On the Flexural Failure of Thick Ice Against Sloping Structures

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Fwu Chyi Teo ◽  
Leong Hien Poh ◽  
Sze Dai Pang
Keyword(s):  
Reference Model ◽  
Ice Sheets ◽  
Axial Loading ◽  
Breaking Load ◽  
Ice Thickness ◽  
Design Code ◽  
Modified Model ◽  
Flexural Failure ◽  
Bending Effect ◽  
Loading Eccentricity

This paper investigates the breaking load of ice sheets up to 6 m thick, against a sloping structure. The reference model by Croasdale, which the design code is based on, neglects the edge moment arising from the loading eccentricity, as well as a second-order bending effect induced by the axial loading in its formulation. In this paper, the model is reformulated to incorporate these effects into the governing equation, as well as to account for the occurrence of local crushing at the point of contact between the ice sheet and sloping structure. For thin ice, predictions from the modified model resemble closely those by Croasdale's model. As the ice thickness increases, however, significant deviations from the reference model can be observed. For thick ice, the terms omitted for brevity in the reference model have a significant influence, without which the breaking load is under-estimated. It is furthermore demonstrated that against sloping structures, the dominant failure mode is that of flexural, except in very limiting cases where it switches to crushing.

Breaking Load of Thick Ice on Sloping Structures

2016 ◽  
Author(s):  
Fwu Chyi Teo ◽  
Leong Hien Poh ◽  
Sze Dai Pang
Keyword(s):  
Failure Modes ◽  
Linear Equations ◽  
Breaking Load ◽  
Dominant Mode ◽  
Second Order ◽  
Ice Thickness ◽  
Flexural Failure ◽  
Level Ice ◽  
Moment Effect ◽  
Bending Failure

Sloping-sided structures have been used in ice-infested waters to reduce ice loads by inducing flexural failure in the incoming level ice, which can be a fraction of the crushing load of the same level ice on vertical walls [1]. Croasdale’s model [2] has been widely used to predict this type of ice loading, which compares well with available field data, such as that measured at the Confederation Bridge [3]. In Croasdale’s formulation, the problem is idealized as a semi-infinite beam on an elastic foundation and neglects the effects of second-order bending and the edge moment arising from eccentricity of axial loadings, i.e. the distance between the point of ice-structure contact and the centroidal axis of the beam. For thin ice, the edge moment effect is indeed negligible due to the small moment arm. However, the edge moment influence on the structural load increases with the ice thickness, as reported in [4]. This suggests that Croasdale’s model may be inadequate for ice thickness beyond a certain threshold. In this paper, we focus on the plane breaking load of thick ice, taking into account the second order bending of the beam as well as the edge moment effect. We also account for the local crushing of level ice that comes into contact with the sloping structure, which creates a surface parallel to the slope prior to the bending failure of ice sheet. This local crushing is assumed to occur until a sufficient surface area is created to provide the bearing capacity required to induce bending failure in the beam. As a result, the eccentricity of axial loading is reduced, lowering the effects of the edge moment and consequently, the predicted load. Taking the above effects into account, the governing equation and the corresponding deflection equation of the refined model are reformulated, and the system of non-linear equations solved with numerically with the Newton-Raphson method. Additionally, the competition between different failure modes, i.e. flexural, crushing and shear, of a level ice encountering a sloping structure is briefly investigated. It is shown that flexural failure remains the dominant mode of failure even for thick ice, for various practical slope angles, ice material properties and ice-structure contact properties.

scholarly journals Elastic properties of floating sea ice from air-coupled flexural waves

2021 ◽  
Author(s):  
Rowan Romeyn ◽  
Alfred Hanssen ◽  
Bent Ole Ruud ◽  
Tor Arne Johansen
Keyword(s):  
Sea Ice ◽  
Elastic Properties ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Flexural Wave ◽  
Ice Thickness ◽  
Linear Filter ◽  
Flexural Stiffness ◽  
Flexural Waves ◽  
Impulsive Source

Abstract. Air-coupled flexural waves appear as wave trains of constant frequency that arrive in advance of the direct air-wave from an impulsive source travelling over a floating ice sheet. The frequency of these waves varies with the flexural stiffness of the ice sheet, which is controlled by a combination of thickness and elastic properties. We develop a theoretical framework to understand these waves, utilizing modern numerical and Fourier methods to give a simpler and more accessible description than the pioneering, yet unwieldly analytical efforts of the 1950's. Our favoured dynamical model can be understood in terms of linear filter theory and is closely related to models used to describe the flexural waves produced by moving vehicles on floating plates. We find that air-coupled flexural waves are a robust feature of floating ice-sheets excited by impulsive sources over a large range of thicknesses, and we present a simple closed-form estimator for the ice thickness. Our study is focussed on first-year sea ice of ~20–80 cm thickness in Van Mijenfjorden, Svalbard, that was investigated through active source seismic experiments over four field campaigns in 2013, 2016, 2017 and 2018. The air-coupled flexural frequencies for sea-ice in this thickness range are ~60–240 Hz. While air-coupled flexural waves for thick sea-ice have received little attention, the higher frequencies associated with thin ice on fresh water lakes and rivers are well known to the ice-skating community and have been reported in popular media. Estimation of ice physical properties, following the approach we present, may allow improved surface wave modelling and wavefield subtraction in reflection seismic studies where flexural wave noise is undesirable. On the other hand, air-coupled flexural waves may also permit non-destructive continuous monitoring of ice thickness and flexural stiffness using simple, relatively inexpensive microphones located in the vicinity of the desired measurement location, either above the ice-sheet or along the shoreline. In this case, naturally forming cracks in the ice may be an appropriate impulsive source capable of exciting flexural waves in floating ice sheets in a passive monitoring context.

scholarly journals Upper and lower limits on the stability of calving glaciers from the yield strength envelope of ice

2011 ◽  
Vol 468 (2140) ◽  
pp. 913-931 ◽  
Author(s):  
J. N. Bassis ◽  
C. C. Walker
Keyword(s):  
Yield Strength ◽  
Water Depth ◽  
Shear Failure ◽  
Ice Sheets ◽  
Direct Consequence ◽  
Ice Thickness ◽  
Tightly Coupled ◽  
The Stability ◽  
Induced Changes ◽  
Lower Limits

Observations indicate that substantial changes in the dynamics of marine-terminating ice sheets and glaciers are tightly coupled to calving-induced changes in the terminus position. However, the calving process itself remains poorly understood and is not well parametrized in current numerical ice sheet models. In this study, we address this uncertainty by deriving plausible upper and lower limits for the maximum stable ice thickness at the calving face of marine-terminating glaciers, using two complementary models. The first model assumes that a combination of tensile and shear failure can render the ice cliff near the terminus unstable and/or enable pre-existing crevasses to intersect. A direct consequence of this model is that thick glaciers must terminate in deep water to stabilize the calving front, yielding a predicted maximum ice cliff height that increases with increasing water depth, consistent with observations culled from glaciers in West Greenland, Antarctica, Svalbard and Alaska. The second model considers an analogous lower limit derived by assuming that the ice is already fractured and fractures are lubricated by pore pressure. In this model, a floating ice tongue can only form when the ice entering the terminus region is relatively intact with few pre-existing, deeply penetrating crevasses.

scholarly journals High-Altitude Radar Measurements of Ice Thickness Over the Antarctic and Greenland Ice Sheets as a Part of Operation IceBridge

2013 ◽  
Vol 51 (2) ◽  
pp. 742-754 ◽  
Author(s):  
Jilu Li ◽  
John Paden ◽  
Carl Leuschen ◽  
Fernando Rodriguez-Morales ◽  
Richard D. Hale ◽  
...  
Keyword(s):  
High Altitude ◽  
Ice Sheets ◽  
Ice Thickness ◽  
Radar Measurements ◽  
The Antarctic

scholarly journals Boundary layer models for calving marine outlet glaciers

2017 ◽  
Vol 11 (5) ◽  
pp. 2283-2303 ◽  
Author(s):  
Christian Schoof ◽  
Andrew D. Davis ◽  
Tiberiu V. Popa
Keyword(s):  
Boundary Layer ◽  
Ice Sheets ◽  
Ice Thickness ◽  
Ice Shelf ◽  
Bedrock Channel ◽  
Extensional Stress ◽  
Grounding Line ◽  
Direct Numerical Solution ◽  
Glacier Ice ◽  
Side Walls

Abstract. We consider the flow of marine-terminating outlet glaciers that are laterally confined in a channel of prescribed width. In that case, the drag exerted by the channel side walls on a floating ice shelf can reduce extensional stress at the grounding line. If ice flux through the grounding line increases with both ice thickness and extensional stress, then a longer shelf can reduce ice flux by decreasing extensional stress. Consequently, calving has an effect on flux through the grounding line by regulating the length of the shelf. In the absence of a shelf, it plays a similar role by controlling the above-flotation height of the calving cliff. Using two calving laws, one due to Nick et al. (2010) based on a model for crevasse propagation due to hydrofracture and the other simply asserting that calving occurs where the glacier ice becomes afloat, we pose and analyse a flowline model for a marine-terminating glacier by two methods: direct numerical solution and matched asymptotic expansions. The latter leads to a boundary layer formulation that predicts flux through the grounding line as a function of depth to bedrock, channel width, basal drag coefficient, and a calving parameter. By contrast with unbuttressed marine ice sheets, we find that flux can decrease with increasing depth to bedrock at the grounding line, reversing the usual stability criterion for steady grounding line location. Stable steady states can then have grounding lines located on retrograde slopes. We show how this anomalous behaviour relates to the strength of lateral versus basal drag on the grounded portion of the glacier and to the specifics of the calving law used.

Indentation and Penetration of Edge-Loaded Freshwater Ice Sheets in the Brittle Range

1987 ◽  
Vol 109 (3) ◽  
pp. 287-294 ◽  
Author(s):  
G. W. Timco
Keyword(s):  
Aspect Ratio ◽  
Ice Sheets ◽  
Ice Thickness ◽  
Test Results ◽  
Tabular Form ◽  
Test Procedures ◽  
Freshwater Ice ◽  
Edge Loading ◽  
Ice Failure ◽  
Penetration Tests

A series of indentation and penetration tests have been performed by edge loading of a vertical indentor into a floating sheet of columnar S2 freshwater ice. The load on the indentor was measured as a function of interaction speed (v = 0.1 – 60 cm-s−1), indentor width (D = 2.54 – 12.7 cm), ice thickness (h = 0.6 – 3.3 cm), strain rate (ε˙ = v/2D = 10−2 – 101 s−1) and aspect ratio (D/h = 0.5 − 22). In total, 66 tests were performed. In this paper, a description of the test procedures is given along with the full results in both graphical and tabular form. Five different ice fracture modes are identified and described. From the test results, an ice-failure mode map is derived which indicates the conditions in which each ice fracture mode predominates.

Model tests of dynamic ice loading on the Chinese JZ-20-2 jacket platform

1992 ◽  
Vol 19 (5) ◽  
pp. 819-832 ◽  
Author(s):  
G. W. Timco ◽  
M. B. Irani ◽  
J. Tseng ◽  
L. K. Liu ◽  
C. B. Zheng
Keyword(s):  
Ice Sheets ◽  
Ice Thickness ◽  
Bohai Bay ◽  
Test Program ◽  
Jacket Platform ◽  
Prototype Structure ◽  
Ice Conditions ◽  
Ice Loads ◽  
Structure Orientation ◽  
Good Agreement

A model test program has been performed to study the dynamic ice loads on a jacket platform used in Bohai Bay, China. The tests were performed at a geometric scale factor of 1:26. The prototype structure/foundation compliance was modelled and the structure was subjected to scaled ice sheets corresponding to the ice conditions in the Bohai Bay. The loads, moments, displacements, and accelerations of the structure were measured. The test variables include the ice thickness, ice speed, elevation of ice cover, and structure orientation with respect to the ice motion. An analysis of the data shows good agreement with measured full-scale information. Key words: ice, loads, dynamic, vibration, jacket structure, foundation, China.

scholarly journals Theoretical limitations to englacial velocity calculations

1994 ◽  
Vol 40 (136) ◽  
pp. 509-518 ◽  
Author(s):  
David B. Bahr ◽  
W. Tad Pfeffer ◽  
Mark F. Meier
Keyword(s):  
Lyapunov Exponent ◽  
Measurement Errors ◽  
Ice Sheets ◽  
Information Loss ◽  
Ice Thickness ◽  
Error Growth ◽  
Numerical Techniques ◽  
Linear And Nonlinear ◽  
Using Data

Abstract To study the dynamics of ice sheets and glaciers, velocities at the bed of a glacier must be measured directly or calculated using data gathered from boreholes and surface surveys. Boreholes to the bed are expensive and time-consuming to drill, so the determination of basal velocity is almost exclusively by numerical inversion of velocities observed at the surface. For non-linearly viscous glaciers, a perturbation analysis demonstrates that inversions for englacial velocities will magnify measurement errors at an exponential rate with depth. The rate at which calculation errors grow is proportional to a Lyapunov exponent, a measure of “information loss” which is shown to be a simple linear function of spatial frequency with a coefficient depending on Glen’s flow-law exponent, n. The coefficient decreases with increasing non-linearity, demonstrating that inversions with non-linearly viscous ice have smaller calculation errors than inversions with linearly viscous ice. In both the linear and nonlinear cases, the Lyapunov exponent (and rate of error growth) increases with decreasing wavelength, which limits velocity calculations at the bed to wavelengths on the order of one ice thickness or greater. This limitation is theoretical and cannot be countered by more accurate survey data or special numerical techniques.

scholarly journals Isochrones and isotherms beneath migrating ice divides

2002 ◽  
Vol 48 (160) ◽  
pp. 95-108 ◽  
Author(s):  
Nadine A. Nereson ◽  
Edwin D. Waddington
Keyword(s):  
Heat Flow ◽  
Migration Rate ◽  
Accumulation Rate ◽  
Ice Sheets ◽  
Temperature Measurements ◽  
Analytical Models ◽  
Ice Thickness ◽  
Ice Flow ◽  
Trailing Edges ◽  
History Of

AbstractWe use simple numerical and analytical models of ice flow and heat flow to characterize the shape of isochrones and isotherms beneath moving ice divides. Both nonlinear ice flow and reduced accumulation (wind scouring) at a divide can cause reduced downward flow in a region about one ice thickness wide under a divide. Greater downward velocities on the flanks cause isochrones and isotherms to become arched at depth. The magnitudes and shapes of these arches depend on the history of divide position. Arch amplitudes decrease by approximately e−1 for each increase in migration rate of 3–5 times the accumulation rate, the arches become asymmetric, with steeper leading edges and more gentle trailing edges, and the arch apex lags behind the divide. Isochrone and isotherm shapes can be used to infer past divide motions. In advection-dominated ice sheets, isochrone shapes record a longer history of divide position than do isotherm shapes. The opposite is true for diffusion-dominated ice sheets, in which a spatial array of ice-temperature measurements might extend the recorded history of divide position.

scholarly journals The EISMINT benchmarks for testing ice-sheet models

1996 ◽  
Vol 23 ◽  
pp. 1-12 ◽  
Author(s):  
Philippe Huybrechts ◽  
Tony Payne ◽  
Keyword(s):  
Large Scale ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Time Dependent ◽  
Ice Thickness ◽  
Operation Model ◽  
Time Dependent Behaviour ◽  
Model Benchmark ◽  
Dependent Behaviour ◽  
Ice Sheet Modelling

We present a series of benchmark experiments designed for testing and comparing numerical ice-sheet models. Following the outcome of two EISMINT workshops organized to intercompare large-scale ice-sheet models currently in operation, model benchmark experiments ate described for ice sheets under fixed and moving margin conditions. These address both steady-state and time-dependent behaviour under schematic boundary conditions and with prescribed physics. A comparison was made of each model’s prediction of basic geophysical variables such as ice thickness, velocity and temperature. Consensus achieved in the model inter-comparison provides reference solutions against which the accuracy and consistency of ice-sheet modelling codes can be assessed.

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