## Confidence intervals from shear strength test (e.g. triaxial test)

## Confidence intervals from shear strength test (e.g. triaxial test)

(OP)

Hi,

I want to share a concept with you and maybe start a discussion about confidence intervals estimation based on the shear strength tests (direct or triaxial).

First, I would like to ask you about your preference. If you interpret such tests, are you asked also for characteristic values estimation? Can you do this solely on the basis of the test results? I know that the most common approach is to take only two numbers from the test - internal friction angle and cohesion (mean/most likely value). Later information about the scatter of the results is "artificially" added based on the prior knowledge (databases or personal experience) and finally, confidence intervals can be estimated [1]. Some researchers utilize the information about the scatter directly from the results [2], but all the solutions that I have found were 'work around'. Together with my colleagues, we proposed a solution directly utilizing well-established formulas from linear regression. There are formulas for estimating the confidence interval of regression line parameters (slope and intercept), so you only need to transform the result from the fitting plane (s'-t, p'-q, or sigma1-sigma3) to the soil parameters. We described this in the paper [3], but I don't expect that engineers would have time to read all the new stuff in the field. Also, there is some algebra behind this method that may be scary at the first glance, but it's not any rocket science. We believe that the proposed method is really useful and easy. So we are trying to make it 'digestible. For this reason, we prepared a video Link briefly discussing this method. It doesn't explain everything, but the paper does. We also prepared an Excel example, so anyone could first try it and check all the formulas in practice (first position of supplementary materials enclosed to the article - open access of course). We will appreciate any feedback.

Cheers,

Karol

[1] Pohl, C. (2011). Determination of characteristic soil values by statistical methods. Geotechnical Safety and Risk. ISGSR 2011, 427-434.

[2] Schneider‐Muntau, B., Schranz, F., & Fellin, W. (2018). The possibility of a statistical determination of characteristic shear parameters from triaxial tests. Beton‐und Stahlbetonbau, 113, 86-90.

[3] Brzeziński, K., Józefiak, K., & Zbiciak, A. (2021). On the interpretation of shear parameters uncertainty with a linear regression approach. Measurement, 174, 108949. Link

P.S. To be honest, I have joined this forum to share our concept with you. It may be interpreted as "promoting" which is against the policy. If so, please let me know. I prefer to remove this post rather than getting banned because it looks that the community here is quite cooperative and I would like to stay here for a longer time.

I want to share a concept with you and maybe start a discussion about confidence intervals estimation based on the shear strength tests (direct or triaxial).

First, I would like to ask you about your preference. If you interpret such tests, are you asked also for characteristic values estimation? Can you do this solely on the basis of the test results? I know that the most common approach is to take only two numbers from the test - internal friction angle and cohesion (mean/most likely value). Later information about the scatter of the results is "artificially" added based on the prior knowledge (databases or personal experience) and finally, confidence intervals can be estimated [1]. Some researchers utilize the information about the scatter directly from the results [2], but all the solutions that I have found were 'work around'. Together with my colleagues, we proposed a solution directly utilizing well-established formulas from linear regression. There are formulas for estimating the confidence interval of regression line parameters (slope and intercept), so you only need to transform the result from the fitting plane (s'-t, p'-q, or sigma1-sigma3) to the soil parameters. We described this in the paper [3], but I don't expect that engineers would have time to read all the new stuff in the field. Also, there is some algebra behind this method that may be scary at the first glance, but it's not any rocket science. We believe that the proposed method is really useful and easy. So we are trying to make it 'digestible. For this reason, we prepared a video Link briefly discussing this method. It doesn't explain everything, but the paper does. We also prepared an Excel example, so anyone could first try it and check all the formulas in practice (first position of supplementary materials enclosed to the article - open access of course). We will appreciate any feedback.

Cheers,

Karol

[1] Pohl, C. (2011). Determination of characteristic soil values by statistical methods. Geotechnical Safety and Risk. ISGSR 2011, 427-434.

[2] Schneider‐Muntau, B., Schranz, F., & Fellin, W. (2018). The possibility of a statistical determination of characteristic shear parameters from triaxial tests. Beton‐und Stahlbetonbau, 113, 86-90.

[3] Brzeziński, K., Józefiak, K., & Zbiciak, A. (2021). On the interpretation of shear parameters uncertainty with a linear regression approach. Measurement, 174, 108949. Link

P.S. To be honest, I have joined this forum to share our concept with you. It may be interpreted as "promoting" which is against the policy. If so, please let me know. I prefer to remove this post rather than getting banned because it looks that the community here is quite cooperative and I would like to stay here for a longer time.

## RE: Confidence intervals from shear strength test (e.g. triaxial test)

I guess one comment to make: conventionally the internal friction angle is calculated from a 'set of three' drained tests (unless you have a stress path device) and the results from multiple 'sets of three' tests plotted to infer the 5th percentile value for a given layer/unit. Are you advocating breaking apart the 'set of three' tests into its constituent parts, then undertaking such analysis?

Also, as a general point, while I appreciate the aim of these confidence-type assessments is essentially to reduce the standard deviation (or, perhaps better yet, the coefficient of variation), that does not necessarily mean the result is any more reliable. For instance, it could mean that numerous results have converged on the same incorrect outcome, for whatever reason. This is always a risk in geotechnical engineering, of course, but I think this is why it is good to tie back to prior knowledge, where available. I think to do this in a statistical manner you would inevitably need incorporate Bayes theorem.

## RE: Confidence intervals from shear strength test (e.g. triaxial test)

Both statistics and geotechnics require some experience, otherwise one can easily fool himself. We just claim that obtaining only single information (point estimation) of cohesion and internal friction angle is a waste of lots of information. Let's say one has nine samples of soil from 'the same location'

*.From what I understand

**, conventionally one would create three 'sets of three', and based on their results would try to estimate the 5th percentile***. What we suggest, is to plot all the points in one figure and compute not only point (mean) estimation, but also confidence intervals. I agree with your general remark that super-accurate estimation of parameters is pointless. However, more samples are better, not necessarily to decrease the coefficient of variation, but at least to estimate it better. Maybe a bootstrap would be a more convincing approach. Instead of taking three 'sets of three' pick as many different sets as you can from nine samples (84 sets of three). And then use the conventional approach for the 5th percentile estimation.*Of course, there is a spatial variability of soil properties. But I think that if one accepts the conventional approach to compute the 5th percentile, he also, assumes it is 'the same' soil in all the samples. Thus, other statistical approaches (including the one proposed by us) are justified as well.**Maybe I am wrong about this. My experience is limited, so such discussions with people from different labs are so valuable :)***Three results from three 'sets' are not much, but I think that rarely one tests much more than that. So I didn't discuss it much in the first point, and only mentioned adding information about the coefficient of variation from prior knowledge.