# Numerical Modeling of 3D Slopes with Weak Zones by Random Field and Finite Elements
## 5 Conclusions  
Aiming at the uneven spatial distribution of weak zones in slopes, this work investigated a mathematical theoretical model based on two-phase random media to characterize a 3D slope with weak zones. Based on the USDFILD platform in ABAQUS software, a Fortran program corresponding to the proposed model was developed, and the 3D finite element modeling of the slope with weak zones was performed. By setting the coordinate rotation angle of the anisotropic correlation structure, the inclination angle of the weak zones in the slope model was controlled. The validity of the proposed model for the analysis of the stability of 3D slopes with weak zones was verified on the basis of existing research results and analytical solutions. At the same time, the calculation results show that the above-mentioned characterization method combined with the finite element method is able to realize the automatic retrieval of the internal slip surface of the slope. By inverting the failure mode of the slope with weak zones, it can be found that the stabilities of slopes with weak zones re dominated by those weak zones.  
Taking the Gangtou tunnel slope as the object of study, a stability analysis of a 3D slope with weak zones was carried out, and the influence of the inclination angle of the weak zones on the slope stability was analyzed using the 3D finite element model. The results show that the weak zones weaken the strength of the slope, leading to a decrease in safety factor. When the inclination angle of the weak zones was approximately parallel to the slope angle, the slope with the weak zones was more prone to instability. These research results provide an important reference for the further quantitative evaluation  
Figure 16: Plastic strain diagram of the slope with 60\({}^{\circ}\) rotation angle of the weak zones. (**a**) The rotation angle of 60\({}^{\circ}\) around the X-axis (\(FOS=1.89\)); (**b**) the rotation angle of 60\({}^{\circ}\) around the Y-axis (\(FOS=1.97\)); (**c**) the rotation angle of 60\({}^{\circ}\) around the Z-axis (\(FOS=1.98\)).  
of landslide susceptibility in the engineering of the slope of the Gangtou tunnel and the selection of excavation slope angles.  
Conceptualization, Y.-X.X., P.C., M.-M.L. and J.H.; methodology, Y.-X.X.; software, Y.-X.X. and P.C.; validation, Y.-X.X. and P.C.; formal analysis, Y.-X.X.; investigation, Y.-X.X., P.C., M.-M.L. and J.H.; resources, Y.-X.X., P.C., M.-M.L. and J.H.; data curation, Y.-X.X.; writing--original draft preparation, Y.-X.X., P.C., M.-M.L. and J.H.; writing--review and editing, Y.-X.X., P.C., M.-M.L. and J.H.; visualization, Y.-X.X.; supervision, Y.-X.X., P.C., M.-M.L. and J.H.; project administration, Y.-X.X., P.C., M.-M.L. and J.H.; funding acquisition, Y.-X.X., P.C., M.-M.L. and J.H. 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 No. 51968019), High Technology Direction Project of the Key Research & Development Science and Technology of Hainan Province, P. R. China (Grant No. ZDYF2021 GXJS020), and the characteristic innovation (Natural Science) projects of scientific research platforms and scientific research projects of Guangdong Universities in 2021(Grant No. 2021 KTSCX139).  
Not applicable.  
The authors declare no conflict of interest.