1. Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China 2. Key Laboratory of Soft Soils and Geoenvironmental Engineering of Ministry of Education, Zhejiang University, Hangzhou 310058, China
The accumulated responses of single batter pile under cyclic loadings (e.g., winds, waves and ocean current) were analyzed. The degradation stiffness model of sand was incorporated into the pile-soil finite element model through the user subroutine. The numerical analysis of cyclic loading characteristics of single pile was realized. Then the accumulated response of single batter pile under various load levels and cycle numbers was analyzed. Results show that the displacement at pile head and the bending moment of pile are gradually increased under lateral static loads when the batter angle changes from ?25° to 25°. The accumulated speeds of the displacement at pile head and the maximum bending moment of pile are decreased under lateral cyclic loads. When the amplitude of the cyclic load is relatively large, the displacement at pile head and the depth of deformation region of the negative batter pile are both smaller than these of the vertical pile, while these of the positive batter pile are the greatest. Fitting analysis of the accumulated displacement at pile head and the maximum bending moment of single batter pile was conducted based on the numerical simulation results. The corresponding methods for predicting the accumulated responses of single batter piles were proposed.
Shuang ZHAO,Kui-hua WANG,Jun-tao WU. Accumulated response of single batter pile under lateral cyclic loading in sand. Journal of ZheJiang University (Engineering Science), 2022, 56(7): 1310-1319.
Fig.1Stress-strain relationship of sand under cyclic loads
Fig.2Flow chart of numerical analysis of cyclic loading characteristics of single pile
土的刚度系数
υs
φ / (°)
ψ / (°)
c / kPa
b1
b2
λ
κ
600
0.6
0.25
35.0
5.0
0.1
0.16
0.38
Tab.1Computational parameters of sand
Fig.3Schematic of numerical model for analyzing cyclic loading characteristics of single piles
土的刚度系数
υs
φ / (°)
ψ / (°)
c / kPa
b1
b2
λ
κ
560
0.6
0.25
34.8
2.9
0.1
0.17
0.43
Tab.2Computational parameters of sand in validation model
Fig.4Comparison of numerical model results and centrifuge model test results
Fig.5Schematic of positive batter pile and negative batter pile
Fig.6Lateral load-displacement curves of single batter piles
Fig.7Fitting analysis of lateral ultimate bearing capacity of single batter piles
Fig.8Accumulated displacement at pile head of single piles under various load levels
Fig.9Fitting analysis results of y1
Fig.10Fitting analysis results of δs
Fig.11Fitting analysis results of ${y_N}$
Fig.12Fitting analysis results of β
Fig.13Distribution of lateral displacement of pile with depth under cyclic loading
Fig.14Accumulation of bending moment of pile with cycle numbers under cyclic loading
Fig.15Fitting analysis results of MmaxN
Fig.16Fitting analysis results of m
[1]
POULOS H G Raked piles: virtues and drawbacks[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2006, 132 (6): 795- 803
doi: 10.1061/(ASCE)1090-0241(2006)132:6(795)
[2]
GEROLYMOS N, GIANNAKOU A, ANASTASOPOULOS L, et al Evidence of beneficial role of inclined piles: observations and summary of numerical analyses[J]. Bulletin of Earthquake Engineering, 2008, 6 (4): 705- 722
doi: 10.1007/s10518-008-9085-2
[3]
ZHANG L, MCVAY M C, LAI P W Centrifuge modelling of laterally loaded single battered piles in sands[J]. Canadian Geotechnical Journal, 1999, 36 (6): 1074- 1084
doi: 10.1139/t99-072
[4]
RAJASHREE S S, SITHARAM T G Nonlinear finite-element modeling of batter piles under lateral load[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2001, 127 (7): 604- 612
doi: 10.1061/(ASCE)1090-0241(2001)127:7(604)
[5]
MANOPPO F J Behaviour of the ultimate bearing capacity of single flexible batter pile under horizontal loads in homogeneous sand[J]. Dinamika Teknik Sipil, 2010, 10 (2): 116- 119
[6]
BAJAJ P, YADU L, CHOUKSEY S K Study on vertical and batter piles subjected to lateral loads in different non-cohesive sub-soil conditions[J]. International Journal of Geotechnical Engineering, 2019, 14 (6): 601- 613
[7]
曹卫平, 樊文甫 水平荷载作用下斜桩承载变形性状数值分析[J]. 中国公路学报, 2017, 30 (9): 34- 42 CAO Wei-ping, FAN Wen-fu Numerical analysis on bearing and deformation behavior of horizontally loaded batter piles[J]. China Journal of Highway and Transport, 2017, 30 (9): 34- 42
doi: 10.3969/j.issn.1001-7372.2017.09.005
[8]
吕凡任. 倾斜荷载作用下斜桩基础工作性状研究[D]. 杭州: 浙江大学, 2004. LV Fan-ren. Study on behavior of batter piles under inclined load [D]. Hangzhou: Zhejiang University, 2004.
[9]
云天铨 线载荷积分方程法分析桩顶受任意荷载的弹性斜桩[J]. 应用数学和力学, 1999, 20 (4): 351- 357 YUN Tian-quan Analysis of sloping elastic pile under arbitrary loads by line-loaded integral equation method[J]. Applied Mathematics and Mechanics, 1999, 20 (4): 351- 357
doi: 10.3321/j.issn:1000-0887.1999.04.004
[10]
ASHOUR M, ALAAELDIN A, ARAB M G Laterally loaded battered piles in sandy soils[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2020, 146 (1): 06019017
doi: 10.1061/(ASCE)GT.1943-5606.0002186
[11]
凌道盛, 任涛, 王云岗 砂土地基斜桩水平承载特性p-y曲线法[J]. 岩土力学, 2013, 34 (1): 155- 162 LING Dao-sheng, REN Tao, WANG Yun-gang A p-y curves method for horizontal bearing characteristics of single batter pile in sands[J]. Rock and Soil Mechanics, 2013, 34 (1): 155- 162
[12]
曹卫平, 夏冰, 赵敏, 等 砂土中水平受荷斜桩的p-y曲线及其应用[J]. 岩石力学与工程学报, 2018, 37 (3): 743- 753 CAO Wei-ping, XIA Bing, ZHAO min, et al p-y curves of laterally loaded batter piles in sand and its application[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37 (3): 743- 753
[13]
曹卫平, 陶鹏, 赵敏, 等 砂土中循环荷载与单调荷载组合作用下斜桩水平承载变形特性[J]. 长安大学学报:自然科学版, 2020, 40 (3): 11- 21 CAO Wei-ping, TAO Peng, ZHAO Min, et al Model test on bearing deformation behavior of batter piles under combined horizontal loads and monotonic loads in sand[J]. Journal of Chang’an University: Natural Science Edition, 2020, 40 (3): 11- 21
[14]
LONG J, VANNESTE G Effects of cyclic lateral loads on piles in sand[J]. Journal of Geotechnical Engineering, 1994, 120 (1): 225- 244
doi: 10.1061/(ASCE)0733-9410(1994)120:1(225)
[15]
LIN S S, LIAO J C Permanent strains of piles in sand due to cyclic lateral loads[J]. Journal of Geotechnical and Geoenvironmental Engineering, 1999, 125 (9): 798- 802
doi: 10.1061/(ASCE)1090-0241(1999)125:9(798)
[16]
ROSQUOET F, THOREL L, GAENIER J, et al Lateral cyclic loading of sand-installed piles[J]. Soils and Foundations, 2007, 47 (5): 821- 832
doi: 10.3208/sandf.47.821
[17]
ZHANG C R, WHITE D, RANDOLPH M Centrifuge modeling of the cyclic lateral response of a rigid pile in soft clay[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2011, 137: 717- 729
doi: 10.1061/(ASCE)GT.1943-5606.0000482
[18]
朱斌, 熊根, 刘晋超, 等 砂土中大直径单桩水平受荷离心模型试验[J]. 岩土工程学报, 2013, 35 (10): 1807- 1815 ZHU Bin, XIONG Gen, LIU Jin-chao, et al Centrifuge modelling of a large-diameter single pile under lateral loads in sand[J]. Chinese Journal of Geotechnical Engineering, 2013, 35 (10): 1807- 1815
[19]
LEBLANC C, HOULSBY G T, BYRNE B W Response of stiff piles in sand to long-term cyclic lateral loading[J]. Géotechnique, 2010, 60 (2): 79- 90
[20]
张勋, 黄茂松, 胡志平 砂土中单桩水平循环累积变形特性模型试验[J]. 岩土力学, 2019, 40 (3): 933- 941 ZHANG Xun, HUANG Mao-song, HU Zhi-ping Model tests on cumulative deformation characteristics of a single pile subjected to lateral cyclic loading in sand[J]. Rock and Soil Mechanics, 2019, 40 (3): 933- 941
[21]
GIANNAKOS S, GEROLYMOS N, GAZETAS G Cyclic lateral response of piles in dry sand: finite element modeling and validation[J]. Computers and Geotechnics, 2012, 44: 116- 131
doi: 10.1016/j.compgeo.2012.03.013
[22]
ACHMUS M, KUO Y S, ABDEL-RAHMAN K Behavior of monopile foundations under cyclic lateral load[J]. Computer and Geotechnics, 2009, 36: 725- 735
doi: 10.1016/j.compgeo.2008.12.003
[23]
张陈蓉, 朱治齐, 于锋, 等 砂土中大直径单桩的长期水平循环加载累积变形[J]. 岩土工程学报, 2020, 42 (6): 1076- 1084 ZHANG Chen-rong, ZHU Zhi-qi, YU Feng, et al Accumulative displacement of long-term cyclic laterally loaded monopiles with large diameter sand[J]. Chinese Journal of Geotechnical Engineering, 2020, 42 (6): 1076- 1084
[24]
HUURMAN M Development of traffic induced permanent strains in concrete block pavements[J]. Heron, 1996, 41 (1): 29- 52
[25]
郭玉樹, 亚克慕斯·马丁, 阿布达雷赫曼·哈里 用循环三轴试验分析海上风力发电机单桩基础侧向位移[J]. 岩土工程学报, 2009, 31 (11): 1729- 1734 KUO Yu-shu, ACHMUS Martin, ABDEL-RAHMAN Khalid Estimation of lateral deformation of monopile foundations by use of cyclic triaxial tests[J]. Chinese Journal of Geotechnical Engineering, 2009, 31 (11): 1729- 1734
doi: 10.3321/j.issn:1000-4548.2009.11.014
[26]
ABDEL-RAHMEN K, ACHMUS M. Finite element modelling of horizontally loaded monopile foundations for offshore wind energy converters in Germany [C]// Proceedings of the International Symposium on Frontiers in Offshore Geotechnics. Perth: [s. n.], 2005: 309-396.
[27]
KUO Y S. On the behavior of large diameter piles under cyclic lateral load [D]. Hannover: Leibniz University of Hannover, 2008.
[28]
刘晋超, 熊根, 朱斌, 等 砂土海床中大直径单桩水平承载与变形特性[J]. 岩土力学, 2015, 36 (2): 591- 599 LIU Jin-chao, XIONG Gen, ZHU Bin, et al Bearing capacity and deflection behaviors of large diameter monopile foundations in sand seabed[J]. Rock and Soil Mechanics, 2015, 36 (2): 591- 599
[29]
ZHU B, LI T, XIONG G, et al Centrifuge model tests on laterally loaded piles in sand[J]. International Journal of Physical Modelling in Geotechnics, 2016, 16 (4): 160- 172
doi: 10.1680/jphmg.15.00023
[30]
王磊, 朱斌, 来向华 砂土循环累积变形规律与显式计算模型研究[J]. 岩土工程学报, 2015, 37 (11): 2024- 2029 WANG Lei, ZHU Bin, LAI Xiang-hua Cyclic accumulative deformation of sand and its explicit model[J]. Chinese Journal of Geotechnical Engineering, 2015, 37 (11): 2024- 2029
doi: 10.11779/CJGE201511012
[31]
ZDRAVKOVIĆ L, TABORDA D M G, POTTS D M, et al. Numerical modelling of large diameter piles under lateral loading for offshore wind applications [C]// Proceeding of 3rd International Symposium on Frontiers in Offshore Geotechnics. Oslo: CRC Press, 2015: 759-764.
[32]
KYUNG D, LEE J Interpretative Analysis of lateral load-carrying behavior and design model for inclined single and group micropiles[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2018, 144 (1): 04017105
doi: 10.1061/(ASCE)GT.1943-5606.0001810
[33]
LITTLE R L, BRIAUD J L. Full scale cyclic lateral load tests on six single piles in sand: TAMU-RR-5640 [R]. Texas: College Station, 1988.
[34]
LI W, IGOE D, GAVIN K Field tests to investigate the cyclic response of monopiles in sand[J]. Proceedings of the Institution of Civil Engineers-Geotechnical Engineering, 2015, 168 (5): 407- 421
doi: 10.1680/jgeen.14.00104
[35]
张勋, 黄茂松 水平循环荷载下砂土中沉井加桩基础累积变形特性[J]. 岩石力学与工程学报, 2016, 35 (6): 1256- 1272 ZHANG Xun, HUANG Mao-song Cumulative deformation of a caisson-piles composite foundation in sand subjected to cyclic lateral loading[J]. Chinese Journal of Rock Mechanics and Engineering, 2016, 35 (6): 1256- 1272
