## 1 Introduction
To restrict the cumulative deformation to a reasonable magnitude, predicting and evaluating the definite value or evolvement tendency of plastic deformation is needed in the first place. Two kinds of approaches are adopted to analyze the characteristics of cumulative deformation under cyclic load. The first is to develop numerical analysis model to predict the development law of cumulative deformation with increasing loading times [7; 8; 9; 10; 11; 12; 13]. This method aims at evaluating the final definite value of the plastic deformation. The other approach focuses on the evolutive states of plastic deformation [14; 15; 16; 17]. Deformation rate is plotted against loading times under different levels of cyclic load so that different plastic stages can be categorized in terms of tracing pattern. With the characteristics of deformation rate clearly classified, the tendency of plastic deformation can be evaluated. As mentioned above, the requirements of restricting the cumulative deformation of subgrade bed is extremely rigid. Especially, the post-construction deformation has been limited to millimeter-scale for the whole substructure and ground for high-speed railway. It seems to be quite difficult to use the first method to predict the definite value due to the extremely small plastic deformation compared with the height of substructure. Therefore, the second approach, which discusses the characteristics of deformation status against loading times, is more popular to predict plastic deformability. In the previous literature, several classifications of plastic deformation tendency have been put forward on a basis of characteristics of deformation rate. [PERSON] [18] and [PERSON] [19] have performed triaxial cyclic loading tests on London clay and Chengdu clay, respectively, and obtained cumulative plastic deformation curve plotted against loading times. They classified the curves into generative pattern and degenerative one, which represents ever-increasing and converging plastic deformation respectively. Obviously, only two states, the steady state and the collapse one, are identified in their framework. [PERSON] [15] has conducted 100 groups of triaxial tests at different stress levels on graded gravel and sandy gravel. Based on the evolving law of cumulative plastic deformation rate, the state of plastic strain has been divided into three categories, i.e., plastic shakedown, plastic creep, and exacerbation. Plastic shakedown implies that plastic strain of fillings tends to a certain value under some cyclic loading level and plastic deformation rate gradually decreased to zero. Meanwhile, exacerbation represents that the deformation rate is continuously increased under cyclic loading, and soil structure is rapidly collapsed with just a few loading times. It should be noted that there is a transitional state termed as plastic creep. In this state, cumulative deformation rate decreases in initial loading stage, and then levels off with the increasing loading times. At the same time, plastic strain is almost linearly increased with loading times, which finally leads to the soil structure broken down. [PERSON] [20] also classified the evolving tendency of plastic deformation under cyclic loading into three groups, i.e., stable state, critical state, and unstable state. However, stability of critical state is ambiguous and need further discussion. In addition, [PERSON] et al. [21] concluded that only elastic strain exists on the condition of small magnitude of cyclic loading. With the increasing loading level, plastic deformation emerges but finally converges to a stable state. When cyclic loading remains relatively large, plastic strain is accumulated and finally makes soil structure break down. Summarily, two ultimate states, which are the stable one that only elastic strain can be observed at low cyclic loading level and the collapsed one that cumulative deformation continuously develops at high loading amplitude, exactly exist.