1. Jiangxi Key Laboratory of Infrastructure Safety Control in Geotechnical Engineering, East China Jiaotong University, Nanchang 330013, China 2. Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China 3. Jiangxi Vocational College of Environmental Engineering, Ganzhou 341000, China 4. National Experimental Teaching Demonstration Center of Civil Engineering, East China Jiaotong University, Nanchang 330013, China
An analytical algorithm for calculating the lateral response of a horizontally loaded step-tapered pile was proposed based on linear elastic subgrade reaction theory. The algorithm assumes a constant subgrade reaction modulus for each soil layer. The pile was segmented according to the variation in the pile section and the different soil layers. The governing equation for every segment was established. Then the iterative relationship of the deflection was derived, and the distribution of internal force and deformation of the pile with given boundary conditions were given by considering the deformation continuity between the adjacent pile segments and the boundary conditions of the pile tips. The obtained results were compared with the finite element calculation results and the field measured data in order to verify the algorithm. The influences of pile parameters such as length-diameter ratio, the position of the reduced diameter or pile-diameter ratio on the internal force and deformation distribution of pile were discussed. Reducing the length-diameter ratio and shifting the position of the reduced diameter to the bottom of the pile can reduce the maximum groundline displacement and increase the maximum bending moment. Reducing the pile-diameter ratio is conducive to reducing the maximum bending moment and coordinating the deformation more effectively.
Wen-tao HU,Dou LIU,Da-xin GENG,Ning WANG,Chang-jie XU,Xing SHANGGUAN,Jie MIN. Internal force and deformation of step-tapered pile under lateral loads. Journal of ZheJiang University (Engineering Science), 2020, 54(4): 739-747.
Fig.1Subdividing of section varied pile under lateral load
Fig.2Calculation flow chart for response of horizontally loaded step-tapered piles
Fig.3Modulus of subgrade reaction around pile
Fig.4Computed horizontal displacement contrast with numerical results and field test results
Fig.5Computed bending moment contrast with numerical results and measurement results
土体类别
t/m
v
Es /kPa
Esoil /kPa
中密砂
4
0.3
22 900
17 011.3
粉砂
1
0.3
29 840
22 166.86
Tab.1Soil parameters in Ismael[1]
Fig.6Computed bending moment contrast with numerical results and field test results
L/D
D
d
d/D
变径位置
10
1
0.6
0.6
40%
12
0.83
0.5
0.6
40%
14
0.7
0.42
0.6
40%
16
0.625
0.375
0.6
40%
18
0.55
0.33
0.6
40%
20
0.5
0.3
0.6
40%
20
0.5
0.3
0.6
20%
20
0.5
0.3
0.6
40%
20
0.5
0.3
0.6
60%
20
0.5
0.3
0.6
80%
20
0.5
0.25
0.5
40%
20
0.5
0.3
0.6
40%
20
0.5
0.35
0.7
40%
20
0.5
0.4
0.8
40%
20
0.5
0.45
0.9
40%
20
0.5
0.5
1.0
40%
Tab.2Pile parameters under different conditions
Fig.7Influence of length-diameter ratio on displacement
Fig.8Influence of length-diameter ratio on moment
Fig.9Influence of location of discontinuity in diameter on displacement
Fig.10Influence of location of discontinuity in diameter on moment
Fig.11Influence of butt diameter to tip diameter on displacement
Fig.12Influence of butt diameter to tip diameter on moment
[1]
ISMAEL N F Behavior of step tapered bored piles in sand under static lateral loading[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2010, 136 (5): 669- 676
doi: 10.1061/(ASCE)GT.1943-5606.0000265
[2]
张玲, 赵明华, 赵衡 双层地基水平受荷桩受力变形分析[J]. 岩土力学, 2011, 32 (Suppl.2): 302- 305 ZHANG Ling, ZHAO Ming-hua, ZHAO Heng Analysis of the deformation of the horizontally loaded piles on the double-layered foundation[J]. Rock and Soil Mechanics, 2011, 32 (Suppl.2): 302- 305
[3]
ZHANG L, ZHAO M, ZOU X Behavior of laterally loaded piles in multilayered soils[J]. International Journal of Geomechanics, 2015, 15 (2): 06014017
doi: 10.1061/(ASCE)GM.1943-5622.0000319
[4]
GABR M A, LUNNE T, POWELL J J Analysis of laterally loaded piles in clay using DMT[J]. Journal of Geotechnical Engineering, 1994, 120 (5): 816- 837
[5]
SHATNAWI E, LIANG R Y, NUSAIRAT J Hyperbolic P-Y criterion for cohesive soils[J]. Jordan Journal of Civil Engineering, 2007, 1 (1): 38
[6]
王国粹, 杨敏 砂土中水平受荷桩非线性分析[J]. 岩土力学, 2011, (Suppl.2): 261- 267 WANG Guo-cui, YANG Min Sandy soil nonlinear analysis of horizontally loaded piles[J]. Rock and Soil Mechanics, 2011, (Suppl.2): 261- 267
[7]
SUITS L D, SHEAHAN T C, YANG K, et al Methods for deriving p-y curves from instrumented lateral load tests[J]. Geotechnical Testing Journal, 2013, 30 (1): 31- 38
[8]
YIN P, HE W, YANG Z J A simplified nonlinear method for a laterally loaded pile in sloping ground[J]. Advances in Civil Engineering, 2018, (5): 1- 9
[9]
尹平保, 聂道流, 杨朝晖, 等 斜坡基桩p-y曲线及水平承载计算方法研究[J]. 岩石力学与工程学报, 2018, 37 (4): 996- 1003 YIN Ping-bao, NIE Dao-liu, YANG Chao-hui, et al Study on calculation method of p-y curve and horizontal load of slope foundation piles[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37 (4): 996- 1003
[10]
POULOS H G, DAVIS E H. Pile foundation analysis and design [M]. [S.l.]: Wiley, 1980: 472-473.
[11]
REESE L C Laterally loaded piles: program documentation[J]. Journal of Geotechnical and Geoenvironmental Engineering, 1977, 103 (12): 287- 305
[12]
MATLOCK H, REESE L C Generalized solutions for laterally loaded piles[J]. Geotechnical Special Publication, 1960, 127 (118): 1220- 1248
[13]
TEHRANI F S, SALGADO R, PREZZI M. A semi-analytical solution for laterally loaded pile groups in multilayered soils [C]//European Conference on Soil Mechanics and Geotechnical Engineering. Edinburgh: [s.n.], 2015.
[14]
ZHAO Heng, YIN Ping-bao, LI Xi-bing Mechanical response of bridge piles in high-steep slopes and sensitivity study[J]. Journal of Central South University: English Edition, 2015, 22 (10): 4043- 4048
doi: 10.1007/s11771-015-2948-1
[15]
赵明华, 杨超炜, 杨明辉, 等 基于有限杆单元法的陡坡段桥梁基桩受力分析[J]. 中国公路学报, 2014, 27 (6): 51- 58 ZHAO Ming-hua, YANG Chao-wei, YANG Ming-hui, et al Mechanical analysis of piles on steep slopes based on finite element method[J]. China Journal of Highway and Transport, 2014, 27 (6): 51- 58
doi: 10.3969/j.issn.1001-7372.2014.06.007
[16]
赵明华, 刘涛, 杨超炜, 等 考虑陡坡效应的横向受荷桩受力分析纽玛克解答[J]. 公路交通科技, 2014, 31 (10): 58- 64 ZHAO Ming-hua, LIU Tao, YANG Chao-wei, et al Stress analysis of laterally loaded piles taking into account the effect of steep slopes Newmark's solution[J]. Journal of Highway and Transportation Research and Development, 2014, 31 (10): 58- 64
doi: 10.3969/j.issn.1002-0268.2014.10.010
[17]
MCCLELLAND B Soil modulus for laterally loaded piles[J]. Soil Mechanics and Foundation Division, 1956, 82: 1- 22
[18]
RANDOLPH M F The response of flexible piles to lateral loading[J]. Geotechnique, 1981, 31 (2): 247- 259
doi: 10.1680/geot.1981.31.2.247
