Does GBSlimited flow occur within glaciers and ice sheets

To provide an overview of the relevance of GBS-limited creep for glacier and ice sheet mechanics, a deformation mechanism map for ice, drawn on axes of grain size and stress, is shown in Fig. 60.3 for T — 268 K. The GBS-limited creep regime and the dislocation creep regime are separated by the solid boundary, along which both mechanisms contribute equally to the strain rate. Within each creep regime, strain-rate contours are calculated using the appropriate flow law for that creep regime. As shown in a (MPa)

Figure 60.2 Plot comparing the composite flow law of Equation (4) (solid lines) with previous laboratory data for coarse-grained ice samples, for T = 268K. The upper solid line is calculated for d = 0.2 mm, the lower for d = 2 mm. The dotted line represents the Glen flow law; the dotted-dashed line represents data from experiments conducted at high confining pressure (Durham et al., 1992). Data points are from ambient pressure tests: d = 0.2 mm, Goldsby & Kohlstedt (2001); □, d > 1mm, Steinemann (1958a); O, d > 1mm, Mellor & Smith (1966); ▲, d > 1 mm, Barnes et al. (1971).

Figure 60.2 Plot comparing the composite flow law of Equation (4) (solid lines) with previous laboratory data for coarse-grained ice samples, for T = 268K. The upper solid line is calculated for d = 0.2 mm, the lower for d = 2 mm. The dotted line represents the Glen flow law; the dotted-dashed line represents data from experiments conducted at high confining pressure (Durham et al., 1992). Data points are from ambient pressure tests: d = 0.2 mm, Goldsby & Kohlstedt (2001); □, d > 1mm, Steinemann (1958a); O, d > 1mm, Mellor & Smith (1966); ▲, d > 1 mm, Barnes et al. (1971).

the figure, strain rates in the dislocation creep regime are independent of grain size (horizontal strain-rate contours), whereas strain rates in the GBS-limited creep regime are strongly dependent on grain size (sloping contours).

As shown in Fig. 60.3, the box bounding the conditions explored in Glen's experiments is transected by the boundary between the two creep mechanisms, illustrating that the Glen flow law is really a composite law containing contributions from both GBS-limited creep and dislocation creep. The overlay of the approximate range of grain size versus stress conditions encountered in glaciers and ice sheets in Fig. 60.3 suggests that flow of these bodies is limited by GBS at all but the highest stresses and largest grain sizes near their bases, where a transition to the dislocation creep regime occurs (see below).

60.4.1 Glaciers

That GBS-limited flow occurs within glaciers (and ice sheets) is supported by numerous field observations, including measurements of borehole tilt and cavity (borehole and tunnel) closure. Subsets of the data from such studies are compared in Fig. 60.4 with calculated relationships between strain rate and stress from Equation (4). In most of the cases shown, at sufficiently low

grain size (mm)

Figure 60.3 Deformation map for ice constructed from the flow laws for GBS-limited creep and dislocation creep for a temperature of 268 K. The heavy solid line of negative slope is the boundary between mechanisms. The dotted-dashed lines are strain-rate contours, calculated using the appropriate flow law for the rate-limiting creep mechanism in each creep regime. The box labelled 'Glen' bounds the approximate s versus d conditions of Glen's experiments (Glen, 1952,1955). The box with dashed lines on three sides outlines the full range of stresses and grain sizes in the Goldsby and Kohlstedt experiments (most of which were conducted at temperatures < 268 K); the solid vertical line on the right edge of this box marks the approximate range of stresses for experiments on samples with grain sizes of ca. 0.2 mm at 268 K (see fig. 3 of Goldsby & Kohlstedt, 2001). The approximate range of stresses in glaciers and ice sheets is shown by the large rectangle.

stresses, the field studies yield a value of n < 2. In some cases (e.g. Meier, 1960; Holdsworth & Bull, 1970), a transition to n > 3 is observed at the highest stresses (ca. 0.1 MPa), indicating a transition to the dislocation creep (n = 4.0) regime. The agreement between the magnitude of the strain rate in the n < 2 regime in the field with that calculated from Equation (4) is in some cases very good (e.g. see data of Gerrard et al., 1952; Meier, 1960), although considerable uncertainty exists in the appropriate value of grain size to use in Equation (4), because grain sizes from field studies are often not reported or only typical or 'average' values are reported. In other cases, strain rates observed in the field are significantly higher than predicted by Equation (4). For example, the strain rate at a given stress observed at the Meserve Glacier site of Holdsworth & Bull (1970) and the Barnes Ice Cap site of Hooke (1973) is in excellent agreement with the strain rate calculated via Equation (4) using a temperature of 273 K and a grain size of 1 mm, although the observed temperatures at the Meserve and Barnes Ice Cap sites were ca. 256 and ca. 263 K, respectively, with grain sizes >1 mm at both sites. Strain rates determined in the Holdsworth & Bull (1970) study are higher than those predicted from Equation (4) by about two orders of magnitude. Such effective shear stress (MPa)

10-4

10_1"

10-12

Figure 60.4 Plot comparing the composite flow law of Equation (4) (solid line) with data from field studies on glaciers and ice sheets. The upper solid line is calculated for d = 2 mm and T = 273 K, the lower solid line for d = 1 mm and T = 255K. The dotted-line parallelogram represents the range of conditions of the experiment on the Barnes Ice Cap by Hooke (1973), which yielded n = 1.65. Data points are from: A,Gerrard etal. (1952),with data reanalysed as in Nye (1953); O, •, Meier (1960); A, Gow (1963); □, Holdsworth & Bull (1970).

10-14

10-4 10-3 10-2 101 10° effective shear stress (MPa)

Figure 60.4 Plot comparing the composite flow law of Equation (4) (solid line) with data from field studies on glaciers and ice sheets. The upper solid line is calculated for d = 2 mm and T = 273 K, the lower solid line for d = 1 mm and T = 255K. The dotted-line parallelogram represents the range of conditions of the experiment on the Barnes Ice Cap by Hooke (1973), which yielded n = 1.65. Data points are from: A,Gerrard etal. (1952),with data reanalysed as in Nye (1953); O, •, Meier (1960); A, Gow (1963); □, Holdsworth & Bull (1970).

discrepancies between laboratory and field data may reflect relatively large uncertainties in the calculated stresses or measured creep rates in the field studies, the effects of impurities on the creep rate due to GBS-limited creep in nature, and/or the effects of strong c-axis fabrics on GBS-limited creep in nature.

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