Effect of Geometry Precision and Load Distribution on Branch Mechanical Response

Round 1

Reviewer 1 Report

This paper addresses the relative accuracy and performance of different finite element models of tree branches, specifically, the relative performance of a 3D solid element model constructed from a 3D laser scan and a geometrically equivalent model constructed of one dimensional beam elements.  

 

I appreciate the intent of the paper, which I take to be to test one of the following, similar hypotheses:

 

1.     Solid element modeling provides better modeling accuracy when compared to beam modeling

2.     Solid element modeling does not provide better modeling accuracy when compared to beam modeling

 

Although the authors refer to their hypotheses, I cannot find a clear statement of which hypothesis they believe they are testing.  In any case, I believe it could be valuable to show that beam models perform as well as solid models and encourage them to pose the research question in that way.  

 

The reason I suggest this could be a valuable study is that, with the advent of any new technology such as 3D laser scanning, there is a rush to use it wherever possible, but technologies such as laser scanning can sometimes provide a false sense of precision and accuracy.  It would therefore be useful to show that standard beam FE models perform well.

 

I have a few additional comments:

 

1.     The finding that beam elements do a good job of predicting deflections of a bare branch is not exactly earth-shattering.  Beam elements are formulated to provide exact solutions to the governing equations of beam theory (without shear deformations) and tree branches, though geometrically complicated, do not exhibit complex mechanical response when subjected to static loads for which the response is in the linear range.  

2.     Though the authors identify the ANSYS beam element used, it would be useful to state whether it is an Euler-Bernoulli or Timoshenko beam element.

3.     The overall relative errors are high.  The most likely explanation is the difficulty in approximating the material elastic modulus and accounting for the bark thickness, though it’s not clear why the error on the beam and solid FE models is in different directions relative to the experiment.

4.     After the validation study, the results are presented in terms of relative error of each model with respect to the experiments, if I read correctly.  Since I understand the hypothesis to relate to the relative performance of the beam models to the solid models, it would be better, I think, to compute relative error between the two models.

5.     The authors address only model response to static loads that keep response in the linear range, yet the introduction they refer to the importance of tree risk and failure analysis. The authors should comment on the importance of their linear elastic results to failure and risk analysis.  As a note, the advantages of a 3D solid model may become more apparent when material nonlinearity and failure come into play as capturing those behaviors in a beam element requires fairly complex calculation of the nonlinear beam moment-curvature relations.

 

 

 

 

None.

Author Response

Responses to Reviewer 1 – Comments

Response to the main comment:

Dear reviewer,

Thank you for your comments, which helped us to improve the manuscript. There were two main hypotheses in the manuscript, one regarding the comparison of geometry and the second one regarding methods of loading, both commonly used in arboriculture practice and mechanical analyses. Due to your comments, we clarified our intentions in the introduction (96-101, 103-105) and abstract (lines 15-16) and also tried to clarify outputs in the results and conclusion (629-633). 

Please find individual comments on your points below.

Regards

Authors collective

Response 1: We agree that the nature of beam elements should provide solutions with satisfying precision, however, there are more influences entering the analysis. First is the procedure of input parameters where the scan geometry should provide exact diameters along the whole branch. In the case of beam geometry, we intentionally measured parameters in-field and from photos, which means that the diameters were measured only in the limited number of points (markers positions, angles of main axis curvature, side branches). The manual measurement contained also a natural degree of inaccuracy. The second main point is in material properties when solid elements allow defining the fully orthotropic model, while beam elements have only limited material inputs. Our aim was not only to compare the solid and beam elements but to do the complex evaluation of the whole procedure based on the usage of scan-based geometry and load definition. We believe that by the changes and explanation mentioned above (in Response to the main comment), we clarified this intention. 

Response 2: Corrected, lines 202-203.

Response 3: Added explanation in lines 387-390, 392-396.

Response 4: The explanation of our hypotheses is mentioned above (in Response to the main comment). Our aim was to point more to the level of simplification in all steps of the model-building procedure which will fit the experiment rather than a comparison of the methods themselves. We improved the description and we hope that the text now presents this idea in a better way. Anyway, it is a good point to show also the comparison of two geometries and we added the comparison by RE into Figures 7 and 8.

Response 5: The methods commonly used for the stability evaluation in practice are based on the non-destructivity; therefore we see the observation of tree response within the elastic-linear range as a crucial starting point. The aim was to provide results that will contribute to the following research aimed at sub-structural modeling, and limit the number of input variables. This approach is described in lines (430-432). The effect of nonlinearity and also dynamic response will be processed in further work. We added an explanation to the methodology (lines 181-184) and clarified that the results are valid for the elastic range in the conclusion line 612. In the original manuscript, we also discussed that the advantage of 3D solid elements has not been fully used in this study (448-453).

Author Response File: Author Response.pdf

Reviewer 2 Report

Line 124. A scheme of diameters to understand vertical and horizontal diameter on the branch, or and scheme of the complete test, is needed.

Line 131. The moisture content is important to obtain the weight of the branch, and others, but there are no references about actual values of moisture content of the wood or the foliage.

Line 150. Fv and Fh denominations are not consistent with the table 1. ELd appears on line 145 but appear as EL on other lines. A review, a clarification and unification of all the terminology along the text is suggested.

Line 133. Frontal area is one of the most important factors to be considered to evaluate the effect of the wind on a tree. I haven’t found references in the text about the expected wind effect on the analysed trees, in terms of load, velocity or drag leaves coefficient, neither the value of the applied loads for the tests in relative comparison with the wind effect (Line 360). In my opinion, the accuracy ant the relevance of the detailed method described in this paper depends, in part at least, on the comparison with the real behaviour of the trees in real conditions. So, an explication of this matter is suggested.

Line 173. How the key points are defined or located along the branch is not clear. Its influence on the mechanical behaviour modelling is important, so I can suggest a better description or justifying.

Line 238. Text in the figure is illegible.

Line 292. If standing trees was mechanically tested in real conditions, an 'apparent' static modulus of elasticity could be obtained for the real branch that includes the effect of the bark, among others. In my opinion, a 70% reduction of the modulus of elasticity because the bark seems quite arbitrary, so a further justify is needed.

Line 299. Moisture content is not so easy to neglect, especially since reference values from the 12% MC are considered and the moisture content of a branch in a standing tree can by higher than 100%. Comparison between considered reference values and conclusions must be described in the paper regarding the effect of the moisture content of the wood in standing trees.

Line 290-305 An important deficiency is not considering real or reliable values of physical or mechanical properties of the wood: bark effect, other values obtained from generic elastic relations, reference values from other species (but similar), moisture content of the wood. It must be very well justified the reasons or the consequences on the conclusions.

Line 371 Text in the image is illegible.

Line 532 The image is illegible

Author Response

Response to Reviewer 2 – Comments

Dear Reviewer,

Thank you for the revision of our manuscript and your comments. We really appreciate your feedback on the deficiency in the definition of material properties, which we reflected by changes in the manuscript and also explained below. We agree that there is a significant simplification in the definition of the material model. However, our novelty in the definition of the orthotropic model which follows the branch orientation in scan-based geometry is a more precise approach than commonly used in other studies. Also, we openly discuss this limitation of our work. According to the recommendation of the second reviewer, we add an explanation of the hypothesis of our work, and we hope that this also contributes to a clear description of the purpose and approach of our study. Please find individual comments on your points below.

Regards

Authors collective

Response 1: Schema is added in Figure 2c. If you will agree, we propose to provide schema in supplementary materials, because of the extension of the manuscript.  

Response 2: Whole branches and pruned parts were weighted immediately after measurement. We did not measure directly the moisture content of the branches. Before and during measurement were branches protected from moisture loss (packaged) and continuously stored in the fridge. Therefore, the change in the moisture content was neglected. Explanation added into lines 130-132.

Response 3: Corrected.

Response 4: We are not sure, if we understood well this comment, but in general we agree that the frontal area is the most important factor, as it is mentioned in the manuscript (lines 258-262). This was also why the scenario with force distributed according to the frontal area of pruned parts was chosen as the reference one (lines 377-378, 455-457). However, the aim of this study was to analyze the level of simplification within the crown structure in FE modeling. The study was intentionally aimed at the higher-order branches on crown edges, which is not always possible to involve in detail in the tree analyses. This study has not ambitious to provide results for overall tree behavior, although these partial results should be used in further work on more complex models. Therefore, we do not see it as relevant to provide values of expected wind loads on whole trees. We expanded the description of our objectives (95-106) and hope that this clarifies the relevance of the methodology and results. In other words, regards “the value of the applied loads for the tests in relative comparison with the wind effect” we would like to accent the fact that the absolute value of applied force (approx.. derived from the geometry of the branch) was important only for numerical model validation (same loading in model and measurement). As the numerical model works in an elastic region and the experimental load was well below the proportional limit, we believe this approach is correct.

Response 5: We added the schema of the end point and the key point to Figure 3. Actually, the key points are all the points used for line definitions in ANSYS.

Response 6: We assume that the readability is influenced by the image resolution reduction in the document. The figure attached in original resolution seems to be well visible. For sure, we increased the size of labels and text in the figures.

Response 7: As was mentioned in response 4, we did not measure whole trees but only higher-order branches. Branches were anchorage in the holder, which did not, provided fully fixed anchorage. Together with the curved shape of the branches, and the unreadability of all markers in image analysis (caused by leaves and positions of side branches – S1, Figure 1,2) we did not consider as reliable to calculate the indirect modulus of elasticity from the deflection. The direct measurement of dynamic wood properties provided general information about the material of each branch and was subsequently used for the calculation of the rest necessary parameters according to literature values (as standard procedure in the modeling, because of the complexity of input material parameters). In relation to our aim, it was not necessary to use precise material properties but to follow the standard feasible process of numerical modeling with suitable simplification, and analyze how the simplification influences results. The reduction of modulus due to bark thickness was derived from the measured bark thickness at the branch base - we computed the theoretical beam deflection (bending of cantilever beam equation) with reduced diameter and derived the elastic modulus corresponding to the same deflection on the beam with original diameter. The approach based on the reduction of diameter corresponded also the other publications. We added an explanation to lines 309,310,312-316.

Response 8: We did not neglect the moisture content in general, since we used the measured (green state) elastic modulus for longitudinal direction. The rest of the constants were calculated based on elastic ratios (adopted for 12% MC), which is the only simplification in relation to moisture content we did. Anyway, as the green wood value of elastic modulus was used as the initial value, values calculated with the use of elastic ratios were close to greenwood too. We understand that there is a high moisture content in trees, it is time-consuming and mainly beyond the purpose of this work to obtain all experimental-based material model parameters for green wood. As the elastic ratios were fixed for all the cases, we believe the above-described simplification does not affect the main hypothesis of the study (geometry and load simplification). Definitely, we add comments in methodology (lines 320,321), results and discussion (lines 408-411,451), and conclusion (line 616). We discussed the possible impact of such simplification and mentioned the moisture content too. 

Response 9: As was mentioned above the aim of the work was not based on the precisely described material properties, but we followed a reliable procedure for the definition of the material model from available data. We added the effect of moisture content (mentioned above), however, the effect of material properties simplification was discussed in the original manuscript (lines 406-413, 427-431,448-453) and included in the conclusions too (lines 614-616). We fully understand and mentioned in conclusions that the material properties and their variability in branches are difficult to detect and contribute to differences in the response of the scan-based model.

Response 10: We assume that the readability is influenced by the image resolution reduction in the document. The figure attached in original resolution seems to be well visible. For sure, we increased the size of labels and text in the figures.

Response 11: We assume that the readability is influenced by the image resolution reduction in the document. The figure attached in original resolution seems to be well visible. For sure, we increased the size of labels and text in the figures.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Text has been improved enough. Text included in some images is still illegible in the paper, any decision about that depends on the editor.

Author Response

Dear reviewer,

thank you for your input which helped us to improve the manuscript. We will solve the issue of images readability with the editor. 

Regards

 Authors collective