Pile Design for Downdrag: Examples and Supporting Materials (2024)
Chapter: Appendix B: Statistical Analyses of t-z and q-z Curve Models
APPENDIX B
Statistical Analyses of t-z and q-z Curve Models
The statistical output for analysis of t-z relationships is included herein. These analyses provide a measurement of validation of the different models that were used to develop t-z curves.
Table B.1. Statistical output for Bohn et al. (2017) Cubic Root relationship.
| Averages | |||||
|---|---|---|---|---|---|
| Bohn et al. (2017) Cubic Root | Mean Bias | COV Bias | NRMSE | ||
| A | Steel | Plastic | 0.97 | 29.84 | 16.7% |
| Granular | 1.02 | 33.50 | 23.8% | ||
| Concrete | Plastic | 0.99 | 34.86 | 20.2% | |
| Granular | 1.00 | 34.55 | 18.1% | ||
| B | Steel | Plastic | 1.00 | 30.46 | 21.9% |
| Granular | 1.03 | 33.34 | 21.1% | ||
| Concrete | Plastic | 1.06 | 27.05 | 20.3% | |
| Granular | 1.01 | 31.89 | 19.4% | ||
Table B.2. Statistical output for Vijayvergiya (1977) relationship.
| Averages | |||||
|---|---|---|---|---|---|
| Vijayvergiya (1977) | Mean Bias | COV Bias | NRMSE | ||
| A | Steel | Plastic | 0.78 | 34.70 | 23.7% |
| Granular | 0.80 | 35.62 | 27.6% | ||
| Concrete | Plastic | 0.74 | 38.88 | 25.8% | |
| Granular | 0.74 | 36.56 | 24.8% | ||
| B | Steel | Plastic | 0.83 | 36.83 | 29.2% |
| Granular | 0.80 | 38.69 | 28.9% | ||
| Concrete | Plastic | 0.77 | 30.96 | 23.0% | |
| Granular | 0.76 | 35.75 | 24.7% | ||
Table B.3. Statistical output for Bohn et al. (2017) Hyperbolic relationship.
| Averages | |||||
|---|---|---|---|---|---|
| Bohn et al. (2017) Hyperbolic | Mean Bias | COV Bias | NRMSE | ||
| A | Steel | Plastic | 1.80 | 44.35 | 16.4% |
| Granular | 1.31 | 45.80 | 24.0% | ||
| Concrete | Plastic | 1.00 | 38.70 | 19.1% | |
| Granular | 1.10 | 34.67 | 18.1% | ||
| B | Steel | Plastic | 2.01 | 48.20 | 23.3% |
| Granular | 1.56 | 48.56 | 23.5% | ||
| Concrete | Plastic | 1.07 | 25.38 | 16.6% | |
| Granular | 1.18 | 37.81 | 17.8% | ||
Table B.4. Statistical output for Mosher (1984) relationship.
| Averages | |||||
|---|---|---|---|---|---|
| Mosher (1984) | Mean Bias | COV Bias | NRMSE | ||
| A | Steel | Plastic | |||
| Granular | 2.65 | 46.66 | 25.3% | ||
| Concrete | Plastic | ||||
| Granular | 1.46 | 39.85 | 25.5% | ||
| B | Steel | Plastic | |||
| Granular | 2.01 | 48.14 | 29.2% | ||
| Concrete | Plastic | ||||
| Granular | 1.40 | 42.98 | 22.2% | ||
*Plastic soils not considered for Mosher (1984), because it was developed for granular soils.
Table B.5. Statistical output for API (2002) relationship.
| Averages | |||||
|---|---|---|---|---|---|
| API (2002) | Mean Bias | COV Bias | NRMSE | ||
| A | Steel | Plastic | 2.14 | 52.33 | 19.5% |
| Granular | 1.05 | 50.69 | 31.8% | ||
| Concrete | Plastic | 0.95 | 45.97 | 22.7% | |
| Granular | 0.81 | 41.46 | 28.0% | ||
| B | Steel | Plastic | 2.45 | 56.16 | 26.4% |
| Granular | 1.14 | 52.78 | 32.4% | ||
| Concrete | Plastic | 0.97 | 29.35 | 17.7% | |
| Granular | 0.85 | 46.38 | 28.1% | ||
Table B.6. Statistical output for Coyle and Reese (1966) relationship.
| Averages | |||||
|---|---|---|---|---|---|
| Coyle and Reese (1966) | Mean Bias | COV Bias | NRMSE | ||
| A | Steel | Plastic | 0.99 | 43.56 | 27.8% |
| Granular | |||||
| Concrete | Plastic | 0.82 | 50.80 | 31.6% | |
| Granular | |||||
| B | Steel | Plastic | 1.95 | 56.18 | 27.8% |
| Granular | |||||
| Concrete | Plastic | 0.93 | 41.78 | 31.3% | |
| Granular | |||||
*Granular soils not considered for Coyle and Reese (1966), because it was developed for plastic soils.
References
API (American Petroleum Institute). (2002). API Recommended Practice 2A-WSD - Planning, Designing, and Constructing Fixed Offshore Platforms – Working Stress Design, 21st ed. American Petroleum Institute.
Bohn, C., Lopes dos Santos, A., and Frank, R. (2017). “Development of Axial Pile Load Transfer Curves Based on Instrumented Load Tests.” Journal of Geotechnical and Geoenvironmental Engineering 143 (1): 04016081.
Coyle, H.M., and Reese, L.C. (1966). “Load Transfer for Axially Loaded Piles in Clay.” Journal of the Soil Mechanics and Foundations Division 92 (2).
Mosher, R.L. (1984). Load Transfer Criteria for Numerical Analysis of Axially Loaded Piles in Sand. U. S. Army Waterways Experiment Station, Automatic Data Processing Center, Vicksburg, Mississippi.
