Buried Piping Modeling and Analysis using CAEPIPE

Stress analyses of buried piping systems pose many complexities which are not encountered while analysing above-ground piping systems. The key challenges are (a) modeling of loads imposed on the buried pipe by the surrounding soil, (b) modeling of restraining support provided by the soil to the buried pipe, and (c) accounting for soil friction opposing the thermal growth/contraction of the buried pipe under operating conditions.

Buried pipes experience soil loads, including vertically downward and upward pressures and lateral pressures from the surrounding soil, which, in turn, support the buried pipes. The soil properties such as its stiffness in different directions and settlement characteristics need to be determined and incorporated in detailed buried piping analysis; this is to ensure that realistic support of buried pipes by the soil is included in the analysis model. Thermal expansion/contraction of buried piping systems may not result in large deformations and stress concentrations compared to above-ground piping, because thermal expansion/contraction is restrained by the surrounding soil and the friction generated at the soil-to-pipe interface. CAEPIPE mathematically models a buried pipe as a “Winkler’s beam on elastic foundation”, that assumes that the soil behaves like a series of independent springs supporting the pipe in vertical and lateral directions with the respective soil stiffness in those directions. For details, refer to CAEPIPE Technical Reference Manual.

CAEPIPE provides an unique user-friendly approach for modeling and analyzing buried piping systems, distinguishing itself from other software options that can be cumbersome. For instance, in CAESAR II, there is an external buried pipe modeler that necessitates exporting and importing the pipe model for generating buried pipe bilinear restraints. This tedious process needs to be repeated whenever there are any changes in the pipe route or supports. Similarly, in AUTOPIPE, buried restraints are manually generated by graphically selecting pipe elements in both horizontal and vertical sections. As the models grow larger, the graphical selection and modification of regions become increasingly time-consuming.

In contrast, CAEPIPE offers an integrated solution where pipe sections with and without soil need to be defined only once. The CAEPIPE interface includes a layout window that simplifies the modeling of buried pipes, resembling the process of writing a script in a log file. Modeling a buried pipe in CAEPIPE is a straightforward three-step process.

Step 1 defines the soil model, taking into account soil properties such as density, moisture content, and lateral earth pressure when analyzing stress distribution in buried pipes.

Step 2 links the defined soils with pipe sections. A section represents the cross-sectional properties of a pipe used to construct a piping model. Sections can be defined for both above-ground and below-ground segments. For example, in the snapshot below, the same pipe section is defined twice, as 20 and 20U, with soil S3 assigned in the soil column input for the buried pipe 20U.

Step 3 assigns the sections 20 and 20U to elements in the "Section" column of the layout window, collectively specifying the range of rows. CAEPIPE automatically generates the buried pipe bilinear restraints. Any changes made to the pipe route or support do not require any additional steps to perform buried pipe analysis by CAEPIPE.

If the user wishes to modify the region of buried pipe or its properties, CAEPIPE offers two useful features: 1) The "Change" command allows block operations, enabling the assignment of sections within a range of rows or changes to the section, or load for a specific span length (i.e., DX, DY, and/or DZ) within a range of rows. Additionally, 2) the user can utilize the "Find and Replace Section" command to replace sections which are discontinuous in the model.

Overall, CAEPIPE streamlines the process of modeling buried pipes by providing an integrated interface and simplifying the steps required for analysis.

To download a free evaluation of CAEPIPE click here: https://www.sstusa.com/piping-software-download.php

Tutorial for Buried Piping Modeling and Analysis using CAEPIPE

The following are the detailed Steps to perform Buried Piping Modeling and Analysis using CAEPIPE.

General

In CAEPIPE, Soil in Buried piping?analysis is modeled using bilinear restraints with an initial stiffness and an ultimate load. After the ultimate load is reached, the displacement continues without any further increase in load, i.e., the yield stiffness is zero. The initial stiffness is calculated by dividing the ultimate load by the yield displacement which is initially assumed to be D/25 where D is outside diameter of the pipe.

Soil modeling is based on Winkler’s model wherein the soil resistance is represented by an infinite number of closely spaced elastic springs. Soil stiffness is calculated for all three directions at each node. Pressure value in the load is suitably modified to consider the effect of static overburden soil pressure. Model is analyzed for operating (W+P1+T1) condition and the displacements in the three global directions are noted. A check is made for whether skin friction is mobilized and the soil has attained the yield state. If true, then the spring is released in that direction indicating that soil no longer offers resistance in that direction. This modified model is again analyzed and checked for yield stage. The iterative process is continued till the percentage difference between displacements at each node for two successive iterations is less than 1%. The final stiffness in each direction is the true resistance offered by the soil to the pipe in that direction.

From the above, you may note that elastic springs representing the soil stiffnesses in the Global X, Y and Z directions are to be added at as many nodes in the buried portion of the Stress model as required to simulate Winkler’s soil model. So, it is important that even long buried straight pipes are discretized so that such elastic springs are added at all intermediate nodes generated along those long buried straight pipes. In addition, it is at the bends, elbows, and branch connections that the highest stresses are found in buried piping subjected to thermal expansion of the pipe. These stresses are due to the soil forces that bear against the transverse run. The stresses are proportional to the amount of soil deformation at the elbow or branch connection. Hence, before performing the analysis, discretize the stress layout as given below.

Piping elements at the junction of bends, elbows, and branch connections as well as long straight buried pipes can be refined through Layout window > Edit > Refine Nodal Mesh > Buried Piping. Refinement length for adding intermediate nodes is based on the influence length computed as below.

Modulus of Subgrade Reaction (k)

This factor k defines the resistance of the soil or backfill to pipe movement due to the bearing pressure at the pipe/soil interface. Several methods for calculating modulus of subgrade reaction (k) have been developed in recent years. As per Trautmann, C.H., and O’Rourke, T.D., “Lateral Force-Displacement Response of Buried Pipes,” Journal of Geotechnical Engineering, ASCE, Vol. 111, No. 9 Sep 1985, pp. 1077-1092, the modulus of subgrade reaction, k, can be calculated as per Eq. (2) in Appendix VII of ASME B31.1-2014 code.

k = C? N? w D

where,

C? = a dimensionless factor for estimating horizontal stiffness of compacted backfill. C? may be estimated at 20 for loose soil, 30 for medium soil, and 80 for dense or compacted soil. In the current version of CAEPIPE, the value of C? is internally set as 80 for both cohesive and cohesionless soil.

D = pipe outside diameter, in

w = soil density, lb/in3

N? = a dimensionless horizontal force factor from Fig. 8 of above stated technical paper. For a typical value where the soil internal friction angle is 30 deg. the curve from Fig. 8 may be approximated by a straight line defined by

N? = (0.285H)/D + 4.3

H = the depth of pipe below grade at the pipe centerline, in

Influence Length (L?)

The influence length is defined as the portion of a buried transverse pipe run which is deflected or “influenced” by pipe thermal expansion along the axis of the buried longitudinal run.

From Hetenyi’s theory, (Beams on Elastic Foundation, The University of Michigan Press, Ann Arbor, Michigan 1967) (also, see Section VII-3.3.2 of Appendix VII of ASME B31.1-2014 code)

where, Pipe / Soil System Characteristics is defined as

E = modulus of elasticity of pipe at reference temperature

I = moment of inertia of pipe cross section

k = modulus of subgrade reaction of soil as detailed above.

Tutorial

Snap shot shown below is a sample model for Buried Piping Modeling and Analysis.

Step 1: First define soils using the command Layout window > Misc > Soils.

Two types of soils can be defined - Cohesive and Cohesionless.

Cohesive soil is hard to break up when dry, and exhibits significant cohesion when submerged. Cohesive soils include clayey silt, sandy clay, silty clay, clay and organic clay.

Cohesionless soil is any free-running type of soil, such as sand or gravel, whose strength depends on friction between particles.

Soil density and Ground level are input for both cohesive and cohesionless soils. The Ground level is used to calculate depth of the buried section. For cohesive soil, Strength is the un-drained cohesive strength (C?). For cohesionless soil, Delta is angle of friction between soil and pipe, and K? is Coefficient of horizontal soil stress.

Ground Level

Ground level for a soil is the height of the soil surface from the global?origin (height could be positive or negative). It is NOT a measure of the depth of the pipe’s centerline.

In the figure below, the height of the soil surface for Soil 1 is 3 feet from the global origin. Pipe node 10 [model origin] is defined at (0,-5, 0). So, at Node 10, the pipe is buried 8’ [= (3’ – (-5’)] deep into the soil. Define similarly for the other soil.

The pipe centerline is calculated by CAEPIPE from the given data.

Depth of Soil above Pipe’s Centerline

When the option “Value entered is Depth of Soil above pipe centerline” is turned ON in Soil input, then CAEPIPE will compute maximum soil loads for the sections buried using the Depth entered. This option will be helpful for modeling pipes that are running up or down a hill with same depth of soil filled above pipe’s centerline as shown in the figure given below.

Warning:

Assign Soil only to those elements that are really buried in soil when the option “Value entered is Depth of Soil above pipe centerline” is turned ON.

Step 2:

Tie the soils defined above with pipe sections through Layout window > Misc > Sections or Ctrl+Shft+S (to list Sections). Double click on the required section property. You will see the field Soil in the bottom right corner. Pick the soil name from the drop-down combo box.

If a part of a piping system uses a certain pipe section with some portion of it buried and the balance not buried, then two separate sections have to be defined, with one of them without soil and the other with soil.

Step 3:

Assign the appropriate section for each buried element on the Layout window with the correct soil around it.

Step 4:

Review the stress layout by highlighting the buried sections of the model in graphics. If your model contains sections that are above ground and buried, then you can selectively see only the buried sections of piping in CAEPIPE graphics by highlighting the section that is tied to the soil. Use the Highlight feature under the Section List window and place highlight on the buried piping section (see Highlight under List window>View menu, or press Ctrl+H). The Graphics window should highlight only that portion of the model that is using that specific section/soil. See the portion shown in green in the figure below.

Step 5:

It is at the bends, elbows, and branch connections that the highest stresses are found in buried piping subjected to thermal expansion of the pipe. These stresses are due to the soil forces that bear against the transverse run. The stresses are proportional to the amount of soil deformation at the elbow or branch connection. Hence, piping elements at the junction of bends, elbows and branch connections are to be refined in the stress layout.

This can be performed through Layout window > Edit > Refine Nodal Mesh > Buried Piping. Please see the section titled “Buried Piping” in CAEPIPE User’s Manual for details on “Nodal mesh generation”.

Step 6:

Now, to best simulate Winkler’s soil model, discretize even the remaining long straight buried pipe elements in the stress layout as detailed below.

Starting from CAEPIPE Version 10.30, a feature is included to discretize the long straight buried pipe elements through Layout Window > Edit > Refine Nodal Mesh > Buried Piping. In other words, the procedure listed below in this step is done automatically using this command.

For example, a long buried pipe element at row no. 3 is split as given below. Since the split length is not known, Influence Length is calculated as explained above by obtaining the properties required from the CAEPIPE model. The resulting length is then used to split the long buried pipe element automatically.

Density of soil S2 = 150 lb/ft3 = 0.087 lb/in3

As explained above, dimensionless factor (C?) is taken as 80 for cohesive and cohesionless soil.

Pipe OD (D) for element at row no. 3 = 30”

Pipe ID (d) for element at row no. 3 = 30”- (2 x 0.874) = 28.252”

Being a sloped pipe, the average height at the middle of the pipe is considered as given below

H = Depth of Pipe below grade = 3’3” + (11’ + 3’)/2 = 10’3” = 125”

N? = (0.285H)/D + 4.3 = (0.285 x 125”/30”) + 4.3 = 5.4875

Modulus Subgrade Reaction, k = C? N? w D

= 80 x 5.4875 x 0.087 x 30 = 1145.79 psi

Moment of Inertia, (I) = π/64 × (D ? – d ?)

= (3.14/64.0) × (30 ? – 28.252 ?) = 8487.99 in?

Modulus of elasticity of Pipe at Reference Temperature, E = 30.8×10? psi

Pipe / Soil System Characteristics =

β = [1145.79 / (4 × 30.8×10? × 8487.99)]?1/?? = 0.0057

Influence Length (L?) = 3π/(4β) = 3 × 3.14 / (4 × 0.0057) = 413 in

Based on the above, number of splits = (Total Length / 413) + 1

= (1758 / 413) + 1 = 5.25 = 6

So, starting from CAEPIPE Version 10.30, the long buried pipe element at row no. 3 is automatically split in 6 equal lengths. The above procedure is followed to automatically split other long buried straight pipe elements in the stress model.

However, in CAEPIPE Version 10.20 or earlier, long straight buried pipe element at row no. 3 in the stress layout needs to be discretized manually using “Multiple Split…” command available through Layout Window > Edit by highlighting the pipe element at row no. 3.

Step 7:

Save the refined model as “BuriedPipingRefined_StPipes.mod”. Analyze the model through File > Analyze. Upon successful analysis, CAEPIPE displays an option “Soil Restraints” in addition to other analysis results.

To download this and other Tutorials on CAEPIPE, please visit https://www.sstusa.com/caepipe-tutorials.php.

To visit SST's website, click here: https://www.sstusa.com/index.php