Fig. 2. Analytical models of pipelines under the external load and ground settlement.

in the other method (indirect method), which is widely used in the analysis of buried tunnels and pipelines, the reaction load between the pipe and soil (Fsoil-pipe) is calculated under the external load and settlement, then interaction of the pipe with soil (under this load only) is analyzed (Fig. 2b).

Apart from modeling of soil and the pipe, pipe-soil interaction is also important, and it can be very effective in the results of analysis. For example, if the pipe displaces due to ground settlement, two different cases can occur depending on the type of soil around the pipe. First case occurs where the soil is adhesive. Therefore, once the pipe is displaced, a gap occurs between the pipe and soil, and no more pressure is exerted on top of the pipe body by soil (Fig. 3a).

However, if the soil is coarse, once the pipe is displaced, soil would also move, and no gap occurs between the pipe and soil. Therefore, there will still be a pressure on top of the pipe body because of the overburden soil (Fig. 3b). So, in modeling the first case, interactions should be defined so as to consider the detachment of pipe-soil nodes.

Pipe-soil interaction is not clearly explained in the original article, and it is just mentioned that interaction is defined as a finite sliding. The authors should discuss the pipe-soil interaction in more detail and explain which friction coefficient was used for tangential friction and how the relative slippage and the separation between the pipe and soil were considered.

Fig. 4. Longitudinal plan of the pipe and soil after deflection.

As shown in Fig. 4, after the foundation settlement, the displacement would be transferred to the pipeline, causing the pipeline to be divided into four sections: unaffected part, transition part, bent part and straight part. In fact, if a deflection occurs, these sections would appear as well. In the numerical model, the length of these sections can be calculated by solving the governing equations.

Restraining Thrust Forces⬇️

Forces Causing Thrust:
1- Static forces (Internal pressure)
2- Dynamic forces (Fluid velocity)

Thrust Force

Thrust Force

Restraining Techniques:⤵️
1- Thrust blocks
2- Restrained joint system
3- Tie rods
4- Combined systems

Types of Thrust Blocks:⤵️
1- Bearing
2- Gravity

Bearing Thrust Block

Bearing Thrust Block

Soil Bearing Strength SB

Bearing Block Construction

Typical Thrust Block Details