_applied sciences_  
_Article_  
**Permanent Deformation and Its Unified Model of Coal Gangue Subgrade Filler under Traffic Cyclic Loading**  
**[PERSON] 1,2**, **[PERSON] 1, [PERSON] 3,*, [PERSON] 1 and [PERSON] 1**  
\begin{tabular}{l l}  & &  
surrounding landscape environment. Therefore, the effective utilization of coal gangue has great theoretical and practical significance.  
The effective utilization of coal gangue waste has always been a hot topic that concerns many scholars. The physical and chemical characteristics of coal gangue are similar to natural gravel, so coal gangue can be broken down into a coarse aggregate of concrete, which can decrease the exploitation of natural gravel but can also save costs and avoid a series of hazards caused by it [6; 7; 8]. Hence, the study on coal gangue concrete has been focused on by many scholars in recent years [9; 10], and the results indicate that the mechanical behaviors of coal gangue concrete, made by replacing a certain amount of gravel with coal gangue, are close to that of ordinary concrete of the same grade. [PERSON] et al. [11] investigated the effect of partial replacement of fly ash with natural loess on gangue-cemented paste backfill (GCPB) performance. Gangue-cemented paste backfill specimens with varying loess doses were produced, and then the rheological properties, macroscopic strength, and microstructural evolution of GCPB were examined. [PERSON] et al. [12] studied the activation and hydration mechanisms of composite activated coal gangue geopolymer, and the results show that coal gangue can be employed as a primary cementitious material after being modified by the proposed activation method. [PERSON] et al. [13] studied the influence of thermally activated coal gangue powder on the structure of the interfacial transition zone in concrete.  
However, compared with traditional concrete, the investigation of the coal gangue concrete still shows many deficiencies. The consumption of coal gangue used as subgrade filler is tremendous, which can effectively solve the problem of coal gangue accumulation. [PERSON] et al. [14] studied the effect of the compactive effort and initial particle gradings on the particle size distribution of mineral waste slag based on screening tests and analyzed the effects of different factors such as the compactive effort, moisture content, coarse grain content (CGC, mass proportion of particles with sizes greater than 5 mm), and forming methods on the engineering properties of mineral waste slag to determine the reasonable roadbed construction parameters. In addition, the research on coarse aggregate subgrade filler has a great reference value for coal gangue subgrade filler [15; 16; 17].  
As mentioned above, coal gangue is widely used as subgrade filler. The coal gangue subgrade is affected by the traffic dynamic loading in the actual environment. However, there is little research reporting the dynamic behaviors of coal gangue, especially considering coarse particles, used as subgrade filler under traffic cyclic loading. Hence, a series of cyclic triaxial tests was carried out using the LSDSTA to research the permanent deformation of CGSF (the maximum particle size is 60 mm) under cyclic loading. The purposes of this study are to (1) study the permanent deformation of coal gangue used as subgrade filler so as to realize resource utilization, (2) explore the effect of \(\sigma_{3}^{\prime}\), \(D_{f}\), and \(D_{c}\) on the permanent deformation to further understand the mechanical properties of CGSF, and (3) establish the unified model of permanent deformation in order to apply this to different types of permanent deformation.