Three-dimensional upper-bound analysis of rock slopes subjected to seepage flows is a classical problem in geotechnical engineering. However, it is difficult to obtain a rigorous upper-bound solution of the safety factor of slopes when seepage flows are involved. In order to address this problem, the three-dimensional (3D) hydraulic head distributions inside a slope under steady state hydraulic conditions are solved numerically. The obtained numerical hydraulic head distributions are further employed to compute the seepage forces applying to the 3D discretized rotational failure mechanism to assess the stability of a rock slope. The Hoek-Brown yield criterion is employed to characterize the failure of rock masses. The generalized tangential technique is employed to formulate the problem as a classical optimization problem. The particle swarm optimization algorithm combined with the Nelder-Mead simplex algorithm is used to search for the best solutions of slope safety factor. The proposed approach is validated by comparing with 2D plane strain analysis results in the literature. Parametric analysis shows that the safety factor increases as $m_i$ or GSI increases, but decreases with the increase of the slope angle $\beta$ and B/H. It is also found that the 3D influence is significant for B/H smaller than 10, beyond which it becomes negligible. The computational results in the form of design tables are presented for practical use in rock engineering.

渗流作用下岩质边坡的三维上界分析是岩土工程中的经典问题。然而，当涉及渗流时，很难得到边坡安全系数的严格上界解。为了解决这个问题，对稳态水力条件下斜坡内的三维 (3D) 水头分布进行了数值求解。获得的数值水头分布进一步用于计算应用于 3D 离散旋转破坏机制的渗流力，以评估岩石边坡的稳定性。Hoek-Brown 屈服准则用于表征岩体的破坏。使用广义切线技术将问题表述为经典优化问题。粒子群优化算法结合Nelder-Mead单纯形算法用于寻找边坡安全系数的最佳解。通过与文献中的二维平面应变分析结果进行比较，验证了所提出的方法。参数分析表明，安全系数随着${米}_{\mathrm{一世}}$ 或 GSI 增加，但随着倾斜角的增加而减少 $\beta$和B / H。还发现 3D 影响对于小于 10 的B / H是显着的，超过该值则可以忽略不计。以设计表的形式给出计算结果，用于岩石工程的实际应用。