EPS颗粒混合轻量土的动变形特性及修正Hardin-Drnevich模型研究

侯天顺; 崔奕翔

doi:10.11779/CJGE202109004

EPS颗粒混合轻量土的动变形特性及修正Hardin-Drnevich模型研究 English Version

西北农林科技大学水利与建筑工程学院,陕西　杨凌　712100

基金项目:

国家自然科学基金项目 51509211

中国博士后基金项目 2016M602863

陕西省留学人员科技活动择优资助项目 2018031

陕西省社会发展科技攻关项目 2015SF260

陕西省博士后基金项目 2017BSHYDZZ50

杨凌示范区科技计划项目 2016GY-01

中央高校基本科研业务费专项资金项目 2452020169

详细信息

作者简介:
侯天顺(1981— ),男,湖北省郧西县人,博士,副教授,主要从事岩土力学、地基基础工程与地质灾害防治方面的教学与科研工作。E-mail：houtianshunyx@sina.com

中图分类号: TU435
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出版历程
- 收稿日期: 2020-10-24
- 网络出版日期: 2022-12-02
- 刊出日期: 2021-08-31

Dynamic deformation characteristics and modified Hardin-Drnevich model for light weight soil mixed with EPS particles

College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling 712100, China

摘要

摘要: 为探究EPS颗粒混合轻量土的动变形特性,通过动三轴试验研究了不同配比、围压对轻量土骨干曲线、Hardin-Drnevich模型参数的影响规律,建立了修正Hardin-Drnevich模型,并对修正模型进行了验证。结果表明：轻量土的骨干曲线呈现出明显的非线性特性与应变硬化特征。轻量土动剪切模量的倒数与剪应变关系曲线符合线性递增的变化规律,其动变形特性可以由Hardin-Drnevich模型描述。最大动剪切模量的倒数和最大动剪应力的倒数随着围压和水泥掺量的增大而减小,随EPS颗粒体积比的增大而增大。在Hardin公式的基础上,引入相对结构度k和广义孔隙比 $e^{'}$ $e^{'}$ ,提出了模型参数的表达式,建立了修正Hardin-Drnevich模型。通过改变应力状态和应力路径对轻量土进行动三轴验证试验,发现模型计算值与试验值间的相对误差均小于11%,修正Hardin-Drnevich模型对轻量土骨干曲线的预测结果良好,这表明修正Hardin-Drnevich模型可以描述轻量土特殊结构性在复杂受力条件下的动力响应。
- 轻量土 /
- 动变形特性 /
- 修正Hardin-Drnevich模型 /
- 相对结构度 /
- 广义孔隙比 /
- 动三轴试验
Abstract: To investigate the dynamic deformation characteristics of light weight soil mixed with EPS particles, the influences of different mixed ratios and confining pressures on the backbone curve and the parameters of Hardin-Drnevich model for light weight soil are studied through the dynamic triaxial tests, and the modified Hardin-Drnevich model is established and verified. The results show that the backbone curve of light weight soil exhibits obvious nonlinear and strain-hardening characteristics. The relationship between reciprocal of dynamic shear modulus and shear strain of light weight soil increases linearly, indicating that the dynamic deformation characteristics of light weight soil can be described by the Hardin-Drnevich model. The reciprocal of the maximum dynamic shear modulus and that of the maximum dynamic shear stress decrease with the increase of confining pressure and cement content, and increase with the increase of volume ratio of EPS particles. On the basis of the Hardin formula, the expression for model parameters is proposed by introducing the relative structure k and the generalized pore ratio e', and the modified Hardin-Drnevich model is established. By changing the stress state and stress path, the relative error between the calculated value and the test value is less than 11%. The predicted results by the modified Hardin-Drnevich model for the backbone curves of light weight soil are good, which shows that the modified Hardin-Drnevich model can describe the dynamic response of the special structure of light weight soil under complex stress conditions.
- light weight soil /
- dynamic deformation characteristic /
- modified Hardin-Drnevich model /
- relative structural degree /
- generalized void ratio /
- dynamic triaxial test

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图 1 不同围压条件下轻量土的骨干曲线

Figure 1. Backbone curves of light weight soil under different confining pressures

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图 2 不同围压条件下动剪切模量倒数1/G_d与动剪应变γ_d的关系曲线

Figure 2. Relationship curves between reciprocal of dynamic shear modulus and dynamic shear strain under different confining pressures

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图 3 模型参数与EPS颗粒体积掺入比b_e的关系曲线

Figure 3. Relationship curves between model parameters and particles content of EPS

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图 4 模型参数与水泥掺量a_c的关系曲线

Figure 4. Relationship curves between model parameters and cement content

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图 5 不同应力状态下模型计算值与试验值的对比

Figure 5. Comparison between calculated and test values under different stress states

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图 6 不同应力路径下模型计算值与试验值的对比

Figure 6. Comparison between calculated and test values under different stress paths

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表 1 土的物理性质指标

Table 1 Physical properties of soil

天然含水率w/%	相对质量密度G_s	天然密度ρ/(g·cm^-3)	塑限w_P/%	液限w_L/%	塑性指数I_P	液性指数I_L	孔隙比e	有机质/%
19.75	2.72	1.702	21.27	33.62	12.35	-0.123	0.91	<5

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表 2 轻量土动三轴试验方案

Table 2 Dynamic triaxial test schemes of light weight soil

影响因素	方案一	方案二	方案三
EPS颗粒体积掺入比b_e/%	20,30,40,50,60	40	0
水泥掺入比a_c/%	10	10,15,20	0
含水率w/%	50	50	21.3
龄期T/d	28	28	0
固结压力σ_c /kPa	50,100,150,200	50,100,150,200	50,100,150,200
固结应力比/K_c	1.0	1.0	1.0
振动频率f/Hz	1	1	1
动剪应力比/s	0.075	0.075	0.075

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表 3 轻量土的相对结构度k的计算结果

Table 3 Calculated results of structural parameter k of light weight soil

配比	素土	b_e=20%a_c=10%	b_e=30%a_c=10%	b_e=40%a_c=10%	b_e=50%a_c=10%	b_e=60%a_c=10%	b_e=40%a_c=15%	b_e=40%a_c=20%
相对结构度k	1	8.952	8.488	7.401	5.303	4.027	8.248	8.709

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表 4 轻量土广义孔隙比 $e^{'}$ $e^{'}$ 的计算结果

Table 4 Calculated results of generalized void ratio $e^{'}$ $e^{'}$ of light weight soil

水泥掺量a_c/%	EPS颗粒体积掺入比b_e/%
水泥掺量a_c/%	0	20	30	40	50	60
0	0.619	—	—	—	—	—
10	—	1.307	1.612	2.018	2.590	3.439
15	—	1.251	1.547	1.938	2.489	3.310
20	—	1.199	1.485	1.865	2.396	3.194

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表 5 最大动剪切模量公式的回归参数值

Table 5 Values of regression parameters of formula for maximum dynamic shear modulus

A	n₁	η₁
0.103	-0.305	14.135

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表 6 参数b经验公式回归参数值

Table 6 Values of regression parameters of empirical formula for parameter b

η₂	n₂	B	n₃	C	n₄
0.0834	1.18	0.037	-12.3	0.437	-0.8

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表 7 改变应力状态的轻量土动三轴验证试验方案

Table 7 Dynamic triaxial validation test schemes of light weight soil by changing stress state

EPS颗粒体积掺入比b_e/%	水泥掺入比a_c/%	含水率w/%	龄期T/d	固结压力σ_c/kPa	固结应力比K_c	振动频率f/Hz	每级循环周数
40	10	50	28	125,175	1	1	10

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表 8 改变应力路径的轻量土动三轴验证试验方案

Table 8 Dynamic triaxial validation test schemes of light weight soil by changing stress path

方案一	方案二	方案三
正弦波	正弦波	正弦波
加载	加载	加载
共6级	共3级	共3级
1/10 τ_max	2/10 τ_max	4/10 τ_max
2/10 τ_max	4/10 τ_max	2/10 τ_max
……	6/10 τ_max	6/10 τ_max
6/10 τ_max

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