岩土热导率预测正三棱柱-准内切球单元结构模型

褚召祥; 王一鸣; 李晓昭; 董凯军; 顾晓滨; 贾国圣

doi:10.11779/CJGE20230900

岩土热导率预测正三棱柱-准内切球单元结构模型 English Version

褚召祥^{1, 2,},
王一鸣¹,
李晓昭^{2, 3},
董凯军⁴,
顾晓滨⁴,
贾国圣⁵

1.
中国矿业大学力学与土木工程学院, 江苏徐州 221116
2.
深地工程智能建造与健康运维全国重点实验室, 江苏徐州 221116
3.
深地科学与工程云龙湖实验室, 江苏徐州 221116
4.
中国科学院广州能源研究所, 广东广州 510640
5.
西安交通大学人居学院, 陕西西安 710049

基金项目:

国家自然科学基金项目 42107156

国家自然科学基金项目 42230704

111创新引智计划 B23003

江苏省自然科学基金项目 BK20231501

徐州市科技计划 KC23383

广东省新能源和可再生能源研究开发与应用重点实验室开放基金项目 E039kf0501

详细信息

作者简介:
褚召祥(1987—)，男，博士，副教授，主要从事岩土传热传质方面的研究工作。E-mail: chulongxiang@cumt.edu.cn

中图分类号: TU432
计量
- 文章访问数: 0
- HTML全文浏览量: 0
- PDF下载量: 0
出版历程
- 收稿日期: 2023-09-14
- 网络出版日期: 2024-05-10
- 刊出日期: 2024-11-30

Regular triangular prism-quasi-inscribed sphere unit cell model for predicting thermal conductivity of geomaterials

1.
School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
2.
State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, Xuzhou 221116, China
3.
Yun Long Lake Laboratory, Xuzhou 221116, China
4.
Guangzhou Institute of Energy Conversion, Chinese Academy of Science, Guangzhou 510640, China
5.
School of Human Settlements and Civil Engineering, Xi'an Jiaotong University, Xi'an 710049, China

摘要

摘要: 借鉴细观力学均质化思想，采用热电类比-集总参数法，在细观尺度建立了固流两相（干燥或饱和）岩土热导率预测正三棱柱-准内切球单元结构(Unit cell)模型，并基于34组文献试验数据和238组模型预测数据进行了对比分析。研究结果表明：①正三棱柱-准内切球单元结构在克服球、圆柱单元结构固有的空间修正缺陷同时，相对立方体-准内切球单元结构（孔隙率0.035~0.473）孔隙率适用范围扩展至0~0.6，可覆盖大部分天然岩土介质孔隙率范围；②MATLAB数据可视化显示正三棱柱-准内切球单元结构模型预测热导率随孔隙率增大呈凹形降低，低孔隙率(< 0.2)岩土热导率预测结果偏低且趋向串联模型下限，高孔隙率（0.4~0.6）岩土热导率预测结果与试验测试值吻合度较高；③两相干燥状态下本模型相对其他单元结构模型预测效果更好，均方根误差RMSE和归一化均方根误差NRMSE最小，分别为0.89 W/m·K和31%；④考虑岩土孔隙水形态和含量，提出的正三棱柱-准内切球单元结构可扩展应用于固液气三相非饱和状态，并基于孔隙颗粒结构、孔隙水形态提出进化视角下固液气多相组分和多孔颗粒结构主导的岩土热导率预测关联式单元结构模型研究的新思路。
- 岩土介质 /
- 表观热导率 /
- 孔隙率 /
- 关联式 /
- 演化
Abstract: Inspired by the homogenization theory in the field of micromechanics, a regular triangular prism-quasi-inscribed sphere unit cell model at the meso-scale for predicting the thermal conductivity of two-phase (dry or water-saturated) geomaterials is proposed by using the lumped parameter thermo-electric analogy method. The performance of the established model is evaluated with 34 sets of thermal conductivity experimental data and 238 sets of thermal conductivity predictions. The results indicated that: (1) The regular triangular prism-quasi-inscribed sphere unit cell is a real representative elementary volume that can characterize the macroscopic continuum geomaterials and overcome the inherent spatial correction defects of the sphere and cylinder unit cell structures. Besides, this model can be used for soil-rocks with the porosity of 0~0.6, covering most porosity range of the natural geomaterials. (2) The MATLAB data visualization illustrate that the proposed model gives thermal conductivities concavely decreasing with porosity, and the model performance is better at relative high porosity (0.3~0.6) than those at low void ratio (< 0.25). (3) Taking the typical geomaterials under two-phase condition as an example, this model has better predictive performance than other unit cell theoretical models, especially under dry condition (the RMSE and NRMSE are, respectively, 0.89W/(m·K) and 31%). (4) Finally, the unit cell model proposed herein can be extended to three-phase unsaturated state (general solid-liquid-gas), and a promising initiative, i.e., to study the effects of component and structure on the effective thermal conductivity of porous- granular geomaterials from an evolutionary perspective, is conjectured based on pore/particle structure and pore water morphology, aiming to provide a new way for further investigating the macroscopic thermo-mechanical behavior of tanglesome geomaterials.
- geomaterial /
- effective thermal conductivity /
- porosity /
- correlation /
- evolution

HTML全文

图 1 本模型在高低孔隙率状态下的3D示意图

Figure 1. 3D schematic diagram of model under high and low porosities

下载: 全尺寸图片幻灯片

图 2 高孔隙率热阻分区及等效网络示意图

Figure 2. Schematic diagram of equivalent thermal resistance partition and network under high porosity

下载: 全尺寸图片幻灯片

图 3 低孔隙率热阻分区及等效网络示意图

Figure 3. Schematic diagram of equivalent thermal resistance partition and network under low porosity

下载: 全尺寸图片幻灯片

图 4 类纺锤体示意图（柱坐标系）

Figure 4. Spindle in a cylindrical coordinate

下载: 全尺寸图片幻灯片

图 5 计算流程图

Figure 5. Flow chart of calculation

下载: 全尺寸图片幻灯片

孔隙率 $\phi$ 随几何特征因子 $\alpha$ 的变化曲线

Variation of porosity $\phi$ with $\alpha$

下载: 全尺寸图片幻灯片

图 7 不同模型两相(干燥/饱和)状态下热导率预测对比

Figure 7. Predictions of effective thermal conductivity of different models under dry or saturated conditions

下载: 全尺寸图片幻灯片

图 8 不同模型随孔隙率变化速率对比

Figure 8. Comparison among various models

下载: 全尺寸图片幻灯片

图 9 不同模型预测结果可视化对比

Figure 9. Comparison of visualization among various models

下载: 全尺寸图片幻灯片

图 10 进化视角下组构主导的岩土热导率研究

Figure 10. Composition-structure dominated ETC of geomaterials from an evolutionary perspective

下载: 全尺寸图片幻灯片

表 1 固流相热导率参考值

Table 1 Thermal conductivity of solid-fluid pse

相态(1 bar, 300K)	热导率(W·(m·K)^-1)	参考文献
固相（石英）	7.69*	^{[10, 13]}
液相（水）	0.6096
气相（空气）	0.02619
*后续定量分析时，黏土 ${\lambda _\text{s}}$ =2 W/(m·K) ^[16]。

下载: 导出CSV

表 2 热导率试验测试结果

Table 2 Experimental data of thermal conductivity

岩土试样	孔隙率Φ	饱和度S_r	热导率/ (W·(m·K)^-1)
砂岩^[19]	0.02	0/1	2.8/3.2
	0.03	0/1	3/3.6
	0.04	0/1	2.5/2.8
	0.06	0/1	2.3/3.3
	0.12	0/1	1.7/3.1
	0.15	0/1	2.1/3.3
	0.16	0/1	1.7/3.0
标准砂^{[13, 18, 20]}	0.354	0/1	0.555/2.968
	0.396	0/1	0.402/2.72
	0.434	0/1	0.333/2.49
	0.472	0/1	0.237/2.25
	0.509	0/1	0.199/2.134
	0.547	0/1	0.141/1.937
黏土^[21]	0.385	0/1	0.67/0.98
	0.418	0/1	0.61/0.97
	0.451	0/1	0.61/0.94
	0.475	0/1	0.57/0.91
注：除黏土外， ${\lambda _\text{s}}$ 均采用Haigh文献中的7.69 W/(m·K)。

下载: 导出CSV

表 3 岩土热导率预测模型对比(RMSE/NRMSE)Table 3 Comparison of prediction models for thermal conductivity of geomaterials 单位：W/(m·K)

模型	Chen^[10]	Series	Parallel	Chu等^[13] (Uncorrected)	Chu等^[13] (Corrected)	Jia等^[14]	本文模型
干燥状态	1.690/0.591	1.211/.424	3.905/1.366	1.309/0.458	1.295/0.453	3.204/1.121	0.889/0.311
饱和状态	2.122/0.789	1.351/0.502	2.880/1.071	1.750/0.651	1.872/0.696	2.611/0.970	1.004/0.373

下载: 导出CSV

参考文献(29)

[1]	徐云山, 肖子龙, 孙德安, 等. 土体导热系数温度效应及其预测模型[J]. 岩土工程学报, 2023, 45(6): 1180-1189. doi: 10.11779/CJGE20220243 XU Yunshan, XIAO Zilong, SUN Dean, et al. Temperature effects and prediction model of thermal conductivity of soil[J]. Chinese Journal of Geotechnical Engineering, 2023, 45(6): 1180-1189. (in Chinese) doi: 10.11779/CJGE20220243
[2]	CHENG P, HSU C T. The effective stagnant thermal conductivity of porous media with periodic structures[J]. Journal of Porous Media, 1999, 2(1): 19-38. doi: 10.1615/JPorMedia.v2.i1.20
[3]	CHU Z X. 1D monodirectional or 2D quasi-uniaxial parallel heat fluxes: a discussion on 'Soil thermal conductivity estimated using a semi-analytical approach'[J]. Geothermics, 2022, 99: 102301. doi: 10.1016/j.geothermics.2021.102301
[4]	GEMANT A. The thermal conductivity of soils[J]. Journal of Applied Physics, 1950, 21(8): 750-752. doi: 10.1063/1.1699752
[5]	DE VRIES D A. Thermal conductivity of soil[J]. Nature, 1956, 178: 1074. doi: 10.1038/1781074a0
[6]	HSU C T, CHENG P, WONG K W. Modified Zehner- Schlunder models for stagnant thermal conductivity of porous media[J]. International Journal of Heat and Mass Transfer, 1994, 37(17): 2751-2759. doi: 10.1016/0017-9310(94)90392-1
[7]	GORI F. A theoretical model for predicting the effective thermal conductivity of unsaturated frozen soils[C]// Proceedings of the fourth international conference on Permafrost, Fairbanks (Alaska). Washington D C: National Academy Press, 1983.
[8]	GORI F, CORASANITI S. Theoretical prediction of the soil thermal conductivity at moderately high temperatures[J]. Journal of Heat Transfer, 2002, 124(6): 1001-1008. doi: 10.1115/1.1513573
[9]	HSU C T, CHENG P, WONG K W. A lumped-parameter model for stagnant thermal conductivity of spatially periodic porous media[J]. Journal of Heat Transfer, 1995, 117(2): 264-269. doi: 10.1115/1.2822515
[10]	CHEN S X. Thermal conductivity of sands[J]. Heat and Mass Transfer, 2008, 44(10): 1241-1246. doi: 10.1007/s00231-007-0357-1
[11]	GORI F, CORASANITI S. New model to evaluate the effective thermal conductivity of three-phase soils[J]. International Communications in Heat and Mass Transfer, 2013, 47: 1-6. doi: 10.1016/j.icheatmasstransfer.2013.07.004
[12]	CORASANITI S, GORI F. Heat conduction in two and three-phase media with solid spherical particles of the same diameter[J]. International Journal of Thermal Sciences, 2017, 112: 460-469. doi: 10.1016/j.ijthermalsci.2016.10.022
[13]	CHU Z X, ZHOU G Q, WANG Y J, et al. A nalytical model for the stagnant effective thermal conductivity of low porosity granular geomaterials[J]. International Journal of Heat and Mass Transfer, 2019, 133: 994-1007. doi: 10.1016/j.ijheatmasstransfer.2018.12.167
[14]	JIA G, MA Z, CAO Y, et al. A new packed-sphere model for geological materials thermal conductivity prediction at moderate porosity range for geothermal utilization[J]. International Journal of Energy Research, 2019, 44: 9479 - 9493.
[15]	JIA G, MA Z, ZHANG Y P, et al. Series-parallel resistance method based thermal conductivity model for rock-soil with low or high porosity[J]. Geothermics, 2020, 84: 101742. doi: 10.1016/j.geothermics.2019.101742
[16]	曾召田, 吕海波, 赵艳林, 等. 广西红黏土热导率测试及理论预测模型研究[J]. 岩石力学与工程学报, 2017, 36(增刊1): 3525-3534. ZENG Zhaotian, LÜ Haibo, ZHAO Yanlin, et al. Study on thermal conductivity test and theoretical prediction model of Guangxi red clay[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(S1): 3525-3534. (in Chinese)
[17]	DONG Y, MCCARTNEY J S, LU N. Critical review of thermal conductivity models for unsaturated soils[J]. Geotechnical and Geological Engineering, 2015, 33(2): 207-221. doi: 10.1007/s10706-015-9843-2
[18]	CHEN S X. Thermal conductivity of sands[J]. Heat and Mass Transfer, 2008, 44(10): 1241-1246. doi: 10.1007/s00231-007-0357-1
[19]	ALBERT K, SCHULZE M, FRANZ C, et al. Thermal conductivity estimation model considering the effect of water saturation explaining the heterogeneity of rock thermal conductivity[J]. Geothermics, 2017, 66: 1-12. doi: 10.1016/j.geothermics.2016.11.006
[20]	LU S, REN T S, GONG Y S, et al. An improved model for predicting soil thermal conductivity from water content at room temperature[J]. Soil Science Society of America Journal, 2007, 71(1): 8. doi: 10.2136/sssaj2006.0041
[21]	肖琳, 李晓昭, 赵晓豹, 等. 含水率与孔隙率对土体热导率影响的室内实验[J]. 解放军理工大学学报(自然科学版), 2008, 9(3): 241-247. XIAO Lin, LI Xiaozhao, ZHAO Xiaobao, et al. Laroratory on influences of moisture content and porosity on thermal conductivity of soils[J]. Journal of PLA University of Science and Technology (Natural Science Edition), 2008, 9(3): 241-247. (in Chinese)
[22]	WHITFIELD J. Survival of the likeliest?[J]. Plos Biology, 2007, 5 (5): 962-965.
[23]	BEJAN A. Shape and Structure, from Engineering to Nature[M]. Cambridge: Cambridge University, 2000.
[24]	陈林根. 构形理论及其应用的研究进展[J]. 中国科学: 技术科学, 2012, 42(5): 505-524. CHEN Lin'gen. Research progress of configuration theory and its application[J]. Scientia Sinica (Technologica), 2012, 42(5): 505-524. (in Chinese)
[25]	MITARAI N, NORI F. Wet granular materials[J]. Advances in Physics, 2006, 55(1/2): 1-45.
[26]	LU N, DONG Y. Closed-form equation for thermal conductivity of unsaturated soils at room temperature[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2015, 141(6): 04015016. doi: 10.1061/(ASCE)GT.1943-5606.0001295
[27]	LU S, LU Y L, PENG W, et al. A generalized relationship between thermal conductivity and matric suction of soils[J]. Geoderma, 2019, 337: 491-497. doi: 10.1016/j.geoderma.2018.09.057
[28]	赵阳升. 岩体力学发展的一些回顾与若干未解之百年问题[J]. 岩石力学与工程学报, 2021, 40(7): 1297-1336. ZHAO Yangsheng. Retrospection on the development of rock mass mechanics and the summary of some unsolved centennial problems[J]. Chinese Journal of Rock Mechanics and Engineering, 2021, 40(7): 1297-1336. (in Chinese)
[29]	何雅玲. 前言: 祝贺过增元院士85华诞专辑[J]. 中国科学: 技术科学, 2021, 51(10): 1135-1136, 1132. HE Yaling. Preface: congratulations on the 85th birthday of academician GUO Zeng Yuan[J]. Scientia Sinica (Technologica), 2021, 51(10): 1135-1136, 1132. (in Chinese)