静力触探修正<i>p-y</i>曲线预测螺旋钢桩横向荷载-位移行为

邵康; 廖汶俊; 赵科威; 邵国霞; 张军伟; 杨水生

doi:10.3969/j.issn.0258-2724.20250400

静力触探修正p-y曲线预测螺旋钢桩横向荷载-位移行为

doi: 10.3969/j.issn.0258-2724.20250400

1.
西南石油大学地球科学与技术学院，四川成都 610500
2.
西南交通大学土木工程学院，四川成都 610031
3.
江西省公路科研设计院有限公司，江西南昌 330002

基金项目: 国家自然科学基金项目（52376210）；江西省交通运输厅青年科技项目（2024QN004）

详细信息

作者简介:
邵康（1991—），男，讲师，研究方向为桩-土相互作用，E-mail：shaokang@swpu.edu.cn

通讯作者:
邵国霞（1975—），女，副教授，博士，研究方向为特殊地基处理技术，E-mail：shaoguoxia@126.com

中图分类号: TU473.1
计量
- 文章访问数: 18
- HTML全文浏览量: 12
- PDF下载量: 1
- 被引次数: 0
出版历程
- 收稿日期: 2025-07-31
- 录用日期: 2026-04-07
- 修回日期: 2025-12-04
- 网络出版日期: 2026-06-30

Modified p–y Curve by Cone Penetration Test for Predicting Lateral Load–Displacement Behavior of Helical Steel Piles

1.
School of Geoscience and Technology, Southwest Petroleum University, Chengdu 610500, China
2.
School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China
3.
Jiangxi Highway Research and Design Institute Co., Ltd., Nanchang 330002, China

摘要

摘要:
为研究螺旋钢桩在砂土中的横向承载-位移行为，考虑桩土间的非线性相互作用，选取3种p-y曲线（p为单位长度土反力，y为桩身横向位移）进行横向承载行为预测比较. 首先，分析现有经典砂土p-y曲线和2种基于CPT参数的p-y曲线（幂函数和双曲线）特点，尤其分析3种方法的不足；其次，通过在螺旋板影响区引入线性变化的修正因子对3种p-y曲线进行修正，以考虑螺旋板的横向承载作用；再次，采用有限差分法求解螺旋钢桩横向受荷弯曲微分方程，通过迭代求解桩身位移；最后，根据文献中进行的螺旋钢桩横向承载现场试验，将3种修正后的p-y曲线预测结果与现场实测值进行误差与统计分析. 结果表明：双曲线修正后p-y曲线预测的荷载-位移结果与实测更为接近，预测结果与实测结果的平均比值为1.04，拟合度达到98.5%；双曲线方法的平均绝对百分比误差为11.63%，而幂函数方法和经典p-y曲线方法的平均绝对百分比误差分别为36.32%和24.35%，双曲线的95%置信区间表明的平均预测误差在−6%～11.9%，而在90%置信区间的平均误差则在−4.6%～10.5%，证明了该方法的可靠性. 研究结果可为螺旋钢桩横向荷载-位移行为准确预测提供参考.
- 桩基础 /
- 螺旋钢桩 /
- p-y曲线 /
- 静力触探 /
- 砂土 /
- 横向承载
Abstract:
In order to investigate the lateral load–displacement behavior of helical steel piles in sand, by considering the nonlinear pile-soil interaction, three p-y curves (p denoted soil reaction per unit length, and y denoted lateral displacement of the pile shaft) were selected to predict and compare lateral bearing behaviors. First, the existing classical sand p-y curve and two CPT-based p-y curves (power function and hyperbola) were analyzed, and their shortcomings were identified. Second, a linearly varying correction factor was introduced within the helical plate influence zone to modify three p-y curves, thereby incorporating the lateral bearing action of the helical plates. Third, the finite-difference method was employed to solve the bending differential equation of the laterally loaded helical steel pile, with pile shaft displacements obtained through iterative solution. Finally, by using the field tests of lateral bearing capacity for helical steel piles conducted in the literature, the prediction results of the three modified p-y curves were subjected to error and statistical analysis against the actual field measurements. The results show that the hyperbola-modified p-y curve produces load–displacement predictions closest to the measurements, with an average predicted-to-measured ratio of 1.04 and a goodness of fit of 98.5%. Among the three methods, the hyperbola approach yields the mean absolute percentage error of 11.63%, compared to 36.32% for the power function method and 24.25% for the classical p-y curve method. Its 95% confidence interval for mean prediction error spans from −6.0% to 11.9%, and the average error of 90% confidence interval spans from −4.6% to 10.5%, which verifies the reliability of the method. These findings provide a robust reference for accurately predicting the lateral load–displacement behavior of helical steel piles.
- pile foundation /
- helical steel pile /
- p-y curve /
- cone penetration test /
- sand /
- lateral bearing

HTML全文

图 1 C₁、C₂、C₃的取值范围^[20]

Figure 1. Value ranges of C₁, C₂, and C₃^[20]

下载: 全尺寸图片幻灯片

图 2 螺旋钢桩结构

Figure 2. Structure of helical steel pile

下载: 全尺寸图片幻灯片

图 3 螺旋板影响区及修正因子分布

Figure 3. Distribution of influence zone of helical plate and correction factors

下载: 全尺寸图片幻灯片

图 4 横向受荷桩的有限差分与受力状态示意

Figure 4. Finite difference and force state of laterally loaded pile

下载: 全尺寸图片幻灯片

图 5 边界条件节点设置示意

Figure 5. Node configuration for boundary conditions

下载: 全尺寸图片幻灯片

图 6 横向位移迭代求解流程

Figure 6. Flow of iterative solution for lateral displacement

下载: 全尺寸图片幻灯片

图 7 误差-迭代次数曲线

Figure 7. Error–iteration count curves

下载: 全尺寸图片幻灯片

图 8 原位测试平面布置图（据Kim等^[32]修改）（单位：m）

Figure 8. In-situ testing layout plan^[32] (modified from Kim et al^[32])(unit: m)

下载: 全尺寸图片幻灯片

图 9 试验场地土层类型与CPT测试（据Kim等^[32]修改）

Figure 9. Soil layer types at test site and CPT (modified from Kim et al^[32])

下载: 全尺寸图片幻灯片

图 10 钻孔取样获得的参数（据Kim等^[32]修改）

Figure 10. Parameters of samples obtained from drilling (modified from Kim et al^[32])

下载: 全尺寸图片幻灯片

图 11 试桩布置参数示意（据Kim等^[32]修改）

Figure 11. Parameter for test pile layout (modified from Kim et al^[32])

下载: 全尺寸图片幻灯片

图 12 位于地面以下1.4 m处的p-y曲线

Figure 12. p−y curves at a depth of 1.4 m below ground surface

下载: 全尺寸图片幻灯片

图 13 3种方法与现场实测的荷载-位移曲线对比流程

Figure 13. Comparison flow of load–displacement curves between three methods and field measured data

下载: 全尺寸图片幻灯片

图 14 7号试验桩荷载-位移示例

Figure 14. Load–displacement plot for test pile No.7

下载: 全尺寸图片幻灯片

图 15 3种方法的预测结果与实测结果比较

Figure 15. Comparison between prediction results of three methods and measured results

下载: 全尺寸图片幻灯片

图 16 不同位移比下3种方法预测结果的算术平均值与置信区间的对比

Figure 16. Comparison of arithmetic means and confidence intervals of prediction results from three methods at different displacement ratios

下载: 全尺寸图片幻灯片

表 1 原位测试选取的试桩结构参数（据Kim等^[32]修改）

Table 1. Structural parameters of test piles selected for in-situ testing (modified from Kim et al^[32])

编号	中心桩轴参数			螺旋板参数
编号	D_p/ mm	t/mm	L/mm	1号螺旋板直径（D_h1）/mm	2号螺旋板直径（D_h2）/mm	3号螺旋板直径（D_h3）/mm	t_h/ mm
1	89.1	3.2	3500	400	200	200	4
2	89.1	3.2	3500	450	300	200	4
3	101.6	3.2	3500	400	200	200	4
4	101.6	3.2	3500	450	300	200	4
5	101.6	4	3500	400	200	200	4
6	101.6	4	3500	450	300	200	4
7	114.3	3.2	3500	400	200	200	4
8	114.3	3.2	3500	450	300	200	4
9	114.3	4	3500	400	200	200	4
10	114.3	4	3500	450	300	200	4
注：试桩上安装深度从小到大依次为1号、2号、3号；D_h1、D_h2、D_h3分别为1号、2号、3号螺旋板直径.

下载: 导出CSV

表 2 3种方法与现场测量的统计误差指标比较

Table 2. Comparison of statistical error metrics between three methods and field measurements

编号	预测方法	ε_mae/ kN	ε_rmse/ kN	ε_mape/ %	R²
7号桩	双曲线	0.233	0.326	5.499	0.989
	幂函数	1.511	1.571	29.812	0.734
	经典 p-y 曲线	1.364	1.484	22.557	0.762

下载: 导出CSV

表 3 不同方法在各位移比下Q_t,pre/Q_t,mea的性能指标

Table 3. Performance metrics of Q_t,pre/Q_t,mea of different methods at specified displacement ratios

方法	D/R/ %	μ	σ	C_COV	样本量
双曲线	1.25	1.095	0.193	0.176	10
	2.50	1.041	0.141	0.135
	3.75	1.004	0.130	0.130
	5.00	0.978	0.113	0.113
幂函数	1.25	0.628	0.200	0.319	10
	2.50	0.596	0.102	0.171
	3.75	0.641	0.050	0.078
	5.00	0.689	0.034	0.049
经典 p-y 曲线	1.25	1.118	0.340	0.304	10
	2.50	1.217	0.248	0.204
	3.75	1.242	0.179	0.144
	5.00	1.190	0.132	0.111

下载: 导出CSV

参考文献(42)

[1]	颜然, 孔纲强, 于江华. 砂土地基中钻进比对螺旋桩安装性能和抗拔承载性能的影响[J]. 岩土力学, 2024, 45(6): 1778-1788. doi: 10.16285/j.rsm.2023.1189 Yan Ran, Kong Gangqiang, Yu Jianghua. Installation and pull-out performance of helical pile embedded in sand influenced by advancing ratio[J]. Rock and Soil Mechanics, 2024, 45(6): 1778-1788. doi: 10.16285/j.rsm.2023.1189
[2]	王乐, 李钰, 徐志军, 等. 不同推进比下螺旋桩在砂土中安装力的离散元研究[J]. 岩土工程学报, 2024, 46(6): 1166-1176. doi: 10.11779/CJGE20230204 Wang Le, Li Yu, Xu Zhijun, et al. Discrete element study of method for installation forces of screw piles in sand under different advancement ratios[J]. Chinese Journal of Geotechnical Engineering, 2024, 46(6): 1166-1176. doi: 10.11779/CJGE20230204
[3]	胡伟, 杨瑶, 刘顺凯, 等. 光伏支架螺旋桩斜向拉拔承载特性试验研究[J]. 太阳能学报, 2022, 43(12): 50-61. Hu Wei, Yang Yao, Liu Shunkai, et al. Experiment study on inclined pullout bearing characteristic of screw anchor pile of photovoltaic bracket[J]. Acta Energiae Solaris Sinica, 2022, 43(12): 50-61.
[4]	邵康, 苏谦, 刘凯文, 等. 竖向受压下考虑安装扰动螺旋钢桩数值模拟分析与现场载荷试验[J]. 岩石力学与工程学报, 2019, 38(12): 2570-2581. doi: 10.13722/j.cnki.jrme.2019.0581 Shao Kang, Su Qian, Liu Kaiwen, et al. Field test and numerical analysis of a helical steel pile under vertical compression loads considering installation effects[J]. Chinese Journal of Rock Mechanics and Engineering, 2019, 38(12): 2570-2581. doi: 10.13722/j.cnki.jrme.2019.0581
[5]	Hao D X, Zhang Y H, Chen Y Z, et al. Numerical analysis of bearing capacity of winged helical anchor in clayed soil[J]. Scientific Reports, 2025, 15: 16380. doi: 10.1038/s41598-025-00571-9
[6]	Asgari A, Ali Arjomand M, Bagheri M, et al. Assessment of experimental data and analytical method of helical pile capacity under tension and compressive loading in dense sand[J]. Buildings, 2025, 15(15): 2683. doi: 10.3390/buildings15152683
[7]	Nowkandeh M J, Choobbasti A J. Numerical study of single helical piles and helical pile groups under compressive loading in cohesive and cohesionless soils[J]. Bulletin of Engineering Geology and the Environment, 2021, 80(5): 4001-4023. doi: 10.1007/s10064-021-02158-w
[8]	Alwalan M F, El Naggar M H. Load-transfer mechanism of helical piles under compressive and impact loading[J]. International Journal of Geomechanics, 2021, 21(6): 04021082. doi: 10.1061/(ASCE)GM.1943-5622.0002037
[9]	Elkasabgy M, El Naggar M H. Axial compressive response of large-capacity helical and driven steel piles in cohesive soil[J]. Canadian Geotechnical Journal, 2015, 52(2): 224-243. doi: 10.1139/cgj-2012-0331
[10]	Elsherbiny Z H, El Naggar M H. Axial compressive capacity of helical piles from field tests and numerical study[J]. Canadian Geotechnical Journal, 2013, 50(12): 1191-1203. doi: 10.1139/cgj-2012-0487
[11]	Cavalcanti Tsuha C de H, Mathias dos Santos Filho J M S, Santos T da C. Helical piles in unsaturated structured soil: a case study[J]. Canadian Geotechnical Journal, 2016, 53(1): 103-117. doi: 10.1139/cgj-2015-0017
[12]	Misaghian M, Hu P, Leo C, et al. Comparative analysis of helical pile uplift behaviour in sand using three different constitutive models[J]. Computers and Geotechnics, 2026, 189: 107651. doi: 10.1016/j.compgeo.2025.107651
[13]	Das D, Billah A M. Axial capacity of helical piles-a state of the art review of field test and design guidelines[J]. Structures, 2025, 80: 109749. doi: 10.1016/j.istruc.2025.109749
[14]	Bittar E, Lehane B M, Blake A, et al. CPT-based design method for helical piles in sand[J]. Canadian Geotechnical Journal, 2024, 61(1): 102-117. doi: 10.1139/cgj-2022-0209
[15]	李心如, 刘润, 王乐, 等. 黏土中海上风电单叶片刚性螺旋桩水平承载特性研究[J]. 岩土工程学报, 2025, 47(9): 1995-2002. doi: 10.11779/CJGE20240526 Li Xinru, Liu Run, Wang Le, et al. Study on horizontal bearing characteristics of single-blade rigid screw pile for offshore wind power in clay[J]. Chinese Journal of Geotechnical Engineering, 2025, 47(9): 1995-2002. doi: 10.11779/CJGE20240526
[16]	Zhang Y P, Ji H X, Liu H, et al. Initial horizontal dynamic impedance of single anti-toppling helical pile for offshore wind turbines[J]. Ocean Engineering, 2024, 306: 118048. doi: 10.1016/j.oceaneng.2024.118048
[17]	Jiang T, Liu C, Zhang X, et al. Experimental study on the deformation of sandy soil around multi-helical anchor piles under horizontal load[J]. Applied Ocean Research, 2023, 139: 103721. doi: 10.1016/j.apor.2023.103721
[18]	Krishnanunni K T, Rathod D, Sasidhar S. Effect of helix position on the lateral resistance of battered single-helix piles located on a sandy slope crest[J]. International Journal of Geomechanics, 2024, 24(3): 04023301. doi: 10.1061/IJGNAI.GMENG-7793
[19]	Jotisankasa A, Tanyacharoen K, Chaiprakaikeow S, et al. Performance of screw piles in bio-stabilized slope based on field monitoring and finite element modelling[J]. Soils and Foundations, 2025, 65(3): 101626. doi: 10.1016/j.sandf.2025.101626
[20]	ANSI/API RP 2GEO—2011 Geotechnical and Foundation Design Considerations[S].
[21]	DNVGL-RP-C212 Offshore soil mechanics and geotechnical engineering[S]
[22]	王亚伟, 朱金, 郑凯锋, 等. 考虑冲刷效应的大跨桥梁地震-风-车-桥耦合振动分析[J]. 西南交通大学学报, 2024, 59(2): 323-331. doi: 10.3969/j.issn.0258-2724.20220091 Wang Yawei, Zhu Jin, Zheng Kaifeng, et al. Coupled vibration analysis of earthquake-wind-vehicle-bridge for long-span bridges considering scouring effect[J]. Journal of Southwest Jiaotong University, 2024, 59(2): 323-331. doi: 10.3969/j.issn.0258-2724.20220091
[23]	Suryasentana S K, Lehane B M. Updated CPT-based p–y formulation for laterally loaded piles in cohesionless soil under static loading[J]. Géotechnique, 2016, 66(6): 445-453. doi: 10.1680/jgeot.14.p.156
[24]	李洪江, 刘松玉, 童立元. 基于CPTU测试p-y曲线法及其在桩基水平承载中的应用[J]. 岩石力学与工程学报, 2017, 36(2): 513-520. doi: 10.13722/j.cnki.jrme.2016.0223 Li Hongjiang, Liu Songyu, Tong Liyuan. A p-y curve method for defermining the horizontal bearing capacity of single pile based on CPTU test and its application[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(2): 513-520. doi: 10.13722/j.cnki.jrme.2016.0223
[25]	陈晓路, 管春雨, 张管武, 等. 近海风力机水平受荷单桩简化p-y曲线研究[J]. 太阳能学报, 2022, 43(5): 366-371. doi: 10.19912/j.0254-0096.tynxb.2020-0427 Chen Xiaolu, Guan Chunyu, Zhang Guanwu, et al. Research on simplified p-y curves of lateral loaded monopile for offshore wind turbines[J]. Acta Energiae Solaris Sinica, 2022, 43(5): 366-371. doi: 10.19912/j.0254-0096.tynxb.2020-0427
[26]	刘金昊, 张帆, 戴国亮. 基于静力触探的黏土中桩基p-y曲线研究[J]. 太阳能学报, 2023, 44(2): 172-180. doi: 10.19912/j.0254-0096.tynxb.2021-1166 Liu Jinhao, Zhang Fan, Dai Guoliang. Research on p-y curve of pile foundation in clay based on cpt data[J]. Acta Energiae Solaris Sinica, 2023, 44(2): 172-180. doi: 10.19912/j.0254-0096.tynxb.2021-1166
[27]	马美玲, 李立辰, 吴文兵, 等. 基于现场试验的海上风电大直径钢管桩p-y曲线特性分析[J]. 海洋工程, 2024, 42(5): 44-53. doi: 10.16483/j.issn.1005-9865.2024.05.005 Ma Meiling, Li Lichen, Wu Wenbing, et al. Characterization of p-y curve for a large-diameter steel pipe pile based on field test[J]. The Ocean Engineering, 2024, 42(5): 44-53. doi: 10.16483/j.issn.1005-9865.2024.05.005
[28]	Kim G, Lee J, Yoon J, et al. CPT-based dynamic p-y analysis method for seismic design of piles embedded in clay[J]. Geomechanics and Engineering, 2023, 35(3): 315-323.
[29]	Kim J, Kim G, Lee J. Dynamic p-y analysis method based on cone penetration test results for monopiles in sand[J]. Soil Dynamics and Earthquake Engineering, 2022, 163: 107503. doi: 10.1016/j.soildyn.2022.107503
[30]	Liu Z T, Zhang Y H, Guo P. A CPT-based p-y model for laterally loaded monopiles in sand[J]. Marine Structures, 2025, 101: 103767. doi: 10.1016/j.marstruc.2024.103767
[31]	Wen K, White D J, Cerfontaine B, et al. Interpretative framework for CPT p-y module tests in drained sands: a practical model for end effect elimination considering sand relative density and surcharge pressure[J]. Computers and Geotechnics, 2025, 183: 107205. doi: 10.1016/j.compgeo.2025.107205
[32]	Kim H J, Reyes J, Dinoy P R T, et al. Modified p-y curves to characterize the lateral behavior of helical piles[J]. Geomechanics and Engineering, 2022, 31(5): 505-518.
[33]	Kim H J, Kim H S, Dinoy P R T, et al. Estimating the lateral profile of helical piles using modified p-y springs[J]. Geomechanics and Engineering, 2023, 35(1): 1-11.
[34]	Reese L C, Cox W R, Koop F D. Analysis of laterally loaded piles in sand[C]//Offshore Technology Conference. Houston: OTC, 1974: OTC-2080-MS.
[35]	Lin Y F, Xiao J D, Le C H, et al. Bearing characteristics of helical pile foundations for offshore wind turbines in sandy soil[J]. Journal of Marine Science and Engineering, 2022, 10(7): 889. doi: 10.3390/jmse10070889
[36]	Khidri M, Liu C, Deng L J. Numerical analysis of screw micropiles under lateral loads via BNWF method[J]. Geotechnical and Geological Engineering, 2025, 43(2): 81. doi: 10.1007/s10706-024-03051-5
[37]	刘红军, 上官士青, 王虎. 水平受荷桩p-y曲线法的数学规划法求解[J]. 工程力学, 2014, 31(4): 225-231. Liu Hongjun, Shangguan Shiqing, Wang Hu. An optimization algorithm solution of the p-y curve method for laterally loaded piles[J]. Engineering Mechanics, 2014, 31(4): 225-231.
[38]	戴自航, 陈林靖. 多层地基中水平荷载桩计算m法的两种数值解[J]. 岩土工程学报, 2007, 29(5): 690-696. Dai Zihang, Chen Linjing. Two numerical solutions of laterally loaded piles installed in multi-layered soils by m method[J]. Chinese Journal of Geotechnical Engineering, 2007, 29(5): 690-696.
[39]	AC358 Acceptance criteria for helical foundation systems and devices[S].
[40]	Khidri M, Deng L J. Field lateral behaviour of full-scale screw micropiles in cohesive and cohesionless soils[J]. Geotechnical and Geological Engineering, 2024, 42(5): 3711-3730. doi: 10.1007/s10706-024-02753-0
[41]	Perlow M J. Helical pile acceptance criteria, design guidelines, and load test verification[C]//Geo-Frontiers 2011. Dallas: .American Society of Civil Engineers, 2011: 94-102.
[42]	Tang C, Phoon K K. Statistical evaluation of model factors in reliability calibration of high-displacement helical piles under axial loading[J]. Canadian Geotechnical Journal, 2020, 57(2): 246-262. doi: 10.1139/cgj-2018-0754