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Shear and compression strain development in sandy model slope under repeated rainfall
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ScienceDirect Soils and Foundations 57 (2017) 920–934 www.elsevier.com/locate/sandf
Shear and compression strain development in sandy model slope under repeated rainfall Katsuo Sasahara a,⇑, Naoki Sakai b b
a Kochi University, 200 Monobeotsu, Nangoku, 783-8502 Kochi, Japan National Institute for Earth Science and Disaster Prevention, 3-1 Tennodai, 305-0006 Tsukuba, Ibaraki, Japan
Received 4 December 2016; received in revised form 2 July 2017; accepted 1 August 2017 Available online 11 November 2017
Abstract Repeated rainfall on natural slope may cause repeated loading and unloading of pore pressure in the slope. The deformation behavior and soil-water conditions in a model slope were monitored under repeated rainfall to examine the influence of repeated rainfall on the deformation of the slope. The results show that the shear and compression deformation of the soil layer developed not only during the wetting process but also during the drying process. The surface and vertical displacement of the slope increased as the groundwater level (G.W.L.) increased during the first wetting process and remained constant during the subsequent drying process. The displacements showed small progress until the maximum G.W.L. of the first wetting process and then increased significantly at the next wetting process. The shear and compression strain remained constant as the suction decreased during the wetting processes and increased with the increase of suction during the drying processes; the strains significantly increased with a small decrease in the suction and then significantly increased with the generation of the pore pressure at the final rainfall event. The relationship between the shear strain and the compression strain was not affected by the repeated loading and unloading of suction. The relationship between the surface displacement and the vertical displacement was also free from the variation of the suction due to the repeated rainfalls. Strain increased with the increase in the pore pressure and the maximum pore pressure at a deeper layer was larger than at a shallower layer. The increase in the vertical displacement to the increase of the surface displacement approaches zero with the increase in the shear strain at the soil layer, denoting a failure state of the soil layer. Ó 2017 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society. This is an open access article under the CC BYNC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Rainfall-induced landslide; Shear strain; Compression strain; Groundwater level; Suction; Pore pressure
1. Introduction Monitoring slope deformation is an effective tool for predicting the onset of landslides. Conventional tilt meters with Micro Electro Mechanical Systems (MEMS) or Global Positioning Systems (GPS) have recently been developed for the measurement of slope deformations. The development of new methods or instruments for monitor-
Peer review under responsibility of The Japanese Geotechnical Society. ⇑ Corresponding author. E-mail address: [email protected] (K. Sasahara).
ing slope deformation is expected to follow the development of Information and Communication Technology (ICT). However, the analysis methods currently used to examine the monitoring data for time prediction of an onset of a landslide are still relatively unsophisticated. A soil creep theory was adopted for this data analysis to predict the onset of a landslide. The creep theory describes the time-displacement relationship before the failure of the soil. It can simulate an accelerative surface displacement just prior to the onset of slope failure. Many formulae for the time prediction of landslides have been established based on soil creep theories (Saito, 1965; Saito and
https://doi.org/10.1016/j.sandf.2017.08.021 0038-0806/Ó 2017 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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Yamada, 1973; Varns, 1983; Fukuzono, 1985; Voight, 1988; Voight, 1989; Crosta and Agliardi, 2003; Xiao et al., 2009; Bozzano and Mazzanti, 2012). Although they have been able to predict the time of the onset of landslides in some cases, these formulae have failed in other cases. They might not have succeeded in predicting the onset of rainfall-induced landslides when the rainfall intensity suddenly decreased prior to the failure. This is because of the change in stress of the landslide body resulting from the change of rainfall intensity. The creep theory cannot describe the deformation generated by the change in stress because it only describes the time-strain (displacement) relationship under a constant stress condition of the soil. A stress-strain relationship is necessary to describe the onset of a landslide resulting from a change in stress. The authors (Sasahara and Tsunaki, 1996; Sasahara and Sakai, 2011, 2014) have reported the stress-strain relationship of the soil in the model slope. They examined the relationship of the volumetric water content (hereafter V.W. C.), the suction, and the groundwater level to the shear strain in a sandy model slope under artificial rainfalls. Although other reports also took the surface displacement and the pore pressure in the model slope or natural slope under artificial rainfall into consideration (Moriwaki et al., 2004; Ochiai et al., 2004), as well as the initiation condition of the failure of a model slope due to artificial rainfall in a flume (Orense et al., 2004; Reid et al., 2009; Wang and Sassa, 2001, 2003), very few studies have examined the influence of the variations in the stress in the slope. Natural slopes are subject to many rainfall events over a long period of time. The stress history, or, more specifically, the repeated loading and unloading of the pore pressure and suction due to repeated rainfalls, may influence the deformation behavior of the slope. Very little research has examined the influence of repeated loading and unloading of the pore pressure or suction on the deformation of a slope. Uchimura et al. (2011) examined the shear deformation behavior of sandy soil in a direct shear apparatus with constant shear stress under the repeated supply (wetting) and drainage (drying) of water. According to the study, shear displacement developed with the increase of the V. W.C. during the first wetting process. The shear displacement remained almost constant until the V.W.C. increased to the maximum of the first wetting stage and then further developed with the increased V.W.C. at the subsequent wetting stage. Although the V.W.C. is not a stress variant in a strict sense, its variation may be closely related to the variation of the suction. Thus, the relationship between the V.W.C. and the shear displacement might be analogous to that between the suction and the shear strain in the direct shear condition. In this study, the V.W.C., the pore pressure (including the suction), and the shear and compression deformation in a sandy model slope were automatically monitored under repeated rainfalls. Analyses were conducted on the relationship between the deformation and the soil-water condition under the repeated loading and unloading of
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pore pressure to seek the constitutive laws between the deformation and the soil-water conditions in the slope under repeated rainfall conditions. 2. Methodology 2.1. Model slope and monitoring equipment Fig. 1 shows the longitudinal section of the model slope and the location of the monitoring devices. Photo 1 shows the model slope with dimensions of 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 is composed of granite soil (Fig. 2 and Table 1) and was made in a steel flume with vertical blades of 1 cm in height at every 50 cm in the longitudinal direction at the base of the slope to prevent slippage between the base of the model and the flume. The surface of the slope is parallel to the base of the slope. The inclination and the thickness of the model slope are based on the fact that most rainfall-induced landslides occur in a topsoil layer on slopes of 30 50 degrees, and the thicknesses of the topsoil layers are typically 0.5 1.5 m in Japan (Osanai et al., 2009). The steel base plate of the model slope models the impermeable surface of the base rock beneath the topsoil. The combination of a topsoil layer on an impermeable base rock is typical of collapsed
Fig. 1. The longitudinal section of the model slope and the arrangement of measurement devices.
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Photo 1. The model slope.
Photo 2. The shear strain gauge.
Fig. 2. The grain size distribution of the granite soil for the model slope.
Table 1 Physical properties of the soil in the model slope. Mean diameter (mm) Coefficient of uniformity Maximum void ratio of the soil emax Minimum void ratio of the soil emin. Void ratio in the model slope e Relative density in the model slope Dr. (%) Water content in the model slope w (%)
1.25 21.88 0.947 0.619 0.652–0.678 82.1–89.9 3.7–4.4
slopes in Japan. The soil is horizontally compacted by human stamping every 20 cm to construct a model slope. Undisturbed soil samples were taken from the surface of the model slope at 50 cm intervals, and the wet and dry unit weights of the samples were measured. The measurements show that the value of the void ratio ranged from 0.65 to 0.68, and the water content of the soil layer was 3.7– 4.4%. The base and upper boundary of the flume were in an impermeable (undrained) condition, while the lower boundary was in a permeable (drained) condition. The shear strain in the slope was measured by a shear strain gauge, which is a series of tilt meters vertically located
Fig. 3. The measurement of the shear strain.
every 9.2 cm in depth. The shear strain is defined at the depth of the center of each tilt meter (4.6, 13.8, 23, 32.2, 41.4, and 50.6 cm). Two tilt meters were connected loosely with a bolt and a nut (Photo 2) so that the meters can only incline in the direction of the slope inclination. The shear strain increment Dc is defined as tan(Dh), while Dh is the inclination increment of the tilt meter (Fig. 3). The tilt meters used for the shear strain gauges were PMP-S10TX models (MIDORI PRECISIONS, Inc.) with a nonlinearity of 0.2 degrees, corresponding to a value of 0.0035 for Dc. The maximum inclination to be measured by the tilt meter is 30 degrees, corresponding to 0.57 for
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shear strain c. The compression strain at a given depth was measured by two vertical displacement gauges and defined as shown in Fig. 4 at depth X1.5, which is the mid-point between depth X1 and depth X2. The vertical displacement gauge is composed of a steel plate (Photo 3) that can move with the soil and a linear displacement gauge (SDP-100R,
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TOKYO SOKKI, Inc.) with an accuracy of 0.2 mm. Both the vertical displacement at the surface and the compression strain were measured by a gauge composed of a steel plate and a linear displacement gauge. The surface displacement between the upper boundary of the flume and the moving pole at the surface of the slope was measured by an extensometer. Moving poles were set at the surface of the slope at distances of 150 cm, 300 cm, and 450 cm from the toe of the slope. Surface displacement was measured by an angle sensor fixed at the upper boundary of the flume (CPP-60, MIDORI PRECISIONS) with a nonlinearity of approximately 0.1 mm. The suction in the slope was measured by a tensiometer (DIK-3023, DAIKI RIKA, Inc.) with an accuracy of 1 kPa, and the V.W.C. was measured by a soil moisture gauge (EC-10, Decagon Devices, Inc.) with an accuracy of 0.02 m3/m3. The groundwater level (hereafter G.W.L.) at the base of the slope was measured by a water level gauge (TD4310, Toyota Koki, Inc.) with an accuracy of 1 cm. The water level gauges were set at the base of the model slope at distances of 0 cm, 150 cm, 300 cm, 450 cm, and 525 cm from the toe of the slope. 2.2. Correction of the compression strain
Fig. 4. The measurement of the compression strain.
Photo 3. Steel plates of a vertical displacement gauge.
It is necessary to correct the compression strain for the examination. To calculate compression strain, both the vertical displacement of the soil layer due to compression and also the horizontal displacement of the soil layer due to shear deformation are taken into account. The vertical displacement due to the compression of the soil layer can be identified from the measured displacement to derive the exact compression strain. The compression strain is calculated from the vertical displacements of the steel plates (Dz1 and Dz2), as shown in Fig. 4. The vertical displacement of a steel plate is measured as the difference of the length of the invar wire between a linear displacement gauge and a steel plate, but is influenced by the horizontal displacement of a steel plate due to the shear deformation of a soil layer (as shown in Fig. 5). When a steel plate moves horizontally, the length of the invar wire increases due to the movement. The increase in the length of the invar wire due to the shear deformation of a soil layer should be deleted from the length of the invar wire between a linear displacement gauge and a steel plate to derive the exact increase of the vertical length of the invar wire due to the compression of a soil layer. The shear strain of a soil layer at the depth of the steel plate is necessary to calculate the horizontal displacement of the steel plate due to the shear deformation. The shear strain is defined as a tangent of the rotation angle ‘h’ of an assumed tilt meter at a depth of a steel plate; the soil layer depth is assumed to be equal to the height of the tilt meter, as shown in Fig. 5. The length of the invar wire increases due to the rotation of an assumed tilt meter caused by the shear deformation of a soil layer. The length of the invar wire between the linear displacement gauge and the tilt meter ‘L’ is defined as follows:
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Fig. 5. The increase of the length of the invar wire of the steel plate of the vertical displacement gauge due to the shear deformation of a soil layer.
L¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðL0 þ DLv Þ2 þ DL2h
ð1Þ
In the equation above, DLv and DLh is defined as DLv ¼ H 0 ð1 cos hÞ
ð2Þ
DLh ¼ H 0 sin h
ð3Þ
By inserting Eqs. (2) and (3) into Eq. (1), qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 L ¼ fL0 þ H 0 ð1 cos hÞg þ H 20 sin2 h
ð4Þ
ð5Þ
The increase of the length of the invar wire can also be due to the compression of the soil layer. When the decrease of a soil layer thickness due to compression is expressed as ‘DV i ’, the increase of the length of the invar wire due to the compression of a soil layer ‘DLc ’ is defined as DLc ¼
DV i cos a
ð6Þ
Because the measured increase of the invar wire ‘DL’ is composed of ‘DLs ’ and ‘DLc ’, the decrease of the soil layer thickness due to the compression of the soil layer ‘DV i ’ is derived as DV i ¼ ðDL DLs Þ cos a DLh H 0 sin h ¼ L0 þ DLv L0 þ H 0 ð1 cos hÞ H 0 sin h 1 a ¼ tan L0 þ H 0 ð1 cos hÞ
Intensity (mm/h)
Duration
Rain Rain Rain Rain
30 30 15 30
Oct.20 Oct.23 Oct.26 Nov.4
1 2 3 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
By inserting Eqs. (5) and (9) into Eq. (7), the vertical displacement due to the compression of the soil layer can be identified and the compression strain can be calculated from the displacement. 2.3. Experimental conditions To simulate the actual soil-water conditions in a natural slope that has experienced numerous rainfall events, three pre-rainfall events (Rain 1, 2, 3, in Table 2) were applied to the model slope before the targeted rainfall event (Rain 4 in Table 2). The surface and the vertical displacement, the shear strain, the compression strain, the G.W.L., the suction, and the V.W.C. in the slope were measured and automatically recorded every 10 s. 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
ð7Þ 3.1. The surface displacement at different location on the model slope
According to Fig. 5, a is derived as tan a ¼
Number
Experiments conducted at 2009.
The increase of the length of the invar wire due to the rotation of the tilt meter ‘DLs ’ is DLs ¼ L L0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ fL0 þ H 0 ð1 cos hÞg2 þ H 20 sin2 h L0
Table 2 Artificial rainfall conditions.
ð8Þ ð9Þ
Fig. 6 shows the time variation of the G.W.L., the vertical displacement, and the surface displacement at different locations on the model slope. The G.W.L. was observed at 0 cm, 150 cm, and 300 cm from the toe of the slope, while
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Rain 4. 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 rainfall events without the G.W.L. generation (Rains 1 2). The displacement also increased during the non-rainfall period after Rain 3. The surface displacement at 450 cm only increased during Rain 4. The surface displacement at 150 cm and 300 cm showed nearly identical magnitudes of increase during Rain 1, Rain 2 and Rain 3 respectively. The results show that the time variations and magnitudes of the G.W.L., the vertical displacement, and the surface displacement at the sections between 150 cm and 300 cm from the toe of the slope are nearly identical. This fact suggests that the G.W.L. increase and the deformation behavior at different locations were almost unique in this section. 3.2. The shear and compression deformation in the model slope
Fig. 6. Time variations of the groundwater level (G.W.L.), the vertical displacement and the surface displacement at different distances from the toe of the model slope.
no G.W.L. was observed at 450 cm and 525 cm from the toe of the slope. The G.W.L. at 0 cm appeared at every rainfall 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, which is the toe of the slope. The vertical displacement at each location increased significantly during rainfall events, while these displacements showed a slight increase immediately following the rainfall events. The displacement increased without the generation of the G.W.L. during Rain 1 and 2, while it increased with the increase of the G.W.L. during Rain 3 and 4; while small increases were recorded during Rains 1–3, the displacement was significant during
Fig. 7 shows the time variation of the V.W.C., the suction, the compression strain, and the shear strain in the model slope. 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 for the Figure. The V.W.C. increased during each rainfall event and decreased gradually after the event. The V.W.C. reached maximum value after termination of Rain 1, 2 and 3. In general, the V.W. C. was greater at shallower layers than at deeper layers. The V.W.C. also became greater during later rainfall events. The suction decreased remarkably during each rainfall event and increased gradually after the events. The suction decreased up to minimum value after termination of Rain 1, 2 and 3. The suction at the shallower layers was generally less than at deeper layers. The minimum suction was nearly identical during Rain 1, Rain 2, and Rain 3, but it was slightly lower during Rain 4. The suction at each depth was positive through the experiment, although the G.W.L. increased beyond the measured depth in some cases. Fig. 6 shows that the G.W.L. rose to 35 cm in depth in the section between 150 cm and 300 cm during Rain 3, while the suction below 35 cm in depth was still positive during Rain 3. The G.W.L. rose to 15 cm in depth at 150 cm and to 0 cm in depth at 300 cm, although suction below 15 cm in depth was still positive during Rain 4. This may be due to quasi-saturation (absorption with air in some pores) beneath the ground water level in the slope. The compression strain at 5 cm, 53.85 cm deep was positive though the duration of the experiment, while it was negative at 15 cm, 25 cm and 35 cm prior to Rain 4. The compression strain at 15 cm, 25 cm deep was still negative during Rain 4, while it became positive at 35 cm, 45 cm deep. The compression strain at 45 cm was negative during Rain 1 and 2 while it turned to positive during Rain 3 and 4. Although the compression strain at 45 cm, 53.85 cm showed pulsating increases between Rain 3 and Rain 4, these were disregarded as electric noise. The compression strain at 5 cm, 45 cm, and 53.85 cm showed increased significantly just
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The shear strain at 32.2 cm and 50.6 cm increased not only during rainfall events (wetting process) but also 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 was relatively low and showed no significant increase prior to Rain 4 and showed significant increase during Rain 4. The shear strain at 13.8 cm and 41.4 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. 4. Discussion 4.1. Relationship between the surface displacement, vertical displacement and the G.W.L
Fig. 7. Time variations of the V.W.C., the suction, the compression strain (ec) and the shear strain (c) in the slope.
after Rains 1–3, while other depths seemed uninfluenced by the rainfall events.
The surface displacement and the vertical displacement are the product of the soil depth to the integration of the shear strain and the compression strain from the surface to the base of the slope. Thus, the relationship between the surface displacement, the vertical displacement and the G.W.L. were examined to assess the deformation behavior of the model slope. Fig. 8(a) shows the relationship between the surface displacement and the G.W.L. at 150 cm and 300 cm from the toe of the slope throughout the duration of the experiment. The blue and red symbols represent data during a rainfall event and after a rainfall event, respectively. Most of the data in the figures are after Rain 3 and during Rain 4 because the variation in the surface displacement before the termination of Rain 3 was much smaller than that after Rain 3. No increase was observed in the surface displacement during Rain 1 and 2 because there was no increase in the G.W.L. The G.W.L. increased to almost 20 cm and decreased to zero once, with a very small increase in the surface displacement during Rain 3; a large increase of G.W.L. created a significant surface displacement at both 150 cm and 300 cm during Rain 4. The relationship at 150 cm was almost same as that at 300 cm until 13 cm of displacement (35–40 cm of G.W. L.); then the surface displacement at 150 cm slightly increased; while that at 300 cm slightly decreased. The rate of the increase of the surface displacement became greater with the increase of the G.W.L. until reaching a peak. Fig. 8(b) shows the relationship between the surface displacement and the G.W.L. at 150 cm and 300 cm, up to 5 cm, to show the detailed relationship under a repeated rainfall event. The G.W.L. increased during the first wetting process and then decreased during the first drying process, with a small increase in the surface displacement. The increase in the surface displacement during the drying process may be an indication of delayed deformation (viscous behavior) of the slope. During the next wetting process, the surface displacement showed small increase until the G.W. L. reached the maximum G.W.L. of the first wetting process, and then increased significantly with increases in the
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1) 150cm
2) 300cm (a) Entire duration of the experiment
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1) 150cm
2) 300cm (b) Small displacement range
Fig. 8. Relationship between the surface displacement and the G.W.L. Blue and red symbol represent data during rainfall event and after rainfall respectively.
G.W.L. The surface displacement showed yielding behavior corresponding to the repeated increase of the G.W.L. Fig. 9(a) shows the relationship between the vertical displacement and the G.W.L. at 150 cm and 300 cm throughout the duration of the experiment. The blue and red symbols represent data during rainfall events and after rainfall events, respectively. As was observed in the relationship between the surface displacement and the G.W.L., the relationship at 150 cm was nearly identical with that at 300 cm until 4 cm of vertical displacement. The vertical displacement showed a greater rate of increase upon increasing the G.W.L. The vertical displacement at 150 cm increased slightly beyond 4 cm of vertical displacement, while it was almost constant at 300 cm beyond 4 cm. Fig. 9 (b) shows the relationship up to 2 cm to examine the detailed relationship under repeated rainfall events. As was observed in the relationship between the surface displacement and the G.W.L., the vertical displacement
increased with increasing G.W.L. during the first wetting process and then showed a small increase during the subsequent drying process. The increase in the vertical displacement during the drying process may be due to the delayed deformation (viscous behavior) of the slope. During the second wetting process, the displacement remained almost constant with increasing G.W.L. until reaching the maximum G.W.L. of the first wetting process; it then increased significantly with increases in the G.W.L. 4.2. Relationship between the shear strain and the suction, the pore pressure Following the overview of the deformation of the model slope, the shear and compression deformation in the model slope relating to rainfall infiltration is examined in detail. The relationship between the shear strain and the suction is shown in Fig. 10. The relationship is different in
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1) 150cm
1) 150cm
2) 300cm
2) 300cm
(a) Entire duration of the experiment
(b) Small displacement range
Fig. 9. Relationship between the vertical displacement and the G.W.L. Blue and red symbol represent data during rainfall event and after rainfall respectively.
shallow and deep layers. Fig. 10(a) shows the relationship between the shear strain and the suction at 23 cm to demonstrate an unsaturated soil layer. The relationship above this depth is almost same with that at 23 cm. The blue and red lines represent the duration of the rainfall event and after the rainfall event, respectively. The suction at the depth of a tilt meter was derived by interpolating and extrapolating the measured suction at every 10 cm of depth. The suction initially decreased with no increase in the shear strain during the wetting process; the shear strain then increased under constant suction after the wetting process. The suction increased without varying the shear strain during the subsequent drying process. This behavior may be attributed to the delay in shear deformation caused by the visco-plastic deformation of the soil. Fig. 10(b) and (c) shows the relationship between the shear strain and the suction at 32.2 cm and 50.6 cm,
respectively, to demonstrate a saturated layer. The arrows indicate the shear strain at the generation of the relative pore pressure head at each depth. The relative pore pressure head is defined as the difference between the G.W.L. and the vertical distance from the center of a tilt meter to the base of the slope (Fig. 11), that is, the pore pressure head at each depth of the slope. The behavior of the shear strain to the variation of the suction at 32.2 cm was similar to that at 23 cm; the shear strain remained almost constant with the suction decrease at wetting processes and then developed with the suction increase at subsequent drying processes at 32.2 cm. The shear strain increased with the decrease in the suction during the wetting processes at 50.6 cm. To be more precise, the shear strain increased not only with the decrease in the suction during the wetting process but also with the increase in suction during the drying process at 50.6 cm. During the next wetting
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Fig. 11. A definition of a relative pore pressure in the slope.
(a) Depth: 23 cm
(b) Depth: 32.2 cm
(c) Depth: 50.6 cm Fig. 10. Relationship between the shear strain and the suction at different depths. c: the shear strain. Blue and red line represent data during rainfall event and after rainfall respectively.
process, the shear strain showed little variation with the decrease in suction until the minimum suction of the previous wetting process and then increased with the decrease in suction. The shear strain increased significantly when it exceeded the value at the generation of the relative pore pressure head. The minimum suction during the last wetting process was a yield stress from the repeated wetting and drying processes. Uchimura et al. (2011) reported the same type of yielding behavior of the shear displacement from the repeated increase and decrease of the V. W.C. for a sandy specimen under direct shear with constant shear stress. This suggests that shear deformation only occurs when the rainfall amount is sufficient to generate even the smallest suction in an actual slope. The shear strain increased with greater decreases in suction after the generation of the pore pressure at each depth. The value of the suction was still positive after the generation of the pore pressure. As previously shown, the relationship between the shear strain and the suction at a shallower layer differed from that at a deeper layer. The shear strain increases under constant suction in a shallower layer, while it increases with the decrease of suction only when the suction decreases beyond the yielding value at a deeper layer. It can be said that the shear deformation at a shallower layer depends more on the visco-plasticity of a soil while it depends more on the decrease of the suction at a deeper layer. The shear deformation shows the yielding behavior to the repeated loading of the suction at a deeper layer. It is recognized that the shear strain significantly increases under the generation of pore pressure (see Fig. 10(b) and (c)). This fact indicates the necessity of examining the relationship between the shear strain and the relative pore pressure in the slope. Fig. 12 shows the relationship between the shear strain and the relative pore pressure head at depths of 23 cm, 32.2 cm, 41.4 cm, and 50.6 cm – where the relative pore pressure was generated. The shear strain at 41.4 cm became negative during Rain 1, Rain 2 and Rain 3, without the generation of relative pore pressure during the unsaturated conditions, while the shear strain increases to positive during Rain 4 with the increase in the relative pore pressure head. The shear
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Fig. 12. Relationship between the shear strain and the pore pressure in the slope. c: the shear strain.
strain at other depths initially increased slightly without the generation of the relative pore pressure head (during unsaturated conditions) and then increased significantly with the increase in the relative pore pressure head. At a depth of 50.6 cm, the pore pressure head increased to 6 cm with an increase in shear strain of 0.28, and then decreased to zero with an increase in shear strain of 0.3. A significant increase in the pore pressure started from the shear strain of 0.39 and resulted in an increase in the shear strain during Rain 4. However, the shear strain increased with a relative pore pressure head of less than 6 cm during Rain 4, even though the relative pore pressure head was less than the maximum value during a previous rainfall event. This means that the shear strain did not demonstrate clear elasto-plastic yielding to the repeated loading in pore pressure in this experiment. The shear strain increases at 32.2 cm and 41.4 cm grew larger with a greater relative pore pressure head until reaching a peak value in the relative pore pressure head during Rain 4. The shear strain showed strain hardening until the peak of the relative pore pressure head at these depths. The maximum pore pressure heads at 23 cm, 32.2 cm and 41.4 cm were shown to be 2.5 cm, 11.9 cm and 21.0 cm, respectively, while the maximum pore pressure at 50.6 cm could not be measured within the range up to 0.57 of the shear strain. This can likely be attributed to the larger maximum pore pressure at a deeper layer. 4.3. Relationship between the compression strain and the suction and the pore pressure The behavior of the compression strain to the suction and the pore pressure in the model slope is examined
following the examination of the shear strain in the model slope. Fig. 13 shows the relationship between the compression strain and the suction at different depths in the model slope. The blue and red lines represent the duration of rainfall event and after the rainfall, respectively. Fig. 13(a) shows the relationship at 4.6 cm to demonstrate a shallow layer. The suction decreased initially without varying the compression strain at each wetting process during rainfall events, and then the compression strain increased with increased suction at each drying process that followed the rainfall events. While the compression strain initially decreased significantly, it then showed considerable increase under almost constant suction after the wetting process of Rain 4. Fig. 13(b) shows the relationship at 23 cm to demonstrate a middle layer. The relationships at 13.8 cm and 32.2 cm are not shown in the figure but are essentially the same as those at 23 cm. The compression strain remained constant during the wetting process and proceeded during the drying processes after Rains 1–3 as well as that at 4.6 cm. The compression strain remained constant initially and then increased significantly with a decrease in suction until the generation of the pore pressure at the wetting process of Rain 4. This value decreased significantly with constant suction after the generation of the pore pressure. The difference between the relationships at 4.6 cm and that at 23 cm is the direction of the proceeding compression strain and behavior during the wetting process of Rain 4. The soil layer at 4.6 cm basically showed compression while that at 23 cm was dilated. Consideration of the reasons for this difference is beyond the scope of this paper. The mechanism of compression of the soil layer due under unsaturated condition need to be examined to investigate this result. The second difference during the wetting process of Rain 4 is that the compression strain increases with constant suction at 4.6 cm while it increases with the decrease of the suction at 23 cm. This is important when examining the compression behavior of the slope during unsaturated conditions because it suggests that the compression behavior at deeper layers depends more on the decrease of suction during the wetting process of Rain 4. The relationship at 41.4 cm is shown in Fig. 13(c). The relationship at 50.6 cm is almost the same as that at 41.4 cm. The compression strain remained constant with the decrease of the suction at wetting processes after Rain 2 and during Rain 3, then increased with increasing suction at subsequent drying processes after Rain 3. It remained constant with the decreased suction, then increased with constant suction, and increased with increasing pore pressure during the final wetting process due to Rain 4. The decrease in the suction after rainfall events might be due to the delay of seepage water infiltration at deeper layers. The compression behavior of the slope to the repeated loading of the suction must be compared with the shear behavior. The elasto-plastic yielding behavior of shear strain to the repeated loading of the suction is clear at a deeper soil layer, while that of the compression strain to the repeated loading of the suction is not clearly observed
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(a) Depth: 4.6 cm
Fig. 14. Relationship between the compression strain and the pore pressure. ec: the compression strain.
(b) Depth: 23 cm
(c) Depth: 41.4 cm Fig. 13. Relationship between the compression strain and the suction in the slope. ec: the compression strain. Blue and red line represent data during rainfall event and after rainfall respectively.
in this examination. The increase in the shear strain under constant suction after the wetting process (or with the increase of the suction during the drying process) is greater at shallow layers. Unlike shear strain, the behavior of the compression strain to the variation of the suction is almost the same at all depths and remained constant with decreasing suction during the wetting process and increased with increasing suction during the drying process at all depths. The behavior of the compression strain after the generation of pore pressure, that is, a large increase in the compression strain with increasing pore pressure, is the same as that observed for the shear strain and the pore pressure. The shear and compression deformation under constant suction (or with increasing suction) may be considered time-dependent deformation due to the wetting of the soil layer. Viscosity might prevent deformation of the soil under large rates of decreased suction during the wetting process, and visco-plastic deformation may occur after the wetting process. Fig. 14 shows the relationship between the compression strain and the pore pressure in the slope. No pore pressure was observed at 4.6 cm or 13.8 cm. At 23 cm, the compression strain reached 0.02 just before the generation of pore pressure during the unsaturated conditions (as shown in Fig. 13(b)) and then decreased almost linearly with the increase in the pore pressure. The compression strain at 32.2 cm initially moved to 0.01 under an unsaturated condition and then increased with the increase in the pore pressure. The compression strain at 41.4 cm also moved to
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Fig. 15. Relationship between the shear strain and the compression strain at 23 cm and 50.6 cm. c: the shear strain, ec: the compression strain.
0.008 under the unsaturated condition. Then it increased up to 0.44 with increasing pore pressure after the generation of pore pressure. The compression strain at 50.6 cm showed small variations under the unsaturated condition, then decreased with the pore pressure until 10 cm, and then finally increased significantly with the increase in the pore pressure. In general, it can be said that the increase in the compression strain became greater with increased pore pressure, and the relationship between the compression strain and the pore pressure can be modified as hyperbolic at depths greater than 32.2 cm. The maximum pore pressure was greater at deeper layers, as was the relationship between the shear strain and the pore pressure. Because the compression strains at all depths only showed significant progress during the wetting process of Rain 4, no influence of repeated loading of the pore pressure could be observed in the relationship between the compression strain and the pore pressure in this experiment. 4.4. Relationship between the shear strain and the compression strain Fig. 15 shows the relationship between the shear strain and the compression strain at 23.3 cm and 50.6 cm throughout the duration of the experiment to examine the dilatancy of the soil in the slope. The relationship at 23.3 cm represents that at a shallower layer while the relationship at 50.6 cm represents that at a deeper layer. The relationship between the compression strain and the shear strain at 23.3 cm and 50.6 cm is a smooth curve that does not fluctuate significantly during Rain 1, Rain 2, Rain 3, and Rain 4. This means that the relationship does not show the yielding behavior for the cyclic loading of either the suction or the pore pressure. The relationship is not affected by the cyclic loading of the suction and the pore pressure under repeated rainfalls.
Fig. 16. Relationship between the surface displacement and the vertical displacement at 300 cm from the toe of the model slope.
4.5. Relationship between the surface displacement and the vertical displacement The result of the examination of the relationship between the shear strain and the compression strain suggests that the relationship between the surface displacement and the vertical displacement is also not affected by the repeated loading of the suction or the pore pressure. Because the surface displacement and the vertical displacement are products of the integration of the shear strain, the compression strain and the depth of a soil layer of the model slope. Fig. 16 shows the relationship between the surface displacement and the vertical displacement at 300 cm from the toe of the model slope. It is clear that the relationship is not disturbed by rainfall events because the shape of the curve showing the relationship is smooth against the loading of the suction and the pore pressure during rainfall events. The slope of the curve approaches zero with the increase in the surface displacement, which implies that the ratio of the increase of the vertical displacement to the surface displacement decreases and it approaches zero toward the failure of the soil. This is similar to the volumetric strain approaching zero toward the critical or residual state under the direct shear condition. It may well be that the ratio of the increase of the vertical displacement to the surface displacement can be used as an indicator of the instability of the slope. Whether or not this is actually the case can be the subject of further research on this topic. 5. Conclusions From the examinations above, the following conclusions can be derived:
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(1) The surface displacement and the vertical displacement increase with the generation of the G.W.L. during rainfall while they show small increases with decreasing G.W.L. after rainfall. The shear and compression strain increase with the V.W.C. increases and the suction decreases during rainfall, while the strains also increase after the rainfall as the V.W.C. decreases and the suction increases. (2) The surface displacement and the vertical displacement increase with increasing G.W.L. during the first wetting process, while they remain almost constant until reaching the maximum G.W.L. (yielding value) of the first wetting process at subsequent wetting process. The displacements increase significantly after the G.W.L. increases beyond the yielding value of the second wetting process. The yielding curve for the relationships between the surface displacement and the G.W.L. (or the vertical displacement and the G. W.L.) can be modeled as hyperbolic. (3) The response of the shear strain to the suction can be described as follows. At shallower layers, the shear strain is almost constant during the wetting processes (with decreased suction) and drying processes (with increased suction), while it proceeds under constant suction before the generation of the pore pressure. The shear strain increases with the decrease of suction during the first wetting process (and the increase of suction during the first drying process) and then remains constant until reaching the minimum suction (yielding value) of the first wetting process; the strain then increases with decreasing suction beyond the yielding value of the subsequent wetting process at deeper layers. The shear strain increases remarkably after the generation of pore pressure. (4) The shear strain shows little increase in the absence of the generation of pore pressure while it increases significantly with increasing pore pressure after the pore pressure is generated. The increase in the shear strain due to the increase in the pore pressure becomes larger with increasing pore pressure. The relationship between the shear strain and the pore pressure head just prior to failure can be modeled as a hyperbolic curve. (5) The compression strain remains constant as the suction decreases during the wetting processes and then proceeds as the suction increases during the drying processes; it proceeds significantly under constant suction during the final rainfall event at all depths. (6) The compression strain proceeds significantly after the generation of pore pressure at soil layers deeper than 13.8 cm. The increment of the compression strain to the increase of the pore pressure grows with increasing pore pressure. (7) The relationship between the shear strain and the compression strain is not affected by the repeated loading of the suction due to the numerous rainfalls.
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(8) The relationship between vertical displacement and surface displacement is not affected by the repeated loading of the suction or the pore pressure. The ratio of the increase in vertical displacement to the increase in surface displacement decreases and approaches zero toward the failure of the slope. It may suggest that this ratio is an indicator of the instability of the slope.
References Bozzano, F., Mazzanti, P., 2012. Assessing of failure prediction methods for slope affected by human activities. In: Eberhardt, E., Froese, C., Turner, A.K., Leroueil, S., (Eds.), Landslides and Engineered Slopes: Proceting Society through Improved Understanding (Proc of 11th Int. and 2nd North American symposium on landslides and Engineered Slopes, Banff, Canada, 3–8 June 2012). CRC Press/Balkema, Leiden, pp. 1465–1471. Crosta, G.B., Agliardi, F., 2003. Failure forecast for large rock slides by surface displacement measurements. Can. Geotech. J. 40, 176–190. Fukuzono, T., 1985. A new method for predicting the failure time of a slope. In: Proc. IVth Intern. Conf. and Field Workshop on Landslides, Tokyo, Japan, pp. 145–150. Moriwaki, H., Inokuchi, T., Hattanji, T., Sassa, K., Ochiai, H., Wang, G., 2004. Failure process in a full-scale landslide experiment using a rainfall simulator. Landslides 4, 277–288. Ochiai, H., Okada, Y., Furuya, G., Okura, Y., Matsui, T., Sanmri, T., Terajima, T., Sassa, K., 2004. A fludized landslide on a natural slope by artificial rainfall. Landslides 3, 211–219. Orense, R.P., Shimoma, S., Maeda, K., Towhata, I., 2004. Instrumented model slope failure due to water seepage. J. Nat. Disaster Sci. 26, 15–26. Osanai, N., Tomita, Y., Akiyama, K., Matsushita, T., 2009. Reality of cliff failure disaster. TECHNICAL NOTE of National Institute for Land and Infrastructure Management No.530, 69–74, (in Japanese). Reid, M.E., Iverson, R.E., Iverson, N.R., LaHusen, R.G., Brien, D.L., Logan, M., 2009. Deciphering landslide behavior using large-scale flume experiments. In: Sassa, K., Canuti, P. (Eds.), LandslidesDisaster Risk Reduction. Springer, Heidelberg, pp. 463–465. Saito, M., 1965. Forecasting the time of occurrence of a slope failure. In: Proc. 6th Intern. Conf. on Soil Mech. and Foundation Eng. Montreal, Canada 2, pp. 537–541. Saito, M., Yamada, G., 1973. Forecasting and result in case of landslide at takabayama. In: Proc. 8th Intern. Conf. on Soil Mech. and Foundation Eng., Moscow, U.S.S.R. 4(3), 325–327. Sasahara, K., Tsunaki, R., 1996. Shear deformation characteristics of sandy soil in steep slope landslides. In: Senneset, K. (Ed.), Landslides (Proc. of the 7th Inter. Symposium on Landslides, 17-21 June 1996, Trondheim, Norway). Balkema, Rotterdam, pp. 877–881. Sasahara, K., Sakai, N., 2011. Shear deformation development and the increase of pore pressure due to rainfall infiltration in sandy model slope under different inclination. Int. J. GEOMAT 1, 64–70. Sasahara, K., Sakai, N., 2014. Development of shear deformation due to the increase of pore pressure in a sandy model slope during rainfall. Eng. Geol. 170, 43–51. Varns, D.J., 1983. Time-deformation relations in creep to failure of earth materials. In: Proc. of 7th Southeast Asian Geotechnical Conference 2, pp. 107–130. Voight, B., 1988. A relation to describe rate-dependent material failure. Science 243, 200–203. Voight, B., 1989. Materials science law applies to time forecasts of slope failure. In: Japan Landslide Society (Eds.), Landslide News 3, Japan Landslide Society, Tokyo, pp. 8–10.
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Uchimura, T., Suzuki, D., Hongkwan, S., 2011. Combined monitoring of water content and displacement for slope instabilty. In: Proc. 4th Japan-Korea Geotech. Eng. Workshop, Japanese Geotechnical Society, Kobe, 67–72. Wang, G., Sassa, K., 2001. Factors affecting rainfall-induced flowslides in laboratory flue tests. Geotechnique 51, 587–599.
Wang, G., Sassa, K., 2003. Pore pressure generation and movement of rainfall-induced landslides: effect of grain size and fine particle content. Eng. Geol. 69, 109–125. Xiao, J.-Q., Ding, D.-X., Xu, G., Jiang, F.-L., 2009. Inverted S-shaped model for nonlinear fatigue in rock. Int. J. Rock Mech. Mining Sci. 46, 643–648.
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ScienceDirect Soils and Foundations 57 (2017) 920–934 www.elsevier.com/locate/sandf
Shear and compression strain development in sandy model slope under repeated rainfall Katsuo Sasahara a,⇑, Naoki Sakai b b
a Kochi University, 200 Monobeotsu, Nangoku, 783-8502 Kochi, Japan National Institute for Earth Science and Disaster Prevention, 3-1 Tennodai, 305-0006 Tsukuba, Ibaraki, Japan
Received 4 December 2016; received in revised form 2 July 2017; accepted 1 August 2017 Available online 11 November 2017
Abstract Repeated rainfall on natural slope may cause repeated loading and unloading of pore pressure in the slope. The deformation behavior and soil-water conditions in a model slope were monitored under repeated rainfall to examine the influence of repeated rainfall on the deformation of the slope. The results show that the shear and compression deformation of the soil layer developed not only during the wetting process but also during the drying process. The surface and vertical displacement of the slope increased as the groundwater level (G.W.L.) increased during the first wetting process and remained constant during the subsequent drying process. The displacements showed small progress until the maximum G.W.L. of the first wetting process and then increased significantly at the next wetting process. The shear and compression strain remained constant as the suction decreased during the wetting processes and increased with the increase of suction during the drying processes; the strains significantly increased with a small decrease in the suction and then significantly increased with the generation of the pore pressure at the final rainfall event. The relationship between the shear strain and the compression strain was not affected by the repeated loading and unloading of suction. The relationship between the surface displacement and the vertical displacement was also free from the variation of the suction due to the repeated rainfalls. Strain increased with the increase in the pore pressure and the maximum pore pressure at a deeper layer was larger than at a shallower layer. The increase in the vertical displacement to the increase of the surface displacement approaches zero with the increase in the shear strain at the soil layer, denoting a failure state of the soil layer. Ó 2017 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society. This is an open access article under the CC BYNC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Rainfall-induced landslide; Shear strain; Compression strain; Groundwater level; Suction; Pore pressure
1. Introduction Monitoring slope deformation is an effective tool for predicting the onset of landslides. Conventional tilt meters with Micro Electro Mechanical Systems (MEMS) or Global Positioning Systems (GPS) have recently been developed for the measurement of slope deformations. The development of new methods or instruments for monitor-
Peer review under responsibility of The Japanese Geotechnical Society. ⇑ Corresponding author. E-mail address: [email protected] (K. Sasahara).
ing slope deformation is expected to follow the development of Information and Communication Technology (ICT). However, the analysis methods currently used to examine the monitoring data for time prediction of an onset of a landslide are still relatively unsophisticated. A soil creep theory was adopted for this data analysis to predict the onset of a landslide. The creep theory describes the time-displacement relationship before the failure of the soil. It can simulate an accelerative surface displacement just prior to the onset of slope failure. Many formulae for the time prediction of landslides have been established based on soil creep theories (Saito, 1965; Saito and
https://doi.org/10.1016/j.sandf.2017.08.021 0038-0806/Ó 2017 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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Yamada, 1973; Varns, 1983; Fukuzono, 1985; Voight, 1988; Voight, 1989; Crosta and Agliardi, 2003; Xiao et al., 2009; Bozzano and Mazzanti, 2012). Although they have been able to predict the time of the onset of landslides in some cases, these formulae have failed in other cases. They might not have succeeded in predicting the onset of rainfall-induced landslides when the rainfall intensity suddenly decreased prior to the failure. This is because of the change in stress of the landslide body resulting from the change of rainfall intensity. The creep theory cannot describe the deformation generated by the change in stress because it only describes the time-strain (displacement) relationship under a constant stress condition of the soil. A stress-strain relationship is necessary to describe the onset of a landslide resulting from a change in stress. The authors (Sasahara and Tsunaki, 1996; Sasahara and Sakai, 2011, 2014) have reported the stress-strain relationship of the soil in the model slope. They examined the relationship of the volumetric water content (hereafter V.W. C.), the suction, and the groundwater level to the shear strain in a sandy model slope under artificial rainfalls. Although other reports also took the surface displacement and the pore pressure in the model slope or natural slope under artificial rainfall into consideration (Moriwaki et al., 2004; Ochiai et al., 2004), as well as the initiation condition of the failure of a model slope due to artificial rainfall in a flume (Orense et al., 2004; Reid et al., 2009; Wang and Sassa, 2001, 2003), very few studies have examined the influence of the variations in the stress in the slope. Natural slopes are subject to many rainfall events over a long period of time. The stress history, or, more specifically, the repeated loading and unloading of the pore pressure and suction due to repeated rainfalls, may influence the deformation behavior of the slope. Very little research has examined the influence of repeated loading and unloading of the pore pressure or suction on the deformation of a slope. Uchimura et al. (2011) examined the shear deformation behavior of sandy soil in a direct shear apparatus with constant shear stress under the repeated supply (wetting) and drainage (drying) of water. According to the study, shear displacement developed with the increase of the V. W.C. during the first wetting process. The shear displacement remained almost constant until the V.W.C. increased to the maximum of the first wetting stage and then further developed with the increased V.W.C. at the subsequent wetting stage. Although the V.W.C. is not a stress variant in a strict sense, its variation may be closely related to the variation of the suction. Thus, the relationship between the V.W.C. and the shear displacement might be analogous to that between the suction and the shear strain in the direct shear condition. In this study, the V.W.C., the pore pressure (including the suction), and the shear and compression deformation in a sandy model slope were automatically monitored under repeated rainfalls. Analyses were conducted on the relationship between the deformation and the soil-water condition under the repeated loading and unloading of
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pore pressure to seek the constitutive laws between the deformation and the soil-water conditions in the slope under repeated rainfall conditions. 2. Methodology 2.1. Model slope and monitoring equipment Fig. 1 shows the longitudinal section of the model slope and the location of the monitoring devices. Photo 1 shows the model slope with dimensions of 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 is composed of granite soil (Fig. 2 and Table 1) and was made in a steel flume with vertical blades of 1 cm in height at every 50 cm in the longitudinal direction at the base of the slope to prevent slippage between the base of the model and the flume. The surface of the slope is parallel to the base of the slope. The inclination and the thickness of the model slope are based on the fact that most rainfall-induced landslides occur in a topsoil layer on slopes of 30 50 degrees, and the thicknesses of the topsoil layers are typically 0.5 1.5 m in Japan (Osanai et al., 2009). The steel base plate of the model slope models the impermeable surface of the base rock beneath the topsoil. The combination of a topsoil layer on an impermeable base rock is typical of collapsed
Fig. 1. The longitudinal section of the model slope and the arrangement of measurement devices.
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Photo 1. The model slope.
Photo 2. The shear strain gauge.
Fig. 2. The grain size distribution of the granite soil for the model slope.
Table 1 Physical properties of the soil in the model slope. Mean diameter (mm) Coefficient of uniformity Maximum void ratio of the soil emax Minimum void ratio of the soil emin. Void ratio in the model slope e Relative density in the model slope Dr. (%) Water content in the model slope w (%)
1.25 21.88 0.947 0.619 0.652–0.678 82.1–89.9 3.7–4.4
slopes in Japan. The soil is horizontally compacted by human stamping every 20 cm to construct a model slope. Undisturbed soil samples were taken from the surface of the model slope at 50 cm intervals, and the wet and dry unit weights of the samples were measured. The measurements show that the value of the void ratio ranged from 0.65 to 0.68, and the water content of the soil layer was 3.7– 4.4%. The base and upper boundary of the flume were in an impermeable (undrained) condition, while the lower boundary was in a permeable (drained) condition. The shear strain in the slope was measured by a shear strain gauge, which is a series of tilt meters vertically located
Fig. 3. The measurement of the shear strain.
every 9.2 cm in depth. The shear strain is defined at the depth of the center of each tilt meter (4.6, 13.8, 23, 32.2, 41.4, and 50.6 cm). Two tilt meters were connected loosely with a bolt and a nut (Photo 2) so that the meters can only incline in the direction of the slope inclination. The shear strain increment Dc is defined as tan(Dh), while Dh is the inclination increment of the tilt meter (Fig. 3). The tilt meters used for the shear strain gauges were PMP-S10TX models (MIDORI PRECISIONS, Inc.) with a nonlinearity of 0.2 degrees, corresponding to a value of 0.0035 for Dc. The maximum inclination to be measured by the tilt meter is 30 degrees, corresponding to 0.57 for
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shear strain c. The compression strain at a given depth was measured by two vertical displacement gauges and defined as shown in Fig. 4 at depth X1.5, which is the mid-point between depth X1 and depth X2. The vertical displacement gauge is composed of a steel plate (Photo 3) that can move with the soil and a linear displacement gauge (SDP-100R,
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TOKYO SOKKI, Inc.) with an accuracy of 0.2 mm. Both the vertical displacement at the surface and the compression strain were measured by a gauge composed of a steel plate and a linear displacement gauge. The surface displacement between the upper boundary of the flume and the moving pole at the surface of the slope was measured by an extensometer. Moving poles were set at the surface of the slope at distances of 150 cm, 300 cm, and 450 cm from the toe of the slope. Surface displacement was measured by an angle sensor fixed at the upper boundary of the flume (CPP-60, MIDORI PRECISIONS) with a nonlinearity of approximately 0.1 mm. The suction in the slope was measured by a tensiometer (DIK-3023, DAIKI RIKA, Inc.) with an accuracy of 1 kPa, and the V.W.C. was measured by a soil moisture gauge (EC-10, Decagon Devices, Inc.) with an accuracy of 0.02 m3/m3. The groundwater level (hereafter G.W.L.) at the base of the slope was measured by a water level gauge (TD4310, Toyota Koki, Inc.) with an accuracy of 1 cm. The water level gauges were set at the base of the model slope at distances of 0 cm, 150 cm, 300 cm, 450 cm, and 525 cm from the toe of the slope. 2.2. Correction of the compression strain
Fig. 4. The measurement of the compression strain.
Photo 3. Steel plates of a vertical displacement gauge.
It is necessary to correct the compression strain for the examination. To calculate compression strain, both the vertical displacement of the soil layer due to compression and also the horizontal displacement of the soil layer due to shear deformation are taken into account. The vertical displacement due to the compression of the soil layer can be identified from the measured displacement to derive the exact compression strain. The compression strain is calculated from the vertical displacements of the steel plates (Dz1 and Dz2), as shown in Fig. 4. The vertical displacement of a steel plate is measured as the difference of the length of the invar wire between a linear displacement gauge and a steel plate, but is influenced by the horizontal displacement of a steel plate due to the shear deformation of a soil layer (as shown in Fig. 5). When a steel plate moves horizontally, the length of the invar wire increases due to the movement. The increase in the length of the invar wire due to the shear deformation of a soil layer should be deleted from the length of the invar wire between a linear displacement gauge and a steel plate to derive the exact increase of the vertical length of the invar wire due to the compression of a soil layer. The shear strain of a soil layer at the depth of the steel plate is necessary to calculate the horizontal displacement of the steel plate due to the shear deformation. The shear strain is defined as a tangent of the rotation angle ‘h’ of an assumed tilt meter at a depth of a steel plate; the soil layer depth is assumed to be equal to the height of the tilt meter, as shown in Fig. 5. The length of the invar wire increases due to the rotation of an assumed tilt meter caused by the shear deformation of a soil layer. The length of the invar wire between the linear displacement gauge and the tilt meter ‘L’ is defined as follows:
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Fig. 5. The increase of the length of the invar wire of the steel plate of the vertical displacement gauge due to the shear deformation of a soil layer.
L¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðL0 þ DLv Þ2 þ DL2h
ð1Þ
In the equation above, DLv and DLh is defined as DLv ¼ H 0 ð1 cos hÞ
ð2Þ
DLh ¼ H 0 sin h
ð3Þ
By inserting Eqs. (2) and (3) into Eq. (1), qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 L ¼ fL0 þ H 0 ð1 cos hÞg þ H 20 sin2 h
ð4Þ
ð5Þ
The increase of the length of the invar wire can also be due to the compression of the soil layer. When the decrease of a soil layer thickness due to compression is expressed as ‘DV i ’, the increase of the length of the invar wire due to the compression of a soil layer ‘DLc ’ is defined as DLc ¼
DV i cos a
ð6Þ
Because the measured increase of the invar wire ‘DL’ is composed of ‘DLs ’ and ‘DLc ’, the decrease of the soil layer thickness due to the compression of the soil layer ‘DV i ’ is derived as DV i ¼ ðDL DLs Þ cos a DLh H 0 sin h ¼ L0 þ DLv L0 þ H 0 ð1 cos hÞ H 0 sin h 1 a ¼ tan L0 þ H 0 ð1 cos hÞ
Intensity (mm/h)
Duration
Rain Rain Rain Rain
30 30 15 30
Oct.20 Oct.23 Oct.26 Nov.4
1 2 3 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
By inserting Eqs. (5) and (9) into Eq. (7), the vertical displacement due to the compression of the soil layer can be identified and the compression strain can be calculated from the displacement. 2.3. Experimental conditions To simulate the actual soil-water conditions in a natural slope that has experienced numerous rainfall events, three pre-rainfall events (Rain 1, 2, 3, in Table 2) were applied to the model slope before the targeted rainfall event (Rain 4 in Table 2). The surface and the vertical displacement, the shear strain, the compression strain, the G.W.L., the suction, and the V.W.C. in the slope were measured and automatically recorded every 10 s. 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
ð7Þ 3.1. The surface displacement at different location on the model slope
According to Fig. 5, a is derived as tan a ¼
Number
Experiments conducted at 2009.
The increase of the length of the invar wire due to the rotation of the tilt meter ‘DLs ’ is DLs ¼ L L0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ fL0 þ H 0 ð1 cos hÞg2 þ H 20 sin2 h L0
Table 2 Artificial rainfall conditions.
ð8Þ ð9Þ
Fig. 6 shows the time variation of the G.W.L., the vertical displacement, and the surface displacement at different locations on the model slope. The G.W.L. was observed at 0 cm, 150 cm, and 300 cm from the toe of the slope, while
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Rain 4. 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 rainfall events without the G.W.L. generation (Rains 1 2). The displacement also increased during the non-rainfall period after Rain 3. The surface displacement at 450 cm only increased during Rain 4. The surface displacement at 150 cm and 300 cm showed nearly identical magnitudes of increase during Rain 1, Rain 2 and Rain 3 respectively. The results show that the time variations and magnitudes of the G.W.L., the vertical displacement, and the surface displacement at the sections between 150 cm and 300 cm from the toe of the slope are nearly identical. This fact suggests that the G.W.L. increase and the deformation behavior at different locations were almost unique in this section. 3.2. The shear and compression deformation in the model slope
Fig. 6. Time variations of the groundwater level (G.W.L.), the vertical displacement and the surface displacement at different distances from the toe of the model slope.
no G.W.L. was observed at 450 cm and 525 cm from the toe of the slope. The G.W.L. at 0 cm appeared at every rainfall 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, which is the toe of the slope. The vertical displacement at each location increased significantly during rainfall events, while these displacements showed a slight increase immediately following the rainfall events. The displacement increased without the generation of the G.W.L. during Rain 1 and 2, while it increased with the increase of the G.W.L. during Rain 3 and 4; while small increases were recorded during Rains 1–3, the displacement was significant during
Fig. 7 shows the time variation of the V.W.C., the suction, the compression strain, and the shear strain in the model slope. 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 for the Figure. The V.W.C. increased during each rainfall event and decreased gradually after the event. The V.W.C. reached maximum value after termination of Rain 1, 2 and 3. In general, the V.W. C. was greater at shallower layers than at deeper layers. The V.W.C. also became greater during later rainfall events. The suction decreased remarkably during each rainfall event and increased gradually after the events. The suction decreased up to minimum value after termination of Rain 1, 2 and 3. The suction at the shallower layers was generally less than at deeper layers. The minimum suction was nearly identical during Rain 1, Rain 2, and Rain 3, but it was slightly lower during Rain 4. The suction at each depth was positive through the experiment, although the G.W.L. increased beyond the measured depth in some cases. Fig. 6 shows that the G.W.L. rose to 35 cm in depth in the section between 150 cm and 300 cm during Rain 3, while the suction below 35 cm in depth was still positive during Rain 3. The G.W.L. rose to 15 cm in depth at 150 cm and to 0 cm in depth at 300 cm, although suction below 15 cm in depth was still positive during Rain 4. This may be due to quasi-saturation (absorption with air in some pores) beneath the ground water level in the slope. The compression strain at 5 cm, 53.85 cm deep was positive though the duration of the experiment, while it was negative at 15 cm, 25 cm and 35 cm prior to Rain 4. The compression strain at 15 cm, 25 cm deep was still negative during Rain 4, while it became positive at 35 cm, 45 cm deep. The compression strain at 45 cm was negative during Rain 1 and 2 while it turned to positive during Rain 3 and 4. Although the compression strain at 45 cm, 53.85 cm showed pulsating increases between Rain 3 and Rain 4, these were disregarded as electric noise. The compression strain at 5 cm, 45 cm, and 53.85 cm showed increased significantly just
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The shear strain at 32.2 cm and 50.6 cm increased not only during rainfall events (wetting process) but also 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 was relatively low and showed no significant increase prior to Rain 4 and showed significant increase during Rain 4. The shear strain at 13.8 cm and 41.4 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. 4. Discussion 4.1. Relationship between the surface displacement, vertical displacement and the G.W.L
Fig. 7. Time variations of the V.W.C., the suction, the compression strain (ec) and the shear strain (c) in the slope.
after Rains 1–3, while other depths seemed uninfluenced by the rainfall events.
The surface displacement and the vertical displacement are the product of the soil depth to the integration of the shear strain and the compression strain from the surface to the base of the slope. Thus, the relationship between the surface displacement, the vertical displacement and the G.W.L. were examined to assess the deformation behavior of the model slope. Fig. 8(a) shows the relationship between the surface displacement and the G.W.L. at 150 cm and 300 cm from the toe of the slope throughout the duration of the experiment. The blue and red symbols represent data during a rainfall event and after a rainfall event, respectively. Most of the data in the figures are after Rain 3 and during Rain 4 because the variation in the surface displacement before the termination of Rain 3 was much smaller than that after Rain 3. No increase was observed in the surface displacement during Rain 1 and 2 because there was no increase in the G.W.L. The G.W.L. increased to almost 20 cm and decreased to zero once, with a very small increase in the surface displacement during Rain 3; a large increase of G.W.L. created a significant surface displacement at both 150 cm and 300 cm during Rain 4. The relationship at 150 cm was almost same as that at 300 cm until 13 cm of displacement (35–40 cm of G.W. L.); then the surface displacement at 150 cm slightly increased; while that at 300 cm slightly decreased. The rate of the increase of the surface displacement became greater with the increase of the G.W.L. until reaching a peak. Fig. 8(b) shows the relationship between the surface displacement and the G.W.L. at 150 cm and 300 cm, up to 5 cm, to show the detailed relationship under a repeated rainfall event. The G.W.L. increased during the first wetting process and then decreased during the first drying process, with a small increase in the surface displacement. The increase in the surface displacement during the drying process may be an indication of delayed deformation (viscous behavior) of the slope. During the next wetting process, the surface displacement showed small increase until the G.W. L. reached the maximum G.W.L. of the first wetting process, and then increased significantly with increases in the
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1) 150cm
2) 300cm (a) Entire duration of the experiment
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1) 150cm
2) 300cm (b) Small displacement range
Fig. 8. Relationship between the surface displacement and the G.W.L. Blue and red symbol represent data during rainfall event and after rainfall respectively.
G.W.L. The surface displacement showed yielding behavior corresponding to the repeated increase of the G.W.L. Fig. 9(a) shows the relationship between the vertical displacement and the G.W.L. at 150 cm and 300 cm throughout the duration of the experiment. The blue and red symbols represent data during rainfall events and after rainfall events, respectively. As was observed in the relationship between the surface displacement and the G.W.L., the relationship at 150 cm was nearly identical with that at 300 cm until 4 cm of vertical displacement. The vertical displacement showed a greater rate of increase upon increasing the G.W.L. The vertical displacement at 150 cm increased slightly beyond 4 cm of vertical displacement, while it was almost constant at 300 cm beyond 4 cm. Fig. 9 (b) shows the relationship up to 2 cm to examine the detailed relationship under repeated rainfall events. As was observed in the relationship between the surface displacement and the G.W.L., the vertical displacement
increased with increasing G.W.L. during the first wetting process and then showed a small increase during the subsequent drying process. The increase in the vertical displacement during the drying process may be due to the delayed deformation (viscous behavior) of the slope. During the second wetting process, the displacement remained almost constant with increasing G.W.L. until reaching the maximum G.W.L. of the first wetting process; it then increased significantly with increases in the G.W.L. 4.2. Relationship between the shear strain and the suction, the pore pressure Following the overview of the deformation of the model slope, the shear and compression deformation in the model slope relating to rainfall infiltration is examined in detail. The relationship between the shear strain and the suction is shown in Fig. 10. The relationship is different in
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1) 150cm
1) 150cm
2) 300cm
2) 300cm
(a) Entire duration of the experiment
(b) Small displacement range
Fig. 9. Relationship between the vertical displacement and the G.W.L. Blue and red symbol represent data during rainfall event and after rainfall respectively.
shallow and deep layers. Fig. 10(a) shows the relationship between the shear strain and the suction at 23 cm to demonstrate an unsaturated soil layer. The relationship above this depth is almost same with that at 23 cm. The blue and red lines represent the duration of the rainfall event and after the rainfall event, respectively. The suction at the depth of a tilt meter was derived by interpolating and extrapolating the measured suction at every 10 cm of depth. The suction initially decreased with no increase in the shear strain during the wetting process; the shear strain then increased under constant suction after the wetting process. The suction increased without varying the shear strain during the subsequent drying process. This behavior may be attributed to the delay in shear deformation caused by the visco-plastic deformation of the soil. Fig. 10(b) and (c) shows the relationship between the shear strain and the suction at 32.2 cm and 50.6 cm,
respectively, to demonstrate a saturated layer. The arrows indicate the shear strain at the generation of the relative pore pressure head at each depth. The relative pore pressure head is defined as the difference between the G.W.L. and the vertical distance from the center of a tilt meter to the base of the slope (Fig. 11), that is, the pore pressure head at each depth of the slope. The behavior of the shear strain to the variation of the suction at 32.2 cm was similar to that at 23 cm; the shear strain remained almost constant with the suction decrease at wetting processes and then developed with the suction increase at subsequent drying processes at 32.2 cm. The shear strain increased with the decrease in the suction during the wetting processes at 50.6 cm. To be more precise, the shear strain increased not only with the decrease in the suction during the wetting process but also with the increase in suction during the drying process at 50.6 cm. During the next wetting
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Fig. 11. A definition of a relative pore pressure in the slope.
(a) Depth: 23 cm
(b) Depth: 32.2 cm
(c) Depth: 50.6 cm Fig. 10. Relationship between the shear strain and the suction at different depths. c: the shear strain. Blue and red line represent data during rainfall event and after rainfall respectively.
process, the shear strain showed little variation with the decrease in suction until the minimum suction of the previous wetting process and then increased with the decrease in suction. The shear strain increased significantly when it exceeded the value at the generation of the relative pore pressure head. The minimum suction during the last wetting process was a yield stress from the repeated wetting and drying processes. Uchimura et al. (2011) reported the same type of yielding behavior of the shear displacement from the repeated increase and decrease of the V. W.C. for a sandy specimen under direct shear with constant shear stress. This suggests that shear deformation only occurs when the rainfall amount is sufficient to generate even the smallest suction in an actual slope. The shear strain increased with greater decreases in suction after the generation of the pore pressure at each depth. The value of the suction was still positive after the generation of the pore pressure. As previously shown, the relationship between the shear strain and the suction at a shallower layer differed from that at a deeper layer. The shear strain increases under constant suction in a shallower layer, while it increases with the decrease of suction only when the suction decreases beyond the yielding value at a deeper layer. It can be said that the shear deformation at a shallower layer depends more on the visco-plasticity of a soil while it depends more on the decrease of the suction at a deeper layer. The shear deformation shows the yielding behavior to the repeated loading of the suction at a deeper layer. It is recognized that the shear strain significantly increases under the generation of pore pressure (see Fig. 10(b) and (c)). This fact indicates the necessity of examining the relationship between the shear strain and the relative pore pressure in the slope. Fig. 12 shows the relationship between the shear strain and the relative pore pressure head at depths of 23 cm, 32.2 cm, 41.4 cm, and 50.6 cm – where the relative pore pressure was generated. The shear strain at 41.4 cm became negative during Rain 1, Rain 2 and Rain 3, without the generation of relative pore pressure during the unsaturated conditions, while the shear strain increases to positive during Rain 4 with the increase in the relative pore pressure head. The shear
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Fig. 12. Relationship between the shear strain and the pore pressure in the slope. c: the shear strain.
strain at other depths initially increased slightly without the generation of the relative pore pressure head (during unsaturated conditions) and then increased significantly with the increase in the relative pore pressure head. At a depth of 50.6 cm, the pore pressure head increased to 6 cm with an increase in shear strain of 0.28, and then decreased to zero with an increase in shear strain of 0.3. A significant increase in the pore pressure started from the shear strain of 0.39 and resulted in an increase in the shear strain during Rain 4. However, the shear strain increased with a relative pore pressure head of less than 6 cm during Rain 4, even though the relative pore pressure head was less than the maximum value during a previous rainfall event. This means that the shear strain did not demonstrate clear elasto-plastic yielding to the repeated loading in pore pressure in this experiment. The shear strain increases at 32.2 cm and 41.4 cm grew larger with a greater relative pore pressure head until reaching a peak value in the relative pore pressure head during Rain 4. The shear strain showed strain hardening until the peak of the relative pore pressure head at these depths. The maximum pore pressure heads at 23 cm, 32.2 cm and 41.4 cm were shown to be 2.5 cm, 11.9 cm and 21.0 cm, respectively, while the maximum pore pressure at 50.6 cm could not be measured within the range up to 0.57 of the shear strain. This can likely be attributed to the larger maximum pore pressure at a deeper layer. 4.3. Relationship between the compression strain and the suction and the pore pressure The behavior of the compression strain to the suction and the pore pressure in the model slope is examined
following the examination of the shear strain in the model slope. Fig. 13 shows the relationship between the compression strain and the suction at different depths in the model slope. The blue and red lines represent the duration of rainfall event and after the rainfall, respectively. Fig. 13(a) shows the relationship at 4.6 cm to demonstrate a shallow layer. The suction decreased initially without varying the compression strain at each wetting process during rainfall events, and then the compression strain increased with increased suction at each drying process that followed the rainfall events. While the compression strain initially decreased significantly, it then showed considerable increase under almost constant suction after the wetting process of Rain 4. Fig. 13(b) shows the relationship at 23 cm to demonstrate a middle layer. The relationships at 13.8 cm and 32.2 cm are not shown in the figure but are essentially the same as those at 23 cm. The compression strain remained constant during the wetting process and proceeded during the drying processes after Rains 1–3 as well as that at 4.6 cm. The compression strain remained constant initially and then increased significantly with a decrease in suction until the generation of the pore pressure at the wetting process of Rain 4. This value decreased significantly with constant suction after the generation of the pore pressure. The difference between the relationships at 4.6 cm and that at 23 cm is the direction of the proceeding compression strain and behavior during the wetting process of Rain 4. The soil layer at 4.6 cm basically showed compression while that at 23 cm was dilated. Consideration of the reasons for this difference is beyond the scope of this paper. The mechanism of compression of the soil layer due under unsaturated condition need to be examined to investigate this result. The second difference during the wetting process of Rain 4 is that the compression strain increases with constant suction at 4.6 cm while it increases with the decrease of the suction at 23 cm. This is important when examining the compression behavior of the slope during unsaturated conditions because it suggests that the compression behavior at deeper layers depends more on the decrease of suction during the wetting process of Rain 4. The relationship at 41.4 cm is shown in Fig. 13(c). The relationship at 50.6 cm is almost the same as that at 41.4 cm. The compression strain remained constant with the decrease of the suction at wetting processes after Rain 2 and during Rain 3, then increased with increasing suction at subsequent drying processes after Rain 3. It remained constant with the decreased suction, then increased with constant suction, and increased with increasing pore pressure during the final wetting process due to Rain 4. The decrease in the suction after rainfall events might be due to the delay of seepage water infiltration at deeper layers. The compression behavior of the slope to the repeated loading of the suction must be compared with the shear behavior. The elasto-plastic yielding behavior of shear strain to the repeated loading of the suction is clear at a deeper soil layer, while that of the compression strain to the repeated loading of the suction is not clearly observed
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(a) Depth: 4.6 cm
Fig. 14. Relationship between the compression strain and the pore pressure. ec: the compression strain.
(b) Depth: 23 cm
(c) Depth: 41.4 cm Fig. 13. Relationship between the compression strain and the suction in the slope. ec: the compression strain. Blue and red line represent data during rainfall event and after rainfall respectively.
in this examination. The increase in the shear strain under constant suction after the wetting process (or with the increase of the suction during the drying process) is greater at shallow layers. Unlike shear strain, the behavior of the compression strain to the variation of the suction is almost the same at all depths and remained constant with decreasing suction during the wetting process and increased with increasing suction during the drying process at all depths. The behavior of the compression strain after the generation of pore pressure, that is, a large increase in the compression strain with increasing pore pressure, is the same as that observed for the shear strain and the pore pressure. The shear and compression deformation under constant suction (or with increasing suction) may be considered time-dependent deformation due to the wetting of the soil layer. Viscosity might prevent deformation of the soil under large rates of decreased suction during the wetting process, and visco-plastic deformation may occur after the wetting process. Fig. 14 shows the relationship between the compression strain and the pore pressure in the slope. No pore pressure was observed at 4.6 cm or 13.8 cm. At 23 cm, the compression strain reached 0.02 just before the generation of pore pressure during the unsaturated conditions (as shown in Fig. 13(b)) and then decreased almost linearly with the increase in the pore pressure. The compression strain at 32.2 cm initially moved to 0.01 under an unsaturated condition and then increased with the increase in the pore pressure. The compression strain at 41.4 cm also moved to
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Fig. 15. Relationship between the shear strain and the compression strain at 23 cm and 50.6 cm. c: the shear strain, ec: the compression strain.
0.008 under the unsaturated condition. Then it increased up to 0.44 with increasing pore pressure after the generation of pore pressure. The compression strain at 50.6 cm showed small variations under the unsaturated condition, then decreased with the pore pressure until 10 cm, and then finally increased significantly with the increase in the pore pressure. In general, it can be said that the increase in the compression strain became greater with increased pore pressure, and the relationship between the compression strain and the pore pressure can be modified as hyperbolic at depths greater than 32.2 cm. The maximum pore pressure was greater at deeper layers, as was the relationship between the shear strain and the pore pressure. Because the compression strains at all depths only showed significant progress during the wetting process of Rain 4, no influence of repeated loading of the pore pressure could be observed in the relationship between the compression strain and the pore pressure in this experiment. 4.4. Relationship between the shear strain and the compression strain Fig. 15 shows the relationship between the shear strain and the compression strain at 23.3 cm and 50.6 cm throughout the duration of the experiment to examine the dilatancy of the soil in the slope. The relationship at 23.3 cm represents that at a shallower layer while the relationship at 50.6 cm represents that at a deeper layer. The relationship between the compression strain and the shear strain at 23.3 cm and 50.6 cm is a smooth curve that does not fluctuate significantly during Rain 1, Rain 2, Rain 3, and Rain 4. This means that the relationship does not show the yielding behavior for the cyclic loading of either the suction or the pore pressure. The relationship is not affected by the cyclic loading of the suction and the pore pressure under repeated rainfalls.
Fig. 16. Relationship between the surface displacement and the vertical displacement at 300 cm from the toe of the model slope.
4.5. Relationship between the surface displacement and the vertical displacement The result of the examination of the relationship between the shear strain and the compression strain suggests that the relationship between the surface displacement and the vertical displacement is also not affected by the repeated loading of the suction or the pore pressure. Because the surface displacement and the vertical displacement are products of the integration of the shear strain, the compression strain and the depth of a soil layer of the model slope. Fig. 16 shows the relationship between the surface displacement and the vertical displacement at 300 cm from the toe of the model slope. It is clear that the relationship is not disturbed by rainfall events because the shape of the curve showing the relationship is smooth against the loading of the suction and the pore pressure during rainfall events. The slope of the curve approaches zero with the increase in the surface displacement, which implies that the ratio of the increase of the vertical displacement to the surface displacement decreases and it approaches zero toward the failure of the soil. This is similar to the volumetric strain approaching zero toward the critical or residual state under the direct shear condition. It may well be that the ratio of the increase of the vertical displacement to the surface displacement can be used as an indicator of the instability of the slope. Whether or not this is actually the case can be the subject of further research on this topic. 5. Conclusions From the examinations above, the following conclusions can be derived:
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(1) The surface displacement and the vertical displacement increase with the generation of the G.W.L. during rainfall while they show small increases with decreasing G.W.L. after rainfall. The shear and compression strain increase with the V.W.C. increases and the suction decreases during rainfall, while the strains also increase after the rainfall as the V.W.C. decreases and the suction increases. (2) The surface displacement and the vertical displacement increase with increasing G.W.L. during the first wetting process, while they remain almost constant until reaching the maximum G.W.L. (yielding value) of the first wetting process at subsequent wetting process. The displacements increase significantly after the G.W.L. increases beyond the yielding value of the second wetting process. The yielding curve for the relationships between the surface displacement and the G.W.L. (or the vertical displacement and the G. W.L.) can be modeled as hyperbolic. (3) The response of the shear strain to the suction can be described as follows. At shallower layers, the shear strain is almost constant during the wetting processes (with decreased suction) and drying processes (with increased suction), while it proceeds under constant suction before the generation of the pore pressure. The shear strain increases with the decrease of suction during the first wetting process (and the increase of suction during the first drying process) and then remains constant until reaching the minimum suction (yielding value) of the first wetting process; the strain then increases with decreasing suction beyond the yielding value of the subsequent wetting process at deeper layers. The shear strain increases remarkably after the generation of pore pressure. (4) The shear strain shows little increase in the absence of the generation of pore pressure while it increases significantly with increasing pore pressure after the pore pressure is generated. The increase in the shear strain due to the increase in the pore pressure becomes larger with increasing pore pressure. The relationship between the shear strain and the pore pressure head just prior to failure can be modeled as a hyperbolic curve. (5) The compression strain remains constant as the suction decreases during the wetting processes and then proceeds as the suction increases during the drying processes; it proceeds significantly under constant suction during the final rainfall event at all depths. (6) The compression strain proceeds significantly after the generation of pore pressure at soil layers deeper than 13.8 cm. The increment of the compression strain to the increase of the pore pressure grows with increasing pore pressure. (7) The relationship between the shear strain and the compression strain is not affected by the repeated loading of the suction due to the numerous rainfalls.
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(8) The relationship between vertical displacement and surface displacement is not affected by the repeated loading of the suction or the pore pressure. The ratio of the increase in vertical displacement to the increase in surface displacement decreases and approaches zero toward the failure of the slope. It may suggest that this ratio is an indicator of the instability of the slope.
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