in the French Alps was used. The first analysis showed that the friction coefficient behaved as a random variable with a smooth and bell-shaped empirical distribution function. Evidence was provided that the friction coefficient varied with the avalanche volume, but any attempt to adjust a one-to-one relationship relating friction to volume produced residual errors that could be as large as three times the maximum uncertainty of field data. A tentative universal friction law is proposed: the friction coefficient is a random variable, the distribution of which can be approximated by a normal distribution with a volume-dependent mean.     

Using AVAL-1D to simulate avalanches in the eastern Pyrenees

The two friction parameters used in the numerical avalanche dynamics program AVAL-1D, were calibrated empirically with data from observed avalanches in the Swiss Alps. The implementation of the model with these friction parameters in other regions with different characteristics can lead to considerable uncertainty if a previous calibration is not performed. However, direct calibration for a specific avalanche path is often not possible since the data available are insufficient. Therefore, we back-calculated twelve well-documented avalanche events from the Catalan Pyrenees to calibrate the friction coefficients to be used in this mountain range. The result of the study reveals that there is a good fit between recorded and simulated avalanche events using the friction parameters originally calibrated for the Swiss Alps, despite the difference in snow climate between these two mountain ranges.     

Effect of the shape of pressure-dependent yield surfaces on solution behaviour near frictional interfaces

The main objective of the present paper is to demonstrate, by means of a problem permitting a semi-analytical solution, the effect of the shape of pressure-dependent yield surfaces on qualitative behaviour of rigid plastic solutions in the vicinity of frictional interfaces. The yield criterion used reduces to the classical Coulomb–Mohr yield criterion at specific values of input parameters and, therefore, can be further reduced to the classical Tresca yield criterion. The solution is singular (some components of the strain rate tensor approach infinity) in the vicinity of the maximum friction surface at sliding if the system of equations is hyperbolic. The dependence of the strain rate intensity factor on input parameters of the double-slip and rotation model based on quite a general plane-strain yield criterion is found, and its consequence on some physical processes in a narrow material layer near frictional interfaces is discussed.     

Can we learn more from the data underlying the statistical α-β model with respect to the dynamical behavior of avalanches?

Hazard and risk assessment in avalanche-prone areas involves estimation of runout distances of potential avalanches. Methods for determination of the runout may be divided into two categories: 1) methods based on statistical approaches such as the well known α-β model or 2) methods based on numerical avalanche models such as the PCM-model or VS-type models (just to name the more traditional ones). Methods in the second group have the advantage that besides the runout distance, velocity and impact pressure distributions along the avalanche track can also be obtained, this being a requisite for meaningful risk assessments. However, the predictive power of dynamical models depends on the use of appropriate rheological models and their parameters.In the statistical α-β model, the maximum runout distance is solely a function of topography. The runout distance equations were found by regression analysis, correlating the longest registered runout distance of several hundred avalanche paths with a selection of topographic parameters.In this paper, we re-evaluate Norwegian and Austrian avalanche data, which served as basis for the α-β model in the respective countries, and additional avalanche data with respect to dynamical measures. As most of those avalanche data originate more or less from extreme events (i.e. avalanches with return periods of the order of 100 years), the dynamical measures may give hints about an appropriate rheology for dynamical models suitable for extreme avalanche events.The analysis raises reasonable doubt whether the classical ansatz for the retarding acceleration of snow avalanches with additive terms involving Coulomb-friction and a velocity-squared dependency, which is used in many avalanche models, is adequate for a physically-based model. Back-calculations of runout distances using a simple block model show a discrepancy between commonly proposed parameter values (and of the underlying rheological models) and the observations.     

A hierarchy of avalanche models on arbitrary topography

We use the non-Cartesian, topography-based equations of mass and momentum balance for gravity driven frictional flows of Luca et al. (Math. Mod. Meth. Appl. Sci. 19, 127–171 (2009)) to motivate a study on various approximations of avalanche models for single-phase granular materials. By introducing scaling approximations we develop a hierarchy of model equations which differ by degrees in shallowness, basal curvature, peculiarity of constitutive formulation (non-Newtonian viscous fluids, Savage–Hutter model) and velocity profile parametrization. An interesting result is that differences due to the constitutive behaviour are largely eliminated by scaling approximations. Emphasis is on avalanche flows; however, most equations presented here can be used in the dynamics of other thin films on arbitrary surfaces.     

A meso-mechanical model for concrete under dynamic tensile and compressive loading

We present a computational model, which combines interface debonding and frictional contact, in order to investigate the response of concrete specimens subjected to dynamic tensile and compressive loading. Concrete is modeled using a meso-mechanical approach in which aggregates and mortar are represented explicitly, thus allowing all material parameters to be physically identified. The material phases are considered to behave elastically, while initiation, coalescence and propagation of cracks are modeled by dynamically inserted cohesive elements. The impenetrability condition is enforced by a contact algorithm that resorts to the classical law of Coulomb friction. We show that the proposed model is able to capture the general increase in strength with increasing rate of loading and the tension/compression asymmetry. Moreover, we simulate compression with lateral confinement showing that the model reproduces the increase in peak strength with increasing confinement level. We also quantify the increase in the ratio between dissipated frictional energy and dissipated fracture energy as the confining pressure is augmented. Our results demonstrate the fundamental importance of capturing frictional mechanisms, which appear to dissipate a similar amount of energy when compared to cracking under compressive loading.     

On a matrix cracking model using Coulomb’s friction law

A matrix cracking model is developed based upon Coulomb friction law instead of a constant frictional shear stress usually assumed in the matrix cracking analyses. A Lamé formulation incorporated with Coulomb friction law is adopted to solve the elastic states of fiber/matrix stress-transfer through a frictionally constrained interface in the slipping region and a modified shear lag model is applied to evaluate the elastic responses in the intact region. By using an energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber reinforced composite is formulated in terms of the frictional coefficient rather than the frictional shear stress usually equated in the matrix cracking stress formulations. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model will be compared with those predicted by the constant frictional shear stress models. The effect of Poisson contraction caused by stress redistribution between the fiber and matrix on the matrix cracking mechanics will be shown and discussed in the present analysis.     

A nonsmooth frictional contact formulation for multibody system dynamics

We present a new node-to-face frictional contact element for the simulation of the nonsmooth dynamics of systems composed of rigid and flexible bodies connected by kinematic joints. The equations of motion are integrated using a nonsmooth generalized-α time integration scheme and the frictional contact problem is formulated using a mixed approach, based on an augmented Lagrangian technique and a Coulomb friction law. The numerical results are independent of any user-defined penalty parameter for the normal or tangential component of the forces and, the bilateral and the unilateral constraints are exactly fulfilled both at position and velocity levels. Finally, the robustness and the performance of the proposed algorithm are demonstrated by solving several numerical examples of nonsmooth mechanical systems involving frictional contact.     

Prediction of electrophoretic mobilities. 4. Multiply charged aromatic carboxylates in capillary zone electrophoresis

The electrophoretic mobilites of aromatic carboxylates and sulfonates at zero ionic strength were correlated with models incorporating both hydrodynamic and dielectric friction. The hydrodynamic friction was predicted using either the Hückel spherical ion model or the Perrin ellipsoidal model. Dielectric friction is the charge-induced drag caused by the reorientation of the solvent dipoles in response to the analyte charge. Based on the Hubbard-Onsager and Zwanzig expressions, the dielectric friction is related to z2/V. Expressions incorporating both the hydrodynamic and dielectric frictional terms successfully predicted infinite-dilution mobilities to within 4.4%. The influence of dielectric friction ranged from 3-8% of the overall drag for singly charged analytes to 39% of the total frictional drag for 1,2,4,5-benzenetetracarboxylate.     

全动操纵面系统中摩擦参数测量方法研究

通过解析方法和数值方法研究了库仑摩擦对结构动响应的影响规律。利用库仑摩擦在时域上能够傅里叶展开为方波函数的特点,得到含库仑摩擦的单自由度系统在简谐激励下的级数响应,结果表明,库仑摩擦的引入导致结构的频域响应中,除了激振频率成分外,还会有奇数倍频的成分,在激振频率为0.605倍固有频率时,奇数倍频成分与激振频率成分的幅值比例是摩擦力的线性函数。通过数值方法证明,上述规律能够推广到二自由度的全动操纵面模型中。利用这一规律,通过动响应试验的方法测量出全动操纵面系统中的库仑摩擦参数,并验证了这种方法的正确性。     

髋关节含库伦摩擦被动行走器动力学建模与仿真研究

被动动力行走是当今双足步行机器人研究的重点之一,学者对被动行走器髋关节的摩擦对其步态影响还存在分歧。该文对髋关节含库伦摩擦的直腿被动动力行走器的建模和仿真,以及摩擦对行走器步态的影响进行了研究。首先推导了髋关节含库伦摩擦的被动行走器的动力学方程,该动力学方程为非线性非光滑的隐式常微分方程组;然后给出了一种基于试算法求解该动力学方程的数值计算方法;最后通过数值仿真分析了髋关节的摩擦对被动行走器步态的影响。研究成果为以后被动动力行走研究提供了一个更接近实际的模型,为数值仿真分析其动力学特性提供了一种工具。     

An effective two-dimensional frictional contact model for arbitrary curved geometry

A finite element model is developed on the basis of a variational formulation of the perturbed Lagrange type and the classical Coulomb law of friction, for the analysis of frictional contact problems in two dimensions. The model accounts for all geometric/kinematic non-linearities associated with large sliding motions as well as arbitrary contact-surface curvatures. Explicit forms for the contact force and tangent stiffness operators and a penalty-type format is utilized in the implementation. An extensive number of numerical simulations are used to demonstrate the effectiveness and practical usefulness of the model.     

The unacknowledged risk of Himalayan avalanches triggering

A “universal” model for avalanche triggering, as well as for collapse of suspended seracs, is presented based on Quantized Fracture Mechanics, considering fracture, friction, adhesion and cohesion. It unifies and extends the classical previous approaches reported in the literature, including the role of the slope curvature. A new size-effect, that on mountain height rather than the classical one on snow slab thickness, is also discussed and demonstrated thanks to glaciers data analysis from the World Glacier Inventory (http://nsidc.org/data/glacier_inventory/browse.html, 2014). The related most noteworthy result is that snow precipitation needed to trigger avalanches at 8,000 m could be up to 4 times, with a realistic value of 1.7 times, smaller than at 4,000 m. This super-strong size-effect may suggest that the risk of Himalayan avalanches is today still unacknowledged. A discussion on the recent Manaslu tragedy concludes the paper.     

Modelling soil removal from snow avalanches: A case study in the North-Western Italian Alps

Snow avalanches can exert considerable erosive forces on soils. If a snow avalanche flows directly over bare ground, basal shear forces may scrape away and entrain soil. Sediments mix up with the avalanche body and may be found within the run-out snow deposit. Based on a previous field campaign aiming to quantify the amount of sediments trapped within avalanche bodies for the study site of Lavancher, in the Aosta Valley, NW-Italy, we developed here a soil erosion model, which we preliminarily applied to that site. An already developed and tested 1-D avalanche dynamics model was modified to include soil erosion. Soil removal was triggered according to two different mechanisms, namely excess of shear and critical velocity. We used equations from the available literature to model the shear stress exerted by the avalanche flow upon the ground underneath. Critical threshold for soil removal of either shear or velocity were also retrieved from the available literature, possibly depending upon soil texture and geotechnical properties. The model performs well in reproducing soil removal for three wet-dense avalanches that occurred in the study site.Use of excess of shear mechanism to evaluate erosion seems more robust, as less dependent upon flow velocity, utmost uncertain. Albeit more accurately measured events of soil eroding avalanches seem necessary to test its performance, the model can be used henceforth as a basis for further refinement concerning geomorphologic contribution of avalanches.     

Curvature‐Controlled Wrinkling Surfaces for Friction

Topographical patterns endow material surfaces with unique and intriguing physical and chemical properties. Spontaneously formed wrinkling has been harnessed to generate surface topography for various functionalities. Despite promising applications in biomedical devices and robot engineering, the friction behavior of wrinkling on curved surfaces remains unclear. Herein, wrinkled surfaces are induced by sputtering metals on soft polymer microspheres. The wrinkle morphologies and length scales can be controlled precisely by tailoring the microsphere radius (substrate curvature) and film thickness. The wrinkled surfaces exhibit controlled friction property, depending on the wrinkling patterns and length scales. An increase in friction force with increasing surface roughness is generally found for dimple patterns and labyrinth patterns. The dimple patterns show the lowest friction due to strong curvature constraint. The herringbone patterns exhibit apparent friction anisotropy with respect to topographic orientation. These results will guide future design of wrinkled surfaces for friction by harnessing substrate curvature.     

An exact analysis of sliding frictional contact of a rigid punch over the surface of magneto-electro-elastic materials

This article performs an exact analysis for a frictional triangular or cylindrical punch acting on the surface of magneto-electro-elastic materials. The punch moves relative to the surface of magneto-electro-elastic materials. Inside the contact area, the Coulomb friction law is applied. Eigenvalue distribution is analyzed, and then appropriate fundamental solutions are given. The stated problem is reduced to a system of singular integral equations of the second kind. The exact solution of the obtained singular integral equations makes it easy to get the explicit expressions of the surface physical quantities. Through plotting figures, the influences of the friction coefficient on contact behavior are shown and interesting results are observed. The in-plane stress, electric displacement and magnetic induction tend to be infinite near the leading edge of the frictional triangular punch, while having spikes at one edge of the frictional cylindrical punch, which may explain why surface damage occurs on the surface of magneto-electro-elastic materials.     

Reibmodelle für elastomere und thermoplastische Werkstoffe und ihre Implementierung in Finite-Elemente-Codes

Polymer Friction Models And Their Implementation Into Finite-Element-Codes In order to support the development of seals and other frictioninvolved parts by numerical simulation methods an exact modeling of the frictional behavior is of essential importance. In case of polymeric materials the friction coefficient significantly depends on real contact area, contact stresses, relative sliding velocity and temperature. This cannot be described with the classical Coulomb-Friction-Model and advanced friction models are not commonly available in commercial FE-Codes. Therefore such advanced friction models have to be formulated and implemented by the users. In this article results of calculations with an implemented friction model are shown. Calculations of contact generation dependent on normal load are compared with the analytical results of the Hertzian Theory. Comparing the results of different FE-models the influence of discretisation is discussed. For verification purposes experimentally determined friction coefficients are listed.