Research On Distribution Model Of Joint Orientations And Its Application To Joint Set Clustering And Rock Slope Uncertainty Analysis

Jointed rock slope is a commonly seen slope type, where joints play a controlling role in the stability of slope. Orientation, as one of the key elements of joint, is the basis of failure mode identification and stability calculation. In practical projects, orientations of joints are generally divided into several sets based on the stereographic projection, and each set is represented by the orientation of contour map center to analyze the rock slop stability. While in fact, orientations are randomly distributed and generally obey some statistical rules, the deterministic calculation methods cannot accurately reflect the stability state of slope. So the researches on the probability distribution of orientations, joint sets identification, and slope stability uncertainty analysis are important to slope engineering. In this paper, a new elliptically symmetrical distribution model is proposed, and is used for joint sets grouping and rock slope uncertainty analysis. The main work and main conclusions in this thesis are listed as follow:(1) The elliptically symmetrical data set is transformed to Fisher distributed set by means of generalized polar coordinate transformation. Based on that, the probability density function, the parameters estimation algorithm, hypothesis testing method, and the orientations simulation method of the elliptical Fisher distribution are deduced. This model has advantages of specific sense of physics and mathematics, convenient calculation, maintaining the advantages of Fisher distribution as well as realized the description of elliptically shaped data. The model is proved to be efficient by the field data measured in a slope rock mass.(2) Based on the mixtures of elliptical Fisher distributions and EM algorithm, joint set grouping and joint orientations simulating are realized. These algorithms are used to group and simulate the joint orientations measured in typical outcrops of candidate area for the geological disposal of high-level radioactive waste in Beishan, Gansu province. The results demonstrate the applicability of the clustering algorithm and the elliptical Fisher distribution.(3) Considering the fact that the existing rock slope stability programs do not cover the any shaped terrain and muti-rock layers condition, a new program that considers the conditions of any shaped terrain, any rock-soil mass combination, any orientations, any number of surcharges, any kind of tensile fissures, as well as considers the influences of earthquake and underground water, is developed. The new program is based on the plane failure and wedge failure modes, and can search out the most dangerous sliding surface automatically.(4) Based on the character that dip and dip angle of orientation are closely related to each other, the idea that the reliability of slope be reflected by the results of Monte Carlo simulation, that the sensitivity of safety factor to orientation be represented by that to spherical distance of normal vector is proposed. It is also suggested that by the means of drawing safety factor and sensitivity contour map on stereonet to visualize the analysis results. These recommended analytical methods are helpful to gain a complete and intuitive view of the effect of joint uncertainty on safety factor, which offer grounds for engineering decision.(5) The elliptical Fisher distribution, the joint set clustering algorithm, the rock slope stability analysis program, the orientation uncertainty based uncertainty analysis method for slope are applied to analyze the high rock slope in the second power plant of Taizhou City, which demonstrate the reasonableness and reliability of these methods, and that the uncertainty of orientations should be considered in rock slope stability analysis.