## 5 Experiment Results and Discussion
### Contrasting Physical Experiment Results against Finite Element Analysis Outcomes
#### 5.3.2 Constraint Definition and Loading Method  
For the simulation on the uniaxial compression process of sandstone, the bottom surface was set to be fixed while the loads were exerted to the head surface. A virtual model with the same size as the physical sandstone specimen was built in the Part section in a module of Abaqus. Figure 17a shows the cylinder part (radius = 25 mm, height = 100 mm), while it also presents the upper (Part 2) and lower (Part 3) compression surfaces which are larger than the cylinder base area. In the Property section of Abaqus, the cylinder object was set to be of elastic materials with the elastic modulus of \(5\times 10^{3}\) MPa and Poisson's ratio of 0.25. Part 2 and Part 3 were set to be rigid, without any deformation during the loading process. Finally, by defining the coupling constraints, three parts were coupled together, as is shown in Figure 17a.  
Figure 17: Coupling and meshing: (**a**) coupling graph; (**b**) meshing graph.  
Meshing (Figure 17b) is critical to the accuracy of the finite element analysis results. In this paper, the three-dimensional cylinder model was divided into grids by gridding seeds with the element division size of 0.01 mm. Then, the axial compressive load was applied to Part 2 by stress with the loading speed at 0.1 MPa/s. Since the above two loading scenarios only have a difference in loading speed, numerical simulation produces similar pattern results. Therefore, only the scenario with the loading speed at 0.1 MPa/s was investigated by the Abaqus simulation.  
During the physical experiments, when the loading reaches the compression limit, a principal crack along the vertical direction appears with multiple minor cracks with an axial angle of around 45\({}^{\circ}\). In Figure 18, it is found that during the compression process, larger strain (shown in red color) occurs in some end areas, as well as the central area, with certain angles away from the axle, which is well consistent with the experiment results shown in Figures 5-11. The perceived pattern and trend consistency between the strain profiles obtained from the two methods of the Abaqus simulation and DIC analysis helps to verify the reliability of DIC results in this study.  
This study predicts that when the loading speed is 0.1 MPa/s, the failure strain lies between 0.004 and 0.011, while for the loading speed of 0.3 MPa/s, the counterpart strain value is between 0.0048 and 0.0093. The projected information should be useful for the prediction of failure on sandstone in real-world engineering applications.  
For the sake of safety, the weakest point of failure should always be given priority. That is to say, for sandstone components under safety monitoring, if the strain value reaches 0.004, there will exist risks of failure which may further lead to accidents. Assuming the safety coefficient is to be 1.5, the calculated allowable strain is then about 0.0027 (=0.004/1.5), and this value is lower than the theoretical result of 0.0037 obtained from the Hill-Tsai criterion. That is to say, when the monitored sandstone strain value reaches 0.0027, caution should be taken, and more attention needs to be paid to strain dynamics to prevent structural damage and engineering failure.