Earthquake-Induced Flow-Type Slope Failure in Weathered Volcanic Deposits—A Case Study: The 16 April 2016 Takanodai Landslide, Japan

: The aim of this paper is to provide new insight into the catastrophic mobility of the earthquake-induced ﬂow-type Takanodai landslide that occurred on 16 April 2016, which had fatal consequences. A geological and geotechnical interpretation of the site conditions and experimental investigations of the mechanical behavior of weathered Kusasenrigahama (Kpfa) pumice are used to characterize the landslide failure mechanism. The results of large-strain undrained torsional shear tests indicate that Kpfa pumice has the potential to rapidly develop very large shear strains upon mobilization of its cyclic resistance. To evaluate the actual ﬁeld performance, a series of new liquefaction triggering analyses are carried out. The liquefaction triggering analyses indicate that Kpfa pumice did not liquefy during the M w 6.2 foreshock event, and the hillslope remained stable. Instead, it liqueﬁed during the M w 7.0 mainshock event, when the exceedance of the cyclic resistance of the Kpfa pumice deposit and subsequent ﬂow-failure type of response can be considered the main cause of the landslide. Moreover, the combination of large cyclic stress ratios ( CSR = 0.21–0.35)— signiﬁcantly exceeding the cyclic resistance ratio CRR = 0.09–0.13)—and static shear stress ratios ( α = 0.15–0.25) were critical factors responsible for the observed ﬂow-type landslide that traveled more than 0.6 km over a gentle sloping surface (6 ◦ –10 ◦ ).


Introduction
On 16 April 2016, a relatively gentle slope (12 • -15 • ) located within the Mt. Aso Volcanic Caldera, in the Prefecture of Kumamoto (Kyushu Island, Japan), failed catastrophically due to severe ground shaking induced by the moment magnitude M w 7.0 2016 Kumamoto Earthquake [1][2][3][4]. The resulting flow-type slide, which involved weathered volcanic soil deposits on a gentle slope, destroyed seven houses (causing five fatalities), damaged critical lifelines and local roads in the small residential Takanodai Housing Complex (Minamiaso Village), and threatened the neighboring Tokyu Country Town community.
Earthquake-induced flow-type landslides in volcanic deposits have occurred many times in the past [5,6]. Despite many research efforts, their mechanisms are still only poorly understood, making it difficult to predict in advance their occurrence and destructive consequences on the natural and built environment. Some of the major limitations in the evaluation of flow-type landslide hazard in similar settings are the lack of experimental data available on the cyclic and dynamic response of volcanic deposits, and the fundamental differences in behavior between such problematic soils and well-understood "textbook" soils (e.g., hard-grained quartz sands). The recent Takanodai flow-type landslide case  [15]); the dashed red rectangles approximate the surface projection of the source model for the Mw7.0 event [16]. (b) Location of the landslide site in southern Japan.

2016 Kumamoto Earthquake Sequence
In April 2016, a series of earthquakes affected the area of the Kumamoto prefecture, Japan. The seismic sequence comprised three events with moment magnitude Mw equal to or greater than 6.0 [1][2][3][4]: Epicentral locations for these seismic events are shown in Figure 1. The figure also shows the approximate surface projection of the finite source model for the Mw7.0 main shock as modeled by Asano and Iwata [16]; other studies on the source rupture process for this seismic event have adopted similar source models (e.g., [17,18]). The landslide site was located about 27 km from the epicenter of the main event, but its Joyner-Boore distance RJB (i.e., the shortest distance between the site and surface projection of a threedimensional rupture) was less than 2 km. The epicentral distances for the 14 April Mw6.2 and 15 April Mw6.0 events were about 25 and 30 km, respectively. Figure 1 shows the location of three K-Net strong motion stations (KMM004, KMM005, and KMM007); all strong motion stations were located 12 km away from the landslide site. Stations KMM004 and KMM007 are underlain by 13-15 m of volcanic ash deposits over volcanic rock, while station KMM005 is underlain by 6 m of sand and 5 m of volcanic ash overlying volcanic rock (K-net [19]). Intensity measures and source-to-site distances for the ground motions recorded by these strong motion stations for the three largest earthquakes of the Kumamoto seismic sequence are summarized in Table 1.  [15]); the dashed red rectangles approximate the surface projection of the source model for the M w 7.0 event [16]. (b) Location of the landslide site in southern Japan.

2016 Kumamoto Earthquake Sequence
In April 2016, a series of earthquakes affected the area of the Kumamoto prefecture, Japan. The seismic sequence comprised three events with moment magnitude M w equal to or greater than 6.0 [1][2][3][4]: Epicentral locations for these seismic events are shown in Figure 1. The figure also shows the approximate surface projection of the finite source model for the M w 7.0 main shock as modeled by Asano and Iwata [16]; other studies on the source rupture process for this seismic event have adopted similar source models (e.g., [17,18]). The landslide site was located about 27 km from the epicenter of the main event, but its Joyner-Boore distance R JB (i.e., the shortest distance between the site and surface projection of a three-dimensional rupture) was less than 2 km. The epicentral distances for the 14 April M w 6.2 and 15 April M w 6.0 events were about 25 and 30 km, respectively. Figure 1 shows the location of three K-Net strong motion stations (KMM004, KMM005, and KMM007); all strong motion stations were located 12 km away from the landslide site. Stations KMM004 and KMM007 are underlain by 13-15 m of volcanic ash deposits over volcanic rock, while station KMM005 is underlain by 6 m of sand and 5 m of volcanic ash overlying volcanic rock (K-net [19]). Intensity measures and source-to-site distances for the ground motions recorded by these strong motion stations for the three largest earthquakes of the Kumamoto seismic sequence are summarized in Table 1.

Field Damage Observations at Takanodai Landslide Site
The Takanodai landslide took place on the gentler lower slopes of the inner caldera and involved the surface cover of volcanic deposits. These soils are known to be sensitive to pore-water pressure changes and earthquake loading, and there have been numerous past studies on rainfall-induced (e.g., [20]) and earthquake-induced (e.g., [6]) landslides in these materials.
As displayed in Figure 2a, the Takanodai landslide traveled in three different directions from a common source. The main slip (cross-section A-A', Figure 2a,b) had a length of about 600 m, a width of 100 m, and a thickness of 5-10 m. Field observations suggest that this was a shallow mobile earth slide. The presence of relatively large intact blocks of soil (Figure 3a,b) that traveled toward the slope toe on a 6 • -10 • angle clearly indicates a translational movement of the soil mass, characterized by a flow-type failure. Numerous tension cracks above the head scarp and at the hilltop, adjacent to the Aso Volcanological Laboratory, were also observed ( Figure 3c). Traces of an orange pumiceous soil were visible on the identified slip surface (Figure 3d), which consisted of a stiff clay-like ash deposit.
As schematically shown in Figure 4a, the soil profile at the Takanodai landslide site consists of an alternating sequence of volcanic deposits: (1) black volcanic ash with high organic matter (OL), (2) brown volcanic ash (AC), (3) weathered orange Kusasenrigahama pumice (Kpfa), (4) stiff brown volcanic ash (Tp), and (5) soft/weathered volcanic rock. Borehole logs in the area indicate that the thickness of the Kpfa pumice layer varies between 0 and 1 m [4,11].
From the field observations, it was inferred that the brown volcanic ash deposits (AC and Tp), within which the Kpfa layer was sandwiched, are less permeable than the Kfpa pumice. The earthquakes were preceded by heavy rainfalls, and water seepage was evident within the pumice soil layer at the time of the first field survey in early May 2016 [4]. This suggests that the Kpfa pumice likely had a high degree of saturation at the time of the Kumamoto earthquakes [4,11].
Following the May 2016 field damage survey, it was hypothesized that the Kpfa pumice was the critical layer associated with the slope failure. Therefore, disturbed and undisturbed samples of the orange Kpfa pumice were retrieved for index testing and to evaluate the undrained response of this soil using torsional simple shear tests. Additional samples of the black (OC) and brown (AC and Tp) ash deposits were also collected to evaluate the unit weight of these deposits (Table 2). samples of the black (OC) and brown (AC and Tp) ash deposits were also collected to evaluate the unit weight of these deposits (Table 2).    samples of the black (OC) and brown (AC and Tp) ash deposits were also collected to evaluate the unit weight of these deposits (Table 2).

Test Material
Kpfa pumice samples were collected from the main slide of the Takanodai landslide (sampling locations shown in Figure 2a). The pumice had a specific gravity of 2.3 (average value) and in situ dry density of approximately 600 kg/m 3 ; the in-situ water content at the time of sampling was 117%. Figure 4a compares its particle size distribution curve (orange curve) with that of the other soil layers OL, AC and Tp. A photo of an intact sample o Kpfa pumice overlaying brown stiff clay (Tp) is shown in Figure 5b, while scanning elec tron microscope (SEM) images are presented in Figure 5c,d. The Kpfa pumice is a pyro clastic soil that consists of silt and sand grains in a semi-continuous anisotropic matrix o halloysite material (Figure 5c,d). Kasama et al. [12] report that the particles of Kpfa pumice are less resistant than those of hard-grained silica sands (such as Toyoura sand), and they can be crushed with fingers.

Test Material
Kpfa pumice samples were collected from the main slide of the Takanodai landslide (sampling locations shown in Figure 2a). The pumice had a specific gravity of 2.3 (average value) and in situ dry density of approximately 600 kg/m 3 ; the in-situ water content at the time of sampling was 117%. Figure 4a compares its particle size distribution curve (orange curve) with that of the other soil layers OL, AC and Tp. A photo of an intact sample of Kpfa pumice overlaying brown stiff clay (Tp) is shown in Figure 5b, while scanning electron microscope (SEM) images are presented in Figure 5c,d. The Kpfa pumice is a pyroclastic soil that consists of silt and sand grains in a semi-continuous anisotropic matrix of halloysite material (Figure 5c,d). Kasama et al. [12] report that the particles of Kpfa pumice are less resistant than those of hard-grained silica sands (such as Toyoura sand), and they can be crushed with fingers.

Test Apparatus
A torsional shear apparatus on hollow cylindrical specimens is recognized to be a good tool to properly evaluate liquefaction soil response [21,22]. In particular, it offers the possibility to reproduce simple shear conditions that are a close representation of field stress conditions during earthquakes [23][24][25][26]. Moreover, in torsional shear tests on hollow cylindrical specimens, it is also currently possible to achieve higher strain levels by increasing the amount of torsional shear displacement that is applied to the soil specimen through the rotation of the top cap [21,27]. For instance, Yasuda et al. [27] investigated the properties of liquefied sand under undrained monotonic torsional shear conditions up to large strains levels of about 50%. Later, Kiyota et al. [21] conducted undrained cyclic torsional simple shear tests up to double amplitude shear strain exceeding 50%. In the latter tests, a correction for the effects of membrane resistance on measured shear stress was carefully applied [21]. Kiyota et al. [22] reported that the maximum amounts of liquefaction-induced ground displacement observed in relevant model tests and field observations are consistent with the limiting value to initiate strain localization observed in torsional shear tests [21]. Therefore, as long as the shear deformation remains uniform, the results of torsional shear tests can be effectively used to estimate the extent of large deformation that will occur in the field during earthquakes [22].
To evaluate the strength, deformation, and cyclic resistance characteristics of Kpfa pumice under simple shear conditions, monotonic and cyclic undrained shear tests were carried out using a fully automated torsional shear apparatus available at the Institute of Industrial Science, University of Tokyo, Japan (Figure 6a). This device is capable of achieving single-amplitude (i.e., one-way) shear strains γSA exceeding 50% (or double-ampli-

Test Apparatus
A torsional shear apparatus on hollow cylindrical specimens is recognized to be a good tool to properly evaluate liquefaction soil response [21,22]. In particular, it offers the possibility to reproduce simple shear conditions that are a close representation of field stress conditions during earthquakes [23][24][25][26]. Moreover, in torsional shear tests on hollow cylindrical specimens, it is also currently possible to achieve higher strain levels by increasing the amount of torsional shear displacement that is applied to the soil specimen through the rotation of the top cap [21,27]. For instance, Yasuda et al. [27] investigated the properties of liquefied sand under undrained monotonic torsional shear conditions up to large strains levels of about 50%. Later, Kiyota et al. [21] conducted undrained cyclic torsional simple shear tests up to double amplitude shear strain exceeding 50%. In the latter tests, a correction for the effects of membrane resistance on measured shear stress was carefully applied [21]. Kiyota et al. [22] reported that the maximum amounts of liquefaction-induced ground displacement observed in relevant model tests and field observations are consistent with the limiting value to initiate strain localization observed in torsional shear tests [21]. Therefore, as long as the shear deformation remains uniform, the results of torsional shear tests can be effectively used to estimate the extent of large deformation that will occur in the field during earthquakes [22].
To evaluate the strength, deformation, and cyclic resistance characteristics of Kpfa pumice under simple shear conditions, monotonic and cyclic undrained shear tests were carried out using a fully automated torsional shear apparatus available at the Institute of Industrial Science, University of Tokyo, Japan ( Figure 6a). This device is capable of achieving single-amplitude (i.e., one-way) shear strains γ SA exceeding 50% (or doubleamplitude, i.e., peak-to-peak, shear strains γ DA exceeding 100%) on hollow cylindrical specimens ranging in dimensions from height H = 200 mm, inner diameter d i = 60 mm, and outer diameter d o = 100 mm to H = 300 mm, d i = 90 mm, and d o = 150 mm [28].
In a hollow cylinder torsional shear apparatus, four independent loading components can be applied: vertical load (Fz), torque (T), inner cell pressure (pi), and outer cell pressure (po). The ensuing stress components (Figure 6b), i.e., axial stress (σz), radial stress (σr), circumferential stress (σθ), and torsional shear stress (τzθ), can be derived as follows [30]: where ro and ri are the outer and inner radii of the specimen, respectively. The average torsional shear strain (γzθ) is defined as where θ is the circumferential angular displacement and H is the specimen height.
The average principal stresses σ1 (major), σ2 (intermediate), σ3 (minor), and the mean stress p are given by   Figure 6. Large-strain torsional shear apparatus used in this study: (a) schematic illustration (adapted from Kiyota et al. [21]; (b) external forces and stress components acting on a hollow cylindrical specimen [29].
In a hollow cylinder torsional shear apparatus, four independent loading components can be applied: vertical load (F z ), torque (T), inner cell pressure (p i ), and outer cell pressure (p o ). The ensuing stress components (Figure 6b), i.e., axial stress (σ z ), radial stress (σ r ), circumferential stress (σ θ ), and torsional shear stress (τ zθ ), can be derived as follows [30]: where r o and r i are the outer and inner radii of the specimen, respectively. The average torsional shear strain (γ zθ ) is defined as where θ is the circumferential angular displacement and H is the specimen height. The average principal stresses σ 1 (major), σ 2 (intermediate), σ 3 (minor), and the mean stress p are given by The device is capable of performing both drained tests, with measurements of volumetric strains, and undrained tests, when drainage is prevented and pore-water pressures u are recorded. Thus, the effective mean stress (p ) can be evaluated as It should be noted that, in this study, p i and p o were kept equal to each other. Measured shear stress and effective mean stress were corrected in real time for the effects of membrane forces, as reported in Chiaro [29].

Test Procedure
All the undrained torsional shear tests presented herein were conducted on reconstituted Kpfa pumice specimens. Previous studies have shown that common specimen preparation methods such as wet tamping, wet pluviation, and dry pluviation are not suitable to prepare volcanic soil specimens (e.g., [31]). Wet tamping usually results in particle crushing. During water pluviation, soil grains tend to float instead of sedimenting into the mold, due to air confined in the inner grain pores. Limitations of the air pluviation method have also been encountered because soil particles tend to segregate due to significant variations in individual grain densities. For these reasons, in this study, specimens were prepared in 15 layers of equal thickness using an ad hoc technique, namely, under-compaction dry tamping. This specimen preparation technique is similar to the under-compaction wet tamping technique proposed by Ladd [32] to prepare homogeneous reconstitute sand specimens, with the exception that the material is compacted under dry conditions. Using this technique, (i) the dry mass required to build each layer was weighed out, (ii) loose soil layers were prepared by gently pouring the soil into a split mold, and (iii) the target dry density (ρ d ) of 600 ± 30 kg/m 3 was achieved by gently tamping the loose soil. The lower layers were compacted to a density slightly less than the desired one as compaction of the upper layers would cause the lower layers to be further compacted and reach the desired density [32]. This allowed preparing homogeneous medium-size hollow cylindrical specimens (r o = 75 mm; r i = 45 mm; H = 300 mm) with uniform density while minimizing particle crushing.
Dual-porosity volcanic soils have high internal grain porosity; therefore, their saturation is challenging and requires a thorough de-airing procedure [31,33]. In this study, the double vacuum method proposed by Ampadu [34] was adopted, followed by application of a back pressure of 200 kPa. In this way, a satisfactory degree of saturation was achieved in all tests, with Skempton's B-values greater than 0.95. After completing the saturation process, the pumice specimens were isotropically consolidated to a target effective mean stress (p 0 ) of 100 kPa. Target values of both density and mean effective stress are representative of the in-situ conditions [7].
Because of the limited amount of soil available, only four strain rate-controlled (0.5%/min shear strain rate) tests were carried out. As summarized in Table 3, they consisted of two monotonic undrained torsional shear tests (Aso#1 and Aso#2) and two cyclic undrained torsional shear tests (Aso#3 and Aso#4).
In monotonic test Aso#2, a static shear stress (τ static ) of 25 kPa was applied by preshearing the specimen under drained monotonic shear conditions, prior to switching to monotonic undrained shearing), to evaluate the effect of sloping ground conditions [35,36]. In the cyclic tests, only level-ground conditions were considered, and no τ static was applied. During cyclic loading, the loading direction was reversed every time the cyclic shear stress (τ cyclic ) amplitude reached a target value of 20 kPa (test Aso#3) or 25 kPa (test Aso#4). To simulate as closely as possible the simple shear stress condition that a soil element undergoes in the field during earthquake shaking [37,38], in all tests, the top cap was mechanically prevented from displacing vertically during the shearing.  Figure 7 shows the results of monotonic test Aso#1 in terms of (a) the stress-strain relationship (τ-γ), and (b) the effective stress path (τ-p ). The simulated monotonic undrained torsional shear response of Toyoura sand at 25% and 45% relative density (D r ) under an initial isotropic consolidation stress of p 0 = 100 kPa is also shown for comparison. The Toyoura sand results were obtained from element-level test simulations performed with the T-sand model calibrated from large-strain torsional simple shear tests on air-pluviated Toyoura sand (Chiaro et al. [39][40][41]).
Geosciences 2022, 12, x FOR PEER REVIEW 11 of 21 [29]. Relatively high effective critical state friction angles (ϕCS' = 38°) were also reported by Picarelli et al. [45] in triaxial compression tests on reconstituted (moist-tamped) specimens of sand-sized volcanic air-fall deposits from Italy which, analogously to the test on Kpfa pumice shown in Figure 7, exhibited undrained instability with a flow-type response.

Monotonic Undrained Response under Initial Static Shear
The presence of a driving static shear stress τstatic in sloping ground conditions may significantly influence the undrained response of soils, under both monotonic and cyclic shear loading conditions [29]. To evaluate the effects of τstatic on the undrained behavior of Kpfa pumice, specimen Aso#2 was pre-sheared by applying an initial shear stress τstatic = 25 kPa (Figure 8) before undrained monotonic shearing. In this case, the specimen response was analogous to that observed in test Aso#1 (τstatic = 0): after the peak shear strength (P) was mobilized, a marked decrease in shear strength was observed with the development of large strains (P-Q), followed by a small recovery of shear strength before specimen failure (F). Although the shear stresses mobilized at the occurrence of instability (P), at the quasi-steady state (Q), and at failure differ between the two tests, the mobilized effective friction angles at these states were the same (Table 4). From the stress-strain response (Figure 7a) one can note that, after an initial peak stress state (P) at 2.5% shear strain, the specimen exhibits strain-softening behavior (with decreasing shear strength as shear strains increase) to a transient minimum in shear strength ("quasi-steady state" Q [42]) at 40% shear strain, when about 80% of the initial effective confining stress has been lost due to the development of excess pore-water pressures. At larger shear strains, the specimen recovers a fraction of its pre-flow shear strength before reaching the final failure state (F), when a continuous shear band formed all around the specimen. In the effective stress space (Figure 5b), attainment of the peak state (P) is followed by the occurrence of unstable behavior, thus identifying a point on the instability line IL (e.g., [43]). From there, the mean effective stress continues to decrease until reaching the failure envelope (FL).
The simulations on Toyoura sand can be taken as reference for the typical undrained behavior of hard-grained sand (e.g., [44]). Toyoura sand at D r = 25% exhibits flow failure, with an initial peak at about 1% shear strain followed by a sudden loss of strength and stiffness. At a nearly zero effective stress state, due to the development of very large excess pore-water pressures, loose Toyoura sand quickly accumulates very large shear strains.
Medium-density (D r = 45%) Toyoura sand exhibits instead a limited flow type of response. After the mobilization of an initial peak shear strength, a temporary loss in strength is observed (quasi-steady state) with accumulation of about 5% shear strain, followed by strain hardening and rapid recovery of shear strength.
The response observed in test Aso#1 on Kpfa pumice can be likened to that of loose (D r = 25%) Toyoura sand, i.e., a flow type of response. Nevertheless, the Kpfa pumice specimen developed significant shear strains despite a high value for the effective friction angle mobilized during flow (at state Q) of φ Q = 42.6 • ; this value of φ is significantly larger than those mobilized by loose Toyoura sand during flow (at failure, φ F = 34 • ) and by medium-density Toyoura sand in the quasi-steady state (φ Q = 31 • ), with limited flow [29]. Relatively high effective critical state friction angles (φ CS = 38 • ) were also reported by Picarelli et al. [45] in triaxial compression tests on reconstituted (moist-tamped) specimens of sand-sized volcanic air-fall deposits from Italy which, analogously to the test on Kpfa pumice shown in Figure 7, exhibited undrained instability with a flow-type response.

Monotonic Undrained Response under Initial Static Shear
The presence of a driving static shear stress τ static in sloping ground conditions may significantly influence the undrained response of soils, under both monotonic and cyclic shear loading conditions [29]. To evaluate the effects of τ static on the undrained behavior of Kpfa pumice, specimen Aso#2 was pre-sheared by applying an initial shear stress τ static = 25 kPa (Figure 8) before undrained monotonic shearing. In this case, the specimen response was analogous to that observed in test Aso#1 (τ static = 0): after the peak shear strength (P) was mobilized, a marked decrease in shear strength was observed with the development of large strains (P-Q), followed by a small recovery of shear strength before specimen failure (F). Although the shear stresses mobilized at the occurrence of instability (P), at the quasi-steady state (Q), and at failure differ between the two tests, the mobilized effective friction angles at these states were the same (Table 4).
by Picarelli et al. [45] in triaxial compression tests on reconstituted (moist-tamped) specimens of sand-sized volcanic air-fall deposits from Italy which, analogously to the test on Kpfa pumice shown in Figure 7, exhibited undrained instability with a flow-type response.

Monotonic Undrained Response under Initial Static Shear
The presence of a driving static shear stress τstatic in sloping ground conditions may significantly influence the undrained response of soils, under both monotonic and cyclic shear loading conditions [29]. To evaluate the effects of τstatic on the undrained behavior of Kpfa pumice, specimen Aso#2 was pre-sheared by applying an initial shear stress τstatic = 25 kPa (Figure 8) before undrained monotonic shearing. In this case, the specimen response was analogous to that observed in test Aso#1 (τstatic = 0): after the peak shear strength (P) was mobilized, a marked decrease in shear strength was observed with the development of large strains (P-Q), followed by a small recovery of shear strength before specimen failure (F). Although the shear stresses mobilized at the occurrence of instability (P), at the quasi-steady state (Q), and at failure differ between the two tests, the mobilized effective friction angles at these states were the same (Table 4).    The presence of a driving shear stress (such as in sloping ground conditions) greater than the quasi-steady state shear strength creates conditions favorable to the generation of landslides with significant runout distances. These could occur after a triggering event, such as an earthquake, causes transient loads greater than the available peak shear strength, after which strain softening would occur, as observed in the two monotonic tests (Aso#1 and Aso#2) presented.

Cyclic Undrained Shear Response
Cyclic undrained torsional shear tests were carried out using two cyclic stress ratio (CSR = τ cyclic /p 0 ) amplitudes of 0.20 and 0.25. Figure 9 shows (a) the stress paths (τ-p ) with the corresponding (d) stress-strain (τ-γ) response and (c) excess pore-water pressure generation relationships (u e -γ) for the two tests.
otonic torsional simple shear tests with and without initial static shear on Kpfa pumice.

Test
Peak State (P) The presence of a driving shear stress (such as in sloping ground conditions) greater than the quasi-steady state shear strength creates conditions favorable to the generation of landslides with significant runout distances. These could occur after a triggering event, such as an earthquake, causes transient loads greater than the available peak shear strength, after which strain softening would occur, as observed in the two monotonic tests (Aso#1 and Aso#2) presented.

Cyclic Undrained Shear Response
Cyclic undrained torsional shear tests were carried out using two cyclic stress ratio (CSR = τcyclic/p0′) amplitudes of 0.20 and 0.25. Figure 9 shows (a) the stress paths (τ-p') with the corresponding (d) stress-strain (τ-γ) response and (c) excess pore-water pressure generation relationships (ue-γ) for the two tests.  In both tests, Kpfa pumice exhibited a cyclic liquefaction type of response [37,46]. The effective stress path (Figure 9a) progressively moved toward the left as excess pore-water pressures accumulated in the initial part of the test, when shear strains remained small (γ < 2-3%). However, as the excess pore-water pressure ratio r u = ∆u/p 0 reached values of 0.75-0.80 (Figure 9g), in both tests, shear strains abruptly increased ("flow") from γ = 2-3% to values larger than γ = 15% in a single half-cycle of loading. Only then, the specimen attained zero-p conditions (i.e., initial liquefaction [47]), with shear strains rapidly growing to γ > 50% in the last stages of the test. Hyodo et al. [31] reported a similar behavior for loose specimens of Shirasu soil (a crushable volcanic soil from southern Kyushu, Japan) subject to cyclic undrained triaxial loading conditions. As shown by Figure 9a, in cyclic test Aso#4 with the higher CSR value of 0.25 (greater than the large-strain shear strength τ F ), flow initiated when the effective stress path touched the stress path of the undrained monotonic test with a similar density. In test Aso#3, where the amplitude of the cyclic stress is less than τ F , the stress path moved toward the failure envelope, and large strains quickly developed when the mobilized friction angle was equal to φ Q (i.e., the stress path crossed the QSSL). Figure 9 also presents the results of undrained cyclic torsional shear tests on two air-pluviated specimens of Toyoura sand with relative densities of 48% (Figure 9b-h) and 73% (Figure 9c-i). These sand specimens were tested at the same CSR value of 0.20. In these tests, the Toyoura sand specimens exhibited a cyclic mobility type of response [37,46]. Excess pore-water pressures increased with each loading cycle, causing the effective stress paths (Figure 9b,c) to move leftward until when p = 0 kPa; this process was accompanied by a gradual accumulation of shear strains. This type of response can be contrasted with that exhibited by the Kpfa pumice specimens, which underwent an abrupt and uncontrolled increase in shear strains in the final part of the cyclic tests.

Cyclic Resistance
The resistance to liquefaction or to cyclic strain accumulation of sands is conventionally defined as the number of cycles to attain a reference value of shear strain (γ SA or γ DA ) or excess pore water pressure ratio r u caused by undrained cyclic shear loading. Figure 10 reports the liquefaction resistance curve of Kpfa pumice corresponding to the attainment of γ DA = 7.5%. In the same figure, liquefaction resistance curves for medium-density (D r = 45% ± 5%) and dense (D r = 67% ± 3%) air-pluviated Toyoura sand from torsional simple shear tests [13] are reported for comparison. From Figure 10, the cyclic resistance ratio (CRR 15 = CSR causing liquefaction at 15 cycles of loading) of the pumice was estimated as 0.22. Despite the differences in cyclic behavior described in the previous sections, the CRR 15 of crushable Kpfa pumice fell between those of hard-grained medium-density to dense Toyoura sand (0.18-0.24). effective stress path (Figure 9a) progressively moved toward the left as excess pore-water pressures accumulated in the initial part of the test, when shear strains remained small (γ < 2-3%). However, as the excess pore-water pressure ratio ru = Δu/p0′ reached values of 0.75-0.80 (Figure 9g), in both tests, shear strains abruptly increased ("flow") from γ = 2-3% to values larger than γ = 15% in a single half-cycle of loading. Only then, the specimen attained zero-p' conditions (i.e., initial liquefaction [47]), with shear strains rapidly growing to γ > 50% in the last stages of the test. Hyodo et al. [31] reported a similar behavior for loose specimens of Shirasu soil (a crushable volcanic soil from southern Kyushu, Japan) subject to cyclic undrained triaxial loading conditions. As shown by Figure 9a, in cyclic test Aso#4 with the higher CSR value of 0.25 (greater than the large-strain shear strength τF), flow initiated when the effective stress path touched the stress path of the undrained monotonic test with a similar density. In test Aso#3, where the amplitude of the cyclic stress is less than τF, the stress path moved toward the failure envelope, and large strains quickly developed when the mobilized friction angle was equal to ϕQ' (i.e., the stress path crossed the QSSL). Figure 9 also presents the results of undrained cyclic torsional shear tests on two airpluviated specimens of Toyoura sand with relative densities of 48% (Figure 9b-h) and 73% (Figure 9c-i). These sand specimens were tested at the same CSR value of 0.20. In these tests, the Toyoura sand specimens exhibited a cyclic mobility type of response [37,46]. Excess pore-water pressures increased with each loading cycle, causing the effective stress paths (Figure 9b,c) to move leftward until when p' = 0 kPa; this process was accompanied by a gradual accumulation of shear strains. This type of response can be contrasted with that exhibited by the Kpfa pumice specimens, which underwent an abrupt and uncontrolled increase in shear strains in the final part of the cyclic tests.

Cyclic Resistance
The resistance to liquefaction or to cyclic strain accumulation of sands is conventionally defined as the number of cycles to attain a reference value of shear strain (γSA or γDA) or excess pore water pressure ratio ru caused by undrained cyclic shear loading. Figure 10 reports the liquefaction resistance curve of Kpfa pumice corresponding to the attainment of γDA = 7.5%. In the same figure, liquefaction resistance curves for medium-density (Dr = 45% ± 5%) and dense (Dr = 67% ± 3%) air-pluviated Toyoura sand from torsional simple shear tests [13] are reported for comparison. From Figure 10, the cyclic resistance ratio (CRR15 = CSR causing liquefaction at 15 cycles of loading) of the pumice was estimated as 0.22. Despite the differences in cyclic behavior described in the previous sections, the CRR15 of crushable Kpfa pumice fell between those of hard-grained medium-density to dense Toyoura sand (0.18-0.24). Figure 10. Liquefaction resistance curves for Kpfa pumice (this study) and air-pluviated Toyoura sand [48] attained by undrained cyclic torsional simple shear tests (100 kPa mean effective stress). Figure 10. Liquefaction resistance curves for Kpfa pumice (this study) and air-pluviated Toyoura sand [48] attained by undrained cyclic torsional simple shear tests (100 kPa mean effective stress).

Outline of the Procedure
This section presents and discusses liquefaction triggering analyses for the Kpfa pumice layer on the Takanodai hillslope for different seismic events of the 2016 Kumamoto earthquake sequence. The cyclic resistance estimated for the Kpfa pumice in the laboratory with the torsional simple shear tests presented above is compared against estimates of the cyclic stress ratio induced by the earthquake according to a state-of-the-practice procedure [49,50]. According to the liquefaction assessment procedure of Idriss and Boulanger [50], the factor of safety against liquefaction triggering is given by where CRR M w =7.5,σ v =100 kPa is the liquefaction resistance for a given soil layer at 100 kPa initial effective vertical stress for a reference moment magnitude M w 7.5 earthquake (corresponding to approximately 15 cycles of loading by a cyclic sinusoidal shear stress history with constant amplitude), CSR M w ,σ v is the seismic demand induced by an earthquake with given moment magnitude M w in a soil deposit under initial vertical effective stress σ v , MSF is a magnitude scaling factor, K σ and K α account for the effects of, respectively, initial consolidation stress and static shear stress on liquefaction resistance, and the factor 0.9 accounts for the effects of multi-dimensional shaking (e.g., [51]). At a depth z below the ground surface, CSR can be estimated as where PGA is the geometric mean peak ground acceleration of the two horizontal components of ground motion, g is the acceleration due to gravity (9.81 m/s 2 ), and σ v and σ v are the initial vertical total and effective stresses, respectively. The nondimensional stress reduction coefficient (r d ) accounts for the flexibility of the soil column and is given by Equation (12) [50].
For the purposes of liquefaction assessment with Equation (10), the cyclic resistance at 15 cycles of Kpfa pumice obtained from cyclic torsional simple shear (CRR N=15, p =100kPa ) was converted from isotropic conditions in the laboratory to anisotropic (i.e., K 0 ) in-situ stress state conditions [52,53] assuming K 0 = 0.5:

Evaluation of K σ for Kpfa Pumice
In quartz sands, an increase in overburden pressure causes a more contractive soil response, resulting in a decrease in CRR. This effect is taken into account in Equation (10) by means of the empirical scaling factor K σ [54,55] applied to the reference CRR value at σ v = 100 kPa. Figure 11 shows K σ as a function of vertical effective stress for a clean sand with D r = 63% (black dashed line), as adopted in the empirical liquefaction triggering procedure of Idriss and Boulanger [50]. For quartz sands, one can note that K σ gradually decreases from 1.1 to 0.9 as the confining stress increases from 50 kPa to 300 kPa. These values of K σ can be contrasted against those computed from the cyclic triaxial test data presented by Hyodo et al. [31] for Shirasu crushable volcanic soil at two values of relative density. For the looser Shirasu soil (D r = 50%), K σ slightly increases from 0.9 at 50 kPa to 1.1 at 300 kPa; the trends are, therefore, opposite to those for quartz sands. In the case of the denser Shirasu soil (D r = 90%), CRR 15 at 50 kPa is about 70% greater than CRR 15 at the standard reference pressure of 100 kPa (i.e., K σ = 1.7), while, when passing from 100 kPa to 300 kPa of confining stress, CRR 15 remains unchanged (i.e., K σ = 1). The data from Hyodo et al. [31] suggest that values of K σ based on tests on quartz sand may not be applicable to soils with crushable grains similar to Kpfa pumice. standard reference pressure of 100 kPa (i.e., Kσ = 1.7), while, when passing from 100 kPa to 300 kPa of confining stress, CRR15 remains unchanged (i.e., Kσ = 1). The data from Hyodo et al. [31] suggest that values of Kσ based on tests on quartz sand may not be applicable to soils with crushable grains similar to Kpfa pumice.
In the subsequent liquefaction triggering assessment of the Kpfa pumice layer, to account for the potential effect of particle crushability on CRR of Kpfa pumice at different confining pressure levels, the overburden correction factor reported in Figure 11 for looser Shirasu soil (Dr = 50%) is adopted. For the soil profile shown in Figure 4 and its geometrical variation along the hillslope [2,8], values of effective vertical stress (σv') acting on the Kpfa pumice layer at the Takanodai landslide site are estimated to vary in the range of 60 kPa (at the toe of the source area) and 120 kPa (at the hilltop), with corresponding Kσ values between 0.86 and 1.02 (as estimated from Figure 11). Figure 11. Overburden stress correction factor Kσ for clean sand [50] and for crushable Shirasu volcanic soil (based on experimental data from Hyodo et al. [31]).

Evaluation of Kα for Kpfa Pumice
The effect of static shear stress ratio (α) on cyclic resistance ratio (CRR) is accounted for by means of a scaling factor Kα = CRRα/CRRα=0, where CRRα is the value of CRR for a given value of α, and CRRα=0 refers to the reference level ground condition (α = 0). Experimental results on different quartz sands at confining pressure less than 300 kPa show that cyclic resistance tends to increase with increasing α in dense sands, and to decrease with increasing α in loose sands. This is shown in Figure 12a using simple shear tests results [23,25] and in Figure 12b using torsional simple shear test results [28]. The authors are not aware of experimental data to estimate values of Kα for crushable volcanic soils; for this reason, the subsequent analyses employ the Kα values for Toyoura sand as simulated by the T-sand model [39][40][41] for air-pluviated Toyoura sand with Dr = 62% in torsional simple shear conditions at σv' = 100 kPa. In these conditions, CRR15,α=0 = 0.22 for both Toyoura sand and Kpfa pumice ( Figure 10). The relationship between Kα and α is shown in Figure   Figure 11. Overburden stress correction factor K σ for clean sand [50] and for crushable Shirasu volcanic soil (based on experimental data from Hyodo et al. [31]).
In the subsequent liquefaction triggering assessment of the Kpfa pumice layer, to account for the potential effect of particle crushability on CRR of Kpfa pumice at different confining pressure levels, the overburden correction factor reported in Figure 11 for looser Shirasu soil (D r = 50%) is adopted. For the soil profile shown in Figure 4 and its geometrical variation along the hillslope [2,8], values of effective vertical stress (σ v ) acting on the Kpfa pumice layer at the Takanodai landslide site are estimated to vary in the range of 60 kPa (at the toe of the source area) and 120 kPa (at the hilltop), with corresponding K σ values between 0.86 and 1.02 (as estimated from Figure 11).

Evaluation of K α for Kpfa Pumice
The effect of static shear stress ratio (α) on cyclic resistance ratio (CRR) is accounted for by means of a scaling factor K α = CRR α /CRR α=0 , where CRR α is the value of CRR for a given value of α, and CRR α=0 refers to the reference level ground condition (α = 0). Experimental results on different quartz sands at confining pressure less than 300 kPa show that cyclic resistance tends to increase with increasing α in dense sands, and to decrease with increasing α in loose sands. This is shown in Figure 12a using simple shear tests results [23,25] and in Figure 12b using torsional simple shear test results [28]. The authors are not aware of experimental data to estimate values of K α for crushable volcanic soils; for this reason, the subsequent analyses employ the K α values for Toyoura sand as simulated by the T-sand model [39][40][41] for air-pluviated Toyoura sand with D r = 62% in torsional simple shear conditions at σ v = 100 kPa. In these conditions, CRR 15,α=0 = 0.22 for both Toyoura sand and Kpfa pumice ( Figure 10). The relationship between K α and α is shown in Figure 13a and is consistent with the laboratory test data reproduced in Figure 12b. One can observe from Figure 13a that K α first decreases with increasing α (detrimental effect of τ static ) and then increases (beneficial effect of τ static ). The resulting values of CRR 15 after application of the scaling factor K α are plotted in Figure 13b.
Assuming infinite slope conditions, α can be calculated as follows [56]: where β is the angle of inclination of the slope. For the Takanodai landslide site, considering β = 6° and 10°, Equation (17) returns values of α for the Kpfa pumice layer of 0.15 and 0.25, respectively; the corresponding Kα values vary between 0.68 and 1.00 (Figure 13a).

Figure 12.
Relationship between Kα factor and static shear stress ratio: (a) simple shear tests [23,25]; (b) torsional simple shear tests [28].  Table 5 summarize the results of the liquefaction assessment for the two largest events of the Kumamoto earthquake sequence, namely, the Mw6. 2 14 April 2016 and the Mw 7.0 16 April 2016. To compare CSR and CRR values, these should be referred to the same earthquake magnitude (i.e., number of equivalent loading cycles). On this purpose, the CSR* values shown in Table 5 and Figures 14 and 15 were obtained by scaling CSR given by Equation (11) as follows: Figure 12. Relationship between K α factor and static shear stress ratio: (a) simple shear tests [23,25]; (b) torsional simple shear tests [28].

Figures 14 and 15, and
tion of the scaling factor Kα are plotted in Figure 13b.
Assuming infinite slope conditions, α can be calculated as follows [56]: where β is the angle of inclination of the slope. For the Takanodai landslide site, considering β = 6° and 10°, Equation (17) returns values of α for the Kpfa pumice layer of 0.15 and 0.25, respectively; the corresponding Kα values vary between 0.68 and 1.00 (Figure 13a).

Figure 12.
Relationship between Kα factor and static shear stress ratio: (a) simple shear tests [23,25]; (b) torsional simple shear tests [28].  Table 5 summarize the results of the liquefaction assessment for the two largest events of the Kumamoto earthquake sequence, namely, the Mw6. 2 14 April 2016 and the Mw 7.0 16 April 2016. To compare CSR and CRR values, these should be referred to the same earthquake magnitude (i.e., number of equivalent loading cycles). On this purpose, the CSR* values shown in Table 5 and Figures 14 and 15 were obtained by scaling CSR given by Equation (11) as follows: Assuming infinite slope conditions, α can be calculated as follows [56]:

Figures 14 and 15, and
where β is the angle of inclination of the slope. For the Takanodai landslide site, considering β = 6 • and 10 • , Equation (17) returns values of α for the Kpfa pumice layer of 0.15 and 0.25, respectively; the corresponding K α values vary between 0.68 and 1.00 (Figure 13a). Table 5 summarize the results of the liquefaction assessment for the two largest events of the Kumamoto earthquake sequence, namely, the M w 6.2 14 April 2016 and the M w 7.0 16 April 2016. To compare CSR and CRR values, these should be referred to the same earthquake magnitude (i.e., number of equivalent loading cycles). On this purpose, the CSR* values shown in Table 5 and Figures 14 and 15 were obtained by scaling CSR given by Equation (11) as follows:

Conclusions
This study re-examined the case study of the Takanodai landslide that occurred in Minami Aso during the 2016 Kumamoto earthquakes. It employed the results of advanced laboratory tests on a pumiceous soil (Kpfa pumice) which previous investigations had identified as the critical layer associated with the slope failure, and it performed liquefaction triggering analyses to assess the in situ performance of the critical layer for two earthquake scenarios of the 2016 seismic sequence. The following conclusions can be drawn:

Conclusions
This study re-examined the case study of the Takanodai landslide that occurred in Minami Aso during the 2016 Kumamoto earthquakes. It employed the results of advanced laboratory tests on a pumiceous soil (Kpfa pumice) which previous investigations had identified as the critical layer associated with the slope failure, and it performed liquefaction triggering analyses to assess the in situ performance of the critical layer for two earthquake scenarios of the 2016 seismic sequence. The following conclusions can be drawn:  For both seismic events, CSR* values were computed considering both lower-bound (Figures 14a and 15a) and upper-bound values (Figures 14b and 15b) of K σ . CRR values were scaled to include the effects of multidirectional shaking and of anisotropic in situ stress conditions (Equations (10) and (16)).
For both earthquake scenarios, in the calculation of CSR, the geometric mean PGA values recorded at the stations KMM005 (located outside the Mt. Aso Caldera, above the rupture surface) and KMM004 (located within the Mt. Aso Caldera, along the faultline projection of the main event) (Figure 1) were selected to account for uncertainty in the estimate of PGA values in the absence of direct strong motion measurements at the site. In this case of the 14 April 2016 foreshock, the source-to-site distance of the landslide site is comprised between the source-to-site distances of the two stations. For the main shock event, due to its location in the proximity of the northern end of the rupture surface, the site likely underwent fault-rupture directivity effects (which were noted in strong motion records, e.g., [16][17][18]) with ground accelerations greater than those recorded at station KMM004 (which is located further away from the rupture surface). Figure 14 shows that, for upper-bound estimates of K σ (Figure 15b), the cyclic demand associated with the M w 6.2 14 April 2016 earthquake, represented by the green shading, did not exceed the cyclic resistance of Kpfa pumice, represented by the blue line, and it was, therefore, insufficient to trigger liquefaction. The factor of safety against liquefaction (F L ) varies between 1.0 and 6.5 ( Table 5), indicating that the seismic demand was significantly lower than the cyclic resistance of the Kfpa pumice deposit. Yet, for the lower-bound estimates of K σ (Figure 15a), the analyses indicate that liquefaction was still possible under strong accelerations (F L = 0.8-6.5), but only if the actual CSR at the landslide site exceeded 0.09. The M w 7.0 16 April 2016 earthquake, however, resulted in greater PGAs which were sufficient to trigger liquefaction, as shown in Figure 15. Concurring low values of K σ and K α (Figure 15a) resulted in CSR values significantly higher than CRR of the pumice layer, as indicated by the yellow shading (F L = 0.3-0.7). It is, therefore, likely that the combination of large inertial forces induced by the main shock earthquake and the presence of a driving initial static shear stress triggered liquefaction in the Kpfa pumice layer, which subsequently initiated a flow-type landslide. The results of these analyses appear, therefore, be consistent with the observed evidence, with the slope at Takanodai remaining stable during the first event, but failing with catastrophic consequences during the main shock.
One should note some limitations of the present analyses. The estimate of CRR for the pumice layer employed in the calculations was derived from laboratory tests on reconstituted soil specimens, prepared in the laboratory. However, soil fabric and structure (i.e., the arrangement of soil particles at the micro and macroscale, e.g., [57]) are primary factors influencing the cyclic strength of soils [58], and they are uniquely associated with the adopted specimen preparation method or the in-situ formation process of a soil deposit. The use of high-quality sampling technique which could provide soil specimens suitable for testing in the laboratory (e.g., [59,60]) would, therefore, provide a significant contribution to the present analyses.
The results of the analyses are significantly influenced by the values adopted for the factors K σ and K α for Kpfa pumice, which, in this case, were based on studies on other soils: a different crushable volcanic soil for K σ , and a hard-grained sand for K α . No studies have addressed so far (at the best of the authors' knowledge) the influence of static shear stress on the cyclic response of pumiceous soils. Such investigations would provide a useful contribution for the assessment of the seismic stability of slopes of these peculiar soil deposits.

Conclusions
This study re-examined the case study of the Takanodai landslide that occurred in Minami Aso during the 2016 Kumamoto earthquakes. It employed the results of advanced laboratory tests on a pumiceous soil (Kpfa pumice) which previous investigations had identified as the critical layer associated with the slope failure, and it performed liquefaction triggering analyses to assess the in situ performance of the critical layer for two earthquake scenarios of the 2016 seismic sequence. The following conclusions can be drawn: •

Laboratory investigations
Large-strain undrained torsional shear tests confirmed that Kpfa pumice has the tendency to show post-peak flow-type failure behavior characterized by an abrupt development of large shear strains exceeding 50% or more when subjected to monotonic shearing.
The presence of an initial driving shear stress may significantly contribute to the observed flow-type failure and associated large deformation.
Under cyclic shear stress condition, tested specimens exhibited a progressive build-up of excess pore water pressure and shear strains. Following the attainment of shear strains of 2-3%, the specimens exhibited a flow-type failure with a rapid development of large (>15%) shear strains.

• Liquefaction triggering analyses
The results of liquefaction triggering analyses are consistent with the response observed in situ, when the slope at Takanodai remained stable during the M w 6.2 14 April 2016 earthquake but failed as a result of the M w 7.0 16 April 2016 earthquake. The concurring effect of high cyclic stress ratios (CSR = 0.21-0.35) induced by the earthquake and static shear stress ratios (α = 0.15-0.25) were the critical factors-leading to the seismic demand exceeding the liquefaction resistance of the Kpfa pumice layer (CRR = 0.09-0.13)-responsible for the observed liquefaction-induced flow-type landslide.