砂土静力触探试验的DEM-FDM耦合数值模拟研究

宋跃; 顾晓强; 胡靖; 郑兴

doi:10.11779/CJGE20240172

砂土静力触探试验的DEM-FDM耦合数值模拟研究 English Version

宋跃^{1, 2,},
顾晓强^{1, 2, ,},
胡靖^{1, 2},
郑兴³

1.
同济大学地下建筑与工程系, 上海 200092
2.
同济大学岩土及地下工程教育部重点实验室, 上海 200092
3.
中国电建集团华东勘测设计研究院有限公司, 浙江杭州 310014

基金项目:

国家自然科学基金项目 42361164615

详细信息

作者简介:
作者简介：宋跃(1992—)，男，博士研究生，主要从事海上风电大直径单桩水平承载特性的研究工作。E-mail: eldembu@tongji.edu.cn

通讯作者:
顾晓强, E-mail: guxiaoqiang@tongji.edu.cn

中图分类号: TU411
计量
- 文章访问数: 301
- HTML全文浏览量: 27
- PDF下载量: 91
出版历程
- 收稿日期: 2024-02-22
- 网络出版日期: 2024-08-20
- 刊出日期: 2025-05-31

DEM-FDM coupled simulation of cone penetration tests in a virtual calibration chamber with sand

SONG Yue^{1, 2,},
GU Xiaoqiang^{1, 2, ,},
HU Jing^{1, 2},
ZHENG Xing³

1.
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China
2.
Key Laboratory of Geotechnical and Underground Engineering of the Ministry of Education, Tongji University, Shanghai 200092, China
3.
Power China Huadong Engineering Corporation Limited, Hangzhou 310014, China

摘要

摘要: 静力触探是岩土工程最重要的原位测试手段之一，然而静力触探不能直接测出土体参数，需借助标定罐试验或数值模拟中已有的锥尖阻力与土体参数的经验关系来确定土体参数。本研究利用离散元（DEM）与有限差分法（FDM）耦合数值方法实现了砂土中标定罐静力触探贯入全过程的高效模拟，探究了影响锥尖阻力的主要因素。模拟中，首先根据砂土单元体宏观力学特性标定了砂土颗粒接触模型参数，并进一步分析了标定罐尺寸、砂土密实度、围压等对锥尖阻力影响，最后建立了归一化锥尖阻力Q和峰值内摩擦角φ_peak的关系。研究结果表明，在离散-连续模型径向尺寸比R_df为0.67且标定罐归一化径向长度R_d为20的情况下，模拟的尺寸效应可忽略。同时，锥尖阻力的模拟结果与小孔扩张理论计算结果吻合良好，验证了数值模拟的可靠性。归一化锥尖阻力Q和峰值内摩擦角φ_peak之间呈指数关系，与原位测试结果接近，进一步验证了耦合模拟方法的准确性，其结果可为砂土静力触探锥尖阻力与土体参数经验关系的建立提供重要参考。
- 静力触探 /
- 标定罐 /
- 离散元 /
- 有限差分 /
- 锥尖阻力
Abstract: The cone penetration test, considered one of the most crucial in-situ testing methods in geotechnical engineering, is unable to directly measure soil parameters. Generally, the empirical relationship between the penetration resistance and the soil parameters is established through tests or numerical simulations. In this research, a coupled numerical approach of the discrete element method (DEM) and the finite difference method (FDM) is employed to simulate the entire cone penetration test process within a calibration chamber and unveil the mechanisms that influence the penetration resistance. Firstly, the microscopic parameters of the sand are calibrated based on its macroscopic behaviors. Additionally, the effects of calibration chamber size, sand density and confining stress on the penetration resistance are thoroughly analyzed. Finally, a relationship is established between the normalized penetration resistance Q and the peak internal friction angle φ_peak. The findings indicate that the size effects in the simulation become negligible when the continuous-discrete model size ratio R_df reaches 0.67 and the normalized radial length R_d of the calibration chamber is set at 20. Furthermore, the simulated penetration resistance closely matches the results obtained by the cavity expansion methods, confirming the reliability of the numerical simulation. An exponential relationship is observed between Q and φ_peak, which closely aligns with the in-situ test results. This further validates the accuracy of the coupled simulation method. These outcomes offer valuable insights for establishing empirical relationships between the cone penetration resistance in sand and the soil parameters in geotechnical engineering.
- cone penetration test /
- calibration chamber /
- discrete element method /
- finite different method /
- cone-tip resistance

HTML全文

图 1 离散-连续耦合数值模拟模型

Figure 1. Details of discrete-continuous simulation model

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图 2 试验和模拟中砂土颗粒级配曲线

Figure 2. Experimental and simulated grain-size distribution curves

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图 3 三轴模拟与试验结果对比

Figure 3. Comparison of triaxial test results in simulation and laboratory

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图 4 标定罐试样高度对锥尖阻力的影响

Figure 4. Influences of height of calibration chamber on cone-tip resistance

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图 5 标定罐试样离散-连续区域径向尺寸对锥尖阻力影响

Figure 5. Influences of discrete-continuous region size ratio on cone-tip resistance

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图 6 标定罐归一化径向尺寸对锥尖阻力影响

Figure 6. Influences of horizontal size of calibration chamber on cone-tip resistance

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图 7 锥尖阻力模拟结果对比

Figure 7. Comparison of simulated results of cone-tip resistance

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图 8 标定罐土体径向位移云图

Figure 8. Displacement contours of calibration chamber

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图 9 等向围压对锥尖阻力的影响

Figure 9. Influences of confining stress on cone-tip resistance

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图 10 锥尖阻力模拟值与计算值的对比

Figure 10. Comparison of predicted and simulated values of q_c

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图 11 锥尖阻力模拟值和预测值对比

Figure 11. Comparison between DEM simulation and analytical solution

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图 12 径向应力的理论解和数值解

Figure 12. Theoretical and numerical solutions of radial stress

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图 13 归一化锥尖阻力与峰值内摩擦角关系

Figure 13. Relationships between normalized cone-tip resistance Q and peak internal friction angle φ_peak

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表 1 砂土颗粒接触模型参数

Table 1 Microscopic contact parameters of sand

参数	数值
颗粒密度(ρ)	2650 kg/m³
刚度系数(k₀)	8×10⁸ N/m²
刚度比(α_s)	0.15
颗粒摩擦系数(μ)	0.45
颗粒抗转动系数(μ_r)	0.35
颗粒法向刚度(k_n)	k_n = k₀×r
颗粒切向刚度(k_s)	k_s = α_s×k_n

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表 2 莫尔-库仑模型参数取值

Table 2 Parameters of Mohr-Coulomb model

相对密实度D_r/%	杨氏模量E/ MPa	泊松比 $\nu$	内摩擦角φ/(°)	剪胀角ψ/(°)
70	60.6	0.3	36.5	10.3
40	36.3	0.3	31.9	3.2
10	30	0.3	30.1	0

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表 3 模型边界及锥体参数

Table 3 Model boundary and cone parameters

参数	数值
耦合墙法向刚度	4×10⁶ N/m
耦合墙切向刚度	6×10⁵ N/m
耦合墙摩擦系数	0.45
耦合墙抗转动系数	0.35
边界墙法向刚度	1×10¹⁰ N/m
边界墙切向刚度	1×10¹⁰ N/m
边界墙摩擦系数	0
边界墙抗转动系数	0
锥体法向刚度	1×10¹⁰ N/m
锥体切向刚度	1×10¹⁰ N/m
锥体摩擦系数	0.2
锥体贯入速度	0.1 m/s

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表 4 莫尔库仑本构模型模拟三轴试验的参数

Table 4 Parameters of Mohr-Coulomb model for simulating triaxial test results

D_r/%	p₀/kPa	q_peak/kPa	E/MPa	$\nu$	ψ_peak/(°)	ϕ_peak/(°)
10	100	205	20.3	0.23	3.9	30.4
40	100	224	36.3	0.25	6.1	31.9
70	100	311	56.5	0.25	18.1	36.5
10	200	405	21.2	0.24	5.1	30.2
40	200	448	38.4	0.26	4.8	31.9
70	200	580	56.7	0.25	16.8	36.3
10	400	801	26.3	0.21	2.9	30.1
40	400	874	40.1	0.27	5.9	31.5
70	400	1132	56.3	0.25	16.1	35.9

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