## 5 Conclusions  
In this paper, the distribution stress of transversely isotropic elastic half-plane surfaces subjected to distributed forces in any direction were investigated. The stress fields were determined, and the effects of the Young's modulus, Poisson's ratio, and the formation dip angle were taken into consideration in the elastic analysis. The accuracy and applicability of the analytical solutions proposed were examined and clarified by calculating some problems. From the analysis conducted, the following conclusions can be obtained:  
(1) The analytical solution of transversely isotropic elastic half-plane surfaces subjected to distributed loading in any direction was proposed, and compared with the numerical solution, the two were in good agreement, which verifies the correctness of the analytical solution of transversely isotropic rock stress deduced in this paper.  
Figure 13: Analytical results for different values of formation dip. (**a**) vertical stress, (**b**) horizontal stress, (**c**) shear stress.  
(2) The stress concentration was closely related to the loading area, when Poisson's ratio stayed the same with the increase of Young's modulus anisotropy ratio, and the concentration degree of horizontal stress, vertical stress, and shear stress on the transversely isotropic plate had a 40%, 20%, and 3% increase in degree compared to that of the isotropic plate. However, with Young's modulus and the increase of Poisson's ratio, the concentration degree of vertical stress, horizontal stress, and shear stress on the transverse isotropic plate slightly decreased by 15%, 10%, and 4%, respectively.  
(3) Along with the increasing value of the dip angle of layered rock mass, the vertical stress in the rock layer presented a slightly upward tendency, while the horizontal stress and shear stress decreased gradually.  
(4) The proposed solution can be used to predict in situ stress. The stability of the working field is maintained after support, which can be further popularized and applied to related fields.  
As a result, the analytical solution and numerical simulation can be capable of characterizing the transversely isotropic layers. However, in this study, the new findings are limited to homogeneous transversely isotropic half-space. In the future, the quantification of stress distributions in an inhomogeneous transversely isotropic half-space should be further studied.  
[PERSON] conceptualized the study; [PERSON] and [PERSON] set up the proposed solution; [PERSON] and [PERSON] carried out the numerical simulation; [PERSON] evaluated the results; [PERSON] wrote the original draft; [PERSON] reviewed and edited the paper; [PERSON] supervised the study. All authors have read and agreed to the published version of the manuscript.  
State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures (KF2020-06), and Financial support for this work was provided by the Outstanding Scholar of [PERSON] (800015Z1179), and Hebei Province Ecological wisdom mine Joint Fund project (E2020402036) and the Fundamental Research Funds for the Central Universities (2009 QZ03).  
The data presented in this study are available on request from the corresponding author.  
The authors would like to thank the editor and the reviewers for their contributions. The authors declare no conflict of interest.