buried piping-c2ug.pdf

Chapter 11:Buried Pipe Modeling

Contents

CAESAR II Underground Pipe Modeler - - - - - 2

Using the Underground Pipe Modeler - - - - - 3

Notes on the Soil Model 9Recommended Procedures12Original Unburied Model13

This chapter describes an

approach to modeling continuous

soil supports using a collection of

point restraints and the CAESAR II

processor that automates the con-

CAESAR II Underground Pipe Modeler CAESAR II - User Guide

11-2 Buried Pipe Modeling

CAESAR II Underground Pipe Modeler

The CAESAR II underground pipe modeler is designed to simplify user input of buried

pipe data. To achieve this objective the Modeler performs the following functions for

users:

Allows the direct input of soil properties. The Modeler contains the equations for

buried pipe stiffnesses that are outlined later in this chapter. These equations are used

to calculate first the stiffnesses on a per length of pipe basis, and then generate the

restraints that simulate the discrete buried pipe restraint.

Breaks down straight and curved lengths of pipe to locate soil restraints. CAESAR II

uses a zone concept to break down straight and curved sections. W here transverse

bearing is a concern (near bends, tees, and entry/exit points), soil restraints are located

in close proximity and where axial load dominates, soil restraints are spaced far apart.

Allows the direct input of user-defined soil stiffnesses on a per length of pipe basis.

Input parameters include axial, transverse, upward, and downward stiffnesses, as well

as ultimate loads. Users can specify user-defined stiffnesses separately, or in conjunc-

tion with CAESAR IIs automatically generated soil stiffnesses.

CAESAR II - User Guide Using the Underground Pipe Modeler

Buried Pipe Modeling 11-3

Using the Underground Pipe Modeler

Users can start the Buried Pipe Modeler by selecting an existing job, and then choosing

Input-Underground from the CAESAR II Main Menu. The Modeler is designed to read

a standard CAESAR II input data file that describes the basic layout of the piping system

as if it was not buried. From this basic input CAESAR II creates a second input data file

that contains the buried pipe model. This second input file typically contains a much larger

number of elements and restraints than the first job. The first job that serves as the pat-

tern is termed the original job. The second file that contains the element mesh refinement

and the buried pipe restraints is termed the buried job. CAESAR II names the buried job

by appending a B to the name of the original job.

Note The original job must already exist and serves as the pattern for the buried pipe

model building. The modeler removes any restraints in the buried section during

the process of creating the buried model. Any additional restraints can be entered

in the resulting buried model. The buried job, if it exists, is overwritten by the

successful generation of a buried pipe model. It is the buried job that is eventually

run to compute displacements and stresses.

When the Buried Pipe Modeler is initially started up, the following screen appears:

This spreadsheet is used to enter the buried element descriptions for the job. The buried

element description spreadsheet serves several functions:

Using the Underground Pipe Modeler CAESAR II - User Guide


allows users to define which part of the piping system is buried.

allows users to define mesh spacing at specific element ends.

allows the input of user-defined soil stiffnesses

Typical buried pipe displacements are considerably different than similar above ground

displacements. Buried pipe deforms laterally in areas immediately adjacent to changes in

directions (i.e. bends and tees). In areas far removed from bends and tees the deformation

is primarily axial. The optimal size of an element (i.e. the distance between a single

FROM and a TO node) is very dependent on which of these deformation patterns is to be

modeled Not having a continuous support model, CAESAR II or the user, must locate

additional point supports along a line to simulate this continuous support. So for a given

stiffness per unit length, either many, closely spaced, low stiffness supports are added or a

few, distant and high stiffness supports are added. Where the deformation is lateral,

smaller elements are needed to properly distribute the forces from the pipe to the soil. The

length over which the pipe deflects laterally is termed the lateral bearing length and can

be calculated by the equation:

Lb = 0.75(pi) [4EI/Ktr] 0.25

Where:

E = Pipe modulus of elasticity

I = Pipe moment of inertia

Ktr = Transverse soil stiffness on a per length basis, (defined later)

CAESAR II places three elements in the vicinity of this bearing span to properly model

the local load distribution. The bearing span lengths in a piping system are called the Zone

1 lengths. The axial displacement lengths in a piping system are called the Zone 3 lengths,

and the intermediate lengths in a piping system are called the Zone 2 lengths. Zone 3 ele-

ment lengths (to properly transmit axial loads) are computed by 100*Do, where Do is the

outside diameter of the piping. The Zone 2 mesh is comprised of up to 4 elements of

increasing length; starting at 1.5 times the length of a Zone 1 element at its Zone 1 end,

and progressing in equal increments to the last which is 50*Do long at the Zone 3 end. A

typical piping system, and how CAESAR II views this element breakdown or mesh

distribution is illustrated on the following page.



Zone Definitions

A critical part of the modeling of an underground piping system is the proper definition of

Zone 1 (or lateral) bearing regions. These regions primarily occur:

On either side of a change in direction

For all pipes framing into an intersection

At points where the pipe enters or leaves the soil

CAESAR II automatically puts a Zone 1 mesh gradient at each side of the pipe framing

into an elbow.

Note It is the users responsibility to tell CAESAR II where the other Zone 1 areas are

located in the piping system.



The left side of the Buried Element Description Spreadsheet displays below:

Buried Element Description Spreadsheet

There are 13 columns in this spreadsheet The eight not shown above carry the user-

defined soil stiffnesses and ultimate loads. The first two columns contain element node

numbers for each piping element included in the original system. The second three col-

umns are discussed in detail below:

Soil Model No. This column is used to define which of the elements in the model

are buried. A nonzero entry in this column implies that the associated element is bur-

ied. A 1 in this column implies that the user wishes to enter user defined stiffnesses,

on a per length of pipe basis, at this point in the model. These stiffnesses must follow

in column numbers 6 through 13. Any number greater than 1 in the SOIL MODEL

NO. column points to a CAESAR II soil restraint model generated using the equa-

tions outlined later under Soil Models from user entered soil data.

From/ To End Mesh Type A check in either of these columns implies that a lateral

loading mesh should be placed at the corresponding element end. For example:

FROM TO SOIL FROM TO

NODE NODE MODEL MESH MESH

5 10 2

The element 5 to 10 is buried. CAESAR II will generate the soil stiffnesses from

user-defined soil dataset #2, and the node 5 end will have a fine mesh so that lateral

bearing will be properly modeled.



Since CAESAR II automatically places lateral bearing meshes adjacent to all buried

elbows, the user must only be concerned with the identification of buried tees and points

of soil entry or exit. The figure below is illustrative:

Lateral Bearing Mesh Definitions

Please note the following:

The user has separated the node numbers in the original piping system by 10s or 20s

instead of the usual 5. This is so that CAESAR II can maintain the normal sequence

of node numbers for the added moves.

From/To Lateral Bearing mesh specifications are not needed for nodes 30, 110 and

130, since CAESAR II places lateral bearing meshes on each side of a bend by

default.

A lateral bearing mesh is not needed at 90 because there is no tendency for the model

to deflect in any direction NOT axial to the pipe.

The tendency for lateral deflection must be defined for each element framing into an

intersection (node 50).



Commands available in this module are

File-OpenOpens a new piping file as the original job.

File-Change Buried Pipe Job NameRenames the buried job (in the

event that the user does not wish to use the CAESAR II default of B

appended to the original job name).

File PrintPrints the element description data spreadsheet.

Soil ModelsAllows the user to specify soil data for CAESAR II to use

in generating one or more soil restraint systems. This is described in detail

below.

Convert InputConverts the original job into the buried job by mesh-

ing the existing elements and adding soil restraints. The conversion pro-

cess creates all of the necessary elements to satisfy the Zone 1, Zone 2,

and Zone 3 requirements, and places restraints on the elements in these

zones accordingly. All elbows are broken down into at least two curved

sections, and very long radius elbows are broken down into segments

whose lengths are not longer than the elements in the immediately adja-

cent Zone 1 pipe section. Node numbers are generated by adding 1 to

the elements FROM node number. CAESAR II checks before using a

node number to make sure that it will be unique in the model. All densi-

ties on buried pipe elements are zeroed, to simulate the continuous sup-

port of the pipe weight. A conversion log is also generated, which details

the process in full.

File-Open

File Print

Soil Models

Convert

CAESAR II - User Guide Notes on the Soil Model


Notes on the Soil Model

The following procedures for estimating soil distributed stiffnesses and ultimate loads

should be used only when the analyst does not have better data or methods suited to the

particular site and problem. COADEs soil restraint modeling algorithm is generally based

on the ideas presented by L.C. Peng in his paper entitled Stress Analysis Methods for

Underground Pipelines, published in 1978 in Pipeline Industry.

Soil supports are modeled as bi-linear springs having an initial stiffness, an ultimate load,

and a yield stiffness. The yield stiffness is typically set close to zero, i.e. once the ultimate

load on the soil is reached there is no further increase in load even though the displace-

ment may continue. The two basic ultimate loads that must be calculated to analyze buried

pipe are the axial and transverse ultimate loads. (Many researchers differentiate between

horizontal, upward, and downward transverse loads, but when the variance in predicted

soil properties and methods are considered, this differentiation is often not warranted.

Note that CAESAR II allows the explicit entry of these data if so desired.)

Once the axial and lateral ultimate loads are known, the stiffness in these directions can be

determined by dividing the ultimate load by the yield displacement. Researchers have

found that the yield displacement is related to both the buried depth and the pipe diameter.

The ultimate loads and stiffnesses computed are on a force per unit length of pipe basis.

The user enters soil data by executing the Soil Models Command. This option

allows the user to specify the soil properties for the CAESAR II buried pipe

equations.

Note Valid soil model numbers start with 2. Soil model number 1 is reserved for user-

defined soil stiffnesses. Up to 15 different soil models may be entered for a single

job.

Upon entry, the soil modeler dialog appears. Either the friction coefficient or the und-

rained shear strength may be left blank. Typically for clays the friction coefficient would

be left blank and would be automatically estimated by CAESAR II as Su/600 psf. Both

sandy soils and clay-like soils may be defined here.

Soil Models

Notes on the Soil Model CAESAR II - User Guide


The soil restraint equations use these soil properties to generate restraint ultimate loads

and stiffnesses. (The TEMPERATURE CHANGE is optional. If entered the thermal

strain is used to compute and print the theoretical virtual anchor length.)

These equations are:

Axial Ultimate Load (Fax)

Fax = D[ (2sH) + (pipt) + (pif)(D/4) ] Where:

= Friction coefficient, typical values are:.4 for silt

.5 for sand

.6 for gravel

.6 for clay or Su/600

Su = Undrained shear strength

D = Pipe diameter

s = Soil density

H = Buried depth to the top of pipe

p = Pipe density

t = Pipe nominal wall thickness

f = Fluid density

Transverse Ultimate Load (Ftr)

Where:

= Angle of internal friction, typical values are:

27-45 for sand

2 2tr sF = (0.5)( )(H+D) [tan(45+/2)] OCMi

CAESAR II - User Guide Notes on the Soil Model


26-35 for silt

0 for clay

OCM = Overburden Compaction Multiplier

If Su is given (i.e. have a clay-like soil), then Ftr as calculated above is multiplied by

Su/250psf.

Note that since in many cases the stiffer the soil, the more conservative the results, Ftris multiplied by the OCM as well. Many experienced pipeline engineers do not wish

to add this "extra conservatism," and prefer to use values that are more in line with

those that have been used in the past. To do this, the OCM is the parameter that is usu-

ally adjusted.

Common practice has been to reduce it (from its default of 8) to values from 5 to 7,

depending on the degree of compaction of the backfill. Backfill efficiency can be

approximated by the Proctor Number, defined in most soils textbooks. (The Proctor

Number is a ratio of unit weights.) The standard practice when the Proctor Number is

known is to multiply the default value 8 by the Proctor Number. This result should

then be used as the compaction multiplier.

Yield Displacement (yd):

yd= Yield Displacement Factor (H+D)

Note The Yield Displacement Factor defaults to 0.015.

Axial Stiffness (Kax) on a per length of pipe basis:

Kax=Fax / yd

Transverse Stiffness (Ktr) on a per length of pipe basis:

Ktr=Ftr / yd

Once the user clicks OK, the soil data is saved in a file entitled .SOI.

Recommended Procedures CAESAR II - User Guide


Recommended Procedures

The recommended procedure for using the buried pipe modeler is outlined below:

1. Select the original job and enter the buried pipe modeler. The original job must

already exist, and will serve as the basis for the new buried pipe model. The original

model should only contain the basic geometry of the piping system to be buried. The

modeler will remove any existing restraints (in the buried portion). Add any under-

ground restraints to the buried model. Rename the buried job if CAESAR II default

name is not appropriate.

2. Enter the soil data using Soil Models.

3. Describe the sections of the piping system that are buried, and define any

required fine mesh areas using the buried element data spreadsheet.

4. Convert the original model into the buried model by the activation of

option Convert Input. This step produces a detailed description of the

conversion.

5. Exit the Buried Pipe Modeler and return to the CAESAR II Main Menu. From here

the user may perform the analysis of the buried pipe job.

A fairly simple buried-pipe example problem is shown in the following section. This

example illustrates the features of the modeler and should in no-way be taken as a guide

for recommended underground piping design.

Soil Models

Convert Input

CAESAR II - User Guide Original Unburied Model


Original Unburied Model

The following input listing represents the unburied model shown above.

Terminal nodes 100 and 1900 are above ground. Nodes 1250 and 1650 (on the sloped

runs) mark the soil entry and exit points.

Soil Model Number 2, a sandy soil, is entered.

Original Unburied Model CAESAR II - User Guide


Elements 1250-1300 through 1600-1650 are buried using soil model number 2. Zone 1

meshing is indicated at the entry and exit points.



Clicking Convert starts the conversion to a buried model.

The screen listing can also be printed.



The original unburied model is shown along with the "buried" model below. Note the

added restraints around the elbows and along the straight runs.

Note the bi-linear restraints added to the buried model. The stiffness used is based upon

the distance to the next node.



Note that the first buried element, 1250-1251, has no density.

The buried job can now be analyzed.

buried piping-c2ug.pdf

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