1 Introduction

The Hokkaido Eastern Iburi earthquake occurred at 3:07 a.m. on September 6, 2018, with a JMA magnitude of Mj = 6.7. It was inland earthquake centered at a depth of approximately 37 km in the eastern Iburi region (Ishikawa et al. 2021). The earthquake caused widespread slope failures in Atsuma. The slope collapse in the Yoshino district of Atsuma-town, where collapsed sediment traveled for a relatively long distance and impacted houses, claimed 36 lives (Fire and Disaster Management Agency 2018; Kawamura et al. 2019; Osanai et al. 2019). Moreover, the number of earthquake-induced slope failures is greatest in Japan (Kawamura et al. 2019). In addition, the number of people affected by earthquake-induced geotechnical events is as large as that in the landslide occurred in Nishinomiya City, Hyogo Prefecture, triggered by the 1995 Hyogo-ken Nanbu earthquake (Sassa et al. 1996). Such large-scale slope failures occur in areas where fallen pumice deposits from volcanic eruptions are distributed on sedimentary rocks (Kawamura et al. 2019), and natural slope failures composed of volcanic-derived soils have been reported from the Kumamoto earthquake (Mukunoki et al. 2016; Kasama et al. 2018) and the Iwate-Miyagi Nairiku earthquake (Kazama et al. 2012). Since Japan is a volcanic country with a number of areas where fallen pumice and volcanic ash soils are distributed, discussion of the mechanism of the widespread and large-scale slope failure in Atsuma, Hokkaido, Japan is of great importance for planning slope disaster prevention and mitigation measures for future earthquakes. Results of laboratory tests on collected samples and stability evaluation of the slopes would provide valuable data for systematization of slope failure phenomena during earthquakes.

A number of studies have been reported for understanding mechanism of the slope failure by the Hokkaido Eastern Iburi earthquake; comprehensive reports by Kawamura et al. (2019) and Osanai et al. (2019) suggest that a fine-grained region with high-water content near the base of a pumice layer called Ta-d, which was deposited approximately 9000 years ago, may have been the slip surface. Zhang et al. (2019) observed grain fracturing and liquefaction at Ta-d. Li et al. (2020) reported occurrence of liquefaction at Ta-d. Li et al. (2020) conducted consolidated-undrained cyclic loading triaxial tests under saturated conditions on an intact sample in an undisturbed and unsaturated state. Aoki et al. (2022) reported that suction in the soil above Ta-d (i.e., Ta-a, b, c) is sensitive to rainfall, while the suction in the soil at Ta-d remains low due to constant high saturation, and no increase or decrease in suction is observed due to rainfall infiltration. The results indicate that the rainfall two days before the earthquake did not affect the slope failure. These studies have been conducted in the fields of geotechnical engineering, geomorphology, and sediment hydraulics, and they all provide important data for understanding the mechanisms of slope failure caused by the Hokkaido Eastern Iburi earthquake from a mechanical viewpoint in geotechnical engineering. For understanding slope failure mechanism from the mechanical point of view, geotechnical stability assessment for examining the mechanical balance of soil mass is important, as it can be used for considering highly risky slopes and reinforcement with steel bars.

Geotechnical stability evaluation requires use of cohesion and internal friction angles as soil strength parameters. Li et al. (2020) evaluated strength properties from stress paths using consolidated-undrained monotonic loading triaxial tests in addition to the consolidated-undrained cyclic loading triaxial tests described above though did not address soil strength parameters. In addition, the mechanisms of slope failure during earthquakes have been investigated by relatively specific tests such as cyclic direct box shear tests (Wakai et al. 2010, Deng et al. 2011a), ring shear tests (Wang and Sassa 2002; Suzuki et al. 2007) and plane strain compression tests (Deng et al. 2011b). Although these tests more faithfully reproduce shear behaviors of soil elements during slope failure, they are rarely used in practice due to the difficulty in testing intact specimens and their special mechanisms. On the other hand, the single-surface shear test, which is used in practice owing to its simple testing device mechanism, easily reproduces K0 states of soil elements before shear and reproduces simple shear states with appropriate shear box spacing (Kim et al. 2012). Therefore, there have been reports (e.g., Shibuya et al., 2007; Kasama et al., 2018) on application of strength parameters obtained from direct shear tests to elucidate collapse mechanisms of geotechnical structures and natural slopes.

Most of the previous studies on the slope failure caused by the Eastern Iburi earthquake in Hokkaido, Japan refers to the particle crushing at the Ta-d. In recent years, studies using X-ray CT scan have been actively conducted in geotechnical engineering, and visualization of particle crushing in shear and loading has been reported (e.g., Otani et al. 2005). Therefore, direct box shear test with a small specimen is advantageous for understanding effects of shear strength and particle crushing.

Based on the above background, in this study, the authors conducted detailed trench observation of the failed slope, portable dynamic cone penetration tests, simple boring survey, and undisturbed specimens sampling at a slope failure site in Atsuma-town, Hokkaido, Japan. The undisturbed samples were subjected to mechanical tests with a direct box shear test apparatus that reproduces low confining pressures of natural slopes, and x-ray CT scans were performed before and after the mechanical tests so as to observe changes in the internal structure after direct box shear tests. The mechanical parameters obtained from the laboratory tests were used to evaluate seismic stability of the target slope as an infinite-length slope, and the failure mechanism was discussed. In this paper, the mechanical parameters from the direct box shear tests, which are standardized by the Japanese Geotechnical Society (JGS), are used to evaluate seismic stability of slope under earthquake conditions, with the aim of developing a method to obtain data for understanding the failure mechanism at an early stage after a disaster by using more convenient testing equipment that is widely used. This paper reports results of the evaluation of slope stability during earthquakes based on the above mechanical parameters.

2 Overview of survey locations and survey content

Figure 1, redrawn after Kawamura et al. (2019), shows a topographic map and the distribution of the failure locations near Atsuma-town, Hokkaio, where a large slope failure (red area in the figure) occurred. Elevation of the mountainous area where the slope failure occurred is approximately 150 to 200 m, and the slope failure occurred north of the epicenter. In the Yoshino district of Atsuma, 36 people lost their lives when a slope collapsed behind their homes. The area surveyed in this study is located in the Uryu district of Atsuma-town, approximately 5 km east of Atsuma-town hall. The maximum horizontal acceleration PGA observed in a seismograph installed by the Hokkaido government at the Atsuma-town hall as a nearby earthquake record (Japan Meteorological Agency 2018) was PGA = 285 Gal for the NS component and PGA = 368 Gal for the EW component. The seismograph installed by the Japan Meteorological Agency in Kanuma, Atsuma-town, approximately10 km south of the survey site, showed PGA = 647 Gal for the NS component and PGA = 838 Gal for the EW component, indicating that the horizontal acceleration was larger than that around the survey site.

Fig. 1
figure 1

Topographical map and seismic waveform around the epicenter of the 2018 Hokkaido Eastern Iburi Earthquake and investigate site (modified Kawamura et al. 2019)

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Figure 2 shows post-earthquake aerial photographs and pre-earthquake topographic maps of the area surrounding the study site (Fig. 2a) and the pre-earthquake surface elevation (Fig. 2b). Figure 2 is based on data published by the GSI (Geospatial Information Authority of Japan). The post-earthquake aerial photographs were taken by GSI on September 6 and 8, 2018. The pre-earthquake surface elevation shows data on the line connecting B-1, B-2, and B-3, where in situ tests were conducted. The failure slope in study is located on the left bank of a small river. The pre-earthquake topographic map shows that the affected area has a valley shape, and slope failures of up to 60 m in width and 180 m in length generally occurred along this valley after the earthquake. In situ tests were conducted at three sites, B-1, B-2 and B-3, whose details are shown in Table 1. In addition to the portable dynamic cone penetration test (DCPT, Japanese Geotechnical Society, 2015), a detailed trench observation of the slope failure section was conducted at each of the locations B-1 ~ 3. Trench observation was also conducted at B-2, where soil samples were collected by simple boring in the uncollapsed area near the observed a trench.

Fig. 2
figure 2

Topographic conditions of the surveyed slopes in this study based on data published by the GSI: a post-earthquake aerial photographs and pre-earthquake topographic maps, b Elevation of the ground surface when B-1, B-2, and B-3 are connected by a straight line

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Table 1 List of field investigation
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Figure 3 shows the main investigation methods used in this study: in situ simple boring, intact specimen sampling, and a direct shear test apparatus that simulates stress conditions at low-confining pressures. In B-1 ~ 2, undisturbed specimens were sampled for the direct box shear test, which was conducted as a mechanical test. In order to perform the direct box shear tests, the Intact specimens were sampled at B1 ~ 2 (Fig. 5), by placing a sharp-edged shoe on one end of a 60 mm inner-diameter acrylic cylinder and slowly pushing it into a ground (see Fig. 3b). The undisturbed specimens were sampled at Nd locally in the depth direction obtained from DCPT.

Fig. 3
figure 3

Overview of the main in situ investigations and direct shear test apparatus conducted in this study: a Status of simple borings on the survey slope, b Intact specimen sampling situation at low-Nd—value layer, c Constant pressure direct box shear test (CP test), d Constant-volume direct box shear test (CV test)

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In this study, we conducted constant pressure direct box shear tests (hereinafter referred to as CP test) corresponding to the drained condition and constant volume direct box shear tests (hereinafter referred to as CV test) corresponding to the undrained condition. The test apparatus used in each test complied with the standards of the Japanese Geotechnical Society (Japanese Geotechnical Society, 2009a, 2009b). The specimens were disks of 60 mm in diameter D of and 20 mm in height H. The results of calibration tests with Toyoura sand for both test apparatuses were comparable to the internal friction angles reported previously (Shibuya et al. 1997). The shear box spacing was 0.4 mm for both CP and CV tests. Shear was applied to a horizontal displacement of D = 7 mm.

Table 2 shows test conditions and results for the CP and CV tests. The vertical stress was σv = 20, 50 kPa for the CP test and σv = 20, 40 kPa for the CV test. The shear rate dD/dt was set to 0.02 mm/min for the CP test, and the CV test was conducted with different dD/dt shown in Table 2 to determine the shear rate dependence of the undrained shear strength, τmax. The CV test was also performed on the Remolded specimens with different dD/dt. dD/dt was determined by considering the performance limitation of the motor of the test apparatus, and it is inferred that the actual rate of slope failure was faster than those of the tests conditions. The Remold specimens were prepared by measuring the density of Intact specimens sampled in the manner shown in (Fig. 3b), then unraveling the specimens and reconstructing them in a shear box for direct box shear tests to obtain the same density. However, the Remold specimens had difficulty in simulating soil structures of the intact specimens and were denser than the intact specimens. In addition, all specimens were tested in an unsaturated state. Moreover, the two specimens shown in Table 2 were X-ray CT scanned before and after the tests to observe changes in their internal structures caused by shear.

Table 2 Test and specimen conditions of direct box shear tests
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3 Results of field survey and laboratory experiments

3.1 Field and physical test results

Figure 4 shows geological profiles estimated from detailed observation of the trench and profile of Nd.at B-1 ~ 3. Pyroclastic deposits (fa) erupted mainly from Trauma (denoted Ta) and Eniwa (denoted En) volcanoes and Shikotsu pumice fall-1 (denoted Spfa) are deposited around the study area (Kawamura et al. 2019). The eruption age of the Shikotsu primary tephra (Spfa-1), to which the volcanic soil belongs, is estimated to be 46,000 years, while those of the En-a and Ta-d deposits are 19,000 to 21,000 years and 9,000 years, respectively. The Ta-b deposit is a white pumice layer formed by the eruption of Trauma volcano in 1667. Here, the subscript alphabet or number indicates the eruption age unit (number) of the pyroclastic fall deposit. Nd obtained from the DCPT is approximately 0–3 up to a depth of approximately 1.5 m, and it tends to increase with depth below this depth, regardless of test sites. At depths greater than 1.5 m, Nd = 20 indicates a base layer, and a relatively low-strength soil layer with Nd = 0 ~ 3 is expected to be deposited on top of this base layer with a slope similar to that of the elevation.

Fig. 4
figure 4

Geological profile estimated from detailed observation of the trench and profile of Nd from DCPT

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Figure 5 shows trench of the soil layer to a depth of approximately 1.4 m at B-2. Between Ta-a, b and Ta-d, we can see black boulders and reworked tephras that were disturbed and redeposited by slope failure and landslide activities. B-1, which is closest to the crown of slope failure, shows pumice deposits from the volcanic activity of Mt. Clay. The undisturbed samples shown in Fig. 3b were sampled from Ta-d above the clay identified in B-1 and B-2. In B-3 at the bottom of the collapsed slope, Ta-a, b, and d were deposited approximately 0.6 m from each other. We also observed weathered mudstone below Ta-d. Although the interpretation of the reworked tephras remains an issue for the collapsed slopes in this study, the geological composition is consistent with the location of Ta-d, which is considered to be a slip surface, at the depth as reported by Zhang et al. (2019), Li et al. (2020), Aoki et al. (2022).

Fig. 5
figure 5

Cross section of trench at B-2 (Corresponds to the geological profile of B-2 in Fig. 4)

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Figure 6 shows the soil properties of the soil samples obtained from B-2 ((a) grain size distributions by sampling depth, (b) natural water content, wn and fine-grain content, Fc). The simple boring method did not allow us to sample a sufficient amount of soil for the physical test for samples up to 1.0 m from the soil surface due to compaction of the soil sample in the sampler, as well as to rhizomes. Therefore, Fig. 6 shows results for depths greater than 1.0 m. At the depths from 1.0 to 1.4 m, where the Nd values were low, the highest coarse grain content of the samples was obtained, and the fine-grain content tended to increase with depth. There is an area with high-water content (wn > 200%) at the depth between 1.2 and 1.7 m. Fc tends to increase with an increase in depth from this high-water content area to Fc > 50%. The area where wn is high and Fc increases corresponds to the boundary between the lower Ta-d layer and the strongly weathered clay in the cross section. These results indicate that the lower part of the Ta-d layer has been weathered. Chigira and Suzuki (2016) studied slope failures similar to that caused by the Hokkaido Eastern Iburi earthquake and reported that the slip surfaces in these failures.

Fig. 6
figure 6

Properties of the soil samples sampled from B-2: a Grain size distribution of sampled soil by each depth, b Profile of water content and fine-grain content

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consisted of halloysite-rich soils. Kameda (2021) reported that the Ta-d, which is assumed to be the slip surface of the slope that collapsed during the Hokkaido Eastern Iburi earthquake, was composed of soil rich halloysite and that this halloysite is tubular in shape and thus has a high-water retentivity. The halloysite is tubular in shape and has a high-water retention property. The high-water retention of Ta-d near the slip surface is consistent with that observed by Aoki et al. (2022). In other words, the areas of high wn and Fc shown in Fig. 6 might be understood as areas with high wn due to increased Fc caused by clays associated with halloysite formation and water retention depending on the shape of the halloysite.

3.2 Mechanical properties by direct box shear test

Wang et al. (2019) analyzed seismic records from the slope failure area of the Hokkaido Eastern Iburi earthquake and found that there was pulse-like acceleration ground motion in the seismic waveforms, which was qualitatively described as a decrease in the strength of the fallen pumice deposits. Ishikawa et al. (2021) found that short-period waves without long-period (> 1 s) components existed in the area north of the epicenter where a number of slope failures occurred and noted that such differences in seismic waveforms affected the risk of slope failure during the earthquake.

Chen et al. (2021) focused on the pulse-like ground motion (PLGM) observed in the Hokkaido Eastern Iburi earthquake and performed discontinuous deformation analysis (DDA). They found that the PLGM may explain the difference in slope failure characteristics between the Kumamoto and the Hokkaido Eastern Iburi earthquakes. As shown above, the influence of ground motion by pulse-like seismic waveforms is pointed out as a cause of slope failure in the Hokkaido Eastern Iburi earthquake. For geotechnical stability assessment for which the influence of such seismic waveforms is considered, the Newmark method, which allows to calculate displacement of an analyzed slope, has been reported to be useful in most cases (Romeo 2000; Kasama et al. 2018; Shinoda et al. 2018, 2019; Kokusho 2019). The Newmark method is effective in evaluating movement of soil masses collapsed by seismic motion. On the other hand, it is also important to use a simpler analytical model to predict location of slope failures easily and quickly in order to predict occurrence of slope failures due to seismic motion in a wide area, as in the case of the Hokkaido Eastern Iburi earthquake. In this study, we focus on the shear strength of the soil elements induced by seismic motion. It is known that the shear strength of soil elements with elasto-viscoplastic properties depends on the shear rate (Ovando-Shelley 1995; Duttine et al. 2008; Shibuya et al., 2008; Kokusho 2019). Kameda (2022) have reported rheological properties for the Ta-d soil type investigated in this study. In this study, direct shear tests were conducted on intact and remolded specimens to investigate the strength properties of Ta-d by varying shear rates and drainage conditions, which are the basic controlling factors for shear strength of soil elements.

Figure 7a, b shows relationship between τ, horizontal displacement, and D obtained from the CV test for the Intact and Remold specimens, respectively. The τ ~ D relationship of the Remold specimen was strain hardening without a clear peak in shear stress (i.e., shear strength, τmax) (see Fig. 7a). For the strain-hardening type, τ at D = 7 mm was defined as τmax. On the other hand, the τ ~ D relationship of the Intact specimen was of the strain-softening type and decreases after the peak shear stress was reached (see Fig. 7b). For the Intact specimens, τmax increases with an increase in dD/dt. However, for the Remolded specimen, the change in τmax with increasing dD/dt was small. Figures 8a, b compare τmax versus dD/dt and the ratio of residual strength, τr to τmax, τmax/τr, respectively. The residual strength τr is defined as τ at D = 7 mm in strain-hardening type. The increase in dD/dt τmax indicates that there was dD/dt dependence of τmax while on the other hand, the experimental results showed that τmax did not increase monotonically with the increase in dD/dt, though rather τmax increased slowly from a certain dD/dt. For the Remold specimens, τmax remained almost the same regardless of dD/dt. The Remold specimens have almost the same shear stress values regardless of dD/dt. dD/dt was small in particular, which may overestimate stability of the collapsed slope. Next, τmax/τr was lower for the Intact specimens than for the Remold specimens at all dD/dt values, τr for the Intact specimens was reduced to approximately 70% of τmax at the highest dD/dt values. Figure 9 shows the τ ~ D relationship in the CV and CP tests of the Intact specimens. In the CP test, the shear displacement given in this experiment was not sufficient for τr as the CP test resulted in a strain-hardening type τ ~ D relationship due to the volume compression during shear.

Fig. 7
figure 7

τ ~ D relationships of CV test group specimens

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Fig. 8
figure 8

τmax, τmax/τf ~ dD/dt relationships of CV test group specimens: a τmax ~ dD/dt, b τmax/τf ~ dD/dt

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Fig. 9
figure 9

τ ~ D relationships of CP test and CV test group specimens

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Figure 10 shows X- ray CT scan results before and after the direct box shear test. Figure 10a shows the CP test (σv = 50 kPa) for the Intact specimen, and Fig. 10b shows the CV test (σv = 20 kPa) for the Remold specimen. The CT scan image becomes whiter with higher density of the material of interest, and blacker with lower density. The voxel size, which indicates resolution of the image, is 0.118 × 0.118 × 0.118 mm3. The pre-shear image of the Intact specimen shows white, dense soil particles. In addition, porous volcanic soil particles with low overall density were observed. These particles were surrounded by fine-grained, weathered soil whose particle shape cannot be identified by the resolution of the CT scan. In the Remold specimen shown in Fig. 10b, the presence of porous soil particles cannot be identified as in the Intact specimen shown in Fig. 10a. This is probably because of particle crushing when the Intact specimen was unraveled and reconstituted. This particle crushing is thought to have released water retained in the porous soil particles, increasing the w and decreasing the e of the specimen (see Table 2). The post-shear image shows that the specimen volume compresses with shear in the CP test, which was a drainage condition. This volume compress indicates that the τ ~ D relationship was strain-hardening type. The undrained CV test specimens also showed volumetric compression after shear, though this was observed as the amount of settlement for σv = 20 kPa loading before shear, and the overall shrinkage of the specimens caused by shear was negligible. However, many of the voids (black areas in Fig. 10b)) seen before shear had disappeared, suggesting that volume changes may have occurred due to partial drainage associated with shear. This resulted in the localized partial drainage (volumetric compression) occurred in the Remold specimen despite constant volume conditions as well as smaller influence of both the porous soil particles, which are easily crushed (Miura et al. 2003), Moreover, the cemented structure to form the high porosity state of the Intact specimen, the τ ~ D relationship was strain-hardening type.

Fig. 10
figure 10

Results of X-ray CT scan a Intact specimen, b Remold sample, White areas indicate high-density areas and black areas low-density areas)

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Figure 11 shows stress paths and Coulomb's fracture reference lines obtained from the CV test on the Intact specimen. Since the pore water pressure was not measured during the shear test, the stress path is shown as total stress. σv in the stress path at dD/dt = 0.02 mm/min decreases immediately after the start of shear, which may indicate occurrence of excess pore water pressure. This may be caused by shear deformation. On the other hand, σv in the stress path with dD/dt = 1.0 mm/min does not decrease in the initial shear phase due to the elasto-viscoplastic properties, indicating that the soil structure and high void ratio shown in (Fig. 15a) were maintained. However, as the shear deformation progresses, σv decreases, as does the stress path at dD/dt = 0.02 mm/min, leading to τmax. The occurrence of excess pore water pressure associated with shear is also confirmed in the results of consolidated-undrained monotonic loading triaxial tests conducted by Li et al. (2020) for saturated specimens. Occurrence of excess pore water pressure associated with shear is also observed in the results of consolidated-undrained monotonic loading triaxial tests performed by Li et al. (2020) for saturated specimens. In other words, the effective stress at Ta-d, which was the slip surface of the slope failure, was such that the effective stress decreased with shear. On the other hand, these test results also suggest the occurrence of excess pore water pressure during shear deformation of unsaturated specimens in their natural hydrous state (note that direct shear tests do not measure pore water pressure). This is caused by the specimens pseudo-saturated due to high-water content, w, and degree of saturation, Sr, even in the unsaturated state, as shown in Table 2. Unno et al. (2008) also reported that liquefaction was caused by excess pore air pressure during repeated loading in consolidated-undrained cyclic loading triaxial tests on unsaturated fine clean sand. The X-ray CT image of the Intact specimen in Fig. 10a) shows that the pores in the Ta-d sample used in the direct box shear test are not continuously connected though most of them are independent in the soil. The wn and Fc of the Ta-d specimens are larger than the fine clean sand used by Unno et al. (2008) in their experiments, and the hydraulic/air conductivity is expected to be lower. This may indicate that even in the unsaturated state of the Ta-d used in the experiments in this study, the increase in excess pore water/air pressure due to shear deformation reduced the effective stress and caused the specimens to fail.

Fig. 11
figure 11

Stress path of intact specimens on CV test

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Here, Fig. 12 shows vertical displacement of the top cap ΔH ~ D during the CV test shown in Fig. 11. For CV testing, the constant volume condition of the sample was satisfied by controlling the air cylinder such that the vertical displacement ΔH of the top cap was ΔH =  ± 0.01 mm (see Fig. 3d). However, with dD/dt = 1.0 mm/sec and σv = 40 kPa, H is not controlled for the volume compress of the specimen in the early shear phase. Therefore, the τ ~ D presents an initial peak (arrows in the figure) and then, τ tends to increase. In consideration of this effect of compliance in the test apparatus, the Coulomb failure criterion line shown in Fig. 15 had been applied to the first peak of τ. In the figure, the internal friction angle, ϕcu, and the cohesion, ccu, at the state of total stress obtained from the Coulomb failure criterion line are shown. ϕcu and ccu increase with the increase in dD/dt.

Fig. 12
figure 12

τ, ΔH ~ D relationships of intact specimens on CV test

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3.3 Seismic stability calculations assuming infinite-length slope

For the failed slopes in this study, surface slip of infinite-length slopes was modeled (Kasama et al. 2018), and the seismic stability was investigated by using mechanical parameters obtained from direct box shear tests. Figure 13 shows forces acting on the infinite-length slope during the earthquake, and Eq. 1 shows the factor of safety Fs obtained from Fig. 13.

$$F_{s} = \, \left\{ {\tan \phi \left( {1 \, - k_{v} - k_{h} \tan \beta } \right) \, + k_{v} \tan \beta + c/\gamma H\cos^{2} \beta } \right\} \, / \, \left( {k_{h} + \, \tan \beta } \right)$$
(1)

where β is the slope gradient, H is the soil layer thickness, γ is the average wet unit weight, ϕ is the internal friction angle, c is the cohesion, kh is the horizontal seismic coefficient, and kv is the vertical seismic coefficient. Note that kv = 0 was also assumed in this study for simplicity, as past studies have reported that the effect of vertical seismic motion is small (Tanaka 1982; Shinoda et al. 2018; 2019).

Fig. 13
figure 13

A force on infinite slope during earthquake (Kasama et al. 2018)

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Figure 14 shows UAV aerial photographs taken during the field survey of the investigated slopes. The slope failures with source heads near B-1 and B-2 occurred at a slight angle to the valley line. Therefore, the representative cross section for the stability analysis based on Eq. 1 was at the location shown in Fig. 15. The slope profile is based on the pre-collapse topographic map published by GSI. Considering that the relatively weak soil layers with Nd = 0 ~ 3 shown in Fig. 4 were deposited at a slope similar to the elevation, the slope outline obtained from the GSI data was used for β.

Fig. 14
figure 14

Aerial photograph of investigation area by UAV (10.29.2018)

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Fig. 15
figure 15

Vertical cross section for stability calculation (based on Geospatial Information Authority of Japan)

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Figure 16 shows the calculated Fs for which seismic motion is not considered when H is varied. In the condition for which seismic motions are not considered, ϕcu and ccu with dD/dt = 0.02 mm/min were used in the calculation, under the assumption that rapid shear rate effect due to seismic motion is small. Fs is greater than Fs = 1.0 regardless of H, indicating that the subject slope was in a stable state before being subjected to seismic excitation force. Figure 17 shows results of Fs for each H as kh is varied for the seismic situation. kh and Fs decrease as H increases. Figure 17 shows kh for NS and EW calculated from the PGA observed near the survey slope (see Fig. 1). Focusing on Fs at kh, which corresponds to PGA = 285 Gal in the NS direction because the orientation of the target slope is close to the NS direction, Fs is below 1.0 from the depth H below 1.0 m. This depth is generally consistent with the collapse depths of most surface collapses observed at Atsuma (Kawamura et al. 2019), and the depths at which Nd is small in DCPT shown in Fig. 4. The above results suggest that on the investigated slopes, although the shear rate effect of the earthquake motion produced a relatively large τmax, the large shear stress acting on the moving soil masses caused their collapse, and the shear strength decreased to below τr, causing movement of the collapsed soil masses for long distances.

Fig. 16
figure 16

Fs ~ H relationships without earthquake load

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Fig. 17
figure 17

Fs ~ kh relationships with earthquake load

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4 Discussion of seismic failure mechanisms of the investigated slopes

Τr in seismic slope failure in fine-grained soils is an important parameter for determining occurrence of long-range movement after the shear forces of the moving soil mass reach τmax and fail due to earthquake-induced excitation forces. Past researches of slope failure during earthquakes have evaluated τmax and τr, and significant cumulative shear displacements ΣD(e.g., ΣD ≥ 200 mm) were observed in cyclic direct box shear and ring shear tests (Ramiah and Purushothamaraj 1971, Skempton 1985, Tika et al. 1996, Tika et al. 1999, Suzuki et al. 2007, Kasama et al. 2018). On the other hand, studies with special plane strain and triaxial compression tests that reproduced large strain ranges have also been reported (Deng et al. 2011a, b).

In this research, direct box shear tests with varying dD/dt showed that the shear strength of the Remold specimens was greater than that of the Intact specimens at low rates, possibly overestimating the stability of the target slope. The reason why we successfully evaluated τmax and τr even at relatively small shear displacements as in this study may be because the specimens used in the experiments were approximately e = 5 ~ 6 and had a large void ratio. Sato and Kuwano (2019) found that volcanic ash soils have effects of cementation between soil particles and high void ratios. They reported results of a series of mechanical tests on a cemented, unplasticized fine-grained soil. The results show that under undrained shear conditions, peak strength of cemented high-void ratio specimens occur in early shear. Therefore, it is likely that the high-void ratio condition of the specimens collected in this study also caused the initial soil structure (i.e., porous soil particles and cemented structure) to be damaged by the slight shear displacement in the direct box shear test, resulting in progressive strength loss. In addition, experiments with varying dD/dt indicated that the shear strength of the Remold specimens was greater than that of the Intact specimens at low velocities, possibly overestimating the stability of the subject slope. In conclusion, the shear strengths obtained from the direct box shear tests on the Intact specimens are highly applicable to evaluation of slope stability during the present earthquake.

These results indicate that the mechanical parameters of a pumice deposit in a high-pore ratio/high-water content condition with cementation effects can be obtained by constant volume direct box shear tests with varying shear rates on Intact samples and that these parameters are applicable to an infinite-length slope model for evaluation of failure caused by seismic motion. In particular, the quantitative data on shear strength and its shear rate dependence under in situ low-confining pressure conditions provide novel data that differ from those obtained from shear behaviors under relatively high-confining pressure conditions presented by Kawamura et al. (2019) and Li et al. (2020). For evaluation of movement of collapsed soil mass, the Newmark method or other methods would be useful for measurement. However, the method described in this paper can reasonably explain the mechanism of seismic destabilization of a pumice soil under conditions of high-void ratio by conducting experiments with different shear rates and a commonly used the direct box shear test apparatus. This can provide useful information for more convenient determination of slope failure during earthquakes and for rapid selection of sites for countermeasures.

5 Conclusion

A field investigation was conducted at a slope failure site in Atsuma-town, Japan, caused by the 2018 Hokkaido Eastern Iburi earthquake, and a series of the direct box shear tests were conducted by using specimens sampled from uncollapsed area. Mechanical parameters obtained from the direct box shear tests were used to investigate seismic stability of the survey slope as an infinite-length slope. The results are summarized below:

  1. 1)

    The Nd values obtained from DCPT were Nd = 0 ~ 3 from the surface to a depth of about 1.5 m, and Nd < 20 at depths deeper than 1.5 m. The boundary area where Nd changes is weathered by the accumulation of pumice from the eruption of Mt. Trauma. The natural water content in this area was high, exceeding 200%.

  2. 2)

    The shear rate dependence of shear strength and the development of residual strength in the Intact and Remold specimens were observed. Constant volume direct box shear tests on the Intact and Remold specimens showed shear rate dependence of shear strength and residual strength in the Intact specimen. This may be related to the porous and volcanic soil particles observed in the X-ray CT scan of the Intact specimens and effects of cementation between the soil particles that forms a high-void ratio state, which was difficult to be reproduced in the Remold specimens. The shear strength did not increase monotonically with increasing shear rate within the range of experiments conducted in this study, suggesting the existence of a critical shear rate at which the shear strength increases.

  3. 3)

    The Shear rate dependence was observed for the mechanical parameters (internal friction angle, ϕcu and cohesion, ccu) in the total stress state obtained from constant volume direct box shear tests on Intact specimens.

  4. 4)

    The factor of safety for the studied slopes was above 1.0 regardless of the collapse depth and was stable before the earthquake, based on the calculations with ϕcu and ccu obtained from direct box shear tests with slow shear rate in the case of normal conditions for which seismic motion is not considered. On the other hand, calculations with ϕcu and ccu obtained from fast shear rates in stability calculations considering horizontal acceleration due to seismic motion showed that the factor of safety was below 1.0 at collapse depths greater than approx. 1.0 m for horizontal accelerations obtained from the most recent seismograph and that the results of simple dynamic cone penetration tests and local calculation results explain the results of the simple dynamic cone penetration test and the collapse conditions at the site.

  5. 5)

    These results indicate that, for pumice deposits with high-void ratio and water content where cementation effects have developed, mechanical parameters are obtained by varying the shear rate on an intact sample through the popular direct box shear tests and applying these parameters to an infinite-length slope model. The results show that applying these parameters to an infinite-length slope model enable to evaluate slope failure caused by seismic motion.

The result of this study has shown that it is possible to evaluate stability of infinite-length slopes by using mechanical parameters for which the velocity dependence is considered caused by seismic motion as a stability evaluation during earthquakes. This result is practically useful in that it allows us to evaluate whether or not slope failure will occur on a weathered, pumice-deposited slope with seismic motion as an external force without the use of special test equipment or analysis programs. As future issues, it is necessary to evaluate long-distance movement of collapsed sediment, which was a characteristic damage form in the Hokkaido Eastern Iburi earthquake, by the Newmark method with mechanical parameters in the critical state after the peak strength is demonstrated, and to evaluate the flowability of Ta-d due to the occurrence of liquefaction.