Technical Papers
Jul 28, 2022

Experimental Formula for the Hydraulic Erosion Rate and Numerical Applications of Soft Bedrock Channels

Publication: Journal of Hydraulic Engineering
Volume 148, Issue 10

Abstract

In this research, laboratory experiments and numerical models were used to develop a new formula for the hydraulic scour rate and a bedrock module for estimating soft bedrock erosion rate, and they were then applied in a study of the Zhuoshui River in Central Taiwan. From laboratory experiments, the relationship between the critical shear stress and hydraulic scour rate with the dominant bedrock property (uniaxial compressive strength) was established. For the soft bedrock module, only one parameter (i.e., the rock erodibility coefficient kv) was calibrated once the bedrock properties were known. An unsteady two-dimensional depth-averaged numerical model incorporating the new formula for hydraulic scour rate and the bedrock module was developed. After calibration and validation, the developed model well reproduced soft bedrock erosion during high-flow periods in this study reach. The simulation results showed that hydraulic scour is dominant in the upstream reach, while abrasive scour accounted for 65%–80% of the total erosion in the downstream reach. In addition, more bedrock erosion was observed at the locations with greater contributions from abrasive scour.

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Data Availability Statement

All data, models, and code that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

This work was financially supported by the Ministry of Science and Technology of Taiwan (Grant No. MOST 103-2221-E-009-155-MY3) and Zhejiang Provincial Natural Science Foundation of China (LY20A020009). The authors appreciate the support of the Water Resources Planning Institute of Water Resources Agency in Taichung, Taiwan, who provided the hydrometric, sediment, and bathymetry data used in the study. In addition, the authors would like to thank Pei-Heng Chung and Shao-Chien Ho who assisted with the experimental preparations, operations, and data collection.

References

Aladejare, A. E., E. D. Alofe, M. Onifade, A. I. Lawal, T. M. Ozoji, and Z. X. Zhang. 2021. “Empirical estimation of uniaxial compressive strength of rock: Database of simple, multiple, and artificial intelligence-based regressions.” Geotech. Geol. Eng. 39 (6): 4427–4455. https://doi.org/10.1007/s10706-021-01772-5.
Altindag, R., and A. Guney. 2010. “Predicting the relationship between brittleness and mechanical properties (UCS, TS and SH) of rocks.” Sci. Res. Essays 5 (16): 2107–2118. https://doi.org/10.5897/SRE.9000753.
Annandale, G. W. 1995. “Erodibility.” J. Hydraul. Res. 33 (4): 471–494. https://doi.org/10.1080/00221689509498656.
Annandale, G. W. 2006. Scour technology, mechanics and engineering, practice. New York: McGraw Hill.
Bollaert, E. F. R., and A. J. Schleiss. 2005. “Physically based model for evaluation of rock scour due to high-velocity jet impact.” J. Hydraul. Eng. 131 (3): 153–165. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:3(153).
Chatanantavet, P., and G. Parker. 2009. “Physically based modeling of bedrock incision by abrasion, plucking, and macroabrasion.” J. Geophys. Res. 114 (F4): F04018. https://doi.org/10.1029/2008JF001044.
Chen, C.-H., Y.-T. Lin, H.-R. Chung, T.-Y. Hsieh, J.-C. Yang, and J.-Y. Lu. 2018. “Modelling of hyperconcentrated flow in steep-sloped channels.” J. Hydraul. Res. 56 (3): 380–398. https://doi.org/10.1080/00221686.2017.1372816.
Cheng, N.-S., and L. H. C. Chua. 2005. “Comparison of sidewall correction of bed shear stress in open-channel flows.” J. Hydraul. Eng. 131 (7): 605–609. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:7(605).
Clifford, S. T. 1991. “An evaluation of the engineering properties of some Nigerian limestones as construction materials for highway pavements.” Eng. Geol. 31 (3–4): 315–326. https://doi.org/10.1016/0013-7952(1)90014-C.
Coleman, S. E., B. W. Melville, and L. Gore. 2003. “Fluvial entrainment of protruding fractured rock.” J. Hydraul. Eng. 129 (11): 872–884. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:11(872).
Dong, J. J., J. Y. Hsu, W. J. Wu, T. Shimamoto, J. H. Hung, E. C. Yeh, Y. H. Wu, and H. Sone. 2010. “Stress-dependence of the permeability and porosity of sandstone and shale from TCDP hole-A.” Int. J. Rock Mech. Min. Sci. 47 (7): 1141–1157. https://doi.org/10.1016/j.ijrmms.2010.06.019.
Dubinski, I. I., and E. Wohl. 2013. “Relationships between block quarrying, bed shear stress, and stream power: A physical model of block quarrying of a jointed bedrock channel.” Geomorphology 180–181 (Jan): 66–81. https://doi.org/10.1016/j.geomorph.2012.09.007.
Gabet, E. J. 2020. “River profile evolution by plucking in lithologically heterogeneous landscapes: Uniform uplift vs. tilting.” Earth Surf. Processes Landforms 45 (7): 1579–1588. https://doi.org/10.1002/esp.4832.
Greimann, B. P., and M. Vandeberg. 2007. Predicting rock scour. Denver: US Dept. of the Interior.
Gu, D. Z., M. R. Jafari, and G. Mostyn. 1993. “An artificial soft rock for physical modelling.” In Proc., Geotechnical Engineering of Hard Soil-Soft Rocks, edited by Anagnostopoulos, 517–524. Rotterdam, Netherlands: A.A. Balkema.
Gunsallus, K. L., and F. H. Kulhawy. 1984. “A comparative evaluation of rock strength measures.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 21 (5): 233–248. https://doi.org/10.1016/0148-9062(84)92680-9.
Hancock, G., and R. S. Anderson. 2002. “Numerical modeling of fluvial strath terrace formation in response to oscillating climate.” Geol. Soc. Am. Bull. 114 (2): 1131–1142. https://doi.org/10.1130/0016-7606(2002)114%3C1131:NMOFST%3E2.0.CO;2.
Hancock, G. S., R. S. Anderson, and K. X. Whipple. 1998. “Beyond power: Bedrock river incision process and form.” In Rivers over rock: Fluvial processes in bedrock channels, edited by K. J. Tinkler and E. E. Wohl, 35–60. Washington, DC: American Geophysical Union.
Hancock, G. S., E. E. Small, and C. Wobus. 2011. “Modeling the effects of weathering on bedrock-floored channel geometry.” J. Geophys. Res. Earth Surf. 116: F03018. https://doi.org/10.1029/2010JF001908.
Hobbs, D. W. 1966. “A study of the behaviour of a broken rock under triaxial compression, and its application to mine roadways.” Int. J. Rock Mech. Min. Sci. 3 (1): 11–43. https://doi.org/10.1016/0148-9062(66)90030-1.
Howard, A. D. 1994. “A detachment-limited model of drainage basin evolution.” Water Resour. Res. 30 (7): 2261–2285. https://doi.org/10.1029/94WR00757.
Hsieh, T.-Y., and J.-C. Yang. 2003. “Investigation on the suitability of two-dimensional depth-averaged models for bend-flow simulation.” J. Hydraul. Eng. 129 (8): 597–612. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:8(597).
Hung, M. C., T. Y. Hsieh, C. H. Wu, and J. C. Yang. 2009. “Two-dimensional nonequilibrium noncohesive and cohesive sediment transport model.” J. Hydraul. Eng. 135 (5): 369–382. https://doi.org/10.1061/(ASCE)0733-9429(2009)135:5(369).
Indraratna, B. 1990. “Development and application of a synthetic material to simulate soft sedimentary rocks.” Géotechnique 40 (2): 189–200. https://doi.org/10.1680/geot.1990.40.2.189.
Inoue, T., T. Iwasaki, G. Parker, Y. Shimizu, N. Izumi, and C. P. Stark. 2016. “Numerical simulation of effects of sediment supply on bedrock channel morphology.” J. Hydraul. Eng. 142 (7): 04016014. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001124.
Inoue, T., J. Mishra, and G. Parker. 2021. “Numerical simulations of meanders migrating laterally as they incise into bedrock.” J. Geophys. Res. Earth Surf. 126 (5): e2020JF005645. https://doi.org/10.1029/2020JF005645.
Inoue, T., S. Yamaguchi, and J. M. Nelson. 2017. “The effect of wet-dry weathering on the rate of bedrock river channel erosion by saltating gravel.” Geomorphology 285 (May): 152–161. https://doi.org/10.1016/j.geomorph.2017.02.018.
ISRM (International Society for Rock Mechanics and Rock Engineering). 1981. Rock characterization testing and monitoring. Oxford, UK: Pergamon Press.
Knight, D. W. 1981. “Boundary shear in smooth and rough channels.” J. Hydraul. Div. Am. Soc. Civ. Eng. 107 (7): 839–851. https://doi.org/10.1061/JYCEAJ.0005695.
Lague, D. 2014. “The stream power river incision model: Evidence, theory, and beyond.” Earth Surf. Processes Landforms 39 (1): 38–61. https://doi.org/10.1002/esp.3462.
Lai, Y. G., B. P. Greimann, and K. Wu. 2011. “Soft bedrock erosion modeling with a two-dimensional depth-averaged model.” J. Hydraul. Eng. 137 (8): 804–814. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000363.
Lamb, M. P., W. E. Dietrich, and L. S. Sklar. 2008. “A model of fluvial bedrock incision by impacting suspended and bed load sediment.” J. Geophys. Res. 113: F03025. https://doi.org/10.1029/2007JF000915.
Lamb, M. P., N. J. Finnegan, J. S. Scheingross, and L. S. Sklar. 2015. “New insights into the mechanics of fluvial bedrock erosion through flume experiments and theory.” Geomorphology 244 (Sep): 33–55. https://doi.org/10.1016/j.geomorph.2015.03.003.
Lamb, M. P., and M. A. Fonstad. 2010. “Rapid formation of a modern bedrock canyon by a single flood event.” Nat. Geosci. 3 (7): 477–481. https://doi.org/10.1038/ngeo894.
Lane, E. W. 1974. “Report of the subcommittee on sediment terminology.” EOS Trans. Am. Geophys. Union 28 (6): 936–938. https://doi.org/10.1029/TR028i006p00936.
Lee, C., C. H. Wu, and J. A. Hoopes. 2004. “Automated sediment erosion testing system using digital imaging.” J. Hydraul. Eng. 130 (8): 771–782. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:8(771).
Liao, C. T., K. C. Yeh, and M. W. Huang. 2014. “Development and application of 2-D mobile-bed model with bedrock river evolution mechanism.” J. Hydro-environ. Res. 8 (3): 210–222. https://doi.org/10.1016/j.jher.2013.03.001.
Lien, H.-C., T.-Y. Hsieh, and J.-C. Yang. 1999. “Use of two-step split-operator approach for 2D shallow water flow computation.” Int. J. Numer. Methods Fluids. 30 (5): 557–575. https://doi.org/10.1002/(SICI)1097-0363(19990715)30:5%3C557::AID-FLD855%3E3.0.CO;2-3.
Nelson, P. A., and G. Seminara. 2015. “Modeling the evolution of bedrock channel shape with erosion from saltating bed load.” Geophys. Res. Lett. 38 (17): L17406. https://doi.org/10.1029/2011GL048628.
Sheorey, P. R. 1997. Empirical rock failure criteria. Rotterdam, Netherlands: A.A. Balkema.
Sklar, L. S., and W. E. Dietrich. 2004. “A mechanistic model for river incision into bedrock by saltating bedload.” Water Resour. Res. 40 (6): W06301. https://doi.org/10.1029/2003WR002496.
Sklar, L. S., and W. E. Dietrich. 2008. “Implications of the saltation–abrasion bedrock incision model for steady-state river longitudinal profile relief and concavity.” Earth Surf. Processes Landforms 33 (7): 1129–1151. https://doi.org/10.1002/esp.1689.
Spasojevic, M., and F. M. Holly. 2008. “Two- and three-dimensional numerical simulation of mobile-bed hydrodynamics and sedimentation.” In Sedimentation engineering processes: Measurements, modeling and practice, edited by M. H. Garcia, 683–761. Reston, VA: ASCE.
Tomkin, J. H., M. T. Brandon, F. J. Pazzaglia, J. R. Barbour, and S. D. Willet. 2003. “Quantitative testing of bedrock incision models for the Clearwater River, NW Washington State.” J. Geophys. Res. 108 (B6): 1–19. https://doi.org/10.1029/2001JB000862.
Vanoni, V. A., and N. H. Brooks. 1957. “Laboratory studies of the roughness and suspended load of alluvial streams.” In Sedimentation laboratory. Pasadena, CA: California Institute of Technology.
Whipple, K. X., G. S. Hancock, and R. S. Anderson. 2000. “River incision into bedrock: Mechanics and relative efficacy of plucking, abrasion, and cavitation.” Geol. Soc. Am. Bull. 112 (3): 490–503. https://doi.org/10.1130/0016-7606(2000)112%3C490:RIIBMA%3E2.0.CO;2.
Williams, G. P. 1970. “Flume width and water depth effects in sediment transport experiments.” In United States Geological Survey Professional Paper, 562-H. Washington, DC: US Government Printing Office.
Wittler, R. J., G. W. Annandale, J. F. Ruff, and S. R. Abt. 1998. “Prototype validation of erodibility index for scour in granular media.” In Proc., Int. Water Resources Engineering Conf. Reston, VA: ASCE.
Wu, W. M. 2007. Computational river dynamics. Leiden, Netherlands: CRC Press.
Zhang, Y., Y. Jia, K. J. Yeh, and C. T. Liao. 2016. “Erosion control plans for Jiji weir downstream channel.” In Proc., 12th Int. Conf. on Hydroscience & Engineering, Hydro-Science & Engineering for Environmental Resilience. Tainan, Taiwan: National Cheng-Kung Univ.

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Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 148Issue 10October 2022

History

Received: Jul 9, 2020
Accepted: Jan 29, 2022
Published online: Jul 28, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 28, 2022

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Chien-Hua Chen [email protected]
Assistant Researcher, Disaster Prevention and Water Environment Research Center, National Yang Ming Chiao Tung Univ., Hsinchu 300, Taiwan. Email: [email protected]
Associate Professor, Ocean College, Zhejiang Univ., Hangzhou 310058, PR China (corresponding author). ORCID: https://orcid.org/0000-0003-0643-5542. Email: [email protected]
Te-Yung Hsieh [email protected]
Research Fellow, Disaster Prevention and Water Environment Research Center, National Yang Ming Chiao Tung Univ., Hsinchu 300, Taiwan. Email: [email protected]
Researcher, Water Resources Planning Institute, Water Resources Agency, Wu-Fong, Taichung 413, Taiwan. Email: [email protected]
Jinn-Chuang Yang [email protected]
Retired Professor, Disaster Prevention and Water Environment Center and Dept. of Civil Engineering, National Yang Ming Chiao Tung Univ., Hsinchu 300, Taiwan. Email: [email protected]

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