## 6 Pipeline Safety Evaluation and Vibration Reduction Solutions  
### Safety Evaluation of Pipeline under Blasting Vibration  
The safety evaluation of pipelines under the impact of a large number of blast holes and multiple batches of blasting is extremely complicated, and no general evaluation system is available presently. Three effective safety assessment methods are proposed in this study.  
(1) Safety standards for vibration velocity  
According to the safety standard [20], the maximum PPV of 79.12 cm/s and 28.32 cm/s obtained under non-electric detonator and electronic detonator blasting significantly exceeded the safe allowable vibration velocity. Blasting causes serious damage to pipelines.  
(2) Safety assessment of the cumulative damage variable \(D\) and range  
Because the water pipeline must undertake important water supply tasks, the engineering safety importance level is high; hence, the threshold of the pipeline variable \(D\) in this study was 0.2 [44]. As shown in Figure 18, the threshold for the damage range of the pipeline is determined to be 4 m. According to the simulation results, the damage range exceeded 4 m, which does not satisfy the safety requirements.  
(3) Safety evaluation of the dynamic tensile strength of the material  
The tensile strength of the material will be significantly increased under high strain rate conditions [45; 46]. In the calculation results, the strain rate at the danger point is close to \(10^{-5}\) s\({}^{-1}\); hence, it is advisable to adopt the dynamic tensile strength. Currently, the dynamic tensile strength of materials under transient loads cannot be directly monitored [47]. In recent years, many researchers have proposed mathematical models for the tensile enhancement coefficient of the brittle materials through the Hopkinson pressure bar test [48; 49]. This test has been widely used in the field of protective structures and impact resistance [50; 51]. Among these, the most widely used is the CEB tensile strength coefficient improvement model [52], as shown in Equation (15). Equation (15) is composed  
Figure 18: Relationship between the cumulative damage degree of pipeline and the number of blast hole detonations.  
of two piecewise functions with a strain rate of 30 s\({}^{-1}\) as the dividing line, and the dynamic tensile strength coefficient can be calculated using different subformulas.  
\[\gamma\big{(}\dot{\epsilon}\big{)}=\left\{\begin{array}{ll}\big{(}\frac{\dot{ \epsilon}}{\dot{\epsilon}_{\rm s}}\big{)}^{1.026\alpha_{\rm s}}&\dot{\epsilon} \leq 30\ \rm{s}^{-1}\\ \zeta_{\rm S}\big{(}\frac{\dot{\epsilon}}{\dot{\epsilon}_{\rm s}}\big{)}^{1/3}& \dot{\epsilon}>30\ \rm{s}^{-1}\end{array}\right. \tag{15}\]  
\[\alpha_{\rm s}=\frac{1}{5+9f_{\rm c}/f_{\rm co}} \tag{16}\]  
\[\zeta_{\rm s}=10^{6.156\alpha_{\rm s}-2} \tag{17}\]  
where the quasi-static strain rate \(\dot{\epsilon}\) is 3 \(\times\) 10\({}^{-5}\)s\({}^{-1}\), \(f_{\rm co}\) is 10 MPa, and \(f_{\rm c}\) is the quasi-static compressive strength of the material.  
The pipeline material used in this study was C50 reinforced concrete with a static compressive strength of 22.4 Mpa. The transverse strain rate at the danger point was the highest; the tensile strength increase coefficient \(\gamma(\dot{\epsilon})\) calculated using the numerical model was 1.80, and the dynamic tensile strength was 3.29 Mpa. As shown in Figure 16, the pipeline at the blasting side (75-105\({}^{\circ}\)) exceeded the dynamic tensile strength; therefore, it is likely to crack.