## 7 Discussion  
This study is the first attempt to apply the twin-shear unified strength theory to calculate the seismic active earth pressure under limited backfill. The influence of a curved slip surface is also considered, which has very important theoretical significance for the seismic earth pressure of limited backfill and the subsequent 3D earth pressure research. In the parameter sensitivity and comparative analysis, the earth pressure distribution form, the intermediate principal stress, the seismic coefficient, and the wall-soil friction angle were discussed.  
The horizontal earth pressure presented a \"convex\" nonlinear distribution, which is consistent with the measured results obtained from the shaking-table test of a retaining structure by [PERSON] and [PERSON] [24]. [PERSON] et al. [40] also carried out theoretical research on seismic active earth pressure and obtained the same distribution form based on a semi-infinite space assumption. However, these previous studies did not comprehensively consider the effects of limited backfill width, intermediate principal stress, and soil arching effects. Therefore, there are still some obvious deviations between the results obtained in this research and previous studies, mainly in the middle and lower parts of the retaining structure. Nevertheless, the overall trend is consistent, and they are all different from the linear distribution of the classical Mononobe-Okabe theory [3,4] or a simple extension of it [22], indicating that the method proposed in this paper is reasonable. The seismic active earth pressure gradually decreased with the intermediate principal stress weight coefficient, by up to 22.96%. This indicates that the intermediate principal stress has a positive effect on further exerting the strength limit of the material, which presents good agreement with previous earth pressure studies considering the intermediate principal stress [32,33]. The lateral earth pressure coefficient \(K\) deduced in this paper was affected by the vertical seismic coefficient \(k_{v}\). \(K\) gradually decreased with \(k_{v}\), which is different from the research by [PERSON] and [PERSON] [23] on the influence of the horizontal seismic coefficient on the earth pressure coefficient. The resultant force action point \(h_{a}\) increased nonlinearly with the wall-soil friction angle \(\delta\), which also indirectly indicates that \(h_{a}\) is significantly affected by the soil arching effects. It is worth noting that \(h_{a}\) began to be greater than the classic resultant force action point \(H/3\) when \(\delta/\varphi_{0}>0.55\). The anti-overturning stability should be strengthened in retaining structure design.  
It should be pointed out that the earth pressure is an approximate calculation. Regardless of which theory is adopted, there will still be a substantial difference between the theoretical value and the actual situation. In addition, the method proposed in this paper is a generalized model. From the perspective of safety, it assumes that the logarithmic spiral angle at the bottom of the retaining structure is \(\theta_{a}=\pi/2+\varphi_{t}-\theta_{cr}\), which makes the formula in this paper have certain limitations--that is, the critical width of the limited backfill under the curved slip surface cannot be given. At present, measurement data on the seismic earth pressure of soil with a limited width is very scarce. The formulas in this study need to be further verified and improved by many experiments in the future.  
Figure 10: Comparison of active earth pressure in previous studies.