Buried Pipe Stress Analysis

Stress Analysis of Buried or Underground piping seems to be difficult for many stress engineers due to the complex soil pipe interaction. But the software Caesar II easily handles that part.  In this article, we will learn the various buried piping analysis methods that are available in Caesar II. The points that will be covered in this article are:

  • The various analysis method of Underground piping
  • Overview of Soil Classification
  • Discuss the current practice of Underground pipe modeling & analysis
  • Examine the data inputs for buried piping and pipeline stress analysis
  • Make a suggestion for sound input data, especially where information is not known or available
  • Learn the inputs, generate some results & conclusions

Caesar II analysis methods for Buried piping

In Caesar II the following four methods are available to perform buried piping stress analysis:

  • CAESAR-II Basic method by LC Peng
  • American lifelines alliance buried pipe– ALA
  • ALA method with 31J
  • ALA method with FEA

Soil Classification According to Grain Size

Fig. 1 below provides the soil classification for the most basic soil types used for underground piping stress analysis.

  • The most basic classification of soil is based on grain-size.
  • Soils with large grains are called “gravel” and soils with small grains “sand”.
  • Internationally it is defined that sand contains grains larger than 0.063 mm and smaller than 2 mm.
  • Gravel contains grains with sizes between 2mm and 63mm.
  • Grains smaller than 0.063 mm are called “silt”.
  • Grains smaller than 0.002 mm are called “clay”.
Soil Classification
Fig. 1: Soil Classification

Shear Stress in Soils

The ability to resist shear stresses depends on friction and cohesion.

When cohesionless soils are poured to the ground from above it will spread due to gravity. Because of friction, the area of spread is limited creating an angle of repose (φ) at the balanced state.

  • From this experiment, the friction force that resists the shear loads may be calculated and the internal friction coefficient (µ) of the soil may be determined:

f = µ ⋅n = µ ⋅w⋅cosϕ —-where f=wsinϕ

µ = tanϕ

  • The friction resistance (s) of any soil in any plane is then expressed as Sliding force ( s ) + Cohesion ( c )

s = n⋅tan(ϕ) + c

The angle (φ) is also called the soil angle of internal friction.

Axial Soil Resistance

  • Frictional Force on the Top of Pipe and at the Bottom Of pipe are different
  • In the case of an idealized model the axial resistance (f) can be determined by the following expression:
Axial Soil Resistance equations
Fig. 2: Axial Soil Resistance equations

Lateral Soil Resistance

  • Lateral Soil Resistance is divided into 3 parts viz. Upward, Downward and Sideways

Upward Resistance (Fig. 3):

Upward soil resistance can be described by the application of the “soil prism theory” also know as “Marston’s load theory”! This theory states that the soil resistance is determined by (a) the weight of a soil prism above the pipe and (b) the shear forces exerted on either side of the prism. ! The shear conditions depend on the installation layout of the pipe and soil, but in this case, negative shear will be assumed. ! Next to the soil prism, the weight of the pipe needs to be taken into consideration as well.

Shear stresses can be found by integrating the friction along both side surfaces of the prism.

Let’s assume cohesionless soil (c=0, e.g. sand); ϕ is the friction angle of the soil.

q = Wt. of Soil Above Pipe + Shear Resistance + Wpipe

q = ρDH + 2H (c + 0.5 ρ H Ka tanФ) + Wpipe = ρDH + ρH2 Ka tanФ

Downward Resistance (Fig. 3):

  • When the pipe moves downwards the soil resistance can be determined from the “vertical bearing capacity”.
  • Detailed geotechnical evaluation is required to determine the vertical bearing capacity.
  • For a general idea, the downward resistance can be roughly estimated to be as twice the horizontal resistance. ! The vertical bearing capacity is the vertical load required to break the soil underneath the pipe over the full width of the pipe.

Horizontal Resistance (Fig. 3):

When pipe moves horizontally, it experiences

  • Passive Force from Front
  • Active Force from Back

Active force is ineffective as pipe moves and a void is created.

qh = ½* ρ (H+D)2 tan2 (45 + Ф/2)  

For cohesive soil (clay) ф = 0, hence less resistance

Upward, Downward and Horizontal Resistance
Fig. 3: Upward, Downward and Horizontal Resistance

How Caesar II models soil?

  • Soil is modeled as a ‘Bilinear Spring’ having ‘initial stiffness, ultimate load, and Yield Stiffness’
  • Ultimate load: Maximum load on the soil beyond which load does not increase but displacement can.
  • Ultimate loads are different in axial, lateral, vertical directions

Modeling Soils in Caesar II

Caesar II simulates the soil surrounding the pipeline using springs of varying stiffness as shown in Fig. 4.

Modeling Soils in Caesar II
Fig. 4: Modeling Soils in Caesar II

About CII  Buried Pipe Modeler

Refer Fig. 5

Underground modeling in Caesar II
Fig. 5: Underground modeling in Caesar II

CAESAR-II Basic method by LC Peng

Caesar II Basic Buried Model
Fig. 6: Caesar II Basic Buried Model

American Lifelines Alliance-ALA

Caesar II American Lifeline Alliance Buried Model
Fig. 7: Caesar II American Lifeline Alliance Buried Model

ALA method with 31J

B31J provides a set of calculations for revised SIFs and flexibility factors, as defined in the upcoming revision to ASME B31J. By using these revised SIFs and flexibilities, your stress analyses produce more accurate results. B31J provides the “more applicable data” referenced in recent editions of the piping codes.

Result Comparison with Various method:

Caesar II Results Comparison for the same model
Fig. 8: Caesar II Results Comparison for the same model


  • Results obtained by ALA Method are more reliable
  • ALA considers more variables based on published data
  • Better method if the soil is changing through the run
  • Peng’s Method gives a very good understanding of the subject and gives quick results for non-critical
  • If the buried pipe is modeled just as a reference in the Above ground Piping Analysis then suggested going for ‘CAESAR II Basic Model’
  • For Pipeline analysis use ‘ALA Method with user-defined stiffness input

Author: This presentation is prepared by Mr. Deepak Sethia who is working in ImageGrafix Software FZCO, the Hexagon CAS Global Network Partner in the Middle East and Egypt. He has extensive experience in using Caesar II and PV Elite software and troubleshooting.

Few more Related articles for you.

Basics for Stress Analysis of Underground Piping using Caesar II
Underground Piping Stress Analysis Procedure using Caesar II
Few Salient Points for Underground / Buried Piping
Training Video: Buried/Underground Piping Stress Analysis
Buried GRP/FRP pipe Laying and Installation Procedure
What if Piping Continuation is Unknown? Part 2. Underground Piping

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Anup Kumar Dey

I am a Mechanical Engineer turned into a Piping Engineer. Currently, I work in a reputed MNC as a Senior Piping Stress Engineer. I am very much passionate about blogging and always tried to do unique things. This website is my first venture into the world of blogging with the aim of connecting with other piping engineers around the world.

2 thoughts on “Buried Pipe Stress Analysis

  1. Dear Anub

    When the ALA method with B31J or FEA is use, Do you use the soil modeler first an then FEA translation or fist FEA and the soil modeler?

  2. When the ALA method with B31J or FEA is use, Do you use the soil modeler first and then FEA translation or fist FEA and then soil modeler?.

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