# Deformation Law and Control Limit of CRTSIII Slab Track under Subgrade Frost Heave
## 6 Conclusions  
By establishing a nonlinear finite element model of CRTSIII slab track, the deformation characteristics of slab track under subgrade frost heave were studied. Further, a millimeter-level control limit of subgrade frost heave was proposed based on the relevant standards of high-speed railway slab track irregularity management. The following conclusions are drawn:  
1. The frost heave displacements of subgrade affects the deformation of its superstructure, leading in turn to cosine track irregularities. Because of the great stiffness of slab track, the amplitude transfer ratio will be greater than 1.0; that is, the deformation mapped to the rail surface will increase.
2. When subgrade frost heave occurs in the middle of the track slab, the track irregularity's change rate reaches the maximum value of 3.15, indicating the worst level of track irregularity. The track irregularity's change rate increases linearly in response to the increase in frost heave but decreases nonlinearly in response to the increase in frost heave wavelength.
3. The frost heave displacements of subgrade leads to the occurrence of interlayer seams between the track structures. Similarly, seam height and length are larger when frost heave acts on the middle section of the track slab. When the frost heave amplitude increases and the frost heave wavelength decreases, the seam length and height also increase. Finally, when the frost heave wavelength exceeds 28 m, it can be considered as having no seams between the self-compacting concrete and base plate.
4. When the frost heave amplitude increases, the seam height increases linearly whilst the seam length increases nonlinearly due to plastic damage of the concrete. In particular, when the frost heave amplitude reaches 35 mm, the concrete on the surface of the base plate produces plastic damage and cracks along the transverse direction, leading to a \"bending\" phenomenon.
5. Based on the relevant standards of slab track irregularity management, the critical values of interlayer seams between the self-compacting concrete and base plate have been selected as the main control indices of subgrade frost heave. Four corresponding wavelength limits (Grades I-IV) are 12 m, 16 m, 19 m and 23 m, respectively.
6. The contribution of this paper is to reveal the deformation transfer law of slab track and subgrade frost heave in a complex environment, to elucidate the occurrence and development law of interlayer seams and to obtain the four-level control limit value  
Figure 17: Control limit of subgrade frost heave based on static results.  
of subgrade frost heave. In practice, once the limit value is exceeded, maintenance workers can promptly carry out remedial work to prevent further deterioration of the track. The limit value of subgrade frost heave control proposed can provide references for new technologies in the design and construction of high-speed railway; it can also strengthen monitoring and timely maintenance during operation.  
Conceptualization, X.C.; software, Q.Z. and Y.Z.; validation, Y.Z. and Q.W.; investigation, Y.Z.; writing--original draft preparation, B.L.; writing--review and editing, Q.Z., Q.W. and A.L.; supervision, G.Y.; project administration, X.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (No. 51778050), the Project of Beijing Municipal Science & Technology Commission (Z191100002519010) and the Science & Technology Research and Development Project of China State Railway Group Corporation (No. P2019G029).  
Not applicable.  
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.