## 5 Conclusions  
In this study, a true triaxial orthogonal test was conducted on frozen calcareous clay to explore its strength change characteristics under the influence of multiple factors, including the degree of influence of each factor. The following conclusions were drawn from the results:  
1. The characteristics of the stress-strain curve of frozen calcareous clay could be divided into three stages: the strain was within 0.5%, showing linear elasticity, and under the effect of pressure, the ice crystals, and their cements were damaged or compressed, and they shrink; at approximately 5%, they showed plastic hardening. The soil particles and ice crystals in the frozen soil recombined and became denser, resulting in irreversible deformation. With the compression process, cracks bred and expanded. The failure stage was manifested as strain hardening due to the test loading conditions. As the deformation increased, the stress also slightly increased. In this stage, the soil sample was squeezed out, and the volume deformation could not represent its true change.
2. Through analytic hierarchy process, the peak stress \(\sigma_{1}\) of each factor under four levels was quantitatively calculated, and the maximum value of influence weight of \(\sigma_{1}\) was A\({}_{4}\) = 0.0431; B\({}_{1}\) = 0.0826; C\({}_{2}\) = 0.0206; and D\({}_{4}\) = 0.1338; E\({}_{4}\) = 0.0289, the maximum and minimum weight was 0.1338 and 0.0197, respectively, and the optimal level was A\({}_{4}\)B\({}_{1}\)C\({}_{2}\)D\({}_{4}\)E\({}_{4}\). By comparing the sum of the weights of the four levels of each factor, the order of primary and secondary influence consistent with the range method was obtained, which was D \(>\) B \(>\) A \(>\) E \(>\) C. Similarly, the maximum and minimum weight of \(\sigma_{2}\) was 1.2239 and 0.014, respectively, and the order of \(\sigma_{2}\) was E \(>\) D \(>\)B \(>\) A \(>\) C.
3. When the interaction was not considered under true triaxial conditions, the effects of the confining pressure and water content on the strength were always significant. The temperature effect was significant only when the significance level \(\Omega>0.05\). The salinity and \(b\) value had a significant effect on the strength. The impact was not significant, and the ranking of the significance of each factor was consistent with the results of the range analysis method and the analytic hierarchy process. When considering the interaction, the interaction factors had different effects on the intensity. When \(\Omega>\) 0.01, A \(\times\) B was equivalent, and the effect of stress was significant, even exceeding that of the temperature. When studying the strength of frozen soil, it was necessary to comprehensively consider the various factors and the interaction between them, to more accurately characterize the mechanical behavior of frozen soil.  
Conceptualization, Z.W. and C.-X.R.; methodology, Z.W. and C.-X.R.; software, Z.W. and Y.C.; validation, C.-X.R., Z.W. and Y.C.; formal analysis, Z.W.; investigation, Q.Y.; resources, Z.W.; data curation, W.L.; writing--original draft preparation, Z.W.; writing--review and editing, Z.W. and W.L.; visualization, Q.Y.; supervision, C.-X.R.; project administration, Z.W.; funding acquisition, C.-X.R. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (grant numbers 51878005 and 51374010); and the Engineering Research Center of the Ministry of Education of Anhui University of Science and Technology in 2020 (grant number: JYBGCZX2020209).  
Data Availability Statement: Not applicable.  
This work was supported by Grants-in-Aid for scientific research from the National Natural Science Foundation of China (51878005, 51374010), Engineering Research Center of the Ministry of Education of Anhui University of Science and Technology in 2020 (JYBGCZX20209).  
The authors declare no conflict of interest.