## 5 Conclusions  
A model is constructed with 0.49 m\({}^{2}\) in cross-sectional area and 0.9m in height. The fillings of the model are mainly composed of angular gravels, which are commonly adopted to construct subgrade bed in railway engineering. Cyclic load is applied by the hydraulic-driven loading system to simulate the train load, and deformations of model filling are monitored in real time by eddy current displacement transducers. The conclusions can be drawn from the model test as follows:  
(1) Both elastic and plastic deformations are produced in the loading process, while only elastic deformation is recoverable in the unloading process. Thus, plastic deformation is accumulated continuously with the effect of cyclic loading. For a given model with certain compaction degree, the development of plastic deformation is significantly affected by the amplitude of cyclic load. The accumulative deformation tends to converge towards a constant value when cyclic amplitude stays at a relatively low level, and is inclined to develop continuously when the amplitude is high enough to make the filling structure break down. (2) With the effect of a given level of cyclic amplitude, models with different compaction degree as well as bearing capacity have quite different evolving characteristics of plastic deformation. An appropriate cyclic amplitude may lead to convergence of plastic deformation for a model with a lower compaction degree, but result in divergence of accumulative settlement for another model with a higher compaction degree. (3) A power function is introduced to investigate the evolving characteristics of plastic deformation rate to subdivide both convergence and divergence status of accumulative deformation. The power function can be expressed as \({v^{\prime}}_{1}=CN^{-m}\). The comprehensive evaluation coefficient \(C\) is an indicator of averaged plastic deformation rate under a given cyclic amplitude. As cyclic amplitude level \(P_{d}/P_{cr}\) increases, the value of \(C\) is also exponentially increased. Thus, the parameter \(C\) can be evaluated with \(P_{d}/P_{cr}\) known. (4) The developing tendency coefficient \(m\) in the power function is a more critical parameter to describe the evolving characteristics of plastic deformation rate. The value of \(m\) shows a sigmoidal curve when plotted against loading times. Subdivision of convergence and divergence status for plastic deformation, which is of great significance to the design of subgrade bed for both ballasted and unballasted railway, can be realized by the analysis of the parameter \(m\). (5) The evolving characteristics of plastic deformation can be classified into four different patterns in terms of the developing tendency coefficient \(m\). The four patterns are rapid stabilization, tardy stabilization, tardy failure, and rapid failure, with \(m\) = 1.5, \(m\) = 0.7\(\sim\)1.0, and \(m\) = 0.4 as boundaries. It should be noted that the three boundaries are corresponding to the cyclic amplitude level \(P_{d}/P_{cr}\) = 0.05, \(P_{d}/P_{cr}\) = 0.15-0.20, and \(P_{d}/P_{cr}\) = 0.6, respectively. The cyclic amplitude level when horizontal displacement starts to increase sharply is quite close to the boundary of \(P_{d}/P_{cr}\) = 0.6 from tardy failure to rapid failure. Such an amplitude level implies that filling structure completely breaks down. (6) Since ballasted railway has a better adaptive capacity for deformation compared to the unballasted one, the requirement for limiting value of plastic deformation should be different for these two types of railways. Plastic deformation of subgrade bed in unballasted railway should locate in the rapid stabilization zone, while plastic deformation in ballasted railway should be controlled to fall into the tardy stabilization zone. Such a principle will provide warranty for both economical construction and enduring service for high-speed railway. **Author Contributions:** Conceptualization, G.L. and Q.L. ; methodology, M.Z. and G.L. ; formal analysis, L.G. and M.Z. ; investigation, G.L. and H.J.