Journal of Shandong University(Engineering Science) ›› 2026, Vol. 56 ›› Issue (4): 145-152.doi: 10.6040/j.issn.1672-3961.0.2025.023

• Civil Engineering • Previous Articles    

Reliability analysis of vertically loaded compressive piles considering uncertainties in material and geometric parameters

Zhang Jun1, Lu Pengxu2, Wang Wei3, Liu Shanwei1*, Tan Xiaohui1   

  1. Zhang Jun1, Lu Pengxu2, Wang Wei3, Liu Shanwei1*, Tan Xiaohui1(1. School of Resources and Environmental Engineering, Hefei University of Technology, Hefei, 230009, Anhui, China;
    2. Power China Construction Group Ltd., Beijing 100120, China;
    3. Anhui Construction Engineering Testing and Research Institute Co., Ltd., Hefei 230051, Anhui, China
  • Published:2026-08-12

Abstract: This paper aims to establish a reliability analysis method for vertically loaded piles in unsaturated soils by considering the uncertainties in soil physic-mechanical parameters and pile-soil geometric parameters. The ultimate bearing capacity of pile foundations was calculated using theoretical formulas, where the β-method was used to determine pile side friction and Terzaghi's formula was employed to evaluate pile tip resistance. Based on the first-order reliability method, the effects of variability in soil layer thickness and pile geometric dimensions on the reliability indices of pile foundations were elucidated. The rationality and accuracy of the proposed calculation method were verified through specific case studies. Parameter analysis showed that the uncertainty in soil layer thickness had little influence on the reliability indices of pile foundations, whereas the uncertainty in pile geometric parameters had a significant impact. Under the same coefficient of variation of the pile geometric parameters, the reliability index of compression piles decreased with increasing groundwater level. However, the influence of groundwater level on the reliability index was less significant than that of the variability in the pile geometric parameters.

Key words: compressive pile, reliability index, ultimate bearing capacity, Monte Carlo Method, uncertainty

CLC Number: 

  • TU43
[1] 胡贺松, 唐孟雄, 刘春林, 等. 大直径随钻跟管桩竖向抗压承载性能试验研究[J]. 土木工程学报, 2022, 55(2): 92-99. Hu Hesong, Tang Mengxiong, Liu Chunlin, et al. Vertical bearing capacity characteristics of large-diameter DPC pipe piles based on field tests[J]. China Civil Engineering Journal, 2022, 55(2): 92-99.
[2] 庄培芝, 张营超, 宋修广, 等. 考虑尺寸效应的桩侧摩阻力修正计算方法[J]. 山东大学学报(工学版), 2021, 51(5): 8-15. Zhuang Peizhi, Zhang Yingchao, Song Xiuguang, et al. Modified calculation method of shaft friction for driven pile considering particle size effect[J]. Journal of Shandong University(Engineering Science), 2021, 51(5): 8-15.
[3] 李连祥, 邢宏侠, 李金良, 等. 喷扩锥台压灌桩最优构造[J]. 山东大学学报(工学版), 2020, 50(6): 82-91. Li Lianxiang, Xing Hongxia, Li Jinliang, et al. Optimal structure of pressure cast-situ-pile with spray-expanded frustum[J]. Journal of Shandong University(Engineering Science), 2020, 50(6): 82-91.
[4] 仉文岗, 王琦, 陈福勇, 等. 考虑岩体空间变异性的边坡可靠度分析及抗滑桩随机响应研究[J]. 岩土力学, 2021, 42(11): 3157-3168. Zhang Wengang, Wang Qi, Chen Fuyong, et al. Reliability analysis of slope and random response of anti-sliding pile considering spatial variability of rock mass properties[J]. Rock and Soil Mechanics, 2021, 42(11): 3157-3168.
[5] 黄广龙, 卫敏, 李娟. 参数变异性对围护结构稳定性影响分析[J]. 岩土力学, 2010, 31(8): 2484-2488. Huang Guanglong, Wei Min, Li Juan. Analysis of influence of parameters variability on retaining structure stability[J]. Rock and Soil Mechanics, 2010, 31(8): 2484-2488.
[6] 杨剑, 黎冰, 鲍安琪, 等. 土体强度的空间分布形式对单桩承载力的影响[J]. 水利水运工程学报, 2022(1): 97-103. Yang Jian, Li Bing, Bao Anqi, et al. Influence of the spatial distribution of soil strength on the bearing capacity of single pile[J]. Hydro-Science and Engineering, 2022(1): 97-103.
[7] 王利群, 赵文, 李艺. 人工挖孔桩桩端阻力经验公式的变异性分析[J]. 东北大学学报(自然科学版), 2010, 31(4): 593-596. Wang Liqun, Zhao Wen, Li Yi. Variability analysis of empirical formula of resistance to pile end on a manually dug hole bottom[J]. Journal of Northeastern University(Natural Science), 2010, 31(4): 593-596.
[8] 谭晓慧, 姚玉川, 林鑫,等. 基于KL展开法的基桩竖向极限承载力可靠度[J]. 地下空间与工程学报, 2023, 19(4): 1250-1258. Tan Xiaohui, Yao Yuchuan, Lin Xin, et al. Reliability of vertical ultimate bearing capacity of foundation pile based on KL expansion[J]. Chinese Journal of Underground Space and Engineering, 2023, 19(4): 1250-1258.
[9] Dong X L,Tan X H,Lin X,et al. Reliability analysis and design of vertically loaded piles in spatially variable soils[J]. International Journal of Geomechanics, 2023, 23(10): 04023175.
[10] 张鹏飞. 基于随机场理论的竖向受荷桩可靠度分析[D]. 合肥: 合肥工业大学, 2024: 15-33. Zhang Pengfei. Reliability analysis of vertically loaded piles based on random field theory[D]. Hefei: Hefei University of Technology, 2024: 15-33.
[11] Skempton A W. Cast in-situ bored piles in London clay[J]. Géotechnique, 1959, 9(4): 153-173.
[12] Burland J B. Shaft friction of piles in clay: a simple fundamental approach[J]. Ground Engineering, 1973, 6(3): 30-42.
[13] Focht J A, Vijayvergiya V N. A new way to predict capacity of piles in clay[C] //Fourth Annual Offshore Technology Conference. Houston, USA: [s.n.] , 1972: 865-871.
[14] Vanapalli S K, Taylan Z N. Design of single piles using the mechanics of unsaturated soils[J]. International Journal of Geomate, 2012, 2(1): 197-204.
[15] Vanapalli S K, Mohamed F M O. Bearing capacity of model footings in unsaturated soils[J]. Experimental Unsaturated Soil Mechanics, 2007, 112: 483-493.
[16] API RP 2A-WSD—2014 Recommended practice for planning, designing and constructing fixed offshore platforms-working stress design[S].
[17] Al-Omari R R, Fattah M Y, Kallawi A M. Bearing capacity of piles in unsaturated soil from theoretical and experimental approaches[J]. IOP Conference Series: Materials Science and Engineering, 2020, 737(1): 012101.
[18] Vanapalli S K, Fredlund D G, Pufahl D E, et al. Model for the prediction of shear strength with respect to soil suction[J]. Canadian Geotechnical Journal, 1996, 33(3): 379-392.
[19] Vanapalli S K, Sheikhtaheri M, Oh W T. Experimental and simple semiempirical methods for interpreting the axial load versus settlement behaviors of single model piles in unsaturated sands[J]. Geotechnical Testing Journal, 2018, 41(4): 698-716.
[20] Terzaghi K. Theoretical soil mechanics[M]. Hoboken: Wiley, 1943: 118-143.
[21] 贡金鑫. 工程结构可靠度计算方法[M]. 大连: 大连理工大学出版社, 2003: 55-56, 155-160.
[22] 杨伟军, 赵传智. 土木工程结构可靠度理论与设计[M]. 北京: 人民交通出版社, 1999: 64-68.
[23] 李继华, 林忠明, 李明顺, 等. 建筑结构概率极限状态设计[M]. 北京: 中国建筑工业出版社, 1990: 151-166.
[24] 谭晓慧, 王建国, 刘新荣, 等. 边坡稳定的有限元可靠度计算及敏感性分析[J]. 岩石力学与工程学报, 2007, 1: 115-122. Tan Xiaohui, Wang Jianguo, Llu Xinrong, et al. Finite element reliability computation and sensitivity analysis of slope stability[J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 1: 115-122.
[25] 谭晓慧, 辛志宇, 沈梦芬, 等. 湿胀条件下合肥膨胀土土-水特征研究[J]. 岩土力学, 2014, 35(12): 3352-3360. Tan Xiaohui, Xin Zhiyu, Shen Mengfen, et al. Study of soil-water characteristics of Hefei expansive soil under moisture-expansion condition[J]. Rock and Soil Mechanics, 2014, 35(12): 3352-3360.
[26] 陈明强. 基于土体参数空间变异性的高桩码头可靠性分析[D]. 大连: 大连海事大学, 2024: 21-35. Chen Mingqiang. Reliability analysis of piled wharf based on the spatial variability of soil parameters[D]. Dalian: Dalian Maritime University, 2024: 21-35.
[27] 陈朔. 变异地层微型桩基础承载机理及试验研究[D]. 合肥: 合肥工业大学, 2023: 38-70. Chen Shuo. Bearing mechanism and experimental study of micropile foundation in composite stratum[D]. Hefei: Hefei University of Technology, 2023: 38-70.
[1] ZHANG Liang, NIU Kai, XU Weihao, ZHAI Mengqi, JIN Qingtong, LIU Juncai, TIAN Li. Study on load carrying performance enhancement and optimization of reinforcing members for power transmission towers in service [J]. Journal of Shandong University(Engineering Science), 2026, 56(1): 122-132.
[2] XU Run, LIU Zhikun, SUN Jianxiu, YU Yang, ZHANG Changyong, LIU Yazhen, YUE Hongya, ZHANG Hongbo. Bearing characteristics of dispersed piles with radial constraints from waste tire grids [J]. Journal of Shandong University(Engineering Science), 2025, 55(6): 142-150.
[3] XU Zhen, ZHANG Tao, GE Xiangdong, GAO Feng, ZHANG Laiyi, ZHANG Xin, TIAN Li. Uncertainty analysis of transmission tower-line system under wind load [J]. Journal of Shandong University(Engineering Science), 2021, 51(4): 99-105.
[4] SUN Donglei, ZHAO Long, QIN Jingtao, HAN Xueshan, YANG Ming, WANG Mingqiang. Bi-level planning of transmission network with solar-storage combination system based on learning theory [J]. Journal of Shandong University(Engineering Science), 2020, 50(4): 90-97.
[5] CHU Xiaodong, TANG Maosen, GAO Xu, LIU Weisheng, JIA Shanjie, LI Sun. Robust optimal dispatch of active distribution networks based on centralized information system [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(6): 20-25.
[6] SUN Yuancheng, YAO Lina. Fault diagnosis and fault tolerant control for non-Gaussian uncertain singular stochastic distribution control systems [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(5): 238-245.
[7] GAO Di, WEI Shou-shui*, REN Xiao-nan, CUI Jian-qiang, XU Cong-juan. Simulation for the light distribution in bio-tissues by the Monte Carlo method [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2010, 40(4): 47-52.
[8] WANG Li-jun, GUAN Xiao-jun*, YU Bao-jun, ZHAO Jian. Research progress on mesoscale-structural simulation models of dynamic recrystallization of deformed metal during hot working [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2010, 40(3): 80-85.
[9] DIAO Wen-Zhong, SHI Jun. Study of power system probability security assessment incomplex power injection space [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2009, 39(6): 135-138.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!