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the Creative Commons Attribution 4.0 License.
| 16 Apr 2024
The effect of propagation saw test geometries on critical cut length
Abstract. For a slab avalanche to release, a crack in a weak snow layer beneath a cohesive snow slab has to initiate and propagate. Information on crack propagation is essential for assessing avalanche triggering potential. In the field, this information can be gathered with the Propagation Saw Test (PST), a field test that provides valuable data on crack propagation propensity. The first PSTs were performed about 20 years ago and standards have since been established. However, there are still differences in how the PST is performed. Standards in North America require the column ends to be cut vertically, whereas in Europe they are typically cut at a normal angle. In this study, we investigate the effect of these different column geometries on the critical cut length. To this end, we conducted 27 pairs of PST experiments, each pair consisting of one PST with slope normal cut ends and one PST with vertical cut ends. Our experiments showed that PSTs with normal cut ends have up to 50 % shorter critical cut lengths, and the difference predominantly depends on the slope angle and slab thickness. We developed two load-based models to convert critical cut lengths between the test geometries: (i) a uniform slab model that treats the slab as one uniform layer and (ii) a layered model that accounts for stratification. For validation, we compare these models with a modern fracture mechanical model. For the rather uniform slabs of our experiments, both load-based models were in excellent agreement with measured data. For slabs with an artificial layering, the uniform load-model predictions reveal deviations from the fracture mechanical model whereas the layered model was still in excellent agreement. This study reveals the influence that the geometry of field tests and the slope angle of the field site have on test results. It also shows that only accurately prepared field tests can be reliable and therefore meaningful. However, we provide models to correct for imprecise field test geometry effects on the critical cut length.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2024-690', Anonymous Referee #1, 03 May 2024
Review:
The effect of propagation saw test geometries on critical cut length,
Bastian Bergfeld, Karl W. Birkeland, Valentin Adam, Philipp L. Rosendahl, and Alec van Herwijnen
This manuscript provides useful information regarding differences in test protocols related to the “propagation saw test”, which is used for snow avalanche stability assessment. There are differences in the test configuration setups that exist between Europe and North America. Field studies carried out in Switzerland and the U.S. compare outcomes associated with the different geometries and two different loading methods are assessed. Accompanying the empirical tests several modeling methods are offered. Notable differences are presented that will be useful in comparing test results or defining a standard.
The paper is well structured, clearly written and offers new relevant results. The title is fitting, and the abstract clear. It is an appropriate topic for NHESS and generally satisfies the criteria for publication in an international journal. In my opinion it will be suitable for publication. That said, I have made some specific recommendations to be addressed to improve the presentation. In particular, it would be beneficial to more robustly present the assumptions made in the mechanical models, as I’ve noted below.
Line 14 “Standards in North America require the column ends to be cut vertically, whereas in Europe they are typically cut at a normal angle.” - As an aside point of curiosity, do you have any knowledge on why (or when) the two different configurations were adopted on the different continents?
Line 46 “methodological differences” - What are different methods? Are these inferring formalized differences, or are you referring to unintended variations during the implementation process?
Line 63 Were weak layer thicknesses measured? Was hardness measured (e.g. hand hardness)?
Line 66 “For 6 pairs we also performed pairs of PSTs in which the weak layer was cut in upslope as well as in downslope direction” – Suggest changing to “For six additional pairs…”. This is clearly presented in the results, but it should be clarified here as well.
Line 67 “Figure 1b” - Fig 1b implies that direction is only considered for the slab cut vertically. The up and down superscript notation does not differentiate PST geometry. However, as presented in fig 2b, both N and V were tested.
Suggest that you show, and reference, the upslope and downslope crack length arrows on Fig 1a, and state that the up and down notation applies to both geometries.
Line 71 “(c) Difference in PST geometry .” - add …at the downhill end of the slope normal beam for an upslope saw cut”.
Line 72 “The main difference is the additional slab load for the slope normal geometry shown by the grey triangle.”- Reading this, my initial thought was that there must be a compensating triangle of snow removed from the uphill end of the slab. (You discuss this later when you bring in downslope saw cuts.) When considering the entire beam there would then be no additional resultant slope normal load. What you are referring to is only the portion of the slab directly above the saw cut plus the grey triangle.
Line 78 (Figure 1b) – Same comment as line 67.
Line 83 “loads” - These would be more appropriately be defined as stresses, rather than loads. Load is typically used to define a force. The stress in this case is defined as the vertical load acting over the inclined weak layer or saw cut area. As developed in appendix A.
Line 99 Eq 3 “𝑟𝑐V” - Should note that eq 3 reduces to eq 2 for the assumptions stipulated there.
Line 106 “smeared springs”- Define smeared springs. Modeled with shear as well as slope normal elastic properties.
Line 178 “This additional load, in normal geometry” what you mean is the additional load above the saw cut area. The total vertical load applied by the beam would be the same. However, it would not be a uniformly distributed vertical load acting over the length of the weak layer + saw cut.
Line 267 “Based on our findings, we suggest that PSTs with slope normal ends should be performed with a saw cut in the upslope direction” - Here you seem to be suggesting that PSTs with saw cuts from the bottom should in general be the standard.
Line 273 “if the PST is to be used as a stability tool without further investigation, the vertical PST configuration should be preferred by practitioners as it allows results to be extrapolated from flatter terrain to steeper slopes with less error.” Here you are suggesting that practitioners should use vertical end cuts.
Line 276 “In general, the use of consistent PST standards will ensure that PST results are easy to interpret, will ensure scientific rigor and will improve the comparability of tests and their results. In addition, standardization and conversion models facilitate the comparison of results between researchers, leading to a deeper understanding of snowpack behavior. Practitioners also benefit from standardized methods and interpretation aids that are invaluable in assessing avalanche risk based on stability tests”. -Not clear what standard you are suggesting. Possibly two different standards? One for researchers and another for practitioners. Although I have the impression that you are advocating the slope normal for everyone, your intention should be clarified. It seems that the PST may be used more frequently by researchers, than by practitioners for routine assessment since the setup requires a substantial time-consuming effort. If it is to be used as a stability test, practitioners may be interested in assessing the influence of slope angle, in which case might the slope normal configuration have an advantage
as a standard? However, this would require using a representative slope that is not in a hazardous area.
Line 292 “Figure A1: (a) Schematic representation of a layered slab in a PST with slope vertical geometry (V-PST).” - The saw cut length in the figure, 𝑟𝑐N, is referencing the N-PST with slope normal geometry instead of 𝑟𝑐V. As sketched in both Figures A1(a) and (b), A indicates a length equal to the saw cut length.
Line 294 “the areas B and C” - B and C should probably be subscripted with an i to indicate the individual areas. Although below, as in line 303 these are defined or inferred to be volumes identifying the masses mA, mB and mC, which physically is the appropriate designation as applied. This referencing of terms A, B, C as length, area and volume for the same terms needs to be cleaned up for consistency.
Line 296 “V-PST (Figure A1a)” - Figure A1(a) shows the saw cut length for the normal beam geometry, although eq A1 is correct.
Line 296 “First for the simpler case of a V-PST (Figure A1a) the mass and load is given by: “- Actually a "stress" acting over the inclined saw cut area, that is in contact with the volume of the slab, A, directly above, as defined by Eq A2. Total vertical load is mA*g.
Line 300 “In the N-PST the Volumes B and C also contribute to the overall mass located above the saw cut:” - Assumes the load (force) is determined through the volume defined by the total volume A+B+C acting vertically over the area of the saw cut.
As I interpret it, for both V-PST and N-PST the assumption is that there is no interaction between the isolated snow over the crack and the rest of the slab. Essentially, snow above the saw crack is considered as a free body in which the normal and shear interacting with the rest of the slab are negligible. That is, the rest of the slab is considered independently. Although not explicitly discussed, the “gravitational pull” of the middle part of the PST is presented in figure 4b. However, I don’t see how this influences the mechanical model presented. This assumption that the part of the slab over the weak layer can be assumed independent of the rest of the slab should be explicitly presented.
Given a bonded slab here is going to be some interaction at the interface of the slab directly over the saw cut and that over the intact weak layer. While on a level surface it may be slight, intuitively, on a slope this interaction would be exacerbated. Given the different properties of the weak layer and the saw crack area this would, it seems, be particularly evident regarding slope parallel shear.
Line 175 “assume that PST beams were long enough, so that the tail end of the PST beam remains mechanically unchanged.” – The length of the beam is not relevant in the model. If it is, please explain.
Line 225 “We suspect that in these PSTs the beam length was too short, the ratio between
slab thickness and beam length was only about 0.5. It is therefore very likely that the geometric difference at the tail end of the beam was also relevant (Bair et al., 2014). However, this is not considered in the models.” – The ratio of thickness to length is provided. Since the length of the beam does not play a role in the model, a more useful metric may be the thickness.
The modeled results show good agreement with field test measurements in Figure 3. Accordingly, they are useful to the overall presentation. It is incumbent upon the authors to discuss the lack of importance of the “rest of the beam” in the PST.
Line 303 “The mass of Volume A remains the same as in Equation A1.” - The mass mA will not be the same in both cases since it depends on the respective saw cut lengths. Should relabel as perhaps mAV and mAN.
Line 15 “normal angle” - Perhaps rephrase to "normal to the slope."
Line 124 Figure 2 - The two circles that look like 8 in the figure are extraneous. Typo.
Line 252 Suggest that “to extrapolate” - is changed “extrapolation to”.
Line 253 “were” - should be changed to “where”
Line 284 “N-PSTS” - drop the S. “N-PST”
Citation: https://doi.org/10.5194/egusphere-2024-690-RC1 - AC1: 'Reply on RC1', Bastian Bergfeld, 16 Sep 2024
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RC2: 'Comment on egusphere-2024-690', Anonymous Referee #2, 30 Jul 2024
The paper is an important step towards standardizing techniques for the PST. Standardization bears potential to facilitate and improve future research as it makes results comparable. For practioners the PST entails limitations due to the time consuming execution of the test. However, the findings and analysis on the test provided in this paper do hold great potential in making fracture mechanics and failure initiation more comprehensible in a teaching environment by combining emperical tests with modeling methods and offering mechanical explanations for the results.
Eventhough I believe the manuscript should be accepted as it is, I would like to offer some suggestions:
- A more precise suggestion on what the findings indicate would be the most suitable standard. It is described that the vertical PST configuration is less susceptible to changes in the slope angle and therefore is suggested to practicioners. To my understanding of the manuscript the benefits also prevail when the crack is initiated from the uphill direction.
- A topic that is touched on in the manuscript but not discussed in much detail is beam length. In the models it is assumed that the "beams were long enough, so that the tail end of the PST beam remains mechanically unchanged when
the saw cut is increased and is therefore not relevant". In addition it is mentioned that this did not apply to some results because the ratio between the depth of the weak layer and the beam lenght was only 0.5. In my opinion it would be intrested to discuss this issue in more depth.
Citation: https://doi.org/10.5194/egusphere-2024-690-RC2 - AC2: 'Reply on RC2', Bastian Bergfeld, 16 Sep 2024
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