## 5 Conclusions  
This study aimed to examine the evolution of the plastic zone at the tip of I-II composite fissures under seepage conditions. An analytical solution was developed based on the Drucker-Prager yield criterion to estimate the plastic zone radius \(r\) at the fracture tip under high and low osmotic pressures. The influence of various parameters on \(r\) was analyzed. The main achievements can be summarized as follows:  
1. The investigation of stress distribution characteristics on the fracture surface under osmotic pressure revealed that the effective positive stress features on the rock body's fracture surface can serve as a criterion to distinguish between high and low osmotic pressures. The stress intensity factor is derived for composite fractures under osmotic pressure, taking into account the effects on rock microfractures.
2. An analytical expression is developed to obtain r in fractures exposed to high and low osmotic pressure. The performed analyses indicated that the value of r in fractured rocks is significantly affected by fracture parameters. When subjected to low osmotic pressure, the fracture plastic zone radius exhibited a decreasing-increasing-decreasing trend as the fracture dip angle \(\theta\) increased, with the peak r occurring at 45\({}^{\circ}\). The fracture length and Poisson's ratio had no notable impact on the fracture r value.
3. Under high osmotic pressure, r increased with increasing \(\theta\). The effect of changes in Poisson's ratio v on the plastic zone radius was more noticeable, with an increase in v from 0.20 to 0.28, resulting in a 10.26% rise in r. Moreover, an increase in fracture length from 10 mm to 30 mm doubled the peak plastic zone radius.  
This study only focuses on the theoretical study of the evolution characteristics of the plastic deformation zone of type I-II composite fractured rock under osmotic pressure. The fracture plastic zone radius of the surrounding rock indicates that it is necessary to continue the evolution characteristics of the seepage field in fractures under the complex stress-permeability coupling environment.  
Conceptualization, methodology, and resources, Z.N.; methodology, data curation, and writing--original draft, Z.N., Y.C.; writing--review and editing, Y.C., T.X. and J.P. All authors have read and agreed to the published version of the manuscript.  
Figure 8: The distribution of \(r\) and \(\theta\) at different fracture lengths (\(P\) = 18 MPa).  
**Funding:** This work was financially supported by the Innovation Capacity Support Plan of Shaanxi Province (No. 2020 TD-005), 2023 High-level Talent Research Project from the Yancheng Institute of Technology (No. xjr2023019), Open Fund Project of Shaanxi Key Laboratory of Geotechnical and Underground Space Engineering (No. YT202302).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request. The data are not publicly available due to privacy.  
**Conflicts of Interest:** The authors declare no conflicts of interest.