Understanding External Load on Buried Flexible Pipes

When pipes are buried underground, they are subjected to external loads primarily from the soil backfill above them and any surface loads. The way a pipe reacts to these loads depends significantly on whether it is a rigid pipe or a flexible pipe.

Rigid vs. Flexible Pipes

• Rigid Pipes: These pipes, like concrete pipes, carry the soil load primarily through their inherent strength. They deflect very little under load.
• Flexible Pipes: These pipes, like PVC or metal pipes, deflect under soil load. This deflection mobilizes lateral passive pressure from the soil backfill at the sides of the pipe, which helps to support the pipe and carry the vertical load. The quality and compaction of the side fill are crucial for flexible pipe performance.

External Load Formula for Flexible Pipes in Narrow Trenches

For flexible pipes buried in a narrow trench with thoroughly compacted side fills, the external load per unit length can be estimated using specific formulas that account for the pipe's interaction with the surrounding soil. One such form of expression commonly used or derived from various theories (like the Iowa formula or White's formula under certain simplifications) involves parameters related to the trench and the pipe itself.

The question asks for the expression for external load per unit length for flexible pipes buried in a narrow trench with compacted side fills.

Let's look at the given options and the typical forms of load calculation:

• Option 1: $\text{P}_{\text{t}} = 3 \cdot \text{H}^3 \cdot \text{P} / (2 \cdot \pi \cdot \text{Z}^5)$ - This expression looks like a form of Boussinesq's formula for stress distribution from a point load, which is not the formula for total external load per unit length on a buried pipe.
• Option 2: $\text{W} = \text{C} \cdot \gamma \cdot \text{B}^2$ - This is a form of Marston's formula for the load on a rigid pipe in a trench, where W is the load per unit length, C is a load coefficient, $\gamma$ is the soil unit weight, and B is the trench width. The load is proportional to the square of the trench width, representing the weight of a prism of soil with a width related to B.
• Option 3: $\text{W} = \text{C}_{\text{p}} \cdot \gamma \cdot \text{B}^2$ - Similar to Option 2, using a different notation for the coefficient.
• Option 4: $\text{W} = \text{C} \cdot \gamma \cdot \text{B} \cdot \text{D}$ - This expression involves the soil unit weight ($\gamma$), the trench width (B), and the pipe diameter (D), along with a coefficient (C). This form suggests that the load is proportional to the volume (and thus weight) of a soil prism defined by the trench width and the pipe diameter over a unit length, modified by a coefficient that accounts for the interaction between the flexible pipe and the compacted side fill. While Marston's rigid pipe formula is $W = C \cdot \gamma \cdot B^2$, formulas for flexible pipes often include terms related to the pipe diameter or trench geometry in a different way, reflecting the load transfer mechanism. The form $\text{W} = \text{C} \cdot \gamma \cdot \text{B} \cdot \text{D}$ is consistent with simplified models where the load is related to the area BxD over unit length.

Given the context of flexible pipes in a narrow trench with compacted side fills, which implies significant side support, the formula representing the load involving trench width (B) and pipe diameter (D) is appropriate. The expression $\text{W} = \text{C} \cdot \gamma \cdot \text{B} \cdot \text{D}$ fits this description as a potential formula for the external load per unit length on flexible pipes under these specific conditions, where:

• $\text{W}$ = External load per unit length on the pipe.
• $\text{C}$ = A coefficient that depends on the trench condition, backfill material, degree of compaction, and settlement ratio.
• $\gamma$ = Unit weight of the soil backfill.
• $\text{B}$ = Width of the trench at the top of the pipe.
• $\text{D}$ = Outer diameter of the pipe.

This formula structure indicates that the load is influenced by the volume of soil directly above and interacting with the pipe within the trench width, scaled by the soil weight and a coefficient. The inclusion of both B and D reflects the geometry of the trench and the pipe's size interacting within it.