Seismic behaviour of reinforced embankments in dynamic centrifuge model tests

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Seismic behaviour of reinforced embankments in dynamic centrifuge model tests Tadao Enomoto a,⇑,1, Tetsuya Sasaki b b

a Ibaraki University, Japan Public Works Research Institute, Japan

Received 9 November 2016; received in revised form 23 October 2017; accepted 7 November 2017

Abstract A series of dynamic centrifuge model tests was conducted to investigate the effects of reinforcement on the seismic behaviour of hillside embankments consisting of sandy soils and resting on stiff base slopes. In total, three types of seismic reinforcements, namely, largescale gabions, drainage-reinforcing piles, and ground anchors with pressure plates, were employed in the tests. The test results showed that: (1) the seismic performance of both lower and higher embankments was remarkably improved by installing large-scale gabions at the toe as they restrained the completion of the formation of sliding planes; (2) the installation of drainage-reinforcing piles at the embankment toe was rather effective in reducing the overall earthquake-induced deformation due to their high permeability and restraint effect against sliding displacement at the reinforced region; and (3) the embankments improved by ground anchors with pressure plates were not vulnerable to earthquake-induced damage due to their constraint effects even under high water table conditions. The improvement effects by the above-mentioned three types of reinforcements were presented by evaluating the global safety factors based on the results of a series of triaxial compression tests. Ó 2018 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: Dynamic centrifuge model test; Embankment; Seismic reinforcement; Laboratory triaxial test; Global safety factor (IGC: D6nD7)

1. Introduction Road embankments constructed on mountainsides and hillsides have frequently experienced catastrophic failures due to past strong earthquakes. In some cases, a long period of time was required to restore the damaged hillside embankments, particularly in the case of the higher ones. For example, according to Hashimoto et al. (2008), it took 44 days to restore embankments for the national highway damaged by the 1994 Hokkaido-Touhouoki earthquake. Tokida (2012) mentioned that the Noto Toll Road,

Peer review under responsibility of The Japanese Geotechnical Society. ⇑ Corresponding author. E-mail address: [email protected] (T. Enomoto). 1 Formerly Public Works Research Institute.

damaged by the 2007 Noto-Hanto earthquake, was opened to the public about one month after the main shock and that the permanent restoration of all the damaged embankments was completed about five months after the temporary recovery. To reduce earthquake-induced damage to embankments, some studies using dynamic centrifuge apparatuses have been conducted (e.g., Kutter and James, 1989; Dobry et al., 1997; Pilgrim, 1998; Okamura et al., 2001; Matsuo et al., 2002; Egawa et al., 2004; Okamura and Tamamura, 2011; Higo et al., 2015). However, these studies focused on the seismic behaviour of embankments with no countermeasures, and the number of investigations on the effectiveness of reinforcement has been limited. As pointed out by Tokida (2012), one of the reasons for this may be that damage to road embankments induced by

https://doi.org/10.1016/j.sandf.2017.12.005 0038-0806/Ó 2018 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/). Please cite this article in press as: Enomoto, T., Sasaki, T., Seismic behaviour of reinforced embankments in dynamic centrifuge model tests, Soils Found. (2018), https://doi.org/10.1016/j.sandf.2017.12.005

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earthquakes is still considered easy to repair, in spite of the above-mentioned examples of having to spend a long period to restore them. Among a limited number of recent studies, the following experimental investigations were conducted on seismic countermeasures for road embankments using dynamic centrifuge apparatuses: (1) The seismic behaviour of embankments with countermeasures for liquefiable subsoil was investigated by Adalier et al. (1998). (2) Hashimoto et al. (2008) examined the effects of reinforcing bars with and without small pressure plates on the seismic performance of embankments. (3) The seismic performance of embankments crestretrofitted with geotextile was confirmed by Ueno et al. (2009). (4) Tokida (2012) reported the effectiveness of crest reinforcement with geosynthetics, the placement of toe rigid blocks, and the installation of rigid barrier walls at the embankment shoulder. However, these experimental studies used model embankments with a height of 10 m or less in prototype scale due to the limited capacities of the shaking table and the soil container, in spite of the susceptibility of embankments more than 15 m in height to earthquakeinduced damage, which was reported by Okimura et al. (1999) and PWRI (2008). The excitation capacities of the shaking tables were also limited (i.e., a peak input acceleration smaller than 0.5 g). In addition, the seismic behaviour of embankments with other types of countermeasures, excluding the above-mentioned retrofit techniques, has not been examined. In view of the above, a series of dynamic centrifuge model tests on the seismic performance of reinforced hillside road embankments, 15 m or 30 m in height, was conducted in the present study by improving the excitation capacity of the shaking table and using a large-scale soil container. This paper focuses on reinforcements by largescale gabions, drainage-reinforcing piles, and ground anchors with pressure plates, where they can often be employed in geotechnical practice. Although the concept of employing large-scale gabions itself was the same as that in the tests conducted by Tokida (2012), the gabions in the present study were stacked in three layers without fixing them in order to reproduce more realistic conditions. Furthermore, to quantify the effectiveness of the abovementioned three seismic countermeasures, the global safety factors of the reinforced embankments were also evaluated based on the results of a series of triaxial compression tests on fill materials. 2. Tested materials Fig. 1 shows the grading curves and the laboratory compaction test data for Edosaki sands from four different

batches used for model and laboratory element tests. Edosaki A and B sands were used for centrifuge test Cases 1, 8, and 9 conducted by Enomoto and Sasaki (2015), where their model embankments had no seismic countermeasures. Edosaki C sand was used in the present study for Cases 13 through 20 with the installation of the above-mentioned reinforcements. Details of the centrifuge model tests are presented later in this paper. Edosaki B, C, and D sands were also used in the present study for laboratory stressstrain tests. The values of the specific gravity (Gs), maximum diameter (Dmax), mean diameter (D50), uniformity coefficient (Uc), fines content (Fc), optimum water content (wopt), maximum dry density (qdmax), plasticity index (Ip), maximum and minimum void ratios (emax and emin), and permeability coefficient (k) of these materials are summarized in Table 1. The values of wopt and qdmax were determined by the A-c method in Japanese Industrial Standards (JIS) A 1210, where the materials were compacted in a cylindrical mould (inner diameter = 100 mm) in three layers with 25 free drops of a 2.5-kg rammer from a height of 30 cm for each layer. The soil properties of Edosaki A through D sands from different batches were quite similar to each other. The initial degree of compaction, Dc0, defined by Eq. (1), was used in the present study as the density index. Dc0 ¼ qd0 =qd max

ð1Þ

where qd0 is the initial dry density of the soil. The k value of Edosaki A sand, shown in Table 1, was evaluated by the constant head permeability test (JIS A 1218), where the specimen was prepared at the same water content and density as in the model and laboratory stressstrain tests (i.e., wopt = 16.7% and Dc0 = 82%, respectively). 3. Laboratory element tests on employed soils 3.1. Test procedures The undrained shear behaviour of saturated Edosaki sand under triaxial conditions was reported by Enomoto and Sasaki (2015). In the present study, a series of drained triaxial compression tests was conducted on this saturated sand, ET1 through ET6, summarized in Table 2. The parameters obtained in these tests are used later in this paper to evaluate the global safety factors of the model embankments. Small-scale cylindrical specimens, 5 cm in diameter and 10 cm in height, were produced by compacting wet materials inside a split mould in five layers using a hammer to Dc0 = 82% under the respective wopt values. The specimen was set into the triaxial apparatus and was saturated under an isotropic state with an effective mean principal stress of p0 ¼ ðr0v þ 2r0h Þ=3 = 20 kPa, where r0v and r0h are the effective vertical and horizontal principal stresses, respectively. After isotropic compression was performed toward the target initial effective confining stress, r00 , shown in Table 2, strain-controlled vertical monotonic load was applied at a

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1.7

100

Edosaki A sand (Case 1)* Edosaki B sand (Case 8 & 9)* Edosaki C sand (Case 13 - 20) Edosaki D sand

70

1.6 3

80

Dry density, ρd (g/cm )

90

Percent finer than D

3

*: tested by Enomoto and Sasaki (2015)

60 50 40 30 20 10

1.5 1.4 1.3

JIS A 1210 (A-c method) Edosaki A sand (Case 1)* Edosaki B sand (Case 8 & 9)* Edosaki C sand (Case 13 - 20) Edosaki D sand

1.2 1.1

*: tested by Enomoto and Sasaki (2015)

0 1E-3

0.01

a)

0.1

1.0

1

2

5

0

10

30

Water content, ω (%)

b)

Particle diameter, D (mm)

20

Fig. 1. Grading and compaction characteristics of sands used for model and laboratory stress-strain tests: (a) grading curves and (b) standard compaction test results. Table 1 Properties of sands used for model and laboratory stress-strain tests. Material Edosaki Edosaki Edosaki Edosaki *

A sand* B sand* C sand D sand

Gs

Dmax (mm)

D50 (mm)

Uc

Fc (%)

xopt (%)

qdmax (g/cm3)

Ip (%)

emax

emin

k (cm/s)

2.657 2.732 2.734 2.727

2.0 2.0 2.0 2.0

0.228 0.278 0.284 0.288

2.91 3.91 3.98 3.06

6.9 9.4 9.2 8.6

16.7 18.1 16.9 16.5

1.604 1.605 1.625 1.671

NP NP NP NP

1.095 – – –

0.609 – – –

9.98  104 – – –

Tested by Enomoto and Sasaki (2015).

Table 2 Conditions of laboratory stress-strain tests and obtained parameters. Edosaki sand

Test code

Test condition

B value

qd0 (g/cm3)

Dc0 (%)

wini(%)

r00 (kPa)

cd (kPa)

/d (deg)

B B B C C C D D D D D D B D D D

ET1 ET2 ET3 ET4 ET5 ET6 ET7 ET8 ET9 ET10 ET11 ET12 ET13 ET14 ET15 ET16

TC-D TC-D TC-D TC-D TC-D TC-D UC UC TC-D TC-U TC-D TC-U TC-U CTL CTL CTL

1.00 1.00 1.00 0.99 1.00 1.00 0.96 – 0.02 0.01 0.03 0.17 0.99 0.09 0.89 0.91

1.314 1.322 1.318 1.342 1.341 1.343 1.370 1.370 1.375 1.377 1.379 1.376 1.317 1.370 1.367 1.367

81.9 82.4 82.1 82.6 82.5 82.6 82.0 82.0 82.3 82.4 82.5 82.3 82.0 82.0 81.8 81.8

18.1 18.1 18.1 16.9 16.9 16.9 16.5 16.5 16.9 16.4 16.4 16.4 18.1 16.5 16.8 16.6

50 100 200 50 100 200 0 0 50 50 100 100 100 100 100 100

2.5 2.5 2.5 0.3 0.3 0.3 – – – – – – – – – –

32.6 32.6 32.6 32.5 32.5 32.5 – – – – – – – – – –

TC-D: Drained triaxial compression test, UC: Unconfined compression test. TC-U: Undrained triaxial compression test, CTL: Undrained cyclic triaxial liquefaction test.

constant vertical strain rate of e_ v = 0.1%/min under drained conditions. The deviator stress, q = r0v  r0h , and vertical strain, ev , were evaluated based on the measurements with a load cell placed inside the triaxial cell and an external displacement transducer, respectively. Meanwhile, the model embankments constructed under the optimum water content condition consisted of saturated and unsaturated regions with and without seepage water, respectively, as will be explained later. The deformation of the embankments can be largely affected by the saturation condition of the fill materials. Therefore, to

evaluate the difference in strength properties between saturated and unsaturated Edosaki sand, another series of laboratory stress-strain tests, ET7 through ET16, shown in Table 2, was also performed in the present study. The same procedure as mentioned above was employed for the specimen preparation, although the saturation process was skipped in some tests. Most of the unsaturated specimens were tested under the same water content as the model embankments without seepage water (i.e., wopt, Skempton’s B value = 0.010.17), while ignoring a small amount of inevitable evaporation during the centrifuge tests. In Test

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ET7, after the specimen had been saturated under the isotropic stress state of p0 = 10 kPa, the effective confining pressure was reduced to 0 kPa for unconfined compression. In this series, vertical monotonic loading or vertical cyclic loading was conducted at e_ v = 0.1%/min or a frequency of 0.1 Hz, respectively. The volume change of the unsaturated specimens in the drained triaxial tests was assumed to be equal to that of the saturated ones consisting of Edosaki C sand tested under otherwise the same condition. For simplicity, the volumetric strain, evol , of the unsaturated specimens was assumed to be zero in undrained shearing. 3.2. Test results Fig. 2 shows the results of drained triaxial compression tests on Edosaki B and C sands. The stress-strain behaviour of all the specimens exhibited strain hardening only. The contractive behaviour became more significant with increasing r00 . This trend in behaviour was similar to that of relatively loose geomaterials. It can also be seen that the difference in behaviour between Edosaki B and C sands was insignificant. The values of the internal friction angle defined at ev = 15%, /d, and cohesion cd, obtained from these test results, are summarized in Table 2. Fig. 3(a) shows the stress-strain behaviour of Tests ET8 through ET12 for unsaturated specimens. In Test ET7, the specimen totally collapsed before shearing due to a rather small impact which was generated when the piston with a top cap was connected to the axial loading device, suggesting that little cohesion existed under the saturated condition. On the other hand, a small peak strength was observed in Test ET8 conducted under the unsaturated condition due to the apparent cohesion. Fig. 3(b) shows the relationship between r00 and the maximum deviator stress, qmax, where the qmax value was defined at ev = 15% for specimens that did not show a distinct peak strength. The data from Test E1, obtained by Enomoto and Sasaki (2015), is also plotted in the figure. Under the drained condition, the strength of the unsaturated specimens was

slightly larger than that of the saturated ones due to the apparent cohesion. On the other hand, under the undrained condition, the qmax value of the unsaturated specimens was extremely larger than that of the saturated ones and was comparable to the drained strength, even taking into account an error in the calculation of the crosssectional area due to the unsaturated condition. In Tests E1 and ET13, using fully saturated specimens, positive excess pore water pressure was observed throughout shearing. Therefore, under the unsaturated condition, the generation of excess pore water pressure may have been restrained due to air bubbles in the specimens, resulting in extremely large strengths. Fig. 3(c) shows the relationship between the cyclic stress ratio, rd =ð2r00 Þ, and the number of cycles to cause double amplitude vertical strain, evðDAÞ , of 5%, Nc, where rd denotes the single amplitude cyclic vertical stress. Some data from Enomoto and Sasaki (2015) are used in the figure. As double amplitude vertical strain of only about 0.1% was observed after 700 cycles in Test ET14, an attempt was made to increase the B value in ET15 and ET16. As shown in Fig. 3(c), the cyclic resistance of the unsaturated specimens was significantly larger than that of the saturated ones. A similar trend for Toyoura sand was reported by Tsukamoto et al. (2002). 4. Procedures of model tests A series of model tests was conducted with a dynamic centrifuge apparatus with an effective radius of 6.6 m at PWRI (Matsuo et al., 1998). The scale factors for the acceleration, density, length, mass, force, stress, strain, time, and viscosity in the dynamic centrifuge model tests are shown in Table 3. In order to simulate the seismic behaviour of hillside road embankments, models with and without reinforcements were constructed on a stiff base slope made of plaster in a soil container. After having applied centrifugal accelerations to the models, a fluid was introduced into the model embankments. When the pore water pressures reached the 6

500

Drained triaxial compression σ '0= 200 kPa

Edosaki B sand Edosaki C sand

400

σ '0= 200 kPa

Volumetric strain, εvol (%)

Deviator stress, q (kPa)

Drained triaxial compression

ET6

300

ET2 ET3

200

ET5

σ '0= 100 kPa ET1

100

0

a)

σ '0= 50 kPa

0

2

4

6

8

10

Vertical strain, εv (%)

14

4 3

ET1 ET4 σ '0= 50 kPa

2 1

ET4

12

σ '0= 100 kPa ET2 ET5

ET3 ET6

Edosaki B sand Edosaki C sand

5

0

16

b)

0

2

4

6

8

10

12

14

16

Vertical strain, εv (%)

Fig. 2. Results of drained triaxial compression tests on Edosaki B and C sands with Dc0 = 82%: (a) q  ev and (b) evol  ev relations.

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a)

b)

c) Fig. 3. Comparison of strength properties between saturated and unsaturated Edosaki sand: (a) q  ev relations of unsaturated specimens, and (b) and (c) static and dynamic strength characteristics, respectively.

5

target values and the global steady state condition was achieved, the model was horizontally shaken. Details of the test procedure are presented below. Typical cross-sections of the models are shown in Fig. 4. The test condition for each model is summarized in Table 4. The models were prepared in a large-scale rigid container, 1.5 m long, 0.3 m wide, and 0.5 m high, with both sides made of high-strength glass to allow for observation. The stiff base slope consisted of two different inclinations, 30 and 5 deg, and was made of plaster. Sand paper was glued to the surface of the base slope to ensure mechanical friction at the interface between the plaster slope and the sand particles. In order to provide seepage water into the embankments, as shown in Fig. 4, a reservoir tank and pipes were installed at the end of the rigid container and in the base slope, respectively. The model embankment, with side slopes of 1:1.8, was made carefully by compacting Edosaki sand to Dc0 = 82% by means of a wooden plate at the respective initial water contents, wini, shown in Table 4. The wopt value was basically employed for 15-m-high embankments as wini, while the model embankments in Cases 8, 9, 16, and 17 were made at the water content which was slightly drier than wopt to avoid the failures that would possibly be caused by the large applied centrifugal acceleration (i.e., 75 g) and their heights. Since the peak internal friction angle and the secant modulus of a similar sandy soil (Inagi sand), obtained from drained plane strain compression tests, were rather independent of the wini values, as confirmed by Tatsuoka (2011), it was assumed in the present study that the effects of the small difference among wini on the seismic performance of the embankments were insignificant. Filling and compaction were repeated for twelve layers of 25- and 33-mm elevations each for the models shown in Figs. 4(a) and (b), respectively. During the model construction, accelerometers (A) and pore water pressure transducers (P) were embedded at the prescribed locations shown in Fig. 4. In addition, mesh lines made of white-coloured silica sand No. 7, and one or two thin reference marks with a diameter of about 8 mm per rectangle and triangle, which were formed by these mesh lines, were placed at the side surface of the embankment to visually observe the model deformation through a transparent glass plate. To eliminate the effects of friction, a thin layer of silicone grease was spread on the side surface of both transparent glass plates. A toe drain consisting of silica sand No. 3 or 4, whose length is shown in Table 4, was installed in all cases, except for Cases 13 and 16.

Table 3 Scale factors in dynamic centrifuge model tests. Scale

Acceleration

Density

Length

Mass

Force

Stress

Strain

Time

Viscosity

Dynamic

Seepage

Prototype Model

1 N

1 1

1 1/N

1 1/N3

1 1/N2

1 1

1 1

1 1/N

1 1/N2

1 1/N

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Fig. 4. Typical cross-sections of test models: (a) Cases 1, 13 through 15, and 18 through 20 and (b) Cases 8, 9, 16, and 17.

In Cases 13 through 19, the respective seismic countermeasures shown in Table 4 and Fig. 5 were taken. To reproduce a more realistic condition in the model tests, it may be necessary to satisfy the similitude law with respect to the strength and stiffness of these seismic countermeasures. Furthermore, the intervals among the respective countermeasures (e.g., distance among drainage-reinforcing piles), as well as their sizes and weights in prototype scale, should be consistent with those usually employed in geotechnical practice. However, it was difficult to find materials satisfying these conditions at the same time. Therefore, in the present study, the interval and the size of the respective countermeasures were designed to be within the actually employed range, as much as possible, while taking into account the capacity of the employed soil container. The model materials for the wire meshes of the large-scale gabions, drainage-reinforcing piles, ground anchors, and pressure plates were selected to withstand large centrifugal force and the strong motion of input excitation. The model gabions consisted of stiff angular gravel with about Dmax = 5 mm and were stacked in three layers inside the embankment toe for Cases 13 and 16, while they were placed with counterweight fill constructed by compacting Edosaki sand according to the same method as that employed for the embankment body in Cases 14, 15, and 17 (Figs. 5(a) and (b)). The embankment toe was in contact with the gabions via a sheet of non-woven fabric for Cases 13 and 16, while a gravel layer for drainage was made between the embankment body and the counterweight fill in Cases 14, 15, and 17. As shown in Fig. 5(c), drainagereinforcing piles were modelled by making a number of holes, 2 mm in diameter, on the side surface of the hollow cylindrical aluminium bars, 6 and 4 mm in outer and inner diameter, respectively, and 400 mm in length. For Case 18, these model piles were inserted into the completed embankment at an inclination of 5 deg. Ground anchors with

pressure plates were employed as a seismic countermeasure in Case 19. As seen from Fig. 5(d), both ends of each ground anchor, which was modelled by wire ropes with 0.7 mm in diameter, were fixed on a pressure plate, modelled by 3mm-thick acrylic plates, by bolts and in the stiff base slope, respectively. All the ground anchors were kept straight with the minimum tensile force throughout the model construction as the anchorage strength at the stiff base slope, which was required to prevent their pull-out, and subsequently, to act as the reinforcement during the shaking, was not evaluated. Therefore, the pre-stressed force applied to the ground anchor may have been small, although it was not measured. In the future, it will be necessary to confirm the effects of the pre-stressed force of the ground anchor on the seismic performance of embankments with an accurate evaluation of the anchorage strength. After the model construction, the models shown in Figs. 4(a) and (b) were spun up to centrifugal accelerations of 50 g and 75 g, respectively. A fluid, methyl-cellulose solution, which was 50 or 75 times more viscous than water, was then introduced into the reservoir tank through the rotary joint of the centrifuge apparatus, while the discharge rate was carefully controlled. Through the process of seepage, the elevation of the phreatic line was monitored based on the measurements with the pore water pressure transducers embedded in the model and images from a high speed camera fixed on the centrifuge apparatus. When the pore water pressures reached the target values and the global steady state condition, the model was horizontally shaken. Fig. 6 shows typical input accelerations for the first shaking step. As shown in Fig. 6(a), the ground motion recorded at the Kobe Maritime Observatory during the 1995 Hyogoken-Nambu earthquake was used for the model shown in Fig. 4(a). Due to a limited excitation capacity of the shaking table under the higher centrifugal acceleration, the same input could not be employed for the model shown in Fig. 4(b). Therefore, the ground motion recorded at the Shichihou Bridge during the 1993 HokkaidoNanseioki earthquake, shown in Fig. 6(b), was inputted for the higher embankment model. As shown in Table 4, for Cases 16 through 20, to confirm the shape of the sliding plane formed in the embankments, the models were furthermore shaken horizontally after the first shaking step by using a sinusoidal wave at a frequency of 1.2 or 0.8 Hz (60 Hz in model scale) with acceleration of a single amplitude of 0.25, 0.3, 0.5 or 0.6 g. Due to a lack of knowledge of the embankment deformation induced by sinusoidal waves under the test conditions employed in the present study, these frequencies and amplitudes were temporarily determined by referring to Matsuo et al. (2002) who had conducted similar model tests. As the deformation of the model embankments induced by the second shaking step was unexpectedly not large enough to confirm the shape of the sliding plane, however, the acceleration amplitude of the third shaking stage was set to be twice larger than that of the second one in Cases 16 through 18. In Cases 19 and 20, due to a temporal restriction, the shaking step by a

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sinusoidal wave with 0.3 g was skipped. The settlement at the crest and the top of the slope, S and S’, respectively (see Fig. 4), was measured with an external displacement transducer throughout the tests.

H95 H93 H93 H95 H95 H95 H93 ? S0.25 ? S0.5 H93 ? S0.25 ? S0.5 H95 ? S0.3 ? S0.6 H95 ? S0.6 H95 ? S0.5

5. Model test results and discussions H95: The 1995 Hyogoken-Nambu earthquake, H93: The 1993 Hokkaido-Nanseioki earthquake. Sa: Sinusoidal wave at frequencies of 1.2 and 0.8 Hz with acceleration of a single amplitude of a (g) for models shown in Figs. 4(a) and (b), respectively (prototype scale). 1 In model scale. 2 In prototype scale. 3 Tested by Enomoto and Sasaki (2015).

– – – Large-scale gabion Counterweight fill with large-scale gabion Counterweight fill with large-scale gabion Large-scale gabion Counterweight fill with large-scale gabion drainage-reinforcing pile Ground anchor with pressure plate – 2.5 21.75 11.25 0 2.5 2.5 0 11.25 2.5 2.5 2.5 16.7 15.3 15.3 15.8 14.8 14.8 14.3 14.3 15.8 15.8 14.8 82.5 81.5 82.2 82.8 82.4 82.2 82.3 82.4 82.2 82.2 82.2 Edosaki Edosaki Edosaki Edosaki Edosaki Edosaki Edosaki Edosaki Edosaki Edosaki Edosaki 15 30 30 15 15 15 30 30 15 15 15 30 40 40 30 30 30 40 40 30 30 30 50 75 75 50 50 50 75 75 50 50 50 13 83 93 13 14 15 16 17 18 19 20

H (cm) Centrifugal acceleration (g) Case

Table 4 Conditions of dynamic centrifuge model tests.

1

H (m)

2

A sand B sand B sand C sand C sand C sand C sand C sand C sand C sand C sand

Dc0 (%) Fill material

wini (%)

Toe drain Length (m)2

Seismic countermeasure

Shaking history

T. Enomoto, T. Sasaki / Soils and Foundations xxx (2018) xxx–xxx

The test results shown in the following sections are discussed in prototype scale. A definition of the acceleration direction is given in Fig. 4. The residual values of S and S’, evaluated from photographs taken after shaking, were used in the following discussions due to the limited measurement capacity of the external displacement transducer (possible measurement range and resolution in model scale of 0–50 mm and 0.1 mm, respectively). In the following sections, to discuss the effects of reinforcements on the seismic behaviour of embankments under the same conditions, the results from the first shaking step are analyzed unless otherwise noted. The earthquake-induced deformations of embankments, which were sketched after the first shaking step, together with water tables for the respective test cases, are shown in Fig. 7. As indicated by the deformed rectangles, which were originally made of white-coloured silica sand No. 7, the deformation of the embankments was concentrated below the water table due possibly to the relatively low strength of saturated Edosaki sand, as seen in Fig. 3. Higo et al. (2015) also reported that embankments with a higher water content than wopt were more vulnerable to earthquake-induced damage due to almost zero suction in the centrifuge model tests. In Cases 1 and 9, after a certain elapsed time from the end of the main shaking, large sliding displacement occurred suddenly near the water table, resulting in the delayed catastrophic failure. The possible reasons for the delayed failure were thoroughly discussed by Enomoto and Sasaki (2015). 5.1. Improvement by Large-scale gabions with and without counterweight fill Fig. 8 shows the relationship between S and S’ obtained from four model tests with an embankment height (in prototype scale), H, of 15 m. Large-scale gabions were employed for the seismic countermeasures in Cases 13 through 15. As shown in Fig. 7, the elevation of the seepage water in Cases 1, 13, and 14 was similar to each other. Enomoto and Sasaki (2015) reported that the earthquake-induced settlement of the embankments with no reinforcement increased with increasing seepage water elevation measured from the plaster surface at the first bench, hw. The definition of hw and its value for each test case are indicated in Fig. 8. It is clearly seen from the figure that the residual values for S and S’ in Case 1 without reinforcement were much larger than those in the other three cases. This suggests that the seismic performance of embankments could be remarkably improved by installing large-scale gabions at the embankment toe. Similar results

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Input acceleration, A (g)

1.0 For embankment with H= 15 m 1995 Hyogoken-Nambu earthquake

0.5 0.0 -0.5

a)

(Prototype scale)

-1.0 0.50 For embankment with H= 30 m

0.25

1993 Hokkaido-Nanseioki earthquake

0.00 -0.25

b)

(Prototype scale)

-0.50 0

5

10

15

20

25

30

35

40

45

50

Time, t (s)

60

c)

45

45

45 45 45

20 30 30 30

Drainage reinforcing pile

300

30 30 30 20

Fig. 6. Typical input accelerations for first shaking step in prototype scale for: (a) Cases 1, 13 through 15, and 18 through 20 and (b) Cases 8, 9, 16, and 17.

180

Case 18 400

(unit: mm) Toe drain

Drainage reinforcing pile

d)

Fig. 5. Details of seismic countermeasures employed in present study: (a) large-scale gabion (Cases 13 and 16), (b) counterweight fill with large-scale gabion (Cases 14, 15, and 17), (c) drainage-reinforcing pile (Case 18), and (d) ground anchor with pressure plate (Case 19).

were reported by Tokida (2012) in centrifuge model tests using toe rigid blocks. The S and S0 values in Case 15 were much smaller than those in the other three cases due to lower water tables. The difference in settlements between Cases 13 and 14 was insignificant; however, the response accelerations were slightly different as will be shown later.

Figs. 9(a) through (c) show photographs of deformed embankments, together with the displaced reference marks, for Cases 1, 13, and 14 taken after the first shaking. It can be seen from Figs. 7 and 9(a) through (c) that the sliding planes in Cases 13 and 14 were slightly shallower than that in Case 1. The possible reason for this behaviour is that the completion of the formation of sliding planes was restrained due to the heavy and stiff gabions with and without counterweight fill. In addition, as indicated by Figs. 9 (d) through (f), which show the earthquake-induced displacement vectors of the reference marks, the model gabions could prevent the occurrence of a catastrophic failure of embankments by restraining the horizontal displacement at the toe, consequently resulting in smaller S and S0 values. These vectors were evaluated by comparing the positions of each reference mark before and after the shaking. Thus, the placement of massive structures, such as the large-scale gabions, at the embankment toe can be successful for reducing seismic damage. Fig. 10 shows the time histories of the response accelerations, Ares, which were recorded with A3, A7, and A10, of the above-mentioned four tests with and without reinforcements by the large-scale gabions. When the data recorded with A3 and A10 for Cases 1 and 14 are compared, it may be seen that the slight amplification of seismic motions was observed at the top of the slope throughout the shaking by having constructed the counterweight fill with the largescale gabions. The data for Case 15 suggest that this trend in behaviour became significant with decreasing seepage water elevation. On the other hand, for Case 13, in which the model gabions were placed inside the embankment toe, the amplification was insignificant. In other words, as the counterweight fill reduced the relative sliding displacement among the large-scale gabions, the model embankments in Cases 14 and 15 may have behaved more rigidly due to the constraint effect. Fig. 11 shows the typical time histories of the excess pore water pressures, Du, which were recorded with P2, P11, and P14, for the above-mentioned four tests. The initial effective vertical stress, r0v0 , which was roughly estimated from the total and submerged densities of the model embankments

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9

No seismic countermeasure

No seismic countermeasure

Before shaking After shaking (with mesh line) Phreatic line

Before shaking After shaking (with mesh line) Phreatic line

b) Case 8

a) Case 1 No seismic countermeasure

Large-scale gabion

Before shaking After shaking (with mesh line) Phreatic line

Before shaking After shaking (with mesh line) Phreatic line

d) Case 13

c) Case 9 Counterweight fill with large-scale gabion

Counterweight fill with large-scale gabion

Before shaking After shaking (with mesh line)

Before shaking After shaking (with mesh line)

Phreatic line

Phreatic line

e) Case 14

f) Case 15 Counterweight fill with large-scale gabion

Large-scale gabion Before shaking After shaking (with mesh line)

Before shaking After shaking (with mesh line)

Phreatic line

Phreatic line

h) Case 17

g) Case 16 Drainage-reinforcing pile Before shaking After shaking (with mesh line) Phreatic line

i) Case 18

No seismic countermeasure Before shaking After shaking (with mesh line) Phreatic line

k) Case 20 Fig. 7. Observed deformations of model embankments after first shaking step.

at each location of P2, P11, and P14, is also indicated in the figure. The drainage gravel layer constructed for Cases 14 and 15 may have not been successful in lowering the seepage water elevation since it was placed outside of the embankment. As a result, no significant difference among Cases 1, 14, and 15 was observed. Similarly, since the seepage water elevations in Cases 1 and 13 were similar to each other, due possibly to the low permeability of the non-woven fabric placed between the embankment toe and the large-scale gabions, no significant difference was observed between these two cases.

5.2. Improvement by large-scale gabions with and without counterweight fill for higher embankments To investigate the applicability of large-scale gabions to higher embankments, as a seismic countermeasure, similar tests were conducted on the models with H = 30 m. Fig. 12 shows the relationship between S and S’ obtained from Cases 8, 9, 16, and 17, where large-scale gabions were installed in the latter two cases. As shown in Fig. 7, the seepage water elevations in Cases 16 and 17 were higher than that in Case 8 without reinforcement, in particular,

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Fig. 8. Residual displacements of 15-m-high embankments with and without reinforcements by large-scale gabions induced by first shaking step.

at the embankment toe. Nevertheless, the residual values of S and S0 in Cases 16 and 17 were much smaller than those in Case 8, suggesting that the seismic reinforcement by the large-scale gabions was effective for higher embankments as well. Fig. 13 shows the time histories of Ares, which were recorded with A3, A11, and A15, of the abovementioned four tests with and without reinforcements by the large-scale gabions. As seen from the data in Cases 8, 9, and 17, the amplification of the seismic motions tended to become significant throughout the shaking with increasing accelerometer elevation due to the counterweight fill with the large-scale gabions. For Case 16, in which the model gabions were placed inside the embankment toe,

the amplification was insignificant at the middle height, which was consistent with the trends in Case 13 with H = 15 m. However, the Ares value was obviously amplified at the top of the slope. Fig. 14 shows the typical behaviour of Du, which was recorded with P3 and P6, in the above-mentioned four tests. The Du value at P3 in Case 8 was almost zero throughout the shaking due to the effect of the long toe drain. At P6, no significant difference among these four cases was observed in general for the same reasons as those described in the above section. In Cases 16 and 17, as mentioned previously, the models were horizontally shaken by using a sinusoidal wave after the first shaking step to confirm the shape of the sliding plane. Fig. 15 shows the earthquake-induced deformations of embankments after the final (third) shaking step for these two cases. The length of the vectors shows the accumulated displacement induced by all the shaking steps from the initial position of each reference mark. As shown in Figs. 15(a) through (d), a few sliding planes were observed in both cases due possibly to their height. The shapes of these sliding planes were rather obscure after the second shaking step in Case 17, while the temporal order of their occurrence by the third shaking step could not be confirmed as the high-speed camera (that had originally been installed) was removed from the apparatus under a centrifugal acceleration of 75 g for safety. On the other hand, in Case 16, two deeper sliding planes were fragmentally generated by the second shaking step. The completion of the formation of the deepest sliding plane was prevented by the heavy and stiff gabions in Case 16; therefore, a shallow one may have been generated in the third shaking step. It can be seen from Fig. 15 that sliding planes

a) Case 1 5m

Displacement vector of reference mark Phreatic line

b) Case 13

e) Case 13 5m

Displacement vector of reference mark Phreatic line

c) Case 14

f) Case 14

Fig. 9. Photographs of deformed embankments taken after first shaking step and earthquake-induced displacement vectors of reference marks.

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T. Enomoto, T. Sasaki / Soils and Foundations xxx (2018) xxx–xxx 0.5

Response acceleration, Ares (g)

0.5

0.5

Case 1

Case 1

|Amax|= 0.507 (g)

-0.5

-0.5

A3

-1.0 0.5

Case 13

0.0

-0.5

|Amax|= 0.515 (g)

A7

-1.0 0.5

-0.5

Case 13

-0.5

A3

-1.0 0.5

Case 14

0.0 -0.5

A3

-1.0 0.5

-0.5

Case 15

|Amax|= 0.579 (g)

0

10

20

Case 15

0.0

-0.5

A3

-1.0

|Amax|= 0.618 (g)

A10

-1.0 0.5

0.0

-0.5

Case 14

0.0

|Amax|= 0.551 (g)

A7

-1.0 0.5

Case 15

0.0

|Amax|= 0.557 (g)

A10

-1.0 0.5

-0.5

|Amax|= 0.535 (g)

Case 13

-0.5

Case 14

0.0

|Amax|= 0.487 (g)

0.0

|Amax|= 0.521 (g)

A7

-1.0 0.5

A10

-1.0 0.5

0.0

|Amax|= 0.476 (g)

Case 1

0.0

0.0

0.0

11

-1.0 30 0

-0.5

|Amax|= 0.571 (g)

A7 10

Time, t (s)

30

|Amax|= 0.742 (g)

A10

-1.0

20

0

10

Time, t (s)

20

30

Time, t (s)

Fig. 10. Time histories of response accelerations of 15-m-high embankments with and without reinforcements by large-scale gabions during first shaking step.

P2

10

Excess pore water pressure, Δ u (kPa)

30

20

15

P11

Case 1

σ 'v 0= 26.7 kPa

Case 1

σ 'v 0= 44.2 kPa

10

P14

20 10

5

0 30

0 20

0 15

Case 13

P11

P2

10

σ 'v 0= 18.1 kPa

5

10

σ 'v 0= 39.4 kPa

Case 13

P2

σ 'v 0= 18.1 kPa

Case 14

σ 'v 0= 42.2 kPa

P11 10

Case 14

10

σ 'v 0= 20.4 kPa

P2

Case 15

P11

σ 'v 0= 47.2 kPa

10

5 0

Case 15

10

20

30

40

50

P14

20

Case 14

σ 'v 0= 82.6 kPa

Case 15

10

0 0

σ 'v 0= 76.8 kPa

0 30

0 20

10

Case 13

P14

20

5 0 15

σ 'v 0= 72.0 kPa

0 30

0 20

10

P14

20

10

0 15

Case 1

σ 'v 0= 75.8 kPa

0 0

10

20

Time, t (s)

30

Time, t (s)

40

50

0

10

20

30

40

50

Time, t (s)

Fig. 11. Time histories of excess pore water pressures of 15-m-high embankments with and without reinforcements by large-scale gabions during first shaking step.

higher embankments, the model gabions can prevent the occurrence of a catastrophic failure, as observed in Case 9, by restraining the horizontal displacement at the toe, as shown in Figs. 15(e) and (f). 5.3. Improvement by drainage-reinforcing piles and ground anchors with pressure plates

Fig. 12. Residual displacements of 30-m-high embankments with and without reinforcements by large-scale gabions induced by first shaking step.

basically formed above the model gabions, which is consistent with the results for the 15-m-high embankments shown in Figs. 7(d) and (e), and 9(b) and (c). In addition, even for

Fig. 16 shows the relationship between S and S’ obtained from four model tests with H = 15 m, where the embankments were improved by drainage-reinforcing piles and ground anchors with pressure plates in Cases 18 and 19, respectively. To confirm these reinforcement effects, the seismic performance of an unimproved embankment with a low seepage water elevation was also examined as Case 20. As seen from Fig. 7, the seepage water elevation of the embankment in Case 19 was similar to and approximately half of those presented in Cases 1 and 20, respectively. On the other hand, the seepage water elevations in Cases 1 and 18 were largely different at the embankment toe due to the effect

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T. Enomoto, T. Sasaki / Soils and Foundations xxx (2018) xxx–xxx 0.5

A3 Case 9

|Amax|= 0.447 (g)

A11

-0.5 0.5

A3

A11

-0.5 0.5

Case 16

|Amax|= 0.267 (g)

A3 Case 17

|Amax|= 0.352 (g) 0.0

-0.5 0.5

A11 |Amax|= 0.372 (g)

A3 0

15

-0.5 45 0

30

A15

-0.5 0.5

Case 17

Case 17

|Amax|= 0.468 (g)

0.0

-0.5

Case 16

|Amax|= 0.433 (g) 0.0

0.0

-0.5 0.5

A15

-0.5 0.5

Case 16

|Amax|= 0.357 (g)

0.0

Case 9

|Amax|= 0.302 (g) 0.0

0.0

-0.5 0.5

A15

-0.5 0.5

Case 9

|Amax|= 0.302 (g)

0.0

Case 8

0.0

0.0

-0.5 0.5

|Amax|= 0.400 (g)

Case 8

|Amax|= 0.372 (g)

0.0

Response acceleration, Ares (g)

0.5

0.5

Case 8

|Amax|= 0.289 (g)

0.0

A11

A15

-0.5 15

Time, t (s)

30

Time, t (s)

45

0

15

30

45

Time, t (s)

Fig. 13. Time histories of response accelerations of 30-m-high embankments with and without reinforcements by large-scale gabions during first shaking step. 20

Case 8 Excess pore water pressure, Δu (kPa)

10

σ'v0= 79.9 kPa

P3 0 20

Case 9 σ'v0= 63.8 kPa

10

P3 0 20

P3 σ'v0= 61.3 kPa Case 16

10 0 20

P3

Case 17 σ'v0= 64.2 kPa

P6

Case 8

Excess pore water pressure, Δu (kPa)

10 0 50 40 30 20 10 0 50 40 30 20 10 0 50 40 30 20 10 0 50 40 30 20 10 0

σ'v0= 163.0 kPa

P6 σ'v0= 146.2 kPa Case 9

P6

σ'v0= 164.5 kPa Case 16 Case 17 σ'v0= 167.8 kPa

P6

0

15

30

45

60

75

Time, t (s) Fig. 14. Time histories of excess pore water pressures of 30-m-high embankments with and without reinforcements by large-scale gabions during first shaking step.

of the drainage-reinforcing piles, although they were similar to each other at the top of the slope. The embankments in Cases 18 and 20 had similar seepage water elevations to each other in the reinforced region. The residual values of S and S’ in Cases 18 and 19 with reinforcements were much smaller than those in Case 1, as shown in Fig. 16. Enomoto and Sasaki (2015) revealed that the seismic performance of the embankments was remarkably improved by lowering the seepage water elevation at the toe by means of a drainage layer. The same conclusion can also be derived from the comparison of data between Cases 1 and 20. Similarly, the difference in the earthquake-induced displacement between Cases 1 and 18 was attributed to the different water tables at the embankment toe. In addition, as shown in the last paragraph of this section, the piles had the restraint effect against the sliding displacement of the embankment in the reinforced region. With respect to Case 19, the seismic performance of the embankment was comparable to that of Case 20 whose seepage water elevation was reduced to about half, as mentioned above. It can also be seen from Fig. 7(j) that the embankment failure can be interrupted forcedly by ground anchors with pressure plates even if the seepage water elevation is high, although the quantitative evidence is presented later. Fig. 17 shows the time histories of Ares, which were recorded with A3, A7, and A10, of the above-mentioned four tests with and without reinforcements. The comparison of data between Cases 1 and 20, both without reinforcements, suggests that the embankment with a lower seepage water elevation behaved more rigidly, which is consistent with the trend between Cases 14 and 15, shown in Fig. 10. The Ares values in Cases 1 and 18 at the top of the slope (i.e., A10) were similar to each other, while the amplification of the seismic motion was obvious at the embankment toe (i.e., A3) due to the improvement by the piles. On the other hand, the amplification of the seismic motion was significant in the positive direction in Case 19, particularly at A3 and A7, suggesting that ground anchors with pressure plates could restrain the embankment

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Before shaking After shaking (with mesh line) Sliding plane

13

Before shaking After shaking (with mesh line) Sliding plane

b) Case 17

a) Case 16

d) Case 17

c) Case 16

7.5 m

7.5 m

Displacement vector of reference mark Phreatic line

Displacement vector of reference mark Phreatic line

f) Case 17

e) Case 16

Fig. 15. Observed deformations of 30-m-high embankments with reinforcements by large-scale gabions after final (third) shaking step.

Crest settlement, S (m)

6 5 4 Case 1 hw= 2.83 m

3 Case 19 hw= 2.69 m

2

Case 20, hw= 1.27 m Case 18, hw= 1.69 m

1 0

0

1

2

3

4

5

6

Settlement at top of slope, S' (m) Fig. 16. Residual displacements of 15-m-high embankments with no seismic reinforcement, drainage-reinforcing piles, and ground anchors with pressure plates induced by first shaking step.

deformation caused by the inertia force acting on the right side of Fig. 7(j). Fig. 18 shows the typical responses of Du, which were recorded with P3, P14, and P16, in the above-mentioned four tests. A comparison of the data between Cases 1 and 18 shows that there was not a large difference in the observed behaviour between the two cases. On the other hand, despite the fact that the Du values at P14 and P16 in Case 19 were a few times larger than those in Case 1, the seismic performance of the embankment improved by the ground anchors with pressure plates was high, as shown in Fig. 16. In Case 20, the Du values recorded with P3 and P16 were almost zero due to the low seepage water elevation.

In Cases 18 through 20, to confirm the shape of the sliding plane, the models were also horizontally shaken by using a sinusoidal wave after the first shaking step. Fig. 19 shows the earthquake-induced deformations of the embankments after the final shaking step for these three cases. The length of the vectors shows the accumulated displacement induced by all the shaking steps from the initial position of each reference mark. The deformation was concentrated above the drainage-reinforcing piles in Case 18. In addition, the comparison between Figs. 19(c) and (i) suggests that the piles had the restraint effect against the sliding displacement of the embankment in the reinforced region, in spite of similar seepage water elevations at the toe. Thus, this effect as well as the low seepage water elevation at the embankment toe resulted in smaller S and S’ values in Case 18. On the other hand, in Case 19, although a similar shape of the sliding plane to Case 1 was observed, its completion was constrained due to the ground anchors with pressure plates. In particular, in spite of the large sliding displacement of the whole embankment, which was comparable to that in Case 1, as shown in Figs. 9 (d) and 19 (f), the occurrence of a catastrophic failure was prevented forcedly, as indicated by Figs. 19 (d) and (e). This prevention effect worked well as complete liquefaction did not occur, as shown in Fig. 18. Once complete liquefaction occurs, the liquefied fill materials may flow completely out through the small clearances among the pressure plates. Changes in the tensile force of the ground anchors during the shaking should be measured in the future in order to discuss the mechanism of the reinforcement more profoundly.

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Case 1

0.0 -0.5

Response acceleration, Ares (g)

0.5

0.5

0.5

-0.5

-0.5

0.0

-0.5

-0.5

|Amax|= 0.643 (g)

A3 0

10

20

|Amax|= 0.636 (g)

|Amax|= 0.498 (g)

A10

-1.0 0.5

Case 20

Case 20

0.0

|Amax|= 0.551 (g)

A7

-1.0 0

30

Case 19

0.0 -0.5

|Amax|= 0.530 (g)

A7

|Amax|= 0.482 (g)

A10

-1.0 0.5

Case 19

-1.0 0.5

Case 20

-1.0

A7

-0.5

0.0

Case 18

0.0 -0.5

0.0

|Amax|= 0.504 (g)

A3

-1.0 0.5

|Amax|= 0.487 (g)

A10

-1.0 0.5

Case 18

0.0

-1.0 0.5

Case 19

0.0

|Amax|= 0.515 (g)

-0.5

|Amax|= 0.714 (g)

A3

-1.0 0.5

A7

-1.0 0.5

Case 18

0.0

Case 1

0.0 -0.5

-0.5

|Amax|= 0.507 (g)

A3

-1.0 0.5

Case 1

0.0

10

20

Time, t (s)

30

-0.5

|Amax|= 0.690 (g)

A10

-1.0 0

10

Time, t (s)

20

30

Time, t (s)

Fig. 17. Comparison of response accelerations of 15-m-high embankments with no seismic reinforcements, drainage-reinforcing piles, and ground anchors with pressure plates during first shaking step.

P3

Excess pore water pressure, Δ u (kPa)

30

20

20 10

P14

Case 1

σ 'v 0= 44.2 kPa

Case 1

σ 'v 0= 75.8 kPa

10

P16

20 10

P14

P3 10

σ 'v 0= 75.3 kPa

10

0 20

P3

10

σ 'v 0= 52.7 kPa

Case 18

σ 'v 0= 46.1 kPa

Case 19

Case 18

P14 10

σ 'v 0= 68.6 kPa

10

20

30

Case 20

σ 'v 0= 82.6 kPa

10

P16

20

σ 'v 0= 31.1 kPa

10

0 0

σ 'v 0= 48.5 kPa

10

40

50

Case 19

0 30

P14

σ 'v 0= 55.4 kPa

P16

20

Case 19

0 20

P3

Case 18

0 30

0 20

Case 20

10

σ 'v 0= 46.9 kPa

P16

20 10

0 20

Case 1

0 30

0 20

0 20

σ 'v 0= 45.2 kPa

0

Case 20

0 0

10

20

Time, t (s)

30

Time, t (s)

40

50

0

10

20

30

40

50

Time, t (s)

Fig. 18. Comparison of excess pore water pressures of 15-m-high embankments with no seismic reinforcements, drainage-reinforcing piles, and ground anchors with pressure plates during first shaking step.

5.4. Evaluation of improvement effects by global safety factors In this section, the improvement effects by the largescale gabions, drainage-reinforcing piles, and ground anchors with pressure plates are summarized by evaluating the global safety factor, Fs. For Cases 13 through 19, the Fs values were calculated for two conditions: (1) with the reinforcements and (2) without those. The Fs value without considering the seismic force was calculated by the following equation based on limitequilibrium analysis: Fs ¼

Rfcd  l þ ½ðW  u  bÞ cos a tan /d g R½W  sin a

ð2Þ

where u is the pore water pressure due to the seepage water in the embankments, W and b are the weight and width of a slice, respectively, l is the length of the arc of a slice, and a is

the angle between the arc of a slice and the horizontal line (see Fig. 20). The employed parameters for the evaluation of Fs are summarized in Table 5, where the constants for the large-scale gabions and stiff base slopes were assumed. As discussed in the previous sections, it is shown that a sliding plane formed above the model gabions as the completion of its formation was restrained due to the heavy and stiff gabions. The /d value of the model gabions was assumed to be similar to that of dense gravel, while the minimum value for cd to reproduce the above-mentioned test results was determined by trial and error. The W value was calculated based on the unit weights of wet and saturated soils, ct and c0sat , respectively, for each embankment model. In all the model cases, the starting point of the sliding plane in the embankments (i.e., Point A presented in Fig. 20) was fixed based on each test result, while the origin (i.e., Point O presented in Fig. 20) was determined numerically by trial and error to produce the minimum value of Fs. Only for Cases 18 and 19, based on the test

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15

Before shaking After shaking (with mesh line) Sliding plane

b) Case 18

a) Case 18 5m

Displacement vector of reference mark Phreatic line

c) Case 18

e) Case 19 Before shaking After shaking (with mesh line) Sliding plane

h) Case 20

g) Case 20

5m

Displacement vector of reference mark Phreatic line

i) Case 20 Fig. 19. Observed deformations of 15-m-high embankments after final shaking step.

Table 5 Constants employed for evaluation of global safety factors. Material

ct (kN/m3)

c0sat (kN/m3)

cd (kPa)

/d (deg)

Edosaki A sand Edosaki B sand Edosaki C sand Base slope Large-scale gabion

14.3–15.31 14.3–15.31 14.3–15.31 18.22 19.02

17.9–18.21 17.9–18.21 17.9–18.21 18.22 19.02

2.52 2.5 0.3 5002 502

32.62 32.6 32.5 40.02 45.02

1

Fig. 20. Schematic diagram for limit-equilibrium analysis to evaluate global safety factors.

results shown in Figs. 19(a) and (d), it was assumed in the analyses that the sliding plane could not pass through the drainage-reinforcing piles and pressure plates due to their high stiffness (Fig. 21). In other words, a sliding plane can form above the drainage-reinforcing piles and can pass through the small clearances among independent pressure plates assumed to be equal to 0.5 m in prototype scale, respectively, in Cases 18 and 19. As a result, potential sliding planes which were similar

2

Determined based on each model test result. Assumed.

to those observed experimentally at the respective final shaking steps were reproduced in the analyses. The Fs values of the embankments assumed to be without reinforcements were also calculated using the same starting point for the sliding plane and the same seepage water elevation for each test case. Fig. 22 shows the increase in the Fs values by the reinforcements. The Fs value increased at least by a factor of 1.05 by installing the respective reinforcements.

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T. Enomoto, T. Sasaki / Soils and Foundations xxx (2018) xxx–xxx

In spite of the large sliding displacement of the whole embankment, the completion of the sliding plane and the occurrence of a catastrophic failure were forcedly interrupted due to the ground anchors with pressure plates.

References

Global safety factor with reinforcement

Fig. 21. Assumption in evaluation of global safety factors for Cases 18 and 19. 1.8 *: Originally with no reinforcement

1:1

Case 18

1.6 Improvement effect Case 19

1.4

Case 16 Case 13

Case 8*

Case 20*

Case 17

1.2 Case 14

Case 1* Case 15

1.0 1.0

Case 9* 1.2

1.4

1.6

1.8

Global safety factor evaluated assuming non-reinforced condition Fig. 22. Comparison between global safety factors with and without reinforcements.

6. Conclusions The following conclusions can be derived from the test results described in this paper: 1. The seismic performance of embankments was remarkably improved by installing large-scale gabions at the embankment toe. The possible reasons for this behaviour are that the completion of the formation of sliding planes was restrained due to the heavy and stiff gabions, and that the gabions were able to prevent the catastrophic failure of the embankments by restraining the horizontal displacement at the toe. Furthermore, since the relative sliding displacement among the large-scale gabions was reduced when they were installed in combination with counterweight fill, the embankments behaved more rigidly due to these constraint effects. 2. The above-mentioned conclusion was also derived from the results of tests on higher embankments. 3. The installation of drainage-reinforcing piles at the embankment toe was rather effective in reducing the overall earthquake-induced deformation due to their high permeability and restraint effect against sliding displacement at the reinforced region. The earthquakeinduced deformation was concentrated above the drainage-reinforcing piles. 4. The embankments improved by ground anchors with pressure plates were not vulnerable to earthquakeinduced damage even under high water table conditions.

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Please cite this article in press as: Enomoto, T., Sasaki, T., Seismic behaviour of reinforced embankments in dynamic centrifuge model tests, Soils Found. (2018), https://doi.org/10.1016/j.sandf.2017.12.005