临界状态土的物理标度律

费建波; 唐昊; 介玉新; 陈湘生

doi:10.11779/CJGE20230435

临界状态土的物理标度律 English Version

费建波^{1, 2, 3,},
唐昊^{1, 2, 3},
介玉新^{4, 5, 6},
陈湘生^{1, 2, 3}

1.
极端环境岩土和隧道工程智能建养全国重点实验室(深圳大学), 广东深圳 518060
2.
滨海城市韧性基础设施教育部重点实验室(深圳大学), 广东深圳 518060
3.
深圳大学土木与交通工程学院, 广东深圳 518060
4.
清华大学水圈科学与水利工程全国重点实验室, 北京 100084
5.
清华大学水利部水圈科学重点实验室, 北京 100084
6.
清华大学水利水电工程系, 北京 100084

基金项目:

国家自然科学基金项目 52178339

国家自然科学基金项目 52090084

深圳市稳定支持计划项目 20220808150117002

详细信息

作者简介:
费建波(1988— )，男，博士，研究员，主要从颗粒岩土工程的研究工作。E-mail: feijianbo@szu.edu.cn

中图分类号: TU441
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出版历程
- 收稿日期: 2023-05-17
- 网络出版日期: 2024-04-18
- 刊出日期: 2024-08-31

Scaling laws for quasi-static granular sand at critical state

FEI Jianbo^{1, 2, 3,},
TANG Hao^{1, 2, 3},
JIE Yuxin^{4, 5, 6},
CHEN Xiangsheng^{1, 2, 3}

1.
State Key Laboratory of Intelligent Geotechnics and Tunnelling, Shenzhen University, Shenzhen 518060, China
2.
Key Laboratory of Coastal Urban Resilient Infrastructures (Shenzhen University), Ministry of Education, Shenzhen 518060, China
3.
College of Civil and Transportation Engineering, Shenzhen University, Shenzhen 518060, China
4.
State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China
5.
Key Laboratory of Hydrosphere Sciences of the Ministry of Water Resources, Tsinghua University, Beijing, 100084, China
6.
Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China

摘要

摘要: 土的临界状态理论描述了土有效应力、抗剪强度与土密实度之间的对应关系，大量土力学试验还揭示了土体强度与加载速率存在相关性。考虑到颗粒物质是自然土体的实际载体，从颗粒物理本源出发，将流态颗粒惯性数I发展为考虑砂土密实程度（即初始颗粒体积分数ϕ₀）的准静态颗粒物理惯性数Q=ϕ₀[ln(I)+α]。以砂土的经典三轴试验数据为基础，探究了处于临界状态土的颗粒物理标度律，发现颗粒的摩擦系数μ与准静态颗粒惯性数Q之间满足简单的μ=ξQ线性关系。新建立的简单物理标度律能够统一刻画处于临界状态砂土的密实状态、剪切速率、围压和粒径等因素与土内摩擦角间复杂的经验关系。为描述受剪颗粒准静态变形的体变规律，进一步探索了临界状态下土颗粒体积分数与准静态颗粒惯性数间的相关性。对三维应力状态情况，引入一个新的无量纲量“中主应力数”对标度律进行拓展，可揭示中主应力对临界状态砂土摩擦特性的影响。
- 颗粒 /
- 临界状态 /
- 标度律 /
- 剑桥模型 /
- 砂土
Abstract: The critical state theory of soils describes the correspondence between effective stress, shear strength and soil density. Numerous soil mechanics experiments have also revealed a correlation between soil strength and loading rate. Considering that the granular matter is the actual medium of natural soils, a quasi-static inertia number is proposed, i.e., Q=ϕ₀[ln(I)+α], for the granular soils considering the particle volume fraction. Based on the classical triaxial test data of soils, the scaling laws of quasi-static deforming sand at the critical state from the perspective of granular physics are explored, and a simple linear relationship i.e., μ=ξQ, is found between the friction coefficient and the quasi-static particle inertia number. The newly established scaling laws can quantitatively describe the influences of the volume fraction, shear rate, confining pressure and particle size on the frictional properties of sand when reaching the critical state. In addition, to quantify the volumetric deformation laws of sand under quasi-static shear, a correlation is obtained between the particle volume fraction ϕ at the critical state and the quasi-static inertia number Q. In attempt to characterize the scaling laws of the three-dimensional stress state, a new dimensionless number (i.e., the intermediate principal stress number) is defined to reveal the influences of the intermediate principal stress on the frictional properties. Thus, the scaling laws are extended.
- granular material /
- critical state /
- scaling law /
- Cambridge model /
- sand

HTML全文

图 1 应变率对不排水强度的影响^[7]，其中s_u为三轴压缩试验的不排水剪切强度，以剪切速率1%/h的强度为参考值， $\dot{ϵ}$ 为剪切速率

Figure 1. Influences of strain rate on undrained strength ^[7] (s_u represents the undrained shear strength from triaxial compression tests, normalized by that at a shear rate of 1%/hour, and $\dot{ϵ}$ is shear rate)

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图 2 颗粒受剪变形分析概化模型，惯性数为微观颗粒重分布时间尺度(左)和宏观变形时间尺度（右）比值

Figure 2. Schematic of granular system under shear (inertia number is defined as time scale ratio between microscopic rearrangement (left) and macroscopic deformation rate (right))

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图 3 密实和疏松土受剪变形的临界状态

Figure 3. The critical state of dense and loose soil under shear

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图 4 颗粒松密程度对摩擦系数μ与ln(I)关系的影响

Figure 4. Definition of internal friction angle at critical state

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图 5 不同密实状态土摩擦系数μ与准静态惯性数Q标度律

Figure 5. Scaling laws between friction coefficient μ and Q for soils at different density states

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图 6 更密实的土颗粒表现出更强的摩擦强度示意Q₁<Q₂

Figure 6. Denser soils exhibiting greater frictional strength, Q₁<Q₂

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图 7 不同毕肖普常数b对μ与ln(I)相关性影响

Figure 7. Influences of intermediate principal stress on relationship between μ and ln(I)

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图 8 通过中主应力数β反映中主应力对标度律的影响

Figure 8. Influences of intermediate principal stress on scaling law through intermediate principal stress number β

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图 9 初始孔隙比对ϕ与ln(I)关系的影响

Figure 9. Effect of initial void ratio on the relationship between ϕ and .ln(I)

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图 10 不同初始孔隙比条件下ϕ与Q间的标度律

Figure 10. Scaling between ϕ and Q for sands with different initial void ratios

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表 1 试验材料的物理指标

Table 1 Physical properties of test materials

材料	G_s	d₅₀/mm	密实状态	e
F-35 Ottawa 砂	2.65	0.36	疏松	0.733
			中等	0.614
			致密	0.494
^#1玻璃砂	2.65	0.36	疏松	0.928
			中等	0.778
			致密	0.638
GS^#40 Columbia grout砂	2.65	0.36	疏松	0.921
			中等	0.762
			致密	0.639

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表 2 3种材料三轴试验数据获取标度律的拟合参数

Table 2 Fitting parameters of scaling law for obtaining triaxial test data for three types of materials

材料	ξ
F-35 Ottawa砂	0.1021
^#1 玻璃砂	0.1173
GS^#40 Columbia grout砂	0.1179

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表 3 主要试验参数

Table 3 Primary experimental parameters

初始孔隙比	G_s	d₅₀/mm	剪切速率
0.360	2.72	14.39	0.6 mm/min	姜景山等^[30]
0.333	2.72	14.39	0.6 mm/min
0.308	2.72	14.39	0.6 mm/min
0.283	2.72	14.39	0.6 mm/min
0.189	2.69	26.48	1 mm/min	Xiao 等^[31]
0.224	2.69	26.48	1 mm/min
0.285	2.69	26.48	1 mm/min
0.317	2.69	26.48	1 mm/min
0.189	2.69	23.48	1 mm/min	Xiao 等^[32]
0.224	2.69	23.48	1 mm/min
0.285	2.69	23.48	1 mm/min
0.317	2.69	23.48	1 mm/min

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