## 5 Conclusions  
In order to obtain the active earth pressure and its action law on the retaining structure under the limited \(c\)-\(\varphi\) soil condition, and to clarify the soil-wall interaction mechanism and the limited \(c\)-\(\varphi\) soil boundary width when the soil arching effect is significant, the theoretical method on the basis of previous studies was improved in this study. Four main conclusions are summarized as below:  
Figure 14: Influence of (**a**) \(B\) and (**b**) \(h\) on \(\sigma_{\text{wh}}\).  
Figure 15: Comparison of each parameters’ effects after standardization on (**a**) the standard resultant force and (**b**) its standard action point.  
* The effect of soil-wall cohesion can be expressed by the soil-wall friction angle. A double-fold line slip surface that considers the soil internal friction angle and the soil-wall friction angle was determined to be suitable for calculating the active earth pressure of a limited \(c\)-\(\varphi\) soil, and a symmetrical catenary arching curve was proposed to simulate the minor principal stress trajectory of a horizontal soil strip.
* An active earth pressure calculation model for a limited \(c\)-\(\varphi\) soil that considers ground surface overload was proposed based on the limit equilibrium method of a horizontal soil strip and the improved soil arching effect theory. The model proposed in this study can be simplified into the classic active earth pressure theory, and it reflects the situation for a limited \(c\)-\(\varphi\) soil better than other theoretical methods. The laterally active earth pressure coefficient of a limited \(c\)-\(\varphi\) soil is a function of burial depth, but it is independent of the limited soil width. The proposed active earth pressure distribution is large in middle and small at both ends, which is consistent with the results of the numerical simulation and the centrifuge model tests.
* An explicit boundary width for a limited \(c\)-\(\varphi\) soil during the active earth pressure calculation was determined. When the distance between the existing large rigid underground structure and the retaining wall of the foundation pit is within the boundary of the limited \(c\)-\(\varphi\) soil width, the active earth pressure model proposed in this study is needed for the calculation. However, the method proposed in this study is not suitable for situations where \(B<(2c\text{cot}\varphi)/(\gamma\text{cot}\delta)\) and \(c\text{cot}\varphi\geq qK_{\text{aw}}\).
* The changes in the active earth pressure due to the limited \(c\)-\(\varphi\) soil parameters were obtained. The factors that have the greatest influence on the resultant force and its action point are the soil internal friction angle and the soil cohesion separately. Thus, the influence of soil cohesion cannot be ignored. The smaller of the limited soil width, the more sensitive the active earth pressure to it. Increasing the wall friction and reducing the limited soil width can reduce the active earth pressure acting on the retaining wall. Reinforced measures should be taken on the upper part of the retaining wall when the ground surface is overloaded.  
Data curation, M.L.; methodology, X.C.; writing, M.L., X.C. and Z.H.; formal analysis, S.L. All authors have read and agreed to the published version of the manuscript.  
This research is supported by the National Natural Science Foundation of China (no. 51938008 and no. L1924061), the China Postdoctoral Science Foundation (no. 2019M660653) and the Special Project on the Integration of Industry, Education and Research of Guangdong Province (no. 192019071811500001).  
The authors declare no conflict of interest.