# Durability-Aimed Design Criteria of Cement-Stabilized Loess Subgrade for Railway
## 1 Introduction  
Loess has good strength and high compressive resistance, which has been widely used in the construction of railway subgrade. However, loess is sensitive to water, so it is prone to significant deformation and settlement after being immersed in water. Cement is usually used to improve the characteristics of loess [1, 2, 3, 4]. Besides, innovative recycled materials such as plastic and glass have been used in railway substructure [5, 6]. The strength of cement-stabilized loess gradually deteriorates under the action of wet-dry cycling, freeze-thaw cycling and repeated load because railway subgrade is exposed to the natural environment. Therefore, when designing the railway subgrade filling, the impact of environment and the train load on the subgrade should be considered to ensure the long-term strength, stability and durability of the subgrade. At present, as for stabilized soil, many engineering departments use unconfined compressive strength \(q_{\text{u}}\) as the strength index in China and other countries [7, 8, 9]. The actual experience of railway departments in China shows that it is safer to choose 7-day saturation strength as the strength of stabilized soil [10]. As for the durability of subgrade, many countries refer to the loss rate of mass or strength after 12 times of wet-dry and freeze-thaw cycling, according to the ASTM (American Society for Testing Material). However, the loss rate of strength after only 5 times of wet-dry and freeze-thaw cycling is used to control the durability of subgrade in China [11], and long-term stability under influences of wet-dry and freeze-thaw cycling is less considered. The strength design criteria of stabilized soil of subgrade bottom and embankment below the subgrade of all grades of the railway are shown in Table 1, which is provided by \"Code for Design of Railway Earth Structure\" [12]. In this study, several inter-city railways in Shaanxi, China, were selected for testing. The first selected loess was not immersed in water with a compaction level of 90%. Its minimum unconfined compressive strength was 420 kPa, which is 1.20 times the required critical strength (350 kPa) of the subgrade bottom. The second selected 8 types of cement-stabilized loess were saturated with water with 90% compaction level and 3% cement dosage. Its minimum 7-day unconfined compressive strength was 514 kPa, which is 1.47 times the required critical strength of the subgrade bottom. It can be seen that the design criteria in Table 1 cannot control the construction quality very well. In fact, the design criteria of filling can be determined by Equation (1) based on strength control. \[[q_{\text{u}}]\ \geq\sigma_{\text{dmax}} \tag{1}\]  
\[[q_{\text{u}}]=k_{\text{f}}\times\eta_{\text{G}}\times\eta_{\text{D}}\times q _{\text{u}} \tag{2}\]  
where  
\([q_{\text{u}}]\) is the strength considering the impact of the environment and train load on the subgrade filling, kPa;  
\(q_{\text{u}}\) is the strength without the impact of the environment and train load on the subgrade filling, kPa;  
\(\sigma_{\text{dmax}}\) is the maximum dynamic stress of subgrade, kPa;  
\(k_{\text{f}}\) is the fatigue reduction coefficient of the subgrade filling under repeated train load;  
\(\eta_{\text{G}}\) is the strength reduction coefficient of the subgrade filling under wet-dry cycling;  
\(\eta_{\text{D}}\) is the strength reduction coefficient of the subgrade filling under freeze-thaw cycling. The strength design criterion \(q_{\text{u}}\) of subgrade filling can be obtained by substituting Equation (2) into Equation (1). \[q_{\text{u}}\geq\sigma_{\text{d}}/(k_{\text{f}}\cdot\eta_{\text{G}}\cdot\eta _{\text{D}}) \tag{3}\]  
Two aspects should be considered when determining the strength design criteria of subgrade filling for the railway. One is \(\sigma_{\text{dmax}}\), and the other is \(\eta_{\text{G}}\) and \(\eta_{\text{D}}\). For dynamic stress, [PERSON] et al.