基于化学反应动力学方程的一维膨胀时程模型

邹维列; 叶云雪; 韩仲

doi:10.11779/CJGE202004017

基于化学反应动力学方程的一维膨胀时程模型 English Version

邹维列^{1, 2,},
叶云雪³,
韩仲^2, ,

1.
西京学院土木工程学院,陕西　西安　710123
2.
武汉大学土木建筑工程学院,湖北　武汉　430072
3.
南昌航空大学土木建筑学院,江西　南昌　330063

基金项目:

国家自然科学基金项目 51779191

国家自然科学基金青年基金项目 51809199

详细信息

作者简介:
邹维列(1969—),男,教授,博士生导师,从事非饱和土特性、土工合成材料应用和道路岩土工程等方面的教学和研究。E-mail: zwilliam@whu.edu.cn

通讯作者:
韩仲, E-mail: zhong.han@whu.edu.cn

中图分类号: TU435
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出版历程
- 收稿日期: 2019-05-23
- 网络出版日期: 2022-12-07
- 刊出日期: 2020-03-31

Chemical reaction kinetics based models for describing evolution of one-dimensional expansion with time

ZOU Wei-lie^{1, 2,},
YE Yun-xue³,
HAN Zhong^2, ,

1.
School of Civil Engineering, Xijing University, Xi'an 710123, China
2.
School of Civil Engineering, Wuhan University, Wuhan 430072, China
3.
School of Civil Engineering and Architecture, Nanchang Hangkong University, Nanchang 330063, China

摘要

摘要: 基于膨胀土的微观膨胀机理,利用二级化学反应动力学方程推导出膨胀土的两种膨胀时程模型：双曲线模型和Logistic模型。前者为两参数模型,其参数物理意义明确；后者为三参数模型,尚有物理意义不明确的参数。通过室内一维膨胀率试验研究了初始含水率和干密度对膨胀时程曲线的影响规律,并对两个模型进行比较。结果表明：①双曲线模型与Logistic模型均能准确地描述膨胀时程曲线；②双曲线模型还可进一步用于预测不同初始含水率和干密度下的膨胀时程曲线；③预测曲线与试验数据具有较好的一致性,且参数的校正过程简单,便于工程应用。推导的膨胀时程模型对于描述膨胀土浸水饱和过程中的体变演化规律具有重要的理论意义。
- 膨胀土 /
- 微观膨胀机理 /
- 膨胀时程 /
- 动力学方程 /
- 模型
Abstract: Two models for describing the evolution of one-dimensional expansion of expansive soils with time are derived based on the second-order chemical reaction kinetic equation, namely, hyperbolic model and Logistic model. The former has two parameters which have clear physical meanings, while the latter has three parameters among which one has an unclear physical meaning. One-dimensional swelling tests on the specimens with different initial water contents and dry densities are conducted to obtain swelling strain-time curves, and the fitting effects using the two models are compared. The results show that both models can accurately describe the swelling strain-time curves. Moreover, the hyperbolic model can also be used to predict the expansion time-history curves of the specimens with different initial water contents and dry densities. The predicted curves have good consistency with the experimental data, and the parameter correction process is simple, which is convenient for engineering applications. The expansion time-history model deduced in this study has important theoretical significance for describing the evolution laws of volume change of expansive soils during the process of water immersion saturation.
- expansive soil /
- microscopic expansion mechanism /
- time-dependence of swelling /
- kinetic equation /
- model

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衷心地感谢西京学院土木工程学院对本文试验工作的大力支持！

图 1 化学反应速率图

Figure 1. Diagram of chemical reaction rate

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图 2 膨胀时程曲线

Figure 2. Swelling-time curves

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图 3 两种模型中共同的参数

Figure 3. Common parameters in two models

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图 4 两种模型的δ_max与t₀的关系

Figure 4. Relationship between δ_max and t₀ in two models

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图 5 两种模型的δ_max与某一给定变量的关系

Figure 5. Relationship between δ_max and a given variable in two models

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图 6 预测的膨胀时程曲线与试验数据的比较

Figure 6. Comparison between predicted curves and experimental data

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表 1 两种模型的膨胀时程曲线参数

Table 1 Parameters in swelling-time curves for two models

干密度/(g·cm^-3)	含水率/%	双曲线模型			Logistic模型
干密度/(g·cm^-3)	含水率/%	δ_max/%	t₀/min	R²	δ_max/%	p	t₀/min	R²
1.7	11.4	23.7	30.7	0.994	23.7	1.01	30.8	0.994
	13.5	20.1	54.9	0.994	20.0	1.08	54.6	0.996
	15.2	17.8	93.2	0.995	17.6	1.12	93.2	0.997
	17.6	14.7	176.1	0.995	14.4	1.06	176.0	0.996
	19.0	13.4	225.3	0.996	13.6	0.94	225.0	0.996
	21.8	9.8	363.2	0.993	9.9	0.93	363.0	0.993
1.6	12.6	15.7	8.7	0.973	15.5	1.14	8.9	0.973
1.6	21.6	8.0	149.1	0.997	8.0	1.00	148.9	0.997
1.5	12.1	12.8	6.9	0.991	12.7	1.11	7.1	0.992
1.5	17.4	10.6	8.4	0.968	11.3	0.65	8.4	0.985
1.4	17.6	9.3	3.1	0.970	9.7	0.60	3.0	0.988
1.4	22.6	6.2	4.2	0.966	6.5	0.59	4.2	0.988

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表 2 预测的荆门弱膨胀土膨胀时程曲线的相关参数

Table 2 Prediction of parameters of expansion time curve of Jingmen expansive soil

$ρ_{d}$ $ρ_{d}$ /(g·cm^-3)	双曲线模型			式（15）			式（16）
$ρ_{d}$ $ρ_{d}$ /(g·cm^-3)	δ_max	t₀/min	R²	α	β	R²	m₂	n₂	R²
1.77	25.4	113.4	0.995	0.015	0.188	0.998	37.912	-41.749	0.999
1.67	21.5	46.6	0.996
1.30	7.6	3.8	0.986

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施引文献(6)

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3.	叶云雪，邹维列，韩仲，谢鹏，张俊峰，徐永福. 考虑初始状态影响的膨胀土一维膨胀特性研究. 岩土工程学报. 2021(08): 1518-1525 . 本站查看