Stuart Savage - Academia.edu (original) (raw)

Papers by Stuart Savage

Annals of Glaciology, 1989

Acta Mechanica, Mar 1, 1991

This paper describes a model to predict the flow of an initially stationary mass of cohesionless ... more This paper describes a model to predict the flow of an initially stationary mass of cohesionless granular material down rough curved beds. This work is of interest in connection with the motion of rock and ice avalanches and dense flow snow avalanches. The constitutive behaviour of the material making up the pile is assumed to be described by a Niohr-Coulomb criterion while the bed boundary condition is treated by a similar Coulomb-type basal friction law assumption. By depth averaging the incompressible conservation of mass and linear momentum equations that are written in terms of a curvilinear coordinate system aligned with the curved bed, we obtain evolution equations for the depth h and the depth averaged velocity ~. Three characteristic length scales are defined for use in the non-dimensionalization and scaling of the governing equations. These are a characteristic avalanche length L, a characteristic height H, and a characteristic bed radius of curvature R. Three independent parameters emerge in the non-dimensionalized equations of motion. One, which is the aspect ratio s = H/L, is taken to be small. By choosing different orderings for the other two, the tangent of the bed friction angle 6 and the characteristic non-dimensional curvature)~ = L/R, we can obtain different sets of equations of motion which appropriately display the desired importance of bed friction and bed curvature effects. The equations, correct to order s for moderate curvature, are discretized in the form of a Lagrangian-type finite difference representation which proved to be successful in the earlier studies of Savage and Hutter [24] for granular flow down rough plane surfaces. Laboratory experiments were performed with plastic particles flowing down a chute having a bed made up of a straight, inclined portion, a curved part and a horizontal portion. Numerical solutions are presented for conditions corresponding to the laboratory experiments. It is found that the predicted temporal-evolutions of the rear and front of the pile of granular material as well as the shape of the pile agree quite well with the laboratory experiments.

The Seventeenth International Offshore and Polar Engineering Conference, 2007

This paper describes the iceberg deterioration component of an iceberg forecasting model. The mod... more This paper describes the iceberg deterioration component of an iceberg forecasting model. The model is intended for operational use by the Canadian Ice Service, and locally by offshore operators. The paper describes the formulation used to account for the various deterioration mechanisms, which consist of melting due to solar radiation, buoyant convection, and forced convection, as well as wave erosion and calving. The work also includes a sensitivity study that examines the role of the environmental input variables and model parameters. Tests examine the influence of water temperature, wind and current velocities, iceberg size, and wave height. The results indicate that wave height plays a major role in iceberg deterioration. Wind velocity and water temperature also play significant roles. In contrast, water current had little influence on iceberg deterioration. Finally, predicted calving intervals are found to be in reasonable agreement with field observations.

Continuum Mechanics and Thermodynamics, 1989

This paper continues a series of studies on the plane flow of a pile of cohesionless granular mat... more This paper continues a series of studies on the plane flow of a pile of cohesionless granular material down a rough inclined plane. Internal and basal friction laws are assumed to obey the Mohr-Coulomb yield criterion but in contrast to previous investigations the angle of friction at the bottom of the pile is considered to depend on the position or on the velocity or on both. Similarity, i.e. shape preserving solutions are constructed. The depth of the pile and the profile of the total minus the centre of mass velocity are determined analytically, but the total length and the position of the centre of mass are calculated numerically. If the basal friction angle is constant, the centre of mass moves with constant acceleration and the length of the pile extends monotonically. These motions change, when the angle of friction varies along the pile-the length of the pile may extend, contract or remain stationary and the centre of mass motion may decelerate or even reach steady state. Eight special cases are exhibited which demonstrate the influence of the friction law on the speed and spread of the pile.

Journal of Fluid Mechanics, Feb 1, 1989

Rock, snow and ice masses are often dislodged on steep slopes of mountainous regions. The masses,... more Rock, snow and ice masses are often dislodged on steep slopes of mountainous regions. The masses, which typically are in the form of innumerable discrete blocks or granules, initially accelerate down the slope until the angle of inclination of the bed approaches the horizontal and bed friction eventually brings them to rest. The present paper describes an initial investigation which considers the idealized problem of a finite mass of material released from rest on a rough inclined plane. The granular mass is treated as a frictional Coulomb-like continuum with a Coulomb-like basal friction law. Depth-averaged equations of motion are derived ; they bear a superficial resemblance to the nonlinear shallow-water wave equations. Two similarity solutions are found for the motion. They both are of surprisingly simple analytical form and show a rather unanticipated behaviour. One has the form of a pile of granular material in the shape of a parabolic cap and the other has the form of an M-wave with vertical faces at the leading and trailing edges. The linear stability of the similarity solutions is studied. A restricted stability analysis, in which the spread is left unperturbed shows them to be stable, suggesting that mathematically both are possible asymptotic wave forms. Two numerical finite-difference schemes, one of Lagrangian, the other of Eulerian type, are presented. While the Eulerian technique is able to reproduce the M-wave similarity solution, it appears to give spurious results for more general initial conditions and the Lagrangian technique is best suited for the present problem. The numerical predictions are compared with laboratory experiments of Huber (1980) involving the motion of gravel released from rest on a rough inclined plane. Although in these experiments the continuum approximation breaks down at large times when the gravel layer is only a few particle diameters thick, the general features of the development of the gravel mass are well predicted by the numerical solutions.

Proceedings of the International Conference on Port and Ocean Engineering Under Arctic Conditions, 2001

ABSTRACT An iceberg drift model has been formulated for eventual operational implementation at th... more ABSTRACT An iceberg drift model has been formulated for eventual operational implementation at the Canadian Ice Service. The model includes air and water drag forces, water pressure gradient, wave radiation stress and the effect of added mass. Besides ...

Acta Mechanica, Nov 1, 1986

Coastal Engineering, 1970

A theoretical and experimental study of the initial development of undular bores in two-dimension... more A theoretical and experimental study of the initial development of undular bores in two-dimensional, rectangular channels with and without boundary friction was performed Equations similar to those of Boussinesq, but including higher order and wall friction terms are presented and solved numerically by an implicit finite difference method A Pohlhausen-type boundary layer momentum integral method is used to obtain the wall shear stress distribution under a developing long wave from the consideration of the boundary layer underneath it The solution is performed in a quasi-iterative manner proceeding from the friction coefficient calculation for an initially assumed wave profile to the inclusion of this coefficient in the calculation of a new wave profile at an advanced time Comparisons of theoretical and experimental results are given For the initial development of the undular bore with which the present work is concerned, the measurements are found to be m reasonable agreement with t...

Journal of the Hydraulics Division, 1976

Solar Energy Engineering, 1977

It has been proposed that nonconvective solar ponds should be used for collecting and storing ene... more It has been proposed that nonconvective solar ponds should be used for collecting and storing energy on a large scale. A solar pond is a shallow body of water about one meter deep containing dissolved salts to generate a stable density gradient with fresh water on top and denser salt water at the bottom. Part of the incident solar radiation

Journal of Applied Mechanics, 1965

Savage has obtained an elegant solution for laminar incompressible flow. It is estimated that the... more Savage has obtained an elegant solution for laminar incompressible flow. It is estimated that the second approximation is sufficiently accurate in the absence of entry effects if Re* = Re (-) <2. Holler [l] 5 has demonstrated that the

Journal of Applied Mechanics, 1964

An analysis is presented for the laminar radial flow of an incompressible fluid between two close... more An analysis is presented for the laminar radial flow of an incompressible fluid between two closely spaced parallel plates. A solution is obtained by perturbing the creeping-flow solution and an expansion is carried out in terms of the downstream coordinate. The solution is found to agree well with experimental measurements except near the channel entrance.

Coastal Engineering 1970, 1970

Hydraulic Engineering, 1993

The paper deals with the mechanics aspects of the modelling of debris flows and will focus on ste... more The paper deals with the mechanics aspects of the modelling of debris flows and will focus on steady, fully developed flows. After a brief review of the types of constitutive equations that have been devised to model these flows, such as the viscoplastic Bingham models, Bagnold dispersive stress models, and generalized viscoplastic models, we shall describe some granular flow kinetic theory models and 'granular dynamics' computer simulations.

IUTAM Symposium on Mechanics of Granular and Porous Materials, 1997

The internal angles of friction for cohesionless assemblies of particles under compression were d... more The internal angles of friction for cohesionless assemblies of particles under compression were determined using molecular dynamics type simulations of biaxial tests. The objective was to determine appropriate internal friction angles to be used for continuum modelling of broken ice covers on waterways. The particles were modelled as random-sized circular disks. Constant confining pressures as well as a constant displacement rate were used for the biaxial tests. The stress-strain curves were obtained for a range of confining pressures. The yield envelopes follow a Mohr-Coulomb criterion of failure. The effect of the interparticle friction coefficient on the global angle of friction was examined. It was found that the internal angle of friction was essentially independent of the interparticle friction angle. Furthermore, assemblies with different particle size distributions were used in order to investigate the effects of this parameter on the internal angle of friction. It was found that as the particle size distribution is made wider, the magnitude of the internal angle of friction increases. Finally, the results obtained using two different contact models were compared in order to verify the effect of this parameter on the results.

Physics of Dry Granular Media, 1998

Some general aspects of modeling in the natural sciences are discussed. Minimum requirements that... more Some general aspects of modeling in the natural sciences are discussed. Minimum requirements that should be satisfied by theories of granular materials are proposed. Some recent work dealing with statics of granular materials is critically reviewed. New calculations of the elusive ‘stress dip’ under a pile of granular material placed on a rough rigid base are described.