1 Introduction

The Great East Japan Earthquake that occurred on March 11, 2011, resulted in tsunami waves reaching vast areas along the Pacific coast of Japan. These waves extended several kilometers inland, engulfing numerous residential areas and resulting in a significant number of victims. Among these, there were instances where embankments constructed for expressways on flatland areas mitigated the tsunami damage. In the vicinity of the Sendai-tobu highway, it was reported that the presence of the highway’s approximately 10-m-high embankment altered the flow direction of the ascending tsunami, preventing the area from being flooded (Goto et al. 2011, Sugawara et al. 2013, Tokida and Tanimoto 2014). Consequently, recent developments in Japan have proposed a multiplied defense system utilizing expressway embankments in flatland areas, with certain regions designating these embankments as tsunami evacuation sites (Sendai city 2011). This represents a significant initiative that assigns a new role to transportation infrastructure in mitigating catastrophic and large-scale natural disasters. However, the current design framework for Japanese road embankments does not require performance specifications to withstand both seismic motion and tsunami impacts. Moreover, during the Great East Japan Earthquake, transportation infrastructure near coastal areas, including roads and railways, suffered extensive damage, resulting in the structural devastation of some sections (Koseki et al. 2012; Koseki and Shibuya 2014). To establish a multiplied defense system against tsunamis utilizing road embankments, it is necessary to present a design philosophy that accounts for the deformation and collapse mechanisms of road embankments affected by tsunamis following seismic events.

Regarding the erosion and failure caused by overtopping flow, such as tsunamis acting on embankments, many research results have been reported. Coleman et al. (2002) meticulously observed the erosion process during overtopping experiments on scaled-down model levees installed in open channels, proposing an equation to estimate the shape of levee erosion. Fujisawa et al. (2007) conducted overtopping experiments on scaled-down model levees, showing that the destruction phenomena involve the formation of an erosional scarp and its upstream movement, suggesting the effectiveness of protective measures against such phenomena. Dazzi et al. (2019) developed a high-accuracy levee breach simulation model by incorporating erosion models for cohesive and non-cohesive ground materials into the 2D shallow water code. However, these studies often focus on river levees and dams, not specifically on transportation infrastructure. In contrast, Watanabe et al. (2020) reported results from scale model experiments targeting railway embankments, demonstrating that even seismically robust railway embankments could be rapidly eroded by overtopping water, with erosion of the base ground accelerating the embankment erosion. They also highlighted the effectiveness of geosynthetic-reinforced soil structures as a countermeasure. The findings presented by Watanabe et al. (2020) indicate the best reinforcement methods for embankments as part of a multiplied defense system. However, studies specifically focusing on road embankments are scarce. To develop effective countermeasures for the safety of the road embankments, it is crucial to clarify the mechanisms of combined disasters involving earthquakes and tsunamis.

Therefore, this study conducted scale model experiments to observe the deformation and erosion behavior of expressway embankments affected by tsunamis following seismic events. The experiments utilized a device equipped with a shaking table to simulate seismic motion at the downstream end of an open channel designed to replicate tsunamis. After subjecting the model embankment to seismic motion, the first wave of breaking bores was introduced, followed by a long-duration overtopping experiment to simulate the effects of a tsunami.

2 Test Materials and Test Procedures

Figure 1 shows a schematic diagram of the experimental apparatus utilized in this study, while Fig. 2 shows a photograph of the experimental setup. The apparatus employed in this research connects a shaking table with a soil container (3000 mm in length) for simulating seismic motion to an open-channel (9000 mm in length) designed to simulate tsunamis and river floods. This setup enables the execution of shaking tests to simulate earthquake motion, followed by hydraulic experiments to mimic tsunamis using a single experimental apparatus. The shaking table’s performance capabilities include a maximum acceleration of 10 m/s2 and a maximum frequency of 7 Hz, allowing it to simulate significant seismic events observed in Japan. In addition, the payload of the shaking table is 30 kN. A soil container measuring 800 mm in height, 3000 mm in length, and 600 mm in width is installed on the shaking table, within which model embankments can be constructed. The open-channel comprises a 5000-mm long water channel and a 4000-mm water storage tank, with a movable weir positioned between them. Simulating breaking bores is possible by storing a predetermined amount of water in the water storage tank and then releasing the movable weir. By controlling the amount of water stored and the elevation speed of the movable weir, the flow speed of the tsunami can be altered. Furthermore, continuous operation of a pump connected to the storage tank via piping enables long-duration overtopping experiments following breaking bores. The sides of the soil container and open-channel are made of reinforced glass, allowing observation of the model embankments’ behavior during shaking and tsunami attacking. Image analysis was performed using high-speed cameras in this experiment. Using this experimental setup, which possesses the aforementioned features, experiments were conducted involving the application of seismic motion to model embankments followed by the impact of tsunamis.

Fig. 1
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Schematic of experimental apparatus for simulating earthquake motion and tsunami. a Elevation view. b Plan view

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Fig. 2
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Photograph of experimental apparatus taken from upstream

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Figure 3 shows a schematic diagram of the model for the expressway embankment. The model embankment is designed based on a provisional two-lane expressway in full scale. The shape of this model embankment was determined with reference to the Do-o Expressway in Hokkaido, Japan, where the road embankment has a typical cross section of Japan’s provisional two-lane expressways, and there is a potential risk of tsunami inundation in that region (Hokkaido Government Office 2022). The scale ratio of the model embankment is 1/20. The model embankment was constructed in the soil container, with a crest width of 720 mm, an embankment height of 300 mm, and a slope gradient of 1:1.8, all built on a horizontal base ground with a thickness of 50 mm. Additionally, a slope with a gradient of 1:1.5 was provided at the upstream end of the base ground to prevent obstruction of the tsunami flow. In this study, model embankments undergo shaking experiments at 1 g. Consequently, the scaling law proposed by Iai (1989) was applied. The validity of the scale-low is shown below. Fujioka et al. (2016) reported a case of highway collapse during the Great East Japan Earthquake. In this report, the maximum settlement of the embankment crest was 2.5 m. Iai (1989) proposed a scaling factor of l1.5 (scale ratio, l = prototype/model) for the displacement caused by a 1-g shaking test. l1.5 was converted to the displacement of the prototype by applying the crest settlement shown in Table 1, and the displacement was 2.84 m for Case 2 and 3.91 m for Case 3. These results were similar to the cases reported by Fujioka et al. (2016). Therefore, the reproducibility of the model embankment used in this study to the actual embankment is ensured with a certain accuracy.

Fig. 3
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Schematic of model embankment and layout of measuring instruments

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Table 1 Summary of experimental conditions
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Figure 4 shows the particle size distribution curve for the geomaterial used in this study, derived from the “Test method for particle size distribution of soils” (JIS A 1204). Furthermore, Fig. 5 shows the compaction curve obtained from the “Test method for soil compaction using a rammer” (JIS A 1210, Method A-a). The embankment and supporting geomaterials consisted of a mixture of Silica sand No.4 and Kasaoka clay in a weight ratio of 9:1. The base ground was compacted to a degree of compaction, Dc (dry density, rd/maximum dry density, rdmax × 100) = 90% and a moisture content, w = 8%, while the embankment was adjusted to a Dc = 85% and w = 8%. The embankment was constructed by compacting in six layers, each 50 mm thick. The rationale for setting these state quantities for both the base ground and the embankment was determined through trial and error with preliminary tests to replicate the damage patterns observed in expressway embankments affected by high intensity shaking (equivalent to a level 2 earthquake in the current design standards for road structures in Japan).

Fig. 4
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Grain size distribution of the geomaterials used in the experiments

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Fig. 5
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Compaction curve of the geomaterials used in the experiment

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Measurement instruments included five pore water pressure transducers on the base ground and eight accelerometers within the embankment. Three laser displacement transducers were installed at the center of embankment crest, the shoulder of the embankment at upstream, and the center of the slope of the embankment at upstream. The embankment’s crest was coated with cement spray to simulate the stiffness of the road pavement surface. The thickness of the coating applied via cement spraying to the model embankment was 5 mm, which corresponds to a scaled representation of a 100-mm pavement in actual dimensions. Additionally, for the purpose of simplifying the visualization of the embankment’s deformation behavior during shaking, a total of 65 markers were placed within the embankment at intervals of 50 mm × 90 mm. Furthermore, high-speed cameras were used to capture the deformation of the cross section of the embankment during shaking and tsunami attacking.

Table 1 summarizes the experimental cases. In this experiment, three cases were conducted with the settlement of the embankment crest as the parameter. The seismic waveform was set to a 5-Hz sine wave with 20 cycles, and three cycles each of tapered waves were added before and after the 20 cycles with uniform acceleration amplitude. In Cases 2 and 3, the initial base acceleration was first set at 1 m/s2 and was increased in increments of 1 m/s2 until 6 m/s2 on Case 2, 7 m/s2 on Case 3. The maximum acceleration almost corresponds to a level 2 earthquake in the current Japanese design standards which has to be considered for the seismic design of important earth structure (Japan Road Association 2019). As for the tsunami conditions, two types of waves were sequentially introduced in this experiment. Initially, breaking bores, which break and envelop as described previously, were generated. This was accomplished by storing a predetermined amount of water in the storage tank located upstream of the experimental apparatus shown in Fig. 1, with the movable weir closed, and then releasing the movable weir. The amount of stored water and the lifting speed of the movable weir were set based on preliminary experiments to a speed at which the tsunami could ascend to the embankment crest. Immediately after confirming that the tsunami had reached the embankment and ascended the slope following the generation of breaking bores, the pump was activated to introduce water into the upstream channel, promptly starting the overtopping experiment. The depth of overtopping was adjusted to 50 mm for Cases 1 and 3, and 100 mm for Case 2. In the assessment of overtopping depth, the reference point was established at the height of the upstream embankment shoulder. For Cases 2 and 3, the reference point was defined as the height of the upstream embankment shoulder post-seismic motion.

3 Test Results and Discussions

3.1 Seismic Behavior of Model Embankment

Figure 6 shows the displacement velocity vectors of the model embankment’s side during shaking at an input acceleration of 5 m/s2 during the 1st, 10th, and 20th cycles in Case 2, estimated through particle image velocimetry (PIV) analysis. The velocity vectors in the figure are represented in warmer colors for larger magnitudes and cooler colors for smaller magnitudes. The entire area is predominantly warmer in color at the 10th wave, indicating overall higher velocities, while at the 20th wave, regions of reduced velocity have emerged. At the 10th wave, the model embankment behaves elastically, with the entire embankment displacing in response to the shaking table’s vibration speed. However, by the 20th wave, increased acceleration responses at the top of the embankment and a reduction in soil stiffness at the elemental level have occurred, leading to the formation of plasticized areas within the model embankment. This results in uneven velocity vectors (displacement distribution).

Fig. 6
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Displacement velocity vectors of the embankment cross section during shaking with the input acceleration amplitude of 5 m/s2 (Case 2)

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Figure 7 shows the condition of the embankment slope after shaking in Case 3, where the height of the embankment was reduced due to the seismic motion. This reduction in height is thought to be influenced by the occurrence of sliding on the slope induced by the shaking. The settlement at the crest of the embankment increased gradually from an acceleration of 5 m/s2, reaching approximately 45 mm at the end of the shaking. Figure 8 shows a sketch of the cracks that developed on the slope and crest of embankment. Cracks were observed at both the crest and the slope. These cracks were visible to the naked eye starting from an acceleration of 5 m/s2, similar to the settlement. Focusing on the markers within the embankment after the shaking ceased, it was evident that those closer to the embankment slope moved towards the toe of the slope, confirming the occurrence of sliding on the slope. This slip line manifested within the embankment and does not extend to the base ground.

Fig. 7
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Deformation of the embankment after shaking in Case 3

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Fig. 8
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Cracks on the embankment surface observed after shaking in Case 3

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The collapse patterns observed in the model embankment align qualitatively with those of expressway embankment failures caused by past earthquakes in Japan, as reported by Tameshige et al. (2009). This suggests that the current experiment, having established soil conditions conducive to simulating the actual phenomena, can be considered a model experiment that generally replicates real embankment occurrences.

3.2 Pore Water Pressure and Erosion Process During Tsunami Attack

In the tsunami experiments, the stability of the upstream slope with and without shaking, as well as the embankment erosion during tsunami overtopping, were observed. The experiments were conducted using a breaking bores generator located upstream. The tsunami flow velocity and overtopping water depth were adjusted by controlling the amount of water stored in the upstream tank and the lifting speed of the movable weir, which serves as the breaking bores device. In each case, immediately after the arrival of the first wave, known as breaking bores, the pump was activated to commence continuous overtopping without delay. There were no significant changes in the condition of the upstream embankment slope following the arrival of the breaking bores in each of the cases. Figure 9 a and b show the changes in pore water pressure, uw during the tsunami attack for Cases 1 and 2, respectively. The elapsed time, t = 0 s in the figures is defined as the moment when breaking bores reached the toe of the upstream slope. uw increased at all measured locations when the breaking bore was reached. This increasement in pore water pressure is not attributed to the infiltration of tsunami water into the embankment, but rather to the arrival of overtopping tsunami water on the embankment surface, which eliminates the space for trapped air to escape, thereby measuring an increase in trapped air. Among the pore pressure observation points, uw − 1 exhibits the lowest effective overburden pressure, s′. At Point A, the maximum ratio of pore air pressure to effective overburden pressure, (uw/s′)max was (uw/s′)max = 0.30 in Case 1 and (uw/s′)max = 0.43 in Case 2 on breaking bore. In Case 2, subjected to seismic motion, the value of (uw/s′)max exhibited a slight increase. Therefore, it is presumed that in the initial phase of the tsunami arrival, the pore pressure within the soil increased due to trapped air, momentarily reducing the effective stress within the embankment.

Fig. 9
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Changes in pore water pressure during a tsunami attack. a Case 1. b Case 2

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The increase in trapped air within the soil is known to act as a barrier to the infiltration line during rainfall events (Cho 2016; Liu et al. 2021). Furthermore, the effects of tsunamis have been reported as a challenge in numerical analyses (Abdollahi and Mason 2019). The behavior of the trapped air increase shown in Fig. 9 represents one of the few datasets measured during tsunami events, serving as foundational data for further detailed studies on variations in air permeability coefficients according to soil properties. Additionally, in Case 2, which has a history of seismic motion, the increase in pore water pressure was greater than in Case 1. This increase is suspected to result from localized water ingress through cracks generated by the seismic motion (Kawajiri et al. 2014).

Figure 10 shows the flow velocity vectors of breaking bores immediately after reaching the shoulder of the embankment and as the tsunami ascends the slope in Case 2. The breaking bores first reached the ground surface at the toe of the embankment on the upstream side. However, no erosion or deformation of the embankment slope was observed after the action of the tsunami. The tsunami, upon ascending the slope, became a plunging flow near the shoulder of the embankment, where a flow resembling a detached stream was identified. Watanabe et al. (2020) reported in their experiments on a railroad embankment that near such upstream crests, tsunami wave overtopping exerted tensile forces that caused the ground to be separating from the slope. Velocity vectors obtained in this study are similar to those of Watanabe et al. (2020), suggesting that separating flow may occur during wave overtopping regardless of the type of embankment.

Fig. 10
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Velocity vector when breaking bores reach the upstream embankment slope

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Figure 11 shows the erosion process of the embankment during overtopping in each experimental case. The moment marked as 0 s in the figure corresponds to the time when overtopping water reached the top of the embankment on the upstream side. The erosion of the model embankment by overtopping water is expected to have a three-dimensional shape. However, in the present study, we evaluated the data on the reinforced glass side of the embankment as a representative cross-sectional data because the erosion process can be observed. Note that, it was visually confirmed that gully erosion did not cause local collapse during and after the overtopping experiment. In Case 1, where no seismic motion was applied, erosion began around the toe of the embankment and progressed towards the back of the slope. However, in Cases 2 and 3, which have a history of seismic motion, the progression of the erosion front was noticeably faster than in Case 1. At 20 s after overtopping commenced in Case 1, only part of the slope was eroded, whereas in Cases 2 and 3, a significant portion of the downstream slope had disappeared. It was anticipated that erosion would progress most rapidly in Case 3 due to the greater settlement of the embankment crest and deeper overtopping water depth compared to Case 2; however, the extent of erosion progression was restrained in Case 3. The precise cause of this observation remains unclear, but it is possibly due to the embankment becoming more compacted from the larger settlement induced by seismic motion, thereby increasing its resistance to overtopping water. Nonetheless, an important insight gained here is that embankments subjected to seismic motion are more susceptible to accelerated erosion by overtopping water. These results indicate that when embankments settle due to an earthquake, leading to relatively higher anticipated inundation depths and the potential for overtopping, measures to prevent the settlement of the crest are necessary for embankments expected to function as part of a multiplied defense system.

Fig. 11
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Erosion process of embankment by overtopping water

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Figure 12 shows the relationship between the subsidence of the embankment crest due to seismic motion and the duration until the embankment crest was eradicated by overtopping water. Evaluating all experimental cases uniformly is challenging due to the variations in overtopping water depth. However, there appears to be a discernible relationship between the settlement of the embankment crest and the time until its eradication. This implies that with an increase in experimental cases, it might be possible to quantitatively assess the durability of embankments against tsunamis using the settlement of the embankment crest.

Fig. 12
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Relationship between the amount of settlement of the embankment crest due to earthquake motion and the time of disappearance of the embankment crest due to overtopping

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4 Conclusions

In this study, model experiments were conducted to observe the deformation and erosion behavior of expressway embankments subjected to tsunamis following seismic motion. After applying seismic motion to the model embankments, the first wave of breaking bores was introduced, followed by a simulation of prolonged overtopping by the tsunami. The findings are summarized as follows:

  • Within the embankments impacted by the tsunami, an immediate rise in what is presumed to be pore air pressure was observed right after the arrival of the breaking bores, followed by an increase in pore water pressure during the subsequent overtopping. In embankment exposed to seismic motion, both pore air pressure and water pressure demonstrated an increase compared to those not subjected to such seismic motion.

  • The breaking bores ascending the slope became a plunging flow near the top of the embankment, leading to the emergence of a flow resembling a detached stream. Such tsunami behavior, which has been demonstrated in previous studies, indicates that tensile forces capable of detaching the soil might act on the slope and near the top of the embankment due to the overtopping of the tsunami. This experiment corroborated the possibility of such forces.

  • Embankments subjected to seismic motion experienced accelerated erosion following the overtopping. These results suggest that when embankments settle due to an earthquake, leading to relatively higher anticipated inundation depths and the potential for overtopping, measures to prevent the settlement of the crest are necessary for embankments expected to function as part of a multiplied defense system.

In this paper, we were able to measure the behavior of pore air and water pressure at the time of tsunami arrival, phenomena not previously studied, and experimentally demonstrated that embankments subjected to seismic motion exhibit lower durability against overtopping tsunami waters. However, these findings are based on limited geotechnical conditions. For instance, embankments composed of cohesive soils may exhibit different deformation modes due to seismic motion and, consequently, may show different durability against subsequent tsunamis compared to the results presented here. Additionally, actual embankments often feature vegetation, and the quantitative assessment of the role of grasses against the action of overtopping water remains a challenge for future research (Zhu and Zhang 2016).