Prediction of the shear deformation of a sandy model slope generated by rainfall based on the monitoring of the shear strain and the pore pressure in the slope

Accepted Manuscript Prediction of the shear deformation of a sandy model slope generated by rainfall based on the monitoring of the shear strain and the pore pressure in the slope

Katsuo Sasahara PII: DOI: Reference:

S0013-7952(16)30542-7 doi: 10.1016/j.enggeo.2017.05.003 ENGEO 4566

To appear in:

Engineering Geology

Received date: Revised date: Accepted date:

23 October 2016 6 May 2017 7 May 2017

Please cite this article as: Katsuo Sasahara , Prediction of the shear deformation of a sandy model slope generated by rainfall based on the monitoring of the shear strain and the pore pressure in the slope. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Engeo(2017), doi: 10.1016/ j.enggeo.2017.05.003

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ACCEPTED MANUSCRIPT Prediction of the shear deformation of a sandy model slope generated by rainfall based on the monitoring of the shear strain and the pore pressure in the slope

Katsuo Sasahara1

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1-(corresponding author) Professor, Kochi University, 200 Monobeotsu, Nangoku,

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783-8502, Kochi, Japan, Tel/Fax: +81-88-864-5341, E-mail:[email protected]

ACCEPTED MANUSCRIPT Abstract It is important to predict shear deformation of a slope due to rainfall infiltration as the basis of the time prediction of an onset of a rainfall-induced landslide. Monitoring of deformations and soil-water conditions in a sandy model slope under artificial rainfall was

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performed to establish the prediction method for shear deformation of the slope due to rainfall infiltration. A prediction method for the relationship between shear strain and pore

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pressure was proposed based on the hyperbolic relationship between shear strain and pore

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pressure measured in the slope. Shear strain is predicted as a function of time before the

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failure of the slope based on the regression analyses of the shear strain – pore pressure relationship and the time - pore pressure relationship. Prediction of the shear strain using

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data until a later time could better simulate the measured values. The predicted shear strain in the deeper layer fit the measured values better than that in the shallower layer. A

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prediction method for the time - surface displacement relationship was also proposed. The procedure for the prediction is the same as that for the prediction of the shear strain, except

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the surface displacement and the groundwater level replace the shear strain and the pore pressure, respectively, in the procedure. The prediction with data even at an early stage of

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the experiment could simulate the time variation of the surface displacement well. The proposed prediction method for the surface displacement produced better simulation results than the prediction method for the shear strain.

ACCEPTED MANUSCRIPT 1. Introduction Landslide disasters result in much damage to human lives and properties; thus, the mitigation of landslides is very important all over the world. However, it is impossible to construct structural countermeasures for all slopes that might collapse and cause damage to

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people, since the construction of countermeasures is expensive and there are too many slopes that pose a potential danger. Thus, an early warning system is an effective tool to

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mitigate the damage caused by landslides. The establishment of an early warning system,

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especially against rainfall- induced landslides, is seriously needed in the east and south-east

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Asia region because they have suffered from many rainfall-induced landslides during the rainy seasons in the region.

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Existing methods for early warning against rainfall- induced landslides are divided into two types. The first is a rainfall threshold. The statistical analysis of the relationships among

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many parameters of rainfall events for past landslide disasters have been conducted to establish the empirical rainfall thresholds. The relationship between rainfall intensity and

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rainfall duration, which is called the I-D threshold (e.g., Caine, 1980; Guzzeti et al., 2007, 2008; Dahal and Hasegawa, 2008), is the most typically used in the world. The relationship

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between an effective rainfall and an hourly rainfall, the combination of two effective rainfalls with different half- lives (MLIT and IDI Japan, 2004) and a parameter that unifies two types of effective rainfall with different half-lives (Nakai, 2004) have been proposed as rainfall thresholds in Japan. Here half-life means the duration in which water storage in the ground decreases to a half of initial water storage. The rainfall threshold is useful to predict the time of onset of a rainfall- induced landslide for an area, but it cannot make a good prediction for a specific slope because the characteristics of the specific slope, such as the geometry, geology and soil properties, cannot be reflected in the threshold. Monitoring of a

ACCEPTED MANUSCRIPT soil-water condition in a specific slope, such as the pore pressure, the groundwater level (hereafter G.W.L.), the volumetric water content (hereafter V.W.C.), and the suction (e.g., Diamanto et al. 2012; Harris et al., 2012; Chae, 2014; Rianna, 2014; Bordoni et. al., 2014; Urciuoli et. al., 2016), has been conducted for the evaluation of the instability of the slope,

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although the soil-water condition is only one of the factors that affect the slope instability. The monitoring of slope deformations, such as the surface displacement, the change of the

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angle of tilt meter due to the shear deformation of the slope (e.g., Saito, 1965; Bozzano and

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Mazzanti, 2012; Jamaludin et al., 2012), has also been conducted for the prediction of the

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times of onset of shallow landslides. Simple formulae for time-prediction based on the monitoring of displacement or deformation were also proposed and utilized for practical

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real-time monitoring in the field (e.g., Saito and Yamada, 1973; Fukuzono, 1985; Varns, 1982; Voight, 1988). Monitoring of the slope deformation is useful for the prediction,

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especially in the case that a targeted slope has already been specified because the behavior of the slope deformation can be measured until the moment of failure of the slope.

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The sediment-related disaster prevention act (Uchida et al., 2009) was enacted in 2001 in Japan. According to the law, a sediment-related disaster hazard area and a special

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sediment-related disaster hazard area (Fig. 1) should be designated by prefectural governors based on the basic survey. The former area is defined as the area vulnerable to sediment-related disasters, while the latter area is defined as the area where damage to buildings or humans by sediment-related disasters can be expected. A warning and evacuation system should be established by municipal governors in the former areas according the act. The monitoring of a slope can be an effective tool for the system in a sediment-related disaster hazard area. Although pore pressure, G.W.L., V.W.C., and suction in a slope are often measured to

ACCEPTED MANUSCRIPT evaluate an instability of the slope, slope instability cannot be directly judged from such measurements because the soil-water condition is only one of the factors which affect the stress state in the slope. Thus, a seepage analysis and a slope stability analysis should be combined with the measurement of the soil-water condition for the early warning. However,

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it is rather difficult to predict these phenomena precisely by the analysis, due to the difficulty of determining model constants and boundary conditions in the analysis. Many

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studies (e.g., Diamanto et al. 2012; Harris et al., 2012; Tiwari, 2014; Bordoni, et. al. 2015)

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have been conducted to develop the seepage analysis and the slope stability analysis and to

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simulate the process of the slope instability using those models. These studies employ suction stress for evaluating the effect of suction and degree of saturation in unsaturated soil

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on shear strength of the soil. Suction stress can be a bridge from seepage analysis to stability analysis in unsaturated slope. Coupling FE-analysis for unsaturated seepage

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analysis to that for deformation analysis (Yang, et. al., 2017) was also proposed based on the suction stress theory. However, the problems described above have not been solved.

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While time-prediction on the monitoring of surface displacement or slope deformation have been already utilized for practice based on the simple formula between time and

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displacement, deformation in the slope (Saito and Yamada, 1973; Fukuzono, 1985; Crosta and Agliardi, 2003; Wang et al.; Bozzano and Mazzanti, 2014; Fung, 2014). It is rather practical way for real-time monitoring. Measurement of the slope deformation can be used to obtain the real movement of the slope. Many methods based on the measurement of the slope deformation have been proposed for time-prediction of the onset of a landslide. Measurements of surface displacement on a slope have been often adopted for time-prediction of the onset of a landslide because of the convenience of installation of monitoring instruments such as extensometers (Saitou, 1965), GPS (Crosta and Agliardi,

ACCEPTED MANUSCRIPT 2003), InSAR (Bozzano and Mazzanti, 2012; Wang et al., 2014) and total stations (Fung, 2014). Most of the methods for time-prediction are based on the empirical relationship between time and displacement in a slope (e.g., Saito and Yamada, 1973; Fukuzono, 1985; Varns, 1982; Voight, 1988). The idealized relationship between time and displacement

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before the failure of a slope is expressed in Fig. 2. It can describe accelerative surface displacement immediately before the onset of the slope failure, and certain formulae for

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predicting the time of onset of a landslide have been established based on this relationship

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(Bozzano and Mazzanti, 2012; Crosta and Agiliard, 2003; Fukuzono, 1985; Saito and

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Yamada, 1973; Saitou, 1965; Verns, 1982; Voight, 1988; Voight, 1989; Xiao, Ding, and Jiang, 2009). They could succeed in the prediction in some cases, while failing in other

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cases. The reason for the failures might be the change of the stress condition in a slope due to the change in rainfall intensity or slope geometry due to cutting the slope or filling soil

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on the slope. The stress-strain relation is necessary to describe the deformation of the slope due to a change in the stress such as a change in pore pressure due to rainfall.

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Sasahara and Sakai (2014) showed the hyperbolic relationship between the pore pressure and the shear strain and between the surface displacement and the G.W.L. in a

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sandy model slope as a result of the increase of the pore pressure due to rainfall infiltration. This fact suggests that the combination of the shear strain with the pore pressure or the combination of the surface displacement with the G.W.L. in the slope might be able to offer the stress-strain relation in the slope and to be applied to evaluate the instability of the slope more directly and mechanically than the slope stability analysis based only on the measurement of soil-water conditions. Very few studies can be found in the literature on the relationship between the shear deformation and the soil-water conditions in a slope. Only Uchimura (2011) showed the hyperbolic relationship between the shear displacement and

ACCEPTED MANUSCRIPT the volumetric water content in a specimen of sandy soil under anisotropic conditions in an inclined direct shear box with the supply of water into the specimen. He also mentioned the possibility of evaluating the instability of the slope based on this relationship. However, he did not examine whether the specimen failed and did not show the process for the

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prediction of the time of onset of the failure of the soil. It is necessary to develop the method for time-prediction of the onset of a landslide based on the relationship between the

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slope deformation and the pore pressure, which is derived from Sasahara and Sakai (2014).

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In this study, monitoring of the deformation and soil-water conditions in a sandy

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model slope under artificial rainfall was conducted, and the measured data were analyzed to examine the relationship between the shear deformation and the pore pressure in the slope.

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Prediction methods for the relationship between time and shear strain, i.e., surface displacement in the slope, are also proposed as the first step of time-prediction of the onset

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2. Methodology

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of rainfall-induced landslides based on the relationship obtained in this paper.

2.1 Model slope and monitoring equipment

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Fig. 4 shows a longitudinal section of the model slope and an arrangement of monitoring devices. Photo 1 shows an oblique view of the model slope. The model is 300 cm in length, 150 cm in width, and 50 cm in depth in the gravitational direction at the horizontal section; and 600 cm in length, 150 cm in width, and 57.7 cm in depth at the slope section with an inclination of 30 degrees. The model slope is composed of granite soil, which has the physical and mechanical properties shown in Table 1 and the grain-size distribution shown in Fig. 5. The model was constructed in a steel flume. Vertical blades of 1 cm in height were located every 50 cm in the longitudinal direction at the base of the slope to prevent

ACCEPTED MANUSCRIPT slippage between the base of the model and the flume. If the soil layer slips on the base, the deformation in the slope cannot be measured adequately; thus, the slip of the soil layer should be avoided. The lateral wall of the flume is made of glass to permit the observation of the lateral side of the model slope. The surface of the slope is parallel to the base of the

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slope. The inclination and the thickness of the model slope are determined from the typical geometry of the topsoil layer in Japan (Osanai et al., 2009). They showed that most

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rainfall-induced landslides occur at topsoil layers on a slope of 30~50 degrees that are

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0.5-1.5 m thick and have an impermeable surface on the base rock. The soil is compacted

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horizontally by human stamping at every 20 cm thickness to construct the model slope. Undisturbed soil samples were taken from the surface of the model slope every 50 cm, and

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the wet and dry unit weights of the samples were measured. The measurements show that the values of the void ratio ranged from 0.652 to 0.678, and the water content of the soil

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layer was 3.7~4.4 %. The base and lateral wall of the flume were impermeable while the lower wall (line CD in Fig.4) was permeable (free drainage). The shear strain in the slope

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was measured by a shear strain gauge, which is a series of tilt meters located vertically at every 9.2 cm in depth. The shear strain is defined at the depth of the center of each tilt

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meter (4.6, 13.8, 23, 32.2, 41.4, and 50.6 cm). The tilt meters were loosely connected to each other with bolts and nuts such that the meters can incline only in the slope inclination direction (Photo 2). The shear strain increment at a depth Δγ is defined as tan(Δθ), where Δθ is the inclination increment of the tilt meter (Fig. 6). The tilt meters used for the shear strain gauges were PMP-S10TX models (MIDORI PRECISIONS, Inc.) with a non- linearity of 0.2 degrees, which corresponds to a value of 0.0035 for Δγ. The maximum inclination that can be measured by the tilt meter is 30 degrees, which corresponds to 0.57 for shear strain γ. The surface displacement between the upper boundary of the flume and

ACCEPTED MANUSCRIPT the moving rod at the surface of the slope was measured by an extensometer. The moving rod moves in the downward direction of the slope due to shear deformation of the model slope. Moving rods were positioned at the surface of the slope at distances of 150 cm, 300 cm, and 450 cm from the toe of the slope. The surface displacement was measured by an

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angle sensor (CPP-60, MIDORI PRECISIONS) fixed at the upper boundary of the flume with a non-linearity of approximately 0.1 mm. The G.W.L. at the base of the slope was

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measured by a water level gauge (TD4310, Toyota Koki, Inc.) with an accuracy of 1 cm

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H2 O. The water level gauges were positioned at the base of the model slope at distances of

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0 cm, 150 cm, 300 cm, 450 cm, and 525 cm from the toe of the slope. The suction in the slope was measured by a tensiometer (DIK-3023, DAIKI RIKA, Inc.) with an accuracy of

Inc.) with an accuracy of 0.02 m3 /m3 .

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1 kPa, and the V.W.C. was measured by a soil moisture gauge (EC-10, Decagon Devices,

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No special care was sent to the installation of the sensors in the slope because they were statically buried at the constitution of a soil layer of the slope. It might be judged that this

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kind of installation of sensors does not give so much disturbance to soil layer in the slope. If the sensors in the slope might inserted from the surface into the slope, the inserting might

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disturbed the soil layer of the slope.

2.2 Experimental conditions To simulate the actual stress history of a natural slope that has experienced so many instances of rainfall before, three pre-rainfall events (Rain 1, 2, 3, in Table 2) were given to the model slope before the targeted rainfall event (Rain 4 in Table 2). The G.W.L.s, the shear strains and the surface displacements in the slope were measured and automatically

ACCEPTED MANUSCRIPT recorded every 10 seconds. The deformation was video recorded from the lateral side of the model slope, and no slippage on the base of the flume could be observed.

3. Experimental results

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3.1 Influence of pre-rainfall events Fig. 7 shows the time variation of the G.W.L. and the surface displacement at different

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locations on the model slope. The G.W.L. was observed at 0 cm, 150 cm, and 300 cm from

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the toe of the slope shown in the Figure. The G.W.L. at 0 cm appeared at every rainfall

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event, while the G.W.L. at 150 cm and 300 cm appeared only during Rain 3 and Rain 4. This may be because the seepage water drained from the slope section accumulated at 0 cm,

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which is the toe of the slope. The surface displacement at 150 cm and 300 cm increased not only during the rainfall event with the G.W.L. generation (Rain 3) but also during the

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rainfall events without the G.W.L. generation (Rain 1~2). The surface displacement at 450 cm only increased during Rain 4. The surface displacement at every location showed nearly

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identical magnitudes of increase.

Fig. 8 shows the time variation of the V.W.C. and the shear strain in the model slope.

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The data of the V.W.C. for depths of 10 cm, 20 cm, 30 cm, 40 cm, and 50 cm at 300 cm from the toe of the slope were used. The V.W.C. increased during each rainfall event and decreased gradually after the event. The V.W.C. also became greater during later rainfall events. The shear strain at 32.2 cm and 50.6 cm increased significantly during rainfall events (wetting process); while it also increased after rainfall events drying process. It should be emphasized that the shear strain also increased during the drying process. The shear strain increase was greater at each successive rainfall event. The shear strain at 4.6 cm and 23 cm significantly increased only during Rain 4. The shear strain at 13.8 cm and 41.4

ACCEPTED MANUSCRIPT cm was actually negative prior Rain 4. This might be due to the reaction of the large inclination of tilt meters just above or below the tilt meter of the targeted depth. The V.W.C. just before Rain 4 was almost same with that at the start of pre-rainfall events at 300 cm from the toe of the slope while the G.W.L. at the toe of the slope just

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before Rain 4 showed positive value. Water supplied by pre-rainfall events could not be

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drained completely and was stored at around the toe of the slope just before Rain 4.

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3.2 Time variation of the surface displacement and the shear strain in the slope Fig. 9 shows the time variation of the surface displacements and the G.W.L.s at 150

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cm and 300 cm from the toe of the model slope during Rain 4. The G.W.L.s at both locations were generated at approximately 11,000-12,000 seconds and increased to

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approximately 35-40 cm H2O at approximately 12,500-14,000 seconds, and then decreased significantly after the failure at 14,400 seconds. The time variations of the

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G.W.L.s at both locations were almost identical. The surface displacements at both locations showed a small increase before 11,000-12,000 seconds when the G.W.L.s at both

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locations were generated. Those movements occurred under unsaturated conditions in the slope. The surface displacements at both locations increased significantly after the generation of the G.W.L. The surface displacement at both locations increased almost identically with the increase of the G.W.L., although it developed slightly even under an unsaturated condition in the experiment. This suggests that the shear deformation is significantly affected by the increase of the pore pressure on the base of the slope. Based on the fact stated above, the influence of the pore pressure in the slope is examined. Fig. 10 shows the time variation of the G.W.L. at 300 cm from the toe of the

ACCEPTED MANUSCRIPT slope (Fig. 10(a)) and the shear strains at the depth of the center of the tilt meter of the shear strain gauge (Fig. 10(b)). The G.W.L. was generated at approximately 11,500 seconds and increased up to 35~37 cm H2 O at 12,600~13,000 seconds; it remained almost constant after that until the failure of the slope at 14,400 seconds. Shear strains in the slope showed slight

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variations until the time of generation of G.W.L. at 300 cm H2O; they developed after that time. The shear strain at 50.6 cm increased significantly just after the time of generation of

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the G.W.L., while the shear strains at other depths developed much less than that at 50.6 cm,

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until the time of maximum G.W.L. at 300 cm. The shear strains at 32.2 cm and 41.4 cm

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(deeper layer) increase to larger values than those at 4.6 cm and 13.8 cm (shallower layer) before the time of maximum G.W.L. at 300 cm. Judging from the fact that the vertical depth

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of the model slope is 57 cm and the maximum G.W.L. is 37 cm H2 O, the soil layer below the depth of 20 cm was saturated. From this, we conclude that shear deformation depends

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mostly on the deeper soil layer saturated with groundwater until the time of maximum G.W.L. Shear deformation of the soil layer develops significantly with the increase of the

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pore pressure until the time of maximum G.W.L.

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3.2 The relationship between the shear strain and the pore pressure in the slope Based on the examination described above, the relationship between the shear strain and the pore pressure in the slope is examined. The relative pore pressure head (hereafter R.P.P.H.) at a certain depth is defined as the vertical distance between the groundwater table and the depth (Fig. 11). The relationship between the shear strain and the pore pressure at each depth is shown in Fig. 12. Shear strains above 20 cm developed without the generation of pore pressure; thus, they are not shown in this figure. The shear strain developed slightly without the generation of pore pressure at first and then increased significantly with the

ACCEPTED MANUSCRIPT increase of the pore pressure below 20 cm. The shear strain without the generation of pore pressure is larger at the shallower layer. It is recognized that the shear strain at the deeper layer depends more on the increase of the pore pressure, while that at the shallower layer depends more on the shear deformation under unsaturated conditions. The increase of the

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shear strain relative to the variation of the G.W.L. is small at first; then becomes larger with the proceeding of shear deformation. The relationship between the shear strain and the pore

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pressure in the saturated layer can be assumed to be hyperbolic. The relationship at 50.6 cm

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is described by two stages of hyperbolic curves. At first, the shear strain slightly increases

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with the sharp increase of the G.W.L.; then it significantly increases with slight variation of the G.W.L. in each hyperbolic curve.

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Based on the relationship between the shear strain and the pore pressure in the slope, local safety factor of soil element at the depth of the measurement might be able to be

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judged by the value of measured shear strain. The ratio of the increase of the shear strain to that of the pore pressure also might be an indicator of the instability of the soil element. The

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larger value of the ration means the state of soil element might be nearer to the failure.

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3.3 The relationship between the surface displacement and the G.W.L. The increase of the surface displacement is also expected to be influenced by the increase of the pore pressure because the surface displacement is recognized as the integration of the shear strain from the surface to the bottom of the slope. The relationships between the surface displacements and the G.W.L. at 150 cm and 300 cm are shown in Fig. 13. Fig. 13 (a) shows the relationship from the beginning of Rain 4 until the failure of the slope. The rates of the increases of the surface displacements relative to the increase of G.W.L were small just after the start of Rain 4 at both locations; they increased gradually

ACCEPTED MANUSCRIPT with the development of the surface displacement until the maximum G.W.L. was reached at 300 cm. The surface displacement still increased with the increase of the G.W.L. until the failure of the slope at 150 cm while it increased under almost constant G.W.L. at 300 cm. The relationships between the surface displacement and the G.W.L. until the maximum

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G.W.L. at both locations can be described by hyperbolic curves. Fig. 13 (b) shows the relationship until the surface displacement of 0.5 cm, to show the slope movement in detail

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just after the start of Rain 4. Surface displacements of up to 0.1 cm at both locations

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developed under the almost constant G.W.L. of 2 cm H2O. Judging from the accuracy of

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the water level gauge, the development of the surface displacement under the G.W.L. of 2 cm H2 O is considered to be under unsaturated conditions. It is recognized from Fig. 13 that

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the surface displacement developed slightly under unsaturated conditions while it increased

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significantly with the increase of the pore pressure under saturated conditions.

4.1 Basic idea

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4. Prediction of the relationship between the time and the shear strain in the slope

It was made clear that the relation between the shear strain and the pore pressure in the

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slope could be modeled by the hyperbolic function. A procedure for the prediction of the time variation of the shear strain in the slope is proposed based on this result. The relations between the shear strain and the pore pressure, and between the time and the pore pressure, are derived through regression analysis of the measured data at any time during the experiment. The formula for simulating the relation between the time and the shear strain is derived by combining those regression equations. All the formulas for the prediction can be derived at any time before the failure occurs, and completely depend on the measurements of the shear strain and the pore pressure in this procedure.

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4.2 Data for the prediction Time-series data of the shear strain and the R.P.P.H., measured at the depth of the center of each tilt meter, were used for this examination. The R.P.P.H. is used instead of the

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pore pressure in the slope because pore pressure was not measured, but the G.W.L. at the base of the model was measured in the experiment. Because the accuracy of the water level

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gauge in the experiment is 1 cm H2 O, data with more than 1 cm H2 O of the difference in

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the R.P.P.H. values at each depth were selected. The data with values less than the

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maximum R.P.P.H. were used for the examination because the hyperbolic function cannot fit the data with decreasing R.P.P.H., which correspond to a strain-softening process after

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reaching the maximum R.P.P.H.

Data for the examinations at the depth of the center of each tilt meter are shown in Fig.

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14. Series of the shear strain and the R.P.P.H. up to the maximum R.P.P.H. are used for the

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examinations. Colored symbols are used for data included in the analysis, while hollow symbols are used for data not included in the analysis. The data at 50.6 cm is not included

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in the analysis because the curve at 50.6 cm is a combination of two hyperbolic curves. Single hyperbolic curves are the target of the analysis in this paper.

4.3 Procedure for the prediction and the results at the depth of 41.4 cm The procedure for the prediction of the time variation of the shear strain and the results of the prediction are explained for the depth of 41.4 cm, as an example. The relation between the shear strain and the R.P.P.H. until a certain time during the experiment is derived by non- linear regression analysis of the data until this time. The hyperbolic function, as given below, is adopted for the relation between the shear strain and

ACCEPTED MANUSCRIPT the R.P.P.H.

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1 Pmax  P G sur . Pmax  P

(1)

where γ is the shear strain, P is the R.P.P.H., and Gsur. and Pmax are experimental constants. Non-linear regression analysis with the hyperbolic function was conducted using Kaleida

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Graph ver. 4.1.1 (Synergy Software). Optimal constants G sur. and Pmax for the function are

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derived by the Levenberg-Marquardt method (Facchinei and Kanzow, 1998) in the software.

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Fig. 15 shows an example of the data analysis. A series of shear strain and the R.P.P.H. until γ/γmax =0.28 were used for the analysis, as shown in the left figure; the result of the

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non- linear regression analysis with the hyperbolic function is shown as the curve in the right figure. γ/γmax is the relative shear strain, which is the ratio of the shear strain γ to the

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maximum shear strain γmax, and it measures how close to failure the condition of the soil is.

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It is recognized that the regression curve can fit the measured data well, even though the regression was conducted only with the data at the early stage of the experiment. Fig. 16

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shows the comparison of the regression curves for the relationship between the shear strain and the R.P.P.H., derived with the data series for different γ/γmax at the depth of 41.4 cm.

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The regression curve for the data up to γ/γmax = 0.09 shows higher R.P.P.H. within the range of the shear strain until 0.03 than the measured data, while the curve with the data until γ/γmax = 0.22 shows lower R.P.P.H. for shear strain greater than 0.09. The other curves for the data up to larger values of γ/γmax coincide relatively well with the measured data. This shows that the regression curves for the data, even at an early stage, can simulate the measured data well. The relation between the time and the pore pressure in the slope is derived by the regression analysis of the measured data until any time during the experiment in this paper

ACCEPTED MANUSCRIPT as the first step of modelling. This kind of empirical relationship cannot take into account soil properties such as void ratio, water content of the soil. Physical modelling based on the seepage analysis should be conducted for taking such properties into account in near future. While regression analysis can produce the relationship between the pore pressure and the

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time easily even if the physical and mechanical properties of the soil in the field might not be known. It is rather practical way for real-time monitoring of the pore pressure. Attention

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should be paid on how well the regression equation can simulate the time variation of the

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pore pressure in this case. Sometimes regression equation might be too simple to simulate

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complicated time variation of the pore pressure. Fig. 17 shows the result of the regression analysis for the data until γ/γmax = 0.28 at the depth of 41.4 cm. The measured data are also

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shown in the figure. The relative time ‘T’’, which is the elapsed time from the moment of the generation of pore pressure at the selected depth, is used instead of the time for the

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horizontal axis in the figure. The power law, as given below, can simulate the measured data better than other functional forms. Here a1 and a2 are experimental constants derived

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by the regression analysis.

P  a1  T ' a2 (2)

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Fig. 17 shows the comparison of the regression curves derived for the data until different γ/γmax . The curves for the data up to γ/γmax = 0.09 and 0.022 are located slightly below the curves for the data up to other γ/γmax. The regression curves for the data until more than γ/γmax = 0.22 show small differences and can simulate the measured relationship well. The equation for the prediction of the shear strain at a certain time during the experiment (equation (3)) is derived by incorporating the regression equation for the relationship between the time and the R.P.P.H. (equation (2)) into the regression equation

ACCEPTED MANUSCRIPT that expresses the relationship between the R.P.P.H. and the shear strain at the same time (equation (1)).



a 1 Pmax  a1  T ' 2 G sur . Pmax  a1  T ' a2

(3)

Fig. 19 shows the regression curves derived from the data until different values of γ/γmax .

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The curve for the data until γ/γmax = 0.09 shows slight increase of the shear strain with time

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and is located far below the measured data. The curves for the data until values of γ/γmax less

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than 0.38 are also located below the measured data, while the other curves simulate the

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measured data relatively well.

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4.4 Results of the prediction at the depths of 23 cm and 32.2 cm Here the results of the prediction of the time variation of the shear strain at the depths

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of 23 cm and 32.2 cm are shown. The prediction was conducted according to the procedure described above for the depth of 41.4 cm. Fig. 20 shows the results of regression analysis

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for the relationship between the shear strain and the R.P.P.H. for data up to different values of γ/γmax . Less data are available for the shallower layer than for the deeper layer because

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the maximum R.P.P.H. in the shallower layer is smaller. Data were recorded at every 1 cm H2 O; thus, less data were recorded in the layer with smaller maximum R.P.P.H. The predicted relationship between the shear strain and the R.P.P.H. with data until γ/γmax = 0.597 is far from the measured data, while the predicted relationships with data until γ/γmax = 0.634 and 1 are within the scatter of the measured data at the depth of 23 cm. The relationship between the shear strain and the R.P.P.H. with data until γ/γmax less than 0.399 cannot simulate the measured data well, while the relationship with data until γ/γmax more than 0.399 can simulate the measured data well at the depth of 32.2 cm. It seems that the

ACCEPTED MANUSCRIPT results of the prediction at 32.2 cm are better than those at 23 cm. Fig. 21 shows the results of regression analysis for the relationship between the relative time and the R.P.P.H. with data until different values of γ/γmax at depths of 23 cm and 32.2 cm. The relative time is defined as the elapsed time from the moment of the generation of the R.P.P.H at each depth.

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The regression curve for data until γ/γmax = 0.634 is far from the measured data, while that with data until γ/γmax = 1 fits the measured data relatively well at the depth of 23 cm.

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Regression curves for data until higher values of γ/γmax at the depth of 32.2 cm are located

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slightly higher and fit the measured data better. The regression curves for data at 32.2 cm

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can simulate the measured data better than those for data at 23 cm in general. Fig. 22 shows the comparison of the regression curves for the relationship between the time and the shear

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strain with data until different values of γ/γmax at depths of 23 cm and 32.2 cm. The regression curve with data until γ/γmax = 0.597 is far from the measured data; those with data

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until higher values of γ/γmax are closer to the measured data at 23 cm. The predicted

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relationship with data until higher γ/γmax can fit the measured data better also at 32 cm.

5. Prediction of the relationship between the time and the surface displacement

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5.1 Procedure of the prediction

It is convenient to adopt the surface displacement instead of the shear strain in the slope for the prediction of the onset of landslides because the measurement of the surface displacement is easier than that of the shear strain in the slope. The measurement of the surface displacement requires the installation of measurement devices only at the surface of the slope, while the measurement of the shear strain requires not only the installation of the measurement devices but also digging into the slope. The procedure for the prediction of the surface displacement is basically the same as that for the prediction of the shear strain in

ACCEPTED MANUSCRIPT the slope. The surface displacement and the G.W.L. replace the shear strain and the pore pressure in the procedure for the prediction of the time variation of the surface displacement. Time series data of the surface displacement and the groundwater level until

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maximum G.W.L. at 300cm from the toe of the slope with more than 1 cm H2 O of the

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difference in the G.W.L. were selected for the analysis.

Fig. 23 shows the comparison of the relations between the surface displacement and

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the G.W.L. derived by the regression analysis of the data until different values of ds/dsmax .

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Values of ds/dsmax is the relative surface displacement (surface displacement / maximum surface displacement). Regression curves for the data at earlier stages show slightly higher

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or lower G.W.L., while the curves for the data until ds/dsmax more than 0.78 are located at intermediate positions between higher and lower G.W.L. from the measured data.

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Regression curves at any time are located within the range of the scatter of the measured

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data and they can simulate the measured relationship well even though the regression analysis was performed on data at the early stage of the experiment.

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The relation between the time and the G.W.L. is derived by regression analysis of the measured data until any time during the experiment. Fig. 24 shows the comparison of the relations derived using the data until different ds/dsmax. The logarithmic function, as given below, is adopted for the regression analysis because this function simulates the relation well, with an R2 value of more than 0.95. GL and T in the equation denote the G.W.L. and time; and 𝑎1 and 𝑎2 are the experimental constants in the equation below.

GL  a1  ln(T )  a 2 (4) It is recognized that regression curves for the data until different values of ds/dsmax show small differences and can simulate the measured data relatively well, except for a duration

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5.2 Evaluation of the error between the measurement and the prediction The error of the prediction of the relationship between the time and the surface

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displacement relative to the measured data is compared with that of the prediction of shear strain as a function of time relative to the measured data in Fig. 25. Average shear strain is

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defined as the surface displacement divided by the depth of the slope and is adopted for the

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evaluation of the error of the prediction of the surface displacement because the surface

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displacement has dimension L1 but the shear strain is dimensionless. The root mean square (hereafter RMSE) of the difference between the results of the prediction using data until

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different values of ds/dsmax and the measured data for the same ds/dsmax is adopted as the error for the evaluation of the prediction of the surface displacement and the shear strain. γ/γmax

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might be able to be an indicator for evaluating error at different depth because it is similar to the stress ratio and it measures how close to failure the condition of the soil is.

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In the cases of the shear strain, the RMSEs at 23 cm and 32.2 cm decrease as γ/γmax increases, while those at 41.4 cm are almost the same, except for the smallest γ/γmax . The

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RMSE with γ/γmax more than 0.7 at any depth is approximately 0.04. This means that the shear strain can be better simulated using the data until larger values of γ/γmax . The RMSEs in the shallower layer are larger for the region of γ/γmax less than 0.7. This means that the shear strain in the deeper layer can be better simulated by the proposed method for prediction of the time variation of the shear strain. The error between the measured data and the values predicted using data until ds/ds max = 0.21 is quite large (0.28) while the error between the measured data and the values predicted using data until larger ds/dsmax is less than 0.05 for the prediction of the surface

ACCEPTED MANUSCRIPT displacement. The error between the measured and the predicted values with data until ds/dsmax = 0.33 ~ 0.66 is less than 0.025. This result shows that time variation of the surface

displacement can be better predicted than that of the shear strain with data until less than 0.6 of ds/dsmax, while the RMSE of the prediction of the surface displacement with data for

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ds/dsmax more than 0.6 is almost equal to that of the prediction of the shear strain.

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5. Conclusions

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It is important to predict the time variation of the shear deformation of a slope as the

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basis for predicting the times of onset of landslides. The monitoring of deformations and soil-water conditions in a sandy model slope under artificial rainfall was performed to

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establish the prediction method for the shear deformation of the slope due to rainfall infiltration. The following results were obtained in this study.

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(1) The shear strain increased slightly without the generation of pore pressure, while it significantly increased with the increase of pore pressure. The surface displacement also

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increased slightly when the groundwater level was unchanged, while it significantly increased with the increase of the groundwater level. The relationship between the shear

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strain and the pore pressure in the slope can be well described as hyperbolic, as can that between the shear strain and the stress ratio in direct shear conditions. The relationship between the surface displacement and the G.W.L. is also well described as hyperbolic. (2) A prediction method for the time variation of the shear strain in the slope was proposed based on the hyperbolic relationship between the shear strain and the pore pressure in the slope. The shear strain in the slope is predicted at a certain time before the failure of the slope based on the regression analyses of the relationship between the shear strain and the pore pressure, and between time and the pore pressure at the same time. Prediction of the

ACCEPTED MANUSCRIPT shear strain using data until a later time could better simulate the measured values. The predicted shear strain in the deeper layer fits the measured value better than in the shallower layer. (3) A prediction method for the time variation of the surface displacement was also

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proposed. The assumptions of the prediction and procedure are same as with the prediction of the shear strain, except the surface displacement and the G.W.L. replace the shear strain

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and the pore pressure, respectively, in the procedure. The prediction using data even at the

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early stage of the experiment could simulate the time variation of the surface displacement

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well. The proposed prediction method for the time variation of the surface displacement produced better simulation results than the prediction method for the time variation of the

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shear strain.

Combination of the measurement of shear strain to pore pressure near the bottom of a

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slope can might contribute prediction of an onset of a rainfall- induced landslide based on the process proposed in this paper. The measurement of surface displacement on a slope

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surface and groundwater level at the bottom of the slope also might contribute prediction of an onset of a rainfall-induced landslide.

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It should be emphasized that the model slope consisted of uniform soil while natural slopes at field consists of non-uniform soil such as different soil layers and macro pores in the soil layers. The application of the relationships found in this paper should be examined to the slopes with a non-uniform soil characteristics in near future.

ACCEPTED MANUSCRIPT References

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monitoring to a simplified slope stability analysis. Engineering Geology 193, 19-37.

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Bozzano, F. and Mazzanti, P., 2012. Assessing of failure prediction methods for slope

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Fig. 1 Sediment-related disaster hazard area and Special sediment-related disaster hazard area

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Fig. 2 The relationship between elapsed time and surface displacement before failure in a slope.

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Fig. 3 Example of the decrease of the surface displacement rate after a rainfall event

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Water level gauge

Soil moisture sensor (10, 20, 30, 40, 50 cm) Tensiometer (5, 15, 25, 35, 45 cm)

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Moving rod of extensometer (150, 300, 450 cm) Shear strain gauge (4.6, 13.8, 23, 32.2, 41.4, 50.6 cm) Vertical displacement gauge (0, 10, 20, 30, 40, 50 cm)

AB, BC：Impermeable CD：Permeable

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Fig. 4 Experimental apparatus and arrangement of measuring instruments

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Photo 1 Model slope

100 80 60 40 20 0 0.001

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Percentage finer （％）

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Grain size （mm）

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Fig. 5 Grain size distribution of the soil of the model slope

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Photo 2 Shear strain gauge

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θ

θ: Increment of inclination angle of tilt meter

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Shear strain γ = tan(θ)

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Fig. 6 Definition of the shear strain

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Fig. 7 Time variation of the surface displacement and the groundwater level in the slope. G.W.L.: groundwater level.

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(a) G.W.L.

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(b) Shear strain

Fig. 8 Time variation of the shear strain and the G.W.L. at 300 cm after 10,000 seconds in the slope. G.W.L.: groundwater level. γ: shear strain.

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Groundwater level Relative pore pressure head at Depth z Depth z

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Fig. 9 Definition of the relative pore pressure head (R.P.P.H.)

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Soil layer depth

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Fig. 10 Relationship between the shear strain and the relative pore pressure at 300 cm in the slope. γ: shear strain. R.P.P.H.: Relative pore pressure head.

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(a) Whole duration (b) Small range of the surface displacement Fig. 11 Relationship between the surface displacement and the groundwater level at 150 cm and 300 cm. G.W.L.: groundwater level.

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R.P.P.H. (cmH2O)

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Depth: 41.4cm

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Fig. 12 Data for the analysis at each depth of the slope. Colored symbols are used for the analysis; hollow symbols are outside of the target of the analysis.

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R.P.P.H . 523.57  19.38R.P.P.H .

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Fig. 13 Example of regression analysis for the relationship between the shear strain and the relative pore pressure head. Depth: 41.4 cm. γ/γ max: 0.28. Colored symbols were used for the analysis; hollow symbols were not used. γ: shear strain. R.P.P.H.: Relative pore pressure head.

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γ/γmax

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Fig. 14 Results of regression analyses for the relationship between the shear strain and the relative pore pressure head with data until different γ/γ max. Depth: 41.4 cm. γ: shear strain. R.P.P.H.: Relative pore pressure head.

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R.P.P.H. (cmH2O)

25 y = 1.1425x0.3997 R² = 0.9128

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Fig. 15 Results of the regression analysis for the relationship between the relative time and the relative pore pressure head. Depth: 41.4 cm. γ/γ max:0.28. T’: Time from the moment when R.P.P.H. was generated (12,270 seconds). R.P.P.H.: Relative pore pressure head.

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Fig. 16 Results of the regression analyses for the relationship between the relative time and the relative pore pressure head with data until different γ/γ max. Depth: 41.4 cm. T’: Time from the moment when R.P.P.H. was generated (12,270 seconds). R.P.P.H.: Relative pore pressure head.

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Fig. 17 Comparison of the regression curves for the relationships between the time and the shear strain with data until different γ/γ max. Depth: 41.4 cm. γ: shear strain.

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γ/γmax 0.597 0.634 1 Measured 4

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(a) Depth: 23 cm (b) Depth: 32.2 cm Fig. 18 Results of regression analyses for the relationship between the shear strain and the relative pore pressure head with data until different γ/γ max. Depth: 23 cm, 32.2 cm. γ: shear strain. R.P.P.H.: Relative pore pressure head.

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Fig. 21 Comparison of the relationships between γ/γ max and RMSE for the predicted time series of the shear strain and the measured one at different depths. RMSE: Root mean square of the error.

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40

G.W.L. (cm H2 O)

30

20 10

30 20

10 Measu…

0 0

5

10

15

20

0

25

0

2

4

6 ds (cm)

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ds (cm)

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G.W.L. (cm H2 O)

40

8

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Fig. 23 Example of regression analysis for the relationship between the groundwater level and the surface displacement. ds/dsmax: 0.21. ds: surface displacement. G.W.L.: groundwater level.

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40 0.12

30

0.21 0.33

20

0.44 0.55 0.66

10

0.78 0.89

0 4

8

1

12

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0

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ds/dsmax

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ds (cm)

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Fig. 24 Results of the regression analyses of the relationship between the groundwater level and the surface displacement with data until different ds/dsmax. ds: surface displacement. G.W.L.: groundwater level.

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50

ds/ds max 0.12 0.21

30

0.33 0.44

20

0.55 0.66

10

0.78

0 11000

0.89

12000

13000

14000

1

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Time (sec.)

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G.W.L. (cm H2 O)

40

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Fig. 25 Results of the regression analyses of the relationship between the time and the groundwater level with data until different ds/dsmax. G.W.L.: groundwater level.

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10.0 ds/dsm ax

0.21

8.0

0.44

6.0

0.55

4.0

0.66

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ds (cm)

0.33

0.78

2.0

0.89

12000

12500

13000

13500

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11500

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1

0.0 11000

Time (sec.)

Measured

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Fig. 26 Comparison of the relationship between the time and the surface displacement with data until different ds/dsmax. ds: surface displacement.

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0.3

RMSE

Depth:23cm 0.2

Depth: 32.2cm

0.1

Depth: 41.4cm

0 0

0.2

0.4 0.6 0.8

1

Surface displacement

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γ/γmax

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Fig. 27 RMSE between the average shear strain derived by the prediction of the surface displacement and that by the measurement in comparison with RMSE for the shear strain at each depth.

ACCEPTED MANUSCRIPT Table 1 Physical and mechanical properties of the soil in the model slope Maximum void ratio of the soil emax

0.947

Minimum void ratio of the soil emin.

0.619

Void ratio in the model slope e

0.652 ~ 0.678

Relative density in the model slope Dr (%)

3.7 ~ 4.4

Hydraulic conductivity ks(cm/sec)

0.0368

Cohesion c’ (kPa)

0.0 34.9

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 ’ (deg.)

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Internal friction angle

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Water content in the model slope w(%)

82.1 ~ 89.9

ACCEPTED MANUSCRIPT Table 2 Artificial rainfall conditions

Time (duration) Oct.20 Oct.23 Oct.26 Nov.4

11:00:36~14:00:00 9:34:25~11:15:00 9:45:00~12:42:43 11:00:00~15:00:00

(2:59:24) (1:39:35) (2:57:43) (3:00:00)

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Event Intensity (mm/h) Rain 1 30 Rain 2 30 Rain 3 15 Rain 4 30 Experiments conducted in 2009.

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The shear strain in the model slope increases with the increase of pore pressure. Prediction of the shear strain based on the monitored pore pressure are proposed. Proposed method can predict the shear strain at deeper soil layer better. Prediction of the surface displacement based on the monitored data is also proposed. The surface displacement can be simulated better than the shear strain in the slope.

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