Run-up Height Research Articles

Study of beach permeability's influence on solitary wave runup with ISPH method

Coastal protections, such as dykes, seawalls, breakwaters and natural beaches can often be considered as porous structures. The accurate prediction of wave motion around porous structures is necessary for the effective design of durable coastal protections. Smoothed particle hydrodynamics (SPH) is a meshless particle-based method suitable for the simulations of violent free-surface flows and their interaction with porous structures. In this paper, an incompressible SPH (ISPH) model is applied to the simulations of solitary wave runup on permeable slopes. The apparent density concept is introduced to allow the smooth particles’ volume to change when shifting between the pure-fluid region and porous region. The present simulations consider both the triangular beaches with uniform permeability and the solid beaches with overlying porous layers. The study focuses on the influence of permeability on the maximum wave runup heights. New runup laws are proposed, which offer guidelines for the design of porous coastal protections.

Full-scale experimental study on wave reflection and run-up at stepped revetments

Stepped revetments are especially suitable in urban areas as they effectively limit wave overtopping whilst offering recreational benefits. A deeper understanding of wave-structure interactions facilitates optimised stepped revetment designs. Wave reflection and wave run-up processes also indirectly provide insights in the wave energy dissipation of stepped revetments. Only few studies have focused on wave reflection from stepped revetments, while the wave run-up process on stepped revetments was studied widely, yet only with small-scale wave flume tests and mostly with regular waves. As the wave overtopping rates in small-scale wave flume tests underestimate those measured in full-scale experiments, these studies are likely affected by scale. This paper investigates wave reflection from and wave run-up on stepped revetments by means of full-scale flume experiments. Two cross-sections, each with a slope of 1:3, were studied with uniform step heights of 0.17 m and 0.50 m. It was found that previous small-scale studies underestimate relative run-up heights by 31–51%. Empirical formulae were derived to estimate wave reflection coefficients and wave run-up heights of stepped revetments. Wave reflection and run-up processes are described and provide further insight in the functioning of stepped revetments.

Displacement behaviour and potential impulse waves of the Gapa landslide subjected to the Jinping Reservoir fluctuations in Southwest China

Landslide failures near water can generate impulse waves that can cause fatalities and property damage. These hazards are extremely prevalent in reservoir areas, such as the 1963 Vajont landslide in Italy and the 2003 Qiangjiangping landslide in China. This study introduces the Gapa landslide which has been reactivated by the impoundment of the Jinping reservoir, Southwest China. According to the geological investigation, the movement of the landslide was based on a deep sliding surface with a displaced body of 13 million m3. However, the landslide did not receive much attention until it exhibited huge displacements and extensive cracking in the upper part of the landslide, which was caused by the rapid drawdown of the reservoir water after rising to its highest level (1880 m asl). At present, the landslide has posed significant threats both to the Wali village on the opposite river bank and the downstream dam site during the subsequent reservoir water fluctuations. Therefore, the landslide's deformation behaviour and mechanism, and its failure mode need to be analyzed, Also, the assessment of the landslide-generated impulse waves is of great necessity.The displacement history of the landslide is presented using surface and underground monitoring data pre-, in-impoundment and subsequent five times fluctuations of the reservoir water. The analysis of daily displacement velocity and inter-annual displacement interprets the comprehensive spatio-temporal displacement characteristics between 2007 and 2020. Based on the interpretation of displacement behaviours, the deformation mechanism is revealed mainly using the hydrostatic and hydrodynamic forces. Additionally, the potential impulse waves have been predicted based on the inferred failure mode of the Gapa landslide. The maximum wave height on the river and the run-up wave height on the opposite bank are estimated to be 45.5 m and 35 m using the empirical and numerical methods. The Wali village below 1915 m asl will be destroyed in a hundred seconds if the landslide collapses overall, thus, a permanent warning line at 1915 m asl is required and residents below the line need to be relocated. The assessment of potential impulse waves related to the Gapa landslide can serve the risk management of the reservoir bank and the hydropower station. We anticipate that this study will provide some important insights into the interpretation of landslide hazard risk in the Jinping Reservoir area and other parts of the world.

Propagation of Solitary Wave Around Conical Island in Level-Set Finite Element Framework

Lee, H., 2021. Propagation of solitary wave around conical island in level-set finite element framework. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 16–20. Coconut Creek (Florida), ISSN 0749-0208. Though the solitary wave is a single wave, it consists of a complex spectrum of frequencies, which enables in-depth analysis and reliable generation both in the laboratory and in the numerical model. For these reasons, solitary waves are known to be a good candidate for the description of waves including tsunamis since they effectively model the important effects of the long wave on the coasts very well. In addition, it is supposed to propagate over constant depth without appreciable changes, allowing for consistent referencing of its offshore or incident wave height. In this study, the level-set scheme, which is combined with the incompressible Navier-Stokes solver based on the fractional step algorithm in the framework of the finite element method, was applied to the modeling of wave propagation and runup on a circular conical island. Unstructured hexahedral meshes were generated for this purpose and MPI (Message Passing Interface) based parallel algorithms were developed to accelerate the computation. The physical behavior of waves are discussed in detail and the numerical results (e.g., runup heights) are compared with the experimental data. The good agreements were observed.

Modelling of mobility of Rissa landslide and following tsunami

Landslides in sensitive clays pose a major threat to life, property and the environment. The lack of warning signs and the extreme mobility of quick clays increase the risk. When occurring along fjords, lakes or large rivers, the landslides can generate destructive tsunamis. Historical records show that 45% of the shoreline landslides in marine sediments in Norway triggered tsunamis with run-up height of 1 to 15 m. To improve the management of the hazard and risk due to landslides in sensitive materials, the profession needs to develop tools for modelling the mobility of landslides and their tsunamigenic potential. The paper back-calculates the 1978 Rissa landslide, one of the largest quick clay landslides in Norway. Because of the quantity of data available, the Rissa landslide provides a unique benchmark to study the mobility of the quick clay, and the tsunami following the landslide. The paper describes a new approach to model landslide mobility and tsunami run-up, and presents the results of the analyses and a comparison of the results with the observations. The back-calculated mobility (runout distance, flow velocity and debris thickness) and wave run-up on the lakeshore agreed well with the measurements.

Numerical Study of Non-Linear Wave Run-Up Around a Circular Cylinder in Regular Waves

Lee, J.-H. and Koo, B., 2021. Numerical study of non-linear wave run-up around a circular cylinder in regular waves. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 554–558. Coconut Creek (Florida), ISSN 0749-0208. In this study, numerical simulations have been carried out to investigate the non-linear wave run-up phenomena of a single cylinder according to wave period and slope. In order to perform numerical analysis on a three-dimensional incompressible viscous turbulent two phase flow, this study used a Volume Of Fluid (VOF) technique and a realizable turbulence model based on the Computational Fluid Dynamics (CFD) commercial code, “STAR-CCM+”. Various incoming wave conditions have been applied to see how the wave steepness and wave periods affect the wave run-up height on the circular cylinder. Finally, the wave run-up estimation results for wave slopes and periods were compared with the related experimental results and they had good agreement. It was confirmed that as the wave steepness increased, the run-up phenomenon appeared largely at the part where the cylinder hit the incident wave.

On the evolution and runup of a train of solitary waves on a uniform beach

In this paper the runup of a train of successive solitary waves is studied. Using a wavemaker with 5-m stroke, a series of evenly-spaced solitary waves, up to nine, is generated in a wave flume. These solitary waves shoal and run up on a 1 on 10 slope. The nonlinearity parameter, i.e., the wave height to water depth ratio, ranges between 0.11 and 0.39. The experimental data show that the runup heights of successive solitary waves reach an asymptotic value after the fourth wave in all cases studied. Depending on the nonlinearity, the runup characteristics can be categorized as either weakly or strongly interacting cases. For the former the runup heights of the successive waves are almost identical to that of a single solitary wave. For the latter, the asymptotic runup value is always lower than that of the first wave. Using the experimental data, two- and three-dimensional Reynolds-Averaged Navier-Stokes equations models are first validated with a high degree of accordance. Additional numerical simulations are performed to extend the experimental database and investigate effects of beach slopes and higher wave nonlinearity values. Finally, using both numerical results and the laboratory data, the unified empirical runup formula for single breaking solitary waves and breaking periodic waves is found applicable to obtain the maximum runup height of successive solitary waves.

Field Insights and Analysis of the 2018 Mw 7.5 Palu, Indonesia Earthquake, Tsunami and Landslides

A devastating Mw 7.5 earthquake and tsunami struck northwestern Sulawesi, Indonesia on 28 September 2018, causing over 4000 fatalities and severe damage to several areas in and around Palu City. Severe earthquake-induced soil liquefaction and landslides claimed hundreds of lives in three villages within Palu. The mainshock occurred at 18:03 local time at a depth of 10 km on a left-lateral strike-slip fault. The hypocenter was located 70 km north of Palu City and the rupture propagated south, under Palu Bay, passing on land on the west side of Palu City. The surface rupture of the earthquake has been mapped onshore along a 30 km stretch of the Palu-Koro fault. We present results of field surveys on the effects of the earthquake, tsunami and liquefaction conducted between 1–3 and 12–19 of October 2018. Seismic intensities on the Modified Mercalli Intensity (MMI) scale are reported for 375 sites and reach a maximum value of 10. We consolidate published tsunami runup heights from several field studies and discuss three possible interrelated tsunami sources to explain the variation in observed tsunami runup heights. Due to limited instrumentation, PGA and PGV values were recorded at only one of our field sites. To compensate, we use our seismic intensities and Ground Motion to Intensity Conversion Equations (GMICEs) and Ground Motion Prediction Equations (GMPEs) developed for similar tectonic regions. Our results indicate that the maximum predicted PGAs for Palu range from 1.1 g for GMICEs to 0.6 g for GMPEs.

Megatsunamis Induced by Volcanic Landslides in the Canary Islands: Age of the Tsunami Deposits and Source Landslides

Evidence for frequent, large landslides on the flanks of the volcanic edifices forming the Canary Islands include outstanding landslide scars and their correlative submarine and subaerial rock and debris avalanche deposits. These landslides involved volumes ranging from tens to hundreds of km3. The sudden entry of large volumes of rock masses in the sea may have triggered tsunamis capable of affecting the source and neighboring islands, with the resulting huge waves dragging coastal and seabed materials and fauna and redepositing them inland. Here, we present new geological evidence and geochronological data of at least five megatsunamis in Tenerife, Lanzarote, and Gran Canaria, triggered by island flank megalandslides, and occasionally explosive eruptions, during the last 1 million years. The exceptional preservation of the megatsunami deposits and the large area they cover, particularly in Tenerife, provide fundamental data on the number of tsunami events and run-ups, and allow proposals on the sources and age of the tsunamis. Tsunami run-up heights up to 290 m above coeval sea level, some of the highest known on Earth in recent geological times, were estimated based on sedimentological, geomorphological, paleontological, and geochronological data. The research results made it possible to estimate the recurrence of tsunamis in the archipelago during the last hundreds of thousands of years, and to establish relationships between tsunami deposits and the probable triggering island flank landslides.

Evidence of Seismic Slip on a Large Splay Fault in the Hikurangi Subduction Zone

AbstractThe Hikurangi subduction zone is capable of producing moderate to large earthquakes as well as regularly repeating slow slip events. However, it is unclear what structures host these different slip styles along the margin. Here we address whether splay faults can host seismic slip at shallow (<1 km) depth by investigating the Pāpaku fault, sampled during International Ocean Discovery Program Expedition 375. We use biomarker thermal maturity to search for evidence of frictional heating within turbiditic sediments of the Pāpaku fault. Four zones of localized high temperature are found near the top of the fault zone, which are interpreted to be zones of localized seismic slip. Thermal modeling shows that the most likely maximum displacement on the shallow Pāpaku fault during each event was 14–17 m. Our results demonstrate that the Pāpaku fault, and potentially other splay faults along the margin, host coseismic slip and have the potential to produce large tsunami (e.g., runup heights of >1 m as observed in the 1947 Poverty and Tolaga Bay earthquakes.

Decadal-scale subaerial beach and dune evolution at Duck, North Carolina

Thirty-nine years of high-resolution data from 1981 to 2019 surveyed by the Field Research Facility (FRF) of the US Army Corps of Engineers at Duck, North Carolina, in the United States, were analyzed for temporal and spatial characteristics of beach morphology evolution employing a range of statistical methods. In the study, emphasis was put on the response of the subaerial part of the beach profile to waves and water levels at several different spatial and temporal scales, ranging from weekly to decadal response. The profile data set was analyzed to determine the subaerial beach evolution, including both the influence of cross-shore sediment transport related to storms and the longshore transport affected by the FRF research pier. The analysis showed that adjacent profile lines exhibit similar beach morphology and evolution with high correlation regarding spatial and temporal patterns. The pier has a noticeable influence on the longshore sediment transport leading to erosion downdrift and accretion updrift of the pier; the dune in the FRF region is rather stable and resistant towards storm erosion, requiring combinations of runup height and water level (i.e., runup level) that reaches the dune face; and erosion high up on the subaerial part of the beach, including the dune, occurs on average due to storms with a return period of 5 years.

Frictional swash hydrodynamics under the improved seaward boundary condition

Effects of the improved seaward boundary condition on the swash zone hydrodynamics with bottom resistance are investigated using the method of characteristics. The characteristic equations including the Chezy-type resistance term are solved numerically by using the specified time interval scheme. Following Guard and Baldock (2007), the improved seaward boundary condition is introduced after incorporating a parameter k. Spatiotemporal distribution of the forward and backward characteristic lines under different bottom frictions and k parameters are specified. Large k parameter postpones the swash flow reversal time and extends the entire swash duration, which enhances/reduces the function of pressure force/bottom friction in swash hydrodynamics. During the late backwash stage, the bottom resistance effect becomes less influential with the increase of parameter k. Shoreline movement is mainly controlled by the bottom friction initially, then by gravity around the swash flow reversal, and by the joint actions of bottom friction and gravity (or hydrostatic pressure and gravity) in the case of k = 0 (or k = 1) near the late backwash stage. With respect to the entire swash duration, the flow reversal time at the shoreline, the maximum run-up height and the maximum backwash velocity, it is confirmed that the effects of the boundary condition parameter k on the swash hydrodynamics become more significant under the large bottom resistance. The present study extends Deng et al. (2016)'s work with the improved seaward boundary conditions and makes it more applicable to the actual swash process. Findings from the present study could further improve our understandings of the frictional swash hydrodynamics.

Analysis of the contributing factors to infragravity swash based on long-term observations

Predicting the runup heights from the offshore waves and beach characteristics has been one of the most important issues in coastal engineering. Various parameters are considered potential contributing factors, but some of them have not been verified in the field. This study discusses the characteristics of infragravity (IG) swash and its relationship with the offshore wave parameters by analyzing the nine-month field observation data of waves and their runup at a sandy beach in Japan. In particular, the contribution of the frequency spread and directional spread was investigated using field data. IG waves developed as bound waves in a shoaling zone, while they caused frequency-dependent dissipation in the surf and swash zone, which affected the IG swash. The lower frequency components of incoming IG waves generated a larger swash than the higher frequency components when IG wave dissipation was not negligible, but the latter was higher without the dissipation. The integrated IG swash was roughly proportional to H0L0, where H0 is offshore wave height and L0 is offshore wavelength. Furthermore, the inclusion of the frequency spread and directional spread improved the IG swash prediction. An increase in the frequency spread and decrease in the directional spread tended to increase the IG swash, which is in qualitative agreement with the bound wave characteristics. The contribution of the directional spread becomes prominent under energetic conditions. The definition of the offshore wave period also affected the swash prediction, and the spectral mean period gave better performance than the peak period during multimodal wave conditions.

Wave Runup for Nowshahr Breakwater at Tide and EBB Scenarios

This study investigates runup design at breakwaters and design criteria under tidal and ebb scenarios for both head and truck of Nowshahr breakwater. First part includes runup height calculations based on shore protection manuals. Based of wave height, frequency, and water depth at the toe runup height has been calculated and Second portion has been dedicated to design of head and truck of Nowshahr port based on Hudson stability formula. Collision of wave and the breakwater head, results in immediate reduction in wave energy. As wave energy propagated gradually decreases when it meets the trunk. The results showed that in both conditions weight of head would be higher than the trunk of breakwater. while, both head and trunk are designed based on high strength materials, but the head has higher degree of importance in terms of design criteria. Hudson formula is responsible for the stability of breakwater structure. Tidal case which considers a non-breaking wave as well as ebb scenario including a breaking wave has been studied to include two extreme conditions occurs to breakwaters. The results showed the higher weight of head is responsible for stability of breakwater at both conditions.

Statistical analysis of three-dimensional run-up heights using Gaussian process emulator of particle method

Statistical analysis of three-dimensional run-up heights using Gaussian process emulator of particle method

Assessing local impacts of the 1700 CE Cascadia earthquake and tsunami using tree-ring growth histories: a case study in South Beach, Oregon, USA

Abstract. We present an investigation of the disturbance history of an old-growth Douglas-fir (Pseudotsuga menziesii) stand in South Beach, Oregon, for possible growth changes due to tsunami inundation caused by the 1700 CE Cascadia Subduction Zone (CSZ) earthquake. A high-resolution model of the 1700 tsunami run-up heights at South Beach, assuming an “L”-sized earthquake, is also presented to better estimate the inundation levels several kilometers inland at the old-growth site. This tsunami model indicates the South Beach fir stand would have been subjected to local inundation depths from 0 to 10 m. Growth chronologies collected from the Douglas-fir stand shows that trees experienced a significant growth reductions in the year 1700 relative to nearby Douglas-fir stands, consistent with the tsunami inundation estimates. The ±1–3-year timing of the South Beach disturbances are also consistent with disturbances previously observed at a Washington state coastal forest ∼220 km to the north. Moreover, the 1700 South Beach growth reductions were not the largest over the >321-year tree chronology at this location, with other disturbances likely caused by climate drivers (e.g., drought or windstorms). Our study represents a first step in using tree growth history to ground truth tsunami inundation models by providing site-specific physical evidence.

Uncertainty quantification for the Hokkaido Nansei-Oki tsunami using B-splines on adaptive sparse grids

Modeling uncertainties in the input parameters of computer simulations is an established way to account for inevitably limited knowledge. To overcome long run-times and high demand for computational resources, a surrogate model can replace the original simulation. We use spatially adaptive sparse grids for the creation of this surrogate model. Sparse grids are a discretization scheme designed to mitigate the curse of dimensionality, and spatial adaptivity further decreases the necessary number of expensive simulations. We combine this with B-spline basis functions which provide gradients and are exactly integrable. We demonstrate the capability of this uncertainty quantification approach for a simulation of the Hokkaido Nansei–Oki Tsunami with anuga. We develop a better understanding of the tsunami behavior by calculating key quantities such as mean, percentiles and maximum run-up. We compare our approach to the popular Dakota toolbox and reach slightly better results for all quantities of interest. References B. M. Adams, M. S. Ebeida, et al. Dakota. Sandia Technical Report, SAND2014-4633, Version 6.11 User’s Manual, July 2014. 2019. https://dakota.sandia.gov/content/manuals. J. H. S. de Baar and S. G. Roberts. Multifidelity sparse-grid-based uncertainty quantification for the Hokkaido Nansei–Oki tsunami. Pure Appl. Geophys. 174 (2017), pp. 3107–3121. doi: 10.1007/s00024-017-1606-y. H.-J. Bungartz and M. Griebel. Sparse grids. Acta Numer. 13 (2004), pp. 147–269. doi: 10.1017/S0962492904000182. M. Eldred and J. Burkardt. Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification. 47th AIAA. 2009. doi: 10.2514/6.2009-976. K. Höllig and J. Hörner. Approximation and modeling with B-splines. Philadelphia: SIAM, 2013. doi: 10.1137/1.9781611972955. M. Matsuyama and H. Tanaka. An experimental study of the highest run-up height in the 1993 Hokkaido Nansei–Oki earthquake tsunami. National Tsunami Hazard Mitigation Program Review and International Tsunami Symposium (ITS). 2001. O. Nielsen, S. Roberts, D. Gray, A. McPherson, and A. Hitchman. Hydrodymamic modelling of coastal inundation. MODSIM 2005. 2005, pp. 518–523. https://www.mssanz.org.au/modsim05/papers/nielsen.pdf. J. Nocedal and S. J. Wright. Numerical optimization. Springer, 2006. doi: 10.1007/978-0-387-40065-5. D. Pflüger. Spatially Adaptive Sparse Grids for High-Dimensional Problems. Dr. rer. nat., Technische Universität München, Aug. 2010. https://www5.in.tum.de/pub/pflueger10spatially.pdf. M. F. Rehme, F. Franzelin, and D. Pflüger. B-splines on sparse grids for surrogates in uncertainty quantification. Reliab. Eng. Sys. Saf. 209 (2021), p. 107430. doi: 10.1016/j.ress.2021.107430. M. F. Rehme and D. Pflüger. Stochastic collocation with hierarchical extended B-splines on Sparse Grids. Approximation Theory XVI, AT 2019. Springer Proc. Math. Stats. Vol. 336. Springer, 2020. doi: 10.1007/978-3-030-57464-2_12. S Roberts, O. Nielsen, D. Gray, J. Sexton, and G. Davies. ANUGA. Geoscience Australia. 2015. doi: 10.13140/RG.2.2.12401.99686. I. J. Schoenberg and A. Whitney. On Pólya frequence functions. III. The positivity of translation determinants with an application to the interpolation problem by spline curves. Trans. Am. Math. Soc. 74.2 (1953), pp. 246–259. doi: 10.2307/1990881. W. Sickel and T. Ullrich. Spline interpolation on sparse grids. Appl. Anal. 90.3–4 (2011), pp. 337–383. doi: 10.1080/00036811.2010.495336. C. E. Synolakis, E. N. Bernard, V. V. Titov, U. Kânoğlu, and F. I. González. Standards, criteria, and procedures for NOAA evaluation of tsunami numerical models. NOAA/Pacific Marine Environmental Laboratory. 2007. https://nctr.pmel.noaa.gov/benchmark/. J. Valentin and D. Pflüger. Hierarchical gradient-based optimization with B-splines on sparse grids. Sparse Grids and Applications—Stuttgart 2014. Lecture Notes in Computational Science and Engineering. Vol. 109. Springer, 2016, pp. 315–336. doi: 10.1007/978-3-319-28262-6_13. D. Xiu and G. E. Karniadakis. The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24.2 (2002), pp. 619–644. doi: 10.1137/S1064827501387826.

A numerical investigation of tsunamis impacting dams

Landslides, rockfalls, and iceberg calving impacting into a water body generate large landslide-tsunamis posing a serious hazard in lakes and reservoirs. These waves can impact and even overtop dams as in the 1963 Vajont disaster in Italy. However, estimating the effects of tsunamis on dams, e.g. pressures and forces, and 3D effects is challenging. An accurate prediction of these effects is also important for a range of coastal and offshore applications. The present study focuses on the numerical modelling of landslide-tsunamis impacting dams with the open source toolbox solids4foam. After a validation with theoretical, experimental, and numerical results, 5th order Stokes, cnoidal, and solitary waves were simulated in 72 2D experiments with dams of steep to vertical inclinations. The wave loading on dams was found to be in agreement with predictions based on an existing empirical approach, significantly expanding its limited validation conditions. New empirical equations are suggested to predict the wave run-up height together with the overtopping volume and depth. These address the cases where no empirical equations are available or existing equations result in large deviations from the numerical results. Novel insight in the dynamic pressure is provided, supported by new semi-empirical equations. Further, simulations in 3D were performed to quantify the effects of the dam curvature and asymmetrical wave impact angles. Both effects combined induce an increase in the run-up height at dam flanks of up to 32%. Such findings support the design of dams and tsunami hazard assessment.

A comparative study of interaction of random waves with a cluster of structures on a berm with RANS and LES models

The interactions of random waves with a cluster of structures positioned in a gridded array are investigated through a series of experiments and high-fidelity RANS and LES simulations. The performances of two different turbulence models, k−ω SST and LES, are evaluated in terms of the predicted flow field and resulting loading on the structures, both in the time and frequency domains. The comparative analyses show that the k−ω SST model predicts the free surface elevations slightly better than that of the LES model. The k−ω SST model fails to resolve the velocity fluctuations leading to the underestimation of the flow kinetic energy. The k−ω SST model underpredicts the wave runup/rundown, as well as the depth-integrated pressure force, compared to the LES model. The wave runup heights and onshore-directed depth-integrated pressure forces are found to follow the Rayleigh distribution. The comparisons of the wave runup heights and corresponding onshore-directed hydrodynamic forces follow a relatively linear trend that is within the ∓95% confidence intervals.

Impact dynamics of debris flow against rigid obstacle in laboratory experiments

Debris-flow impact against rigid obstacle involves instant redirection of flow velocity and elevation of flow depth, and could serve as a stringent approach for verification of the two-phase flow models. In this study, kinetic and dynamic behavior of debris-flow impact with varying flow regime has been analyzed on the basis of laboratory tests with distributed measurement. Debris flows interact with obstacle in the modes of vertical jet (deflected vertically) and momentum jump (reflected upstream). The experimental results are further adopted to verify the predictability of vertical jet model and momentum jump model. Our findings highlight that, due to the elevated confining stress in the impact area, the liquefaction ratio increases, resulting in a more “fluid-like” state of debris flow. The two analytical models could distinguish the runup height around the threshold Froude number 3–4. However, the impact loads under both modes could be very close, because the effective impact in the vertical jet mode only concentrates in the lower portion of runup height. The potential threat of flip-through impact (shock impact by a steep or concave wave front) should also be considered, as its impulse load could be much higher than the predicted load by vertical jet and momentum jump models.