Sir,
I agree with the first comment of R. A. Sommerfeld that it would be very convenient if the large-volume strength could be derived from measurements on smaller volumes. I only showed (Gubler 1978[a], [b]) that the extrapolation to larger volumes depends strongly on the link-strength distribution chosen. Sommerfeld remarks that technical reasons impede a determination of the exact distribution type for the strength of the fundamental units or test samples from field measurements. But if future experiments allow the determination of the strength distribution of the microscopic links defined by Gubler (1978[b]), an exact extrapolation from measured smaller-volume strength to large volumes would be possible. (If the snow under investigation is homogeneous in a macroscopic sense.) Concerning shear strength and Daniels’ statistics, Sommerfeld seems to imply that his test samples are not conclusively identical with the fundamental units. So each test sample may consist of an unknown number of fundamental units. If the link number per test sample is high enough, Daniels’ theory predicts a constant expectation for its strength independent of the number of links per sample. If Sommerfeld’s test samples consist only of several links, he has to develop a method which enables him to determine the original link-strength distribution. Daniels’ suppositions cearly require a logical definition for the links. The theory implies the existence of only two states of a link: completely broken or surviving. But Sommerfeld’s test volumes may break in part during natural stress increase showing that they cannot be considered as the fundamental links. For these reasons, it seems to me that one has to know the strength distribution of the logical links in order for it to be permissible to apply Daniels’ statistics. There still remains a second problem: the stress-rates applied to the test samples are at least three orders of magnitude higher than the natural stress-rates. This fact together with the well-known high stress-rate dependence of strength of snow indicates that it is not possible to determine ductile shear strength using the sampling methods described by Sommerfeld together with Daniels’ statistics. The problems arising from natural macroscopic weak flaws which in general are not distributed at random in the potential avalanche starting zone are already discussed in the original paper (Gubler, 1978[a]).
H. Gubler
Eidg. Institut für Schnee- und Lawinenforschung,
7260 Weissfluhjoch/Davos, Switzerland
2 February l979
