# Shear Mechanical Properties of Rock Joints Under Non-Uniform Load Based on DEM
## 6 Conclusions  
In this study, we constructed a non-uniform load mechanical model using the strip division method to investigate the effect of non-uniform load on the shear mechanical properties of joint surfaces. We then conducted a series of shear test simulations based on PFC software to analyze how different load distribution forms affect main shear parameters (cohesion and internal friction angle), crack expansion patterns, and energy evolution laws. Finally, we used machine learning methods to develop a quantitative prediction model for shear strength. (1) Taking into account the common overburden loads on joint surfaces in engineering projects, we established a non-uniform-load mechanics model for joint surfaces using the strip partitioning method. This resulted in three representative forms of load distribution: far-field concentration (FFC), near-field concentration (NFC), and focus on central (FOC). Additionally, based on idealized mathematical hypotheses, we derived load distribution formulas for these three conditions. (2) The proximity of load concentration to the distal shear direction correlated positively with peak shear displacement and strength. Compared to NFC, cohesion increased by 12.4% (FOC) and 30.76% (FFC), whereas internal friction angles decreased marginally by 0.91% (FOC) and 1.44% (FFC). Fracture analysis revealed distinct failure modes: NFC and FOC specimens exhibited one through-crack at the peak shear stress, while FFC developed two. Initial loading stages in NFC/FOC prioritized tensile cracks, transitioning to shear-dominated failure. Notably, shear cracks comprised >50% of total crack propagation in FFC. Energy dissipation metrics showed hierarchical trends: deformation energy (U) and elastic energy (Ue) followed FFC > FOC > NFC, while dissipated energy (Ud) ranked FFC > NFC > FOC, reflecting crack evolution differences under varying loading configurations. (3) According to the characteristics of deformation, strength, crack formation, and energy evolution under different load distribution forms, the farther the maximum load location was along the shear direction, the stronger the resistance to damage and stability of rock mass was. In engineering practice, it is advisable to position the maximum load as far away as possible from the joint along the shear direction. (4) By using the XGBoost algorithm, we proposed five quantitative shear strength prediction models: the Whale, Genetic, Bayesian, and Particle Swarm algorithms. By \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Normal Stress (MPa)**} & \multicolumn{4}{c}{**Shear Strength Simulation (MPa)**} \\ \cline{2-5}  & **NFC** & **FOC** & **FFC** & **UD** \\ \hline
1.5 & 4.29 & 4.71 & 5.28 & 4.74 \\
1.6 & 4.41 & 4.67 & 5.31 & 4.76 \\
1.7 & 4.52 & 4.84 & 5.31 & 4.92 \\
1.8 & 4.52 & 4.74 & 5.44 & 5.06 \\
1.9 & 4.66 & 5.06 & 5.58 & 4.84 \\
2 & 4.79 & 5.2 & 5.75 & 5.13 \\
2.1 & 5.05 & 2.16 & 5.77 & 5.1 \\
2.2 & 5.01 & 5.28 & 5.88 & 5.22 \\
2.3 & 5.12 & 5.4 & 5.91 & 5.34 \\
2.4 & 5.19 & 5.53 & 5.97 & 5.46 \\
2.5 & 5.24 & 5.58 & 5.94 & 5.56 \\
2.6 & 5.3 & 5.63 & 6.21 & 5.67 \\
2.7 & 5.35 & 5.69 & 5.29 & 5.71 \\
2.8 & 5.38 & 5.7 & 6.21 & 5.75 \\
2.9 & 5.41 & 5.81 & 6.26 & 5.83 \\
3 & 5.6 & 5.91 & 6.31 & 5.8 \\ \hline \end{tabular}
\end{table} 
Table 3: _Cont._comparing the predicted values with the test values, we obtained the Genetic-XGBoost algorithm prediction model with the highest prediction accuracy (R\({}^{2}\) = 0.973). The weight of the load distribution mode was 76.7%, which was considerably higher than that of the load value at 23.2%. This indicates that load distribution form is a primary factor affecting shear strength. Conceptualization, C.Y. ; Methodology, H.L. ([PERSON]) and X.Z. ; Software, X.Z. and Y.C. ; Validation, H.L. ([PERSON]) and K.O. ; Formal analysis, H.L. ([PERSON]), X.Z., H.L. ([PERSON]), Y.C., C.Y. and K.O. ; Resources, H.L. ([PERSON]), H.L. ([PERSON]) and Y.C. ; Writing--original draft, [PERSON] ([PERSON]) and [PERSON]; Writing--review & editing, [PERSON] ([PERSON]).