Journal of Shandong University(Engineering Science) ›› 2021, Vol. 51 ›› Issue (5): 8-15.doi: 10.6040/j.issn.1672-3961.0.2021.161

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Modified calculation method of shaft friction for driven pile considering particle size effect

Peizhi ZHUANG1(),Yingchao ZHANG1,Xiuguang SONG1,He YANG1,*(),Zhicheng GUO1,2,Yan HU3   

  1. 1. School of Qilu Transportation, Shandong University, Jinan 250002, Shandong, China
    2. Lunan High Speed Railway Co., Ltd., Jinan 250102, Shandong, China
    3. Shandong High-Speed Jinan Development Co., Ltd., Jinan 250100, Shandong, China
  • Received:2021-04-09 Online:2021-10-20 Published:2021-09-29
  • Contact: He YANG;


This study aimed to investigate the influence of particle size on the micropile by conducting theoretical analysis and model tests. The empirical relationship between the critical friction angle and the relative roughness at the pile-soil interface was established, and thus the critical friction angle could be determined quantitively in consideration of the particle size of sands. To emphasis the influence of particle size on the additional normal stress at the soil-pile interface, the shear band at the soil-pile interface was modelled as a hollow cylinder and then a new modified method was proposed based on the elastic cavity expansion theory. Only two new parameters, Poisson's ratio and the thickness of the shear band, were involved in the modified method, which was validated by comparison with model tests. It was found that the pile shaft friction was mainly determined by the pile roughness and the ratio of pile diameter to sand median size and the critical state angle at the pile-soil interface, while the additional normal stress mainly results from the pile roughness and the ratio of pile diameter to sand median size, respectively. The research could provide the valueable reference for the bearing capacity design of micropiles.

Key words: micropile, shaft friction, particle size effect, sand, cavity expansion theory

CLC Number: 

  • TU473


Relationship between the interface critical state angle and relative surface roughness"


Analytical model of pile-soil interface shear theory"


Relationship between additional normal stress and the relative pile diameter"


Predicted scale effect of Δσrd with comparison to experimental results"


The calibration chamber and cone penetrator in the model tests"

Table 1

Properties of Leighton Buzzard Sand"

类型 中值粒径d50/mm 密度Gs/(103kg·m-3) 最大孔隙比emax 最小孔隙比emin 极限摩擦角φcs/(°)
FC砂 0.51 2.65 0.805 0.550 32
FE砂 0.12 2.65 1.014 0.613 32


Comparison of uplift shaft capacity between theoretical and experimental results"


Comparison of penetrations shaft capacity between theoretical and experimental results"

1 刘修成, 徐杰, 游新鹏, 等. 珊瑚礁地质大直径钢管打入桩承载特性研究[J]. 海洋工程, 2019, 37 (6): 157- 163.
LIU Xiucheng , XU Jie , YOU Xinpeng , et al. Study on bearing behavior of large diameter driven steel pipe pile in coral reef geology[J]. The Ocean Engineering, 2019, 37 (6): 157- 163.
2 龚晓怡, 邓振洲, 李存兴, 等. 基于标准贯入度试验的桩基轴向承载力估算[J]. 水运工程, 2020, (10): 165- 171.
doi: 10.3969/j.issn.1002-4972.2020.10.030
GONG Xiaoyi , DENG Zhenzhou , LI Cunxing , et al. Estimation on axial bearing capacity of pile foundation based on standard penetration test[J]. Port & Waterway Engineering, 2020, (10): 165- 171.
doi: 10.3969/j.issn.1002-4972.2020.10.030
3 朱斌, 杨永垚, 余振刚, 等. 海洋高桩基础水平单调及循环加载现场试验[J]. 岩土工程学报, 2012, 34 (6): 1028- 1037.
ZHU Bin , YANG Yongyao , YU Zhengang , et al. Field tests on lateral monotonic and cyclic loadings of offshore elevated piles[J]. Chinese Journal of Geotechnical Engineering, 2012, 34 (6): 1028- 1037.
4 RANDOLPH M F , DOLWIN R , BECK R . Design of driven piles in sand[J]. Géotechnique, 1994, 44 (3): 427- 448.
doi: 10.1680/geot.1994.44.3.427
5 TOOLAN F, LINGS M, MIRZA U. An appraisal of API RP2A recommendations for determining skin friction of piles in sand[C]//Proceeding 22nd Offshore Technology Conference. Houston, America: Offshore Technology Conference, 1990: 33-42.
6 BUSTAMANTE M, GIANESELLI L. Pile bearing capacity prediction by means of static penetrometer CPT[C]//Proceedings of the 2nd European Symposium on Penetration Testing. Paris, France: CRC Press, 1982: 493-500.
7 DE KUITER J , BERINGEN F . Pile foundations for large North Sea structures[J]. Marine Georesources & Geotechnology, 1979, 3 (3): 267- 314.
8 KOLK H, BAAIJENS A, SENDERS M. Design criteria for pipe piles in silica sands[C]//Proceeding 1st International Symposium on Frontiers in Offshore Geotechnics. Balkema Perth, Australia: CRC Press, 2005: 711-716.
9 SCHMERTMANN J H. Guidelines for cone penetration test: performance and design[R]. Washington, USA: Federal Highway Administration, 1978.
10 蔡国军, 刘松玉. 基于CPTU测试的桩基承载力预测新方法[J]. 岩土工程学报, 2010, 32 (增刊2): 479- 482.
CAI Guojun , LIU Songyu . New method based on CPTU data to evaluate pile bearing capacity[J]. Chinese Journal of Geotechnical Engineering, 2010, 32 (Suppl.2): 479- 482.
11 严凯, 庞玉麟, 李卫超, 等. 基于CPT的锤击桩贯入分析理论模型[J]. 建筑科学, 2020, 36 (增刊1): 68- 76.
YAN Kai , PANG Yulin , LI Weichao , et al. CPT-based model for penetration simulation of hammer installed piles[J]. Building Science, 2020, 36 (Suppl.1): 68- 76.
12 JARDINE R , CHOW F , OVERY R , et al. ICP design methods for driven piles in sands and clays[M]. London, UK: Thomas Telford, 2005.
13 LEHANE B , SCHNEIDER J , XU X . The UWA-05 method for prediction of axial capacity of driven piles in sand[J]. Frontiers in Offshore Geotechnics, 2005, 221 (12): 683- 689.
14 史乃伟. 钙质砂界面摩擦特性研究[D]. 天津: 天津大学, 2018.
SHI Naiwei. Research on the properties of interface friction between calcareous sand and structure[D]. Tianjin: Tianjin University, 2018.
15 郭聚坤, 雷胜友, 魏道凯, 等. 粗糙度对结构物-细砂界面剪切特性的影响[J]. 水利水运工程学报, 2019, (3): 85- 94.
GUO Jukun , LEI Shengyou , WEI Daokai , et al. Effects of roughness on shear properties of structure-sands interface[J]. Hydro-Science and Engineering, 2019, (3): 85- 94.
16 郭聚坤, 雷胜友, 王瑞, 等. 结构物-标准砂界面剪切机理试验研究[J]. 地下空间与工程学报, 2020, 16 (3): 722- 733.
GUO Jukun , LEI Shengyou , WANG Rui , et al. Study on interface shear mechanism between structures and standard sand[J]. Chinese Journal of Underground Space and Engineering, 2020, 16 (3): 722- 733.
17 UESUGI M , KISHIDA H . Frictional resistance at yield between dry sand and mild steel[J]. Soils and Foundations, 1986, 26 (4): 139- 149.
doi: 10.3208/sandf1972.26.4_139
18 JARDINE RJ, LEHANE BM, EVERTON SJ. Friction coefficients for piles in sands and silts[C]//Offshore Site Investigation and Foundation Behaviour. Dordrecht, Netherlands: Springer, 1993: 661-677.
19 FROST J , DEJONG J , RECALDE M . Shear failure behavior of granular-continuum interfaces[J]. Engineering Fracture Mechanics, 2002, 69 (17): 2029- 2048.
doi: 10.1016/S0013-7944(02)00075-9
20 GARNIER J , GAUDIN C , SPRINGMAN SM , et al. Catalogue of scaling laws and similitude questions in geotechnical centrifuge modelling[J]. International Journal of Physical Modelling in Geotechnics, 2007, 7 (3): 1- 23.
doi: 10.1680/ijpmg.2007.070301
21 BOULON M, FORAY P. Physical and numerical simulation of lateral shaft friction along offshore piles in sand[C]//Proc. 3rd Int. Conf. on Numerical Methods in Offshore Piling. Nantes, France: Institut Francais du Petrol Nantes, 1986: 127-147.
22 LINGS M , DIETZ M . The peak strength of sand-steel interfaces and the role of dilation[J]. Soils and Foundations, 2005, 45 (6): 1- 14.
doi: 10.3208/sandf.45.1
23 PAIKOWSKY S G , PLAYER C M , CONNORS P J . A dual interface apparatus for testing unrestricted friction of soil along solid surfaces[J]. Geotechnical Testing Journal, 1995, 18 (2): 168- 193.
doi: 10.1520/GTJ10320J
24 DIETZ M S. Developing an holistic understanding of interface friction using sand with direct shear apparatus[D]. Bristol: University of Bristol, 2000.
25 TURNER J P , KULHAWY F H . Physical modeling of drilled shaft side resistance in sand[J]. Geotechnical Testing Journal, 1994, 17 (3): 282- 290.
doi: 10.1520/GTJ10103J
26 BALACHOWSKI L . Scale effect in shaft friction from the direct shear interface tests[J]. Archives of Civil and Mechanical Engineering, 2006, 6 (3): 13- 28.
doi: 10.1016/S1644-9665(12)60238-6
27 DEJONG J T , WESTGATE Z J . Role of initial state, material properties, and confinement condition on local and global soil-structure interface behavior[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2009, 135 (11): 1646- 1660.
doi: 10.1061/(ASCE)1090-0241(2009)135:11(1646)
28 FIORAVANTE V . On the shaft friction modelling of non-displacement piles in sand[J]. Soils and Foundations, 2002, 42 (2): 23- 33.
doi: 10.3208/sandf.42.2_23
29 HO T Y K , JARDINE RJ , ANH-MINH N . Large-displacement interface shearbetween steel and granular media[J]. Geotechnique, 2011, 61 (3): 221- 234.
doi: 10.1680/geot.8.P.086
30 LECHANE BM , GAUDIN C , SCHNEIDER JA . Scale effects on tension capacity forrough piles buried in dense sand[J]. Geotechnique, 2005, 55 (10): 709- 719.
doi: 10.1680/geot.2005.55.10.709
31 TEHRAANI FS , HAN F , SALGADO R , et al. Effect of surface roughness on the shaft resistance of non-displacement piles embedded in sand[J]. Geotechnique, 2016, 66 (5): 386- 400.
doi: 10.1680/jgeot.15.P.007
32 YANGZ , JARDINE RJ , ZHU B , et al. Sand grain crushing and interface shearing during displacement pile installation in sand[J]. Geotechnique, 2010, 60 (6): 469- 482.
doi: 10.1680/geot.2010.60.6.469
33 FORAY P, BALACHOWSKI L, RAULT G. Scale effect in shaft friction due to the localisation of deformations[C]//Proceedings of the International Conference Centrifuge. Tokyo, Japan: A.A. Balkema, 1998: 211-216.
34 GARNIER J, KONIG D. Scale effects in piles and nails loading tests in sand[C]//Proceedings of the Int-ernational Conference Centrifuge. Tokyo, Japan: A.A. Balkema, 1998: 205-210.
35 LAST N. Cone penetration tests on samples of dry Hokksund sand in a rigid walled chamber[R]. Norwegian Geotechnical Institute, 1979.
36 BOLTON M D , GUI M W , GARNIER J , et al. Centrifuge cone penetration tests in sand[J]. Géotechnique, 1999, 49 (4): 543- 552.
doi: 10.1680/geot.1999.49.4.543
37 SCHNEIDER J A. Analbnysis of piezocone data for displacement pile design[D]. Western Australia: University of Western Australia, 2007.
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