The Potential for Fracture Growth in Stepped Subglacial Topography as a Quarrying Mechanism

Understanding the rates and mechanisms of erosion by subglacial quarrying is a major unsolved problem in geomorphology. Stress enhancement due to load concentration on bedrock ledges between cavities is hypothesized to drive the growth of fractures. Prior work assumed the formation of vertically oriented tensile fractures at the downstream margins of cavities as the controlling process, but did not account for the evolution of the stress field as fractures lengthen, and in particular the dominance of the shearing mode at fracture tips. We used 2D finite element analysis and J-integral methods to analyze stress intensity factors and fracture growth potentials at the tips of preexisting fractures in loaded bedrock steps, taking into account normal and shear components and measured rock strengths. By examining different step heights, step riser angles, rock types, prior fracture locations and orientations, and extents of ice-rock contact zones, we identified some situations favorable for fracture growth, especially in brittle rock types. Typically, however, the growth direction will not be vertically downward but angled up-glacier away from the step riser, a situation unfavorable for quarrying. Moreover, in many situations, the normal stress across fracture planes will be compressive. Non-vertical step risers buttress the bedrock and also suppress fracture growth. In contrast, reducing the sizes of ice-rock contact zones not only increases the loading magnitude, as previously recognized, but also increases intensification of tensile stress at the tips of fractures located just up-glacier. Thus, larger cavities, and hence, fast sliding and low effective pressures, favor quarrying more strongly than previously recognized.