ANALYSIS OF PILE DRIVING IN VERTICAL AND HORIZONTAL DIRECTIONS USING A HYBRID MODEL

Transcription

1 ANALYSIS OF PILE DRIVING IN VERTICAL AND HORIZONTAL DIRECTIONS USING A HYBRID MODEL TATSUNORI MATSUMOTO i) PASTSAKORN KITIYODOM ii) EIJI KOJIMA iii) HIROMICHI KUMAGAI iv) SATOSHI NISHIMOTO v) and KOUICHI TOMISAWA vi) ABSTRACT In order to etimate the deformation and load ditribution of a ingle pile ubjected to dynamic horizontal load a well a vertical load, a implified method of three-dimenional numerical analyi, KWaveHybrid program, i developed uing a hybrid model. In the hybrid model, the pile i modelled a elatic beam, and the oil at each pile node i treated a pring and dahpot in both vertical and horizontal direction. KWaveHybrid i alo able to analye the tatic repone of the pile. Validity of the newly developed program i examined through comparion with theoretical value and horizontal dynamic and tatic pile load tet reult. Key Word : Pile load tet, Pile driving analyi, Hybrid model, Horizontal loading, Vertical loading, Cae tudy 1. INTRODUCTION It ha been believed that the tatic load tet i the mot reliable method to obtain the load-diplacement relation of a pile. Mot tatic load tet are conducted uing reaction pile a the reaction ytem. In the work of Kitiyodom et al. 1), it i uggeted that the influence of the reaction pile on the meaured load-diplacement relation may not be neglected, and that an interpretation of the meaured data i required to obtain a true load-diplacement relation of the pile. For axial compreive pile load tet, the dynamic load teting or the rapid load teting i widely ued becaue of the fact that thee method are unuceptible to reaction pile, and require le time and cot compared with the conventional tatic load tet where reaction pile are employed. The dynamic load teting and the rapid load teting, however, require interpretation of the meaured ignal to derive a correponding tatic load-diplacement relation. Epecially, for dynamic load tet in which wave propagation phenomena in the pile cannot be neglected, wave matching analyi i indipenable. In a eimic area uch a Japan, application of the dynamic or rapid pile load tet to horizontal pile load teting would be very ueful in the eimic deign of the pile foundation. Several computer program for analying the one-dimenional wave propagation in a 1 pile have been developed, uch a Smith method 2), CAPWAP 3), WEAP ), TNOWAVE 5), KWave 6) and KWaveFD 7). However, all of thee program can be applied to the problem in vertical direction only. In thi tudy, a computer program KWaveHybrid ha been developed baed on a hybrid model. In KWaveHybrid, the horizontal reitance of the pile i incorporated into the hybrid model o a to be able to analye the deformation and load ditribution of a ingle pile ubjected to horizontal load a well a vertical load. The program can be alo ued to calculate the tatic load-diplacement relation of the pile in both horizontal and vertical direction. In order to examine the validity of the newly developed program, verification analye are carried out firt. Then the program i applied to the tatic and dynamic horizontal load tet of actual teel pipe pile. 2 METHOD OF ANALYSIS Figure 1 illutrate the hybrid modelling of the pile and the oil ued in thi tudy. The pile i modelled a beam element with mae and the oil i treated a pring and dahpot. Figure 2 how the dynamic haft oil reitance model incorporated into KWaveHybrid. The value of the vertical pring, k, the horizontal pring, k x and k y, the vertical radiation damping, c, and the horizontal I) Profeor, Graduate School of Natural Science and Technology, Kanazawa Univerity, Kodatuno 2--2, Kanazawa, , Japan. ii) Reearch Aociate, Graduate School of Natural Science and Technology, Kanazawa Univerity, Kodatuno 2--2, Kanazawa, , Japan. iii) Japan Pile Corporation, Shinkawa , Chuo-ku, Tokyo, 1-33, Japan iv) Japan Pile Corporation, Shinkawa , Chuo-ku, Tokyo, 1-33, Japan v) Civil Engineering Reearch Intitute of Hokkaido, Hiragihi , Toyohira-ku, Sapporo, , Japan vi) Civil Engineering Reearch Intitute of Hokkaido, Hiragihi , Toyohira-ku, Sapporo, , Japan Manucript wa received for review on May 9, 25.

2 MATSUMOTO, KITIYODOM, KOJIMA, KUMAGAI, NISHIMOTO AND TOMISAWA radiation damping, c x and c y, per unit haft area are approximated by mean of Equation (1) and (2), baed on the work of Novak et al. 8). 2.75G x y G k, k k d d G x y.5g c, c c V V where G and V are the hear modulu and the hear wave velocity of the urrounding oil repectively, and d i the outer diameter of the pile. k k 2 c k 1 c 1 k n c 2 c n (K p ) 1 m m 1 (K p ) 3 m 2 m n k b c b c b m b c h n k h c h k h 1 (K p ) 2 c h 1 (K p ) n k h 2 c h 2 k h n Fig. 1. Hybrid modelling of the pile and the oil. Slider max tatic or q h Pile node Dahpot c v (vicou) (1) (2) The lider value i equal to the tatic maximum haft max reitance, tatic, in the vertical direction and i equal to the limit horizontal preure, q h, in the horizontal direction. The total dynamic friction in vertical direction, total, i generally taken a a non-linear function of velocity, according to 1 vv / ( v = 1 m/) (3) max total tatic where v i a reference velocity and v i the relative velocity between the pile and the adjacent oil. Non-linear vicou law imilar to Equation (3) have been propoed by Gibon and Coyle 9), Heerema 1), and Litkouhi and Pokitt 11), all of whom ugget a value of cloe to.2, with the parameter varying from about.1 for and, to unity for clay oil 12). The relation in Equation (3) wa introduced into the vicou damping in Figure 2 for vertical haft reitance model. Figure 3 how the dynamic vertical pile bae reitance model. The value of the oil pring at the pile bae, k b, the damping, c b, and the lumped oil ma, m b, per unit bae area can be etimated a follow 13) : kb 8G d(1 ) () cb 3. G (1 ) V (5).1 mb 16r o (1 ) (6) in which and are the Poion ratio and the denity of the oil repectively. The equation of motion of the pile i expreed a K w C w M w F (7) where [K], [C] and [M] are the tiffne matrix, the damping matrix and the ma matrix repectively. { F} i the external force vector. The tiffne matrix i formed from the pile tiffne matrix and the oil tiffne matrix. The damping matrix i equal to the oil damping matrix. The ma matrix i formed from the pile ma matrix and the lumped oil ma at the pile bae. Soil adjacent to pile Pile node Spring k Dahpot c (radiation) Slider q b Dahpot c b Soil far from pile (fixed) Fig. 2. Vertical and horizontal haft reitance model. Spring k b Lumped Dahpot cb ma M b 2

3 Fig. 3. Vertical bae reitance model. When the tre at a pile-oil interface nodal point reache the oil yield tre, the oil pring tiffne and the dahpot value at that point are et to. In order to conider alo the nonlinearity of the oil pring tiffne, Equation (7) i rewritten in incremental form a: F K w C w M w F (8) t t t t t t t t t t t t Equation (8) can be olved for the pile ettlement, deflection and rotation from which the axial force, the hear force and the bending moment can be obtained. Note that Newmark method 1) i ued for olving Equation (8). In the analyi of tatic pile load tet, the tatic vertical haft oil pring, k tatic, i etimated by mean of Equation (9) and (1) following Randolph and Wroth 15). ktatic (2 / 2.75 ) k, ln[5.(1 ) l/ d ] (9) where l i the pile embedment length. The tatic horizontal haft oil pring value at each pile node are etimated baed on Mindlin olution 16) which i imilar to the olution of the integral equation method ued by Poulo and Davi 17). The equation become k k E l (1) x y tatic tatic pd / ue (11) where p i the horizontal ditributed force acting uniformly over the pile element and u i the correponding horizontal diplacement at each pile node calculated uing the integral equation method. Note that the hear reitance at the pile bae ha not been incorporated in the preent program. More detail of the tatic analyi method can be found in Reference 18) and 19). 3 ACCURACY OF THE PROPOSED METHOD 3.1 Impact on pile without oil reitance Vertical impact on a homogeneou pile and a non-homogeneou pile without oil reitance are calculated by the program KWaveHybrid, and the calculated reult are compared with the theoretical value. Table 1 how the pecification of a homogeneou pile to be analyed here. Table 1. Specification of a homogeneou pile Length (m) 1 Diameter (mm) Cro-ectional area (m 2 ).126 Young' modulu (kn/m 2 ) Bar wave velocity (m/) 5 Denity (ton/m 3 ) Ma (ton) 1.51 Figure how the vertical impact force applied to the pile head. Figure 5 how the calculated and theoretical ditribution of axial force along the pile. Theoretically, the front of compreion force reache the pile bae at t = 2 m becaue the bar wave velocity i 5 m/. The compreion force i reflected at the pile bae, and the reflected force goe back to the pile head a the tenion force and reache the pile head at t = m. The calculated reult are in good agreement with thee theoretical olution. Figure 6 how the time v pile diplacement at the middle point (z = 5 m). A good agreement between the theoretical and calculated value can be een again. Force Force Fig.. Pile head force. (t = 2 m) (t = m) Theoretical (t = 2 m) Theoretical (t = m) t = m t = 2 m Pile ditance (m) Pile diplacement (mm) Fig. 5. Ditribution of axial force along the pile. 3 2 Theoretical 1 z = 5 m Fig. 6. Time v pile diplacement Table 2. Specification of a non-homogeneou pile Upper Lower Length (m) 5 5 Diameter (mm) Cro ection area (m 2 ) Young' modulu (kn/m 2 ) Bar wave velocity (m/) 5 5 Denity (ton/m 3 )

4 MATSUMOTO, KITIYODOM, KOJIMA, KUMAGAI, NISHIMOTO AND TOMISAWA A non-homogeneou pile with no oil reitance hown in Table 2 wa alo analyed uing the propoed method. The pile conit of two ection having the ame material but different cro-ectional area. The cro-ectional area of the lower ection i twice that of the upper ection. The impact force hown in Figure wa applied to the pile head. Figure 7 and 8 how time v velocity and time v pile head diplacement, repectively. Good agreement between the calculated and theoretical value can be een in both the velocity and diplacement. 3.2 Friction pile with elatic oil repone A perfect friction pile with elatic friction repone i analyed, and the calculated reult are compared with the theoretical olution of the ingle ma ytem hown in Figure 9. Specification of the pile to be analyed here are the ame a thoe hown in Table 1. The value of the vertical haft pring tiffne, k, and the vertical radiation damping, c, were et a k = kn/m 3 and c = 5. kn/m 3 along the pile haft uniformly for convenience. The correponding value of the total vertical pring tiffne, K, and the total vertical damping, C, in the ingle ma ytem are hown in Figure 9. Figure 1 and 11 how time v diplacement of the middle point of the pile without damping (c = ) and with damping, repectively. Overall, the calculated reult are in good agreement with the theoretical olution in both cae. Periodical ocillation can be een in the calculated reult. Thee ocillation in the calculation reult reflect the wave propagation phenomena in the pile, which cannot be imulated uing the ingle ma ytem. Velocity (m/) Pile head dip. (mm) 6 2 Theoretical Fig. 7. Time v pile head velocity Theoretical Fig. 8. Time v pile head diplacement Pile diplacement (mm) M = 1.51 ton K = kn/m Fig. 9. Single ma ytem. C = 62.8 kn/m z = 5 m -8 Theoritical Fig. 1. Time v pile diplacement (without damping). Pile diplacement (mm) 12 8 Peak from olution with damping - -8 z = 5 m Theoritical Fig. 11. Time v pile diplacement (with damping). CASE STUDY.1 Tet decription The tet piling on two teel pipe pile wa performed. Figure 12 how the profile of oil layer and the SPT N-value at the tet ite. Two tet pile, deignated a P1 and P2, were intalled by preboring. So there i no oil plug inide the pile. The tet pile pecification are ummaried in Table 3. The ditance between the centre of the two pile i 3.5 m. Table 3. Specification of tet teel pile P1 P2 Length (m) Embedment length (m) Outer diameter (mm) 6 5 Inner diameter (mm) Cro-ectional area (cm 2 ) Young' modulu (kn/m 2 ) Shear wave velocity (m/) Denity (ton/m 3 ) Pile ma (ton).9 1.1

5 Both tatic and dynamic horizontal load tet were carried out on each pile. The dynamic pile load tet wa carried out prior to the tatic pile load tet. In the dynamic pile load tet, the pile wa hit horizontally by a hammer ma of.96 ton at the point z =.25 m below the pile head. Applied force, horizontal diplacement and acceleration were meaured at the ame level of the hit point with a ampling rate of 15. After the dynamic pile load tet, two tatic horizontal pile load tet with different loading method were conducted on each pile. Static horizontal pile load tet with tep loading method 2) wa conducted firt. Load tep equence for the tep loading i hown in Figure 13, following JSF T ). In vertical pile load tet tandard JGS ), two loading method are recommended which are the tep loading method and the continuou loading method. However, in JSF T32-83, only the tep loading method i precribed. In thi tudy, the tatic horizontal pile load tet with the continuou loading method wa alo conducted. The load tep equence of continuou loading i alo hown in Figure 13. The tatic horizontal load wa applied at the ame loading point a the dynamic horizontal pile load tet. The horizontal diplacement of the pile and the applied force were monitored throughout the tatic pile load tet. Force, F ta Depth from G.L. (m) Clay Clayed Sand Sandy Clay Fine Sand Silt Clay SPT N-value P1 P2 1 Fig. 12. Profile of oil layer and SPT N-value Step loading (JSF T32-83) Cont. loading Time (min) Fig. 13. Load tep equence of tatic pile load tet. 5 Horizontal Dip., u (mm) (a) force (b) and etimated horizontal diplacement Acceleration, (m/ 2 ) Velocity, v (m/) (c) acceleration (d) Velocity (integrate of acceleration by time) Fig. 1. Dynamic pile load tet ignal of P1..2 tatic and dynamic tet ignal The dynamic tet ignal of P1 and P2 are hown in Figure 1 and 15, repectively. The meaured force increae and decreae rapidly with time and have a peak of about 5 kn. The loading duration i about 5 m. Figure 16 and 17 how the meaured tatic and dynamic horizontal load-horizontal diplacement relation of P1 and P2, repectively. It can be een from the figure that there are good agreement between the meaured load diplacement relation from the tatic

6 MATSUMOTO, KITIYODOM, KOJIMA, KUMAGAI, NISHIMOTO AND TOMISAWA load tet with continuou loading and that from the tatic load tet with tep loading. On the other hand, the meaured load diplacement relation from the dynamic load tet are totally different from the meaured tatic load diplacement relation. Therefore, in order to obtain the tatic load diplacement relation of the pile from the meaured ignal of the dynamic load tet, wave matching analyi of the meaured dynamic ignal wa carried out uing KWaveHybrid. Horizontal Dip., u (mm) (a) force (b) and etimated horizontal diplacement Acceleration, (m/ 2 ) Velocity, v (m/) (c) acceleration (d) Velocity (integrate of acceleration by time) Fig. 15. Dynamic pile load tet ignal of P2. Force, F Horizontal Diplacement, u (mm) Fig. 16. load-diplacement relation of P1. Force, F Fig. 17. load-diplacement relation of P2..3 Wave matching analyi reult Matching analyi wa repeated with aumed value for the maximum haft limit horizontal preure, q h, and the oil hear modulu, G, uing the meaured F dyn a the force boundary condition at the loading point, until a good matching between the calculated and the meaured pile diplacement wa obtained. Soil parameter ued in the final matching of P1 are lited in Table. Figure 1(b) and Figure 18 how the diplacement v time and load diplacement relation of P1 in the final matching analyi, compared with the meaured value. It can be een that the calculated dynamic pile diplacement underetimated the meaured value after the peak diplacement. Thi i thought to be due to the oil pring model. At the preent, the value of the oil pring in KWaveHybrid during the loading and unloading tate are the ame. It can be een from the meaured reult (Figure 16 and 17) that the value of the oil pring during the loading and unloading tate hould be different. Thee extenion are left for future work. 6

7 Table. Soil parameter for final matching of P1. Depth (m) G (kpa) q h (kpa) to > Elatic range Table 5. Soil parameter for final matching of P2. Depth (m) G (kpa) q h (kpa) to > Elatic range Uing the ame oil parameter a hown in Table, the tatic load diplacement relation of P1 wa etimated uing KWaveHybrid. Figure 19 how the comparion of the etimated tatic load diplacement relation of P1 with the meaured value. It can be een that the etimated reult matche very well with the meaured one. The ame analyi procedure a P1 were carried out for P2. Soil parameter ued in the final matching of P2 are lited in Table 5. Figure 15(b) and Figure 2 how the diplacement v time and load diplacement of P2 in the final matching analyi, compared with the meaured value. Figure 21 how the comparion of the etimated tatic load diplacement relation of P2 with the meaured value. Again there i a good agreement between the etimated and the meaured reult Fig. 18. Dynamic pile load tet reult of P1. Force, F ta Etimated Fig. 19 Static pile load tet reult of P Fig. 2. Dynamic pile load tet reult of P2. Force, F ta Etimated Fig. 21 Static pile load tet reult of P1.. Prediction analyi In actual contruction ite, it would be very ueful to etimate the tatic load diplacement relation of the actual pile from the dynamic load tet of another pile having maller diameter. In thi work, the oil parameter of P2 (Table 5), which ha a maller diameter than P1, were employed to predict the load diplacement relation of P1. Figure 22 how the predicted diplacement v time and the predicted dynamic load diplacement relation of P1, compared with the meaured value. Figure 23 how the predicted tatic load diplacement relation of P1, compared with the meaurement. It can be een from the figure that although the predicted diplacement overetimate the meaured value, there are reaonable agreement between the predicted and the meaured value. 5 CONCLUSIONS A new numerical program KWaveHybrid for analying pile driving a well a tatic load tet in vertical and horizontal direction ha been developed in thi tudy. Performance of the program wa verified through comparion with theoretical olution The developed program wa then applied to the dynamic and tatic horizontal load tet on two teel pipe pile. A good matching between the calculated and

8 MATSUMOTO, KITIYODOM, KOJIMA, KUMAGAI, NISHIMOTO AND TOMISAWA meaured behaviour of the pile during driving and during tatic load tet wa obtained. The identified oil reitance parameter of the maller diameter pile were ued to predict the behaviour of the bigger pile, and a good prediction wa obtained. Horizontal Dip., u (mm) Predicted (a) and predicted horizontal diplacement Predicted (b) and predicted load-diplacement relation Fig. 22. Predicted dynamic reult of P1. Force, F ta Predicted Fig. 23. Predicted tatic load-diplacement of P1. REFERENCES 1) Kitiyodom, P., Matumoto, T. and Kanefua, N. (2): Influence of reaction pile on the behaviour of tet pile in tatic load teting. Canadian Geotechnical Journal, 1(3), ) Smith, E. A. L. (196): Pile driving analyi by the wave equation. Journal of the Soil Mechanic and Foundation Diviion ASCE, 86(SM), ) Rauche, F., Moe, F. and Goble, G. G. (1972): Soil reitance prediction from pile dynamic Journal of the Soil Mechanic and Foundation Diviion ASCE, 98(SM9), ) Goble, G. G. and Rauche, F. (1976): Wave equation analyi of pile driving-weap program, prepared for the U.S. department of tranportation, federal highway adminitration, implementation diviion, office of reearch and development. 5) TNO (1977): Dynamic pile teting. Report No. BI ) Matumoto, T. and Takei, M. (1991): Effect of oil plug on behaviour of driven pipe pile. Soil and Foundation, 3(2), ) Wakiaka, T., Matumoto, T., Kojima, E. and Kuwayama S. (2): Development of a new computer program for dynamic and tatic pile load tet. Proceeding of the 7 th International Conference on the Application of Strewave Theory to Pile, Kuala Lumpur, ) Novak, M., Nogami, T. and Aboul-Ella F. (1978): Dynamic oil reaction for plane train cae. Journal of Mechanical Engineering ASCE, 1(EM), ) Gibon, G. and Coyle, H. M. (1968): Soil damping contant related to common oil propertie in and and clay. Report No , Texa Tranport Intitute, Texa A&M Univerity. 1) Heerema, E. P. (1979): Relationhip between wall friction diplacement, velocity and horizontal tre in clay and in and for pile driveability analyi. Ground Engineering, 12(1). 11) Litkouhi, S. and Pokitt, T. J. (198): Damping contant for pile driveability calculation. Géotechnique, 3(1), ) Randolph, M. F. and Deek A. J. (1992): Dynamic and tatic oil model for axial pile repone. of the th International Conference on the Application of Strewave Theory to Pile, The Hague, ) Deek, A. J. and Randolph, M. F. (1995): A imple model for inelatic footing repone to tranient loading. International Journal for Numerical and Analytical Method in Geomechanic, 19, ) Newmark, N. M. (1959): A method of computation for trucural dynamic. Journal of the Engineering Mechanic Diviion ASCE, 85(EM3), )Randolph, M. F. and Wroth, C. P. (1978): Analyi of deformation of vertically loaded pile. Journal of Geotechnical Engineering ASCE, 1(12), ) Mindlin, R. D. (1936): Force at a point interior of a emi-infinite olid. Phyic, 7, ) Poulo, H. G. and Davi E. H. (198): Pile Foundation Analyi and Deign, Wiley, New York. 18) Kitiyodom, P. and Matumoto, T. (22): A implified analyi method for piled raft and pile group foundation with batter pile. International Journal for Numerical and Analytical Method in Geomechanic, 26, ) Kitiyodom, P. and Matumoto, T. (23): A implified analyi method for piled raft foundation in non-homogeneou oil. International Journal for Numerical and Analytical Method in Geomechanic, 27, ) Japanee Society of Soil Mechanic and Foundation Engineering. (1983): JSSMFE tandard method for lateral loading tet for a pile. Japanee Society of Soil Mechanic and Foundation Engineering, Tokyo. 21) Japanee Geotechnical Society. (22): Standard of Japanee Geotechnical Society for vertical load tet of pile. Japanee Geotechnical Society, Tokyo.