Parallel Line Explosive Charge

Introduction

Parallel explosive charge are complex methods which have been simplified in many cases to into equivalent parallel line or point sources. The estimate of the standard error for parallel equations can be as high as 34%; However, if the standoff distance between the pipe and explosive line is greater, then it can be approximated by a single point source. : A=R

A=R

The minimum distance from the pipeline to the nearest explosive charge must be greater than two times the outside pipe diameter. : A<\frac{2D}{12}\~\S_h=\frac{PD}{2t}

A<\frac{2D}{12}\\~
\\S_h=\frac{PD}{2t}

Where:

R − Distance from the Charge to the Pipeline(ft)

P − MAOP−Maximum Allowable Operating Pressure(psi)

D − Pipeline Outside Diameter(in)

t − Pipe Wall Thickness(in)

S_ℎ − Hoop Stress(psi)

L=N_1L_1\~\W=N_1W_1

L=N_1L_1\\~\\W=N_1W_1

Where:

L − Total Length of Explosive Line(ft)

L₁ − Spacing Length Between Charges in Explosive Line(ft)

W − Total Charge Weight(lbs)

W₁ − Weight of Single Charge(lbs)

N₁ − Number of Charges in Explosive Line

\begin{align} \text{If } R >L: \ & S_c = 4.44E \left( \frac{nW}{\sqrt{(Et)(R^{2.5})}} \right)^{0.77} \ \text{If } R < L: \ & S_c = 4.44E \left( \frac{1.4n \frac{W_1}{L_1}}{\sqrt{(Et)(R^{1.5})}} \right)^{0.77}\ \text{A=R:}\ & S_{nc} = 4.44E \left( \frac{nW_1}{\sqrt{(Et)(A^{2.5})}} \right)^{0.77}\ \text{If } S_{nc} > S_c \text{ Then } S_c = S_{nc} \ &S_t=S_H+S_c\ &S=\sqrt{S_t^2-(S_tS_c)+S_c^2} \end{align}\

\begin{align*}
 \text{If } R >L: \\
& S_c = 4.44E \left( \frac{nW}{\sqrt{(Et)(R^{2.5})}} \right)^{0.77} \\
 \text{If } R < L: \\
& S_c = 4.44E \left( \frac{1.4n \frac{W_1}{L_1}}{\sqrt{(Et)(R^{1.5})}} \right)^{0.77}\\
\text{A=R:}\\
& S_{nc} = 4.44E \left( \frac{nW_1}{\sqrt{(Et)(A^{2.5})}} \right)^{0.77}\\
 \text{If } S_{nc} > S_c \text{ Then } S_c = S_{nc} \\
&S_t=S_H+S_c\\
&S=\sqrt{S_t^2-(S_tS_c)+S_c^2}
\end{align*}\\

Where:

S_𝑐 − Maximum Circumferential = S_𝑙 − Maximum Longitudinal Stress(psi)

n − Equivalent Energy Release Ratio

W − Weight of Single Charge(lbs)

E − Modulus of Elasticity

t − Pipe Wall Thickness(in)

S_𝑡 − Combined Hoop and Circumferential Stress(psi)

Calculated\,\%\,SMYS=\frac{S}{SMYS}100

Calculated\,\%\,SMYS=\frac{S}{SMYS}100

 Blasting Conditions for combined Stress Level

𝐶𝑎𝑙𝑆𝑀𝑌𝑆 >%𝑆𝑀𝑌𝑆 − NOT ACCEPTABLE/𝐶𝑎𝑙𝑆𝑀𝑌𝑆 <%𝑆𝑀𝑌𝑆 − ACCEPTABLE

Schematics

N1 – Number of Charges in Explosive Line

L1 – Spacing Length Between Charges in Explosive Line

L – Length of an Explosive Line

W1 – Weight of Each Charge in Explosive Line

R – Perpendicular Distance of the Explosive Line to Pipeline

Case Guide

Part 1: Create Case

Input Parameters

• Pipe Outside Diameter
• Pipe Wall Thickness
• Specified Minimum Yield Strength
• Maximum Allowable Combined Stress Level – SMYS
• Manufacturer
• Explosive Type
• Equivalent energy release ratio
• MAOP – Maximum Allowable Operating Pressure
• N1 – Number of Charges in Explosive Line
• L1 – Spacing Length Between Charges in Explosive Line
• W1 – Weight of Single Charge
• n – Equivalent Energy Release Ratio
• R – Distance of the Charge to Pipeline

Part 2: Outputs/Reports

Results

• Total Length of Explosive Line
• Total Charge Weight
• Sh – Hoop Stress
• Sc-Maximum Circumferential = Sl-Maximum Longitudinal Stress
• St – Combined Hoop && Circumferential Stress
• S – Total Combined Stress
• Calculated Percent of SMYS
• Blasting Conditions for Combined Stress Level:

References

• SWRI – Pipeline Response to Buried Explosive Detonations – Volume I
• SWRI – Pipeline Response to Buried Explosive Detonations – Volume II
• PRCI – Pipeline Response to Blasting in Rock

FAQ