Maximum Impact Load & Penetration Depth – Liquid

Introduction

The focal point of this application is to assess strain due to a falling object such as a piece of construction equipment, material or vehicle falls over an operating pipeline.

Some of the limitations of this calculation are as follows: drop height, maximum load at the soil surface, type of soil, etc. to determine the penetration depth.

Maximum Impact Load:

L_{max}=\sqrt{\frac{32WH_fGr_o}{\pi^2 (1-v)} }[lbs]

L_{max}=\sqrt{\frac{32WH_fGr_o}{\pi^2 (1-v)}  }[lbs]

Where:
𝐿_𝑚𝑎𝑥 − Maximum Load at Soil Surface (lbs)
𝑊 − Weight of Falling Object (lbs)
𝐻_𝑓 − Drop Height (in)
𝑟_𝑜 − Least Horizontal Radius of Falling Object (in)
𝐺 − Soil Shear Modulus (psi)
𝑣 − Poisson’s Ratio for Soil (dimensionless)

For large strains, near the region of impact, the shear modulus is one tenth the low amplitude shear modulus. : G=\frac{\rho V_s^2}{10}

G=\frac{\rho V_s^2}{10}

Where:
𝑉_𝑠 − Shear Wave Velocity of Near Surface Soils (in/sec)
𝜌 − Mass Density of Near Surface Soil (Unit Weight of Soil/ Acceleration/ due to Gravity)(lb.sec²/in⁴)

Penetration Depth:

x_p=kP_a\log(1+\frac{V^2}{215000})[ft]

x_p=kP_a\log(1+\frac{V^2}{215000})[ft]

Where:
𝑥_𝑝 − Penetration Depth (ft)
𝑃_𝑎 − Weight per Unit Impact Area (lb/ft²)
𝑉 − Impact Velocity (equal to (√2𝑔𝐻_𝑓 )(ft/sec)
𝑘 − Empirical Coefficient of Penetration
(𝑘 = 0.0367 for Sandy Soil, k = 0.0482 for Soil with Vegetation, k = 0.0732 for Soft Soil)

Case Guide

Part 1: Create Case

Input Parameters

• Weight of Falling Object (lbs)
• Drop Height (ft)
• Impact Area Diameter (ft)
• Unit Weight of Soil: (70-150) (lbs/ft³)
• Poisson’s Ratio for Soil
• Shear Wave Velocity of Near Surface Soil (in/sec)
• Empirical Coefficient of Penetration

Part 2: Outputs/Reports

Results

• Soil Shear Modulus (psi)
• Maximum Load at the Soil Surface (lbf)
• Impact Velocity (ft/sec)
• Impact Pressure (psi)
• Weight per Unit of Impact Area (psi)
• Penetration Depth (ft)

References

• ASME B31.8 – Gas Transmission and Distribution Piping Systems
• API 5L, API 5LS and API 5LX – Specification of Pipe Grade
• ASTM – Various – Weld Joint Factor
• CFR Code Part 192
• MMS Regulations
• USDA-SCS Modified (Permissible Velocity of Water and Soil Erodibility)
• FHWA-HEC
• Pipeline Rules of Thumb Handbook

FAQ