Numerical Investigation on Hydrodynamic Characteristics of Landslide-Induced Impulse Waves in Narrow River-Valley Reservoirs

Landslide-induced impulse waves in a river-valley reservoir region have become a serious threat to life and property intactness. Compared with previous studies focusing on landslides in open-water regions, this article systematically carried out numerical investigations on the hydrodynamic characteristics of landslide-induced impulse waves in narrow river-valley reservoirs by applying software package FLOW3D. To verify the computational reliability of FLOW3D, necessary experimental work was conducted. The predicted temporal evolutions of water elevation at selected wave gauges are in good agreement with that recorded during the corresponding experiment. The effects of some prominent factors, such as the drop height of the slide, still-water depth, slide volume, and slide slope, on the propagation and magnitude of landslide-induced impulse waves are investigated in detail by systematically analyzing both simulation and experimental results. Based on simulation results, we proposed empirical formulas for predicting the landslide-induced impulse waves by performing dimensionless analysis and applying nonlinear regression methods. Then, the proposed empirical formulas were applied to predict the impulse waves induced by four landslide accidents. It is believed that the findings drawn from this article could greatly enhance our understanding on the hydrodynamic characteristics of landslide-induced impulse waves in narrow river-valley reservoir regions, and the proposed empirical formulas can be used as quick technical support for the safe navigation of such rivers.


I. INTRODUCTION
Landslide-induced impulse waves with large volume and high velocity have become a serious potential threat to the safety of riverside residents and the intactness of navigation vessels in the river-valley reservoir region, characterized by narrow reservoir geometries and steep shores. During the past few decades, many river reservoirs have been gradually constructed in the mountainous areas, directly causing serious riverbank-slope instability problems, and the reservoir regions have become significantly vulnerable to landslides, The associate editor coordinating the review of this manuscript and approving it for publication was Jenny Mahoney. especially under the influence of long-period high-waterlevel conditions and regular reservoir operations. Compared with landslides in open-water regions, landslides in narrow river-valley reservoir regions can generate impulse waves with greater transverse and longitudinal propagation, resulting in worse consequences. There are many examples of significant damage to infrastructure, especially large reservoirs and dams, due to serious landslide-induced impulse waves that happened in water-conservancy construction projects around the world. For example, at 22:39 of October 9th 1963, a massive landslide that occurred in the Vajont reservoir in Italy caused a tragic event that shocked the world. The volume of the landslide body was 260 million m 3 , which generated VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ huge impulse waves, 250 m in height at the opposite shore, and the impulse waves cross over the top of dam, leading to about 2000 deaths and the complete destruction of several villages and towns [1], [2]. In June 2015, a 6 m high impulsewave was generated by a 24,000 m 3 Wushan landslide that fell into the Yangtze River in Chongqing, China. It resulted in the sinking of 21 small ships berthing on the opposite side Fig. 1, and at least one death and five injuries [3], [4]. Therefore, it is necessary to understand the underlying physics during the process of impulse waves generation, propagation, and their final impact on infrastructure, as well as attenuation for proper site selection for wharfs and safer navigation-route design in river-valley reservoir regions.
In the past, hydrodynamic characteristics of landslideinduced impulse waves in open-water regions have been extensively studied by many researchers through theoretical [5], [6], experimental [1], [7], [8], and numerical approaches [9]- [11], focusing on impulse-wave height and propagation characteristics. Regarding the theoretical studies, Noda et al. [12] simplified the landslide problem into horizontal or vertical landslides, and derived analytical solutions by using linear approximation and infinite approximation, respectively. By applying the wavelet-transform method, Panizzo et al. [13] analyzed the evolution of impulse waves height induced by landslides. Using linear theory, Risio and Sammarco [14] derived a new analytical solution to study the propagation law of impulse waves, which can predict the height and period of impulse waves For the experimental work, Heller and Hager [15] studied the generation and propagation of impulse waves induced by bulk landslides by carrying out a flume experiment, revealing the seven prominent factors determining the maximum impulse-wave height. Since a landslide-induced impulse-wave has extremely strong three-dimensional (3D) characteristics, a two-dimensional (2D) flume experiment has inherited drawbacks. Zweifel and Hager [16], and Fritz [17] carried out a series of 2D experiments on impulse waves induced by artificial granular material entering water in the Hydraulic Laboratory (VAW) of Zurich University (ETH). They also derived analytical formulas for predicting the propagation of impulse waves and the corresponding wave period. Enet et al. [39] Studied landslide impulse wave caused by underwater rigid-body landslides through large-scale three-dimensional experiments. A high-speed camera is used to record the trajectory of the landslide body. The miniature accelerometer in the landslide model measures the acceleration of the landslide body. The analytical law of the landslide motion is deduced from the measurement data, and the dispersion and nonlinear effects of the impulse-wave are analyzed. Zu et al. [18] established a four-dimensional mathematical model among wave-height transmissibility rate, initial wave height, water depth, and azimuth angle, as well as propagation distance, through utilizing the tensor space-mapping method. They summarized the general regularity of the propagation and attenuation of landslide-induced impulse waves. Their findings can be applied to analyze and forecast a landslide-induced impulse waves, and scientifically and accurately determine the damage range of landslide-induced impulse waves. Along with experimental studies, numerical investigation has become increasingly popular, and various numerical models have been established to study the hydrodynamic characteristics of landslide-induced impulse waves. Based on the methods reported by Yin et al. [19] and Grilli et al. [20] modified the seabed landslide-generated surge-source model to form an initial source model for underwater landslide-generated impulse waves; this improved model can be used to predict potential impulse waves disasters at different water levels in mountainous reservoir areas. Mao et al. [21] developed a three-phase finite-element numerical model to evaluate the devastating hazards of landslide-induced impulse waves, due to huge energy-carrying capability during the process of impulse waves generation and propagation. Recently, Huang et al. [22] established a fully coupled numerical model for landslide-induced impulse waves based on the noncoherent granular flow-governing equation. This has been used to analyze the characteristics of the landslide motion and generated impulse waves, and predict the final deposition and wave run-up height.
It is not hard to find that earlier studies mainly focused on the study of wave type, shape change, maximum impulse waves height, and propagation characteristics caused by the landslide entering the water. Among them, the study on maximum impulse waves height and wave-velocity characteristics caused by the landslide entering the water in the cross section of the river channel is relatively common. Some people pointed out that the height of an impulse waves depends mainly on landslide volume and Froude number [12], [23]. Subsequently, some scholars further studied the effects of slope, water depth, landslide-body size, and shape-to-swell height, and derived a series of empirical formulas [24], [25]. In addition, Zhang et al. [40] Used the ''Tsunami squared'' numerical method to study the effect of reservoir width changes in the Three Gorges Reservoir area on landslide impulse-wave propagation. Compared with the convergent reservoir, the divergent reservoir geometry has a greater effect on wave propagation attenuation. Heller et al. [42] obtained the maximum amplitude, wave height, period and along the propagation deformation equation through the experiment of 144 slides under the three parameter system changes of Froude number, relative slide mass and slide thickness.
Obviously, the current landslide-wave model tests can comprehensively consider influencing factors such as landslide shape, velocity, landslide volume, and water depth. However, the study on the influence of channel configuration on the impulse waves has not been thoroughly carried out. Most river-landslide models are established for relatively wide rivers. Very limited research has been carried out to investigate the hazard potential of landslide-induced impulse waves in narrow river-valley reservoirs of mountainous areas. The generating and propagating phenomena of landslide-induced impulse waves in narrow river-valley reservoir regions are significantly different from those in open-water regions, since the propagation of impulse waves can be greatly influenced by strong reflected waves formed at the opposite riverbank, making the generation mechanism of landslide-induced impulse waves more complicated. Therefore, it is now urgently needed to meet the knowledge gap on landslide-induced impulse waves in narrow river-valley reservoirs and their hydrodynamic influence in the surrounding environment.
In this study, to enhance our understanding on landslideinduced impulse waves in narrow river-valley reservoir regions, a series of experimental work was conducted. In addition, with the development of CFD technology, more and more research work adopts CFD technology [9]- [11], [43], software package FLOW-3D, as a 3D twophase flow model was applied to systematically study the generation and propagation of landslide-induced surge waves in narrow reservoir river regions at a laboratory scale, and it has been approved to be effective research tools for studies on landslide-induced impulse waves [26]- [30]. In present paper, 3D experimental data is used to verify the reliability of our 3D numerical model (FLOW-3D). Then, the simulation results of the verified 3D numerical model have been used to derive our empirical formulas in predicting impulse waves in both lateral and longitudinal directions. For landslide accidents happened in the narrow river-valley reservoir regions, we apply the limited measured results to further verify the reliability of our empirical formula in predicting impulse waves in realscale landslide problem. The rest of the paper is organized as follows. Governing equations and corresponding numerical methods of the software packages, model validations are described in Section 2. Section 3 discusses the hydrodynamic characteristics of the generation and propagation of landslideinduced impulse waves, and proposes empirical formulas for predicting the initial maximum surge height, and longitudinal and lateral attenuation based on both experimental and numerical results. Moreover, Section 3 further verifies the accuracy and reliability of the proposed empirical formulas by performing four landslide accidents. The main conclusions drawn from this study are listed in Section 4.

II. METHODS
The 3D landslide-induced impulse-wave model is established using the full three-dimensional commercial code Flow-3D (Flow Science, Inc., Santa Fe, NM). The model has been widely applied to study the characteristics of impulse-wave generation and propagation caused by landslides into reservoirs [29], [30]. The model solves the Reynolds-Averaged Navier-Stokes Equations and the continuity equation for incompressible flow along with the true volume-of-fluid method (VOF, Hirt and Nichols, 1981) in order to compute free-surface motion. The general moving-object module (GMO) was selected to simulate the interaction between moving objects and the fluid for the purpose of modelling landslide-generated waves. Source terms were added in the continuity equation and the VOF transport equation in order to describe the hydrodynamic effects of moving objects. In particular, shear velocity at the moving-object boundaries is accounted for into shear-stress terms in momentum equations (Flow Science, 2007). Therefore, the resulting general 3D continuity and momentum equations considering fluid motion, GMO motion, the viscosity of the fluid, and porous media are: In Equation (1), ρ is the density of water, (A x , A y , A z ) are the fraction areas of fluids in the x, y, and z directions, (u, v, w) are the velocity components in the x, y, and z directions, and R SOR is a mass source. The mass-source term, when the FAVOR (Fractional Area Volume Obstacle Representation) is used, also accounts for the additional volume source generated on the boundary of a moving object. In Equation (2) V F is the fraction volume open to flow, (G x , G y , G z ) are the gravitational acceleration in the x, y, and z directions, (f x , f y , f z ) are the viscous terms in the x, y, and z directions, and (b x , b y , b z ) are flow losses in porous media. The final terms account for the injection of mass at a source represented by a geometry component; in fact, the term (u w , v w , w w ) represents the velocity of the source component that is generally nonzero for a mass source at a GMO. The term (u s , v s , w s ) is the fluid velocity at the surface of the source relative to the source itself.
Fluid configurations are defined in terms of a VOF function, F (x, y, z, t), which represents the volume of fluid per unit volume and satisfies the equation: F DIF is a different diffusion term for two-fluid mixing, and the term F SOR is the time rate of change of the volume fraction of fluid associated with the mass source.
In the above model, the RNG k-ε turbulence model [34], [35] was implemented as the turbulence closure, the second-order finite-difference method was utilized to discretize the momentum equations, the TruVOF [31], [32] method was used to capture the interface between air and water, and the pressure and velocity was coupled by GMRES Pressure-Velocity Solvers [33].

A. MODEL SETUP AND VALIDATION 1) EXPERIMENTAL SETUP
Experiments were carried out in the Key Laboratory of Water and Sediment Science and Water Disaster Prevention and Control in Hunan Province at the Changsha University of Science and Technology. The wave flume was 1.8 m in height, 1.5 m in width, and 60 m in length (60m × 1.5m × 1.8m). The experimental layout is depicted in Fig. 2, which represents a typical layout for a landslide accident near a dam reservoir region with a scale ratio of about 1:200. As observed in Fig. 2a, the configuration of the slide was cuboid with 0.2 m in length and 0.1 m in width. The model is based on the Froude similarity rule, so other similarity ratios can be obtained as shown in table 3. In the experimental work, the density of the slide was 2560 kg/m 3 , and the volume of the slide could be directly adjusted by varying its thickness or height. As shown in Fig. 2, the wave height was recorded by eight gauges. Three of them were arranged transversely with wave-gauge G1 locating in the middle of the domain. Wave-gauge G4 was used to measure the run-up height of the impulse waves. Six wave gauges were arranged longitudinally. As reported in Fritz [17], the slide would readily collapse, if the slope of the riverbank were in the 60 to 90 degrees range. Hence, we set the bank slope at 75 degrees. Other parameters designed for different experimental runs are listed in Table 1. In the present paper, each experimental run was repeated five times, and the recorded data were averaged to satisfy accuracy requirements and reduce possible experimental errors.

2) NUMERICAL SETUP
The computational domain was 8 m in length, 1.5 m in width, and 1.8 m in height. A high-resolution computational mesh with 2 million grids was generated to resolve the freesurface profile in high fidelity, as shown in Fig. 3. Simulation duration was 8 s. To meet the numerical-stability requirement, an adaptive time step was selected. In addition to the value of the slope used in the experimental work, three more bank slopes were selected: 30, 35, and 40 degrees. Table 2 lists the parameter setup for all simulation runs. These simulation runs were designed to systematically analyze the influence  of prominent factors, such as falling, on the generation and spread of landslide-induced impulse waves.

3) NUMERICAL SETUP MODEL VALIDATION
In this section, the computational capability of our numerical model in predicting landslide-induced impulse waves is validated by reproducing experimental runE2, describe in the experimental setting section. Fig. 4 plots the comparison of the time series of water elevation between prediction and measurement recorded at three selected wave gauges. As observed in Fig. 4, they are in good agreement with respect to wave period and wave height. To further verify the accuracy of the computation, the skill number was calculated using Equation (4) [36]: where X num and X exp represent predictions and measurements, respectively. It appeared that the skill numbers for all water-elevation comparisons plotted in Fig. 4 were greater than 0.9. The difference between measurement and simulation results at G1 alone was relatively noticeable, which can be due to complicated wave interactions, especially the reflected wave from the opposite channel shore. Based on the results demonstrated above, our numerical model could simulate hydrodynamic characteristics of an impulse-wave well and with high accuracy.

A. HYDRODYNAMICS OF LANDSLIDE-INDUCE IMPULSE WAVES
This section describes the hydrodynamic characteristics of landslide-induced impulse waves in detail. The simulation result for S13 is demonstrated and discussed in this section. Fig. 5 shows snapshots of the water body at different time instances during the process of impulse-wave generation, propagation, run-up, and recession from the opposite VOLUME 8, 2020 channel shore. As seen in Fig. 5, the temporal evolution of the landslide-induced impulse waves can generally be summarized as three stages: 1) During the first stage, the water body is squeezed to spread around the entering site. As shown in Fig. 5a, just when the slide enters the water body, a impulse-wave bore traveling forward is generated in a very short time, behaving as an impact-wave. At t = 0.58 s, after the slide completely enters the water body, it replaces the volume of the original water body, causing the surrounding water body to rise up, as observed in Fig. 5b.
2) Propagation and attenuation of the impulse waves occur during the second stage. After t = 1.6s, the impulse-wave spreads laterally to reach the opposite channel shore Fig. 5c. Meanwhile, it also gradually propagates along the channel in a longitudinal direction. The intensity of impulse waves can be attenuated to some extent due to the viscous effects of the water Fig. 5d.
3) In the third stage, the impulse-wave runs up onto the opposite channel shore Fig. 5e. Once the landslide-induced impulse-wave reaches its maximum run-up height, it retreats under the influence of gravity Fig. 5f. Fig. 6 plots the temporal evolution of water elevation recorded at five selected wave gauges arranged in both the longitudinal and lateral directions, where η is the impulsewave height. As observed in Fig. 6a, impulse-wave height gradually decreases with the distance measured from the slide entering the site in the longitudinal direction. The attenuation rate of the impulse-wave also decreases with distance. In addition, it is observed that the attenuation rate of impulse waves in the lateral direction is slightly attenuated with distance compared with that in the longitudinal direction Fig. 6b. This is possibly due to the narrow river reach and the relatively large slide volume. Furthermore, when the wave gauge is located close to the slide entering the site (y = 10 cm), the wave height also is slightly lower than other measuring points.

B. EFFECT OF PROMINENT FACTORS 1) INITIAL MAXIMUM IMPULSE-WAVE HEIGHT IN THE LATRAL DIRECTION
In this section, the effects of prominent factors, such as drop height (H), on the variation of the initial maximum wave height of landslide-induced impulse waves are discussed in detail. Fig. 7 shows the initial maximum wave height as function of slide volume, drop height, slide slope, and water depth. And Fig. 8 also shows the relationship between initial maximum wave height and relevant parameters. It can be seen that wave height increases almost linearly with slide volume (Fig. 7a and Fig. 8a). This is because an increase in slide volume can greatly enlarge both the final kinetic energy  of the slide and the contact surface area between the slide and the water. As observed in Fig. 7b and Fig. 8b, impulsewave height also increases linearly with the increasing of the drop height of the slide. Since an increase in the slide slope can significantly reduce the magnitude of frictional force between the surface of the slide and the sliding plane, resulting in higher final kinematic energy for the slide before it enters the water, wave height increases with increasing slide slope Fig. 7c. As seen fromFig. 7d and Fig. 8c, wave height gradually decreases with still-water depth. It is due to this reason that increasing the water depth will reduce VOLUME 8, 2020 the drop height of the slide, thus the energy will be reduce which the slider kinetic energy is converted into a wave energy. In addition, an increase in still-water depth results in an increase in the surface area of the reservoir. Hence, the energy-carrying capability by unit width of the water body increases, and landslide-induced impulse-wave height decreases. This can become more obvious for narrow rivervalley reservoirs, since any change in still-water depth can cause the width of the reservoir area to rapidly change when the slope of the river shore is large.

2) CHARACTERISTICS OF WAVE PROPAGATION IN THE LONGITUDINAL DIRECTION
In this section, we discuss the hydrodynamic characteristics of the propagation of landslide-induced impulse waves in the longitudinal direction. Variations of the maximum impulsewave height of a landslide-induced impulse-wave as function of slide volume, drop height, slide slope, and still-water depth along the centreline of the channel are plotted in Fig. 9. As can be seen from Fig. 9a, the larger the slide volume is, the higher the impulse wave can be. Meanwhile, wave height gradually decreases with the longitudinal distance measured from the entering site of the slide while the reducing rate of the maximum impulse-wave height decreases. Basically, similar to the maximum impulse-wave height under different slide volumes, the maximum impulse-wave height gradually increases with the drop height Fig. 9b. It is also observed that the attenuation rate of impulse-wave height is very high, with a distance of 0.5m. For instance, as an impulse-wave propagates from x = 0.5 to x = 1.3 m, the maximum impulse-wave height reduces from 1.64 to 0.86 cm. However, the attenuation rate of the impulse wave reduces greatly when the impulse waves propagates from x = 2.1 to x = 2.9 m, since the maximum height of the impulse wave only reduces from 0.84 to 0.51 cm. Variations of impulse-wave height under different bank slopes along the centreline of the channel are plotted in Fig. 9c. As observed in Fig. 9c, the bank slope has very limited influences on the propagation of impulse waves in a longitudinal direction. Fig. 9d demonstrates the variation of maximum impulse-wave height under different still-water depth. As seen from Fig. 9d, maximum impulse-wave height decreases with still-water depth, especially when still-water depth increases from 0.4m to 0.6 m.

3) LATERAL WAVE PROPAGATION
The hydrodynamic characteristics of impulse-wave propagation in the lateral direction are discussed in this section. Fig. 10 depicts variations of maximum impulse-wave height in the lateral direction as function of slide volume, drop height slide slope, and still water depth. Variation of maximum impulse-wave height under different slide volumes is plotted in Fig. 10a. It shows that the larger the slide volume is, the greater the impulse waves height will be. The attenuation rate of an impulse-wave within a lateral distance of 0.1 m is relatively large. The maximum attenuation rate of wave  height within the first lateral distance of 0.1 m is about 17%. It was also found that the drop of the slide had very limited influence on the maximum impulse-wave height along the center line of the channel, but it did have noticeable influence on the maximum impulse-wave height when the drop of the slide was larger than 0.12 m Fig. 10b. Similar to the variation of maximum impulse-wave height in the longitudinal direction, the maximum impulse-wave height increases with the slide slope Fig. 10c, but decreases with still-water depth Fig. 10d.

C. EMPIRICAL FORMULAS FOR LANDSLIDE-INDUCED IMPULSE WAVES
In this section, based on the simulation results presented above, we derive the empirical formulas for predicting initial maximum impulse-wave height and evaluating the attenuation of an impulse wave in both longitudinal and lateral directions by performing dimensionless analysis and applying nonlinear regression methods [37], [38]. The initial maximum impulse-wave height can be calculated with Equation (5), which systematically considers the influence of slide volume, drop height, slide slope, and still-water depth.
Comparison of the predicted initial maximum impulsewave height and the calculations by Equation (5) is plotted in Fig. 11. Corresponding correlation-coefficient R 2 is 0.925, indicating the reliability of Equation (5). Hence, we can use Equation (5) as a technical tool to make fast predictions of the initial maximum impulse-wave height by comprehensively reflecting the influences of slide volume, drop height, slide slope, and still-water depth. Liu [38] proposed a theoretical formula for the rapid estimation of the attenuation of a landslide-induced impulsewave in the Three Gorges reservoir area, as follows: where η r is the wave height in the longitudinal direction, η 0 is the initial maximum impulse-wave height, h is the still-water depth of the reservoir area, x is the distance measured from the entering site of the slide, and p and q are constants.
In this article, to systematically consider the joint influences of slide volume, drop height, slide slop, and stillwater depth, we derive a formula by adapting Liu's formula, as follows: where a, b, c, d, and p are constants. By applying the regression method, the following empirical formula is derived based on simulation results: Fig. 12 plots the comparison of predicted impulse-wave heights in the longitudinal direction and the calculations by Equation (8). As seen from Fig. 12, the empirical formula has good accuracy in predicting variations of impulsewave height in the longitudinal direction. Corresponding correlation-coefficient R2 is 0.94. In addition, a similar formula is derived for evaluating the attenuation of an impulse-wave in the lateral direction, as shown in Equation (9): Fig. 13 depicts the comparison of the predicted impulsewave heights in the lateral direction and the calculations by Equation (9). It shows that the predicting accuracy of Equation (9) is acceptable, and that the correlation coefficient is 0.97.

D. CASE STUDY 1) STUDY AREA
The Yellow River section in Qinghai province is a typical narrow river-valley reservoir river. The most bank of the Qinghai Yellow River consists of cliffs. The Yellow River is meandering and the water flow condition is complicated.    Fig. 14b. Hence, this region becomes vulnerable to landslide accident. Tangjiaxi, located in Zhexi reservoir, Hunan province, China, was hit by a landslide on July 16, 2014 due to several days of rainfall [22]. The Gongjiafang landslide is located in China's Three gorges reservoir on the Yangtze river, In November 2008, a 380000m 3 slide volume rushed into the water to generate waves [41]. Tafjord is a branch of Stavfjord in western Norway. On April 7, 1934, the impact of possibly 3000000m 3 of rock into Tafjord generated huge waves [17].

2) VALIDATION OF EMPIRICAL FORMULA IN PREDICTINGINITIAL MAXIMUM SURGE HEIGHT
To verify the reliability of our proposed Formula (5) in predicting initial maximum impulse-wave height, we calculated the maximum initial impulse-wave height for four landslide events. and the results were compared with actual measurements and the prediction by Liu's formula [38]: (10) where v is the sliding speed, l is slide length, w is slide width, t is slide height, b is river width, and h is water depth. The established empirical formula uses water depth to make the parameters dimensionless, so that the empirical formula can be extended to a large scale. Table 4 shows the four   specific landslide events of various parameters. Table 5 lists the comparison of the initial maximum impulse-wave height among measurement, prediction by Liu's formula, and our prediction with Equation (5). As can be seen from table 5 that Equation (5) has a significant improvement over the formula for predicting the maximum initial impulse-wave height. In the Shenguotan landslide, the errors between Equation (5) and Equation (10) and the measured values are 2% and 5%, respectively. In the Tangjiaxi landslide, the errors of Equation (5) and Equation (10) are 5.6% and 9.2%, respectively. In the Gongjiafang landslide, the errors of Equation (5) and Equation (10) are 1.5% and 12%, respectively. In the Tafjord landslide event, the errors of Equation (5) and Equation (10) were 3.3% and 5.3%, respectively. And the average error between Equation (5) and Equation (10) and the measured values is 5.1% and 7.8%, respectively. This comparison indicates that Equation (5) is reliable in predicting a large leading wave height in narrow river-valley reservoir areas.

IV. CONCLUSION
Landslide-induced impulse waves have become a serious threat to life safety and property intactness, especially in narrow river-valley reservoir areas. This article systematically carried out numerical investigations on the hydrodynamic characteristics of landslide-induced impulse waves in narrow river-valley reservoirs by applying software package FLOW3D. To verify the computational reliability of FLOW3D, new laboratory experiments were performed. The main conclusions are drawn as follows: 1) Compared with previous research on landslides in open-water areas, we conducted a series of experimental work and a 3D numerical simulation on landslide-induced impulse waves in a narrow rivervalley reservoir region. The effects of prominent factors such as slide volume, drop height of the slide, slide slope, and still-water depth, on the hydrodynamic characteristics of an impulse-wave have been discussed in detail. It was found that the initial maximum impulsewave height increased with the slide volume, the drop of the slide, and the slide slope, but decreased with still-water depth. An impulse-wave could be gradually attenuated as it propagates to the surrounding water, and the attenuation rate of the impulse-wave could be greatly affected by slide volume, slide slope, and stillwater depth. 2) Based on the simulation results, we derived empirical formulas for predicting the initial maximum impulsewave height, variations of impulse-wave height, along both longitudinal and lateral directions in the narrow river-valley by performing dimensionless analysis and applying nonlinear regression methods. The accuracy and reliability of the proposed formulas are well-validated by comparing their calculations with corresponding experiment data and simulation results. It can be seen from the formula that as the drop height, and the slide volume, and the landslide angle increase, the initial impulse wave height also increases, which can be found from the numerical analysis results and experimental results. The greater the drop height and the landslide angle can increase the speed of the slider into the water, increase the kinetic energy of the landslide body, the more energy converted into the water body, and the increase in the volume of the landslide, the more the volume of discharged water, the increase in impulse height. When other conditions are constant, the initial impulse wave height decreases as the water depth increases. This is because increasing the water depth is equivalent to reducing the drop height of the slide, which reduces the water inlet speed and kinetic energy of the slide. 3) Four landslide events were used to further verify the reliability of our proposed formula in analyzing the hydrodynamic characteristics of landslide-induced impulse-wave in actual landslide accident. The analytical solutions of the proposed formulas were compared, and were in a good agreement with the field-observation data. It is believed that the findings drawn from this article could greatly enhance our understanding on landslide-induced impulse-wave in narrow river-valley reservoir areas, and our proposed analytical formulas could act as are liable technical tool for evaluating the potential hazards of landslideinduced impulse waves. KE QU received the Ph.D. degree in environment water resources from The City College of New York, The City University of New York, USA. He is currently an Associate Professor with the School of Hydraulic Engineering, Changsha University of Science and Technology, Changsha, China. His current research interests include two-phase flow modeling, storm surge modeling, wave-structure interaction, and multiscale coastal flow model development, with over 30 publications in these areas. VOLUME 8, 2020