基于凝胶分形模型膨润土侵蚀质量的计算方法

徐永福

doi:10.11779/CJGE202004016

基于凝胶分形模型膨润土侵蚀质量的计算方法 English Version

徐永福^{1, 2,}

1.
上海交通大学土木工程系,上海　200030
2.
皖江工学院,安徽　马鞍山　243000

基金项目:

国家自然科学基金项目 41630633

国家自然科学基金项目 41877211

安徽省自然科学基金项目 1808085MD106

详细信息

作者简介:
徐永福(1967—),男,江苏泰兴人,博士,教授,从事分形介质力学､非饱和（特殊）土力学和地基处理的研究。E-mail: yongfuxu@sjtu.edu.cn

中图分类号: TU471
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出版历程
- 收稿日期: 2019-05-19
- 网络出版日期: 2022-12-07
- 刊出日期: 2020-03-31

Calculation of erosion mass of bentonite based on fractal model for colloids

XU Yong-fu^{1, 2,}

1.
Department of Civil Engineering, Shanghai Jiaotong University, Shanghai 200030, China
2.
Wanjiang Institute of Technology, Maanshan 243000, China

摘要

摘要: 地下水沿围岩裂隙对高放废物地质处置库膨润土缓冲/回填层产生侵蚀作用,膨润土的侵蚀质量与地下水流量密切相关。不同于砂粒,膨润土以凝胶形式赋存于地下水中,形成悬浊液。膨润土凝胶具有分形结构,基于膨润土凝胶的分形结构,导出膨润土的侵蚀质量（m_s）与地下水流量（V_w）的理论关系,表示为 $m_{s} = β V_{w}^{α}$ ,指数 $α$ 表示为膨润土凝胶分维（D）的函数, $α = D / (6 - D)$ 。采用Börgesson等和Suzuki等对MX-80膨润土的侵蚀试验结果,验证膨润土的侵蚀质量与地下水流量的理论关系。膨润土凝胶的分维根据Svensson等的X-射线小角度衍射结果计算,膨润土在不同浓度NaCl溶液中的侵蚀质量与盐溶液流量的关系都符合基于膨润土凝胶分形模型的理论关系。
- 膨润土 /
- 侵蚀质量 /
- 流量 /
- 凝胶 /
- 分维
Abstract: The water inflow into the deposition holes and tunnels in a repository will mainly take place through fractures in the rock and will lead to that the buffer and backfill will be wetted and eroded. If the counter pressure and strength of the buffer or backfill are insufficiently high, piping erosion will take place. An erosion model to estimate the erosion mass (m_s) of bentonite buffer in saline solution for a certain water inflow rate during a certain time based on the fractal model for bentonite colloids is proposed as $m_{s} = β V_{w}^{α}$ , in terms of a power law, V_w is the accumulated volume of water flow. The exponent parameter (α) is related to the fractal dimension (D) of bentonite colloids as $α = D / (6 - D)$ . The relationship between the erosion mass (m_s) and the accumulated volume of water flow (V_w) is verified by the experiments of MX-80 bentonite piping erosion in NaCl solutions by Börgesson et al and Suzuki et al. The fractal dimension (D) of bentonite colloids is calculated according to the small-angle X-ray scattering (SAXS) of MX-80 bentonite by Svensson & Hansen (2013).
- bentonite /
- erosion mass /
- accumulated volume of water flow /
- colloid /
- fractal dimension

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图 1 膨润土侵蚀迁移示意图^[8]

Figure 1. Schematic illustration for the processes of bentonite erosion^[8]

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图 2 膨润土侵蚀引起膨胀力衰减现象^[11]

Figure 2. Reduction of expansive pressure due to bentonite erosion

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图 3 膨润土凝胶的分形结构示意图^[31]

Figure 3. Schematic illustration of fractal bentonite colloids

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图 4 MX-80膨润土凝胶的分维^[32]

Figure 4. Fractal dimension of MX-80 bentonite colloids ^[32]

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图 5 MX-80膨润土侵蚀质量预测结果^[19]

Figure 5. Prediction of MX-80 bentonite erosion mass^[19]

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图 6 MX-80膨润土侵蚀质量预测结果^[16]

Figure 6. Prediction of MX-80 bentonite erosion mass^[16]

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表 1 典型黏土凝胶的分维

Table 1 Fractal dimension of clay colloids

材料	性状	测试方法	D	文献
Kunigel V1膨润土		膨胀变形试验	2.15	[23]
MX-80膨润土	蒸馏水	X射线小角度衍射	2.92	[32]
	1% NaCl溶液		2.29
	2% NaCl 溶液		2.09
	3.5% NaCl溶液		1.81
膨润土	粒径0.6 μm	沉淀试验	2.13	[33]
高岭石	粒径2.0 μm		2.35
磷酸酯	粒径12.0 μm		2.21
钻孔泥浆	粒径6 μm		1.52-1.59	[34]
硅粉			1.75	[35]

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参考文献(35)

[1]	XU Y F, JIANG H, CHU F F, et al. Fractal model for surface erosion of cohesive sediments[J]. Fractals, 2014, 22(3): 1440006. doi: 10.1142/S0218348X14400064
[2]	XU Y F. Peak shear strength of compacted GMZ bentonites in saline solution[J]. Eng Geol, 2019, 251: 93-99. doi: 10.1016/j.enggeo.2019.02.009
[3]	徐永福, 孙德安, 董平. 膨润土及其与砂混合物的膨胀试验[J]. 岩石力学与工程学报, 2003, 22(3): 451-451. doi: 10.3321/j.issn:1000-6915.2003.03.022 XU Yong-fu, SUN De-an, DONG Ping. Swelling tests on bentonite and sand-bentonite mixture[J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(3): 451-451. (in Chinese) doi: 10.3321/j.issn:1000-6915.2003.03.022
[4]	叶为民, 黄伟, 陈宝, 等. 双电层理论与高庙子膨润土的体变特征[J]. 岩土力学, 2009, 30(7): 1899-1904. doi: 10.3969/j.issn.1000-7598.2009.07.004 YE Wei-min, HUANG Wei, CHEN Bao, et al. Diffuse double layer theory and volume change behavior of densely compacted Gaomiaozi bentonite[J]. Rock and Soil Mechanics, 2009, 30(7): 1899-1904. (in Chinese) doi: 10.3969/j.issn.1000-7598.2009.07.004
[5]	秦冰, 陈正汉, 刘月妙, 等. 高庙子膨润土的胀缩变形特性及其影响因素[J]. 岩土工程学报, 2008, 30(7): 1005-1010. doi: 10.3321/j.issn:1000-4548.2008.07.010 QIN Bing, CHEN Zheng-han, LIU Yue-miao, et al. Swelling-shrinkage behaviour of Gaomiaozi bentonite[J]. Chinese Journal of Geotechnical Engineering, 2008, 30(7): 1005-1010. (in Chinese) doi: 10.3321/j.issn:1000-4548.2008.07.010
[6]	孙德安, 张龙. 盐溶液饱和高庙子膨润土膨胀特性及预测[J]. 岩土力学, 2013, 34(10): 2790-2795. doi: 10.16285/j.rsm.2013.10.035 SUN De-an, ZHANG Long. Swelling characteristics of Gaomiaozi bentonite saturated by salt solution and their prediction[J]. Rock and Soil Mechanics, 2013, 34(10): 2790-2795. (in Chinese) doi: 10.16285/j.rsm.2013.10.035
[7]	张虎元, 贾灵艳, 周浪. 高效废物处置库的混合型缓冲回填材料压缩特性研究[J]. 岩土力学, 2013, 34(6): 1546-1552. doi: 10.16285/j.rsm.2013.06.037 ZHANG Hu-yuan, JIA Ling-yan, ZHOU Lang. Compression behaviors of compacted bentonite-sand mixtures as buffer material for HLW disposal[J]. Rock and Soil Mechanics, 2013, 34(6): 1546-1552. (in Chinese) doi: 10.16285/j.rsm.2013.06.037
[8]	BAIK M H, CHO W J, HAHN P S. Erosion of bentonite particles at the interface of a compacted bentonite and a fractured granite[J]. Eng Geol, 2007, 91: 229-239. doi: 10.1016/j.enggeo.2007.02.002
[9]	XU Y F. Approach to the erosion threshold of cohesive sediments[J]. Ocean Engineering, 2019, 172: 183-190. doi: 10.1016/j.oceaneng.2018.11.036
[10]	XU Y F, GAO Z R, CHU F F, et al. Fractal model for erosion mass of bentonite colloids[J]. Environ Earth Sci, 2016, 75: 1330. doi: 10.1007/s12665-016-6101-8
[11]	XU Y F, LI X Y. Fractal approach to erosion threshold of bentonites[J]. Fractals, 2018, 26(2): 1840012. doi: 10.1142/S0218348X18400121
[12]	BIRGERSSON M, BÖRGESSON L, HEDSTRÖM K, et al. Bentinite Erosion[R]. Stockholm, SKB TR-09-34, Swedish Nuclear Fuel and Waste Management Co., 2009.
[13]	SKB. Detailed Program for Research and Development 1999-2004[R]. Stockholm: Swedish Nuclear Fuel and Waste Management Co., 1998.
[14]	POSIVA Oy. TKS-2009 Nuclear Waste Management at Olkiluoto and Loviisa Power Plants: Review of Current Status and Future Plans for 2010-2012[R]. 2010.
[15]	徐永福. 高放废物地质处置库中膨润土的侵蚀机理和模型研究综述[J]. 地球科学进展, 2016, 32(10): 1050-1061. doi: 10.11867/j.issn.1001-8166.2017.10.1050 XU Yong-fu. Mechanisms and models for bentonite erosion used for geologic disposal of high level radioactive waste: a review[J]. Advances in Earth Science, 2017, 32(10): 1050-1061. (in Chinese) doi: 10.11867/j.issn.1001-8166.2017.10.1050
[16]	BÖRGESSON L, SANDÉN T. Piping and Erosion in Buffer and Backfill Materials[R]. Clay Technology AB, SKB R-06-80, Svensk Kärnbränslehantering AB, 2006.
[17]	JANSSON M. Laboratory Studies of Bentonite Erosion[R]. Report, Nuclear Chemistry, Royal Institute of Technology, KTH, Stockholm, 2009.
[18]	SANE P, LAURILA T, OLIN M, et al. Current Status of Mechanical Erosion Studies of Bentonite Buffer[R]. POSIVA 2012-45, 2012.
[19]	SUZUKI K, ASANO H, YAGAG R. Experimental investigations of piping phenomena in bentonite-based buffer materials for an HLW repository[J]. Clay Miner, 2013, 48: 363-382. doi: 10.1180/claymin.2013.048.2.15
[20]	XU Y F, JIANG H, CHU F F, et al. Fractal model for surface erosion of cohesive sediments[J]. Fractals, 2014, 22(3): 1440006. doi: 10.1142/S0218348X14400064
[21]	SCHAEFER D W, MARTIN J E, WILTZIUS P, et al. Fractal geometry of colloidal aggregates[J]. Phys Rev Lett, 1984, 52(26): 2371-2375. doi: 10.1103/PhysRevLett.52.2371
[22]	FRANKS G V, ZHOU Y, YAN Y-D, et al. Effect of aggregate size on sediment bed rheological properties[J]. Phys Chem Chem Phys, 2004, 6: 4490-4498. doi: 10.1039/b402580f
[23]	XU Y F, XIA X H. Fractal model for virgin compression of pure clays[J]. Mech Res Commun, 2006, 33: 206-216. doi: 10.1016/j.mechrescom.2005.06.008
[24]	AUBERT C, CANNELL D S. Restructuring of colloidal silica aggregates[J]. Phys Rev Lett, 1986, 56: 738. doi: 10.1103/PhysRevLett.56.738
[25]	SINKÓ K, TORMA V, KOVÁCS A. SAXS investigation of porous nanostructures[J]. J of Non-Crystalline Solids, 2008, 354: 5466-5474. doi: 10.1016/j.jnoncrysol.2008.08.021
[26]	WOIGNIER T, PHALIPPOU J, VACHER R, et al. Different kinds of fractal structures in silica aerogels[J]. J of Non-Crystalline Solids, 1990, 121: 198-201. doi: 10.1016/0022-3093(90)90131-5
[27]	COURTENS E, VACHER R. Porous silica[M]//THORPE M F, MITKOVA M I. Amorphous Insulators and Semiconductors, NATO ASI Series, 3 High Technology, Kluwer Academic Publishers, 1997: 255-288.
[28]	ZHOU Y, FRANKS G V. Flocculation mechanism induced by cationic polymers investigated by light scattering[J]. Langmuir, 2006, 22: 6775-6786. doi: 10.1021/la060281+
[29]	XI Y, CHEN J J, XU Y F, et al. Yield stress of fractal aggregates[J]. Fractals, 2015, 23(3): 1550028. doi: 10.1142/S0218348X15500280
[30]	MEAKIN P. Fractal aggregates[J]. Advances in Colloid and Interface Sci, 1988, 28: 249-331.
[31]	KRONE R B. A Study of Rheologic Properties of Estuarial Sediments[R]. U.S. Army Corps of Engineers Committee on Tidal Hydraulics Technical Bulletin No. 7, Vicksburg, MS, 1963.
[32]	SVENSSON P D, HANSEN S. Combined salt and temperature impact on monmorillonite hydration[J]. Clays and Clay Minerals, 2013, 61(4): 328-341. doi: 10.1346/CCMN.2013.0610412
[33]	KLIMPEL R C, HOGG R. Evaluation of floc structures[J]. Colloids and Surf, 1991, 55: 279-288. doi: 10.1016/0166-6622(91)80099-A
[34]	HUANG H. Porosity-size relationship of drilling mud flocs: fractal structure[J]. Clays and Clay Minerals, 1993, 41: 373-379. doi: 10.1346/CCMN.1993.0410314
[35]	SCHAEFER D W, MARTIN J E, WILTZIUS P, et al. Fractal geometry of colloidal aggregates[J]. Phys Rev Lett, 1984, 52: 2371-2374. doi: 10.1103/PhysRevLett.52.2371