A Stochastic Rockfall Model Related to Random Ground Roughness Based on Three-Dimensional Discontinuous Deformation Analysis

The use of feasible 3-D numerical methods has become essential for addressing problems related to rockfall hazard. Although several models with various degrees of complexity are available, certain trajectories and impact dynamics related to some model inputs could fall in the rockfall observations area but are rarely calibrated against reflecting its range, especially the lateral deviations. A major difficulty exists in the lack of simulating the apparent randomness during the impact-rebound process leading to both ground roughness and block irregularities. The model presented here is based on three-dimensional discontinuous deformation analysis (3-D DDA). Despite similarities to previous simulations using 3-D DDA, the model presented here incorporates several novel concepts: (1) ground roughness is represented as a random change of slope angle by height perturbation at a grid point in DEM terrain; (2) block irregularities are modelled directly using polyhedron data; (3) a scaled velocity restitution relationship is introduced to consider incident velocity and its angle. Lateral deviations of rebound velocity, both direction and value, at impact are similarly accounted for by perturbing the ground orientation laterally, thus inducing scatter of run-out directions. With these features, the model is capable to describe the stochastic rockfall dynamics. In this study, 3-D DDA was then conducted to investigate the dynamic behavior of the rockfall and examine the role of sphericity of the rock block travelling on bench slopes with different ground roughness levels. Parametric analyses were carried out in terms of cumulative distribution function (CDF) to investigate for spatial distribution (both runout distance and lateral displacement), velocity and jumping height. The effects of block shape and ground roughness revealed by these factors were discussed. It suggests that ground roughness amplifies the randomness and plays important roles on the dynamic behavior of the system; irregularity from block sphericity will further amplify the randomness especially when the size of the rock is relatively small compared to the roughness level. Both irregularities should be taken into consideration in simulating rockfall problems. Further calibration of the new model against a range of field datasets is essential.

Reproduction Method of Rockfall Geologic Hazards Based on Oblique Photography and Three-Dimensional Discontinuous Deformation Analysis

Rockfall geologic hazards are widely distributed. Due to their concealed nature, rockfalls are difficult to investigate using traditional contact survey methods, and the hazards they pose affect major projects and people’s safety. Reproducing methods, including scene survey and movement process analysis, are primary tasks used to prevent these hazards; however, few reconstruction methods can directly apply the parameters of the rockfall geologic hazards obtained by the scene survey to evaluate the movement process. To address this problem, a method of reproduction based on oblique photography and three-dimensional discontinuous deformation analysis (3D-DDA) is proposed; the method consists of three key techniques (oblique photography, 3D rock block system modeling, and 3D rock block system analysis). First, geometric characteristic parameters of the terrain, rockfall, and discontinuities are extracted based on oblique photography using an unmanned aerial vehicle (UAV). Second, the block system model of rockfall is reconstructed by using 3D computational geometry theory and taking these geometric characteristic parameters as an input. Finally, the whole evolution process of rockfall geologic hazard, including initiation, movement, and accumulation, is simulated by the 3D-DDA method. To verify the practicability of this reproduction method, a typical rockfall geologic hazard, located in the K8 + 050 section of the Gaohai expressway, Yunnan, China, is studied. In addition, the characteristics of 19 dangerous rock masses in the survey area are clarified, and the geometric features of the discontinuities in the rock masses are extracted based on oblique photography using an UAV. The block system model of a potential rockfall is reconstructed, the movement trajectory is simulated by the 3D-DDA method, and the evolution process of velocity and kinetic energy of the rockfall verifies that the spatial layout of the current three-level passive protective nets system is reasonable. The case study indicates that the proposed method provides a geological and mechanical model for the risk assessment of rockfall geologic hazards.