基于Kozeny-Carman方程的酶诱导碳酸钙沉淀固化砂土的渗流数学模型

doi:10.16285/j.rsm.2024.1135

岩土力学 ›› 2025, Vol. 46 ›› Issue (8): 2376-2386.doi: 10.16285/j.rsm.2024.1135CSTR: 32223.14.j.rsm.2024.1135

基于Kozeny-Carman方程的酶诱导碳酸钙沉淀固化砂土的渗流数学模型

靳贵晓^{1, 2}，林劭聪²，姜启武^{3, 4}，黄明^{3, 4}，李熹⁵

1. 福建理工大学生态环境与城市建设学院，福建福州 350118；2. 福建理工大学土木工程学院，福建福州 350118； 3. 福州大学土木工程学院，福建福州 350108；4. 武汉大学土木建筑工程学院，湖北武汉 430072； 5. 福州市建设发展集团有限公司，福建福州 350014

收稿日期:2024-09-13 接受日期:2024-12-02 出版日期:2025-08-11 发布日期:2025-08-14
通讯作者: 姜启武，男，1999年生，博士研究生，主要从事微生物岩土工程方面的研究。E-mail：2024102100022@whu.edu.cn
作者简介:靳贵晓，女，1984年生，博士，副教授，主要从事环境岩土工程方面的研究工作。E-mail：jinguixiao2008@126.com
基金资助:
国家自然科学基金（No. 41972276，No. 52378392）；国家特支人才项目（No. 00387088）；福建省科技计划引导项目（No. 2024H0020）。 This work was supported by the National Natural Science Foundation of China (41972276，52378392), the National Special Support Talent Project of China (00387088) and the Science and Technology Plan Guidance Project of Fujian Province (2024H0020).

Seepage mathematical model of enzyme-induced calcium carbonate precipitation-treated sandy soil based on the Kozeny-Carman equation

JIN Gui-xiao^{1, 2}, LIN Shao-cong², JIANG Qi-wu^{3, 4}, HUANG Ming^{3, 4}, LI Xi⁵

1. School of Ecological Environment and Urban Construction, Fujian University of Technology, Fuzhou, Fujian 350118, China; 2. School of Civil Engineering, Fujian University of Technology, Fuzhou, Fujian 350118, China; 3. College of Civil and Engineering, Fuzhou University, Fuzhou, Fujian 350108, China; 4. School of Civil Engineering, Wuhan University, Wuhan, Hubei 430072, China; 5. Fuzhou City Construction Development Group Co., Ltd., Fujian, Fuzhou 350014, China

Received:2024-09-13 Accepted:2024-12-02 Online:2025-08-11 Published:2025-08-14

摘要/Abstract

摘要： 目前关于酶诱导碳酸钙沉淀（enzyme-induced calcium carbonate precipitation，EICP）技术固化砂土的渗流数学模型研究较少，现有的渗流模型未考虑EICP矿化反应中生成的碳酸钙晶体，难以预测EICP固化砂土的渗透性能。为此，基于Kozeny-Carman（K-C）方程，考虑碳酸钙晶体对孔隙填充作用、迂曲度和比表面积的影响，建立EICP固化砂土的渗流数学模型。将模型理论结果与试验结果进行对比，验证了模型的可行性和合理性，分析了孔隙率、平均粒径、碳酸钙含量和比表面积对试样渗透系数的影响。研究结果表明：提出的渗流数学模型能较好地反映不同颗粒级配以及不同胶结程度条件下EICP固化砂土的渗透系数，适用范围较广；渗透系数k 随孔隙率n 和平均粒径D₅₀的增加而增大，k 对n的敏感性远高于D₅₀；k随碳酸钙含量和比表面积的增加而显著下降。随着碳酸钙含量的增加，试样孔隙率逐渐下降，迂曲度逐渐增加，附着于碳酸钙晶体的水膜逐渐变厚，渗透系数显著下降。研究成果可为EICP固化砂土的工程应用提供一定的理论基础。

关键词: 酶诱导碳酸钙沉淀（EICP）, Kozeny-Carman方程, 碳酸钙晶体, 渗流模型, 砂土固化

Abstract: There is currently a limited amount of research on mathematical models for seepage in enzyme-induced calcium carbonate precipitation (EICP) solidified sand. Existing seepage models neglect the influence of calcium carbonate crystals formed during the EICP mineralization process, thereby rendering them insufficient in predicting the permeability behavior of EICP-solidified sand. To address this issue, this study establishes a mathematical model for seepage in EICP-solidified sand based on the Kozeny-Carman (K-C) equation, incorporating the effects of calcium carbonate crystals on pore filling, tortuosity, and specific surface area. By comparing the theoretical results of the model with experimental data, the feasibility and rationality of the model are validated. Furthermore, the impact of porosity, mean particle size, calcium carbonate content, and specific surface area on the permeability coefficient of the samples is analyzed. The research findings indicate that: 1) The proposed mathematical seepage model can effectively represent the permeability coefficient of EICP-solidified sand under various particle size distributions and cementation degrees, demonstrating broad applicability. 2) The permeability coefficient (k) increases with the rise in porosity (n) and mean particle size (D₅₀), with k being more sensitive to changes in porosity than mean particle size. 3) The permeability coefficient decreases significantly with increasing calcium carbonate content and specific surface area. As calcium carbonate content increases, the sample porosity gradually decreases, tortuosity increases, and the water film adhering to the calcium carbonate crystals thickens, leading to a substantial drop in permeability coefficient. The results of this study provide a theoretical foundation for the engineering application of EICP-solidified sand.

Key words: enzyme-induced calcium carbonate precipitation (EICP), Kozeny-Carman equation, calcium carbonate crystals, seepage modeling, sand solidification

中图分类号: TU 42

靳贵晓, 林劭聪, 姜启武, 黄明, 李熹, . 基于Kozeny-Carman方程的酶诱导碳酸钙沉淀固化砂土的渗流数学模型[J]. 岩土力学, 2025, 46(8): 2376-2386.

JIN Gui-xiao, LIN Shao-cong, JIANG Qi-wu, HUANG Ming, LI Xi, . Seepage mathematical model of enzyme-induced calcium carbonate precipitation-treated sandy soil based on the Kozeny-Carman equation[J]. Rock and Soil Mechanics, 2025, 46(8): 2376-2386.

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基于Kozeny-Carman方程的酶诱导碳酸钙沉淀固化砂土的渗流数学模型

Seepage mathematical model of enzyme-induced calcium carbonate precipitation-treated sandy soil based on the Kozeny-Carman equation

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