Finite element simulation of impulse wave generated by landslides using a three-phase model and the conservative level set method

A numerical model has been developed using the finite element method for the simulation of impulse waves generated by landslides. The fluid-like landslide is modeled as a generalized non-Newtonian visco-plastic fluid. A three-phase flow model based on the incompressible viscous Navier–Stokes equations is solved using the finite element method to describe the motion of the three types of fluid in landslide. The conservative level set method is expanded to n-phase flow cases and employed to capture the interface of the three phases: air, water, and the landslide. The overall performance of the approach is checked by a number of validation cases: a Rayleigh–Taylor instability problem to illustrate the capability of the proposed method to deal with interface capturing, a benchmark test of a subaerial landslide generated by an impulse wave is carried out and compared with the published experimental data and numerical results, and finally, the 1958 Lituya Bay landslide generated impulse wave, and its results are compared against a scaled-down experiment and other published numerical results. It can be noted that the current model has an excellent ability to capture the complex phenomena that occurs during the whole process of the landslide-generated impulse wave, and considering the simplified treatment of the landslide and the numerical model, fairly good agreement between computed and experimental results has been observed for all simulation cases.     

Visualization of tsunami waves with Amira package

In recent years numerical investigations of tsunami wave propagation have been spurred by the magnitude 9.3 earthquake along the Andaman–Sumatra fault in December, 2004. Visualization of tsunami waves being modeled can yield a much better physical understanding about the manner of wave propagation over realistic seafloor bathymetries. In this paper we will review the basic physics of tsunami wave propagation and illustrate how these waves can be visualized with the Amira visualization package. We have employed both the linear and nonlinear versions of the shallow-water wave equation. We will give various examples illustrating how the files can be loaded by Amira, how the wave-heights of the tsunami waves can be portrayed and viewed with illumination from light sources and how movies can be used to facilitate physical understanding and give important information in the initial stages of wave generation from interaction with the ambient geological surroundings. We will show examples of tsunami waves being modeled in the South China Sea, Yellow Sea and southwest Pacific Ocean near the Solomon Islands. Visualization should be a part of any training program for teaching the public about the potential danger arising from tsunami waves. We propose that interactive visualization with a web-portal would be useful for understanding more complex tsunami wave behavior from solving the 3-D Navier–Stokes equation in the near field.     

海底滑坡海啸的颗粒流耦合模型

海底滑坡的运动可能引发海啸,破坏离岸设施,威胁海岸带安全。国内外关于海底滑坡引发海啸的研究方兴未艾。采用Mih颗粒流模型控制具弱黏聚力的砂土滑坡运动,利用两相流模型计算岩土体-水体相互作用及RNG湍流模型控制水体运动,构建了基于颗粒流模型的海底滑坡海啸全耦合数值分析方法。通过简单水槽水下滑坡案例进行了海底滑坡海啸全过程研究。数值分析再现了变形滑体的不均一运动、密度分异流动、水滑机制和以波谷为典型特征的涌浪波等典型海底滑坡及海啸现象,这表明数值模型具有有效性。许多海域（包括中国南海北部）都存在弱黏聚力和无黏聚力的水下滑坡,该数值方法值得推广和进一步研究完善。     

The hydrodynamics of landslide tsunamis: current analytical models and future research directions

Landslide-generated tsunamis are lesser-known yet equally destructive than earthquake tsunamis. Indeed, the highest tsunami wave recorded in recent history was generated by a landslide in Lituya Bay (Alaska, July 9, 1958) and produced run-up in excess of 400 m. In this paper, we review the state of the art of landslide tsunami analytical modelling. Within the framework of a linearised shallow-water theory, we illustrate the dynamics of landslide tsunami generation and propagation along beaches and around islands. Finally, we highlight some intriguing new directions in the analytical modelling of landslide tsunamis to support early warning systems.     

A new landslide-induced tsunami simulation model and its application to the 1792 Unzen-Mayuyama landslide-and-tsunami disaster

By combining landslide dynamics research and tsunami research, we present an integrated series of numerical models quantitatively simulating the complete evolution of a landslide-induced tsunami. The integrated model simulating the landslide initiation and motion uses measured landslide dynamic parameters from a high-stress undrained dynamic-loading ring shear apparatus. It provides the numerical data of a landslide mass entering and moving under water to the tsunami simulation model as the trigger of tsunami. The series of landslide and tsunami simulation models were applied to the 1792 Unzen-Mayuyama megaslide and the ensuing tsunami disaster, which is the largest landslide disaster, the largest volcanic disaster, and the largest landslide-induced tsunami disaster to have occurred in Japan. Both the 1792 megaslide and the tsunami portions of the disaster are well documented, making this an excellent test of the reliability and precision of the new simulation model. The simulated tsunami heights at the coasts well match the historical tsunami heights recorded by “Tsunami-Dome-Ishi” (a stone showing the tsunami reaching point) and memorial stone pillars.     

A non-hydrostatic model for the numerical study of landslide-generated waves

This paper proposes and demonstrates a two-layer depth-averaged model with non-hydrostatic pressure correction to simulate landslide-generated waves. Landslide (lower layer) and water (upper layer) motions are governed by the general shallow water equations derived from mass and momentum conservation laws. The landslide motion and wave generation/propagation are separately formulated, but they form a coupled system. Our model combines some features of the landslide analysis model DAN3D and the tsunami analysis model COMCOT and adds a non-hydrostatic pressure correction. We use the new model to simulate a 2007 rock avalanche-generated wave event at Chehalis Lake, British Columbia, Canada. The model results match both the observed distribution of the rock avalanche deposit in the lake and the wave run-up trimline along the shoreline. Sensitivity analyses demonstrate the importance of accounting for the non-hydrostatic dynamic pressure at the landslide-water interface, as well as the influence of the internal strength of the landslide on the size of the generated waves. Finally, we compare the numerical results of landslide-generated waves simulated with frictional and Voellmy rheologies. Similar maximum wave run-ups can be obtained using the two different rheologies, but the frictional model better reproduces the known limit of the rock avalanche deposit and is thus considered to yield the best overall results in this particular case.     

The August 27, 2014, rock avalanche and related impulse water waves in Fuquan,Guizhou, China

At about 8:30 p.m. on 27 August 2014, a catastrophic rock avalanche suddenly occurred in Fuquan, Yunnan, southwestern China. This landslide and related impulse water waves destroyed two villages and killed 23 persons. The impulse waves occurred after initiation of the landslide, caused by the main part of the slide mass rapidly plunging into a water-filled quarry below the source area. The wave, comprising muddy water and rock debris, impacted the opposite slope of the quarry on the western side of the runout path and washed away three homes in Xinwan village. Part of the displaced material traveled a horizontal distance of about 40 m from its source and destroyed the village of Xiaoba. To provide information for potential landslide hazard zonation in this area, a combined landslide–wave simulation was undertaken. A dynamic landslide analysis (DAN-W) model is used to simulate the landslide propagation before entering the quarry, while Fluent (Ansys Inc., USA) is used to simulate the impulse wave generation and propagation. Output data from the DAN-W simulation are used as input parameters for wave modeling, and there is good agreement between the observed and simulated results of the landslide propagation. Notably, the locations affected by recordable waves according to the simulation correspond to those recorded by field investigation.     

Modeling the 2004 Sumatra tsunami at Seychelles Islands: site-effect analysis and comparison with observations

The M _w = 9.1 mega-thrust Sumatra–Andaman earthquake that occurred on December 26, 2004, was followed by a devastating tsunami that killed hundreds of thousands of people and caused catastrophic effects on human settlements and environments along many coasts of the Indian Ocean, where even countries very far from the source were affected. One of these cases is represented by the Republic of Seychelles, where the tsunami reached the region about 7 h after the earthquake and produced relevant damages, despite the country was more than 4,500 km far from the seismic source. In the present work, we present and discuss a study of the 2004 Sumatra tsunami by means of numerical simulations with the attention focused on the effects observed at the Seychelles Archipelago, a region never previously investigated with this approach. The case is interesting since these islands lay on a very shallow oceanic platform with steep slopes so as the ocean depth changes from thousands to few tens of meters over short distances, with significant effects on the tsunami propagation features: the waves are strongly refracted by the oceanic platform and the tsunami signal is modified by the introduction of additional frequencies. The study is used also to validate the UBO-TSUFD numerical code on a real tsunami event in the far field, and the results are compared with the available observations, i.e., the sea level time series recorded at the Pointe La Rue station, Mahé Island, and run-up measurements and inundation lines surveyed few weeks after the tsunami at Praslin Island, where the tsunami hit during low tide. Synthetic results are found in good agreement with observations, even though some of the observations remain not fully solved. Moreover, simulations have been run in high-tide condition since the 2004 Sumatra tsunami hitting at high tide can be taken as the worst-case scenario for the Seychelles islands and used for tsunami hazard and risk assessments.     

Numerical modeling of a landslide-generated tsunami following a potential explosion of the Montserrat volcano

The explosion of the Montserrat volcano (Caribbean Sea) could trigger a major landslide and lead to the generation of a tsunami in the Caribbean Sea. In the worst case scenario, the volume of material reaching the sea has been estimated at 80 millions of cubic meters. The sliding of this mass and the generation of the associated tsunami have been simulated numerically, assuming that the debris behave like a heavy fluid flowing into the sea. The numerical model solves the 3D Navier-Stokes equations for a mixture composed of rocks and water. The generated water waves is then propagated around the coast of Montserrat by means of a shallow water model. The numerical results show that the water heights above sea level are higher than 5 meters within a radius of 5 km of the source.     

Numerical Simulation of the 1969 Portuguese Tsunami by a Finite Element Method

On 28 February 1969, the coasts of Portugal, Spain and Morocco were affected by sea waves generated by a submarine earthquake (Ms = 7.3) with its epicenter located off Portugal. The propagation of this tsunami has been simulated by a finite element numerical model solving the Boussinesq equations. These equations have been discretized using the finite element Galerkin method and a Crank–Nicholson scheme in time. The model is validated by investigating the propagation of a solitary wave over a flat bottom. The grid sizes for the 1969 event have been determined by one-dimensional tests offshore and in shallow water regions. The two-dimensional simulation of the 1969 tsunami is carried out using the hydraulic source calculated from the geophysical model of Okada and seismic parameters of Fukao. The modeled waves are compared with the recorded ones with respect to travel times, maximum amplitudes and periods of the signal. The comparison between Boussinesq and shallow-water models shows that the effects of frequency dispersion are minor. Good agreement is found for most of the studied gauges.     

A critical review of potential tsunamigenic sources as first step towards the tsunami hazard assessment for the Napoli Gulf (Southern Italy) highly populated area

Catastrophic tsunami events like those occurred in Papua New Guinea in 1998, Sumatra in 2004 and Japan in 2011, attracted the attention of the scientific community and promoted the development of different tools for assessing tsunami hazard. A preliminary step towards this goal is the knowledge of the events which might affect a specific coastal zone. In this context, we propose a method to identify the tsunami events possibly occurring in areas characterized by scarce data and a non-conservative environment. Accordingly, we propose different indices to summarize the knowledge on tsunami triggering mechanisms (earthquakes, landslides, volcanic eruptions), the characteristics of those mechanisms (magnitude of earthquakes, volume of landslide, Volcanic Explosivity Index) and tsunami features (water height, run-up, wave amplitude, propagation time). This knowledge, considered over a wider area than that of interest, allows for a paramount vision of possible hazardous events that could affect a particular coastal zone. Moreover, the tsunami simulation data and the analysis of potentially tsunamigenic slides which occurred on the Campania continental margins were also considered in the analysis. We focused our attention on Napoli megacity, because the high population density (about 1 million of people live on a territory of 117 km²), together with the presence of active volcanic areas (Ischia, Somma-Vesuvio and Campi Flegrei), make this city potentially exposed to tsunami risk. The main outcome of such an approach shows that in the near field a tsunami amplitude varying from a few centimetres (30–40 cm) to some metres (1–4 m) might be expected at the coastline if the tsunami event was triggered by volcanic activity, whereas no relevant tsunami event should be expected given the peculiar seismicity of the Neapolitan volcanic areas, with earthquakes rarely exceeding 4 Mw, if any possible cascade effects are overlooked. A morphometric analysis of high-resolution bathymetry collected between Ventotene Island and the Gulf of Salerno has shown that the submarine southern sectors of the Ischia Island and the Sorrento Peninsula are characterized by a high density of landslide scars, being thus a potential source area of landslide-generated tsunamis. However, despite the susceptibility of these areas to recurrent slope failures, only four submarine landslide scars were found to be potentially tsunamigenic with estimated tsunami amplitude of few metres at the coastline as predicted by coupling slide morphometry with tsunami amplitude equations. Concerning the tsunamis generated by earthquakes in the Western Mediterranean, only those triggered by high magnitude events (value ≥ 6–7 Mw) might affect the city of Napoli with an amplitude not exceeding 0.5 m, in about 30′.     

Insights on the small tsunami from January 28, 2020, Caribbean Sea MW7.7 earthquake by numerical simulation and spectral analysis

A major left-lateral strike-slip Mw7.7 earthquake occurred in the vicinity of the Caribbean Sea on January 28, 2020. As a result, a small-scale tsunami was generated. The properties of the seismogenic source were described using observational data gathered for the earthquake and tsunami, as well as information on the regional tectonic setting. The tsunami was simulated with the COMCOT model and Okada’s dislocation model from finite fault solutions for M_W7.7 Caribbean Sea earthquakes published by the United States Geological Survey. The simulation results were compared to tide gauge records to validate whether the seafloor’s vertical displacement generated by the strike-slip fault caused a small-scale tsunami. We conducted a spectral analysis of the tsunami to better understand the characteristics of tsunami records. The tsunami simulation results showed that the co-seismic vertical displacement caused by a strike-slip M_W7.7 earthquake could have contributed to the small-scale tsunami, but the anomalously large high-frequency tsunami waves recorded by the George Town tide gauge 11 min after the earthquake were unrelated to the earthquake-generated tsunami. According to the spectrum analysis, the predominant period of noticeable high-frequency tsunami waves recorded by the George Town tide gauge occurred only two minutes after the earthquake. This indicates that the source of the small-scale tsunami was close to the George Town station and the possible tsunami source was 150 km away from George Town station. These facts suggest that a submarine landslide was caused by the strike-slip earthquake. The comprehensive analysis showed that the small-scale tsunami was not caused solely by co-seismic seafloor deformation from the strike-slip event but that an earthquake-triggered submarine landslide was the primary cause. Therefore, the combined impact of two sources led to the small-scale tsunami.

     

Modelling December 2004 Indian Ocean tsunami: a coastal study

December 2004 tsunami in the Indian Ocean region has been simulated using MIKE-21 HD model. The vertical displacement of the seabed is incorporated into the numerical simulation by using time-varying bathymetry data. In the open ocean, sea surface height from altimeter observation has been used to validate the model results. To the west of the rupture zone, the crest is observed to precede the trough of the tsunami waves while to the east, trough preceded the crest. The model performance along the coastal region has been validated using de-tided sea levels from tide gauge measurements at Tuticorin, Chennai, Vishakapattanam, and Paradip ports along the east coast of India. Unique coastal characteristics of the tsunami waves, wave height, and wave celerity are reasonably simulated by the numerical model. Spectral analysis of tide gauge observations and corresponding model results has been done, and the distribution of frequency peaks from the analysis of gauge observations and the model results is observed to have a reasonable comparison. Low-frequency waves, contributed from the coastally trapped edge waves, are found to dominate both the tide gauge observations and the model results. The subsequent increase in the tsunami wave height observed at Chennai, Vishakapattanam, and Paradip has been explained on the basis of coastally trapped edge waves. From the validation studies using altimeter data and tide gauge data, it is observed that the model can be used effectively to simulate the tsunami wave height in the offshore as well as in the coastal region with satisfying performance.     

Use of tsunami waveforms for earthquake source study

Tsunami waveforms recorded on tide gauges, like seismic waves recorded on seismograms, can be used to study earthquake source processes. The tsunami propagation can be accurately evaluated, since bathymetry is much better known than seismic velocity structure in the Earth. Using waveform inversion techniques, we can estimate the spatial distribution of coseismic slip on the fault plane from tsunami waveforms. This method has been applied to several earthquakes around Japan. Two recent earthquakes, the 1968 Tokachi-oki and 1983 Japan Sea earthquakes, are examined for calibration purposes. Both events show nonuniform slip distributions very similar to those obtained from seismic wave analyses. The use of tsunami waveforms is more useful for the study of unusual or old earthquakes. The 1984 Torishima earthquake caused unusually large tsunamis for its earthquake size. Waveform modeling of this event shows that part of the abnormal size of this tsunami is due to the propagation effect along the shallow ridge system. For old earthquakes, many tide gauge records exist with quality comparable to modern records, while there are only a few good quality seismic records. The 1944 Tonankai and 1946 Nankaido earthquakes are examined as examples of old events, and slip distributions are obtained. Such estimates are possible only using tsunami records. Since tide-gauge records are available as far back as the 1850s, use of them will provide unique and important information on long-term global seismicity.     

海啸和海啸沉积

综述海啸沉积特征,认为岸上细粒海啸沉积物具有以下特点:（1）地层层序上向上变细、减薄;（2）水流方向的重复反向（即重复的双向水流）;（3）含有撕裂的碎屑;（4）较差的分选性;（5）向陆地延伸更远;但将以上任何单一特征看成是海啸沉积的特征性依据都是不恰当的,需要将以上特征结合起来判断,才能作为海啸沉积的依据。而有关岸上巨砾的海啸或是风暴来源,至今仍争论不清,但较一致认为巨砾堤坝复合体是风暴成因。浅水碎屑海啸岩通常为夹在低能稳定状态的背景沉积粉砂—黏土层内的一套独特砂层,可以根据海啸能量的增加到衰减分为Tna—Tnd四个不同单元;而地震海啸岩通常具有震积岩—海啸岩的沉积序列;碳酸盐海啸岩则显示了与海啸入射流和回流相关的冲刷—充填结构。深海的海啸沉积作用机制仍然不清。尽管海啸传播阶段可以产生地中海A型均质岩,但深海海啸岩可能主要与海啸回流有关,如目前讨论最多的K—T撞击海啸岩。尽管目前的研究促进了对海啸的认识,但存在诸如海啸沉积机制仍然不明确,海啸沉积识别依然困难等许多问题,海啸沉积学的进一步发展将为解决这些问题提供坚实基础。     

A new empirical equation for predicting the maximum initial amplitude of submarine landslide-generated waves

Landslides - The accurate prediction of landslide tsunami amplitudes has been a challenging task given large uncertainties associated with landslide parameters and often the lack of enough...     

库区滑坡的次生灾害分析与研究——以藕塘滑坡为例

滑坡除直接成灾外,还会产生次生灾害,滑坡体落入江河中,可形成巨大涌浪,造成较大的危害。涌浪高度除受滑速、失稳体积、水深等重要因素的影响外,波浪的形成还要受水库地形、库面宽度、滑坡入库过程的持续时间以及滑坡体的宽度等因素的影响,尤其在峡谷地区更为显著,且波浪在传播过程中,还受到河谷两岸的阻碍、往返的折射以及波群的相互干扰或迭加等影响。以藕塘滑坡为例,在滑波局部失稳情况下采用潘家铮涌浪算法,计算和预测滑体冲入库区后的滑速和造成的涌浪高度,并且考虑了地震作用和滑坡前缘泡在水中所产生的阻力。     

Tsunami deposits in the geological record

A review is presented here of tsunami deposits in the geological record. It begins with a discussion of the relationships between the processes of tsunami generation and propagation and the sedimentary responses. This is followed by a consideration of the sedimentary processes associated with the passage of tsunami waves across coastlines. Attention is also given to the sedimentary processes associated with tsunami-triggered gravity backwash flows and comparisons are made with turbidity current action. We observe that despite sedimentary evidence for recent tsunamiites, geological research on ancient tsunamis has not identified stratigraphic units associated with onshore tsunami sedimentation. Equally, it is noted that nearly all published studies of sedimentary processes associated with modern tsunamis have not considered patterns of sediment transport and deposition in the offshore zone.     

Subaqueous landslide-triggered tsunami hazard for Lake Zurich,Switzerland

Subaqueous landslides can induce potentially damaging tsunamis. Tsunamis are not restricted to the marine environment, but have also been documented on lakes in Switzerland and worldwide. For Lake Zurich (central Switzerland), previous work documented multiple, assumedly earthquake-triggered landslides. However, no information about past tsunamis is available for Lake Zurich. In a back-analysis, we model tsunami scenarios as a consequence of the earthquake-triggered landslides in the past. Furthermore, on the basis of a recent map of the earthquake-triggered subaqueous landslide hazard, we present results of a tsunami hazard assessment. The subaqueous landslide progression, wave propagation and inundation are calculated with a combination of open source codes. Although no historic evidence of past tsunamis has been documented for Lake Zurich, a tsunami hazard exists. However, only earthquakes with long return periods are assumed to cause considerable tsunamis. An earthquake with an exceedance probability of 0.5% in 50 years (corresponding to an earthquake with a return period of 9975 years) is assumed to cause tsunamigenic landslides on most lateral slopes of Lake Zurich. A hypothetical tsunami for such an event would create damage especially along the shores of the central basin of Lake Zurich with estimated peak flow depths of up to ~?4.6 m. Our results suggest that for an earthquake with an exceedance probability of 10% in 50 years (i.e., mean return period of 475 years), no considerable tsunami hazard is estimated. Even for a worst-case scenario, the cities of Zurich and Rapperswil, located at the northern and southern ends of the lake, respectively, are assumed to experience very little damage. The presented first-order results of estimated wave heights and inundated zones provide valuable information on tsunami-prone areas that can be used for further investigations and mitigation measures.