Angled Line Explosive Charge

Introduction

An angled-line source that is simplified into an equivalent parallel line source if the its standoff distance is equal to or less than the effective length of the line. The calculation uses a point source solution that simplifies methods for an angled line source.

Minimum distance from the pipeline to the nearest explosive charge must be greater than two times outside pipe diameter. :R=A<\frac{2D}{12} \~\ B>90

R=A<\frac{2D}{12} \\~\\ B>90

Maximum allowable angle between pipe and explosive line must be less than 90˚

S_h=\frac{PD}{2t}

S_h=\frac{PD}{2t}

Where:

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

B − Angle Between Pipe and Grid(deg), convert to Radians = 𝐵(0.0175)

P − MAOP−Maximum Allowable Operating Pressure(psi)

D − Pipeline Outside Diameter(in)

t − Pipe Wall Thickness(in)

S_ℎ − Hoop Stress(psi)

R_{gc} = A + \frac{(N_1 – 1)L_1 \sin B}{2} \
R = \frac{R_{gcl}}{\cos B} \~\
L = N_1 L_1 \
W = N_1 W_1

R_{gc} = A + \frac{(N_1 - 1)L_1 \sin B}{2} \\
R = \frac{R_{gcl}}{\cos B} \\~\\
L = N_1 L_1 \\
W = N_1 W_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

\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}\

\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

A – Distance to Nearest Charge

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 and Explosive Line

B – Angle Between Pipe and Explosive Line

Rgcl – Distance Between Geometric Center of Explosive Line and Pipe

R – Effective Standoff Distance

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
• A – Distance of the Nearest Charge to Pipeline
• B – Angle Between Pipe and Grid

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