Here is the analysis reformatted into standard **UBB Code**. You can copy the text inside the code block below and paste it directly into your forum post.
I have optimized the formatting to ensure mathematical symbols (like φ) display correctly on most standard engineering forums, and I have used `
` blocks for the data to ensure alignment.
### **Copy the code below:**
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[b][size=4]Geotechnical Analysis: Characteristic Value of Peak Friction Angle (φ'peak)[/size][/b]
[b]Reference:[/b] EN 1997-1 (Eurocode 7) & Frank et al. (2004), [i]Designers' Guide to EN 1997-1[/i].
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[b]1. Data Statistics[/b]
Based on the provided dataset for the peak angle of friction, the statistical parameters are derived as follows:
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Dataset (φ) : {32.5, 36.1, 34.3, 38.1, 39.3, 31.8, 33.6, 37.0}
Count (n) : 8
Mean (m) : 35.34°
Std. Dev (s): 2.71°
COV : 7.7%
According to EN 1997-1 Clause 2.4.5.2, the characteristic value must be a "cautious estimate of the value affecting the occurrence of the limit state."
Frank et al. (2004) distinguish between:
- Local Failure: Governed by the 5% fractile (rare for friction angles).
- Large Volume Failure: Governed by the cautious estimate of the mean (standard for slope stability and bearing capacity).
For this analysis, we assume a failure mechanism involving a significant volume of ground; therefore, we calculate the
lower 5% confidence limit of the mean using the Student's t-distribution for small sample sizes.
3. CalculationThe formula for the characteristic value
Xk is:
Xk = m - t * (s / √n)Where:
- t = Student's t-factor (for n=8, degrees of freedom=7, 5% confidence) = 1.895
- Standard Error = 2.71 / √8 = 0.958°
Xk = 35.34 - (1.895 * 0.958)
Xk = 35.34 - 1.815
Xk = 33.525°
4. Final Determination The characteristic value of the peak angle of friction for design is:
φ'k = 33.5° (Rounded to the nearest 0.1°)Note on Uncertainty: We can state with 95% confidence that the true mean friction angle of the soil stratum is at least 33.5°. The reduction from the mean (35.3°) to the characteristic value (33.5°) reflects the uncertainty inherent in the small sample size (n=8).
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