Keywords

1 Introduction

Mt. Kurikoma is located in the center of the Tohoku region, the northeastern portion of Honshu, the largest island of Japan, at an elevation of 1626 meters. It is a complex stratovolcano comprising some volcanic edifices with inferred eruption centers (Fujinawa et al. 2001). Lava flows from these eruption centers cover the secondary volcaniclastic deposits, the “reworked” products of the “direct” products of volcanic eruptions. Most of them are weakly cemented rhyolitic tuffs and, therefore, highly susceptible to mass wasting events once exposed.

A 7.2 Magnitude (Moment Magnitude Mw: 6.8) earthquake occurred about 10 km northeast of Mt. Kurikoma at 8:43 JST on June 14, 2008. The overwhelming majority of the reported failures are geotechnical. The earthquake caused over 3000 mass-wasting events within the aftershock area, which gives a reasonable estimate of the fault rupture area of the main quake, encompassing Kurikoma Volcano’s flank on the hanging side of the earthquake fault (Miyagi et al. 2011). One of the most spectacular mass-wasting events was the Aratozawa Landslide at an upstream section of the Aratozawa Dam in Kurihara, Miyagi Prefecture. The volume of the sliding body near the dam is estimated to be about 68 million cubic meters. A foot of the landslide mass (4.22 million cubic meters) entered the water of the reservoir of Aratozawa Dam, causing a tsunami (seiche) in the reservoir. Though the quake hit the rural area, and thus, sparsely distributed dwellings suffered minor damage, 17 were confirmed dead, and six were still missing. Out of those with known causes, only two cases had no connection to sediment disasters. In other words, mass-wasting events were blamed as the primary cause of deaths in this earthquake, which included seven people believed to have been buried by a fluidized debris mass at the Komanoyu hot spring.

Though the area suffered severe damage, the earthquake left tremendous marks of soil deformations and tsunami runups along a dam reservoir, which provided unique opportunities to gain insights into the dynamics of the mass-wasting events. This paper summarizes the findings from our observations in the referred papers (Nomura et al. 2009; Rahman and Konagai 2016, 2017).

2 Geological and Geomorphological Setting of the Epicentral Area

Figure 1 shows a hill-shade map of the epicentral area encompassing Mt. Kurikoma and its widespread mountainside. Red circles and line segments on the southeastern flank of Mt. Kurikoma are the discontinuous fault ruptures identified through field surveys and LiDAR image interpretations by Maruyama et al. (2009). These red circles and line segments align with the southeastern bound of the group of the aftershocks’ epicenters (white circles) observed from 8:43 JST on June 14 to 24:00 on June 15, 2008.

Fig. 1
A terrain map of the epicentral area encompassing Mount Kurikoma and its widespread mountain-side. The locations of epicenter of the main shock in the north is marked. Other locations are Komano Yu hotspring, Aratozawa landslide, and Aratozawa dam.

Hill-shade illustration of the epicentral area encompassing Mt. Kurikoma and its widespread mountainside: Open circles indicate the locations of aftershock epicenters recorded on June 14 and 15, 2008. Redline segments and red circles are locations of surface fault ruptures that the reconnaissance team of the Research Institute of Earthquake and Volcano Geology, the National Institute of Advanced Industrial Science and Technology (AIST), identified and reported (Yoshimi et al. 2008a, b; Maruyama et al. 2009)

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As said, Mt. Kurikoma is a complex stratovolcano comprising some volcanic edifices with inferred eruption centers (Fujinawa et al. 2001). On the southeastern flank of Kuricoma Volcano, there are some eruption centers, such as pyroclastic cones and lava domes, with solidified lava flows spreading from them to lower elevations. These lava flows cover the secondary volcaniclastic deposits, the “reworked” products of the “direct” products of volcanic eruptions. This hill-shade relief shows that valley density above a specific elevation, ranging from 450 to 550 m a.s.l., is relatively low. In contrast, valleys below this elevation cut mountain slopes down to lower elevations. This feature suggests the presence of harder caprock (radiating lava flows and Ignimbrite) overlying relatively soft secondary volcaniclastic deposits (rhyolitic tuff), and the terrain below this elevation shows clear traces of not only soil mass movements triggered by this earthquake but also those of the past events, indicating that the area has been suffering from frequent geotechnical disasters.

3 Debris Flow that Hit the Komano-Yu Hot Spring Inn

Figure 2 shows a path that the 1.5 million m3 debris mass flowed down from its source right beneath the snow remaining around the eastern peak of Mt. Higashi-Kurikoma (38.9584°N 140.8061°E), one of the volcanic edifices making up the Kurikoma volcano. The fluidized debris mass ran down along the Dozozawa River Channel. A part of the mud flow of about a 0.5 million m3 volume, whose path was clogged with another landslide mass (38.9389°N 140.8406°E), surged up to “Komano-Yu” hot spring inn (38.9377°N 140.8378°E), where seven people were killed in soil and rubble.

Fig. 2
A terrain map of the Dozozawa River Channel and Komano-Yu Hot Spa inn. The locations marked are Landslide that clogged the valley in the South east. The Mount Higashi Kurikoma is in the North west.

Dozozawa River Channel and Komano-Yu Hot Spa inn (38.93779°N, 140.83756°E)

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Some eyewitness accounts vaguely tell us the fluidized debris mass reached the “Komano-Yu hot spring inn” 6 to 9 min after they felt the intense quake (Ikeya et al. 2009). Though these testimonies tell little about the exact times of the succeeding post-quake events till the debris mass hit the hot spring inn, it was a vital testimony of Mr. Sugawara, one of the inn owners, that a guest, who was staying in the inn’s annex, ran up to him and reported that a landslide took place across the valley, whose mass seemed to have clogged up the valley before the debris flow reached the inn. Given these testimonies and mud marks remaining on the valley walls, Ikeya et al. (2009) first estimated the peak discharges of the debris mass at several curved channels with remaining mud marks of super-elevations. Then they used a numerical method by Miyamoto and Ito (2002) to simulate the non-steady debris flow associated with erosional and depositional processes. The simulation showed that the fluidized debris reached the landslide mass blocking the river channel at the “Komano-Yu hot spring inn” and started stagnating about 9 min after the quake. Then the slurry started flowing upstream along the southern valley wall, hitting the inn’s buildings (9 min. 40 s after the quake). They also ran a simulation assuming that the landslide mass didn’t block the river channel and concluded that the inn would not have been hit by the debris mass. So, it was a sequence of unfortunate events that eventually claimed seven lives there.

Nomura et al. (2009) used the Depth-Averaged Material Point Method (DAMPM) developed by Abe and Konagai (2017), Abe et al. (2007) to simulate the flowing process of the fluidized debris mass. DAMPM is based on the concept of describing a debris mass as a cluster of upright material columns that move through cells of computational fixed Eulerian mesh (Konagai and Numada 2002), and a simple semi-empirical model for describing equivalent fluid (Hungr 1995) has been implemented for the material columns. The idea to describe material columns through a fixed computational grid is based on the scheme for the Material Point Method proposed by Sulsky et al. (1994). The advantage of this scheme is that it can represent large deformation and provide a Lagrangian description that is not subject to mesh tangling. In the DAMPM, governing equations are integrated along the z direction to ignore the motions of particles within each column. Eventually, this procedure leads to shallow water and consolidated elastoplastic assumptions for liquefied and coherent debris mass flows, respectively.

Figure 3 shows a material column in the DAMPM. The net driving force acting on a boundary block between the columns consists of the tangential component of weight, the basal resisting force, T, and the tangential internal pressure resultant, P. The resultant pressure term, P, is described by the pseudo-three-dimensional Drucker-Prager model whose yield surface is assumed to circumscribe the Mohr-Coulomb yield surface expressed in terms of the material cohesion, c, and the angle of internal friction, φ.

Fig. 3
A drawing presents a material column in the DAM P M. The net driving force acting on a boundary block between the columns consists of the tangential component of weight, the basal resisting force, T, and the tangential internal pressure resultant, P.

Forces acting on an upright column other than weight: P=tangential internal pressure resultant, T=basal resisting force (Hungr 1995)

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In the DAMPM, the Voellmy bi-parametric model (Eq. (1)) defines the basal resisting force, T, because it gives the most consistent results with field-measured data.

$$ T=A\left\{\rho g h\left(\cos \alpha +\frac{a_c}{g}\right)\left(1-{r}_u\right)\mu +\rho g\frac{{\overline{v}}^2}{\xi}\right\} $$
(1)

where, A = basal area, ρ = bulk unit density of the column, g = gravitational acceleration, h = height of the column, α = bed slope angle, ac = centrifugal acceleration, dependent on the vertical curvature radius of the flume, ru = pore-pressure coefficient (ratio of pore pressure to the total normal stress at the base of the column), μ = the basal frictional coefficient, \( \overline{v} \) = local depth-averaged velocity, and ξ = turbulence coefficient that describes the thickness of the basal layer, dilatant flow, viscosity, and turbulence.

The number of necessary Lagrangian parameters for the DAMPM simulation is seven, as listed in Table 1. These seven parameters were then calibrated to adjust the simulated debris flow velocities to the velocities estimated from super-elevations of the debris flow. Figure 4 shows a simulated debris flow at t = 0.6, 15, 30, 60, 120, 180, 300, 420, and 600 s (10 min) after the debris mass started flowing, consistent with witness accounts.

Table 1 Parameters used for the Dozozawa debris flow
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Fig. 4
Ten contour graphs plot the simulated debris flow at t equals 0.6, 15, 30, 60, 120, 180, 300, 420, and 600 seconds after the debris mass started flowing, consistent with witness accounts. The debris source elevation is 1350 above mean sea level. The Komano-Yu hot spring inn Elevation is 655 above mean sea level.

Simulated debris flow (Nomura et al. 2009)

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A super-elevation, which is the difference in flow surfaces at the outer and inner boundaries of the channel, characterizes the open channel flow in a bend with radius Rc. Assuming that the velocity \( \overline{v} \) of an open channel flow is uniform across the channel width B and the radius Rc is substantially larger than the channel width B, we can relate the super-elevation ∆h to the flow velocity by equating fluid pressure to centrifugal force:

$$ \overline{v}=\sqrt{R_c{g}^{\prime}\frac{\varDelta h}{B}} $$
(2)

where g′ = g cos α with g being acceleration due to gravity and α being the channel inclination.

However, the debris flow velocity is not uniform across the channel. Moreover, the energy can dissipate through the flowing process of the viscous slurry. This equation was modified and applied to debris flows by introducing a correction factor k to estimate debris-flow velocities vmud (e.g., Hungr et al. 1984; Chen et al. 2014; Bulmer 2002; Prochaska et al. 2008):

$$ {v}_{mud}=\sqrt{\frac{R_c{g}^{\prime }}{k}\frac{\varDelta h}{B}} $$
(3)

This k, which is 1 for a pure water flow with uniform velocity across the channel, is often empirically set at a value larger than 1, considering the viscous features of debris flows. Ikeya et al. (2009) set k at 10 in their simulations of the debris flow that hit the “Komano-Yu hot spring inn.” Nomura et al. (2009) also adjusted the geotechnical parameters (Table 1) to make the simulated debris velocities to become close to the super-elevation-based flow velocities for k = 10 in Eq. (3).

Even though practicing engineers have widely used super-elevations and channel geometries in post-event field surveys to estimate flow velocities, extracting these parameters from the field is challenging. The determination of bend radius and super-elevation is especially affected by the unsteady flow traces and terrain morphology. The selection of the radius of curvature depends on the curve of the natural channel with abrupt changes. Another significant anomaly is that only the highest flow marks of an unsteady debris flow are seen on site; these marks often estimate the super-elevation, which is lower than the actual maximum super-elevation that the particular cross-section experiences during the flow. Figure 5 illustrates the scenario that happens in situ. Measurement of super-elevation from the mud marks inaccurately predicts the speed of flowing slurry, as was proven by the previous research work (Iverson et al. 1994). Extensive study is thus required to develop or modify the strategy for plausible estimation of velocities.

Fig. 5
A U shaped cross section with three points t 1, t 2 and t 3 marked in one of the slopes. The height of the point t 3 is delta h actual. Another point is marked in the opposite slope which is at a vertical distance of delta H mud from t 3.

Problems encountered in reality when determining super-elevation from mud marks: We are dealing with an unsteady flow whose surfaces differ at different times, t1, t2, and t3. Therefore, the actual maximum super-elevation ∆hactual differs from the observable post-event super-elevation ∆hmud (Rahman and Konagai 2016, 2017)

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To seek better ways to fix this anomaly, Rahman and Konagai (2016, 2017) carried out a series of three-dimensional numerical curved flume tests using smoothed particle hydrodynamics (SPH). The first procedure of this method is to determine the radii of curvature along an irregularly curved natural flume. This procedure is based on a simplified assumption that the time T for a flowing slurry to reach its maximum super-elevation is associated with the sloshing period Ts of the slurry confined within a representative transverse cross-section of this curved flume. The SPH simulations showed that the time T nearly equals 1/3 of the sloshing period, Ts.

The second procedure estimates the maximum flowing slurry velocities from the observable super-elevations remaining at particular locations of the flume, where super-elevations are not identical to the maximum super-elevations reached during the event. Velocities vreal are often underestimated, particularly near the debris source where the unsteady nature of the flowing debris slurry is more predominant. A number of SPH simulations for a variety of flume configurations showed that the mud-mark-based estimates of the velocities vmud, obtained from Eq. (3) with the k value set at 1.0, can be related to vreal by the following equation:

$$ \frac{v_{mud}}{v_{real}}=1-{e}^{-\beta X}\kern0.62em for\;X>1\kern0.62em \mathrm{with}\;\beta =0.4880 $$
(4)

where, β is an adjustment factor and X is the normalized distance given by:

$$ X=\frac{x}{L}=\frac{\mathrm{Distance}\ \mathrm{from}\ \mathrm{source}\ \mathrm{front}}{\mathrm{Initial}\ \mathrm{source}\ \mathrm{length}} $$
(5)

Rahman and Konagai (2017) chose the Newtonian fluid model to describe the debris slurry’s flowing nature, and the above Eq. (4) is found to be almost identical to that derived in their previous study for Bingham-type debris flows (Rahman and Konagai 2016), except that the adjustment factor β in Eq. (4) is slightly larger for the Bingham-type flows and is about 0.5721. Equation (4) is thus used to adjust the super-elevation-based estimates of velocities.

Rahman and Konagai (2017) used the iterative approach (the first procedure mentioned above) to determine bend radii along the Dozozawa River Channel objectively. They chose locations of the point of highest super-elevations. Then at each point of the highest super-elevation, an arbitrarily chosen stretch along the curved ravine was approximated by an arc in the least square sense. Several transverse cross-sections were taken strip-wise along this stretch to obtain the average cross-sectional shape. The length of the selected stretch was then updated from the sloshing period of the slurry confined within the obtained average cross-section, and the procedure was repeated until sufficient convergence was reached.

Substituting the obtained bend radii along the river channel in Eq. (3) (k = 1) yielded the mud-marks-derived velocities vmud and then Eq. (4) estimated the actual slurry velocities vreal at these bends (Fig. 6). The slurry velocity for each section between two adjacent bends is assumed as the average of the slurry velocities at these two bends. The travel-time curve was obtained by summing up the sectional times, as shown in Fig. 7. Figure 7 shows that it took around 8 min for the debris mass to reach Komano-Yu hot spring inn. This travel time, obtained by adjusting the mud-marks-derived velocities using Eq. (4), is slightly shorter than 9 min and 40 s, and 10 min estimated by Ikeya et al. (2009) and Nomura et al. (2009), respectively.

Fig. 6
A scatterplot between velocity in meters per second and normalized distance X, plots the real and mud velocities.

Mud mark-based estimation of velocities and adjusted velocities for the debris flow that hit the Komano-Yu hot spring inn (Rahman and Konagai 2017)

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Fig. 7
A line graph between normalized distance X and time in seconds. A line with an increasing trend is present.

Travel-time curve of the debris flow that hit the Komano-Yu hot spring inn (Rahman and Konagai 2017)

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4 Aratozawa Landslide

The earthquake caused a massive landslide, about 1300 m long, 900 m wide, and thicker than 100 m, to be detached from the gentle mountain flank of Kurikoma, the secondary volcaniclastic deposits (weakly cemented rhyolitic tuffs), leaving a vast depression akin to a hole punched in the mountainside (Fig. 8). The total volume of the detached soil mass, estimated to be 67 million m3, broke into some blocks and moved over an underlying gentle slip surface dipping at about 2.6 degrees south-southwest and developed through a layer of alternating sandstones and siltstones beneath the rhyolitic tuff (Kazama et al. 2012).

Fig. 8
An aerial view of a large mass of land caved in at the top of a mountain.

Aratozawa Landslide and Mt. Kurikoma (Photo by K. Konagai, June 15, 2008)

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Figure 9 compares the pre- and post-earthquake topographies of the Aratozawa Landslide area. The mountain flanks on the west and east sides of the landslide exhibited a tiered profile, suggesting similar mountain blocks fell one on the other in past similar landslide events. Fig. 9(b) also shows one of the fault ruptures traces that the reconnaissance team of the Research Institute of Earthquake and Volcano Geology, the National Institute of Advanced Industrial Science and Technology (AIST), identified and reported (Yoshimi et al. 2008a, b; Maruyama et al. 2009). Though the causal relationship is unclear, scars of the significant landslides, including those that occurred in the past (recognized from the mountain flank’s tiered surface profile), line up on the extension of this fault rupture (See Cross-section AA’ in Fig. 9(b)).

Fig. 9
Two aerial terrain maps which marks the location of the tributary of the Nihasama river and the surface rupture. A line graph between elevation in meters and distance in meters. A line begins at (0, 500) and drops to (780, 300). Values are estimated.

Hill-shade maps of the (a) Pre-quake terrain of Aratozawa: The photogrammetric image was obtained by using aerial photos of Sept. 23, 2006, Geospatial Information Authority of Japan), and the (b) post-quake terrain of Aratozawa: Orthophoto of the area immediately after the quake was laid over the hill-shade illustration as a semi-transparent layer. Surface rupture trace was reported by Yoshimi et al. (2008a, b). Yellow broken lines show the landslide extent

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Most blocks of the landslide mass moved over 200 to 300 m toward open areas along a small tributary of the Nihasama River flowing from north to south and the reservoir of Aratozawa Dam. The frontal blocks hit the eastern valley wall of the small tributary, and a fraction of the landslide mass of about 1.5 million m3 entered the reservoir, causing a sunami (seiche).

This fraction of soil mass, about 2% of the total volume of the landslide mass, was calculated from both the changes in bathymetries before and after the earthquake and the 2.4 m increase in the reservoir’s water level from 268.5 m to 270.9 m. Due to this unusual tsunami surge, mud marks remained along the shores of the reservoir, indicating the tsunami inundation heights shown in Fig. 10 (Johansson et al. 2008). Based on the measured tsunami inundation heights, Nomura et al. (2009) attempted to estimate the velocity of the landslide mass that entered the reservoir.

Fig. 10
An aerial map with several bars marked over several points with a number at the end.

Seiche heights (unit: m), with respect to lake elevation before the earthquake (268.5 m), as measured in the field on July 13 and July 25, 2008. (Johansson et al. 2008)

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Numerical simulations of the tsunami surge were conducted based on the nonlinear long-wave theory. The governing equations for the tsunami surge with the effect of the reservoir bed uplifts are given on the Cartesian coordinates (x, y) as:

$$ \frac{\partial \eta }{\partial t}+\frac{\partial M}{\partial x}+\frac{\partial N}{\partial y}-\frac{\partial \xi }{\partial t}=0 $$
(6)
$$ {\displaystyle \begin{array}{l}\frac{\partial M}{\partial t}+\frac{\partial }{\partial x}\left(\frac{M^2}{D}\right)+\frac{\partial }{\partial y}\left(\frac{MN}{D}\right)+ gD\frac{\partial \eta }{\partial x}\\ {}+{f}_B\frac{M\sqrt{M^2+{N}^2}}{D^2}=0\end{array}} $$
(7)
$$ {\displaystyle \begin{array}{l}\frac{\partial N}{\partial t}+\frac{\partial }{\partial x}\left(\frac{MN}{D}\right)+\frac{\partial }{\partial y}\left(\frac{N^2}{D}\right)+ gD\frac{\partial \eta }{\partial y}\\ {}+{f}_B\frac{N\sqrt{M^2+{N}^2}}{D^2}=0\end{array}} $$
(8)

where, M = uD = flux in x direction with u= velocity in x direction, N = vD = flux in y direction with v = velocity in y direction, h = initial depth of water, η = change in water level, D = h + η = total depth of water, ξ = reservoir bed’s uplift, and fB = gn2/D1/3 = frictional coefficient of reservoir bed with n = Manning’s coefficient.

Equation (6) shows the mass conservation law, including the effect of dam bed uplifts. Equations (7) and (8) describe motions in the x and y directions. They have advection terms, hydrostatic pressure terms, and frictional terms based on Manning’s formula for free surface flows.

Figure 11(a) shows the change in the depths of the reservoir bed, which was obtained by subtracting bathymetry data in 1998 from that immediately after the earthquake (from June to July 2008). The simulation reproduced the effect of debris mass entering the reservoir by lifting reservoir-bottom elements one by one from where the debris mass first entered the reservoir to the point where the frontal end of the mass finally stopped (see Fig. 11(b)). The mass’s inflow velocity, V, was obtained by dividing the entire stretch of the debris mass immersed in water by the time for the whole reservoir-bed uplift process.

Fig. 11
A map of the reservoir bed which is color coded for the depth ranging from 100 to negative 10 meters. The debris mass entered the reservoir from the North and flew through the south.

(a) Change in the depths of the reservoir bed and (b) schematic presentation of the way to reproduce the effect of debris mass entering the reservoir by lifting reservoir-bottom elements one by one (after Nomura et al. 2009)

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Bars and lines in Fig. 12 are, respectively, the measured and simulated tsunami inundation heights at the points along the reservoir shoreline where the heights of the tsunami marks were measured (Fig. 10). The simulated inundation heights are affected mainly by the velocity V of the debris mass that entered the reservoir and the reservoir’s bed frictional coefficient fB in Eqs. (6) to (8). Gradually changing these key parameters, the numerical simulation result was accommodated to the optimum solution in the least square sense.

Fig. 12
1. Three bar graphs plots the inrushing velocity in meters per second for velocities 13.3, 6.7, 4.4 meters per second. 2. Three bar graphs plots the inrushing velocity in meters per second for frictional coefficient of 0.005, 0.01, and 0.02.

Observed and simulated tsunami run-up heights along the reservoir shore line (Nomura et al. 2009)

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The left side of Fig. 12 shows the effect of the inflow velocity on the simulated tsunami heights, while the right side shows the effects of reservoir bed friction. Simulated tsunami heights are highly susceptible to the landslide mass velocity, while they are less sensitive to the reservoir bed friction. This tendency is particularly true near the source of the tsunami wave (open circles in Fig. 12). Through the least square optimization of the tsunami heights, the inflow velocity V was estimated to be around 4.4 m/s (see Fig. 13).

Fig. 13
A line graph plots the root mean square of error in meters and inrushing debris mass velocity in meters per second. The line begins at (2.5, 1.9), drops to (4, 1.4), rises slightly to (7, 1.6) and remains flat up to (14, 1.6). Values are estimated.

Root mean square error between estimated and measured tsunami inundation heights (Nomura et al. 2009)

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It is probably premature to deduce that the entire landslide mass had this velocity of 4.4 m/s only from the abovementioned simulations for the tsunami caused by the 2% volume of the whole landslide mass. As for the frontal blocks of the landslide mass that hit the eastern valley wall of the small tributary of the Nihasama River, Kazama et al. (2012) considered that these blocks that hit the valley wall might have caused a ground motion, which may have been recorded by seismographs at Aratozawa dam, and nearby seismometer stations. Examining seismic records at these stations and assuming that the propagating velocity of the impact-induced ground motion was about 3 km/s, they deduced that the blocks hit the valley wall 60 s after the landslide initiation. During the 60 s, the frontal blocks moved over about 320 m distance. Thus, they estimated that the velocity of the blocks was about 5.3 m/s, which was slightly faster than the tsunami-mark-based velocity of the debris mass that entered the reservoir.

5 Conclusions

A 7.2 Magnitude earthquake occurred about 10 km northeast of Mt. Kurikoma, a complex stratovolcano comprising some volcanic edifices, at 8:43 JST on June 14, 2008. Though the quake hit the rural area, and thus sparsely distributed dwellings suffered minor damage, 17 were confirmed dead, and six are still missing. Though the quake-induced mass-wasting events were blamed as the primary cause of deaths in this earthquake, they left tremendous marks of soil deformations and tsunami runups along a dam reservoir, which provided unique opportunities to gain insights into the dynamics of the mass-wasting events. This paper summarized the findings from our observations in the referred papers (Nomura et al. 2009; Rahman and Konagai 2016, 2017) and compared these findings with the other researchers’ inferences from different approaches.

Ikeya et al. (2009) and Nomura et al. (2009) estimated the time for the fluidized debris mass from the eastern flank of Mt. Higashi-Kurikoma to reach the “Komano-Yu” hot spring inn (38.9377°N 140.8378°E), where seven people were killed in wet soil and rubble. They both used maximum flowing slurry velocities calculated from the observable super-elevations remaining at particular locations of the Dozozawa River Channel to adjust the parameters for the numerical tools that they used (A numerical simulation tool introducing the erosion rate equation (Miyamoto and Ito 2002) and the Depth-Averaged Material Point Method (DAMPM) by Abe and Konagai (2017), Abe et al. (2007), respectively. The estimated times were 9 min and 40 s (Ikeya et al. 2009) and 10 min (Nomura et al. 2009). As a matter of course, they are very close to each other.

We must be aware that the mud-mark-based super-elevations are not identical to the maximum super-elevations reached during the unsteady debris flow event. The actual peak velocities of vreal are often underestimated, particularly near the debris source where the unsteady nature of the flowing debris slurry is more predominant. Rahman and Konagai (2016, 2017) conducted a number of SPH simulations for a variety of flume configurations. Their result showed that the mud-mark-based estimates of the velocities vmud can be related to vreal by the following equation (same as Eq. (4)):

$$ \frac{v_{mud}}{v_{real}}=1-{e}^{-\beta X}\kern0.62em for\;X>1\;\mathrm{with}\;\beta =0.4880 $$

where, X is the normalized distance given by:

$$ X=\frac{x}{L}=\frac{\mathrm{Distance}\ \mathrm{from}\ \mathrm{source}\ \mathrm{front}}{\mathrm{Initial}\ \mathrm{source}\ \mathrm{length}} $$

Rahman and Konagai (2016, 2017) also developed an iterative approach to determine objectively bend radii along a natural flume with abrupt changes. Adjusting the slurry velocities using the above equations, Rahman and Konagai (2017) estimated that the debris mass reached Komano-Yu hot spring inn about 8 min after the debris flow initiation.

The earthquake caused a massive landslide, about 1300 m long, 900 m wide, and thicker than 100 m, to be detached from the gentle mountain flank of Mt. Kurikoma (Aratozawa Landslide). The total volume of the detached soil mass, estimated to be 67 million m3, broke into some coherent blocks. These blocks moved over 200 to 300 m toward open areas along a small tributary of the Nihasama River flowing from north to south and the reservoir of Aratozawa Dam. The frontal blocks hit the eastern valley wall of the small tributary, and a fraction of the landslide mass of about 1.5 million m3 entered the reservoir, causing a tsunami. Nomura et al. (2009) attempted to estimate the velocity of the landslide mass from the remaining tsunami inundation marks. Through the least square optimization of the tsunami heights by changing two critical parameters for the simulation, namely the velocity of the landslide mass entering the reservoir and the friction of the reservoir’s bed, they estimated the velocity to be around 4.4 m/s. This velocity is slightly smaller than that (5.3 m/s) of the frontal blocks to move over a 320 m distance until it hit the valley wall of the small tributary of the Nihasama River; Kazama et al. (2012) deduced this velocity by examining seismic records from Aratozawa Dam and nearby seismometer stations.

As stated above, mud-marks-based estimation of velocities of mass-wasting processes from different approaches showed similar results. In every approach, it was unavoidable that we had unknown parameters because we were dealing with a mass-wasting process whose interior can hardly be seen and inferred. We must keep comparing and reviewing different approaches because we will always need clarification about the unknown parameters in each approach and refine the estimated results, which will help us be prepared for the next significant events in similar areas.