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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 1758651, 7 pages
Research Article

Modified Maag’s Spherical Diffusion Model of Vacuum Penetration Grouting

School of Engineering & Technology, China University of Geosciences, Beijing 100083, China

Correspondence should be addressed to Jianguo Lyu

Received 13 August 2017; Revised 11 December 2017; Accepted 25 December 2017; Published 21 January 2018

Academic Editor: Stefano de Miranda

Copyright © 2018 Feng Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The penetration grouting is very widely used in geotechnical engineering nowadays, but the slurry diffusion radius is not long enough because of low grouting pressure. The vacuum grouting method is proposed to solve this problem. However, there is no diffusion theory model of vacuum grouting, which makes the practical application lack scientific basis. In this paper, the distribution law of vacuum negative pressure in soil is deduced. Then, the boundary conditions of Maag’s spherical diffusion model are modified by the vacuum pressure distribution law. After that, the vacuum modification model is deduced. Finally, Maag’s model and modified model are analyzed according to a published experiment, which proves that the vacuum modification model is suitable for predicting the slurry diffusion of vacuum grouting. The proposed model provides a reference for the theoretical study of vacuum grouting.