Restrained and Unrestrained Zones of Buried Pipelines

ASME B31.8, ASME B31.4, GB 50251-2015, GB 50253-2014 codes divides the pipeline into "Restrained" and "Unrestrained" zones with different strength criteria. What does it mean?

The main problem for every pipeline designer: how to find the virtual anchor points and divide pipeline into restrained and unrestrained zones? The answer for this question and solutions are below.

Before we begin, let’s say that actually, there are three conditions of pipe behavior instead of two described in ASME B31.4 and B31.8 codes:

Please see here the detailed explanation what is restrained and unrestrained pipes.

Restrained pipe section

Piping in which soil or supports prevent axial displacement or flexure at bends is “restrained.” Restrained piping may include the following:

Buried Pipeline

1 - Virtual anchor points, 2 - restrained section, 3 - unrestrained section

Aboveground pipe, restrained between two rigid anchors

Unrestrained pipe section

Piping that is freed to displace axially or flex at bends is “unrestrained.” Unrestrained piping may include the following:

Restrained and Unrestrained Zones in the Buried Pipelines

Buried gas and oil pipelines usually are very long and have a small temperature difference. In this case all three types of pipe condition occur: unrestrained, totally restrained and partially restrained.

Let’s assume that soil model is ideal plastic:

In this case the axial stress and axial displacement diagram along the pipeline will be as follows:

q - Longitudinal friction force

As we see unrestrained zone on the right end of the pipe is a very small. The most length of pipeline consists of totally restrained and partially restrained zones.

Anchor load in restrained zone will be:

Axial force at restrained zone is:

Stress at restrained zone is:

Axial force at unrestrained zone is:

Stress at unrestrained zone is:

Balance equation:

Therefore virtual anchor length (sliding zone length) is

Virtual anchor length can be calculated using Start-Elements.

Stress function in unrestrained zone is:

Displacement function in unrestrained zone is:

Axial displacement at restrained zone is zero. Therefore:

For more complex and more realistic Elastic-plastic soil model that is used in PASS/START-PROF pipe stress analysis software the zero displacement (totally restrained) zones is absent:

Let’s assume that restrained zone begins when axial displacement is very small, for example 1% of maximum displacement. Bypassing complex calculations the sliding zone length that is used in PASS/START-PROF software is:

- Soil longitudinal displacement resistance factor from soil database


Actually, division by restrained and unrestrained zones are conditional. For example if "x" is a very small then pipe is "almost" restrained. There's no criteria how small should be "x" to consider the zone as "restrained".

We add a special option in Project Settings called "Autodetect". It allows software to automatically decide what strength criteria it should use for each pipe element - Restrained or Unrestrained.

Start will automatically use "restrained" equations for the pipe if following equation is truth:


where F - axial force in pipe, E - Young's modulus, SH - hoop stress, v - Poisson's ratio.

It means that start will consider N/Nmax>97.5% pipe as fully restrained and N/Nmax<97.5% as fully unrestrained.

Manual option is not recommended because it seriously slows down the design process. Autodetect option is not recommended, because the strength criteria will be sometimes too conservative and sometimes less conservative for partially restrained pipes.

It is not best solution, because some points of "intermediate" zone of pipe can be overstressed SL>0.9Sy. And for some parts of "intermediate" zone the strength criteria will be too conservative. The best and universal solution is suggested below.

Start Smart Check

ASME B31.8, ASME B31.4, GB 50251-2015, GB 50253-2014 code has no strength criteria for "Intermediate" zone. How to check it? Solution can be can be borrowed from Russian codes and design experience GOST R 55596-2013, GOST 32388-2013, SNIP 2.05.06-85.

In real design practice the determination where the restrained zones is consume a lot of time. For example on the screenshot below the restrained zones of a very long gas pipeline are shown.

That’s why we decided to create universal strength criteria that automatically meets the B31.4 and B31.8 code strength requirements, but can be used for any type of piping. The problem is that ASME B31.4 and B31.8 has unclear requirements for stress analysis.

ASME B31.4 code 402.6.2 requires that longitudinal stress in unrestrained pipe should be less than  and  for occasional loads.

This requirement can be extended for all pipe conditions, no matter restrained or unrestrained, but for primary loads. Longitudinal stress in any type of piping from sustained primary loads (weight and pressure) should be less than 0.75Sy:

M and Fa should be calculated by software including Bourdon effect.

ASME B31.4 code 402.6.1 requires that longitudinal stress in restrained pipes should be less than 0.9Sy, the equivalent stress should be less than 0.9Sy.

This requirement can also be extended for all pipe conditions, but for primary and secondary loads acting simultaneously (weight, pressure, and thermal expansion).

M and Fa should also be calculated by software including Bourdon effect.

The expansion stress should be checked for both restrained and unrestrained pipes. The same way ASME B31.8 strength criteria can be improved.

Based on these main ides of ASME B31.4 we suggest the universal strength criteria, that is suitable for "Restrained", "Unrestrained", and any "Intermediate" states of pipes and fittings.

The summary of strength criteria we show in the following tables.

Table 1. Original ASME B31.4 Strength Criteria


Table 2. Start Smart Check ASME B31.4 Improved Strength Criteria


Table 3. Original ASME B31.8 Strength Criteria


Table 4. Start Smart Check ASME B31.8 Improved Strength Criteria


We called these strength criteria "Start Smart Check". This option can be enabled in Project Settings. It guarantee that original code strength criteria with manual division of the pipe to the restrained and unrestrained zones will be met too. But if you enable "Start Smart Check" you can easily analyze any complex pipeline/piping model in PASS/START-PROF without thinking about restrained and unrestrained zones. This method is reliable and successfully used in Russian codes for buried pipelines of any complexity since 1985. The same criteria was developed for ASME B31.8, GB 50251-2015, GB 50253-2014 codes by PASS/START-PROF authors.

See Also

Modeling Main Pipeline Stations, Bourdon Effect, Restrained and Unrestrained Pipes, Virtual Anchor Length