A theory of glacial quarrying for landscape evolution models

Abstract

Quarrying rate from adhesive wear theory: Equation 2 of the articleErosion of solid surfaces in sliding contact is referred to as "wear" in materials science. Owing to asperities (bumps) on solid surfaces, the real area of contact along the sliding interface is less than the total area. The theory of adhesive wear uses the frequency of asperity-junction formation during slip and posits a probability k of asperity breakage at a junction to determine the volume of wear fragments Q v :where x is the slip displacement, N is the number of asperity junctions formed per unit distance of slip, and V e is the volume of material eroded if an asperity breaks, which depends on the load normal to the slip surface, the hardness of the material, and the asperity geometry (Rabinowicz, 1965). In materials science applications involving microscopic asperities, k is a wear constant. If a specific asperity geometry and spacing are assumed, the value of k can be determined through experiments in which solids are slid past each other and surface erosion is measured (for example, k for metals is typically 0.5-160 ×10 -3 ) (Rabinowicz, 1965).For the two-dimensional stepped glacier bed of the model (Fig. 1), with steps of tread length L, the total number of steps is n s = L T /L, where L T is the total length of the bed. For each unit distance of displacement, ice will traverse a step 1/L times, so that N = n s /L, or

Experimental determination of a double-valued drag relationship for glacier sliding

“…Motivation for emphasizing ice/bed separation comes from both extensive evidence of cavities on formerly glaciated bedrock (e.g. Walder and Hallet, 1979;Hallet and Anderson, 1980;Hooyer and others, 2012) and their centrality in models of glacier surging (Kamb and others, 1985;Kamb, 1987), hydrology (Walder, 1986;Kamb, 1987;Schoof, 2010) and bedrock erosion (Hallet, 1996;Iverson, 2012). Motivation for neglecting regelation comes from the common scarcity on formerly glaciated bedrock of obstacles sufficiently small to be accommodated mainly by regelation (Kamb, 1970;Hooke, 2005), which probably reflects the tendency for small obstacles to be worn flat by abrasion (Hooke, 2005).…”

“…Sliding speed also controls the rate of bedrock erosion by glaciers (e.g. Hallet, 1979;Iverson, 2012) and thus needs to be calculated in numerical models aimed at simulating the long-term topographic evolution of glaciated mountain belts and their constituent landforms (Egholm and others, 2009;Herman and others, 2011).…”

Ice flow models and glacial erosion over multiple glacial–interglacial cycles

“…154 R. M. Headley and T. A. Ehlers: Ice flow models and glacial erosion over multiple glacial-interglacial cycles complex processes such as the influence of subglacial hydrology (Egholm et al, 2011;Herman et al, 2011;Iverson, 2012). Despite these advances, other mechanisms are still represented by simplified assumptions and approximations, particularly the underlying physics of ice flow.…”

“…In many orogenic-scale models, glacial flow and erosion have been represented using simplifying assumptions, such as the shallow ice approximation (SIA) for glacial flow (Kessler et al, 2008;Iverson, 2012). This approximation simplifies the ice flow equation (Glen flow law) by only considering the first-order simple shear stresses (Cuffey and Paterson, 2010).…”

Morphotectonic implication of the Paleoproterozoic Mid-Lithuanian Suture Zone

“…Fur ther more, the per sis tent ac tiv ity of the MLSZ in ev i ta bly led to for ma tion of the wide zone of in creased frac tur ing in the over ly ing sed i mentary cover. The ev i dence pro vided from dif fer ent re gions im plies in creased rates of ero sion of frac tured lithologies (Dühnforth et al, 2010) that is also con sis tent with mod el ling re sults (Iverson, 2012). The spac ing of frac tures also con trol the pre vail ing mecha nism (e.g.…”