Distribution-free estimation for average trace length of rock discontinuities within 3D large sampling window of complex high-steep slope

The trace length as an important indicator reflecting the size of discontinuity, can usually be estimated by setting a sampling window on the surface of the rock mass. However, in high-steep rock slopes with cliffy topography and uneven terrain, traditional methods are difficult to select suitable plane sampling windows. Therefore, estimating the average trace length accurately in this situation has become an urgent problem to be solved. This study proposes a distribution-free method for estimating the average trace length of discontinuities within large windows in complex high-steep slopes. By introducing a cuboid sampling window, the estimation method has been extended to three-dimensional for the first time. Additionally, the proposed method addresses the limitations of existing methods, making it applicable for larger sampling areas. In addition, the new method considers the proportion of three types of traces intersecting the sampling area and their angles with the sampling area, and corrects the new method using the weight of visible traces at both ends, eliminating the impact of sampling biases such as censoring bias, orientation bias, and size bias. The reliability of the proposed method was validated by generating nine sets of simulated trace data with different angles and distribution types. Finally, the new method is applied to a complex high-steep slope with an elevation difference of nearly 600 m on the southeastern edge of the Qinghai Tibet Plateau. The results indicate that for the estimation of trace length in high-steep slope, the new method has smaller errors and lower error volatility. When selecting an appropriate sampling area size, the error of the new method is less than 6 %, and the error fluctuation is less than 4 %. And this study is of great significance for evaluating the stability of high-steep rock mass structures in major projects in hard mountain areas.