13th World Conference on Earthquake Engineering Vancouver, B.C., Canada

August 1-6, 2004 Paper No. 3294

STUDY ON SEIMIC BEARING CAPACITY OF GROUPED PILES WITH BATTERED PILES

Akira KOMATSU1, Yoshito MAEDA2, Takahiro SAKATA 3

SUMMARY This report presents an evaluation of the design method of the seismic bearing capacity of group piles. By model tests using the aluminum bar-laminar, it was found that the concept of effective width depending on load eccentricity can be used to evaluate the bearing capacity of grouped piles in the same manner as the calculation method for shallow foundations. The lateral bearing capacity equation of battered piles was derived by using the admissible velocity field method, and the proposed equation gave satisfactory agreement with the results of laboratory tests.

INTRODUCTION In the seismic design of bridge foundations regarding a large earthquake, the pile foundation is designed to prevent fall-down. The vertical resistance-deflection (PV-z) relationship and the lateral soil resistance-deflection (PH –y) relationship are used as a elasto-plastic formulation (Japan Road Association1997) in which the ultimate vertical and lateral resistance is defined. In order to realize more optimum seismic design of the group pile foundation, it was concluded that the following studies were required: (1) Application of the design method using the effective width depending on the load eccentricity for group piles as the deep foundation: (2) Establishment of the equation for the ultimate lateral bearing capacity of the battered pile which is a more rigid structure to lateral loads than the vertical pile. In order to study the items described above, (1) model tests using aluminum bar-laminar were performed, (2) the failure mechanism of the battered pile was evaluated, and (3) the equation of the ultimate bearing resistance used by the admissible velocity field method was derived, then the results of the analyses using the equation were compared with the test results.

MODEL TESTS Experimental setup

A two-dimensional testing vessel having internal dimensions of 1500mm in length, 900mm in height, and 50mm in width as shown in Figs.1and 2 was used. Aluminum bar-laminar was used as the soil model.

1 Engineer, Nippon Steel Corporation, Tokyo, Japan. Email: komatsu.akira@eng.nsc.co.jp 2 Professor, KyusyuKyoritu University, Kitakyusyu, Japan. Email: maeda@kyukyo-u.ac.jp 3 Senior Engineer, CTI Engineering Corporation, Tokyo, Japan. Email: sakata@ctie.co.jp

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 10 20 30 40 50 60

単杭

単杭の5倍の計算値

群杭（n=5）

鉛直

荷重

　Ｐ

v（kN）

鉛直変位　δv（mm）

群杭効果

Fig.4 Vertical load – displacement curves of vertical single pile and group piles

Group effect

Vertical Displacement (mm)

Ver

tica

l loa

d P

v (k

N)

○ : Single Pile

□ : 5 x Single pile

◇ : group piles (5pcs)

Fig.3 Deformation at ultimate vertical load

Aluminum bars having a radius of 3mm and of 1.6mm were mixed at the rate of 3 to 2, respectively. This aluminum bar-laminar has unit weights of 16.7 kN/m3, and an internal friction angle of 21˚obtained from the shear test. Vertical and lateral loads were applied to the pile head through a rigid loading rod by an air jack. The applied load and deflection of the pile head were measured with a load cell and the potentiometer. Loads were applied to the pile head in increments of n×25N/min for vertical loads and n×7.5N/min for lateral loads where n is the number of piles. A flexible model pile was made from an aluminum plate 650mm long, 5mm thick, and 600mm in embedded depth on the tip of which a small aluminum plate of 30mm was connected in order to sustain vertical loading capacity. Pile spacing center to center is 150mm. Then a rigid model pile was made from an aluminum rectangular bar of 50mm × 50mm in width, 650mm in length, and 325mm in embedded depth. Results of model tests using flexible test piles are shown in Fig.3. The group effect and battered effect on the lateral resistance of the piles was found to be dependent on the number of piles, pile spacing, and the head fixity condition. In this paper, the pile battered in the direction of the horizontal load is described as the in-batter pile, and the opposite pile is described as the out-batter pile.

Group effect Deformation at ultimate vertical load (50mm) for a single pile and group piles is shown in Fig.3. Vertical load – displacement curves for a single pile and group piles are shown in Fig.4. In case of cohesionless soil, vertical bearing capacity of group piles has been found to be greater than that of the single pile multiplied. In this model test using aluminum bar-laminar, the same results were obtained.

Fig-1 Photograph of the experimental set-up Fig-2 Photograph of model piles

Behavior to Eccentric load of group piles Vertical eccentric loads (e=0,50,100,150,200,250,300mm) were applied to the group piles (5 piles). The results of the experiment on the effect of the vertical eccentric loads are shown in Fig.5. Vertical bearing capacity of group piles decreases with increasing eccentricity. The relation between vertical bearing capacity of group piles and eccentricity of vertical loads is shown in Fig.6. In the same manner as for the design method for shallow foundations, the vertical bearing load multiplied by piles in the effective width B’=B-2e centering on a loading position is shown in Fig.6. Two line graphs of vertical bearing capacity in Fig.6 shows different values, but have good correlation. These different values in the lines depend on the group effect described in the section above. Consequently, a design method that the ultimate vertical bearing capacity of group piles is evaluated by using the concept of effective width depending on the load eccentricity allows in the same manner as for shallow foundations.

Bearing Capacity of battered pile Deformation of the flexible model pile and aluminum bar-laminar after lateral loading (50mm) is shown in Figs.7 and 8. Comparison of lateral bearing capacity with respect to the degree of the battered pile is shown in Fig.9. The zone of the passive earth resistance for the in-batter pile is larger than that for the out-batter pile, and the deformation of the in-batter pile is smaller than that of the out-batter pile. Therefore, the lateral bearing capacity of the battered pile was found to increase in accordance with the degree. Deformation after vertical and lateral load tests of group piles (5 piles. / ±20° ) is shown in Figs.10 and 11, respectively. Deformation of aluminum bar-laminar between battered piles is larger than that of Aluminum bar-laminar beside the vertical pile. Load-deflection curves of the vertical and lateral loading test of group piles are shown in Figs.12 and 13, respectively. Vertical bearing capacity of group piles was found to decrease slightly in accordance with the increase of the degree of the battered piles. On the other hand, the lateral bearing capacity of group piles was found to increase at the rate of 0.6 to 2.0 in accordance with the increase of the inclination degree of the battered piles as shown in Fig.14.

0

0.5

1

1.5

2

2.5

3

0 10 20 30 40 50 60

鉛直

支持

力Ｐ

Ｖ(kN)

鉛直変位 δＶ (mm)

0

0.5

1

1.5

2

2.5

3

0 10 20 30 40 50 60

鉛直

支持

力Ｐ

Ｖ(kN)

鉛直変位 δＶ (mm)

○ e=0 □ e=7 5 ◇ e= 150

● e= 225 ■ e= 300 m m

Vertical Displacement (mm)

Ver

tica

l loa

d P

v (k

N)

Fig.5 Vertical load – displacement curves under eccentric loads Eccentricity e (mm)

Ver

tica

l bea

ring

cap

acit

y P

v (k

N)

○ :Test results of group piles △ :Sum of capacity in effective width

Fig.6 Comparison of bearing capacity on eccentric loads

鉛直

支持力

ＰＶ（

kN）

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250 300偏心量 e (mm)

ＰＶ

Ｂ′

ｅ

CL

○ 荷重･変位曲線から得られた支持力値

△ 有効載荷幅 B′内の単杭の支持力の合計

鉛直

支持力

ＰＶ（

kN）

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250 300偏心量 e (mm)

ＰＶ

Ｂ′

ｅ

CL

○ 荷重･変位曲線から得られた支持力値

△ 有効載荷幅 B′内の単杭の支持力の合計

○: Test results of group piles △: Sum of capacity in effective width

Ver

tica

l bea

ring

cap

acit

y P

V (

kN)

Eccentricity e (mm)

Fig.7 Deformation of the flexible pile ( -10°) at the ultimate lateral load Fig.8 Deformation of flexible pile ( + 10°)at the

ultimate lateral load

0.0

0.5

1.0

1.5

2.0

2.5

- 20 - 15 - 10 - 5 0 5 10 15 20

杭の傾斜角α （° ）

支持

力比

η

δ =50mm

δ =降伏点

Fig.10 Deformation at ultimate vertical load

P

Fig.11 Deformation of group piles with battered piles under lateral loading

Bea

ring

cap

acity

rat

io η

Dgree of the battered pile

■: deflection = 50 mm ◆: yield point

Fig.9 Relationship between inclination of flexible battered pile and lateral bearing capacity ratio

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 10 20 30 40 50 60

（n=5,e=0）

鉛直荷重PV

V （kN）

鉛直変位δ v （㎜）

△ α =15 ° ◇ α =10 ° □ α =5 ° ○ α =0 °

▽ α =20 ° Ver

tica

l loa

d P

v (k

N)

Vertical Displacement (mm)

Fig.12 Vertical load – displacement curves of group piles

EQUATION OF LATERAL RESISTANCE OF PILE

Mechanism of lateral resistance of battered pile Battered piles remain the most efficient structural component for resisting lateral loads due to earthquake. The group pile system with battered piles results in a more rigid frame than one with vertical piles only. In seismic design analysis, the bi-linear PH-y curve is applied to obtain the lateral resistance of piles. The maximum value of soil resistance (lateral bearing capacity) is assumed to be the passive earth pressure strength of the soil behind the pile. In Japan, for the coefficient of the lateral subgrade reaction of the battered pile inclined in the vertical, a correction is formulated in the design standard [Technical Standards for Port and Harbor Facilities and Explanation (1989)]. In this paper, lateral loading tests using the rigid model pile in aluminum bar-laminar ground were carried out so as to evaluate the mechanism of ground failure on the battered pile. Based on the failure mechanism obtained, an equation of the passive earth pressure strength of the battered pile is proposed by using the admissible velocity field method. It is obvious that the passive earth resistance zone for in-batter pile is greater than that for the out-batter pile. Failure mechanism of the ground behind batter pile In order to evaluate the failure mechanism of the ground behind the battered pile, the lateral loading tests using the rigid model pile (a aluminum rectangular bar of 50m × 50m width, 650mm in length) were conducted and analyzed by using the tracking vision system. Tests using three different degree (-10˚,0˚,+10˚) of the pile were conducted. The photographs and deformation graphs of the soil by using the tracking vision system after loading are shown in Figs.15 and 16. These experiments show the sliding wedge beneath the pile is not the straight slope on that is assumed in the Coulomb theory, and has the zone of radial shear. This is due to the friction between the pile and the ground. Then, the boundary of the passive Rankine zone is at an angle 34.5˚ (=π/4-φ/2) with the horizontal surface of the ground.

Fig.13 Horizontal load – deflection curves of grouped pile with battered piles

0

0.1

0.2

0.3

0.4

0.5

0 10 20 30 40 50 60

（n=5,e=0）

水

平

荷

重P H

（k

N）

水平変位δ H （㎜）

水平荷重 （ｋ

Lta

ral l

oad

Pv

(kN

)

Horizontal deflection (mm)

Fig.14 Relationship between inclination of flexible battered pile and lateral bearing capacity ratio

Inclination of battered pile B

earin

g ca

paci

ty ra

tio

○ : Lateral capacity (deflection=50mm) □ : Lateral capacity (yield point) ◇ : Vertical capacity (deflection=50mm) △ : Vertical capacity (yield point)

Fig.17 The admissible velocity field of battered pile

○＋ α

Z

R

RH

V0

V1

δ

O

a b

c

e f dl

φ φ

ω

∆ω ω1

(A)

(B)

D

V

z=Zcosα

ω1−φ−α π/2−ω1+α

H

Equation of the lateral earth pressure for battered pile Based on the failure mechanism in Figs.15 and 16, the passive earth resistance zone shall be composed of the radial shear zone and the passive Rankine zone due to the friction between the pile and the ground. Accordingly, the equation of the passive ground pressure for the battered pile was derived by using the admissible velocity method as shown in Fig.17. The lateral ultimate resistance of the battered pile is described as follows:

zcp

KBazR pH ・・・・ γδγ=)( (1)

γγ

γδ

NNz

c

Rzcp

K

c

H

+

⋅=

2

2

12

＝

γ

(2)

δcos'cc NN = (3)

δγγ cos'NN = (4)

( ) ( ) ( )( )

−

−−−−+=

φφωω

φφωδ

tan

1

sin

coscos

tan

1tan2exp

cos

cos'

1

11

α

φα

α

αNc (5), α

φπω ++=

241 (6)

( ) ( )21cos

cos' IIN +

+=

α

αη

δγ

(7)

( ) ( )

( ) ( ){[

( )} ( )]ααφαω　　　

αωφφω

α

cossintan3cos

sintan3tan3exp1tan9

1

sintan3exp

1

112

01

1

++−−

−+

=

+−= ∫

φ

ωωφωω

dI

(8) ( ) ( ) ( )

( )α

αα

−−−−

=φω

φωωφω

1

1112 sin

tan3expsincoscosI (9)

where, RH: ultimate resistance normal to the axis of the battered pile, B: the pile diameter, Kpγed: the coefficient of lateral earth pressure (ratio of horizontal to vertical normal effective stress) with friction angle between the soil and pile wall, γ: effective unit weight of soil, z: depth below soil surface, α

p:correction factor regarding three-dimensional expansion effect (αp=2 for clay, αp=3 for sand), α: degree of battered pile to the vertical , φ: angle of internal friction of sand, η: correction factor for the accurate potential energy analyzed by Maeda(2002).

PH

Fig-15 Deformation of rigid pile (-10°)

(＋10°)

Fig-16 Deformation of rigid pile (+10°)

PH

(-10°)

CONCLUSION

In the present study, the evaluation for the design method of seismic bearing capacity of group piles was investigated to realize an optimum and economical seismic design. The main conclusions are given, as follows: (1) A design method allows the ultimate vertical bearing capacity of group piles to be evaluated by using the concept of effective width depending on the load eccentricity in the same manner as for shallow foundations. (2) The lateral bearing capacity of the battered pile (degree>0) is larger than that of the vertical pile, and in contrast, the lateral bearing capacity of the battered pile (degree<0) is smaller. Then the lateral bearing capacity of the group piles with the battered pile increased more significantly than the group piles with the vertical piles. It is found that the structure of group piles with the battered pile has both the effect of rigid resistance due to the inclination of the pile and the effect of pile head fixity. (3) The proposed equation for the lateral resistance of the battered pile using the admissible velocity field method agrees satisfactorily with the results of the model tests.

REFERENCES 1. Japan Road Association (1997): “Specifications for road bridges,” Vol. Ⅳ. 2. The Japan Port and Harbor Association (1989): Technical Standards for Port and Harbor Facilities

and Explanation (in Japanese) 3. Maeda, Y., Ochiai, H., Yokota, Y. (2002): “Bearing capacity formula of shallow foundations

considering effects of inclinations and subsoil stratum,” Proceedings of the Japan Society of Civil Engineer, Vol.715, p107-115 (in Japanese)

4. Komatsu, A., Maeda, R. (2003) : “Laboratory loading test of bearing capacity characteristic of grouped piles (Bearing capacity under eccentric and inclined load, and for battered pile),” Proceedings of Symposium on Japan Geotechnical Engineering, No.48, p129-134 (in Japanese)

Lat

eral

bea

ring

cap

acit

y ra

tio

0.0

0.5

1.0

1.5

2.0

2.5

- 30 - 20 - 10 0 10 20 30

斜杭角度（° ）

支持

力比

試験

解析

Lat

eral

bea

ring

cap

acit

y ra

tio

Inclination of battered pile

■ : test ○:computed

Fig.18 Relationship between inclination of flexible pile and lateral bearing

i i

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

-30 -20 -10 0 10 20 30 斜杭角度（°）

試験 解析

Fig. 19 Relationship between inclination of flexible pile and lateral bearing

Inclination of battered pile

■ : test ○ : computed