3 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August -6, 4 Paper No. 394 STUDY ON SEIMIC BEARING CAPACITY OF GROUPED PILES WITH BATTERED PILES Akira KOMATSU, Yoshito MAEDA, 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 (P V -z) relationship and the lateral soil resistancedeflection (P H y) relationship are used as a elasto-plastic formulation (Japan Road Association997) 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: () Application of the design method using the effective width depending on the load eccentricity for group piles as the deep foundation: () 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, () model tests using aluminum bar-laminar were performed, () 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 5mm in length, 9mm in height, and 5mm in width as shown in Figs.and was used. Aluminum bar-laminar was used as the soil model. Engineer, Nippon Steel Corporation, Tokyo, Japan. Email: komatsu.akira@eng.nsc.co.jp Professor, KyusyuKyoritu University, Kitakyusyu, Japan. Email: maeda@kyukyo-u.ac.jp 3 Senior Engineer, CTI Engineering Corporation, Tokyo, Japan. Email: sakata@ctie.co.jp
Aluminum bars having a radius of 3mm and of.6mm were mixed at the rate of 3 to, respectively. This aluminum bar-laminar has unit weights of 6.7 kn/m 3, and an internal friction angle of 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 5N/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 65mm long, 5mm thick, and 6mm in embedded depth on the tip of which a small aluminum plate of 3mm was connected in order to sustain vertical loading capacity. Pile spacing center to center is 5mm. Then a rigid model pile was made from an aluminum rectangular bar of 5mm 5mm in width, 65mm in length, and 35mm 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. Fig- Photograph of the experimental set-up Fig- Photograph of model piles Group effect Deformation at ultimate vertical load (5mm) 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. Vertical load Pv (kn) 鉛直荷重 Pv(kN) 3..5..5. : Single Pile : 5 x 単杭 Single pile 単杭の 5 倍の計算値 : group piles (5pcs) 群杭 (n=5) Group 群杭効果 effect Fig.3 Deformation at ultimate vertical load 3 4 5 6 鉛直変位 δv(mm) Vertical Displacement (mm) Fig.4 Vertical load displacement curves of vertical single pile and group piles
Behavior to Eccentric load of group piles Vertical eccentric loads (e=,5,,5,,5,3mm) 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-e 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. Vertical load Pv (kn) 鉛直支持力 P V (kn) 3.5.5 e= e=75 e=5 e=5 e=3m m 3 4 5 6 Vertical Displacement 鉛直変位 δ(mm) V (mm) Fig.5 Vertical load displacement curves under eccentric loads Vertical bearing capacity PV (kn) Vertical bearing capacity Pv (kn) 鉛直支持力 PV(kN) 3.5.5 : 荷重 変位曲線から得られた支持力値 :Test results of group piles : Sum of capacity in effective width 有効載荷幅 :Sum of capacity B 内の単杭の支持力の合計 in effective width C P V L e B 5 5 5 3 Eccentricity 偏心量 e e (mm) Eccentricity e (mm) Fig.6 Comparison of bearing capacity on eccentric loads Bearing Capacity of battered pile Deformation of the flexible model pile and aluminum bar-laminar after lateral loading (5mm) 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 outbatter 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. / ± ) is shown in Figs. and, 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. and 3, 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.6 to. in accordance with the increase of the inclination degree of the battered piles as shown in Fig.4.
Fig.7 Deformation of the flexible pile ( - ) at the ultimate lateral load Fig.8 Deformation of flexible pile ( + )at the ultimate lateral load.5 Bearing capacity ratio η 支持力比 η..5. : deflection = 5 mm δ=5mm : yield point δ = 降伏点 - -5 - -5 5 5 杭の傾斜角 α ( ) Dgree of the battered pile Fig.9 Relationship between inclination of flexible battered pile and lateral bearing capacity ratio Fig. Deformation at ultimate vertical load P 3. Fig. Deformation of group piles with battered piles under lateral loading 鉛直荷重 P Vertical load V Pv (kn) (kn) V.5..5. α = α =5 α = α =5 α = 3 4 5 6 Vertical 鉛直変位 Displacement δ ( mm ) v (mm) (n=5,e=) Fig. Vertical load displacement curves of group piles
(k N) 水平荷重 Ltaral load Pv (kn) (k 水平 H 荷重 P.4.3.. 3 4 5 6 水平変位 δ Horizontal deflection ( mm ) H (mm) (n=5,e=) Bearing capacity ratio : Lateral capacity (deflection=5mm) : Lateral capacity (yield point) : Vertical capacity (deflection=5mm) : Vertical capacity (yield point) Fig.3 Horizontal load deflection curves of grouped pile with battered piles Inclination of battered pile Fig.4 Relationship between inclination of flexible battered pile and lateral bearing capacity ratio 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 P H -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 (989)]. 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 5m 5m width, 65mm in length) were conducted and analyzed by using the tracking vision system. Tests using three different degree (-,,+ ) 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.5 and 6. 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/) with the horizontal surface of the ground.
P H (- ) P H (+ ) Fig-5 Deformation of rigid pile (- ) Fig-6 Deformation of rigid pile (+ ) Equation of the lateral earth pressure for battered pile Based on the failure mechanism in Figs.5 and 6, 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.7. The lateral ultimate resistance of the battered pile is described as follows: R ( z) = a p B K z () pcδ H K = RH p cδ z () c = N c + N z N c = N c ' cosδ (3) N = N ' cos δ (4) ( δ + α ) z=zcosα Z R H a φ + α H O R ω π/ ω +α ω δ ω D V V (A) e dl V φ b Fig.7 The admissible velocity field of battered pile ( ω ) cos ( ω φ ) f (B) ω φ cos cos φ π Nc ' = exp( ω tan φ ) (5), ω = + φ + α cosα tan φ sin tan φ 4 (6) cos ( δ + α ) N ' = η ( I + I ) (7) cos α ω I = exp ( 3ω tan φ ) sin ( + ω ) dω = [ exp 9 tan φ + ( 3ω tanφ ){ 3 tanφ sin ( ω ) cos ( ω )} + ( 3 tanφ sin α + cosα )] ( ω ) cosφ sin( ω ) exp( 3ω tanφ) sin( ω φ ) (8) I cos = (9) where, R H : ultimate resistance normal to the axis of the battered pile, B: the pile diameter, K ped : the coefficient of lateral earth pressure (ratio of horizontal to vertical normal effective stress) with friction angle between the soil and pile wall, : effective unit weight of soil, z: depth below soil surface, α p:correction factor regarding three-dimensional expansion effect (α p = for clay, α p =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(). c
Lateral bearing capacity ratio 支持力比.5..5. : test :computed 試験 解析 - 3 - - 3 Inclination 斜杭角度 of battered ( ) pile Fig.8 Relationship between inclination of flexible pile and lateral bearing i i Lateral bearing capacity ratio.6.4...8.6 : test.4 : computed 試験. 解析 -3 - - 3 斜杭角度 ( ) Inclination of battered pile Fig. 9 Relationship between inclination of flexible pile and lateral bearing 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: () 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. () The lateral bearing capacity of the battered pile (degree>) is larger than that of the vertical pile, and in contrast, the lateral bearing capacity of the battered pile (degree<) 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. Japan Road Association (997): Specifications for road bridges, Vol. Ⅳ.. The Japan Port and Harbor Association (989): Technical Standards for Port and Harbor Facilities and Explanation (in Japanese) 3. Maeda, Y., Ochiai, H., Yokota, Y. (): Bearing capacity formula of shallow foundations considering effects of inclinations and subsoil stratum, Proceedings of the Japan Society of Civil Engineer, Vol.75, p7-5 (in Japanese) 4. Komatsu, A., Maeda, R. (3) : 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, p9-34 (in Japanese)