Evaluation of ultimate behavior of actual large-scale pile group foundation by in-situ lateral loading tests and numerical analysis

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ScienceDirect Soils and Foundations 58 (2018) 819–837 www.elsevier.com/locate/sandf

Evaluation of ultimate behavior of actual large-scale pile group foundation by in-situ lateral loading tests and numerical analysis Shuntaro Teramoto a,⇑,1, Tomonari Niimura b, Tomihiro Akutsu c, Makoto Kimura d a

Setsunan University, Osaka 572-8508, Japan b Osaka Gas Co., Ltd, Japan c Obayashi Co., Ltd, Japan d Kyoto University Graduate School of Engineering, Japan Received 27 January 2017; received in revised form 12 February 2018; accepted 28 March 2018 Available online 27 August 2018

Abstract Structures resting on a liquefied natural gas (LNG) base must be completely stable during an earthquake in order to ensure a steady gas supply. Thus, the stability of the foundations on which these large-scale structures rest is one of the most significant factors for realizing the safety and ease of maintenance in the event of an earthquake. Problems can potentially occur when the actual bearing capacity of an in-service practical LNG tank foundation has not been verified, and when the operative design method for the pile-group effect is inadequate, especially for large-scale pile groups. To date, no prediction method capable of appropriately simulating the mechanical behavior of large-scale pile groups has been established. Therefore, in this study, in-situ lateral loading tests were conducted on a real-life practical tank foundation upon the demolition of an LNG tank after 40 years of service. A 3D elasto-plastic finite element method (FEM) analysis was also conducted. From the results, the bearing capacity and the failure level of the practical LNG tank foundation were investigated and its soundness was confirmed. In addition, the behavior of a large-scale pile group foundation for load share distribution was observed and compared with the operative design. Ó 2018 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society.

Keywords: LNG tank; Pile group; In-situ test; Lateral loading test; FEM; Pile group effect (IGC: E04)

1. Introduction The Tohoku earthquake of March 11, 2011 provided an opportunity to diversify energy sources and to address global environmental problems. Natural gas discharges lower amounts of CO2, NO2, and SO2 during combustion than other fossil fuels. It is also said to be capable of providing a huge amount of stable clean energy and, even though

Peer review under responsibility of The Japanese Geotechnical Society. ⇑ Corresponding author. E-mail address: [email protected] (S. Teramoto). 1 Former affiliation: Doctoral student, Kyoto University Graduate School of Engineering, Japan.

recovery takes years longer than that for oil, natural gas deposits can be found all over the world. Imported natural gas arrives at LNG bases as
162 °C liquefied natural gas (henceforth, LNG). The devolatilization of natural gas compresses its volume to 1/600 of its original volume and improves the efficiency of its transport. It is supplied through pipelines after storage, re-evaporation, and odorization. In earthquake-prone countries, like Japan, the safety and maintenance of an LNG-receiving terminal are critical when servicing an LNG base. The LNG tank is an extremely important facility whose foundation is composed of multiple piles to support the superstructure. The superstructure must be capable of supporting the vertical load of its weight during normal operations, as well as

https://doi.org/10.1016/j.sandf.2018.03.011 0038-0806/Ó 2018 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society.

S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

Unit horizontal subgrade reaction force

820

pHU

tan-1kHE

pHU =

p

p

pU

kHE =

k

k

kH p:

0

Horizontal displacement

1.0 2/3 (1)

k:

H (m)

kHE : Coefficient of horizontal subgrade reaction (kN/m3) pHU : Maximum unit horizontal subgrade reaction force (kN/m3) kH : Coefficient of horizontal subgrade reaction during earthquakes (kN/m2) pU : Earth pressure strength during earthquakes (kN/m2)

0.5 2/3 (2)

0.5 2/3 (3)

0.5 2/3 (4)

0.5 2/3 (100)

Loading direction

k

: Correction factor of coefficient of horizontal subgrade reaction at single pile

p

: Correction factor of maximum unit horizontal subgrade reaction force at single pile

k

: Correction factor of coefficient of horizontal subgrade reaction at group pile

p

: Correction factor of maximum unit horizontal subgrade reaction force at group pile

Fig. 1. 2-D framework analysis design in Specification for Highway Bridges.

the lateral load and the bending moment caused by the inertial forces of earthquakes. Problems related to pile groups subjected to lateral loading have been investigated by many researchers, and the pile-group effect has been found to be a significant factor in the design of pile foundations. From the 1960s to 1980s, an elastic theoretical analysis of the pile-group effect (Poulos, 1964), small-scale model tests (Tamaki et al., 1971), and an elastic numerical analysis using the theory developed by Poulos (Randolph, 1981) were conducted. In these studies, algebraic equations were suggested for the pile-group effect which considered the spacing between piles, the matrix of a pile group, the fixation of a pile head, and the relative stiffness between a pile and the ground. However, these equations were shown to have limitations in terms of the elastic ranges they could cover. In the 1980s and 1990s, along with the development of mechanical devices and measurement systems, centrifuge model tests (Adachi et al., 1994; McVay et al., 1998) and realscale tests (O’Neil et al., 1985; Pedro et al., 1997) were performed. In the real-scale tests, in-situ lateral loading tests on a 9-pile group, including the ultimate behavior (Kimura et al., 1994), and 3-D elastic perfectly-plastic FEM analyses of the tests (Kimura et al., 1995) were conducted, and the results became the basis for an evaluation of the pile-group effect in the current design for Specification for Highway Bridges (Japan Road Association, 2012). In recent years, large-scale seismic loading model tests (Shirato et al., 2008) and non-linear seismic numerical analyses (Zhang et al., 2002a) have been conducted to investigate the dynamic mechanical behavior of pile groups. To simulate the dynamic behavior of RC pile groups, a new beam model (AFD model), capable of considering the axial-force dependency in the nonlinear moment-curvature relation, was introduced. In the development of rational foundation structures, jacket-type foundations using batter piles (Zhang et al., 2002b) and steel

pipe pile foundations, supporting integrated columns with multiple steel pipe piles (Shinohara et al., 2013) have been carefully studied. In addition, the mechanical behavior of seismic reinforced foundations for pile groups in an improved ground (Bao et al., 2013), as well as reinforced existing foundations with steel pipe sheet piles (Isobe et al., 2014) and additional piles (Teramoto et al., 2016) have been examined. In terms of the pile-group effect considered in the current 2D framework analysis design in the Specification for Highway Bridges, shown in Fig. 1, the back piles are assumed to have half the maximum subgrade reaction of the front-most pile (without considering the pile number). From past studies, however, it is clear that the number of piles increases the pile-group effect, and that there is a risk of the miscalculation in large-scale pile groups due to the evaluation method in the design stage. Considering the fact that pile group foundations are usually built to be large for the sake of seismic reinforcement, it is important that the actual pile-group effect be clarified. Little progress has been made in the research on the lateral behavior of the large-scale pile groups typically used as foundations for LNG tanks. This is due to the difficulty of conducting in-situ loading tests with large-scale practical pile groups, and of finding agreement between the numerical analysis results and the in-situ loading test results. For these reasons, the actual bearing capacity of an inservice practical LNG tank foundation has yet to be determined. The challenges of conducting research on pile-group foundations are summarized as follows: (1) the actual bearing capacity of an in-service practical LNG tank foundation has not been determined, (2) the operative design method for the pile-group effect is inadequate, especially for large-scale pile groups, due to the difficulty of conducting in-situ loading tests, and (3) there is no predication method capable of simulating the mechanical behavior of large-scale pile groups that can sufficiently consider the pile-group effect.

S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

The objectives of the present study are (1) to determine and then verify the lateral behavior of an in-service practical LNG tank foundation, (2) to confirm the pile-group effect of a large-scale pile group and to evaluate an operative design method, and (3) to develop and evaluate a prediction method capable of simulating the mechanical behavior of large-scale pile groups that gives appropriate consideration to the pile-group effect. In-situ lateral loading tests were conducted with a 7  9 pile group (m  n pile group: arranged in n lines orthogonal to the loading direction, and m lines parallel to the loading direction), and with a 3  1 pile group used as part of the practical tank foundation. This was in accordance with the demolition of an LNG tank after 40 years of service at Osaka Gas Senboku LNG Receiving Terminal 1. An investigation of the lateral bearing capacity of the LNG tank foundation was carried out. It was possible to observe the behavior of the tank from the yielding mode to the ultimate mode to the destruction mode since the LNG tank foundation was completely demolished after the tests. Simultaneously, a simulation was also conducted by means of a 3D elastoplastic FEM analysis. In the analysis, the soil model for the subloading tij model (Nakai et al., 2004) and the pile model for the hybrid model (Zhang et al., 2000) were capable of appropriately simulating the pile-group effect of large-scale pile groups. However, the ordinary simplified models that were used in the past, such as the 2D model, the no volume beam alone model, and the contracted pile group model, have been shown to be inadequate for simulating the pile-group effect. The pile-group effect and the mechanism of the large deformation of large-scale pile groups are discussed considering both sets of results. In this study, the ultimate bearing capacity of a practical foundation after its service is determined, the yield load to the ultimate load, and the foundation deformation (including the yielding of the pile head and the residual deformation of the pulled-out piles) are observed, and the lateral mechanical behavior of a large-scale pile group, especially in terms of the pile-group effect, is clarified. A comparison between the load share distribution of a practical pile group and the design in the Specification for Highway Bridges validates the design method. Finally, a simulation method which is applicable to large-scale pile groups is developed. In this analysis, the model pile simulates the pile-group effect properly and the soil model simulates the ground around the cyclically-loaded largescale pile group. With this method, the hard-to-predict behavior of large-scale pile groups can also be simulated before a loading test. 2. Outline of lateral loading tests on 7  9 pile group foundation 2.1. Structure of demolished LNG tank The demolished LNG tank used for the loading tests is shown in Fig. 2, and a top view of the foundation is given

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in Fig. 3. Photo 1 shows the externals of the specimen and the reaction piles for loading. The tank is a double-walled metal tank with a maximum capacity of 45,000 m3. The foundation consists of a slab and 496 steel pipe piles. Details of the piles are shown in Fig. 4. The slab is 48 m in diameter, 0.8 m in thickness, and is made of reinforced concrete. The piles are 23.5 m in length, 406.4 mm in diameter, 12.7 mm in thickness in the upper part, and 9.5 mm in thickness in the lower part. There is a distance of 0.8 m between the bottom of the slab and the ground surface. The ground around the edge of the tank is improved to an N-value of about 15 by means of sand compaction piles. Each pile is an open-toe type of end-supported pile and the N-value of the bearing ground located at the pile tip is around 50. The upper part of the pile is filled with reinforced concrete to a depth of 6 m. The upper part of the pile, 0.8 m above the ground surface and 0.3 m under the ground, is covered with protective concrete, is rectangular in shape, and has a thickness of 150 mm. 2.2. Preparation of specimens The positions of the 7  9 and the 3  1 pile group specimens in the slab are shown in Fig. 3. The specimens were loaded laterally using the right side of the slab as a reaction pile, as shown in Photo 1. The specimens were prepared by removing other parts of the slab, so that only the specimens remained. However, the piles around the specimens remained in the ground. The protective concrete over the ground surface was removed so as to enable the direct measurement of the pile shaft, while the concrete under the ground was left intact. 2.3. Measurement A contact-type displacement transducer was employed to measure the pile and slab specimens by using the reference piles located in front of each specimen (Figs. 3 and 5). However, because these reference piles were likely to be affected by the pile group displacement at loading, the displacement of these piles was measured with the total station set up a distance of 25 m from the specimen (orthogonal to loading direction). The shear strain and bending strain of the piles were measured with the strain gauge, the inclination of the piles was measured with the inclinometer, and the applied load was measured as shown in Fig. 5. The pile-group effect in the loading direction was investigated by measuring seven piles in the center line, while those orthogonal to the loading direction were investigated by measuring the five piles in the front line. The strain, the inclination, and the displacement of the part of the piles in the ground were not measured due to the difficulty of measuring piles filled with concrete. This point was complemented by a numerical analysis.

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Reaction piles

3×1pile group

Loading direction

6000

7×9 pile group 14000

2000

Double-walled metal tank 45,000 [kL]

18000

Photo.1

48 m

23.5 m

ColuN mnar sec- value tion 0 20 40

Bearing ground (N = 46) Fig. 3. Elevated view of LNG tank.

single pile

2×1pile group 2000 750 2250

7×9 pile group

3×1 pile group

2000 2250 750

19@2000=38000 48000

Reaction piles

7×9 pile group 5,000 kN jack (two series) Loading plate Base (H-steel)

Displacement gauge SDP-300D, Strain gauge Displacement gauge CDP-100, Strain gauge Fixed inclinometer

5,000 kN jack

Reference pile

Fig. 2. Specimen and measurement arrangement.

Reaction piles

Photo 1. Externals of specimen and reaction piles.

2.4. Loading stages and determination of maximum load

3. FEM analysis conditions

The loading stages of the 7  9 and the 3  1 pile groups are shown in Figs. 6 and 7, respectively. The unidirectional multiple-cycle, multiple-step loading method was selected as the lateral loading test method. There were five cycles and ten loading steps, amounting to a total loading time of about 5 h, as the lateral load was applied with six hydraulic jacks of 5000 kN, as seen in Fig. 3 and Photo 1. The outputs of the six jacks were controlled by an oil pressure device which also simultaneously measured the pressure. In order to observe the ultimate behavior of the 7  9 pile group, it was necessary to predict the deformation while determining the maximum load (capacity of the jack). Firstly, the yield load per pile, 247 kN, was calculated by Y. L. Chang’s formula (fixed pile head condition). A yield load of 15,561 kN (247 kN was multiplied by 63) was assumed for the 7  9 pile group. Secondly, an analysis using a 3-dimensional elasto-plastic FEM was conducted before the tests on the 7  9 pile group. The results were used to establish the maximum load in the loading tests; it was set at 30,000 kN (with the six 5000 kN jacks).

3.1. FEM code and FEM mesh The FEM code DBLEAVES (Ye et al., 2007) was used for the FEM analysis. The analysis area and the FEM mesh are shown in Figs. 8 and 9. In this analysis, the 7  9 pile group and the piles remaining around them were simulated precisely. 3.2. Modeling of pile foundation As shown in Fig. 10, each pile was modeled by a hybrid element with the same volume as the pile. This was necessary to simulate the pile-group effect properly because the pile-group effect is the interaction between one pile and the other piles and depends on the pile spacing. The pilegroup effect can be simulated more precisely with a hybrid element than with a beam element alone. The parameters of the pile foundation were determined through the use of the design values of the specimen according to the calculation flow shown in Fig. 10. The piles around the specimens that remained in the ground were also modeled to simulate the actual condi-

S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

Fig. 8. Analysis area and FEM mesh.

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S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

tions, as shown in Fig. 10. To investigate the influence of the remaining piles, a comparison analysis was conducted before the tests in which the remaining piles were removed. Consequently, it was confirmed that the 7  9 pile group without any remaining piles had a 10% larger displacement than the 7  9 pile group with remaining piles. 3.3. Constitutive models of soils Loading direction

The ground was modeled by the subloading tij model (Nakai et al., 2004). This model is regarded as one of the most useful elastoplastic models because it can consider the intermediate principal stress by adapting the concept of modified stress tij. A comparison of the tensors and scalars related to the stress and strain increments (between the ordinary concept and the tij concept) is shown in Table 1. The influence of the stress-path dependency of the density and/or the confining pressure on the deformation and strength characteristics was considered.

EI

EI

EA

column

EA

column

EI

Bending moment (kN*m)

Column element (elastic model) Beam element (bilinear model) beam

EA

Fig. 9. Details of FEM mesh around 7  9 pile group.

beam

Beam element EI beam EA beam

Mp

Fully plastic moment Mp = 416 (kN m) (Design value of actual pile) Degradation factor of stiffness after fully plastic tan tan = 1/10 (1/1000 for pile head)

Column element EI column EA column Actual pile

Curvature

Pile model in FEM

(1/m)

Outer diameter 0.406 m

Actual pile Esp = 2.0×108[kN/m2] Steel pipe Asp = 0.0157[m2] Isp = 3.04×10-4[m4] Esc = 2.82×107[kN/m2] Concrete Asc = 0.114[m2] Isc = 1.03×10-3[m4] Thickness 12.7 mm

(EA)pile = Esp × Asp + Esc × Asc = 6.35 ×106[kN] (EI)pile = Esp × Isp + Esc × Isc = 8.98 ×104[kN*m2]

0.1 ( EI ) pile

0.9 ( EI ) pile

Column element

0.4 m

( EI ) column

0.4 m

I column

Ecolumn

Beam element

0.1 EI pile

0 .4 4 12

( EI ) beam

8.98 103

Abeam 2.1 10

EI column I column

3

m

4

Pile heart 4.21 10 6 kN / m 2

Ebeam

I beam

0.9 E pile Asp EA

0.0157 m 2 pile

Abeam

EI beam Ebeam

Fig. 10. Modeling of pile and calculation flow of parameters.

8.08 10 4 [kN * m 2 ]

4.04 108 kN / m 2

2.0 10

4

m4

S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

Strain increment normal to reference plane Deviatoric strain increment tensor Strain increment parallel to reference plane

gij ¼ sij =p

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g ¼ q=p ¼ ð3=2Þgij gij

xij ¼ t0ij =tN X ¼ ts =tN ¼

pffiffiffiffiffiffiffiffiffiffi xij xij

dev ¼ deij dij

deSMP ¼ deij aij

deij ¼ deij
13 dev dij qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ded ¼ 23 deij deij

de0ij ¼ deij
dev SMP aij qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dcSMP ¼ de0ij de0ij

600

Beam

Unit : mm

Fig. 11. Outline of loading tests on 1  2 pile group prior to 7  9 tests.

Bending moment [×10 2 kN m] -16 -12 -8 -4 0 0.0

FEM

[Test] 500 kN 1000 kN 1500 kN 1900 kN

-1.0 -2.0

1000

Depth (m)

Lateral load (kN)

Footing

800

Test

500

0

1200 Jack

2000

1500

7000

Elevated view 1200

0

4200

tij ¼ rik akj tN ¼ tij aij t0ij ¼ tij
tN aij qffiffiffiffiffiffiffiffi ts ¼ t0ij t0ij

3000

rij p ¼ rij dij =3 sij ¼ rij
pdij pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q ¼ ð3=2Þsij sij

1200

Stress ratio

aij

50

Stress ratio tensor

dij ðunittensorÞ

Jack

100

Deviatric stress

tij concept

800

400

Tensor normal to reference plane Stress tensor Mean stress Deviatoric stress tensor

Ordinary concept

Top view

600

Table 1 Tensors and scalars related to stress and strain increment in ordinary concept and tij concept.

825

20 40 60 80 Lateral displacement of pile top (mm)

100

-3.0

-4.0 -5.0

[FEM] 500 kN 1000 kN 1500 kN 1900 kN

-6.0

Fig. 12. Results of simulation analysis on 1  2 tests prior to 7  9 tests.

The main superiority of the subloading tij model in this analysis is shown below. In simulating the cyclic lateral loaded pile group, the soil around the piles must be modeled such that it can consider the stress path during unloading and reloading, and it is simulated by the subloading surface concept (Hashiguchi, 1980). The specifics of this model enable it to simulate not only clay soil behavior, but also sand behavior without any distinction between normally consolidated and overconsolidated soil. On the other hand, the Cam-clay model cannot simulate sand behavior. And, in general, to simulate laterally loaded piles, an interface element is typically arranged between the piles and the soil behind them to demonstrate the delamination behavior of the pile surface. At this point, the model can simulate delamination behavior without the interface element by decreasing the deformation modulus of the soil according to the decrease in confined pressure. The input parameters of the soil, except for k and j, were determined by the results of soil tests and standard penetration tests. Compression index k and swelling index j were determined with the results of parallel 1  2 lateral loading tests conducted near the LNG tank foundation (prior to the 7  9 tests). An outline of the 1  2 tests is shown in

Fig. 11, while the test and analysis results (load–displacement and bending moment distributions) are shown in Fig. 12. FEM parameters k and j were determined with sufficient accuracy with the 1  2 tests, which were conducted before the 7  9 tests. The calculation flows for all the input parameters of the soil are shown in Figs. 13 and 14 and Table 2. The improved area given in Fig. 13 shows that the ground has been improved (N = 15) by the sand compaction pile method during the construction of the LNG tank. The area is distributed around the circumference of the LNG tank (Figs. 8 and 13). In the analysis of the 7  9 and 3  1 tests, the j determined by the 1  2 tests was converted to consider the difference in the N-value distribution according to the flow shown in Fig. 13. 3.4. Analysis procedure Firstly, the initial stresses of the ground were generated by a self-weight analysis under an elastic ground condition. Secondly, the elastic ground was replaced by subloading tij model soil and hybrid element piles. However, the initial stresses remained. Finally, footing nodes were applied at the actual loading positions and under the same condition as that of the tests (Figs. 6 and 7).

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S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837 250 m

Estimated ground surface strength

150 m

Tank used for this test series

Strong

Weak

1 2

average N-value of (N ,0Nm~, N8 are m in ground surface 0

SCP ground improved area (N = 15)

1

2

N0 = N-value of B-1 = 5

N1 = average N-value of A-1~A-4 = 7.5

A-4(5)

A-3(11)

0

(

Previous 1×2 test area N0, Unimproved ground area N1, Improved ground area N2,

B-1(5)

Previous loading test of 1×2 pile group

N2 = 15

3×1

1

2 3

0

,

2

1 3

0

Assumption 7×9

3(1 2 0 )(1 e0 ) p E0 E0 2800 N

2×1

Single

48 m

A-1(9)

1 N

Position of SPT ( ) : AVG N-value in surface 8 m area

A-2(5)

( 0, e0, p are taken the same value in all cases)

N-value N-value N-value N-value N-value 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70

0

AVG N-value = 9

AVG N-value = 5

AVG N-value = 11

AVG N-value = 5

AVG N-value = 5

5 Depth of max. bending moment distribution in FEM analysis

Filling soil

8

Depth (m)

10

15

20

Depth of pile tip 25 A-1

A-2

A-3

Fig. 13. Conversion method for j and SPT data.

A-4

B-1

S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

~ Parameters except

and

~

~ Parameters and

[Reference of past study]

a = 500

827

~

[Assumption]

Filling layer ~ 8 m

= 1.5

8m~

Self weight analysis

[Assumption of ordinal value] K0

a, , , , e0, Rf

1

decide as to past 2×1 test result are simulated

[soil test, standard penetration test] e0 Rf

m (= p)

N

6 sin (3 sin )

as right section

decide

degree

Input parameters of prediction analysis of 7×9 group pile Fig. 14. Calculation flow of input soil parameters for prediction analysis of 7  9 pile.

Table 2 Input parameters of soil. Depth of layer (m)

Soil classifycation

Failure stress ratio RCS

Nvalue N

Poisson’s ratio m

Unit weight c (kN/m3)

Coefficient of earth pressure at rest K0

Void ratio e0

Compression index k

Swelling index j Unimproved ground j1

Improved ground j2

0.175 0.525 0.875 1.225 1.65 2.2 2.85 3.6 4.5 5.5 6.5 8 10.5 14 18 22.5

Filling soil (Gravel)

2.8 2.8 2.8 2.3 2.3 2.5 2.5 2.4 3.1 1.9 1.9 3.5 3.4 3.5 2.8 4.6

17 17 17 13 13 6 6 5 4 3 3 9 8 36 13 46

0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

17.9 17.9 17.9 8.1 8.1 8.1 8.1 8.1 8.1 8.1 8.1 8.1 8.1 8.1 8.1 8.1

0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43

0.80 0.80 0.80 0.95 0.95 0.77 0.77 0.77 0.75 0.95 0.95 1.70 0.57 1.00 0.72 0.45

0.0018 0.0018 0.0018 0.0018 0.0018 0.0018 0.0018 0.0018 0.0018 0.0018 0.0018 0.0018 0.0009 0.0009 0.0009 0.0009

0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0004 0.0004 0.0004 0.0004

0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004

Filling soil (Silty-sand)

Filling soil (Silty-fine clay) Gravel Gravel sand Silty-clay Gravel

4. Test and FEM analysis results 4.1. Load displacement results The load displacement results for the 7  9 pile group at the loading position (average displacement at both sides of the slab surface) are presented in Fig. 15. Fig. 15 is shown in Fig. 16 as the logarithmic axis for reading the yielding point. The maximum load of the tests was 25,400 kN and the displacement at the time was 240.5 mm (=60%  d). The residual displacement after the tests was 158 mm. Compared to the design yield of 15,561 kN, calculated with the Chang’s equation, the lateral stiffness in

the test results, given in Fig. 15, was actually seen to have decreased. However, the ductile deformation progressed and the load gradually increased without the occurrence of brittle failure. From a comparison of the results of the prediction analysis before the tests and the test results, the analysis was shown to have predicted the test results with high accuracy until around 40 mm (=10%  d). However, there was little decrement in the lateral stiffness in the analysis. This is because the characteristic of the hybrid element simulates the piles. At the pile head, as shown by the blue circle in Fig. 17, the solid elements arranged in the hybrid element have high stress due to the fixation of the pile

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S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837 36000

Displacement revised by the reference pile

32000

Jacks capacity 30,000 kN Cycle 5 121.0 mm

24000

+39 mm

Unload

+19 mm Cycle 4 65.7 mm

20000

Load (kN)

Cycle 6 Maximum load 25,408 kN Displacement 240.5 mm

Continue loading

28000

+10 mm 16000

Cycle 3 32.1 mm

Yield load of pile head in design 15,561 kN (Y. L. Chang s formula)

12000

+9 mm Test

8000

4000

0 0

20

40

60

80

100

120

140

160

180

Lateral displacement at loading point

200

220

240

260

280

mm

Fig. 15. Load displacement results of 7  9 tests, prediction analysis, and analysis after the tests.

head, and the solid elements share higher shear force. Therefore, this increase in shear force in the solid elements results in a decrease in the plastic deformation of the beam element. The results indicate that the model for the pile head is improved after the tests, as presented in Fig. 17. The plastic deformation in the large deformation phase, shown by the blue line in Fig. 15, was able to simulate the test results more appropriately due to the improvement. However, the deformation was still underestimated at the maximum load in the analysis. The main reason is that the analysis was not able to simulate the falling of the pile head from the slab (shown in Photo 2) because the pile head and the slab share the same nodes in the FEM analysis. If an interface element is used to simulate the falling for the next improvement, some tests have to be conducted to determine the parameters of the interface element; that issue can be addressed in the future. On the other hand, given the shape of the unloading and reloading cycles, FEM was able to simulate the test results with high accuracy. This is because the subloading tij model introduces a subloading surface concept, which ordinary elasto-plastic models cannot simulate. The load displacement results for the 3  1 pile group in the loading position are shown in Fig. 18. FEM sim-

ulates the initial stiffness of the test results as lower than that of the 7  9 pile group. However, the accuracy was higher at around 60 mm (=15%  d). These results indicate the possibility that FEM underestimated the soil parameter since the lateral stiffness depends more on the ground stiffness than on the pile stiffness in the initial phase. 4.2. Deformation mode of large-scale pile group The deformation modes for the inclination of the piles during the tests and FEM are shown in Fig. 19. The pulled-out piles (front-most and back-most piles) after the tests are shown in Photo 3. Both the experimental results and those of the analysis indicate that the front-most pile inclined more than the back-most pile at an applied phase of 8000 kN kN, while the inclination of the front-most pile increased exponentially at an applied phase of 25,400 kN. As is to be expected from the large inclination of the pile, the pile and the slab did not cross orthogonally in the tests. This is because the pile head and the slab surface both fail because of the large deformation, as shown in Photo 2. The falling of the pile head from the slab and the falling away of the slab skin reduce the pile head connectivity.

S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

After pile yielding

20000

Load (kN)

Pile yielding area 55 mm, 15000 kN

12000 10000 9000 8000 7000 6000 5000

After ground yielding before pile yielding 8 mm, 6000 kN

4000 3000

Initial stiffness

2000

1000 1

10 100 Lateral displacement at loading point (mm)

30000

After pile yielding

FEM results 20000

Pile yielding area

Load (kN)

12000 10000 9000 8000 7000 6000 5000

55 mm, 14000 kN

After ground yielding before pile yielding

4000

7 mm, 4000 kN

3000 2000

Initial stiffness

1000 1

10 100 Lateral displacement at loading point (mm)

Fig. 16. Load displacement results shown as common logarithmic axis.

Hybrid element

Ground surface

Slab (elastic) Beam

Slab (elastic)

Hybrid element

The bending moment distributions of the 7  9 and the 3  1 pile groups at a displacement of 30 mm (7.5%  d) are presented in Fig. 21. Only the FEM analysis results are shown because no measurements were taken in the ground. For comparison, Fig. 22 shows the results of past in-situ lateral loading tests on a 3  3 pile group at a displacement of 7.5%  d (Kimura et al., 1994). The value beside the maximum bending moment represents the bending moment of each pile normalized by the front-most pile in the center line. In all cases, the front-most pile had the largest bending moment and its position in the ground was the shallowest. A strict comparison of these cases is difficult due to the difference in test conditions. The bending moment distributions for the 7  9 and the 3  1 pile groups were similar to those of the past 3  3 tests. From a comparison of the middle pile (pile 4 in the 7  9 pile group case) and the back-most pile, the distributions were nearly the same as those in the 3  1 pile group case. However, the bending moment of the middle pile in the 7  9 pile group case was smaller. The maximum bending moments of the middle pile and the back-most pile were deeper in the 7  9 pile group case due to the larger pilegroup effect generated in the 7  9 pile group. Considering that the depth of the ground has an influence on the lateral bearing capacity, equal to 1/b (b: characteristic value of the pile), and that b is proportional to kH1/4(kH: coefficient of horizontal subgrade reaction), the kH of the

Test results

80 cm

4.3. Difference in bending moment distribution between scales of pile group

30000

90 cm

Moreover, the analysis results indicate that the maximum point of the bending moment of the front-most pile was shallower than that of the back-most pile. As shown in Photo 3, the pulled-out front pile actually deformed more than the back pile, and the maximum point of the bending moment was shallower again. Due to the failure of the front-most pile head, there was a distinct change in the supporting structure of the pile group, and the position of the maximum bending moment of the front-most pile was shallower, resulting in a dramatic incline in the front-most pile over the ground. The inclination of the slab is shown in Fig. 20. This inclination was calculated from the vertical displacement of the slab surface, as measured by the contact-type displacement transducer. The inclination of the slab increased with the load increments. However, from around 16,000 kN, the inclination was seen to decrease in the test results. This decrement was attributed to the failure of the front-most pile head. However, FEM cannot simulate this decrement in inclination, because the pile head of the FEM mesh is modeled as a continuum and is not capable of simulating the pile head desorption shown in Photo 2. In addition, it is also the reason why the displacement at the maximum load from the FEM analysis was still underestimated, as is shown in Fig. 15.

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Prediction analysis

Analysis after the tests

Fig. 17. Improvement in modeling of pile.

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S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

1400

Falling out of the pile head from the slab

Loading direction

1200

Load (kN)

1000 800

Yield load of pile head in design 741 kN (Y. L. Chang s formula)

Falling away of slab skin

600 400 200 Front-most pile

0

0

10

20

30

40

50

60

70

80

90

Photo 2. Desorption of pile head and slab surface.

100

Lateral displacement (mm) Fig. 18. Load displacement results of 3  1 tests and simulation.

Front Inclina -tion FEM Test

0.30° 0.22°

-2.1 m

Back

Loading direction

-2.5 m

0.27°

-2.8 m

0.24° 0.16°

0.25°

-3.0 m

-3.1 m

0.24°

-3.2 m

0.25°

0.26° 0.19°

40 cm

40 cm

Pile head

Pile head

-3.2 m

Position of the maximum bending moment from FEM results

Front-most pile

Back-most pile

Photo 3. Deformation of pulled-out piles after tests.

FEM Test

Back

Loading direction

2.2° 4.1°

1.8°

1.7°

1.5° 3.0°

1.5°

1.5°

1.6° 3.0°

10000

Rotational angle of footing θ (μrad)

Front

FEM Test

1000

-1.4 m -2.4 m

-2.9 m

-3.4 m

-3.6 m

-3.8 m

-3.9 m

Position of the maximum bending moment from FEM results

Fig. 19. Pile deformation in ground (FEM) and inclination of piles (Test, FEM).

middle pile in the 7  9 pile group case is lower and has deeper ground effects. This decrement in kH is the pilegroup effect. 4.4. Bending moment distribution according to loading Fig. 23 shows the evolution of the bending moment distribution for the underground 7  9 pile group in the FEM analysis. As was stated previously, the front-most pile had the largest bending moment and the shallowest position.

100

Measured displacement

Measured displacement Loading

θ

10

Back

Front

0

4000

8000

12000 16000 Load (kN)

20000

24000

28000

Fig. 20. Inclination of slab.

From the initial phase to around 12,000 kN, the position of the maximum bending moment becomes deeper with incremental increases in the load for all piles. After 12,000 kN, the position was deeper in the back-most pile, remained constant in the middle pile, and was shallower in the front-most pile. This is because of a decrease in kH (it becomes deeper) and the yielding of the pile head (it become shallower). As with the back-most pile, if the pile head did not yield, the position in the front-most pile was deeper.

S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

Bending moment (kN*m)

Bending moment (kN*m) -200 2

-100

0

100

200

300

-200 2

Slab

1

Position (m)

-7 -8

1.13 1.00 0.80 0.63

Front-most center pile (1) Middle center pile (4) Back-most center pile (7) Front-most outer pile (8)

300

Middle pile

-4

Back-most pile

1.00 0.89

-5 -6

Lateral load = 600 kN (7.5%×d)

-7 -8

(7)

(4)

(1) center

Loading direction

Loading direction

-9 -10

-11 back

-12

Front-most pile

-3

(8) outer

Lateral load = 9,000 kN (7.5%×d)

-9 -10

200

Ground surface

-2

Position (m)

-3

-6

100

-1

-2

-5

0

0

Ground surface

-1

-4

-100

Slab

1

0

831

outer front

-13

7×9 pile group

Back-most Middle Front-most pile pile pile

-11 -12 -13

3×1 pile group

Fig. 21. Results of bending moment distribution in FEM analysis.

The influence of the yielding pile head in the front-most pile, at 14,640 kN, became larger than the influence of the decrease in kH. This influence of the yielding pile head is that the position of the maximum bending moment was shallower, while the decrease in kH results in a deeper maximum bending moment. Therefore, the position of the maximum bending moment of the front-most pile was shallower. Subsequently, once the front-most pile head yields, the foundation leans forward. The more forward the pile, the deeper the position of the maximum bending moment. Therefore, it is understood that the influence of the decrement in kH (the pile-group effect) and the influence of the yielding of the pile head are nearly equal for the middle pile. These variations in the depth of the maximum bending moments and other factors are summarized in Fig. 24.

9m

19.4 m Reaction piles

(2)

(1)

9m 3×3 pile group

Sand gravel (filling) N-value = 5~10

Pile diameter : 1.2 m Lateral load : 12,000 kN Pile spacing : 2.5d (7×9 test is 5d) (7.5%×d) Bending moment (kN*m) -2000 -1000 0 1000 2000 3000 0 Ground surface 5

Position (m)

10 13 15

20 Front-most pile (1) 25

Diluvium

4.5. Load share of large-scale pile group The load share of each pile normalized by the frontmost pile is shown in Fig. 25. This shared load is calculated from the shear force measured by the strain gauge attached to the pile surface above the ground. In all loading stages, the front-most pile shares the largest load, and at around the fourth pile, it shares the smallest load. These results are the same as those seen in past model tests (Shibata et al., 1989). The load share of the back-most piles decreases according to the increase in applied load; FEM can simulate this tendency in the evolution of the load share distribution. The load share distribution of the framework analysis design in the Specification for Highway Bridges is shown

(3)

9m

Loading direction

Middle pile (2) Back-most pile (3)

30 Fig. 22. Outline and bending moment distribution results of past in-situ lateral loading tests on 3  3 pile group (Kimura et al., 1994).

S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

4,000 kN 12,000 kN 20,000 kN

-12

Fully-plastic moment at 14,640 kN

-8

Fully-plastic moment at 21,840 kN

-6

-14

Front-most pile (1) Bending moment (kN*m) -500 -400 -300 -200 -100 0 100 200 300 400 500 2 Slab 0

Fully-plastic moment at 16,840 kN

-4 -6 -8 -10 -12

Less than fully-plastic moment

Position (m)

-2

-14

Middle pile (4) Bending moment (kN*m) -500 -400 -300 -200 -100 0 100 200 300 400 500 2 Slab 0 -2 -4

Fully-plastic moment at 17,280 kN

The followability of the ground with adjacent piles, the range of influence of the pile group, and the evolution of the ground deformation form are discussed in this section. Distributions of the lateral displacement of the ground at 4000 kN and 25,400 kN are shown in Fig. 26. The displacement was normalized by the average lateral displacement of the pile at the ground surface. According to the increase in loading, the inner ground of the pile group began to follow the pile group as a clod.

(1)

back front Bending moment (kN*m) -500 -400 -300 -200 -100 0 100 200 300 400 500 2 Slab 0 Ground surface -2 Procedure of depth of -4 maximum bending moment

-10

Position (m)

4.7. Lateral deformation of ground

(4)

25,400 kN

4.6. Ground subsidence around 7  9 and 3  1 pile groups The ground behind the front-most and the back-most piles after testing is shown in Photos 4 and 5, respectively; the loading system at the maximum load is shown in Photo 6. The crack generated at the backside of the front-most pile presumably was caused by the separation of the rectangular protective concrete of the pile and the ground. Behind the back-most pile, large ground subsidence was generated, and this exacerbated the unstable condition of the jacks. A subsidence of 200–350 mm was measured, indicating a slide down of the ground between the back-most pile and the remaining piles underground. The prediction analysis indicates that this subsidence would be around 170 mm. The quantity evaluated by FEM was smaller due to the difficulty of simulating the slide down. However, this analysis is a useful prediction method for the ground subsidence around a pile group. To compare the scale of the pile group, an additional analysis of the 3  1 pile group (loaded at the same displacement as the 7  9 pile group) was conducted. The results indicate that the ground subsidence of the 3  1 pile group was 40 mm, which is smaller than the 170 mm subsidence of the 7  9 pile group. Therefore, the larger subsidence of the 7  9 pile group can be assumed to be specific to large-scale pile groups.

(7)

-6 -8 -10 -12 -14

Less than fully-plastic moment

in Fig. 25. In the results for a load of 16,000 kN (assuming the ground reaches the maximum subgrade reaction), the load share averages of the back piles ((2)–(7)) are 0.56 in the test and 0.48 in FEM. While the averages are approximately equal, the subgrade reaction in the design is overestimated in the center and underestimated in both the second and the back-most piles. These results indicate that the design is at risk of overestimating the maximum subgrade reaction in cases where the pile number increases to more than 7, as the number of overestimated center piles does partly increase. Moreover, the results indicate that the reduction rate for the maximum subgrade reaction at the back piles (=0.5 currently) must be properly determined when designing each pile.

Position (m)

832

Back-most pile (7) Fig. 23. Evolution of bending moment distribution of 7  9 pile group in FEM analysis.

S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

4.8. Investigation of stress distribution of soil around 7  9 pile group and deformation of piles The increment distributions of tN (p of the common elasto-plastic model, Table 1) at 4000 kN and the lateral displacement distribution of the piles are shown in Fig. 27. On the front side of the piles in the ground, an increase is generated from a depth of
1.5 m in the forward-depth direction, while the increment is larger for the front-most piles. On the back side of the piles in the ground, a decrease is generated in the back-depth direction, while the decrement is larger at the back-most piles. Our earlier results showed that the front-most piles are supported by the forward ground, and the back-most piles are supported by both the forward and the backside ground. Additionally, from the deformation distributions of the piles, the shallow part of the front-most pile deformed considerably (arrow A) due to a large subgrade reaction from the shallow front side of the pile, while the deep part of the back-most pile deformed largely (arrow B) due to a large subgrade reaction from the deep backside of the pile. 4.9. Influence of subgrade reaction on load share mechanism The cause of the above load share distribution and its behavior are discussed here using the reaction force of the piles. As shown in Fig. 28, the subgrade reaction is calculated as rx (stress of the loading direction) at the front

-400

0

Bending moment (kN*m) 0 -400 -200 0 -400

-200

-200

0

Ground surface -2 -4

Position (m)

[Main factor] Influence of -6 the yielding pile head -8 [Main factor] Influence of -10 the decrease in kH

Influence of the decrease in kH and the yielding pile head are equal

[Main factor] Influence of the decrease in kH

[Main factor] Influence of the decrease in kH

-12 -14

Front-most pile (1)

Middle pile (4)

Back-most pile (7)

Fig. 24. Evolution of depth of maximum bending moment.

8,000 kN

4,000 kN

12,000 kN

16,000 kN

FEM Test

1 Load share of each pile normalized by front-most pile

In particular, the large ground deformation of the inner backside of the ground apparently affected the decrease in the load share, as shown in Fig. 25. From the representative contour line for the 10% displacement, the range of influence of the 7  9 pile group was wide in all directions, especially in the loading direction, compared with the 3  1 pile group. In the case of the 7  9 pile group, the range increased for the vertical direction (from 13d to 15.5d) and for the loading direction (from 15d to 25d) according to the increase in load. However, the range decreased for the orthogonal to the loading direction. This reduction can be attributed to the large deformation of the pile group caused by the shear failure of the ground beside the pile group, and the decrease in the followability of the ground. From the representative contour line of 40% near the distribution of maximum bending moments, the contour has a symmetrical shape in the 4000 kN phase. However, according to the increase in loading, the contour starts to have a downward-sloping shape. This change is due to the position of the maximum bending moment in the front-most piles, which do not become deeper due to the yielding of the pile head. Thus, the deformation of the pile group affects the shallow forward ground around the frontmost piles and the deep ground. According to the above results, the loading influence on the ground around a pile group is expanded horizontally and vertically by expanding the scale.

833

0.9

(1)

(7)

front

0.8

back

0.7 0.6 0.5 Design 0.5

0.4

Ave. of (2)~(7) 0.48

Ave. of (2)~(7) 0.56

0.3

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Front

Back

Fig. 25. Load share distribution of 7  9 pile group.

The front-most pile

Crack

Photo 4. Crack behind front-most pile.

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S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

Reaction piles

7×9 pile group

Gap of jack and base

The backmost pile 160 cm

Settlement of base

35 cm

20 cm

Position of remaining piles under ground Photo 6. Situation of loading system at maximum load.

Photo 5. Subsidence behind back-most pile.

Ground surface

Ground surface 2.5 m = 6.3d

60

80

10

80 60 40

20 40 10 m = 25d

20 10

90

170 mm subsidence

20 10 25,400 kN (6.4 mm = 42%×d)

Loading direction front

2.9 m = 7.3d

Depth (m)

0 1 2 3 4 5 6 7 8

80

90 80 60 40

4,000 kN (6.4 mm = 1.6%×d) Ground surface 6080 40 20 1.6 m = 4d 10

60

6.2 m = 15.5d

0 1 2 3 4 5 6 7 8

20 40 6 m = 15d

5.2 m = 13d

Depth (m)

10

1.7 m = 4.3d

back

Lateral displacement of ground normalized by lateral displacement of pile at ground surface (%) 0 20 40 60 80 100

section 2.4 m = 6d

front

back

Position of the maximum bending moment

200 kN (6.4 mm = 1.6%×d) Fig. 26. Distribution of displacement of ground around 7  9 pile group (FEM).

and rear faces of the hybrid element. Subsequently, the reaction force of the pile is calculated by the vertical integration of the subgrade reaction (from the ground surface to the pile tip). The reaction forces at the front face and the rear face of the pile are shown in Fig. 29(a), while the total of these reaction forces is shown in Fig. 29(b). Additionally, the dis-

tribution of initial stress rx0 and the stress at 16,000 kN, rx, are shown in Fig. 30. In this figure, the compression in front of the pile results in an increase in the reaction force, but the compression behind the pile results in a decrease in the reaction force. From the results of the reaction force at the front face, the front-most pile receives the largest reaction force and the

S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

Deformation of pile (mm) 7 6 5 4 3 2 1

-20

0

tN increment (kPa) 0 20

4,000 kN

-5

A -2.85 m

-5

-5

-5

-5

20 10

B

10

5 10 m

Depth (m)

1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

8

835

5

10 5

5

-5

5

Front-most pile

-5

Back-most pile

Remaining piles

Front-most pile

Middle pile

-5 -10

-10

-5

Middle pile

-2.85 m

5

5

5

5

-5

Back-most pile

Fig. 27. Relation between ground stress distribution around pile group and deformation of piles (FEM).

Loading direction

Element for calculation of subgrade reaction at front face of pile

Column element solid element that has 1/10 EI of actual pile

Pile heart beam element that has 9/10 EI of actual pile Element for calculation of subgrade reaction at rear face of pile Not used for calculation due to small shear force

Fig. 28. Elements using calculation of subgrade reaction.

back-most pile receives a negative reaction force. This is due to the deformation of the ground in front of the pile shown in Fig. 30. This negative reaction shows the decrement of the initial stress and does not exceed the initial stress. The results of the reaction force at the rear face indicate that the posterior pile has a large reaction force. The reaction force at the rear face does not become greater than that at the front face. This is because the reaction force at the rear face cannot exceed the initial stress. Therefore, the reaction force at the rear face of the back-most pile is almost equal to the reaction force at the front face of the front-most pile in the initial phase. However, depending on the loader, it can be relatively small. This mechanism of the reaction forces explains the almost symmetrical U-shape in the initial phase for the load share ratio distribution shown in Fig. 25. However, the shape changes as the load-share ratio of the backmost piles decreases.

5. Conclusion In-situ lateral loading tests on large-scale pile groups and a 3D elasto-plastic FEM analysis of the tests were conducted to investigate the bearing capacity of an in-service practical LNG tank foundation and the mechanical behavior of the pile groups.

In this study, the resisting forces of the in-service practical foundation were checked for the first time with a simulation method capable of assessing the behavior of laterally loaded large-scale pile groups. (1) By using predictions from the FEM analysis of the soil tests, and lateral loading tests performed before the soil tests, the load displacement results for 7  9 and 3  1 pile groups were predicted with accuracy, including the shape of the unloading and reloading cycles. This has helped render an appropriate determination of the test conditions. An analysis performed after the tests that improved the pile modeling was able to simulate the behavior of the 7  9 pile group, after yielding, to some extent. (2) The foundation yield around the load was calculated with Chang’s formula along with the increase in load to the ultimate load of 25,400 kN. At the ultimate load, the falling of the pile head from the slab and the falling away of the slab skin were predominantly observed at the front-most pile. However, brittle failure was not observed. (3) The deformation of the piles in the FEM results was found to correspond to the deformation of the pulled-out piles after the tests. The difference between each line was found to be close to that seen in past insitu lateral loading tests on a 3  3 pile group.

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S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

4,000 kN Front face Rear face

8,000 kN Front face Rear face

Total

12,000 kN Front face Rear face

Total

500

500

450

450

Total

Total

400

400 (1)

(7)

300 250

front

(1)

350

Reaction force of pile (kN)

350

Reaction force of pile (kN)

16,000 kN Front face Rear face

back

200 150 100 50

(7)

300 250 front

back

200 150 100 50

0

0

-50

-50

-100

-100 -150

-150

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(1)

(2)

(a) Reaction force at front and rear face

(3)

(4)

(5)

(6)

(7)

(b) Total of reaction force

Fig. 29. Evolution of reaction force of each pile.

x:

Stress of loading direction 200

150

100

50

0 0

x

50

Stress of loading direction at 16,000 kN kPa

x0 :

Initial stress of loading direction

Stress of loading direction 100

150

200

200

150

100

50

20 m

Stress increase at rear face (negative reaction force)

x

50

kPa 100

150

200

Stress decrease at rear face (positive reaction force)

Stress increase at front face (positive reaction force)

Stress increase at front face (positive reaction force)

00

Stress decrease at front face (negative reaction force)

Can t decrease under 0

20 m

Loading direction

Stress decrease in total (negative reaction force) (a) Fro nt-mo st p ile

(b) Back-mo st p ile

Fig. 30. Transition of ground stress distribution at front-most and back-most piles.

(4) The affected range of the ground (lateral and vertical displacement) increased in all directions with the 7  9 pile group compared to the 3  1 pile group. These results indicate the scale effect of the pile group.

(5) The maximum subgrade reaction of each pile for the framework analysis design in the Specification for Highway Bridges is different from the load share distribution of the 7  9 test and the FEM results; however, their averages are nearly equal. Therefore, the

S. Teramoto et al. / Soils and Foundations 58 (2018) 819–837

reduction rate of the maximum subgrade reaction at the back piles (= 0.5 currently) must be properly determined when designing each pile. (6) According to the yield of the pile heads of the frontmost piles, the deformation of the ground around these piles changed modes. Thus, a different tendency was seen at the back-most piles. (7) From the stress distribution results, the front-most piles were supported by the forward ground, while the back-most piles were supported by the forward and backside ground. This variation caused a difference in the pile deformation at the pile positions. (8) The back-most pile received the reaction force as a decrement in stress due to the initial stress, since that quantity had limitations. Therefore, according to the increase in load, the total reaction force at the backmost pile was small compared to that at the frontmost pile. This difference in reaction forces is why the load-share ratio distribution had an almost symmetrical U-shape in the initial phase. However, the shape changed as the load-share ratio of the backmost piles decreased. In the next study, the applicability of the above analysis to large-scale pile groups will be shown under a oneboundary condition in in-situ lateral loading tests. Changing the pile number by means of this analysis method, a parametric analysis will be conducted and the influence of the pile number on the pile-group effect will be investigated quantitatively. Subsequently, the mechanical behavior of large-scale pile groups subjected to seismic loads will be investigated with this method along with the pile number being applied to the design of pile groups. Acknowledgements This was a collaborative research effort by Osaka Gas Co., Ltd, Kyoto University, and Obayashi Co., Ltd. Sincere thanks are given to T. Nishizaki of Osaka Gas Co., Ltd and A. Inoue of Obayashi Co., Ltd, for their valuable suggestions. Thanks are also extended to the interested parties for their support and encouragement. References Adachi, T., Kimura, M., Kobayashi, H., Morimoto, A., 1994. Behavior of laterally loaded pile groups in dense sand. Proc. Int. Conf. Centrifuge 94, 509–514. Bao, X., Morikawa, Y., Kondo, Y., Nakamura, K., Zhang, F., 2013. Shaking table test on reinforcement effect of partial ground improvement for pile group foundation and its numerical simulation. Soils Found. 52 (6), 1043–1061. Hashiguchi, K., 1980. Constitutive equation of elastoplastic materials with elasto-plastic transition. J. Appl. Mech., ASME 102 (2), 266–272.

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