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Basic Approach to Evaluate Seismic Induced Stresses in Buried Steel Pipes

Designing underground steel pipes to withstand earthquake stresses is a critical task in civil and structural engineering. This comprehensive note will detail the key considerations, design methodologies, related formulas, and provide a sample calculation to illustrate the process.

Overview

Underground steel pipes, such as those used for water, gas, and oil transmission, must be designed to resist the stresses induced by seismic activities. The design process involves understanding the seismic forces, pipe-soil interaction, and the inherent properties of the pipe material.

Design Considerations

Material Selection: Steel is often chosen for its ductility, which is crucial for withstanding seismic forces without fracturing.

Pipe Diameter and Wall Thickness: Larger diameters and thicker walls can increase resistance but may also require more sophisticated installation techniques.

Depth of Burial: Deeper burial can provide more protection from surface seismic waves, but also increases the load on the pipe.

Analytical Methods

Static Analysis: Used for preliminary assessments, estimating the stresses using static forces as a representation of seismic effects.

Dynamic Analysis: This includes:

Modal Analysis: Evaluates the natural frequencies of the pipe system.

Time History Analysis: Simulates the specific input of an earthquake record.

Response Spectrum Analysis: Uses a spectrum of possible responses to different frequencies of input motion.

Relevant Formulas

The design of underground steel pipes for seismic stresses often involves the following calculations:

Stress due to External Pressure (Οƒ):

𝜎 = [𝑝×𝐷/2×𝑑]

Where p is the external pressure, 𝐷 is the diameter of the pipe, and 𝑑 is the wall thickness.

Hooper’s Formula: Used to calculate the bending moments and shear forces in buried pipes. It considers the wave propagation along the pipeline:

𝑀 = 𝑍×𝐻×𝐷× [1βˆ’π‘’βˆ’π›ΌΓ—π‘₯]

Where 𝑍 is the seismic coefficient, 𝐻 is the depth of burial, 𝐷 is the diameter, 𝛼 is the attenuation factor, and π‘₯ is the distance along the pipe.

Newmark’s Method: Calculates the displacement of the pipe due to ground shaking:

Ξ” = [π‘Žπ‘”Γ—π‘†/𝑔] ​

Where π‘Žπ‘”β€‹is the peak ground acceleration, 𝑆 is the response modification factor, and 𝑔 is the acceleration due to gravity.

Sample Calculation

Scenario: Consider a DN800 steel pipe (800 mm diameter) with a wall thickness of 12 mm, buried 4 meters underground in a Seismic Zone 3 area.

To evaluate the seismic-induced stresses in a DN800 steel pipe buried underground, we need to consider both the mechanical and seismic stresses. This includes calculating the stresses due to external pressure and the additional stresses induced by seismic activity.

Input Parameters:

Diameter of the Pipe (D) = 800 mm = 0.8 m

Wall Thickness (t) = 12 mm = 0.012 m

Depth of Burial (H) = 4 m

Soil Density (ρ) = typical value around 1,800 kg/m³

Peak Ground Acceleration (PGA) = typical value for Seismic Zone 3, assume 0.3 g (g = 9.81 m/sΒ²)

  1. Calculation of External Pressure:

The external pressure due to the soil can be approximated by the formula: 𝑝 = πœŒΓ—π‘”Γ—π» Substituting the values: 𝑝 = 1,800 kg/m3Γ—9.81 m/s2Γ—4 m = 70,579.2 Pa

  1. Calculation of Stress due to External Pressure:

The hoop stress 𝜎 induced by this external pressure is calculated using:

𝜎 = [𝑝×𝐷/2×𝑑] ​

Substituting the values:

𝜎 = 70,579.2 PaΓ—0.8 m2Γ—0.012 m = 2,356,640 Pa (π‘œπ‘Ÿβ€‰2.36 MPa)

  1. Seismic Load Calculation:

Seismic loads can be approximated by considering the additional dynamic pressure applied laterally due to seismic acceleration: π‘π‘ π‘’π‘–π‘ π‘šπ‘–π‘ = [πœŒΓ—PGA×𝑔×𝐻]

π‘π‘ π‘’π‘–π‘ π‘šπ‘–π‘ = 1,800Γ—0.3Γ—9.81Γ—4 = 21,173.76 Pa

  1. Seismic Stress Calculation:

The stress πœŽπ‘ π‘’π‘–π‘ π‘šπ‘–π‘β€‹induced by seismic loads is then: πœŽπ‘ π‘’π‘–π‘ π‘šπ‘–π‘ = [π‘π‘ π‘’π‘–π‘ π‘šπ‘–π‘Γ—π·/2×𝑑]

β€‹πœŽπ‘ π‘’π‘–π‘ π‘šπ‘–π‘ = 21,173.76 PaΓ—0.8 m2Γ—0.012 m = 706,459 Pa (π‘œπ‘Ÿβ€‰0.71 MPa)

  1. Total Stress in the Pipe:

The total stress in the pipe wall, combining both soil-induced and seismic-induced stresses, is: πœŽπ‘‘π‘œπ‘‘π‘Žπ‘™ = 𝜎+πœŽπ‘ π‘’π‘–π‘ π‘šπ‘–π‘

πœŽπ‘‘π‘œπ‘‘π‘Žπ‘™ = 2.36 MPa+0.71 MPa = 3.07 MPa

This stress value of 3.07 MPa is a basic approximation. In real-world applications, detailed dynamic analyses are required to account for factors like soil-structure interaction, the pipe’s flexibility, and local seismic response factors.

About the Author:

Dr. Sabarna Roy, Head – Research & Development, Kejriwal Castings Limited

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