Underground Pipe Stress Analysis 

Underground piping systems behave very differently compared to aboveground or plant piping. When a pipe is buried in soil, it interacts continuously with the surrounding ground. This interaction creates additional forces that must be carefully considered during piping stress analysis.

In this article, we explain underground pipe stress analysis. The concepts are explained step by step so that students, beginners, and junior piping stress engineers can easily understand.

Why Underground Piping Analysis Is Different

Aboveground piping systems are mostly supported on racks, sleepers, or structures. These supports are well defined and easy to model.

However, underground piping systems are surrounded by soil on all sides. The soil:

• Restrains pipe movement
• Creates friction resistance
• Applies pressure on the pipe
• Opposes thermal expansion and contraction

Because of this, underground piping analysis requires special modeling techniques.

Main Challenges in Underground Pipe Stress Analysis

The biggest challenge in underground piping analysis is accurate soil–pipe interaction modeling. Unlike steel supports, soil behavior is complex and nonlinear.

The soil resistance acting on the pipe is mainly divided into two categories:

• Axial friction forces
• Lateral soil pressure forces

Both of these forces resist pipe movement and must be included in stress calculations.

Axial Friction in Underground Pipes

Axial friction occurs when the pipe tries to move along its length due to:

• Thermal expansion
• Pressure changes
• Settlement effects

The surrounding soil resists this axial movement by friction. This friction force acts opposite to the direction of pipe movement.

How Axial Friction Force Is Calculated

Axial friction force depends on:

• Pipe weight
• Weight of soil above the pipe
• Pipe diameter
• Soil properties

In simple terms, axial friction force is calculated as:

Axial friction force = Coefficient of friction × Normal force

The normal force is the combined weight of:

• The pipe and its contents
• The soil resting above the pipe

This force is usually calculated per unit length of pipe.

Coefficient of Friction Between Pipe and Soil

The coefficient of friction depends on soil type. If soil test data is available, it should always be used. Otherwise, typical values are:

• Silt: 0.3
• Sand: 0.4
• Gravel: 0.5
• Clay: 0.6 to 2.4 (depending on strength)

Clay soil behaves differently from sand or gravel because it has cohesive properties.

Weight of Soil Acting on the Pipe

The soil weight acting on the pipe depends on trench geometry. There are two common cases:

• Trenched pipe
• Direct buried pipe

For shallow trenches, the full soil weight above the pipe is considered. For deeper trenches, soil arching effects may reduce the effective soil load.

In most conservative designs, the full soil weight is used.

Lateral Soil Resistance in Underground Pipes

When a buried pipe expands or moves sideways, it pushes against the soil. The soil resists this movement by developing lateral pressure.

This lateral resistance is critical in:

• Thermal expansion analysis
• Seismic analysis
• Settlement analysis

Types of Lateral Soil Movement

Lateral movement of underground pipes can occur in three directions:

• Upward movement
• Downward movement
• Sideward movement

Each direction creates different soil resistance patterns.

Soil Resistance Behavior

Soil resistance does not behave like a rigid support. Initially, resistance increases with displacement. After a certain point, the soil reaches its maximum resistance.

This behavior is represented using a force–displacement curve.

The curve typically has:

• An elastic region (initial stiffness)
• A plastic region (maximum resistance)

Once the maximum resistance is reached, additional displacement does not increase soil force.

Bi-Linear Soil Restraint Model

In piping stress software, soil resistance is usually modeled using a bi-linear restraint.

This model includes:

• Elastic stiffness (initial slope)
• Plastic stiffness (usually zero)

This approach closely matches real soil behavior and avoids overestimating restraint forces.

Soil Elastic Stiffness

Soil elastic stiffness depends on:

• Soil modulus of elasticity
• Pipe diameter
• Depth of burial

The stiffness is calculated per unit length of pipe and applied in the lateral direction.

Higher soil stiffness means more resistance to pipe movement.

Ultimate Soil Resistance

Ultimate soil resistance is the maximum force the soil can apply to the pipe.

It depends on:

• Soil friction angle
• Soil density
• Depth of cover
• Pipe diameter

Once this force is reached, the soil yields and allows further pipe movement.

Pressure Effects in Underground Piping

Internal pressure in underground piping creates additional axial forces.

Pressure tries to:

• Expand the pipe
• Increase axial stress
• Push the pipe against surrounding soil

The soil resists this movement and adds to overall pipe stress.

Modeling Underground Pipes in Stress Software

To accurately simulate underground piping behavior, the following steps are usually followed:

1. Define soil properties
2. Calculate axial friction
3. Define lateral soil restraints
4. Apply bi-linear stiffness
5. Validate displacements and stresses

Because soil restraints act continuously, underground pipes often require finer element mesh compared to aboveground piping.

Importance of Fine Mesh Modeling

Soil restraints act along the entire pipe length. If the mesh is too coarse:

• Soil resistance may be underestimated
• Stress distribution may be inaccurate

Using smaller element lengths improves accuracy but increases model size. A balance between accuracy and efficiency is required.

Common Mistakes in Underground Pipe Analysis

• Ignoring soil friction
• Using rigid restraints instead of soil springs
• Overestimating soil stiffness
• Not checking displacement results

Understanding real soil behavior is more important than blindly applying formulas.

Best Practices for Underground Pipe Stress Analysis

• Use soil test data whenever possible
• Apply conservative assumptions if data is unavailable
• Use bi-linear soil restraints
• Check axial and lateral displacements
• Review stress contours carefully

Conclusion

Underground pipe stress analysis is a specialized area of piping engineering. Soil–pipe interaction plays a major role in determining pipe stresses and movements.

By correctly modeling axial friction, lateral soil resistance, and pressure effects, engineers can design safe and reliable underground piping systems.

Although the analysis may appear complex, breaking it into simple steps makes it easier to understand and apply.

A well-modeled underground piping system not only ensures safety but also reduces maintenance and failure risks over the life of the plant.