Using System Reliability Concepts to Derive Partial Safety Factors for Punching Shear with Shear Reinforcement: An Explorative Analysis

No.

Comments

Response

1.

“The main contribution of this work needs to be further highlighted. Is this the first reliability analysis of this structure in this article? What parts of the reliability analysis methodology used in this article are original?“

Firstly, it should be clarified here that this manuscript was developed in the context of a research initiative promoted by the German Federal Ministry for Economic Affairs and Energy (in German: Bundesministerium für Wirtschaft und Energie). One of the goals of this research project was the development of an open-source software package for structural reliability computation. The software package, named as TesiproV, was developed in the programming language R and has the ultimate goal to facilitate and promote the use of reliability-based methods among structural engineering practitioners and scientific communities.

During the development of the TesiproV software package – and ultimately, of the research project – distinct system reliability problems (i.e., structural engineering problems with multiple limit state functions) were selected and considered for testing and analysis. The structural system with multiple failure modes addressed in this manuscript is a well-known systems reliability problem to some of the co-authors, namely Prof. Hegger and Prof. Ricker – experienced researchers in the field of punching shear. Therefore, the selected problem was perceived as having the potential to be calculated and analysed within the framework of the above-mentioned project, and, particularly using the TesiproV package. 

It shall be also highlighted that despite the Authors of this manuscript having previously worked on the reliability assessment of punching shear resistance models (see e.g., Ricker et al, 2020), the reliability-based methods addressed in the manuscript are part of the structural reliability fundamentals, which have been long-studied in the extensive field literature. Therefore, and as stated in along the manuscript, the reliability-based methods used in this investigation are not intellectual property of the Authors. Yet, to the best of the Authors‘s knowledge, no similar investigation is available in literature and the parametric study conducted to tackle this system reliability problem is, indeed, original.

Further clarifications concerning this remark were added to the manuscript (Section 1).

References:

·       Ricker, M., Feiri, T., Nille-Hauf, K., Adam, V., & Hegger, J. (2021). Enhanced reliability assessment of punching shear resistance models for flat slabs without shear reinforcement. Engineering Structures, 226, 111319.

2.

“Why current analysis methodology was used for this problem?“

For simplicity reasons and considering the explorative nature of this investigation, it was the intention of the Authors to use a Level II method in combination with the Simple Bounds of Cornell. Please note that when supported by a computational tool for structural reliability calculation, as the above-mentioned TesiproV package, these methods can be easily used by structural engineering practitioners with relatively little effort.

Yet, to be able to verify the accuracy of the system reliability results produced by Level II methods, the Authors decided also to use Level III methods, which are those where failure probabilities are calculated more ‘‘exactly’’ by means of numerical integration, which typically involve the use of simulation methods. Within the large scope of Level III methods available, the Authors selected two Monte-Carlo simulation methods with variance reduction as further detailed in the manuscript: Importance Sampling (MC-IS) and Subset Sampling (MC-SuS). In a nutshell, MC-IS is a classical approach to calculate failure probabilities by sampling around the so-called a design-point, which is typically determined with support of Level II methods and needs to be searched at the beginning of each simulation run.

The MC-SuS method is a more modern approach known for not using any specific information about the reliability problem other than the input–output model, and therefore, for being independent of the inherent properties of the structural system being analysed. Nonetheless, both methods are known for being highly effective and efficient, making them especially attractive to tackle structural reliability problems of practical interest (e.g., Ricker et al., 2022).

Finally, it should be also noted that as concluded in this investigation, the use of Level III methods might actually be an add-value to this type of analysis provided that computational power is available to practitioners to attain more precise results and  avoid unsafe decisions.

References:

·       Ricker, M., Feiri, T., & Nille-Hauf, K. (2022). Contribution to efficient structural safety assessments: A comparative analysis of computational schemes. Probabilistic Engineering Mechanics, 69, 103285.

3.

“The contents of the second section are suggested to be reduced.“

Indeed, the Authors are aware that Section 2 of the present manuscript – referring to the design provisions in DIN EN 1992-1-1 together with the German National Annex DIN EN 1992-1-1+NA(D) for punching shear with and without shear reinforcement – is somewhat extensive and, very likely, already known to the main target audience of this investigation. Nonetheless, the Authors also believe that these provisions are a vital part of the theoretical background needed to contextualise this study and to support readers to avoid any misinterpretation of the results.

Furthermore, your counterpart reviewer – Reviewer 2 – made some remarks about this Section that require explanation and, in some cases, additional or complementary details. 

Based on these arguments, the Authors would like to maintain the structure and the content of Section 2 as it is.

4.

“Typos should be carefully checked and corrected.“

The manuscript was carefully checked and revised as recommended.

Number

Comments

Response

1)

“Please use the terminology "partial factor" instead of "partial safety factor." See for example the fib Bulletin 80 "Partial factor methods for existing concrete structures."

Suggestion accepted: All the “partial safety factor” terms were replaced by the “partial factor” terms.

2)

„The paragraph in lines 65-67 is hard to follow, please rephrase for clarity.“

The paragraph was adjusted and further clarified as recommended.

3)

„In line 120 "web-crushing limit" - are you referring to the concrete struts?“

The term “web-crushing limit” refers to the crushing of the compressive strut. This reference was added to the manuscript. 

4)

„In line 133 you cite the recommended values for ?. However, these are major simplifications. This should be at least commented on with regards to uncertainties it introduces in the analysis.“

The Authors are aware that the recommended values for  are major simplifications (e.g., Ricker et al, 2022). Further reference to specific methods that allow to determine more accurate -values was added to the manuscript (Section 2.2).

However, since this investigation only covers the resistance side, the Authors did not consider the scatter of the model behind the -values.

References:

·       Ricker, M., Häusler, F., & Hegger, J. (2022). Punching of edge column–slab connections–comparison of tests and codes. Proceedings of the Institution of Civil Engineers-Structures and Buildings, 175(3), 202-214.

5)

„The same comment goes for the strip of 3d over which reinforcement is averaged - the activation/yielding of reinforcement can be over a larger or smaller length - this is a further approximation/uncertainty and should be at least acknowledged. “

Indeed, the reinforcement is averaged over the strip of a 3d distance. In this investigation, the Authors considered an even distribution of the reinforcement region, as it is also common in punching shear tests. This was further clarified in the manuscript (Table 4, Section 4.3.1).

6)

„Lines 235-236 - please double-check this statement on uncorrelated series system failure. “

The statement was verified and adjusted.

7)

„The database you use - is it available in open access? I suggest you also mention (or try and calculate the model error) on the new punching database by the fib: https://www.fib- international.org/commissions/databases.html)“

No, the database used in this investigation is not available in open access. However, the basis of this database is the fib /ACI database. Note that the fib /ACI database was evaluated by the CEN Task Group 4, responsible for the revision of Eurocode 2. During this revision process, the fib /ACI database was evaluated and extended. Thus, despite not being the same, the database used in this investigation is very similar to the fib /ACI database.

8)

„Line 247 - how exactly did you decide which tests to assign to several failure modes?“

As mentioned in the previous point, the Task Group 4 checked the failure modes of each test in the database. The Authors used the failure modes previously defined in the database.

As it is also stated in the manuscript, it is clear in the database that some tests could not be directly attributed to a specific failure mode. Such tests were used for the evaluation of more than one failure mode.

9)

„You cite Table 3 before Table 2. Switch the order/names.“

The citation order of Tables 2 and 3 was adjusted as recommended.

10)

„Lines 301-303 explain in more detail how experiments were predicted - taking partial factors = 1, provided measured average material properties, etc.?“

Further explanation was added to the manuscript (Section 4.2): For the comparison of prediction and experimental results, the punching shear  was used, all the partial factors in the design equations were taken as unity and the mean value of the concrete compressive strength (cylinder) was adopted.

11)

„In Table 1 the sigma,LND value of 0.192 for C25 seems to me to be incorrect if you used the JCSS formula of s*sqrt(nu*n/((n-1)(nu-2))). Please double-check!

The Reviewer is right. The Authors apologise for the typo. The new value ( 0.164) is now corrected in Table 1.

12)

“I suggest adding at least some graphs to show the model error vs main parameters. You say later there is no space in the paper for this. But this is because you spend a huge amount of space explaining theory that will be known to an expert reader and then only limited space on the results themselves. This is not a book and the theoretical background needn't be so extensive, I'd prefer to see more analysis and scrutiny of the results.“

The graphs for the derivation of the model uncertainties are quite large and, therefore, cannot be all included in the manuscript. Nonetheless, for the sake of illustration, the graphs of one of the failure modes were inserted in the manuscript (see new Figure 3).

13)

“Can you compare the outlier detection using a box-and-whiskers plot (Q1-1.5IQR and Q3+1.5IQR)?“

It is a fact that boxplots (also known as 1.5 IQR test) can be used to identify any observation falling outside 1.5-times the range of the inner two quartiles of observations (or values). Boxplots are typically uncomplicated methods to detect outliers, by giving a decent visual indication of potential outliers. Hence, they are typically seen as graphical methods. However, the models behind graphical methods normally lack robust statistical rules and, therefore, are perceived to be more suitable for preliminary or “high-level” outlier detection analysis.

For this reason, the Authors selected a more robust test that includes statistical rules and considerations, as the David-Hartley Pearson Test, which is a statistical test suitable for the detection of multiple outliers in a dataset of values.

14)

“Please justify your choice of interior column - what about edge and corner columns? This are typically more problematic and thus it is more interesting to know the reliability of those cases.“

The Authors agree with the Reviewer. Nonetheless, edge and, specially, corner column test data tend to be rare or limited, which would invalidate the results of an investigation as the one presented in this manuscript.

15)

“So you chose a beta,target of 3.8 - explain why and from where (structural/reliability class, service life, etc.). However, you do not consider loads as probabilistic, i.e. they are deterministic. In this case you are calibrating only the resistance side and according to Eurocode 1990 your beta,target becomes betaR = alphaR*beta,target with alpha,R = 0.8. In other words you are calibrating for betaR = 0.8*3.8 ~ 3. See for example:

Bairán, Jesús Miguel, Nikola Tošić, and Albert de la Fuente. "Reliability-based assessment of the partial factor for shear design of fibre reinforced concrete members without shear reinforcement." Materials and Structures 54, no. 5 (2021): 1-16.“

The  target value was taken from DIN EN 1990 and refers to the recommended value for a Reliability Class 2 (RC2) and for a 50-year reference period. This RC2 is associated with the Consequence Class 2 (CC2) mostly related to common structures where consequences of failure are medium(e.g., residential and office buildings, public buildings).

For this analysis, only the resistance side was considered both to limit the computational effort and to evaluate the potential of the proposed approach.

To decouple the resistance and the load sides, the Authors applied a constant sensitive value  equal to 0.80 based on the provisions of DIN EN 1990. Thus, the resulting -values were then divided by 0.8, which enabled making comparisons with the more common target value of 3.8 recommended in DIN EN 1990.  

Further clarifications were added in the manuscript (Sections 4.3.1 and 5.1).

16)

“Figures 3-6 deserve more explanation and discussion.“

Additional explanation and discussion were added to these Figures.

17)

“Instead of changing gamma,C perhaps you can change parameters of the equations? For instance Crd,c?“

The Authors agree with the Reviewer. If the potential of the proposed approach is later used in the structural code, the empirical pre-factor  can be potentially reduced, while going further with . Nonetheless, the Authors would like to highlight that the goal of the present investigation was to evaluate the approach’s potential. To this, the Authors decided to focus on the variation of  since the impact of the results would be more prominent and a clearer image of the approach’s potential could be outlined. Yet, the Authors see this remark as a valuable recommendation for further applications and developments and took the freedom to include it in the last section of the manuscript.