Multiple Nonlinear Regression Models for Predicting Deformation Behavior of Concrete-Face Rockfill Dams
Publication: International Journal of Geomechanics
Volume 21, Issue 2
Abstract
Deformation assessment and control are important issues in the construction of concrete face rockfill dams (CFRDs). The design and construction of CFRDs require deformation behavior that can be estimated rapidly to support engineering optimization and safety assessment. This study aims to develop robust empirical prediction models with physical meaning for predicting key indices of CFRD deformation behavior based on in-service case history data. A database of 87 case histories of in-service CFRD constructed over the past 50 years was compiled. A multiple regression method is adopted to develop empirical relationships between three key indices (crest settlement, internal settlement, and face slab deflection) and six dam construction-related control variables (dam height, void ratio, foundation condition, intact rockfill strength, valley shape, and operation time). The internal correlation between the key indices and control variables is discussed. Dam height, intact rockfill strength, and foundation condition are found to be the important factors influencing the three key indices. The developed models are compared with some published methods to discuss model rationality and accuracy. The feasibility and application of the models are further validated considering one case study.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study was supported by the National Natural Science Foundation of China (Grant Nos. 51909215 and 52039008), the Natural Science Basic Research Program of Shaanxi (Program No. 2020JQ-641), China Postdoctoral Science Foundation (Program No. 2020M683527), the Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 19JS047), the Young Talent Fund of University Association for Science and Technology in Shaanxi, China (Program No. 20200417), and the National Natural Science Foundation of China (Grant Nos. 51722907 and 51979224).
Notation
The following symbols are used in this paper:
- A, B, C, D, E, F
- coefficients in the regression model;
- A1
- upstream slope face area;
- a, b, c, α, β
- empirical formula coefficients;
- bi
- regression coefficient;
- D, Hi, d, hi
- geometric parameters for rockfill modulus;
- E
- natural constant;
- ej
- residual error;
- H, CL
- dam height and crest length, respectively;
- Hr
- reference value of dam height;
- L
- leakage after reservoir filling;
- n, k
- number of case and control variable, respectively;
- R2,
- determination coefficient and adjusted determination coefficient, respectively;
- S
- conditional standard deviation;
- Xi
- control variable in the regression model;
- Yi
- deformation parameter;
- yave
- mean of dependent variable;
- yj,
- observed value and predicted value for the jth-dependent variable, respectively;
- γ, γw
- density of rockfill and water, respectively;
- ɛ
- random error;
- Λ
- bias factor; and
- σɛ
- standard deviation of random error.
References
Behnia, D., K. Ahangari, A. Noorzad, and S. R. Moeinossadat. 2013. “Predicting crest settlement in concrete face rockfill dams using adaptive neuro-fuzzy inference system and gene expression programming intelligent methods.” J. Zhejiang Univ. Sci. A 14 (8): 589–602. https://doi.org/10.1631/jzus.A1200301.
Charles, J. A. 2008. “The engineering behaviour of fill materials: The use, misuse and disuse of case histories.” Géotechnique 58 (7): 541–570. https://doi.org/10.1680/geot.2008.58.7.541.
Clements, R. P. 1984. “Post-construction deformation of rockfill dams.” J. Geotech. Eng. 110 (7): 821–840. https://doi.org/10.1061/(ASCE)0733-9410(1984)110:7(821).
Fell, R., P. Macgregor, D. Stapledon, and G. Bell. 2005. Geotechnical engineering of dams. London: Balkema.
Gurbuz, A. 2011. “A new approximation in determination of vertical displacement behavior of a concrete-faced rockfill dam.” Environ. Earth Sci. 64 (3): 883–892. https://doi.org/10.1007/s12665-011-1070-4.
Habibagahi, G. 2002. “Post-construction settlement of rockfill dams analyzed via adaptive network-based fuzzy inference systems.” Comput. Geotech. 29 (3): 211–233. https://doi.org/10.1016/S0266-352X(01)00025-8.
Hunter, G., and R. Fell. 2003. “Rockfill modulus and settlement of concrete face rockfill dams.” J. Geotech. Geoenviron. Eng. 129 (10): 909–917. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:10(909).
Hunter, G. J. 2003. The pre- and post-failure deformation behaviour of soil slopes. Sydney, Australia: Univ. of New South Wales.
ICOLD (International Commission on Large Dams). 2004. Concrete face rock fill dams concepts for design and construction. Committee on materials for fill dams. Paris: ICOLD.
Jia, J. S., Y. Xu, J. T. Hao, and L. M. Zhang. 2016. “Localizing and quantifying leakage through CFRDs.” J. Geotech. Geoenviron. Eng. 142 (9): 06016007. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001501.
Jiang, G., and K. Cao. 1993. “Concrete face rockfill dams in China.” In Proc., Int. Symp. on High Earth-Rockfill Dams, 25–37. Beijing, China: China Society for Hydropower Engineering.
Kermani, M., J.-M. Konrad, and M. Smith. 2017. “An empirical method for predicting post-construction settlement of concrete face rockfill dams.” Can. Geotech. J. 54 (6): 755–767. https://doi.org/10.1139/cgj-2016-0193.
Kim, M. K., S. H. Lee, Y. W. Choo, and D. S. Kim. 2011. “Seismic behaviors of earth-core and concrete-faced rock-fill dams by dynamic centrifuge tests.” Soil Dyn. Earthquake Eng. 31 (11): 1579–1593. https://doi.org/10.1016/j.soildyn.2011.06.010.
Kim, Y.-S., and B.-T. Kim. 2008. “Prediction of relative crest settlement of concrete-faced rockfill dams analyzed using an artificial neural network model.” Comput. Geotech. 35 (3): 313–322. https://doi.org/10.1016/j.compgeo.2007.09.006.
Kim, Y.-S., M.-W. Seo, C.-W. Lee, and G.-C. Kang. 2014. “Deformation characteristics during construction and after impoundment of the CFRD-type Daegok Dam, Korea.” Eng. Geol. 178: 1–14. https://doi.org/10.1016/j.enggeo.2014.06.009.
Kutner, M. H., C. J. Nachtsheim, J. Neter, and W. Li. 2004. Applied linear statistical models. 5th ed. New York: McGraw-Hill.
Lawton, F. L., and M. D. Lester. 1964. “Settlement of rockfill dams.” In Proc., 8th ICOLD Congress, 599–613. Paris, France: International Commission on Large Dams.
Ma, G., W. Zhou, T.-T. Ng, Y.-G. Cheng, and X.-L. Chang. 2015. “Microscopic modeling of the creep behavior of rockfills with a delayed particle breakage model.” Acta Geotech. 10 (4): 481–496. https://doi.org/10.1007/s11440-015-0367-y.
Marandi, S. M., S. M. VaeziNejad, and E. Khavari. 2012. “Prediction of concrete faced rock fill dams settlements using genetic programming algorithm.” Int. J. Geosci. 3 (3): 601–609. https://doi.org/10.4236/ijg.2012.33060.
Pinto, N. L. S., and F. P. Marques. 1998. “Estimating the maximum face deflection in CFRDs.” Int. J. Hydropower Dams 5: 28–31.
Pramthawee, P., P. Jongpradist, and R. Sukkarak. 2017. “Integration of creep into a modified hardening soil model for time-dependent analysis of a high rockfill dam.” Comput. Geotech. 91: 104–116. https://doi.org/10.1016/j.compgeo.2017.07.008.
Rousseeuw, P. J. 1998. Handbook of statistical methods for engineers and scientists, 17.1–17.15. 2nd ed. New York: McGraw-Hill.
Saberi, M., C. D. Annan, and J. M. Konrad. 2018. “Numerical analysis of concrete-faced rockfill dams considering effect of face slab–cushion layer interaction.” Can. Geotech. J. 55 (10): 1489–1501. https://doi.org/10.1139/cgj-2017-0609.
Seo, M.-W., I. S. Ha, Y.-S. Kim, and S. M. Olson. 2009. “Behavior of concrete-faced rockfill dams during initial impoundment.” J. Geotech. Geoenviron. Eng. 135 (8): 1070–1081. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000021.
Sherard, J. L., and J. B. Cooke. 1987. “Concrete-face rockfill dam: I. Assessment.” J. Geotech. Eng. 113 (10): 1096–1112. https://doi.org/10.1061/(ASCE)0733-9410(1987)113:10(1096).
Shi, Y., J. Yang, J. Wu, and J. He. 2017. “A statistical model of deformation during the construction of a concrete face rockfill dam.” Struct. Control Health Monit. 25 (2): 1–11.
Sigtryggsdóttir, F. G., J. T. Snæbjörnsson, and L. Grande. 2018. “Statistical model for dam-settlement prediction and structural-health assessment.” J. Geotech. Geoenviron. Eng. 144 (9): 04018059. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001916.
Sowers, G. F., R. C. Williams, and T. S. Wallace. 1965. “Compressibility of broken rock and the settlement of rockfills.” In Proc., 6th Int. Conf. on Soil Mechanics and Foundation Engineering, 561–565. Toronto, ON: Canadian Society for Civil Engineering.
Sukkarak, R., P. Jongpradist, and P. Pramthawee. 2019. “A modified valley shape factor for the estimation of rockfill dam settlement.” Comput. Geotech. 108: 244–256. https://doi.org/10.1016/j.compgeo.2019.01.001.
Wen, L., J. Chai, Z. Xu, Y. Qin, and Y. Li. 2017. “Monitoring and numerical analysis of behaviour of Miaojiaba concrete-face rockfill dam built on river gravel foundation in China.” Comput. Geotech. 85: 230–248. https://doi.org/10.1016/j.compgeo.2016.12.018.
Wen, L., J. Chai, Z. Xu, Y. Qin, and Y. Li. 2018. “A statistical review of the behaviour of concrete face rockfill dams based on case histories.” Géotechnique 68 (9): 749–771. https://doi.org/10.1680/jgeot.17.P.095.
Wen, L., Y. Qin, J. Chai, Y. Li, X. Wang, and Z. Xu. 2015. “Behaviour of concrete-face rockfill dam on sand and gravel foundation.” Proc. Inst. Civ. Eng. Geotech. Eng. 168 (5): 439–456. https://doi.org/10.1680/jgeen.14.00103.
Won, M.-S., and Y.-S. Kim. 2008. “A case study on the post-construction deformation of concrete face rockfill dams.” Can. Geotech. J. 45 (6): 845–852. https://doi.org/10.1139/T08-020.
Xu, Y., and L. M. Zhang. 2009. “Breaching parameters for earth and rockfill dams.” J. Geotech. Geoenviron. Eng. 135 (12): 1957–1970. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000162.
Yilmazkaya, E., G. Dagdelenler, Y. Ozcelik, and H. Sonmez. 2018. “Prediction of mono-wire cutting machine performance parameters using artificial neural network and regression models.” Eng. Geol. 239: 96–108. https://doi.org/10.1016/j.enggeo.2018.03.009.
Zhou, W., J. Hua, X. Chang, and C. Zhou. 2011. “Settlement analysis of the Shuibuya concrete-face rockfill dam.” Comput. Geotech. 38 (2): 269–280. https://doi.org/10.1016/j.compgeo.2010.10.004.
Zhou, X., G. Ma, and Y. Zhang. 2019. “Grain size and time effect on the deformation of rockfill dams: A case study on the Shuibuya CFRD.” Géotechnique 69 (7): 606–619. https://doi.org/10.1680/jgeot.17.P.299.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 21 • Issue 2 • February 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Mar 2, 2020
Accepted: Sep 10, 2020
Published online: Dec 2, 2020
Published in print: Feb 1, 2021
Discussion open until: May 2, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.