Deformation and localisation behaviours of reinforced gravelly backfill using shaking table tests

H. Munoz, T. Kiyota

Institute of Industrial Science, The University of Tokyo, Tokyo, Japan

Keywords:Geosynthetic-reinforced soil (GRS)Retaining wall (RW) model Shaking table test Digital image correlation (DIC)Localisation

A B S T R A C T To understand the deformational behaviours of geosynthetics-reinforced soil retaining walls(GRS RWs),a series of plane-strain shaking table tests was conducted on retaining wall models. The backfill of the models was made of poorly graded gravel. Deformations and strains in the gravelly backfill induced by seismic loading are recorded in real time, which are of importance to understand the seismic strength and stability of the GRS RW systems,as strain localisation development in the backfill and foundation is related to the degree of strength degradation of the system.In the present study,we aimed at quantifying the induced deformations of the GRS RW models due to shaking. Digital image correlation (DIC) technique was then employed to analyse and provide full-field deformation and motion images with the models. It is demonstrated that, unlike conventional contact devices that are yet limited to provide quantities of a singular and fixed location, DIC provides deformation and motion of the area of interests to reveal the evolution of localisation.

1. Introduction

Geosynthetic-reinforced soil retaining walls (GRS RWs) and integral bridges (GRS IBs) are the stable structures, in contrast to conventional unreinforced soil structures, when subjected to high seismic loads under cost-effective requirements (Munoz et al.,2012; Tatsuoka et al., 2014). Inherent features of GRS structures include a stage-constructed full-height rigid (FHR) facing having the reinforcement layers connected firmly to its face. The stagedconstruction of the FHR facing provides high confining pressure in the backfill, which promotes high stiffness and strength of the backfill.This feature contributes to the improvement of the GRS RW strength to withstand higher seismic loading(Tatsuoka et al.,1997,2015;Tatsuoka,2008).GRS technology has become the standard for engineering design and construction of reinforced soil structures in Japan:very important(Rank I),important(Rank II)and other noncritical soil structures (Rank III) (Railway Technical Research Institute, 2012). Geogrid layers, as planar tensile reinforcements,are conventionally used to reinforce the backfill of GRS structures in terms of tensile strength. Notwithstanding, the authors and their colleagues proposed to investigate the performance of alternative tensile reinforcement types other than geogrids (i.e. geocells),which are able to interact well with large-size particle soils(Kiyota et al.,2009;Han et al.,2017),to alleviate the requirements of high quality backfill for GRS and construct new types of GRS RWs.In this case, the present paper discusses the advantages of reinforcing large-size particle backfill with geocells on reducing excessive deformations and displacements of GRS RW models subjected to seismic shaking tests.

Deformation and displacement measurements by direct contact devices are in general costly for densely instrumented models,and are yet limited to provide quantities of a singular and fixed location.These drawbacks may lead to oversight of valuable information that could be extracted from physical tests. Digital image correlation(DIC) is a class of non-contact measurement method that acquires images of an object, stores images in digital form and performs image analysis to extract full-field deformation, displacement and motion measurements of an object (Sutton et al., 2009). DIC has been used to study the deformation characteristics of different material specimens(Heinz and Wiggins,2010;Munoz et al.,2016a,b, 2017; Munoz and Taheri, 2019), full-scale and model structures(e.g.Fukuda et al.,2010,2013;Busca et al.,2014;Ribeiro et al.,2014;Feng et al., 2015). In the present study, DIC applied to the models was demonstrated with the advantages of having a natural speckle pattern provided by the gravel(i.e.the backfill)that eliminated any requirement of installing artificial targets (e.g. Fukuda et al., 2010,2013; Busca et al., 2014; Ribeiro et al., 2014) to track deformations and displacements of the backfill.

2. Geosynthetic-reinforced soil retaining wall model

2.1. Similitude rules for models in 1g testing

Despite the advantages of testing models with 1g shaking table,the results may somehow be different from the behaviour of the conceived prototype structures(Munoz et al.,2012;Tatsuoka et al.,2012)due to(i)pressure level and(ii)particle size effects,i.e.effects of the ratio of particle size to model size. Nonetheless, GRS RW model tests are likely to be suitable for stability analysis of the prototype structures.Despite the possible effects of the two factors as mentioned above, it suggests that there is no significant difference from prototypes and conceived models. The scale factors for the primary parameters in a small-scale model test are presented in Table 1 (Munoz et al., 2012; Tatsuoka et al., 2012).

2.2. Construction of geosynthetic-reinforced soil retaining wall models

The models corresponding to GRS RWs are constructed with a stage FHR facing. The FHR facing has reinforcement layers firmly attached to its face at small spans, and it is a much simpler and thinner structure, which makes unnecessary the use of a large footings and/or pile foundation for strong supporting ground(Tatsuoka et al., 2013). Three types of FHR-facing models of GRS RWs were constructed:(i)Model 1:the geogridC-reinforced model,(ii)Model 2:the geogridM-reinforced model,and(iii)Model 3:the geocell-reinforced model.The scaled model to prototype factors are summarised in Table 1.

The models were designed considering a scale-down factor of λ=10 in length and in stress σ(Munoz et al.,2012;Tatsuoka et al.,2012). The GRS RW models were backfilled with poorly graded gravel.The wall model(40 cm in width,50 cm in height,and 3 cm in thickness) was made of duralumin. Its back face and bottom surface,in direct contact with the backfill and supporting ground,were made roughly by covering them with a sheet of sandpaper.The GRS RW models were erected inside a rectangular prismatic steel box(180 cm long,40 cm wide and 87.5 cm high)fixed to a shaking table.Fig.1a shows a picture of a GRS RW model mounted on the shaking table used in the present study.The front and back sides of the box comprise a transparent-tempered glass window which allowed observation of in-plane displacements and deformation of the models during shaking. In general, the frictional resistances along the granular soil-glass interface are sensitive to the applied mean vertical stress, which decreases rapidly with increase in vertical stress, as the apparent frictional angle is inversely proportional to the vertical stress (Tatsuoka et al., 1984; Tatsuoka and Haibara,1985). In the present study, the vertical stresses in magnitude of 5-12 kPa were dominant in the backfill; therefore, an apparent friction angle of 8°-10°along the granular soil-glass interface could be expected. These values are much lower than the friction angle(65°) of the gravel used as backfill in the models; therefore, the frictional effects of soil-glass (window) interface, if any, can be negligible in the shaking tests with respect to the behaviours of the backfill.

Table 1 Scaled factors for different physical quantities in small-scale model.

2.3. Reinforcement of the backfill

The backfill was reinforced in a region with dimension of 40 cm × 50 cm × 36 cm (width × height × length), as shown in Fig.1b. In total,10 layers of reinforcement for a height of 39.5 cm were arranged at a vertical spacing of 5 cm in the backfill. The reinforcement layers were firmly connected to the wall facing by either bolts or clamps,as shown in Fig.1c.Under this arrangement,high connection strength between the reinforcement layers and the wall face was ensured. In all the models, the backfill and supporting ground were made of dry-tamping poorly-graded gravel (gravel size D50= 14.2 mm, coefficient of uniformity Uc= 1.44, specific gravity Gs= 2.65, and maximum dry density Dmax= 1.87 g/cm3) to a prescribed dry density of about 0.95Dmax= 1.78 g/cm3(void ratio e = 0.49).

Three types of reinforcement layers were used for the Models 1-3:

(1) Model 1 (the geogridC-reinforced model): this model uses a polyester geogrid of 1 mm in thickness having an aperture of 6.3 mm × 6.3 mm. This geogrid is typically used as tensile reinforcement material in practical applications.

(2) Model 2(the geogridM-reinforced model):this model uses a phosphor-bronze grid of 1 mm in thickness having its surface made rough by sand gluing in order to promote grid-gravel friction. The phosphor-bronze grid has an aperture of 35 mm × 35 mm (Munoz et al., 2012).

(3) Model 3 (the geocell-reinforced model): this model uses a square-shaped cell mattress with dimension of 50 mm × 60 mm × 25 mm (Han et al., 2017). This reinforcement model is made of polyester.

2.4. Instrumentation of the models

The models were instrumented by associated measurement devices placed at relevant locations to monitor the displacements by displacement transducers LVTD (LV1-LV3) or laserdisplacement sensors (LD1-LD3), earth pressures (LC1-LC3) and accelerations. A set of small-size accelerometers was set up in the models, i.e. one on the shaking table (AC7), one on the upper wall(AC6) and five embedded within the backfill (AC2-AC5) and foundation ground (AC1) (Fig. 1b). Once the models were constructed and instrumented, they were subjected to a scale-down time-history of accelerations applied to the base of a shaking table apparatus.

3. Seismic loading on the models

Fig. 1. (a) Shaking table, GRS RW model and image acquisition setup; (b) Typical instrumentation of the models; and (c) A FHR facing with geogridC.

To examine whether prototype structures can withstand high seismic demands,the models were subjected to a sinusoidal timehistory of accelerations scaled to represent the characteristics of an earthquake event by the peak ground acceleration (PGA), predominant frequency (fp) and magnitude. The 1995 Hyogoken-Nambu earthquake (i.e. the Kobe earthquake) was considered as input for the models (PGA of 818 cm/s2and a predominant frequency fpof 1-3 Hz). A shaking frequency between 3.2 Hz and 9.6 Hz used in the model would be representative for relatively high shear-strain levels induced in the unreinforced backfill,which is expected to occur under high seismic loading demands. Therefore, in all the model tests, the base acceleration was applied at a natural frequency, i.e. fi= 5 Hz to simulate severe earthquakes.Fig. 2 shows the typical base acceleration applied to the shaking table and recorded by AC7.Each model was subjected to a history of sinusoidal acceleration(i.e.base acceleration,¨ubfor time t)with 20 sinusoidal cycles of a base acceleration amplitude increasing 100 gal (1 gal = 0.01 m/s2) per stage, i.e. Stage I (～100 gal), Stage II(～200 gal),etc.,till failure or collapse of the structures.In addition,to simulate the actual weight of pavement for railways or highways,a surcharge of 1 kPa made of lead shot bags was placed on the crest of the backfill of the models.

The above base shaking events were applied by using a shaking table at the facilities of the Institute of Industrial Science of the University of Tokyo.

4. Two-dimensional digital image correlation method

The principle of two-dimensional (2D) DIC technique is to record image points in time using a single digital camera. Some fundamental concepts of optics are briefly introduced below. The geometric model for a camera requires three elementary transformations, as shown in Fig. 3 (Sutton et al., 2009).The first transformation relates the world coordinates of a point RW(XW，YW，ZW)to coordinates in the camera system RC.RWand RCtransformation requires both rotation by a tensor([Rij]) and translation by vector t({tx，ty，tz}-1). The second transformation is projection RConto the image retinal system Rrby a pure perspective projection.The third transformation is to transform the point Rr(xi，yi)into the sensor coordinate system Rs(xs，ys)in units of pixels.In summary, the core transformation, eliminating the scale factor,yields

where the symbol f represents the image distance, and ^cxand ^cyare the translation parameters.

In image matching, the grey value of the position of a single pixel can be found at thousands of other pixels in the second image being compared, and no unique correspondence can be matched;while mandatorily, the matching process has to correspond to a unique matching position. To solve the correspondence problem,the object surface textures have to exhibit non-periodic and random textures,such as speckle patterns (Sutton et al., 2009).

4.1. Inherent speckle pattern and correlation

DIC method relies on a contrasting random texture as speckle patterns in the surface of the specimen. In typical tests using DIC technique, the pattern adheres to the surface of the object under study and the pattern deforms as the surface does. Therefore, no loss of correlation occurs, even under events of large translation and deformation.Although a hand-made speckle pattern is usually needed for optimal measurement, some materials such as wood,concrete,sand and gravel may display an inherent speckle pattern.The latter was the case for the gravelly backfill of the models in the present study.Fig.4 shows the natural speckle pattern provided by the gravel in the backfill of the GRS RW models. This pattern was characterised by high contrast, i.e. a random pattern exhibiting no bias to an orientation and showing a grey spectrum adequate in size for high-strain resolution. Thus under these conditions, very sensitive defocus was avoided(Sutton et al.,2009;Munoz et al.,2016a).

Fig. 2. Typical time-history of base acceleration ¨ub recorded by AC7 applied to the models.

In Fig.4a,a couple of images of the area of interest of the backfill under examination are presented. Herein, a reference image (undeformed object) and an image of the deformed model with their respective field of subsets are shown for coordinates(xi，yi) and?in the reference and deformed images, respectively. Numerical evaluation and optimisation of the similarities between the undeformed and deformed subsets were adopted in order to identify the matching positions in the image of the deformed model (e.g. the zero-mean normalised sum of squared difference(ZNSSD) criterion).

4.2. Digital image correlation setup and testing

Fig.3. Three elementary transformations of the pinhole camera model and associated coordinate systems (Sutton et al., 2009).

To record the digital images during the shaking tests, a digital video camera(Sony HDR-CX590V)was set up pointing directly onto the plane of the transparent acrylic window of the testing box.The video camera was able to capture image frames at 30 Hz,i.e.higher than the shaking frequency of 5 Hz throughout the tests. During testing, the camera system was fixed on ground (i.e. a fixed observer in earth)focussing symmetrically to centre of the models.Continuous and uniform illumination across the entire models was provided by a conveniently adjusted halogen light to ensure adequate contrast. A series of monochromatic (grey-scale) images was stored and analysed to create 2D shape and displacements. A typical monochromatic image of the area of interest under study is shown in Fig.4a.The images acquired during the shaking tests were firstly corrected for minor lens distortions, if any, to compute deformation and motion.A start image,when base shaking was not applied yet,was selected to provide an initial reference to recreate the deformation field on the subsequent images. For deformation and strain computations,a map of 70×70 pixel subsets and a step size of 20 pixels were used. Having the camera system fixed to an observer on earth, the raw displacements obtained by DIC correspond to total displacements utof an element. The total displacement is composed of the base displacement ub(i.e. the displacement of the rigid box of the shaking table)plus the relative displacement of the element in question u to the base, i.e.ut(t) = ub(t)+u(t) for time t. An example of the field of ut(t) in Model 1 is shown in Fig. 4b.

5. Direct contact and digital image correlation measurements

in t he backfill for Model 1 (geogridC-reinforced model) measured by accelerometers AC1, AC2, AC3 and AC5(see locations in Fig.1b)are presented in Fig. 5a, b, respectively. The time-history of displacements ut(t) was back-calculated in view of acceleration records by a double integration method. To do so, the acceleration records were linear-baseline corrected and then filtered using a fourth-order Butterworth filtering procedure with a band-pass at 3-25 Hz. The diagrams of Fourier amplitude versus frequency demonstrated that the filtering procedure to acceleration above only band-passed small acceleration amplitudes(i.e.noise)at small(＜3 Hz)and large frequencies(＞25 Hz).Hence,no alteration of the nature of base shaking (5 Hz) and response was incurred.

The time-histories of accelerations(t)and displacements ut(t)

Fig.4. (a)Inherent speckle pattern of the gravelly backfill and undeformed and deformed subsets;and(b)Field of lateral displacement ut(t)at the end of Stage VI(600 gal)in Model 1.

The time-history of lateral displacements ut(t) in the backfill obtained by DIC corresponding to Model 1 for locations A1-A5 is presented in Fig. 6. In this figure, it is evident that progressive accumulation of lateral deformation,at different rates,took place in the backfill (see the increase in displacement amplitude experienced by A1-A5 from Stage I (100 gal) to Stage VII (700 gal) with the increases in both the number of loading cycles and base acceleration level). The points A1-A5 are located approximately at the perpendicular projection of points AC1-AC5 onto the acrylic window of the testing box, respectively. Thus, in a general sense,under the plane-strain testing conditions herein, it was expected that the displacements of points A1-A5(by DIC)should match the displacements of AC1-AC5(back-calculated from accelerometers),respectively.Note that for the latter,the back-calculation method of displacement by double integration ut(t) uses base correction techniques so that the displacements in this case do not take into account any residual nor accumulation of displacements in the deformable backfill. In contrast, the DIC method is able to fully capture and depict the displacements(deformations)accumulated cycle by cycle during shaking tests. Hence, a base correction was applied to the DIC quantities in order to compare them with the amplitude of displacements ut(t) obtained by accelerometers, as presented in Fig. 7. This figure shows the amplitude of ut(t) on average and their standard deviation (average of 20 waves under steady shaking in a stage) for loading Stages I-VII. A linear correlation was found with y ≈x and R2≈0.998 for the examined points.The differences (in the order of 3%) may be attributed to the fact that the accelerometers captured displacements of the embedded gravel,while DIC captured the displacements of the gravel in direct contact with the acrylic window. Therefore, it can be concluded that the DIC method applied herein captured fairly the deformations taking place in backfill.

6. Full-field deformation and strains of the models

DIC analysis provided quantitative evidence of the nature of development of deformation and strains in the backfill of the models. In general, it was observed that the backfill deformed progressively with increases of base acceleration cycles and amplitude. In a similar fashion, the shear strains were localised in the backfill and foundation, which led to strength degradation of the backfill and foundation. The paper focuses merely on the deformation characteristics of the models at the residual state of Stage VI (600 gal), as illustrated in Figs. 8-10. These figures show the field of lateral displacements related to the base, i.e. u(t) for time t.For this,a vector processing task was performed to have u(t)by simply making u = ut-ub.In addition,the field of shear strains at time t presented herein corresponds to the total shear strains,which is composed of the cyclic (γcyc) and average (γave) shear strains (Kramer,1996).

Fig. 5. Time-history of (a) accelerations ¨ut(t) and (b) displacements ut(t) at locations AC1-AC5 in the backfill and foundation in Model 1.

6.1. Model 1: GeogridC-reinforced model

Fig. 6. Time-history of displacements ut(t) at locations A1-A5 in the backfill and foundation measured by DIC.

The field of lateral displacements u(t)for Model 1 is presented in Fig. 8a. The accumulated lateral displacements in the backfill took place in compliance with the active and passive movements of the wall. Thus, at this residual state, large lateral deformation was accumulated in the crest of the backfill close to the wall, which decreased progressively from the wall to remote locations in the backfill(see the wedge of displacement gradients in Fig.8a).At the crest of the backfill in contact with the wall, residual lateral deformation reached about 37 mm (～7.5% of the wall height).Fig. 8b presents the field of settlements (vertical displacements).This figure shows the interaction between two bodies in the backfill: a block defined by the stiff reinforced zone and a wedge formed in the unreinforced zone (immediately behind the reinforced zone).The formation of this wedge may be attributed to the difference in stiffness between these zones, and the successive mobilisation of active and passive cyclic displacements of the reinforced zone and the wall. The wedge in the unreinforced zone of the backfill experienced relatively large settlements.In a general sense,the crest of this wedge settled from 7 mm to 16 mm(～1.5%-～3%of the wall height).On the other hand,settlements in the crest of the reinforced zone reached only about 5 mm on average(～1%of the wall height). Negligible settlements took place outside the reinforced zone and unreinforced zone wedge, as well as in the foundation soil (see the gradient colour in Fig. 8b).

The field of shear strains developed in the backfill is presented in Fig.8c.This figure shows that developed shear strain in the backfill was localised in the following regions (see numbers 1 to 4 in the figure):

(1) At the contact between the reinforced and unreinforced zones.It was found that the largest values of shear strains in the backfill took place at this interface. In this case, strains developed in the magnitude of 10% on average.

(2) At the bottom of the reinforced zone. Localisation of strains took the form of an inclined plane having its origin at the toe of wall. In this case, this localised plane inclined only few degrees with respect to the horizontal, about 8°.

(3) Along an inclined plane of a wedge formed in the unreinforced zone. This plane was inclined about 29°with respect to the horizontal direction.

Fig. 7. Relation between the amplitude of displacements ut(t) obtained from accelerometers (back-calculated) and DIC methods in Model 1.

Fig. 8. Fields of (a) lateral displacements u(t), (b) settlements and (c) shear strains in Model 1 (geogridC-reinforced) at residual state of Stage VI (600 gal).

Fig. 9. Fields of (a) lateral displacements u(t), (b) settlements and (c) shear strains in Model 2 (geogridM-reinforced) at residual state of Stage VI (600 gal).

(4) A minor localisation extent is reported at wall toe-foundation interface, and the contact in between the wall face and reinforced zone.

Fig.10. Fields of(a)lateral displacements u(t),(b)settlements and (c)shear strains in Model 3 (geocell-reinforced) at residual state of Stage VI (600 gal).

It is important to note that, in non-localised zones within the reinforced zone and unreinforced zone wedge, strains developed only at about 2%-3%, suggesting that the soil there remained stiff and was less degraded.Finally,marginal strains were found outside the regions as described above, including depth into the foundation.

6.2. Model 2: GeogridM-reinforced model

In general, large deformation and strains encountered with Model 1 were alleviated under the reinforcement conditions of the backfill with Model 2(i.e.phosphor-bronze grid).In Fig.9a,similar to above discussion, in compliance with the rotation and translation of the wall,most of the lateral deformation in the backfill did take place in the crest of the reinforced zone close to the wall,and the lateral deformation decreased from this location to remote locations in the backfill. The lateral deformation in the crest of the reinforced zone reached only 20 mm on average(～4.5%of the wall height);in contrast,deformation at comparable location in Model 1 reached about 37 mm(～7.5%of the wall height).Fig.9b shows the field of settlements for Model 2.The formation of two main blocks in the backfill was also identified, i.e. a block defined by the stiff reinforced zone and a wedge in the unreinforced zone formed immediately behind the reinforced zone. This figure shows that settlements in the crest of the unreinforced zone wedge were in the magnitude of ～3 mm-～7 mm(～0.6%-～1.5%of the wall height).On the other hand, the crest of the reinforced zone experienced minor settlements,which were less than 1 mm(～0.2%of the wall height). Other locations in the backfill, other than the abovementioned ones, experienced marginal settlements.

The field of shear strains with Model 2 is shown in Fig.9c.In this figure,similar to Model 1,shear strain developed and was localised in regions 1-4 as discussed above.In region 1,about 5%strain was localised at the contact in between the reinforced and unreinforced zones. In region 2, a plane with localising strains inclined about～9°with respect to the horizontal.In region 3,shear strains did not fully localise along the inclined plane, and in region 4, strains were localised in a minor extent between 2% and 3%. The soil in non-localised zones within the reinforced zone and wedge in the unreinforced zone of the backfill developed with strains of about 1%-3%. Other than that, strains were negligible outside the above locations.

6.3. Model 3: Geocell-reinforced model

With Model 3, relatively large deformation and strains developing in the backfill,previously encountered with Models 1 and 2,were greatly alleviated. With Model 3, in compliance with the rotation and translation of the wall, lateral deformation reached only about 9 mm(～2%of the wall height)on average(see Fig.10a).This deformation was the smallest experienced by the models compared with the 20 mm (～4.5% of the wall height) and the 37 mm(～7.5%of the wall height)lateral displacements of Models 2 and 1,respectively.The field of settlements of Model 3 is presented in Fig.10b.Similar to the case with Models 1 and 2,a block defined by the stiff reinforced zone and a wedge in the unreinforced zone were also identified. This figure shows that the crest of the reinforced zone experienced a minor vertical deformation, and so did the reinforced body.The settlement here reached less than 0.4 mm(～0.08%of the wall height)on average,i.e.the smallest settlement when compared with settlements experienced by Models 1 and 2.Also,the crest of wedge in the unreinforced zone of Model 3 settled the lowest, about 0.8 mm-3 mm (～0.2%-～0.6% of the wall height).

The field of shear strains of Model 3 is shown in Fig.10c. Similarly, as discussed above, the developed shear strain was localised in regions 1-4. In region 1, shear strains were localised and developed only in the magnitude of ～2%on average,in contrast to the rest of the backfill. This strain level was the lowest when compared with 10%and 5%in Models 1 and 2,respectively.In region 2,shear strains were localised in an inclined plane of about 26°with respect to the horizontal. In contrast, this plane inclined～8°and ～9°in Models 1 and 2,respectively.No major localisation of strains occurred along the inclined plane of region 3 and in region 4.Again,the soil in non-localised zones within the reinforced zone and wedge in the unreinforced zone of the backfill developed with strains of between ～0.4% and ～1%. Other than the above locations, strains development was marginal.

7. Conclusions

To understand the deformational behaviours of GRS RW having a FHR facing subjected to earthquake excitations,model tests were constructed and tested. The models had their backfill made of large-size poorly graded gravel reinforced with three different types of reinforcements. The models were densely instrumented with direct contact devices. DIC method was implemented and applied to examine the full-field deformation patterns of the GRS RW backfill when subjected to earthquake shaking. The natural surface of the gravelly backfill served well as speckle patterns to conduct DIC, hence, no physical targets for particle tracking were employed. The applicability and reliability of DIC were demonstrated. DIC method can provide advantages in contrast with conventional contact displacement measurements as DIC is able to generate the full-field deformation of the models to gain insights into strain localisation in the backfill and failure patterns of the models.

Declaration of Competing Interest

We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Acknowledgments

The first author would like to thank the Japan Society for the Promotion of Science and their financial support through the JSPS Fellowship Programme to conduct research activities at the University of Tokyo. The assistance of X. Han, T. Mera and T. Katagiri,from the Institute of Industrial Science of the University of Tokyo,with performing the shaking table experiments is greatly acknowledged. The authors also thank all their previous and current colleagues for their help.