## 4 Effects of Particle Shape, Initial Void Ratio, and Inter-Particle Friction Angle  
In addition to the above-mentioned simulations concerning the influence of inherent anisotropy, the effects of particle shape, initial void ratio, and inter-particle friction coefficient on \(K_{0}\)-value are studied by a further series of simulations. Meanwhile, variations of these factors can induce changes of strength parameters (peak strength and critical state strength) of the specimen, thus the relationship between \(K_{0}\) values and strength parameter can be better investigated. Particle number and particle size distribution of all specimens in this section are identical to those described in Section 3. Three different kinds of shape (shown in Figure 3) were used to investigate the effect of both particle shape and potential particle rotation. Aspect  
Figure 11: Evolution of \(a_{n}\) in different initial anisotropy specimens. Figure 12: Evolution of \(a_{t}\) in different initial anisotropy specimens. ratio is represented by AR below for conciseness. Specimen formation and consolidation mode are the same as the isotropic specimens in Section 4. The initial void ratio of these specimens is controlled by adjusting inter-particle friction coefficient during the consolidation stage. Summary information about all specimens in these simulations is listed in Table 2. After completion of specimen formation, five different inter-particle friction coefficients (0.3, 0.35, 0.45, 0.5, and 0.7) are adopted during loading stage for each specimen. Besides the one-dimensional compression experiment described in Section 4, triaxial tests are also conducted to obtain corresponding macroscopic strength parameters. Figures 13 and 14 show the variations of \(K_{0}\)-values with void ratio from two aspects. Figure 13 focuses on the impact of inter-particle friction coefficient whereas Figure 14 focuses on particle shapes. According to Figure 7, \(K_{0}\)-value tends to reach a stable value when vertical stress is large enough. Therefore, \(K_{0}\)-values were determined at the end of the loading process (at vertical stress of 900 kPa). The void ratio was determined after consolidation completed before one-dimensional loading. The results presented in Figures 13 and 14 show an increasing trend of \(K_{0}\)-value, with increasing specimen initial void ratio for specimens with any inter-particle friction coefficient and particle shape in the tested range. Furthermore, according to Figure 13, \(K_{0}\)-value decreases with inter-particle friction coefficient increasing. This trend matches with existing laboratory tests [23,42]. For real granular material specimens, the difference of inter-particle friction coefficient between particles reflects the difference in mineral composition and particle grinding roundness. The effect of particle shape on \(K_{0}\) can be observed from Figure 14. Although there is a slight difference in the initial void ratio range corresponding to each particle shape, we can still find that the \(K_{0}\)-value decreases with the increase of the aspect ratio. This trend is well observed in previous literature [23,42]. [PERSON] [23] believed that this trend stemmed from the fact that changes in the aspect ratio of particles caused changes in the branch vector (see its literature for a specific explanation), thus changing the mechanical properties of the material. [PERSON] [42] thought that the change of self-locking effect caused by the change of particle shape was the main reason. The stronger the self-locking effect [43] is, the weaker the relative sliding between particles is, thus less lateral stress is required under the same