## 3 Performance Evaluation
### Cone Penetration Test  
A series of cone penetration tests of Ticino sand in a virtual calibration chamber were performed using the DEM code PFC3D [62; 63], which were simulated in this study for comparison. The chamber was a cylindrical container with a height \(H\) of 0.7 m and a diameter \(D\) of 1.2 m. The cone had a diameter \(d_{\rm c}\) of 71.2 mm, and its tip had an angle of 60\({}^{\circ}\), as shown in Figure 9a. The cone tip and frontal section of the shaft with a length of 0.1 m had a friction coefficient of 0.35. Figure 8: Influence factors on acceleration effect. Figure 9: Configurations in the numerical model of cone penetration test (**a**) size of cone (**b**) particle size distribution of sand. The grain size distribution of the Ticino sand is shown in Figure 9b, which was scaled by a factor of 50 and represented as \(d_{10}\) = 18 mm, \(d_{30}\) = 22 mm, \(d_{50}\) = 26 mm, \(d_{70}\) = 32 mm, and \(d_{90}\) = 40 mm. The uniformity coefficient was \(C_{\rm u}\) = 1.61 (well sorted). Therefore, a total of 65,000 particles were initialised, corresponding to the characteristic ratios \(D/d_{50}\) = 46 and \(d_{\rm c}/d_{50}\) = 2.74. The boundary effect from the container could be eliminated with the sufficiently large value of \(D/d_{50}\), while the penetration resistance will fluctuate due to the relatively low value of \(d_{\rm c}/d_{50}\). Using the real particle sizes in reality, there would be more than 8,125,000,000 particles involved, which would overwhelm the computational capacity. The initial void ratio was 0.66. The density of the particles was 2643 kg/m\({}^{3}\). The self-gravity of the particles was not considered. The normal and tangential stiffness of the particles were taken as 300 MPa and 75 MPa, respectively, and the friction coefficient was 0.35. A local damping ratio of 0.7 was used to accelerate the equilibrium process. The specimens were created to the target void ratio using the radius expansion method under a confining pressure of 100 kPa. In the penetration operations, the cone penetration was driven at a rate of 0.1 m/s. The key measurable quantity for the cone penetration test is the cone factor\(f_{\rm c}\), which is the force measured at the cone surface divided by the cone area. The DEM predictions with different particle numbers are shown in Figure 10, in which the raw vibrating curves are fitted using an equation [63]:  
\[f_{\rm c}=a[1-\exp(-bw)] \tag{20}\]  
where \(a\) and \(b\) are the fitting coefficients; \(w\) is the penetration depth. The value of \(a\) characterises the ultimate bearing capacity of the cone below a particular depth. The prediction of \(a\) in this study is 1.25, which is higher than that obtained by [PERSON] et al. [63] of 1.17 for 7%, which is mainly attributed to the inaccuracy of the DEM algorithm itself. Smaller particle sizes were adopted with the ratio \(d_{\rm c}/d_{50}\) modified to 3.45, 5.5, 11, 22 and 55, making the particle numbers increase to 150,000, 520,000, 1,001,000, 2,002,000 and 4,881,200. The fitted value of \(a\) by the DEM using 150,000 particles (1.21) is similar to the fitted \(a\) with 65,000 particles (1.25), both of which are much higher than the value with 540,000 particles (0.6). Fewer fluctuations occur in the resistance profile using more particles. The comparison hints that an obvious scale effect exists in the cone penetration test relating to the value of \(d_{\rm c}/d_{50}\). The scenario with smaller particles is not simulated in  
Figure 10: Cone factors predicted by DEM simulations. this study, as the focus here is on the parallel effect. The scale effect in the cone penetration test has been studied by References [64; 65]. The transient velocity and the force chain of the particles around the cone with \(d_{\rm c}/d_{50}=3.45\) (65,000 particles) are shown in Figure 11. The average runtimes in 10,000 incremental steps were compared between the CPU sequential, CPU parallel, and GPU parallel simulations (Table 3).