Buried Pipe Modeling

7/23/2019 Buried Pipe Modeling

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Modeler Overview ................................................................ 10-2

Using the Underground Pipe Modeler .................................. 10-3Notes on the Soil Model........................................................ 10-8

Recommended Procedures.................................................... 10-15Example ................................................................................ 10-16

C H A P T E R 1 0

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The CAESAR II Underground Pipe Modeler is designed to simplify user input of buried pipe data. This

processor will take anunburied layout and bury it. The Modeler

Allows the direct input of soil properties. The

performs the following functions for users:

Modeler

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

contains the equations for buried pipestiffnesses that are outlined later in this chapter. These equations are used to calculate first thestiffnesses on a per length of pipe basis, and then generate the restraints that simulate the discrete

buried pipe restraint.

Breaks down straight and curved pipe so that when axial loads dominate, soil restraints are spacedfar apart.

uses a zone

concept to break down straight and curved sections. Where transverse bearing is a concern forexample near bends, tees, and entry/exit points soil restraints are located in close proximity.

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.You can specify user-defined stiffnesses separately, or in conjunction with sautomatically generated soil stiffnesses.



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You can start the Buried Pipe Modelerby selecting an existing unburiedjob, 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 creates a second input data file that contains the buried pipe model. This second input file typicallycontains 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 piperestraints is termed the buried job. names the buried job by appending a B to the name of theoriginal job.

Note

When the

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 in the buried section can be entered in the resulting buried model. Theburied 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.

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

This spreadsheet is used to enter the buried element descriptions for the job. The buried element descriptionspreadsheet serves several functions:

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

allows you to define mesh spacing at specific element ends.

allows the input of user-defined soil stiffnesses



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Typical buried pipe displacements are considerably different than similar above ground displacements. Buriedpipe 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 distancebetween 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,

L

or the user, must locate additional point supportsalong 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 bythe equation:

b = 0.75( ) [4EI/Ktr]

Where:

0.25

E = Pipe modulus of elasticity

I = Pipe moment of inertia

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

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 Zone2 lengths. Zone 3 element lengths (to properly transmit axial loads) are computed by 100*Do, where Do is theoutside 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 lastwhich is 50*Do long at the Zone 3 end. A typical piping system, and how views this element

breakdown or mesh distribution is illustrated below. All pipe density is set to zero for all pipe identified asburied, so that deadweight causes no bending around these point supports.

Zone Definitions



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Note: automatically puts a Zone 1 mesh gradient at each side of the pipe framing into anelbow. It is your responsibility to tell

A critical part of the modeling of an underground piping system is the proper definition of Zone 1

where the other Zone 1 areas are located in the pipingsystem.

or lateralbearing regions

On either side of a change in direction.

. These bearing regions primarily occur:

For all pipes framing into an intersection.

At points where the pipe enters or leaves the soil.

Using any user-defined node within or near Zone 1.

The left side of the Buried Element Description Spreadsheetdisplays 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 theoriginal system. The next three columns Soil Model No, From End Mesh Type, To End Mesh Type, arediscussed in detail below:

Soil Model No.This column is used to define which of the elements in the model are buried. A nonzero entry



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in this column implies that the associated element is buried. A 1 in this column implies that the user wishes toenter user defined stiffnesses, on a per length of pipe basis, at this point in the model. These stiffnesses mustfollow in column numbers 6 through 13. Any number greater than 1 in the SOIL MODEL NO. column points

to a soil restraint model generated using the equations outlined later under Soil Models from userentered soil data.

From/ To End Mesh Type

FROM TO SOIL FROM TO

A check in either of these columns implies that a Zone 1 should be placed at the

corresponding element end. For example:

NODE NODE MODEL MESH MESH

5 10 2

The element 5 to 10 is buried. will generate the soil stiffnesses from user-defined soil dataset #2, andthe node 5 end will have a fine mesh so that lateral bearing will be properly modeled. Since 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:

Please note the following:

The user has separated the node numbers in the original piping system by varying the incremental

range by 20. This is so can maintain the sequence of node numbers for the added nodes.This is not required but is useful in comprehending results. For very long runs, node increments of100 may be helpful.



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From/To Lateral Bearing mesh specifications are not needed for nodes 30, 110 and 130, since

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.

places lateral bearing meshes on each side of a bend by default.

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 JobName

Renames the buried job (in the event that the user does not wish to use the 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 to use in generating one or moresoil restraint systems. This is described in detail below.

ConvertConverts the original job into the buried job by meshing the existing elements and

adding soil restraints. The conversion process creates all of the necessary elements to

satisfy the Zone 1, Zone 2, and Zone 3 requirements, and places restraints on theelements in these zones accordingly. All elbows are broken down into at least twocurved sections, and very long radius elbows are broken down into segments whose

lengths are not longer than the elements in the immediately adjacent Zone 1 pipe

section. Node numbers are generated by adding 1 to the elements FROM nodenumber. checks before using a node number to make sure that it will beunique in the model. All densities on buried pipe elements are zeroed to simulate thecontinuous support of the pipe weight. A conversion log is also generated, which

details the process in full.



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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. Our soil restraint

modeling algorithms are based on the ideas presented by (1) The CAESAR II Basic Model L.C. Peng in hispaper entitled Stress Analysis Methods for Underground Pipelines, published in 1978 in Pipeline Industry and(2) Appendix B: Soil Spring Representation from the Guidelines for the Design of Buried Steel Pipe by the

American Lifelines Alliance http://www.americanlifelinesalliance.org/pdf/Update061305.pdf.

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 displacement may continue. The two basic ultimate loads that must be

calculated to analyze buried pipe are the axial and transverse ultimate loads. Many researchers differentiatebetween horizontal, upward, and downward transverse loads, but when the variance in predicted soil propertiesand methods are considered, this differentiation is often not warranted. Note that

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

allows the explicit

entry of these data if so desired.

The user enters soil data by executing the Soil Models Command. This option allows the user tospecify the soil properties for the CAESAR II Buried Pipe Equations.

Note

Upon entry, the soil modeler dialog appears. Select either the

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.

CAESAR II Basic Model (Peng) or the AmericanLifeLines Alliance.

http://www.americanlifelinesalliance.org/pdf/Update061305.pdf.http://www.novapdf.com/http://www.novapdf.com/http://www.americanlifelinesalliance.org/pdf/Update061305.pdf.


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Either the friction coefficient or the undrained shear strength may be left blank. Typically for clays the frictioncoefficient would be left blank and would be automatically estimated by as Su/600 psf. Both sandysoils and clay-like soils may be defined here.

The soil restraint equations use these soil properties to generate restraint ultimate loads and stiffnesses. TheTEMPERATURE 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

F

)

ax = D[ (2 sH) + ( pt) + ( f

Where:

)(D/4) ]

0.4 for silt

ent, typical values are:

0.5 for sand

0.6 for gravel

0.6 for clay or Su

S

/600

u H = Buried depth to the top of pipe= Undrained shear strength (specified for clay-like soils)

D = Pipe diameter p = Pipe density

s t = Pipe nominal wall thickness= Soil density

f = Fluid density



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Transverse Ultimate Load (Ftr

F

)

tr = 0.5 s (H+D)2[tan(45 + /2 2

If S

OCM

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

Where:

/250 psf.

27-45 for sand

= Angle of internal friction, typical values are:

26-35 for silt

0 for clay

The OCM is an artificial

Notes on the Overburden Compaction Multiplier (OCM)

CAESAR II term used to allow you to take a conservative approach when modeling

uncertain soil response. Since a higher stiffness will generally produce conservative results, you may wish to

increase the transverse soil stiffness, CAESAR II

Users have reduced the OCM (from its default of 8) to values ranging from 5 to 7, depending on the degree ofcompaction of the backfill. There is no theory which suggests that the OCM cannot equal 1.0.

uses the OCM to serve this purpose.

For a strict implementation of Peng's Theory as discussed in his articles (April 78 and May 78 issue of Pipeline

Industry) you should use a value of 1.0 for the OCM.

Yield Displacement (yd

y

):

d = Yield Displacement Factor(H+D)

Note:

Axial Stiffness (K

The Yield Displacement Factor defaults to 0.015(suggested for H = 3D).

ax

K

) on a per length of pipe basis:

ax=Fax / y

Transverse Stiffness (K

d

tr

K

) on a per length of pipe basis:

tr=Ftr / y

Once you click

d

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

The following information references the American Lifelines Alliance document "Guidelines for the Design of

Buried Steel Pipe " Appendix B: Soil Spring Representation

http://www.americanlifelinesalliance.org/pdf/Update061305.pdf. This document provides bilinear stiffness of

soil for axial, lateral, uplift and bearing. Each stiffness term has a component associated with sandy soils

(subscripted q) and a component associated with clays (subscripted c). Data can be entered for pure granular

soils and pure clays.

Soil stiffness for both clay and sand (cohesive and granular soils, respectively) are defined through the following

parameters supplied by the user:

soil cohesion representative of the soil backfill

H soil depth to top of pipe (this is converted by C2 to depth to pipe centerline in ALA calculations)

http://www.americanlifelinesalliance.org/pdf/Update061305.pdf.http://www.novapdf.com/http://www.novapdf.com/http://www.americanlifelinesalliance.org/pdf/Update061305.pdf.


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effective unit weight of soil

total dry unit weight of fill

0K

coefficient of earth pressure at rest (can be calculated based on internal friction angle of soil)

f coating-dependent factor relating the internal friction angle of the soil to the friction angle at thesoil-pipe interface

internal friction angle of soil

Elastic range of soil is either fixed or a function of D & H with limits based on D.

Axial Length units

Lateral Multiple of D 0.04(H+D/2)

Upward Multiple of HMinimum

(dQu) Upward Multiple of D

Downward Multiple of D



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Axial:

tan12

0KDHcDTu

uT

peak friction force at pipe-soil interface maximum axial soil force per unit length that can betransmitted to pipe)

pipe OD

adhesion factor (for clays only)

1

695.0

1

274.0123.0608.0

32 ccc

where c is in ksf

soil cohesion representative of the soil backfill (undrained shear strength)

H depth of cover to pipe centerline

effective unit weight of soil

0K

coefficient of earth pressure at rest

The ratio of the horizontal effective stress acting on a supporting structure and the vertical effective stress in thesoil at that point. At rest indicates the pipe does not move for this calculation.

interface angle of friction for pipe and soil,f

f coating-dependent factor relating the internal friction angle of the soil to the friction angle atthe soil-pipe interface

Concrete 1.0

Coal Tar 0.9

Rough Steel 0.8

Smooth Steel 0.7

Fusion Bonded Epoxy 0.6

Polyethylene 0.6



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internal friction angle of soil

t axial displacement to develop

uT

= 0.1 inch for dense sand= 0.2 inch for loose sand

= 0.3 inch for stiff clay

= 0.4 inch for soft clay

Lateral:

HDNcDNP qhchu

uP maximum horizontal soil bearing capacity (maximum lateral soil force per unit length that can betransmitted to pipe)

chN horizontal soil bearing capacity factor for clay (0 for c=0)

qhN

9)1()1( 32 x

d

x

cbxaNch

)()()()( 432 xexdxcxbaNqh

Nch 0 H/D 6.752 0.065 -11.063 7.119 --

Nqh 20 H/D 2.399 0.439 -0.03 1.059E-3 -1.754E-5

Nqh 25 H/D 3.332 0.839 -0.090 5.606E-3 -1.319E-4

Nqh 30 H/D 4.565 1.234 -0.089 4.275E-3 -9.159E-5

Nqh 35 H/D 6.816 2.019 -0.146 7.651E-3 -1.683E-4

Nqh 40 H/D 10.959 1.783 0.045 -5.425E-3 -1.153E-4

Nqh 45 H/D 17.658 3.309 0.048 -6.443E-3 -1.299E-4

p horizontal displacement to develop u

DD

H 01.0)2

(04.0to 0.15D



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Vertical Uplift:

HDNcDNQuqvcv

uQ maximum vertical upward soil bearing capacity (maximum vertical uplift soil force per unit length

that can be transmitted to pipe)

cvN

vertical upward soil bearing capacity factor for clay (0 for c=0)

qvN vertical upward soil bearing capacity factor for sand (0 forqqv

ND

HN )

44(

)

10)(2D

HN

cv

applicable for (H/D)

qqv ND

HN )

44(

)2

45(tan)tanexp( 2qN

qu vertical displacement to develop uQ

= 0.01H to 0.02H for dense to loose sands < 0.1D

= 0.1H to 0.2H for stiff to soft clays < 0.2D

Vertical Bearing:

2

2D

NHDNcDNQqcd

dQ maximum vertical bearing soil force per unit length that can be transmitted to pipe

cN

, qN

,N

vertical downward soil bearing capacity factors

}1)2

001.045(tan)]001.0tan()]{exp[001.0[cot( 2cN

)2

45(tan)tanexp( 2qN

)5.218.0(eN

total dry unit weight of fill

qd vertical displacement to develop dQ

= 0.1D for granular soils

= 0.2D for cohesive soils



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

1 Select the original unburied job and enter the buried pipe modeler. The original job must alreadyexist, and will serve as the basis for the pipe model. The original model need only contain the basic

geometry of the piping system. The modeler will remove any existing restraints in the buriedportion. Add any additional underground restraints ( e.g. thrust block) to the buried model. Rename

the buried job if the default name (JOBNAME

2 Enter the soil data using Soil Models or collect any user-defined soil data.

B) is not appropriate.

3 Describe the sections of the piping system that are buried, and define any required fine mesh areasusing the buried element data spreadsheet or enter user-defined soil data (columns 6-13).

4 Convert the original model into the buried model by clicking Convert Input

5 Exit the

. This step produces adetailed description of the conversion.

Buried Pipe Modeler and return to the CAESAR II Main Menu

A 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.

. From here the user mayreview and edit the buried model and perform the analysis of the buried pipe job.



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The following input listing represents theunburiedmodel 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.



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

Elements 1250-1300 through 1600-1650 are buried using soil model number 2. Zone 1 meshing is indicated atthe entry and exit points.



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Clicking Convert on the toolbar to begins the conversion to a buried model.



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The screen listing can also be printed.



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The original unburied model is shown along with the "buried" model below. Note the added restraints around theelbows and along the straight runs.

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

nodes.



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



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The buried job can now be analyzed.

Documents

Buried Pipe Modeling