# Current Practices of Railway Ballastless Track Design Methods in China
## 2 Ballastless Track Structure Design Method
### Limit State Method  
The LSM analyzes, evaluates and controls the structure based on its performance under the limit state. It takes the limit state that prevents the structure or sections from reaching the requirements of certain functions as the basis and can ensure the safety and reliability of the structure under extreme loads and severe conditions. Theoretically, the LSM is more advanced than the ASM [35]. According to the Code for the Design of Railway Tracks (Limit State Method) (Q/CR 9130-2018) [31], the main process of the limit state method is shown in Figure 4.  
Figure 3: Force balance calculation diagram for allowable stress method.  
According to the specification [31], the loads considered in the LSM are similar to those of the ASM.  
The determination of the temperature gradient load, bulk temperature load, bridge defection load and subgrade settlement load of the LSM are same as those of the ASM. However, the train loads of the two methods have some differences. For the LSM, according to the specification [31], the vertical load and lateral load adopt the standard value. The calculation method is as follows:  
The standard value of the vertical train load is as follows:  
\[P_{k}=2\cdot P_{j} \tag{7}\]  
which is double the static wheel weight in any working condition.  
The standard value of the lateral train load is expressed as:  
\[Q_{k}=0.8\cdot P_{j} \tag{8}\]  
In Figure 4, \(M_{dk}\), \(M_{dk}\), \(M_{tk}\), \(M_{n\
eq k}\) and \(M_{cjk}\) are the standard values of moment effects under train load, temperature gradient load, bulk temperature load, bridge defection load and subgrade settlement load, which can also be calculated using the formula or FEM.  
For unit structures and piecewise structures, the combination of moment effect \(M\) is calculated as a basis of reinforcement, and the combination methods include fundamental combination, accidental combination and standard combination. But for longitudinal connected structure, the load effect is considered in the form of axial force \(F\) with a different calculation system, which is not introduced in this paper, and more details can be found in the specification [31].  
Figure 4: Design process of limit state method.  
Similar to the ASM, for unit structures, the train load, temperature gradient load, bridge defection load or subgrade settlement load are considered. For piecewise structures, the bulk temperature load (including concrete shrinkage load) should also be considered.  
Different from the ASM, which uses the safety factor \(K\) as the only and unified factor to create safety allowance, the LSM uses the partial coefficient \(\gamma\) and load combination factor \(\psi\) in effect combination to consider the structural failure probability under different limit states. The combination formulas are shown in Figure 4, and the specific parameter values are defined in the specification [31].  
The calculation for the reinforcement of the limit state depends on the principle that combination effect \(M\) should be no more than the resistance of structure \(M_{R}\), which is mainly afforded by the steel bar in tension and the concrete in compression. Different from the ASM, when calculating \(M_{R}\), the reinforced concrete material is converted to homogeneous concrete material using an equivalent method, and the height of the compression zone after conversion is \(x\). The meanings of other parameters are shown in Figure 5. According to force balance, the cross-sectional area of the steel bar \(A_{s}\) is preliminary calculated.  
When calculating the reinforcement according to the LSM, the effect combination should take the larger value between the fundamental combination and the accidental combination, and the result should be verified by the maximum height of compression zone and the minimum reinforcement ratio. What is more, it is necessary to check the crack limit using the standard combination effect. Finally, the result that meets all these criteria will be the final reinforcement scheme.