# Influence of Fracture Geometric Characteristics on Fractured Rock Slope Stability
## 1 Introduction  
A rock slope comprises many spatially varying fractures such as layers, joints, fissures, and faults. Ideally, in addition to the variability in properties of the rock matrix, a complete characterization of the geometric characteristics of these fractures, such as length, orientation, spacing, connectivity, density, and properties of the fractures, such as the shear strength and the hydraulic conductivity in the rock slope are required for a rock slope stability analysis. Because a complete characterization of the slope is impractical, our slope stability analysis is always fraught with uncertainty [1; 2; 3]. As a result, probabilistic analysis of rock slope stability is thus appropriate [4; 5; 6; 7].  
Many studies have been conducted to perform a non-deterministic rock slope stability analysis taking into account the inherent variability of strength parameters in rock mass and random fractures [8; 9; 10]. However, few researchers have investigated the impact of variability in fracture geometric characteristics on the slope stability. Hence, it is critical to focus on the fracture geometric characteristics and their effects on rock slope stability.  
Previous slope stability investigations in rock slopes have emphasized the influence of the fracture geometry on the slope instability [11; 12; 13; 14]. Combined with the strength reduction method (SRM), some scholars evaluated the slope stability using the discrete fracture network (DFN) model [15; 16]. [PERSON] et al. [17] integrated remote sensing andDFN approaches to simulate kinematic block failure in the UK-based mine quarry slope and found a considerable effect of fractures on the block stability. [PERSON] et al. (1998) investigated the natural variability of the fracture geometric parameters (e.g., persistence, spacing, and orientation) on the rock slope stability using a 3D distinct element code. They found that fractures with unfavorable persistence (fully extended) and both fixed spacing and orientation values do not always show a conservative solution. In addition, many authors have investigated the impact of rock bridges and fractures using FEM, DEM, and hybrid numerical modeling codes ([PERSON] et al., 2009; [PERSON] et al., 2010; [PERSON] et al., 2011; [PERSON] et al., 2012). [PERSON] and [PERSON] ([PERSON] and [PERSON], 2013) conducted experimental studies to examine the impact of non-persistent discontinuity on the strength of the rock mass.  
[PERSON] et al. (2014) evaluated the ability of different probabilistic methods to model slope stability uncertainty, including the point estimate method (PEM), response surface method (RSM), Monte Carlo simulation (MCS), and Latin hypercube method (LHM). It was found that there are challenges in applying most probabilistic methods to modeling fracture variability, and MCS is the only method that can readily handle uncertainty problems caused by discrete fractures without any special treatment or adaptation. Hence, this paper uses MCS to conduct the probabilistic analysis.  
This study investigates the influences of fracture geometric characteristics (i.e., the fracture trace length, dip, and spacing) on the mean stability of fractured rock slopes. Based on the DFN-DEC model, a series of slope stability calculatations were performed using the strength reduction method for the probabilistic slope stability analysis.  
This paper is organized as follows. Section 2 shows the methodology of the DFN-DEC model and the probabilistic analysis for slope stability. The rock slope model and results of the probabilistic analysis are displayed in Section 3. Then, the influences of the fracture trace length, dip, and spacing on the mean stability of rock slopes are investigated in Section 4. The article draws conclusions in Section 5.