A Mathematical Model for the Analysis on the Injection and Distribution of Chemical Grout in Soils
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概要
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A mathematical model for analyzing the motion of chemical grout in soils has been developed in this paper. The proposed model combines the analysis of fluid flow and the mass transport of chemicals and lends itself to obtaining information on pressure distribution and concentration profile of the injected chemical grout in soils. The model employs the theory of miscible displacement in porous media and consists of two sets of governing differential equations which are solved for pressure head and concentration of the grout solution injected in the soils. The flow equation assumes transient grout permeation in deformable and saturated or unsaturated soil medium. It also takes the effect of density and viscosity variation of the grout into consideration. The transport equation expresses the dilution of injected grout due to dispersion (mechanical dispersion and molecular diffusion) and adsorption of chemicals during the permeation process. These equations exhibit nonlinear behavior in the solution of which requires advanced numerical procedures. For the solution of the flow equation the standard Galerkin scheme was applied but due to the domination of the convective term, an upstream weighted residual method was employed to yield oscillatory free solutions for the transport equation. An attempt was made to determine the optimal upstream weighting parameter for minimizing false dispersions typically observed in a convective-dominated transport equation. Using the proposed model and the resulting computer program, the chemical grout permeation process was analyzed for one- and three-dimensional spherical and cylindrical injection under various mechanical, hydraulic and geological conditions. The numerical results obtained were compared with the laboratory grouting experiments conducted on the equal geometrical and hydraulic conditions to validate the model. The results of this study are conducive to the assessment of chemical grout distribution in a soil mass and can serve as basis for the development of a rational and efficient design methodology for chemical grouting. It should be noted that the results and conclusions advanced in this study are applicable to other granular media and fractured rocks if the distribution of voids can be considered as uniform.
- 東海大学の論文
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