Direct estimation of snow density using CPT

Direct estimation of snow density using CPT A.B. McCallum University of the Sunshine Coast, Queensland, Australia

ABSTRACT: A recently devised correlation allows for the direct derivation of soil unit weight from CPT data qt and fs. However, the direct application of this technique to another geomaterial, snow, is not possible; the variable bonding within snow complicates the correlation. To examine the relationship between CPT data and snow unit weight, data from almost one hundred CPTs in Antarctica were analyzed. Snow unit weight is seen to vary with CPT sleeve friction and a significant relationship exists between CPT net sleeve friction data and snow unit weight. Variations in CPT tip resistance and sleeve friction data for polar snow of the same unit weight may provide insight into the microstructure or level of bonding within the snow pack.

1 INTRODUCTION Typically, snow density is determined gravimetrically; a snow pit is dug and snow samples are extracted and then weighed. However, increasingly, the desire for rapid in situ density estimates have resulted in the application of other technologies including the neutron probe (Morris and Cooper, 2003) where a radioactive source is lowered down a bore hole or the Mostly Automated Borehole Logging Experiment (MABLE), that performs in situ measurements of borehole wall hardness with cm-scale vertical resolution and near-infrared reflectivity with 5 mm vertical resolution (Breton and Hamilton, 2012). However, neither of these methods provides rapid and reliable highresolution in situ assessment of snow density. In soils, unit weight, or density multiplied by gravity, is usually determined by obtaining undisturbed samples, however, this can be a difficult and costly process. Robertson and Cabal (2010) outline numerous existing relationships to derive soil unit weight from in situ testing data and then present a new correlation incorporating the work of Marchetti (1980) and Mayne (2007) allowing soil unit weight to be estimated directly from CPT tip resistance and sleeve friction data. McCallum (2012) extensively outlined the use of CPT in polar snow and briefly noted the viability of deriving snow density from CPT data. In this paper, the Robertson and Cabal (2010) methodology is applied to historical data from CPT in snow, to ascertain whether the method is applicable to bonded polar snow; then, the relationship between snow density and CPT data is further examined.

2 METHODS Modified CPT equipment was used in the vicinity of Halley Station, Antarctica to conduct almost one hundred CPTs in dry polar snow, typically to depths of 5 m. A number of tests were conducted in the immediate vicinity of two snow pits which were excavated to depths of approximately 5 m in order to allow direct comparison between gravimetrically estimated snow density and CPT data. 36.7 mm diameter scientific cones rated to 20 kN tip resistance were used to measure tip resistance and sleeve friction. Snow samples for density analysis were retrieved using cylindrical density tubes, one tube of length 247 mm and diameter 73 mm and the second measuring 250 mm with diameter 35 mm. The large sampling tube was used when possible, however, limited layer thickness often necessitated the use of the smaller tube. Samples were weighed using an Acculab ‘Econ’ portable balance, precise to ± 1.0 g and three samples were taken per layer. Snow data recorded included layer thickness, density, grain size, hardness and snow type.

3 EXISTING RELATIONSHIPS FOR SOIL (Robertson and Cabal, 2010) developed a correlation allowing estimation of soil unit weight using only direct CPT measurements for qt (or qc) and fs. The figure from Robertson and Cabal (2010) is shown in Figure 1.

Figure 1. Dimensionless unit weight calculated using representative CPT data for polar snow in Equation 2 plots within data for soil compiled by Robertson and Cabal (2010), aligning with SBT Zone 6.

Using Figure 1 along with representative CPT data for polar snow results in a dimensionless unit weight (γ/γw) of 1.6 (see Table 1). Table 1. Representative CPT data from Halley Research Station for polar snow and resultant unit weight estimated via correlation for soil from Robertson and Cabal (2010). qc MPa fs MPa pa MPa (estimated) Dimensionless unit weight γ/γw 1.65

0.01

0.1

1.6

This unit weight equals a density of 1830 kg m−3, three to four times the typical density for hard polar snow. Hence, the Robertson and Cabal (2010) correlation for soil is not directly applicable to snow. However, Robertson and Cabal (2010) also suggested a modified correlation to account for variations in specific gravity, resulting in the following:

0.27 log

0.36 log

1.236

2.65

(1)

where Rf is friction ratio, qt is corrected cone resistance, pa is atmospheric pressure (in same units as qt), γ is soil unit weight, γw is unit weight of water and Gs is average specific gravity.

When this equation is applied to the representative data obtained for snow in Table 1 then a dimensionless unit weight (γ/γw) of 0.32 is obtained, equivalent to a density of 320 kg m−3. This is a typical density for newly fallen snow and approximately 75 % of the typical snow densities recorded at Halley; Figure 2 shows gravimetrically derived density data from a snow pit dug at Halley; measured density is in the right-hand column.

Figure 2. Snow pit data showing layer hardness, crystal type, grain size and density.

The modified correlation to account for variation in specific gravity (Robertson and Cabal, 2010) generates representative unit weights or densities for snow, another geomaterial, as long as a modifying value of average specific gravity is used. However, this relationship is general and is not sufficient to accurately estimate snow density using only CPT data. This is consistent with Mayne (2007), noted by Robertson and Cabal (2010), that any correlation between cone resistance and unit weight is complicated by cementation, suggesting that any relationship derived for typically unbonded soils, is probably not directly applicable to a highly-bonded geomaterial, snow.

4 PROPOSED CORRELATION Colbeck (1998) says that it is the amount of bonding within snow that determines its strength and therefore resistance measured by CPT. McCallum (2013), using data from penetrometer testing in Greenland and Antarctica, showed that both tip-resistance and sleeve-friction increase with increasing snow density; friction probably increasing because of “increased normal force acting upon the friction sleeve caused by less efficient packing of fractured particles at the cone shoulder as density of the snow undergoing penetration increases.” McCallum (2013) showed that the relationship between tip resistance and sleeve-friction may provide an assessment of snow microstructure or the level of bonding, noted earlier as the primary determinant of snow strength or resistance to penetration (Colbeck, 1998) and that snow density may be estimated solely by using CPT sleeve-friction data.

This relationship is now further explored. When sleeve friction values averaged over friction-sleeve length are compared with snow density, qualitative correlation is apparent. Figure 3 shows density variation with depth plotted against sleeve friction, normalized for comparison purposes.

400

500

600

Density (kg m−3) 700

0

800

900

1000

4

5

6

Averaged Friction Stratigraphy

0.5

1

Depth (m)

1.5

2

2.5

3

3.5

4

4.5 0

1

2

3

Resistance (MPa)

Figure 3. Comparison of sleeve-friction averaged over friction-sleeve length and normalized for comparison purposes, with snow density.

The cross-correlation function between these data suggests a correlation of 0.6. This suggests that the envisaged relationship may be valid, however, accurate comparison between any CPT data and density is difficult because of the variation in resolution. CPT data were recorded every 5 mm of penetration whilst density variation was typically observed over a scale of hundreds of millimeters. What is evident from Figure 3 is the increase in sleeve friction with depth versus the largely depth-independent density data. This suggests that sleeve friction increases with depth. CPT sleeve friction data for snow is not routinely modified to incorporate the increase in vertical stress with depth, but this is only because such data has never previously been reported before the work done by McCallum (2012). In that investigation, McCallum investigated the effect of overburden on sleeve friction data and concluded that mean sleeve friction varied significantly with amount of overburden and thus vertical stress, see Figure 4.

Figure 4. Significant variation of mean sleeve friction with amount of overburden removed. Line of best fit has gradient -0.003 ± 0.0004; each point on the graph is the mean of 195 data points.

If estimated values for snow unit weight are used to remove this frictional increase with depth ( 17 % per m) from the friction data presented in Figure 3, then a much closer fit is qualitatively observed between net sleeve friction and snow density, see Figure 5.

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Density (kg m−3) 480 500 520

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Resistance (MPa)

Figure 5. Comparison of net sleeve-friction averaged over friction-sleeve length and normalized for comparison purposes, with snow density.

5 SUMMARY Higher resolution density data is necessary to enable further quantification of the relationship between snow density and sleeve friction. However, preliminary analysis suggests that there is a significant relationship between net sleeve friction obtained from CPT and snow density. Because snow is a bonded geomaterial, tip resistance data is not used in establishing this relationship, indeed, the combination of tip resistance and sleeve friction CPT data for polar snow may provide insight into the microstructure or level of bonding within the snow pack. This is the subject of ongoing research.

6 ACKNOWLEDGEMENTS This research was only possible due to the generous assistance of Lankelma and Gardline Geosciences and the British Antarctic Survey, both in Cambridge, UK and Halley Research Station, Antarctica.

REFERENCES

Breton, D. J. and Hamilton, G. S. (2012), “Travels with MADGE and MABEL: near-situ and in-situ investigations of firn at Titan Dome, Antarctica”, Abstract C13G-06 presented at 2012 Fall Meeting, AGU, San Francisco, Calif., 3-7 Dec.

Colbeck, S. C. (1998), “Sintering in a dry snow cover”, Journal Of Applied Physics, 84(8), 4585–4589. Marchetti, S. (1980), “In-situ tests by Flat Dilatometer”, Journal of Geotechnical Engineering, ASCE, 106(3), 299–321. Mayne, P. W. (2007), Characterization & Engineering Properties of Natural Soils, vol. 3, chap. In-situ test calibrations for evaluating soil parameters, Taylor & Francis, London, 1602–1652. McCallum, A. B. (2012), Cone Penetration Testing in polar snow, Ph.D. thesis, University of Cambridge. McCallum, A. B. (2013), “Cone Penetration Testing (CPT): a valuable tool for investigating polar snow”, New Zealand Journal of Hydrology (In print). Morris, E. M. and Cooper, J. D. (2003), “Instruments and methods - Density measurements in ice boreholes using neutron scattering”, Journal Of Glaciology, 49(167), 599–604. Robertson, P. K. and Cabal, K. (2010), “Estimating soil unit weight from CPT”, in: “2nd International Symposium on Cone Penetration Testing, Huntington Beach”.