# Safety Analysis of Buried Corrosion-Defect Gas Pipeline in Ceramic Soil Layer Under Blasting Action
## 3 Theoretical Determination of Explosion Load  
The tube-soil interaction is extremely complicated because of the complex nonlinear and inelastic characteristics of the soil medium. It is generally believed that the method of calculating the tube-soil interaction separately from the tube does sufficiently account for the tube-soil interaction. This does not accord with the actual stress state of the buried pipeline and affects the accuracy of the results. The pipe-soil interaction is a complex coupling system, and its exact working form is still unclear. At present, there is no universal force model which can be applied to any tube-soil force model. Therefore, it is necessary to simplify the design of different stress models to correspond to their respective stress characteristics. According to the dynamic response monitoring data of ductile iron pipe under blasting vibration, the dynamic response of large-diameter cast iron pipe under a blasting load based on Timoshenko beam theory is calculated. The vibration response prediction model of large-diameter cast iron pipe under blasting vibration is established, and the accuracy of the simulation of the pipe-soil interaction by Kelvin foundation beam theory is verified. The explosive detonates in the rock mass, and the stress wave propagates through the rock-soil interface and reaches the pipe after transmission. If the distance between the pipe and the explosion source is far enough, the explosion stress wave can be assumed to propagate on the plane formed by the pipe and the explosion source, that is, the explosion stress wave is considered as a plane wave, and the propagation path of the stress wave is shown in Figure 4.  
Figure 3: Field test diagram. Figure 2: Schematic diagram of experimental monitoring arrangement. According to the research results of [PERSON], [PERSON] et al., the blasting load adopts exponential-decay-type load [4]:  
\[p(t)=p_{s}e^{-mt} \tag{1}\]  
where \(p_{s}\) is the peak explosion pressure, and \(m\) is the attenuation coefficient. \[m=\sqrt{2}\omega \tag{2}\]  
\[\omega=\frac{2\sqrt{2}c_{p}}{3r_{f}} \tag{3}\]  
\(c_{p}\) is the longitudinal wave velocity, and \(rf\) is the radius of the crushing zone. When explosive explodes, it will instantly produce a large blasting pressure in the gun hole, directly acting on the hole wall. The formula of detonation pressure is as follows:  
\[p_{b}=\frac{\rho_{e}D^{2}}{2(\gamma+1)} \tag{4}\]  
where \(p_{b}\) is the detonation pressure at the gun hole, \(\rho_{e}\) is the explosive density, \(D\) is the explosive detonation speed, and \(\gamma\) is the isentropic index, usually 3.0. In the process of rock blasting, the crushing zone and elastic zone will be produced under the action of explosion shock wave and stress wave with the detonation source as the center. When it reaches the crushing zone, the attenuation is due to the stress wave. Both the shock wave and stress wave show exponential attenuation, and the attenuation index is as follows [11]:  
\[m_{1}=2+\frac{\mu_{r}}{1-\mu_{r}},\ m_{2}=2-\frac{\mu_{r}}{1-\mu_{r}} \tag{5}\]  
In the formula, \(\mu_{r}\) is the rock dynamic Poisson ratio, \(m_{1}\) is the attenuation index for the shock wave, and \(m_{2}\) is that for the stress wave. After the stress wave reaches the edge of the crushing zone, it enters the elastic zone. At this time, the action of the stress wave can only produce elastic vibration, and the explosion pressure function is:  
\[p_{e}=\frac{\rho_{e}D^{2}}{2(\gamma+1)}\bigg{(}\frac{r_{c}}{r_{b}}\bigg{)}^{- m_{1}}\bigg{(}\frac{r_{f}}{r_{c}}\bigg{)}^{-m_{2}} \tag{6}\]  
where \(p_{e}\) is the explosion pressure at the elastic boundary, \(r_{b}\) is gun hole radius, and \(r_{c}\) is crushing zone radius. Figure 4: Cross-section of stress wave propagation path.