# Investigation of Rock Joint and Fracture Influence on Delayed Blasting Performance
## 4 Analysis of Stress and Displacement Distribution around Joints  
By substituting the transmission wave function of the joint interface in Figure 2 into Equations (12) and (13) and combining them with the delayed blasting model, the contour plots of stresses and deformation are calculated in Figure 3.  
It can be seen from Figure 3a that at the joint end, \(\sigma_{x}\) is positive in the direction of 0\({}^{\circ}\)-330\({}^{\circ}\) and subjected to tensile stress, whereas it is negative in the direction between 330\({}^{\circ}\) and 360\({}^{\circ}\) under compressive stress. \(\sigma_{x}\) is not symmetrical along the joint interface, and \(\sigma_{x}\) stress gradient increases rapidly in the direction of 300\({}^{\circ}\)-330\({}^{\circ}\), forming a stress concentration area. Figure 3b shows that at the joint end, \(\sigma_{y}\) is positive in the direction of 0\({}^{\circ}\)-180\({}^{\circ}\) under tensile stress. On the other hand, it is negative in the direction of 180\({}^{\circ}\)-360\({}^{\circ}\) and subjected to compressive stress. Although stress is symmetrically distributed along the joint interface, it can be clearly found from the figure that the \(\sigma_{y}\) stress field is not distributed symmetrically. Comparing Figure 3a,b, however, there are normal stress components in \(\sigma_{x}\), and \(\sigma_{y}\) and \(\sigma_{x}\) had a larger stress range. It can be seen from Figure 3c that the lateral displacement of the joint end is affected by the stress components in both directions. Although an intuitive understanding of the stress field distribution at the joint end can be obtained from the stress contour diagram, the asymmetry and continuous changes in the whole process still cannot be analyzed from the contour plot. Thus, the numerical simulation method is used to analyze the stress change in the wave acting on the mass point on the left side of the joint. Based on the following three figures, the stress field of the joint particle is asymmetric.  
Based on Figure 3a, the stress on the left side of the joint is tensile. According to the gradient change in the stress value with the distance from the joint, the stress distribution in the contours is denser, indicating it is manifested as tensile stress. A failure is more likely to appear in this area. Figure 3b shows the contour plot of longitudinal stress along the joint. It can be seen from the figure that the compressive stress distribution area and value are very small and the rock material is not damaged at this time. In addition, the stress concentration appears in the lower-right position. However, the vibration velocity of the particles on both sides of the joint interface change from time to time; the maximum force position also changes accordingly.  
Figure 3: Stress and deformation contour of joints post blasting shock wave.  
To verify the propagation of the detonation wave incident on the jointed rock mass and discuss the distribution of the stress field of the jointed rock mass under the blasting, a finite element model is used. To assess the effect of the blast shock wave on the stress field around the joint, the peak strain value is used as the only parameter (positive values represent tensile stress, and negative values represent compressive stress) in the numerical simulation [25; 26]. By setting parameters such as time step, the influence of the joint on the stress field around the incident joint subject to explosion stress wave can be analyzed.