## 5 Conclusions  
Based on the theory of two-phase seepage, the theory of porous media seepage, and the principle of effective stress in porous media, a two-phase fluid-solid coupling mathematical model in saturated zone of subgrade considering the effects of fine particles migration is established. The mathematical model is numerically calculated with the software COMSOL Multiphysics(r). The two-phase seepage characteristics in saturated zone of the subgrade and the deformation characteristics of the solid skeleton are studied, and the following conclusions are obtained:  
Figure 22: (**a**) The relation curves of porosity change and cumulative volume fraction of fine particles; (**b**) the relation curves of porosity change and vertical displacement.  
Under the action of fluid seepage, the erosion and migration of the fine particles in saturated zone of subgrade gradually occurred, and the volume fraction of fine particles increased with the increase of time, and as the time goes on, only skeleton particles and particles with large sizes are left in the subgrade, the volume fraction of fine particles gradually decreased to the initial value. The constant erosion of fine particles inside the subgrade and the constant migration of fine particles with fluid from the lower part of the subgrade to the upper part of the subgrade caused that the volume fraction of fine particles in the upper part of the subgrade is larger than that in the lower part of the subgrade at the same time.  
With the increase of time, the porosity, the velocity of fluid, the velocity of fine particles, and the permeability of the subgrade show the trend of first increasing and then stabilizing; the pore water pressure in the subgrade has no significant changes with time.  
The vertical displacement is distributed symmetrically on the central axis of the subgrade. With the increase of time, the vertical displacement increases first and then decreases slightly and finally tends to be stable.  
For the filler with a larger initial volume fraction of fine particles, the maximum value of the volume fraction of fine particles in the subgrade caused by fluid seepage is larger, and the time required to reach the maximum value is shorter. It can be concluded that in actual engineering, the volume fraction of fine particles in the subgrade filler should be minimized on the premise so that the filler gradation meets the requirements of the specification.  
The main purpose of this research is to explore the characteristics of the two-phase seepage and the deformation of solid skeleton in saturated zone of the subgrade considering the effects of fine particles migration, in order to explain the internal mechanisms of the mud pumping disease. Therefore, the dynamic characteristics of the subgrade filler and the fluid-solid two-phase seepage characteristics considering the effects of fine particles migration and sedimentation under train loads have more practical engineering significance, which will also be the focus of the next research.  
Conceptualization, Y.D. and Y.J.; methodology, J.-s.Z., X.-b.C., and X.W.; software, F.M.; validation, Y.D. and Y.J.; formal analysis, Y.D.; investigation, Y.J.; resources, J.-s.Z.; data curation, Y.J.; writing--original draft preparation, Y.D.; writing--review and editing, Y.D.; visualization, Y.D.; supervision and project administration, J.-s.Z.; funding acquisition, X.-b.C. All authors have read and agreed to the published version of the manuscript.  
The research was funded by the National Natural Science Foundation of China under grant number CNNSF 51608533. The laboratory tests were partially supported by the China Railway Corporation Science and the Technology Development Project under grant number 2017G008-A.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.